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Triaxial Testing of Soils
Triaxial Testing of Soils
Poul V Lade
This edition first published 2016copy 2016 by John Wiley amp Sons Ltd
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Disclaimer All reasonable attempts have been made to contact the owners of copyrighted material used in this book [Figures 112 338 341 450 451 455ab Table 71] However if you are the copyright owner of any source used in this book which is not credited please notify the Publisher and this will be corrected in any subsequent reprints or new editions
Library of Congress Cataloging‐in‐Publication data applied for
ISBN 9781119106623
A catalogue record for this book is available from the British Library
Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic books
Set in 1012pt Palatino by SPi Global Pondicherry India
1 2016
Contents
Preface xiiiAbout the Author xvii
1 Principles of Triaxial Testing 111 Purpose of triaxial tests 112 Concept of testing 113 The triaxial test 214 Advantages and limitations 315 Test stages ndash consolidation and shearing 4
151 Consolidation 5152 Shearing 5
16 Types of tests 5161 Simulation of field conditions 6162 Selection of test type 12
2 Computations and Presentation of Test Results 1321 Data reduction 13
211 Sign rule ndash 2D 13212 Strains 13213 Cross‐sectional area 23214 Stresses 24215 Corrections 25216 The effective stress principle 25217 Stress analysis in two dimensions ndash Mohrrsquos circle 25218 Strain analysis in two dimensions ndash Mohrrsquos circle 27
22 Stressndashstrain diagrams 28221 Basic diagrams 28222 Modulus evaluation 37223 Derived diagrams 41224 Normalized stressndashstrain behavior 48225 Patterns of soil behavior ndash error recognition 49
23 Strength diagrams 51231 Definition of effective and total strengths 51232 MohrndashCoulomb failure concept 51233 MohrndashCoulomb for triaxial compression 54234 Curved failure envelope 55235 MIT pndashq diagram 57236 Cambridge pndashq diagram 59237 Determination of best‐fit soil strength parameters 60238 Characterization of total strength 60
24 Stress paths 61241 Drained stress paths 61242 Total stress paths in undrained tests 61243 Effective stress paths in undrained tests 61244 Normalized pndashq diagrams 66245 Vector curves 68
vi Contents
25 Linear regression analysis 72251 MIT pndashq diagram 72252 Cambridge pndashq diagram 74253 Correct and incorrect linear regression analyses 75
26 Three‐dimensional stress states 76261 General 3D stress states 76262 Stress invariants 76263 Stress deviator invariants 80264 Magnitudes and directions of principal stresses 81
27 Principal stress space 83271 Octahedral stresses 83272 Triaxial plane 84273 Octahedral plane 86274 Characterization of 3D stress conditions 87275 Shapes of stress invariants in principal stress space 89276 Procedures for projecting stress points onto a common
octahedral plane 90277 Procedure for plotting stress points on an octahedral plane 96278 Representation of test results with principal stress rotation 97
3 Triaxial Equipment 9931 Triaxial setup 99
311 Specimen cap and base 99312 Membrane 103313 O‐rings 105314 Drainage system 106315 Leakage of triaxial setup 112316 Volume change devices 113317 Cell fluid 113318 Lubricated ends 120
32 Triaxial cell 125321 Cell types 125322 Cell wall 127323 Hoek cell 128
33 Piston 128331 Piston friction 129332 Connections between piston cap and specimen 132
34 Pressure supply 133341 Water column 133342 Mercury pot system 134343 Compressed gas 135344 Mechanically compressed fluids 136345 Pressure intensifiers 137346 Pressure transfer to triaxial cell 137347 Vacuum to supply effective confining pressure 138
35 Vertical loading equipment 139351 Deformation or strain control 139352 Load control 140353 Stress control 141354 Combination of load control and deformation control 141355 Stiffness requirements 143
Contents vii
356 Strain control versus load control 14336 Triaxial cell with integrated loading system 143
4 Instrumentation Measurements and Control 14541 Purpose of instrumentation 14542 Principle of measurements 14543 Instrument characteristics 14744 Electrical instrument operation principles 149
441 Strain gage 149442 Linear variable differential transformer 151443 Proximity gage 153444 Reluctance gage 153445 Electrolytic liquid level 154446 Hall effect technique 154447 Elastomer gage 154448 Capacitance technique 155
45 Instrument measurement uncertainty 155451 Accuracy precision and resolution 156452 Measurement uncertainty in triaxial tests 156
46 Instrument performance characteristics 158461 Excitation 158462 Zero shift 159463 Sensitivity 159464 Thermal effects on zero shift and sensitivity 159465 Natural frequency 159466 Nonlinearity 159467 Hysteresis 159468 Repeatability 159469 Range 1594610 Overload capacity 1604611 Overload protection 1604612 Volumetric flexibility of pressure transducers 160
47 Measurement of linear deformations 160471 Inside and outside measurements 160472 Recommended gage length 162473 Operational requirements 162474 Electric wires 163475 Clip gages 163476 Linear variable differential transformer setup 167477 Proximity gage setup 168478 Inclinometer gages 170479 Hall effect gage 1714710 X‐ray technique 1714711 Video tracking and high‐speed photography 1714712 Optical deformation measurements 1724713 Characteristics of linear deformation measurement devices 174
48 Measurement of volume changes 178481 Requirements for volume change devices 178482 Measurements from saturated specimens 180483 Measurements from a triaxial cell 189484 Measurements from dry and partly saturated specimens 192
viii Contents
49 Measurement of axial load 195491 Mechanical force transducers 195492 Operating principle of strain gage load cells 197493 Primary sensors 197494 Fabrication of diaphragm load cells 198495 Load capacity and overload protection 198
410 Measurement of pressure 1994101 Measurement of cell pressure 1994102 Measurement of pore pressure 1994103 Operating principles of pressure transducers 2014104 Fabrication of pressure transducers 2014105 Pressure capacity and overpressure protection 201
411 Specifications for instruments 201412 Factors in the selection of instruments 202413 Measurement redundancy 202414 Calibration of instruments 203
4141 Calibration of linear deformation devices 2034142 Calibration of volume change devices 2044143 Calibration of axial load devices 2044144 Calibration of pressure gages and transducers 204
415 Data acquisition 2064151 Manual datalogging 2064152 Computer datalogging 206
416 Test control 2064161 Control of load pressure and deformations 2064162 Principles of control systems 207
5 Preparation of Triaxial Specimens 21151 Intact specimens 211
511 Storage of samples 211512 Sample inspection and documentation 212513 Ejection of specimens 214514 Trimming of specimens 215515 Freezing technique to produce intact samples of granular materials 217
52 Laboratory preparation of specimens 217521 Slurry consolidation of clay 217522 Air pluviation of sand 219523 Depositional techniques for silty sand 222524 Undercompaction 227525 Compaction of clayey soils 232526 Compaction of soils with oversize particles 234527 Extrusion and storage 235528 Effects of specimen aging 235
53 Measurement of specimen dimensions 235531 Compacted specimens 235
54 Specimen installation 235541 Fully saturated clay specimen 236542 Unsaturated clayey soil specimen 237
6 Specimen Saturation 23961 Reasons for saturation 23962 Reasons for lack of full saturation 239
Contents ix
63 Effects of lack of full saturation 24064 B‐value test 241
641 Effects of primary factors on B‐value 241642 Effects of secondary factors on B‐value 243643 Performance of B‐value test 246
65 Determination of degree of saturation 24966 Methods of saturating triaxial specimens 250
661 Percolation with water 250662 CO2‐method 251663 Application of back pressure 252664 Vacuum procedure 258
67 Range of application of saturation methods 262
7 Testing Stage I Consolidation 26371 Objective of consolidation 26372 Selection of consolidation stresses 263
721 Anisotropic consolidation 264722 Isotropic consolidation 267723 Effects of sampling 268724 SHANSEP for soft clay 268725 Very sensitive clay 272
73 Coefficient of consolidation 272731 Effects of boundary drainage conditions 272732 Determination of time for 100 consolidation 272
8 Testing Stage II Shearing 27781 Introduction 27782 Selection of vertical strain rate 277
821 UU‐tests on clay soils 277822 CD‐ and CU‐tests on granular materials 277823 CD‐ and CU‐tests on clayey soils 277824 Effects of lubricated ends in undrained tests 282
83 Effects of lubricated ends and specimen shape 282831 Strain uniformity and stability of test configuration 282832 Modes of instability in soils 284833 Triaxial tests on sand 284834 Triaxial tests on clay 290
84 Selection of specimen size 29285 Effects of membrane penetration 293
851 Drained tests 293852 Undrained tests 293
86 Post test inspection of specimen 293
9 Corrections to Measurements 29591 Principles of measurements 29592 Types of corrections 29593 Importance of corrections ndash strong and weak specimens 29594 Tests on very short specimens 29695 Vertical load 296
951 Piston uplift 296952 Piston friction 296953 Side drains 298954 Membrane 301
x Contents
955 Buoyancy effects 308956 Techniques to avoid corrections to vertical load 309
96 Vertical deformation 309961 Compression of interfaces 309962 Bedding errors 309963 Techniques to avoid corrections to vertical deformations 311
97 Volume change 312971 Membrane penetration 312972 Volume change due to bedding errors 317973 Leaking membrane 317974 Techniques to avoid corrections to volume change 319
98 Cell and pore pressures 319981 Membrane tension 319982 Fluid self‐weight pressures 319983 Sand penetration into lubricated ends 319984 Membrane penetration 319985 Techniques to avoid corrections to cell and pore pressures 320
10 Special Tests and Test Considerations 321101 Introduction 321
1011 Low confining pressure tests on clays 3211012 Conventional low pressure tests on any soil 3211013 High pressure tests 3221014 Peats and organic soils 322
102 K0‐tests 322103 Extension tests 322
1031 Problems with the conventional triaxial extension test 3231032 Enforcing uniform strains in extension tests 324
104 Tests on unsaturated soils 3261041 Soil water retention curve 3261042 Hydraulic conductivity function 3271043 Low matric suction 3271044 High matric suction 3291045 Modeling 3301046 Triaxial testing 331
105 Frozen soils 331106 Time effects tests 333
1061 Creep tests 3331062 Stress relaxation tests 333
107 Determination of hydraulic conductivity 335108 Bender element tests 335
1081 Fabrication of bender elements 3361082 Shear modulus 3371083 Signal interpretation 3381084 First arrival time 3381085 Specimen size and geometry 3401086 Ray path analysis 3401087 Surface mounted elements 3401088 Effects of specimen material 3411089 Effects of cross‐anisotropy 341
Contents xi
11 Tests with Three Unequal Principal Stresses 343111 Introduction 343112 Tests with constant principal stress directions 344
1121 Plane strain equipment 3441122 True triaxial equipment 3451123 Results from true triaxial tests 3481124 Strength characteristics 3531125 Failure criteria for soils 355
113 Tests with rotating principal stress directions 3601131 Simple shear equipment 3601132 Directional shear cell 3621133 Torsion shear apparatus 3641134 Summary and conclusion 370
Appendix A Manufacturing of Latex Rubber Membranes 373A1 The process 373A2 Products for membrane fabrication 373A3 Create an aluminum mold 374A4 Two tanks 374A5 Mold preparation 374A6 Dipping processes 374A7 Post production 375A8 Storage 375A9 Membrane repair 375
Appendix B Design of Diaphragm Load Cells 377B1 Load cells with uniform diaphragm 377B2 Load cells with tapered diaphragm 378B3 Example Design of 5 kN beryllium copper load cell 378 B31 Punching failure 379
References 381Index 397
Preface
The triaxial test is almost always chosen for studies of new phenomena because it is rela-tively simple and versatile The triaxial test is the most suitable for such studies and it is required in geotechnical engineering for the purposes of design of specific projects and for studying and understanding the behavior of soils
The first triaxial compression test apparatus shown in Fig P1 was designed by von Kārmān (1910 1911) for testing of rock cores The scale may be deduced from the fact that the specimen is 4 cm in diameter (Vaacutesaacuterhelyi 2010) However his paper was not noticed or it was forgotten by 1930 when Casagrande at Harvard University wrote a letter to Terzaghi at the Technical University in Vienna in which he describes his visit to the hydraulics laboratory in Berlin Here he saw an apparatus for measuring the permea-bility of soil Casagrande suggested that the cylindrical specimen in this apparatus could be loaded in the vertical (axial) direction to indi-cate its strength Therefore he was going to build a prototype and Terzaghi proposed that he build one for him too This appears to be the begin-ning of triaxial testing of soils in geotechnical engineering The apparatus was immediately employed by Rendulic (Terzaghi and Rendulic 1934) for tests with and without membranes the results of which played an important role in understanding the effective stress principle as well as the role of pore water pressure and consolidation on shear strength at a time when the effective stress principle was still being questioned (Skempton 1960 de Boer 2005)
Previous books on the developments of tech-niques for triaxial testing have been written by Bishop and Henkel (1957 1962) and by Head (1986) The proceedings from a conference on Advanced Triaxial Testing of Soil and Rock (Donaghe et al 1988) was published to summa-
rize advances in this area Other books have not appeared since then To understand the present book the reader is required to have a background in basic soil mechanics some experience in soil mechanics laboratory testing and perhaps in foundation engineering
In addition to triaxial testing of soils the contents of the book may in part apply to more advanced tests and to the testing of hard soils ndash soft rocks It is written for research workers soil testing laboratories and consulting engineers The emphasis is placed on what the soil speci-men is exposed to and experiences rather than the esthetic appearance of the equipment There will be considerable use of physics and mathe-matics to illustrate the arguments and discus-sions With a few exceptions references are made to easily accessible articles in the literature Much of the book centers on how to obtain high quality experimental results and the guiding concepts for this purpose have been expressed by the car industry in their slogans ldquoQuality is Job Onerdquo (Ford Motor Company) and ldquoQuality is never an accident it is always the result of excellent workmanshiprdquo (Mercedes)
The book is organized in a logical sequence beginning with the principles of triaxial testing in Chapter 1 and the computations and presen-tations of test results in Chapter 2 The triaxial equipment is explained in Chapter 3 and instrumentation measurements and control is reviewed in Chapter 4 Preparation of triaxial specimens is presented in Chapter 5 and satu-ration of specimens is described in Chapter 6 The two testing stages in an experiment are made clear in Chapter 7 Consolidation and in Chapter 8 Shearing Chapter 9 accounts for the corrections to the measurements Chapter 10 informs about special tests and test conditions and Chapter 11 puts the results from triaxial tests in perspective by reviewing results from
xiv Preface
tests with three unequal principal stresses Appendices are provided to explain special experimental techniques Information on ven-dors for the various types of equipment may be obtained from the internet
The authorrsquos background for writing this book consists of a career in laboratory experi-mentation at university level to study and model the behavior of soils More specifically he received an MS degree in 1967 from the Technical University of Denmark for which he wrote a thesis on the influence of the intermedi-ate principal stress on the strength of sand and in retrospect ended up with the wrong conclu-sion on the basis of perfectly correct results He received a PhD from the University of California at Berkeley in 1972 with a dissertation on ldquoThe StressndashStrain and Strength Characteristics of Cohesionless Soilsrdquo which included results
from triaxial compression tests true triaxial tests and torsion shear tests to indicate the effects of the intermediate principal stress on sand behavior as well as a three‐dimensional elasto‐plastic constitutive model for the behavior of soils
With his students the author developed testing equipment performed experiments and built constitutive models for the observed soil behavior while a professor at the University of California at Los Angeles (UCLA) (1972ndash1993) Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015) Many of the experimental techniques developed over this range of years are explained in the present book
Great appreciation is expressed to John F Peters of the US Army Engineer Research and Development Center in Vicksburg MS for his careful review of the manuscript and for his many comments Special thanks go to Afshin Nabili for his invaluable assistance with drafting a large number of the figures and for modifica-tion of other diagrams for the book
Poul V Lade October 2015
References
Bishop AW and Henkel DJ (1957) Measurement of Soil Properties in Triaxial Test Edward Arnold London
Bishop AW and Henkel DJ (1962) The Measurement of Soil Properties in the Triaxial Test 2nd edn St Martinrsquos Press New York NY
de Boer R (2005) The Engineer and the Scandal Springer Berlin
Donaghe RT Chaney RC and Silver ML (eds) (1988) Advanced Triaxial Testing of Soil and Rock ASTM STP 977 ASTM Philadelphia PA
Head KH (1986) Manual of Soil Laboratory Testing ndash Volume 3 Effective Stress Tests Pentech Press London
von Kārmān T (1910) Magyar Meacuternoumlk eacutes Ėpiteacuteszegylet Koumlzloumlnye 10 212ndash226
B
b
c
aD1
D2
Figure P1 Triaxial apparatus designed and con-structed for testing of rock cores by von Kārmān (1910 1911)
Preface xv
von Kārmān T (1911) Verhandlungen Deutsche Ingenieur 55 1749ndash1757
Skempton AW (1960) Terzaghirsquos discovery of effec-tive stress In From Theory to Practice in Soil Mechanics (eds L Bjerrum A Casagrande RB Peck and AW Skempton) pp 42ndash53 John Wiley and Sons Ltd London
Terzaghi K and Rendulic L (1934) Die wirksame Flaumlchenporositaumlt des Betons Zeitschrift des Ōsterreichischen Ingenieur‐ und Architekten Vereines 86 1ndash9
Vaacutesaacuterhelyi B (2010) Tribute to the first triaxial test performed in 1910 Acta Geology and Geophysics of Hungary 45(2) 227ndash230
About the Author
Poul V Lade received his MS degree from the Technical University of Denmark in 1967 and he continued his studies at the University of California at Berkeley where he received his PhD in 1972 Subsequently his academic career began at the University of California at Los Angeles (UCLA) and he continued at Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015)
His research interests include application of appropriate experimental methods to determine the three‐dimensional stressndashstrain and strength behavior of soils and the development of consti-tutive models for frictional materials such as soils concrete and rock He developed laboratory experimental apparatus to investigate monotonic loading and large three‐dimensional stress rever-
sals in plane strain true triaxial and torsion shear equipment This also included studies of effects of principal stress rotation stability instability and liquefaction of granular materials and time effects The constitutive models are based on elasticity and work‐hardening isotropic and kinematic plasticity theories
He has written nearly 300 publications based on research performed with support from the National Science Foundation (NSF) and from the Air Force Office of Scientific Research (AFOSR) He was elected member of the Danish Academy of Technical Sciences (2001) and he was awarded Professor Ostenfeldrsquos Gold Medal from the Technical University of Denmark (2001) He was inaugural editor of Geomechanics and Engineering and he has served on the editorial boards of eight international journals on geotechnical engineering
Triaxial Testing of Soils First Edition Poul V Lade copy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd
Principles of Triaxial Testing1
11 Purpose of triaxial tests
The purpose of performing triaxial tests is to determine the mechanical properties of the soil It is assumed that the soil specimens to be tested are homogeneous and representative of the material in the field and that the desired soil properties can in fact be obtained from the triaxial tests either directly or by interpretation through some theory
The mechanical properties most often sought from triaxial tests are stressndashstrain relations volshyume change or pore pressure behavior and shear strength of the soil Included in the stressndashstrain behavior are also the compressibility and the value of the coefficient of earth pressure at rest K0 Other properties that may be obtained from the triaxial tests which include time as a component are the permeability the coefficient of consolidation and properties relating to time dependent behavior such as rate effects creep and stress relaxation
It is important that the natural soil deposit or the fill from which soil samples have been taken in the field are sufficiently uniform that the soil samples possess the properties which are approshypriate and representative of the soil mass in the field It is therefore paramount that the geology at the site is well‐known and understood Even then samples from uniform deposits may not
ldquocontainrdquo properties that are representative of the field deposit This may happen either (a) due to the change in effective stress state which is always associated with the sampling process or (b) due to mechanical disturbance from sampling transshyportation or handling in the laboratory The stressndashstrain and strength properties of very senshysitive clays which have been disturbed cannot be regenerated in the lab oratory or otherwise obtained by interpretation of tests performed on inadequate specimens The effects of sampling will briefly be discussed below in connection with choice of consolidation pressure in the trishyaxial test The topic of sampling is otherwise outshyside the scope of the present treatment
12 Concept of testing
The concept to be pursued in testing of soils is to simulate as closely as possible the process that goes on in the field Because there is a large number of variables (eg density water content degree of saturation overconsolidation ratio loading conditions stress paths) that influence the resulting soil behavior the simplest and most direct way of obtaining information pertinent to the field conditions is to duplicate these as closely as possible
2 Triaxial Testing of Soils
However because of limitations in equipment and because of practical limitations on the amount of testing that can be performed for each project it is essential that
1 The true field loading conditions (including the drainage conditions) are known
2 The laboratory equipment can reproduce these conditions to a required degree of accuracy
3 A reasonable estimate can be made of the sigshynificance of the differences between the field loading conditions and those that can be proshyduced in the laboratory equipment
It is clear that the triaxial test in many resshypects is incapable of simulating several imporshytant aspects of field loading conditions For example the effects of the intermediate princishypal stress the effects of rotation of principal stresses and the effects of partial drainage durshying loading in the field cannot be investigated on the basis of the triaxial test The effects of such conditions require studies involving other types of equipment or analyses of boundary value problems either by closed form solutions or solutions obtained by numerical techniques
To provide some background for evaluation of the results of triaxial tests other types of laboratory shear tests and typical results from such tests are presented in Chapter 11 The relashytions between the different types of tests are reviewed and their advantages and limitations are discussed
13 The triaxial test
The triaxial test is most often performed on a cylindrical specimen as shown in Fig 11(a) Principal stresses are applied to the specimen as indicated in Fig 11(b) First a confining pressure σ3 is applied to the specimen This pressure acts all around and therefore on all planes in the specimen Then an additional stress difference σd is applied in the axial direction The stress applied externally to the specimen in the axial direction is
σ σ σ1 3= +d (11)
and therefore
σ σ σd = minus1 3 (12)
In the general case three principal stresses σ1 σ2 and σ3 may act on a soil element in the field However only two different principal stresses can be applied to the specimen in the convenshytional triaxial test The intermediate principal stress σ2 can only have values as follows
σ σ2 3= Triaxial compression (13)
σ σ2 1= Triaxial extension (14)
The condition of triaxial extension can be achieved by applying negative stress differshyences to the specimen This merely produces a reduction in compression in the extension direcshytion but no tension occurs in the specimen The state of stress applied to the specimen is in both cases axisymmetric The triaxial compression test will be discussed in the following while the triaxial extension test is discussed in Chapter 10
The test is performed using triaxial apparashytus as seen in the schematic illustration in Fig 12 The specimen is surrounded by a cap and a base and a membrane This unit is placed in a triaxial cell in which the cell pressure can be applied The cell pressure acts as a hydrostatic confinement for the specimen and the pressure is therefore the same in all directions In addition
σ1
(a) (b)
σ1 = σd + σ3
σ2 = σ3
σd = σ1 ndash σ3σ3
σ3σ3
σ3
σd
Figure 11 (a) Cylindrical specimen for triaxial testing and (b) stresses applied to a triaxial specimen
Principles of Triaxial Testing 3
a deviator load can be applied through a piston that goes through the top of the cell and loads the specimen in the axial direction
The vertical deformation of the specimen may be measured by a dial gage attached to the piston which travels the same vertical distance as the cap sitting on top of the specimen Drainage lines are connected to the water saturated specishymen through the base (or both the cap and the base) and connected to a burette outside the trishyaxial cell This allows for measurements of the volume changes of the specimen during the test
Alternatively the connection to the burette can be shut off thereby preventing the specimen from changing volume Instead the pore water pressure can be measured on a transducer conshynected to the drainage line
The following quantities are measured in a typical triaxial test
1 Confining pressure2 Deviator load3 Vertical (or axial) deformation4 Volume change or pore water pressure
These measurements constitute the data base from which other quantities can be derived
[eg stress difference (σ1 ndash σ3) axial strain ε1 and volumetric strain εv]
14 Advantages and limitations
Whereas the triaxial test potentially can proshyvide a substantial proportion of the mechanical properties required for a project it has limitashytions especially when special conditions are encountered and necessitates clarification based on experimentation
The advantages of the triaxial test are
1 Drainage can be controlled (onndashoff)2 Volume change or pore pressure can be
measured3 Suction can be controlled in partially satushy
rated soils4 Measured deformations allow calculation of
strains and moduli5 A larger variety of stress and strain paths
that occur in the field can be applied in the triaxial apparatus than in any other testing apparatus (eg initial anisotropic consolidashytion at any stress ratio including K0 extension active and passive shear)
The limitations of the triaxial test are
1 Stress concentrations due to friction between specimen and end plates (cap and base) cause nonuniform strains and stresses and therefore nonuniform stressndashstrain volume change or pore pressure response
2 Only axisymmetric stress conditions can be applied to the specimen whereas most field problems involve plane strain or general three‐dimensional conditions with rotation of principal stresses
3 Triaxial tests cannot provide all necessary data required to characterize the behavior of an anisotropic or a cross‐anisotropic soil deposit as illustrated in Fig 13
4 Although the axisymmetric principal stress condition is limited it is more difficult to apply proper shear stresses or tension to soil in relatively simple tests
The first limitation listed above can be overcome by applying lubricated ends on the
Pore pressure transducer
On-Off valve
Burette
Piston
Dial gage
Triaxial cell
P = σd middot A
Aprime
σcell
σ3
σ3 σ3= σcell
Figure 12 Schematic diagram of triaxial apparatus
4 Triaxial Testing of Soils
specimen such that uniform strains and stresses and therefore correct soil response can be proshyduced This is discussed in Chapter 3 In addishytion to the limitations listed above it should be mentioned that it may be easier to reproduce certain stress paths in other specialty equipment than in the triaxial apparatus (eg K0‐test)
Although the triaxial test is limited as explained under points 2 and 3 above it does combine versatility with relative simplicity in concept and performance Other equipment in which three unequal principal stresses can be applied or in which the principal stress direcshytions can be rotated do not have the versatility or is more com plicated to operate Thus other types of equipment have their own advantages and limitations These other equipment types
include plane strain true triaxial simple shear directional shear and torsion shear apparatus All these pieces of equipment are with the excepshytion of the simple shear apparatus employed mainly for research purposes Their operational modes capabilities and results are reviewed in Chapter 11
15 Test stages ndash consolidation and shearing
Laboratory tests are made to simulate field loadshying conditions as close as possible Most field conditions and the corresponding tests can be simplified to consist of two stages consolidation and shearing
Axis of symmetry
1Eh
1Eh
1Ghv
1Ev
ndashmicrohvEh
ndashmicrohvEn
2(1 + microhh)En
ndashmicrohhEn
ndashmicrohvEh
ndashmicrohvEh
ndashmicrohhEh
0
h
h
v
0 0
σh
σh
σv
τhv
τhv
τvh
τvh
σh
σv
σh
τhv
τvh
τhh
τhh τhh
ϵh
ϵv
ϵh
γhv
γvh
γhh
0
Require tests withapplication of
shear stresses
0 0
0
0 0 0 00
1Ghv0 0 0 00
0 0 0 0 0
0 0
bull =
Figure 13 Cross‐anisotropic soil requiring results from more than triaxial tests for full characterization
Principles of Triaxial Testing 5
151 Consolidation
In the first stage the initial condition of the soil is established in terms of effective stresses and stress history (including overconsolidation if applicable) Thus stresses are applied correshysponding to those acting on the element of soil in the field due to weight of the overlying soil strata and other materials or structures that exist at the time the mechanical properties (stressndashstrain strength etc) are sought Sufficient time is allowed for complete consolidation to occur under the applied stresses The condition in the field element has now been established in the triaxial specimen
152 Shearing
In the second stage of the triaxial test an addishytional stress is applied to reach peak failure and beyond under relevant drainage conditions The additional stress applied to the specimen should correspond as closely as possible to the change in stress on the field element due to some new change in the overall field loading situashytion This change may consist of a vertical stress increase or decrease (eg due to addition of a structure or excavation of overlying soil strata) or of a horizontal stress increase or decrease (eg due to the same constructions causing the vertical stress changes) Any combination of vertical and horizontal stress changes may be simulated in the triaxial test Examples of vertishycal and horizontal stress changes in the field are shown in Fig 14
Usually it is desirable to know how much change in load the soil can sustain without failshying and how much deformation will occur under normal working conditions The test is therefore usually continued to find the strength of the soil under the appropriate loading condishytions The results are used with an appropriate factor of safety so that normal working stresses are always somewhat below the peak strength
The stressndashstrain relations obtained from the triaxial tests provide the basis for determinashytion of deformations in the field This may be done in a simplified manner by closed‐form
solutions or it may be done by employing the results of the triaxial tests for calibration of a constitutive model used with a numerical method in finite element or finite difference computer programs
16 Types of tests
The drainage conditions in the field must be duplicated as well as possible in the laboratory tests This may be done by appropriate drainage facilities or preventions as discussed above for the triaxial test In most cases the field drainage conditions can be approximated by one of the following three types of tests
1 Consolidated‐drained test called a CD‐test or just a drained test
2 Consolidated‐undrained test or a CU‐test3 Unconsolidated‐undrained test or a UU‐test
Additionalload
Excavation
ΔσV asymp 0
ΔσV asymp 0
ΔσV gt 0
ΔσV lt 0
Δσh lt 0
Δσh gt 0
Δσh lt ΔσV
Δσh
Figure 14 Examples of stress changes leading to failure in the field
6 Triaxial Testing of Soils
These tests are described in ASTM Standards D7181 (2014) D4767 (2014) and D2850 (2014) respectively
Which condition of drainage in the laboratory test logically corresponds to each case in the field depends on a comparison of loading rate with the rate at which the water can escape or be sucked into the ground Thus the permeability of the soil and the drainage boundary conditions in the field together with the loading rate play key roles in determination of the type of analysis and the type of test drained or undrained that are appropriate for each case Field cases with partial drainage can be correctly duplicated in laboratory tests if the effective stress path is determined for the design condition However the idea of the CD‐ CU‐ and UU‐tests is to make it relatively simple for the design engineer to analyze a condition that will render a sufficient factor of safety under the actual drainage condishytion without trying to estimate and experimenshytally replicate the actual stress path
It has been determined through experience and common sense that the extreme conditions are drained and undrained with and without consolidation As a practical matter in a commershycial laboratory it is easier to run an undrained test than a drained test because it is easier and faster to measure pore pressures than volume change Therefore even drained parameters are more likely to be estimated from a CU‐test than from a CD‐test
161 Simulation of field conditions
Presented below is a brief review of the three types of tests together with examples of field cases for which the tests are appropriate and with typishycal strength results shown on Mohr diagrams
Drained tests
Isotropic consolidation is most often used in the first stage of the triaxial test However anisoshytropic consolidation with any stress ratio is also possible
The shearing stage of a drained test is pershyformed so slowly the soil is so permeable and the drainage facilities are such that no excess
pore pressure (positive or negative) can exist in the specimen at any stage of the test that is
∆u = 0 (15)
It follows then from the effective stress principle
prime = minusσ σ u (16)
that the effective stress changes are always the same as the total stress changes
A soil specimen always changes volume during shearing in a drained test If it contracts in volume it expels pore fluid (usually water or air) and if it expands in volume (dilates) then it sucks water or air into the pores If a non‐zero pore pressure is generated during the test (eg by performing the shearing too fast so the water does not have sufficient time to escape) then the specimen will expel or suck water such that the pore pressure goes towards zero to try to achieve equilibrium between externally applied stresses and internal effective stresses Thus there will always be volume changes in a drained test Consequently the water content the void ratio and the dry density of the specimen at the end of the test are most often not the same as at the beginning
The following field conditions can be simushylated with acceptable accuracy in the drained test
1 Almost all cases involving coarse sands and gravel whether saturated or not (except if confined in eg a lens andor exposed to rapid loading as in eg an earthquake)
2 Many cases involving fine sand and someshytimes silt if the field loads are applied reashysonable slowly
3 Long term loading of any soil as for examplea) Cut slopes several years after excavationb) Embankment constructed very slowly in
layers over a soft clay depositc) Earth dam with steady seepaged) Foundation on clay a long time after
construction
These cases are illustrated in Fig 15The strength results obtained from drained
tests are illustrated schematically on the Mohr diagram in Fig 16 The shear strength of soils increases with increasing confining pressure
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
Triaxial Testing of Soils
Triaxial Testing of Soils
Poul V Lade
This edition first published 2016copy 2016 by John Wiley amp Sons Ltd
Registered officeJohn Wiley amp Sons Ltd The Atrium Southern Gate Chichester West Sussex PO19 8SQ United Kingdom
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All rights reserved No part of this publication may be reproduced stored in a retrieval system or transmitted in any form or by any means electronic mechanical photocopying recording or otherwise except as permitted by the UK Copyright Designs and Patents Act 1988 without the prior permission of the publisher
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Limit of LiabilityDisclaimer of Warranty While the publisher and author(s) have used their best efforts in preparing this book they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose It is sold on the understanding that the publisher is not engaged in rendering professional services and neither the publisher nor the author shall be liable for damages arising herefrom If professional advice or other expert assistance is required the services of a competent professional should be sought
Disclaimer All reasonable attempts have been made to contact the owners of copyrighted material used in this book [Figures 112 338 341 450 451 455ab Table 71] However if you are the copyright owner of any source used in this book which is not credited please notify the Publisher and this will be corrected in any subsequent reprints or new editions
Library of Congress Cataloging‐in‐Publication data applied for
ISBN 9781119106623
A catalogue record for this book is available from the British Library
Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic books
Set in 1012pt Palatino by SPi Global Pondicherry India
1 2016
Contents
Preface xiiiAbout the Author xvii
1 Principles of Triaxial Testing 111 Purpose of triaxial tests 112 Concept of testing 113 The triaxial test 214 Advantages and limitations 315 Test stages ndash consolidation and shearing 4
151 Consolidation 5152 Shearing 5
16 Types of tests 5161 Simulation of field conditions 6162 Selection of test type 12
2 Computations and Presentation of Test Results 1321 Data reduction 13
211 Sign rule ndash 2D 13212 Strains 13213 Cross‐sectional area 23214 Stresses 24215 Corrections 25216 The effective stress principle 25217 Stress analysis in two dimensions ndash Mohrrsquos circle 25218 Strain analysis in two dimensions ndash Mohrrsquos circle 27
22 Stressndashstrain diagrams 28221 Basic diagrams 28222 Modulus evaluation 37223 Derived diagrams 41224 Normalized stressndashstrain behavior 48225 Patterns of soil behavior ndash error recognition 49
23 Strength diagrams 51231 Definition of effective and total strengths 51232 MohrndashCoulomb failure concept 51233 MohrndashCoulomb for triaxial compression 54234 Curved failure envelope 55235 MIT pndashq diagram 57236 Cambridge pndashq diagram 59237 Determination of best‐fit soil strength parameters 60238 Characterization of total strength 60
24 Stress paths 61241 Drained stress paths 61242 Total stress paths in undrained tests 61243 Effective stress paths in undrained tests 61244 Normalized pndashq diagrams 66245 Vector curves 68
vi Contents
25 Linear regression analysis 72251 MIT pndashq diagram 72252 Cambridge pndashq diagram 74253 Correct and incorrect linear regression analyses 75
26 Three‐dimensional stress states 76261 General 3D stress states 76262 Stress invariants 76263 Stress deviator invariants 80264 Magnitudes and directions of principal stresses 81
27 Principal stress space 83271 Octahedral stresses 83272 Triaxial plane 84273 Octahedral plane 86274 Characterization of 3D stress conditions 87275 Shapes of stress invariants in principal stress space 89276 Procedures for projecting stress points onto a common
octahedral plane 90277 Procedure for plotting stress points on an octahedral plane 96278 Representation of test results with principal stress rotation 97
3 Triaxial Equipment 9931 Triaxial setup 99
311 Specimen cap and base 99312 Membrane 103313 O‐rings 105314 Drainage system 106315 Leakage of triaxial setup 112316 Volume change devices 113317 Cell fluid 113318 Lubricated ends 120
32 Triaxial cell 125321 Cell types 125322 Cell wall 127323 Hoek cell 128
33 Piston 128331 Piston friction 129332 Connections between piston cap and specimen 132
34 Pressure supply 133341 Water column 133342 Mercury pot system 134343 Compressed gas 135344 Mechanically compressed fluids 136345 Pressure intensifiers 137346 Pressure transfer to triaxial cell 137347 Vacuum to supply effective confining pressure 138
35 Vertical loading equipment 139351 Deformation or strain control 139352 Load control 140353 Stress control 141354 Combination of load control and deformation control 141355 Stiffness requirements 143
Contents vii
356 Strain control versus load control 14336 Triaxial cell with integrated loading system 143
4 Instrumentation Measurements and Control 14541 Purpose of instrumentation 14542 Principle of measurements 14543 Instrument characteristics 14744 Electrical instrument operation principles 149
441 Strain gage 149442 Linear variable differential transformer 151443 Proximity gage 153444 Reluctance gage 153445 Electrolytic liquid level 154446 Hall effect technique 154447 Elastomer gage 154448 Capacitance technique 155
45 Instrument measurement uncertainty 155451 Accuracy precision and resolution 156452 Measurement uncertainty in triaxial tests 156
46 Instrument performance characteristics 158461 Excitation 158462 Zero shift 159463 Sensitivity 159464 Thermal effects on zero shift and sensitivity 159465 Natural frequency 159466 Nonlinearity 159467 Hysteresis 159468 Repeatability 159469 Range 1594610 Overload capacity 1604611 Overload protection 1604612 Volumetric flexibility of pressure transducers 160
47 Measurement of linear deformations 160471 Inside and outside measurements 160472 Recommended gage length 162473 Operational requirements 162474 Electric wires 163475 Clip gages 163476 Linear variable differential transformer setup 167477 Proximity gage setup 168478 Inclinometer gages 170479 Hall effect gage 1714710 X‐ray technique 1714711 Video tracking and high‐speed photography 1714712 Optical deformation measurements 1724713 Characteristics of linear deformation measurement devices 174
48 Measurement of volume changes 178481 Requirements for volume change devices 178482 Measurements from saturated specimens 180483 Measurements from a triaxial cell 189484 Measurements from dry and partly saturated specimens 192
viii Contents
49 Measurement of axial load 195491 Mechanical force transducers 195492 Operating principle of strain gage load cells 197493 Primary sensors 197494 Fabrication of diaphragm load cells 198495 Load capacity and overload protection 198
410 Measurement of pressure 1994101 Measurement of cell pressure 1994102 Measurement of pore pressure 1994103 Operating principles of pressure transducers 2014104 Fabrication of pressure transducers 2014105 Pressure capacity and overpressure protection 201
411 Specifications for instruments 201412 Factors in the selection of instruments 202413 Measurement redundancy 202414 Calibration of instruments 203
4141 Calibration of linear deformation devices 2034142 Calibration of volume change devices 2044143 Calibration of axial load devices 2044144 Calibration of pressure gages and transducers 204
415 Data acquisition 2064151 Manual datalogging 2064152 Computer datalogging 206
416 Test control 2064161 Control of load pressure and deformations 2064162 Principles of control systems 207
5 Preparation of Triaxial Specimens 21151 Intact specimens 211
511 Storage of samples 211512 Sample inspection and documentation 212513 Ejection of specimens 214514 Trimming of specimens 215515 Freezing technique to produce intact samples of granular materials 217
52 Laboratory preparation of specimens 217521 Slurry consolidation of clay 217522 Air pluviation of sand 219523 Depositional techniques for silty sand 222524 Undercompaction 227525 Compaction of clayey soils 232526 Compaction of soils with oversize particles 234527 Extrusion and storage 235528 Effects of specimen aging 235
53 Measurement of specimen dimensions 235531 Compacted specimens 235
54 Specimen installation 235541 Fully saturated clay specimen 236542 Unsaturated clayey soil specimen 237
6 Specimen Saturation 23961 Reasons for saturation 23962 Reasons for lack of full saturation 239
Contents ix
63 Effects of lack of full saturation 24064 B‐value test 241
641 Effects of primary factors on B‐value 241642 Effects of secondary factors on B‐value 243643 Performance of B‐value test 246
65 Determination of degree of saturation 24966 Methods of saturating triaxial specimens 250
661 Percolation with water 250662 CO2‐method 251663 Application of back pressure 252664 Vacuum procedure 258
67 Range of application of saturation methods 262
7 Testing Stage I Consolidation 26371 Objective of consolidation 26372 Selection of consolidation stresses 263
721 Anisotropic consolidation 264722 Isotropic consolidation 267723 Effects of sampling 268724 SHANSEP for soft clay 268725 Very sensitive clay 272
73 Coefficient of consolidation 272731 Effects of boundary drainage conditions 272732 Determination of time for 100 consolidation 272
8 Testing Stage II Shearing 27781 Introduction 27782 Selection of vertical strain rate 277
821 UU‐tests on clay soils 277822 CD‐ and CU‐tests on granular materials 277823 CD‐ and CU‐tests on clayey soils 277824 Effects of lubricated ends in undrained tests 282
83 Effects of lubricated ends and specimen shape 282831 Strain uniformity and stability of test configuration 282832 Modes of instability in soils 284833 Triaxial tests on sand 284834 Triaxial tests on clay 290
84 Selection of specimen size 29285 Effects of membrane penetration 293
851 Drained tests 293852 Undrained tests 293
86 Post test inspection of specimen 293
9 Corrections to Measurements 29591 Principles of measurements 29592 Types of corrections 29593 Importance of corrections ndash strong and weak specimens 29594 Tests on very short specimens 29695 Vertical load 296
951 Piston uplift 296952 Piston friction 296953 Side drains 298954 Membrane 301
x Contents
955 Buoyancy effects 308956 Techniques to avoid corrections to vertical load 309
96 Vertical deformation 309961 Compression of interfaces 309962 Bedding errors 309963 Techniques to avoid corrections to vertical deformations 311
97 Volume change 312971 Membrane penetration 312972 Volume change due to bedding errors 317973 Leaking membrane 317974 Techniques to avoid corrections to volume change 319
98 Cell and pore pressures 319981 Membrane tension 319982 Fluid self‐weight pressures 319983 Sand penetration into lubricated ends 319984 Membrane penetration 319985 Techniques to avoid corrections to cell and pore pressures 320
10 Special Tests and Test Considerations 321101 Introduction 321
1011 Low confining pressure tests on clays 3211012 Conventional low pressure tests on any soil 3211013 High pressure tests 3221014 Peats and organic soils 322
102 K0‐tests 322103 Extension tests 322
1031 Problems with the conventional triaxial extension test 3231032 Enforcing uniform strains in extension tests 324
104 Tests on unsaturated soils 3261041 Soil water retention curve 3261042 Hydraulic conductivity function 3271043 Low matric suction 3271044 High matric suction 3291045 Modeling 3301046 Triaxial testing 331
105 Frozen soils 331106 Time effects tests 333
1061 Creep tests 3331062 Stress relaxation tests 333
107 Determination of hydraulic conductivity 335108 Bender element tests 335
1081 Fabrication of bender elements 3361082 Shear modulus 3371083 Signal interpretation 3381084 First arrival time 3381085 Specimen size and geometry 3401086 Ray path analysis 3401087 Surface mounted elements 3401088 Effects of specimen material 3411089 Effects of cross‐anisotropy 341
Contents xi
11 Tests with Three Unequal Principal Stresses 343111 Introduction 343112 Tests with constant principal stress directions 344
1121 Plane strain equipment 3441122 True triaxial equipment 3451123 Results from true triaxial tests 3481124 Strength characteristics 3531125 Failure criteria for soils 355
113 Tests with rotating principal stress directions 3601131 Simple shear equipment 3601132 Directional shear cell 3621133 Torsion shear apparatus 3641134 Summary and conclusion 370
Appendix A Manufacturing of Latex Rubber Membranes 373A1 The process 373A2 Products for membrane fabrication 373A3 Create an aluminum mold 374A4 Two tanks 374A5 Mold preparation 374A6 Dipping processes 374A7 Post production 375A8 Storage 375A9 Membrane repair 375
Appendix B Design of Diaphragm Load Cells 377B1 Load cells with uniform diaphragm 377B2 Load cells with tapered diaphragm 378B3 Example Design of 5 kN beryllium copper load cell 378 B31 Punching failure 379
References 381Index 397
Preface
The triaxial test is almost always chosen for studies of new phenomena because it is rela-tively simple and versatile The triaxial test is the most suitable for such studies and it is required in geotechnical engineering for the purposes of design of specific projects and for studying and understanding the behavior of soils
The first triaxial compression test apparatus shown in Fig P1 was designed by von Kārmān (1910 1911) for testing of rock cores The scale may be deduced from the fact that the specimen is 4 cm in diameter (Vaacutesaacuterhelyi 2010) However his paper was not noticed or it was forgotten by 1930 when Casagrande at Harvard University wrote a letter to Terzaghi at the Technical University in Vienna in which he describes his visit to the hydraulics laboratory in Berlin Here he saw an apparatus for measuring the permea-bility of soil Casagrande suggested that the cylindrical specimen in this apparatus could be loaded in the vertical (axial) direction to indi-cate its strength Therefore he was going to build a prototype and Terzaghi proposed that he build one for him too This appears to be the begin-ning of triaxial testing of soils in geotechnical engineering The apparatus was immediately employed by Rendulic (Terzaghi and Rendulic 1934) for tests with and without membranes the results of which played an important role in understanding the effective stress principle as well as the role of pore water pressure and consolidation on shear strength at a time when the effective stress principle was still being questioned (Skempton 1960 de Boer 2005)
Previous books on the developments of tech-niques for triaxial testing have been written by Bishop and Henkel (1957 1962) and by Head (1986) The proceedings from a conference on Advanced Triaxial Testing of Soil and Rock (Donaghe et al 1988) was published to summa-
rize advances in this area Other books have not appeared since then To understand the present book the reader is required to have a background in basic soil mechanics some experience in soil mechanics laboratory testing and perhaps in foundation engineering
In addition to triaxial testing of soils the contents of the book may in part apply to more advanced tests and to the testing of hard soils ndash soft rocks It is written for research workers soil testing laboratories and consulting engineers The emphasis is placed on what the soil speci-men is exposed to and experiences rather than the esthetic appearance of the equipment There will be considerable use of physics and mathe-matics to illustrate the arguments and discus-sions With a few exceptions references are made to easily accessible articles in the literature Much of the book centers on how to obtain high quality experimental results and the guiding concepts for this purpose have been expressed by the car industry in their slogans ldquoQuality is Job Onerdquo (Ford Motor Company) and ldquoQuality is never an accident it is always the result of excellent workmanshiprdquo (Mercedes)
The book is organized in a logical sequence beginning with the principles of triaxial testing in Chapter 1 and the computations and presen-tations of test results in Chapter 2 The triaxial equipment is explained in Chapter 3 and instrumentation measurements and control is reviewed in Chapter 4 Preparation of triaxial specimens is presented in Chapter 5 and satu-ration of specimens is described in Chapter 6 The two testing stages in an experiment are made clear in Chapter 7 Consolidation and in Chapter 8 Shearing Chapter 9 accounts for the corrections to the measurements Chapter 10 informs about special tests and test conditions and Chapter 11 puts the results from triaxial tests in perspective by reviewing results from
xiv Preface
tests with three unequal principal stresses Appendices are provided to explain special experimental techniques Information on ven-dors for the various types of equipment may be obtained from the internet
The authorrsquos background for writing this book consists of a career in laboratory experi-mentation at university level to study and model the behavior of soils More specifically he received an MS degree in 1967 from the Technical University of Denmark for which he wrote a thesis on the influence of the intermedi-ate principal stress on the strength of sand and in retrospect ended up with the wrong conclu-sion on the basis of perfectly correct results He received a PhD from the University of California at Berkeley in 1972 with a dissertation on ldquoThe StressndashStrain and Strength Characteristics of Cohesionless Soilsrdquo which included results
from triaxial compression tests true triaxial tests and torsion shear tests to indicate the effects of the intermediate principal stress on sand behavior as well as a three‐dimensional elasto‐plastic constitutive model for the behavior of soils
With his students the author developed testing equipment performed experiments and built constitutive models for the observed soil behavior while a professor at the University of California at Los Angeles (UCLA) (1972ndash1993) Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015) Many of the experimental techniques developed over this range of years are explained in the present book
Great appreciation is expressed to John F Peters of the US Army Engineer Research and Development Center in Vicksburg MS for his careful review of the manuscript and for his many comments Special thanks go to Afshin Nabili for his invaluable assistance with drafting a large number of the figures and for modifica-tion of other diagrams for the book
Poul V Lade October 2015
References
Bishop AW and Henkel DJ (1957) Measurement of Soil Properties in Triaxial Test Edward Arnold London
Bishop AW and Henkel DJ (1962) The Measurement of Soil Properties in the Triaxial Test 2nd edn St Martinrsquos Press New York NY
de Boer R (2005) The Engineer and the Scandal Springer Berlin
Donaghe RT Chaney RC and Silver ML (eds) (1988) Advanced Triaxial Testing of Soil and Rock ASTM STP 977 ASTM Philadelphia PA
Head KH (1986) Manual of Soil Laboratory Testing ndash Volume 3 Effective Stress Tests Pentech Press London
von Kārmān T (1910) Magyar Meacuternoumlk eacutes Ėpiteacuteszegylet Koumlzloumlnye 10 212ndash226
B
b
c
aD1
D2
Figure P1 Triaxial apparatus designed and con-structed for testing of rock cores by von Kārmān (1910 1911)
Preface xv
von Kārmān T (1911) Verhandlungen Deutsche Ingenieur 55 1749ndash1757
Skempton AW (1960) Terzaghirsquos discovery of effec-tive stress In From Theory to Practice in Soil Mechanics (eds L Bjerrum A Casagrande RB Peck and AW Skempton) pp 42ndash53 John Wiley and Sons Ltd London
Terzaghi K and Rendulic L (1934) Die wirksame Flaumlchenporositaumlt des Betons Zeitschrift des Ōsterreichischen Ingenieur‐ und Architekten Vereines 86 1ndash9
Vaacutesaacuterhelyi B (2010) Tribute to the first triaxial test performed in 1910 Acta Geology and Geophysics of Hungary 45(2) 227ndash230
About the Author
Poul V Lade received his MS degree from the Technical University of Denmark in 1967 and he continued his studies at the University of California at Berkeley where he received his PhD in 1972 Subsequently his academic career began at the University of California at Los Angeles (UCLA) and he continued at Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015)
His research interests include application of appropriate experimental methods to determine the three‐dimensional stressndashstrain and strength behavior of soils and the development of consti-tutive models for frictional materials such as soils concrete and rock He developed laboratory experimental apparatus to investigate monotonic loading and large three‐dimensional stress rever-
sals in plane strain true triaxial and torsion shear equipment This also included studies of effects of principal stress rotation stability instability and liquefaction of granular materials and time effects The constitutive models are based on elasticity and work‐hardening isotropic and kinematic plasticity theories
He has written nearly 300 publications based on research performed with support from the National Science Foundation (NSF) and from the Air Force Office of Scientific Research (AFOSR) He was elected member of the Danish Academy of Technical Sciences (2001) and he was awarded Professor Ostenfeldrsquos Gold Medal from the Technical University of Denmark (2001) He was inaugural editor of Geomechanics and Engineering and he has served on the editorial boards of eight international journals on geotechnical engineering
Triaxial Testing of Soils First Edition Poul V Lade copy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd
Principles of Triaxial Testing1
11 Purpose of triaxial tests
The purpose of performing triaxial tests is to determine the mechanical properties of the soil It is assumed that the soil specimens to be tested are homogeneous and representative of the material in the field and that the desired soil properties can in fact be obtained from the triaxial tests either directly or by interpretation through some theory
The mechanical properties most often sought from triaxial tests are stressndashstrain relations volshyume change or pore pressure behavior and shear strength of the soil Included in the stressndashstrain behavior are also the compressibility and the value of the coefficient of earth pressure at rest K0 Other properties that may be obtained from the triaxial tests which include time as a component are the permeability the coefficient of consolidation and properties relating to time dependent behavior such as rate effects creep and stress relaxation
It is important that the natural soil deposit or the fill from which soil samples have been taken in the field are sufficiently uniform that the soil samples possess the properties which are approshypriate and representative of the soil mass in the field It is therefore paramount that the geology at the site is well‐known and understood Even then samples from uniform deposits may not
ldquocontainrdquo properties that are representative of the field deposit This may happen either (a) due to the change in effective stress state which is always associated with the sampling process or (b) due to mechanical disturbance from sampling transshyportation or handling in the laboratory The stressndashstrain and strength properties of very senshysitive clays which have been disturbed cannot be regenerated in the lab oratory or otherwise obtained by interpretation of tests performed on inadequate specimens The effects of sampling will briefly be discussed below in connection with choice of consolidation pressure in the trishyaxial test The topic of sampling is otherwise outshyside the scope of the present treatment
12 Concept of testing
The concept to be pursued in testing of soils is to simulate as closely as possible the process that goes on in the field Because there is a large number of variables (eg density water content degree of saturation overconsolidation ratio loading conditions stress paths) that influence the resulting soil behavior the simplest and most direct way of obtaining information pertinent to the field conditions is to duplicate these as closely as possible
2 Triaxial Testing of Soils
However because of limitations in equipment and because of practical limitations on the amount of testing that can be performed for each project it is essential that
1 The true field loading conditions (including the drainage conditions) are known
2 The laboratory equipment can reproduce these conditions to a required degree of accuracy
3 A reasonable estimate can be made of the sigshynificance of the differences between the field loading conditions and those that can be proshyduced in the laboratory equipment
It is clear that the triaxial test in many resshypects is incapable of simulating several imporshytant aspects of field loading conditions For example the effects of the intermediate princishypal stress the effects of rotation of principal stresses and the effects of partial drainage durshying loading in the field cannot be investigated on the basis of the triaxial test The effects of such conditions require studies involving other types of equipment or analyses of boundary value problems either by closed form solutions or solutions obtained by numerical techniques
To provide some background for evaluation of the results of triaxial tests other types of laboratory shear tests and typical results from such tests are presented in Chapter 11 The relashytions between the different types of tests are reviewed and their advantages and limitations are discussed
13 The triaxial test
The triaxial test is most often performed on a cylindrical specimen as shown in Fig 11(a) Principal stresses are applied to the specimen as indicated in Fig 11(b) First a confining pressure σ3 is applied to the specimen This pressure acts all around and therefore on all planes in the specimen Then an additional stress difference σd is applied in the axial direction The stress applied externally to the specimen in the axial direction is
σ σ σ1 3= +d (11)
and therefore
σ σ σd = minus1 3 (12)
In the general case three principal stresses σ1 σ2 and σ3 may act on a soil element in the field However only two different principal stresses can be applied to the specimen in the convenshytional triaxial test The intermediate principal stress σ2 can only have values as follows
σ σ2 3= Triaxial compression (13)
σ σ2 1= Triaxial extension (14)
The condition of triaxial extension can be achieved by applying negative stress differshyences to the specimen This merely produces a reduction in compression in the extension direcshytion but no tension occurs in the specimen The state of stress applied to the specimen is in both cases axisymmetric The triaxial compression test will be discussed in the following while the triaxial extension test is discussed in Chapter 10
The test is performed using triaxial apparashytus as seen in the schematic illustration in Fig 12 The specimen is surrounded by a cap and a base and a membrane This unit is placed in a triaxial cell in which the cell pressure can be applied The cell pressure acts as a hydrostatic confinement for the specimen and the pressure is therefore the same in all directions In addition
σ1
(a) (b)
σ1 = σd + σ3
σ2 = σ3
σd = σ1 ndash σ3σ3
σ3σ3
σ3
σd
Figure 11 (a) Cylindrical specimen for triaxial testing and (b) stresses applied to a triaxial specimen
Principles of Triaxial Testing 3
a deviator load can be applied through a piston that goes through the top of the cell and loads the specimen in the axial direction
The vertical deformation of the specimen may be measured by a dial gage attached to the piston which travels the same vertical distance as the cap sitting on top of the specimen Drainage lines are connected to the water saturated specishymen through the base (or both the cap and the base) and connected to a burette outside the trishyaxial cell This allows for measurements of the volume changes of the specimen during the test
Alternatively the connection to the burette can be shut off thereby preventing the specimen from changing volume Instead the pore water pressure can be measured on a transducer conshynected to the drainage line
The following quantities are measured in a typical triaxial test
1 Confining pressure2 Deviator load3 Vertical (or axial) deformation4 Volume change or pore water pressure
These measurements constitute the data base from which other quantities can be derived
[eg stress difference (σ1 ndash σ3) axial strain ε1 and volumetric strain εv]
14 Advantages and limitations
Whereas the triaxial test potentially can proshyvide a substantial proportion of the mechanical properties required for a project it has limitashytions especially when special conditions are encountered and necessitates clarification based on experimentation
The advantages of the triaxial test are
1 Drainage can be controlled (onndashoff)2 Volume change or pore pressure can be
measured3 Suction can be controlled in partially satushy
rated soils4 Measured deformations allow calculation of
strains and moduli5 A larger variety of stress and strain paths
that occur in the field can be applied in the triaxial apparatus than in any other testing apparatus (eg initial anisotropic consolidashytion at any stress ratio including K0 extension active and passive shear)
The limitations of the triaxial test are
1 Stress concentrations due to friction between specimen and end plates (cap and base) cause nonuniform strains and stresses and therefore nonuniform stressndashstrain volume change or pore pressure response
2 Only axisymmetric stress conditions can be applied to the specimen whereas most field problems involve plane strain or general three‐dimensional conditions with rotation of principal stresses
3 Triaxial tests cannot provide all necessary data required to characterize the behavior of an anisotropic or a cross‐anisotropic soil deposit as illustrated in Fig 13
4 Although the axisymmetric principal stress condition is limited it is more difficult to apply proper shear stresses or tension to soil in relatively simple tests
The first limitation listed above can be overcome by applying lubricated ends on the
Pore pressure transducer
On-Off valve
Burette
Piston
Dial gage
Triaxial cell
P = σd middot A
Aprime
σcell
σ3
σ3 σ3= σcell
Figure 12 Schematic diagram of triaxial apparatus
4 Triaxial Testing of Soils
specimen such that uniform strains and stresses and therefore correct soil response can be proshyduced This is discussed in Chapter 3 In addishytion to the limitations listed above it should be mentioned that it may be easier to reproduce certain stress paths in other specialty equipment than in the triaxial apparatus (eg K0‐test)
Although the triaxial test is limited as explained under points 2 and 3 above it does combine versatility with relative simplicity in concept and performance Other equipment in which three unequal principal stresses can be applied or in which the principal stress direcshytions can be rotated do not have the versatility or is more com plicated to operate Thus other types of equipment have their own advantages and limitations These other equipment types
include plane strain true triaxial simple shear directional shear and torsion shear apparatus All these pieces of equipment are with the excepshytion of the simple shear apparatus employed mainly for research purposes Their operational modes capabilities and results are reviewed in Chapter 11
15 Test stages ndash consolidation and shearing
Laboratory tests are made to simulate field loadshying conditions as close as possible Most field conditions and the corresponding tests can be simplified to consist of two stages consolidation and shearing
Axis of symmetry
1Eh
1Eh
1Ghv
1Ev
ndashmicrohvEh
ndashmicrohvEn
2(1 + microhh)En
ndashmicrohhEn
ndashmicrohvEh
ndashmicrohvEh
ndashmicrohhEh
0
h
h
v
0 0
σh
σh
σv
τhv
τhv
τvh
τvh
σh
σv
σh
τhv
τvh
τhh
τhh τhh
ϵh
ϵv
ϵh
γhv
γvh
γhh
0
Require tests withapplication of
shear stresses
0 0
0
0 0 0 00
1Ghv0 0 0 00
0 0 0 0 0
0 0
bull =
Figure 13 Cross‐anisotropic soil requiring results from more than triaxial tests for full characterization
Principles of Triaxial Testing 5
151 Consolidation
In the first stage the initial condition of the soil is established in terms of effective stresses and stress history (including overconsolidation if applicable) Thus stresses are applied correshysponding to those acting on the element of soil in the field due to weight of the overlying soil strata and other materials or structures that exist at the time the mechanical properties (stressndashstrain strength etc) are sought Sufficient time is allowed for complete consolidation to occur under the applied stresses The condition in the field element has now been established in the triaxial specimen
152 Shearing
In the second stage of the triaxial test an addishytional stress is applied to reach peak failure and beyond under relevant drainage conditions The additional stress applied to the specimen should correspond as closely as possible to the change in stress on the field element due to some new change in the overall field loading situashytion This change may consist of a vertical stress increase or decrease (eg due to addition of a structure or excavation of overlying soil strata) or of a horizontal stress increase or decrease (eg due to the same constructions causing the vertical stress changes) Any combination of vertical and horizontal stress changes may be simulated in the triaxial test Examples of vertishycal and horizontal stress changes in the field are shown in Fig 14
Usually it is desirable to know how much change in load the soil can sustain without failshying and how much deformation will occur under normal working conditions The test is therefore usually continued to find the strength of the soil under the appropriate loading condishytions The results are used with an appropriate factor of safety so that normal working stresses are always somewhat below the peak strength
The stressndashstrain relations obtained from the triaxial tests provide the basis for determinashytion of deformations in the field This may be done in a simplified manner by closed‐form
solutions or it may be done by employing the results of the triaxial tests for calibration of a constitutive model used with a numerical method in finite element or finite difference computer programs
16 Types of tests
The drainage conditions in the field must be duplicated as well as possible in the laboratory tests This may be done by appropriate drainage facilities or preventions as discussed above for the triaxial test In most cases the field drainage conditions can be approximated by one of the following three types of tests
1 Consolidated‐drained test called a CD‐test or just a drained test
2 Consolidated‐undrained test or a CU‐test3 Unconsolidated‐undrained test or a UU‐test
Additionalload
Excavation
ΔσV asymp 0
ΔσV asymp 0
ΔσV gt 0
ΔσV lt 0
Δσh lt 0
Δσh gt 0
Δσh lt ΔσV
Δσh
Figure 14 Examples of stress changes leading to failure in the field
6 Triaxial Testing of Soils
These tests are described in ASTM Standards D7181 (2014) D4767 (2014) and D2850 (2014) respectively
Which condition of drainage in the laboratory test logically corresponds to each case in the field depends on a comparison of loading rate with the rate at which the water can escape or be sucked into the ground Thus the permeability of the soil and the drainage boundary conditions in the field together with the loading rate play key roles in determination of the type of analysis and the type of test drained or undrained that are appropriate for each case Field cases with partial drainage can be correctly duplicated in laboratory tests if the effective stress path is determined for the design condition However the idea of the CD‐ CU‐ and UU‐tests is to make it relatively simple for the design engineer to analyze a condition that will render a sufficient factor of safety under the actual drainage condishytion without trying to estimate and experimenshytally replicate the actual stress path
It has been determined through experience and common sense that the extreme conditions are drained and undrained with and without consolidation As a practical matter in a commershycial laboratory it is easier to run an undrained test than a drained test because it is easier and faster to measure pore pressures than volume change Therefore even drained parameters are more likely to be estimated from a CU‐test than from a CD‐test
161 Simulation of field conditions
Presented below is a brief review of the three types of tests together with examples of field cases for which the tests are appropriate and with typishycal strength results shown on Mohr diagrams
Drained tests
Isotropic consolidation is most often used in the first stage of the triaxial test However anisoshytropic consolidation with any stress ratio is also possible
The shearing stage of a drained test is pershyformed so slowly the soil is so permeable and the drainage facilities are such that no excess
pore pressure (positive or negative) can exist in the specimen at any stage of the test that is
∆u = 0 (15)
It follows then from the effective stress principle
prime = minusσ σ u (16)
that the effective stress changes are always the same as the total stress changes
A soil specimen always changes volume during shearing in a drained test If it contracts in volume it expels pore fluid (usually water or air) and if it expands in volume (dilates) then it sucks water or air into the pores If a non‐zero pore pressure is generated during the test (eg by performing the shearing too fast so the water does not have sufficient time to escape) then the specimen will expel or suck water such that the pore pressure goes towards zero to try to achieve equilibrium between externally applied stresses and internal effective stresses Thus there will always be volume changes in a drained test Consequently the water content the void ratio and the dry density of the specimen at the end of the test are most often not the same as at the beginning
The following field conditions can be simushylated with acceptable accuracy in the drained test
1 Almost all cases involving coarse sands and gravel whether saturated or not (except if confined in eg a lens andor exposed to rapid loading as in eg an earthquake)
2 Many cases involving fine sand and someshytimes silt if the field loads are applied reashysonable slowly
3 Long term loading of any soil as for examplea) Cut slopes several years after excavationb) Embankment constructed very slowly in
layers over a soft clay depositc) Earth dam with steady seepaged) Foundation on clay a long time after
construction
These cases are illustrated in Fig 15The strength results obtained from drained
tests are illustrated schematically on the Mohr diagram in Fig 16 The shear strength of soils increases with increasing confining pressure
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
Triaxial Testing of Soils
Poul V Lade
This edition first published 2016copy 2016 by John Wiley amp Sons Ltd
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ISBN 9781119106623
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Set in 1012pt Palatino by SPi Global Pondicherry India
1 2016
Contents
Preface xiiiAbout the Author xvii
1 Principles of Triaxial Testing 111 Purpose of triaxial tests 112 Concept of testing 113 The triaxial test 214 Advantages and limitations 315 Test stages ndash consolidation and shearing 4
151 Consolidation 5152 Shearing 5
16 Types of tests 5161 Simulation of field conditions 6162 Selection of test type 12
2 Computations and Presentation of Test Results 1321 Data reduction 13
211 Sign rule ndash 2D 13212 Strains 13213 Cross‐sectional area 23214 Stresses 24215 Corrections 25216 The effective stress principle 25217 Stress analysis in two dimensions ndash Mohrrsquos circle 25218 Strain analysis in two dimensions ndash Mohrrsquos circle 27
22 Stressndashstrain diagrams 28221 Basic diagrams 28222 Modulus evaluation 37223 Derived diagrams 41224 Normalized stressndashstrain behavior 48225 Patterns of soil behavior ndash error recognition 49
23 Strength diagrams 51231 Definition of effective and total strengths 51232 MohrndashCoulomb failure concept 51233 MohrndashCoulomb for triaxial compression 54234 Curved failure envelope 55235 MIT pndashq diagram 57236 Cambridge pndashq diagram 59237 Determination of best‐fit soil strength parameters 60238 Characterization of total strength 60
24 Stress paths 61241 Drained stress paths 61242 Total stress paths in undrained tests 61243 Effective stress paths in undrained tests 61244 Normalized pndashq diagrams 66245 Vector curves 68
vi Contents
25 Linear regression analysis 72251 MIT pndashq diagram 72252 Cambridge pndashq diagram 74253 Correct and incorrect linear regression analyses 75
26 Three‐dimensional stress states 76261 General 3D stress states 76262 Stress invariants 76263 Stress deviator invariants 80264 Magnitudes and directions of principal stresses 81
27 Principal stress space 83271 Octahedral stresses 83272 Triaxial plane 84273 Octahedral plane 86274 Characterization of 3D stress conditions 87275 Shapes of stress invariants in principal stress space 89276 Procedures for projecting stress points onto a common
octahedral plane 90277 Procedure for plotting stress points on an octahedral plane 96278 Representation of test results with principal stress rotation 97
3 Triaxial Equipment 9931 Triaxial setup 99
311 Specimen cap and base 99312 Membrane 103313 O‐rings 105314 Drainage system 106315 Leakage of triaxial setup 112316 Volume change devices 113317 Cell fluid 113318 Lubricated ends 120
32 Triaxial cell 125321 Cell types 125322 Cell wall 127323 Hoek cell 128
33 Piston 128331 Piston friction 129332 Connections between piston cap and specimen 132
34 Pressure supply 133341 Water column 133342 Mercury pot system 134343 Compressed gas 135344 Mechanically compressed fluids 136345 Pressure intensifiers 137346 Pressure transfer to triaxial cell 137347 Vacuum to supply effective confining pressure 138
35 Vertical loading equipment 139351 Deformation or strain control 139352 Load control 140353 Stress control 141354 Combination of load control and deformation control 141355 Stiffness requirements 143
Contents vii
356 Strain control versus load control 14336 Triaxial cell with integrated loading system 143
4 Instrumentation Measurements and Control 14541 Purpose of instrumentation 14542 Principle of measurements 14543 Instrument characteristics 14744 Electrical instrument operation principles 149
441 Strain gage 149442 Linear variable differential transformer 151443 Proximity gage 153444 Reluctance gage 153445 Electrolytic liquid level 154446 Hall effect technique 154447 Elastomer gage 154448 Capacitance technique 155
45 Instrument measurement uncertainty 155451 Accuracy precision and resolution 156452 Measurement uncertainty in triaxial tests 156
46 Instrument performance characteristics 158461 Excitation 158462 Zero shift 159463 Sensitivity 159464 Thermal effects on zero shift and sensitivity 159465 Natural frequency 159466 Nonlinearity 159467 Hysteresis 159468 Repeatability 159469 Range 1594610 Overload capacity 1604611 Overload protection 1604612 Volumetric flexibility of pressure transducers 160
47 Measurement of linear deformations 160471 Inside and outside measurements 160472 Recommended gage length 162473 Operational requirements 162474 Electric wires 163475 Clip gages 163476 Linear variable differential transformer setup 167477 Proximity gage setup 168478 Inclinometer gages 170479 Hall effect gage 1714710 X‐ray technique 1714711 Video tracking and high‐speed photography 1714712 Optical deformation measurements 1724713 Characteristics of linear deformation measurement devices 174
48 Measurement of volume changes 178481 Requirements for volume change devices 178482 Measurements from saturated specimens 180483 Measurements from a triaxial cell 189484 Measurements from dry and partly saturated specimens 192
viii Contents
49 Measurement of axial load 195491 Mechanical force transducers 195492 Operating principle of strain gage load cells 197493 Primary sensors 197494 Fabrication of diaphragm load cells 198495 Load capacity and overload protection 198
410 Measurement of pressure 1994101 Measurement of cell pressure 1994102 Measurement of pore pressure 1994103 Operating principles of pressure transducers 2014104 Fabrication of pressure transducers 2014105 Pressure capacity and overpressure protection 201
411 Specifications for instruments 201412 Factors in the selection of instruments 202413 Measurement redundancy 202414 Calibration of instruments 203
4141 Calibration of linear deformation devices 2034142 Calibration of volume change devices 2044143 Calibration of axial load devices 2044144 Calibration of pressure gages and transducers 204
415 Data acquisition 2064151 Manual datalogging 2064152 Computer datalogging 206
416 Test control 2064161 Control of load pressure and deformations 2064162 Principles of control systems 207
5 Preparation of Triaxial Specimens 21151 Intact specimens 211
511 Storage of samples 211512 Sample inspection and documentation 212513 Ejection of specimens 214514 Trimming of specimens 215515 Freezing technique to produce intact samples of granular materials 217
52 Laboratory preparation of specimens 217521 Slurry consolidation of clay 217522 Air pluviation of sand 219523 Depositional techniques for silty sand 222524 Undercompaction 227525 Compaction of clayey soils 232526 Compaction of soils with oversize particles 234527 Extrusion and storage 235528 Effects of specimen aging 235
53 Measurement of specimen dimensions 235531 Compacted specimens 235
54 Specimen installation 235541 Fully saturated clay specimen 236542 Unsaturated clayey soil specimen 237
6 Specimen Saturation 23961 Reasons for saturation 23962 Reasons for lack of full saturation 239
Contents ix
63 Effects of lack of full saturation 24064 B‐value test 241
641 Effects of primary factors on B‐value 241642 Effects of secondary factors on B‐value 243643 Performance of B‐value test 246
65 Determination of degree of saturation 24966 Methods of saturating triaxial specimens 250
661 Percolation with water 250662 CO2‐method 251663 Application of back pressure 252664 Vacuum procedure 258
67 Range of application of saturation methods 262
7 Testing Stage I Consolidation 26371 Objective of consolidation 26372 Selection of consolidation stresses 263
721 Anisotropic consolidation 264722 Isotropic consolidation 267723 Effects of sampling 268724 SHANSEP for soft clay 268725 Very sensitive clay 272
73 Coefficient of consolidation 272731 Effects of boundary drainage conditions 272732 Determination of time for 100 consolidation 272
8 Testing Stage II Shearing 27781 Introduction 27782 Selection of vertical strain rate 277
821 UU‐tests on clay soils 277822 CD‐ and CU‐tests on granular materials 277823 CD‐ and CU‐tests on clayey soils 277824 Effects of lubricated ends in undrained tests 282
83 Effects of lubricated ends and specimen shape 282831 Strain uniformity and stability of test configuration 282832 Modes of instability in soils 284833 Triaxial tests on sand 284834 Triaxial tests on clay 290
84 Selection of specimen size 29285 Effects of membrane penetration 293
851 Drained tests 293852 Undrained tests 293
86 Post test inspection of specimen 293
9 Corrections to Measurements 29591 Principles of measurements 29592 Types of corrections 29593 Importance of corrections ndash strong and weak specimens 29594 Tests on very short specimens 29695 Vertical load 296
951 Piston uplift 296952 Piston friction 296953 Side drains 298954 Membrane 301
x Contents
955 Buoyancy effects 308956 Techniques to avoid corrections to vertical load 309
96 Vertical deformation 309961 Compression of interfaces 309962 Bedding errors 309963 Techniques to avoid corrections to vertical deformations 311
97 Volume change 312971 Membrane penetration 312972 Volume change due to bedding errors 317973 Leaking membrane 317974 Techniques to avoid corrections to volume change 319
98 Cell and pore pressures 319981 Membrane tension 319982 Fluid self‐weight pressures 319983 Sand penetration into lubricated ends 319984 Membrane penetration 319985 Techniques to avoid corrections to cell and pore pressures 320
10 Special Tests and Test Considerations 321101 Introduction 321
1011 Low confining pressure tests on clays 3211012 Conventional low pressure tests on any soil 3211013 High pressure tests 3221014 Peats and organic soils 322
102 K0‐tests 322103 Extension tests 322
1031 Problems with the conventional triaxial extension test 3231032 Enforcing uniform strains in extension tests 324
104 Tests on unsaturated soils 3261041 Soil water retention curve 3261042 Hydraulic conductivity function 3271043 Low matric suction 3271044 High matric suction 3291045 Modeling 3301046 Triaxial testing 331
105 Frozen soils 331106 Time effects tests 333
1061 Creep tests 3331062 Stress relaxation tests 333
107 Determination of hydraulic conductivity 335108 Bender element tests 335
1081 Fabrication of bender elements 3361082 Shear modulus 3371083 Signal interpretation 3381084 First arrival time 3381085 Specimen size and geometry 3401086 Ray path analysis 3401087 Surface mounted elements 3401088 Effects of specimen material 3411089 Effects of cross‐anisotropy 341
Contents xi
11 Tests with Three Unequal Principal Stresses 343111 Introduction 343112 Tests with constant principal stress directions 344
1121 Plane strain equipment 3441122 True triaxial equipment 3451123 Results from true triaxial tests 3481124 Strength characteristics 3531125 Failure criteria for soils 355
113 Tests with rotating principal stress directions 3601131 Simple shear equipment 3601132 Directional shear cell 3621133 Torsion shear apparatus 3641134 Summary and conclusion 370
Appendix A Manufacturing of Latex Rubber Membranes 373A1 The process 373A2 Products for membrane fabrication 373A3 Create an aluminum mold 374A4 Two tanks 374A5 Mold preparation 374A6 Dipping processes 374A7 Post production 375A8 Storage 375A9 Membrane repair 375
Appendix B Design of Diaphragm Load Cells 377B1 Load cells with uniform diaphragm 377B2 Load cells with tapered diaphragm 378B3 Example Design of 5 kN beryllium copper load cell 378 B31 Punching failure 379
References 381Index 397
Preface
The triaxial test is almost always chosen for studies of new phenomena because it is rela-tively simple and versatile The triaxial test is the most suitable for such studies and it is required in geotechnical engineering for the purposes of design of specific projects and for studying and understanding the behavior of soils
The first triaxial compression test apparatus shown in Fig P1 was designed by von Kārmān (1910 1911) for testing of rock cores The scale may be deduced from the fact that the specimen is 4 cm in diameter (Vaacutesaacuterhelyi 2010) However his paper was not noticed or it was forgotten by 1930 when Casagrande at Harvard University wrote a letter to Terzaghi at the Technical University in Vienna in which he describes his visit to the hydraulics laboratory in Berlin Here he saw an apparatus for measuring the permea-bility of soil Casagrande suggested that the cylindrical specimen in this apparatus could be loaded in the vertical (axial) direction to indi-cate its strength Therefore he was going to build a prototype and Terzaghi proposed that he build one for him too This appears to be the begin-ning of triaxial testing of soils in geotechnical engineering The apparatus was immediately employed by Rendulic (Terzaghi and Rendulic 1934) for tests with and without membranes the results of which played an important role in understanding the effective stress principle as well as the role of pore water pressure and consolidation on shear strength at a time when the effective stress principle was still being questioned (Skempton 1960 de Boer 2005)
Previous books on the developments of tech-niques for triaxial testing have been written by Bishop and Henkel (1957 1962) and by Head (1986) The proceedings from a conference on Advanced Triaxial Testing of Soil and Rock (Donaghe et al 1988) was published to summa-
rize advances in this area Other books have not appeared since then To understand the present book the reader is required to have a background in basic soil mechanics some experience in soil mechanics laboratory testing and perhaps in foundation engineering
In addition to triaxial testing of soils the contents of the book may in part apply to more advanced tests and to the testing of hard soils ndash soft rocks It is written for research workers soil testing laboratories and consulting engineers The emphasis is placed on what the soil speci-men is exposed to and experiences rather than the esthetic appearance of the equipment There will be considerable use of physics and mathe-matics to illustrate the arguments and discus-sions With a few exceptions references are made to easily accessible articles in the literature Much of the book centers on how to obtain high quality experimental results and the guiding concepts for this purpose have been expressed by the car industry in their slogans ldquoQuality is Job Onerdquo (Ford Motor Company) and ldquoQuality is never an accident it is always the result of excellent workmanshiprdquo (Mercedes)
The book is organized in a logical sequence beginning with the principles of triaxial testing in Chapter 1 and the computations and presen-tations of test results in Chapter 2 The triaxial equipment is explained in Chapter 3 and instrumentation measurements and control is reviewed in Chapter 4 Preparation of triaxial specimens is presented in Chapter 5 and satu-ration of specimens is described in Chapter 6 The two testing stages in an experiment are made clear in Chapter 7 Consolidation and in Chapter 8 Shearing Chapter 9 accounts for the corrections to the measurements Chapter 10 informs about special tests and test conditions and Chapter 11 puts the results from triaxial tests in perspective by reviewing results from
xiv Preface
tests with three unequal principal stresses Appendices are provided to explain special experimental techniques Information on ven-dors for the various types of equipment may be obtained from the internet
The authorrsquos background for writing this book consists of a career in laboratory experi-mentation at university level to study and model the behavior of soils More specifically he received an MS degree in 1967 from the Technical University of Denmark for which he wrote a thesis on the influence of the intermedi-ate principal stress on the strength of sand and in retrospect ended up with the wrong conclu-sion on the basis of perfectly correct results He received a PhD from the University of California at Berkeley in 1972 with a dissertation on ldquoThe StressndashStrain and Strength Characteristics of Cohesionless Soilsrdquo which included results
from triaxial compression tests true triaxial tests and torsion shear tests to indicate the effects of the intermediate principal stress on sand behavior as well as a three‐dimensional elasto‐plastic constitutive model for the behavior of soils
With his students the author developed testing equipment performed experiments and built constitutive models for the observed soil behavior while a professor at the University of California at Los Angeles (UCLA) (1972ndash1993) Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015) Many of the experimental techniques developed over this range of years are explained in the present book
Great appreciation is expressed to John F Peters of the US Army Engineer Research and Development Center in Vicksburg MS for his careful review of the manuscript and for his many comments Special thanks go to Afshin Nabili for his invaluable assistance with drafting a large number of the figures and for modifica-tion of other diagrams for the book
Poul V Lade October 2015
References
Bishop AW and Henkel DJ (1957) Measurement of Soil Properties in Triaxial Test Edward Arnold London
Bishop AW and Henkel DJ (1962) The Measurement of Soil Properties in the Triaxial Test 2nd edn St Martinrsquos Press New York NY
de Boer R (2005) The Engineer and the Scandal Springer Berlin
Donaghe RT Chaney RC and Silver ML (eds) (1988) Advanced Triaxial Testing of Soil and Rock ASTM STP 977 ASTM Philadelphia PA
Head KH (1986) Manual of Soil Laboratory Testing ndash Volume 3 Effective Stress Tests Pentech Press London
von Kārmān T (1910) Magyar Meacuternoumlk eacutes Ėpiteacuteszegylet Koumlzloumlnye 10 212ndash226
B
b
c
aD1
D2
Figure P1 Triaxial apparatus designed and con-structed for testing of rock cores by von Kārmān (1910 1911)
Preface xv
von Kārmān T (1911) Verhandlungen Deutsche Ingenieur 55 1749ndash1757
Skempton AW (1960) Terzaghirsquos discovery of effec-tive stress In From Theory to Practice in Soil Mechanics (eds L Bjerrum A Casagrande RB Peck and AW Skempton) pp 42ndash53 John Wiley and Sons Ltd London
Terzaghi K and Rendulic L (1934) Die wirksame Flaumlchenporositaumlt des Betons Zeitschrift des Ōsterreichischen Ingenieur‐ und Architekten Vereines 86 1ndash9
Vaacutesaacuterhelyi B (2010) Tribute to the first triaxial test performed in 1910 Acta Geology and Geophysics of Hungary 45(2) 227ndash230
About the Author
Poul V Lade received his MS degree from the Technical University of Denmark in 1967 and he continued his studies at the University of California at Berkeley where he received his PhD in 1972 Subsequently his academic career began at the University of California at Los Angeles (UCLA) and he continued at Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015)
His research interests include application of appropriate experimental methods to determine the three‐dimensional stressndashstrain and strength behavior of soils and the development of consti-tutive models for frictional materials such as soils concrete and rock He developed laboratory experimental apparatus to investigate monotonic loading and large three‐dimensional stress rever-
sals in plane strain true triaxial and torsion shear equipment This also included studies of effects of principal stress rotation stability instability and liquefaction of granular materials and time effects The constitutive models are based on elasticity and work‐hardening isotropic and kinematic plasticity theories
He has written nearly 300 publications based on research performed with support from the National Science Foundation (NSF) and from the Air Force Office of Scientific Research (AFOSR) He was elected member of the Danish Academy of Technical Sciences (2001) and he was awarded Professor Ostenfeldrsquos Gold Medal from the Technical University of Denmark (2001) He was inaugural editor of Geomechanics and Engineering and he has served on the editorial boards of eight international journals on geotechnical engineering
Triaxial Testing of Soils First Edition Poul V Lade copy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd
Principles of Triaxial Testing1
11 Purpose of triaxial tests
The purpose of performing triaxial tests is to determine the mechanical properties of the soil It is assumed that the soil specimens to be tested are homogeneous and representative of the material in the field and that the desired soil properties can in fact be obtained from the triaxial tests either directly or by interpretation through some theory
The mechanical properties most often sought from triaxial tests are stressndashstrain relations volshyume change or pore pressure behavior and shear strength of the soil Included in the stressndashstrain behavior are also the compressibility and the value of the coefficient of earth pressure at rest K0 Other properties that may be obtained from the triaxial tests which include time as a component are the permeability the coefficient of consolidation and properties relating to time dependent behavior such as rate effects creep and stress relaxation
It is important that the natural soil deposit or the fill from which soil samples have been taken in the field are sufficiently uniform that the soil samples possess the properties which are approshypriate and representative of the soil mass in the field It is therefore paramount that the geology at the site is well‐known and understood Even then samples from uniform deposits may not
ldquocontainrdquo properties that are representative of the field deposit This may happen either (a) due to the change in effective stress state which is always associated with the sampling process or (b) due to mechanical disturbance from sampling transshyportation or handling in the laboratory The stressndashstrain and strength properties of very senshysitive clays which have been disturbed cannot be regenerated in the lab oratory or otherwise obtained by interpretation of tests performed on inadequate specimens The effects of sampling will briefly be discussed below in connection with choice of consolidation pressure in the trishyaxial test The topic of sampling is otherwise outshyside the scope of the present treatment
12 Concept of testing
The concept to be pursued in testing of soils is to simulate as closely as possible the process that goes on in the field Because there is a large number of variables (eg density water content degree of saturation overconsolidation ratio loading conditions stress paths) that influence the resulting soil behavior the simplest and most direct way of obtaining information pertinent to the field conditions is to duplicate these as closely as possible
2 Triaxial Testing of Soils
However because of limitations in equipment and because of practical limitations on the amount of testing that can be performed for each project it is essential that
1 The true field loading conditions (including the drainage conditions) are known
2 The laboratory equipment can reproduce these conditions to a required degree of accuracy
3 A reasonable estimate can be made of the sigshynificance of the differences between the field loading conditions and those that can be proshyduced in the laboratory equipment
It is clear that the triaxial test in many resshypects is incapable of simulating several imporshytant aspects of field loading conditions For example the effects of the intermediate princishypal stress the effects of rotation of principal stresses and the effects of partial drainage durshying loading in the field cannot be investigated on the basis of the triaxial test The effects of such conditions require studies involving other types of equipment or analyses of boundary value problems either by closed form solutions or solutions obtained by numerical techniques
To provide some background for evaluation of the results of triaxial tests other types of laboratory shear tests and typical results from such tests are presented in Chapter 11 The relashytions between the different types of tests are reviewed and their advantages and limitations are discussed
13 The triaxial test
The triaxial test is most often performed on a cylindrical specimen as shown in Fig 11(a) Principal stresses are applied to the specimen as indicated in Fig 11(b) First a confining pressure σ3 is applied to the specimen This pressure acts all around and therefore on all planes in the specimen Then an additional stress difference σd is applied in the axial direction The stress applied externally to the specimen in the axial direction is
σ σ σ1 3= +d (11)
and therefore
σ σ σd = minus1 3 (12)
In the general case three principal stresses σ1 σ2 and σ3 may act on a soil element in the field However only two different principal stresses can be applied to the specimen in the convenshytional triaxial test The intermediate principal stress σ2 can only have values as follows
σ σ2 3= Triaxial compression (13)
σ σ2 1= Triaxial extension (14)
The condition of triaxial extension can be achieved by applying negative stress differshyences to the specimen This merely produces a reduction in compression in the extension direcshytion but no tension occurs in the specimen The state of stress applied to the specimen is in both cases axisymmetric The triaxial compression test will be discussed in the following while the triaxial extension test is discussed in Chapter 10
The test is performed using triaxial apparashytus as seen in the schematic illustration in Fig 12 The specimen is surrounded by a cap and a base and a membrane This unit is placed in a triaxial cell in which the cell pressure can be applied The cell pressure acts as a hydrostatic confinement for the specimen and the pressure is therefore the same in all directions In addition
σ1
(a) (b)
σ1 = σd + σ3
σ2 = σ3
σd = σ1 ndash σ3σ3
σ3σ3
σ3
σd
Figure 11 (a) Cylindrical specimen for triaxial testing and (b) stresses applied to a triaxial specimen
Principles of Triaxial Testing 3
a deviator load can be applied through a piston that goes through the top of the cell and loads the specimen in the axial direction
The vertical deformation of the specimen may be measured by a dial gage attached to the piston which travels the same vertical distance as the cap sitting on top of the specimen Drainage lines are connected to the water saturated specishymen through the base (or both the cap and the base) and connected to a burette outside the trishyaxial cell This allows for measurements of the volume changes of the specimen during the test
Alternatively the connection to the burette can be shut off thereby preventing the specimen from changing volume Instead the pore water pressure can be measured on a transducer conshynected to the drainage line
The following quantities are measured in a typical triaxial test
1 Confining pressure2 Deviator load3 Vertical (or axial) deformation4 Volume change or pore water pressure
These measurements constitute the data base from which other quantities can be derived
[eg stress difference (σ1 ndash σ3) axial strain ε1 and volumetric strain εv]
14 Advantages and limitations
Whereas the triaxial test potentially can proshyvide a substantial proportion of the mechanical properties required for a project it has limitashytions especially when special conditions are encountered and necessitates clarification based on experimentation
The advantages of the triaxial test are
1 Drainage can be controlled (onndashoff)2 Volume change or pore pressure can be
measured3 Suction can be controlled in partially satushy
rated soils4 Measured deformations allow calculation of
strains and moduli5 A larger variety of stress and strain paths
that occur in the field can be applied in the triaxial apparatus than in any other testing apparatus (eg initial anisotropic consolidashytion at any stress ratio including K0 extension active and passive shear)
The limitations of the triaxial test are
1 Stress concentrations due to friction between specimen and end plates (cap and base) cause nonuniform strains and stresses and therefore nonuniform stressndashstrain volume change or pore pressure response
2 Only axisymmetric stress conditions can be applied to the specimen whereas most field problems involve plane strain or general three‐dimensional conditions with rotation of principal stresses
3 Triaxial tests cannot provide all necessary data required to characterize the behavior of an anisotropic or a cross‐anisotropic soil deposit as illustrated in Fig 13
4 Although the axisymmetric principal stress condition is limited it is more difficult to apply proper shear stresses or tension to soil in relatively simple tests
The first limitation listed above can be overcome by applying lubricated ends on the
Pore pressure transducer
On-Off valve
Burette
Piston
Dial gage
Triaxial cell
P = σd middot A
Aprime
σcell
σ3
σ3 σ3= σcell
Figure 12 Schematic diagram of triaxial apparatus
4 Triaxial Testing of Soils
specimen such that uniform strains and stresses and therefore correct soil response can be proshyduced This is discussed in Chapter 3 In addishytion to the limitations listed above it should be mentioned that it may be easier to reproduce certain stress paths in other specialty equipment than in the triaxial apparatus (eg K0‐test)
Although the triaxial test is limited as explained under points 2 and 3 above it does combine versatility with relative simplicity in concept and performance Other equipment in which three unequal principal stresses can be applied or in which the principal stress direcshytions can be rotated do not have the versatility or is more com plicated to operate Thus other types of equipment have their own advantages and limitations These other equipment types
include plane strain true triaxial simple shear directional shear and torsion shear apparatus All these pieces of equipment are with the excepshytion of the simple shear apparatus employed mainly for research purposes Their operational modes capabilities and results are reviewed in Chapter 11
15 Test stages ndash consolidation and shearing
Laboratory tests are made to simulate field loadshying conditions as close as possible Most field conditions and the corresponding tests can be simplified to consist of two stages consolidation and shearing
Axis of symmetry
1Eh
1Eh
1Ghv
1Ev
ndashmicrohvEh
ndashmicrohvEn
2(1 + microhh)En
ndashmicrohhEn
ndashmicrohvEh
ndashmicrohvEh
ndashmicrohhEh
0
h
h
v
0 0
σh
σh
σv
τhv
τhv
τvh
τvh
σh
σv
σh
τhv
τvh
τhh
τhh τhh
ϵh
ϵv
ϵh
γhv
γvh
γhh
0
Require tests withapplication of
shear stresses
0 0
0
0 0 0 00
1Ghv0 0 0 00
0 0 0 0 0
0 0
bull =
Figure 13 Cross‐anisotropic soil requiring results from more than triaxial tests for full characterization
Principles of Triaxial Testing 5
151 Consolidation
In the first stage the initial condition of the soil is established in terms of effective stresses and stress history (including overconsolidation if applicable) Thus stresses are applied correshysponding to those acting on the element of soil in the field due to weight of the overlying soil strata and other materials or structures that exist at the time the mechanical properties (stressndashstrain strength etc) are sought Sufficient time is allowed for complete consolidation to occur under the applied stresses The condition in the field element has now been established in the triaxial specimen
152 Shearing
In the second stage of the triaxial test an addishytional stress is applied to reach peak failure and beyond under relevant drainage conditions The additional stress applied to the specimen should correspond as closely as possible to the change in stress on the field element due to some new change in the overall field loading situashytion This change may consist of a vertical stress increase or decrease (eg due to addition of a structure or excavation of overlying soil strata) or of a horizontal stress increase or decrease (eg due to the same constructions causing the vertical stress changes) Any combination of vertical and horizontal stress changes may be simulated in the triaxial test Examples of vertishycal and horizontal stress changes in the field are shown in Fig 14
Usually it is desirable to know how much change in load the soil can sustain without failshying and how much deformation will occur under normal working conditions The test is therefore usually continued to find the strength of the soil under the appropriate loading condishytions The results are used with an appropriate factor of safety so that normal working stresses are always somewhat below the peak strength
The stressndashstrain relations obtained from the triaxial tests provide the basis for determinashytion of deformations in the field This may be done in a simplified manner by closed‐form
solutions or it may be done by employing the results of the triaxial tests for calibration of a constitutive model used with a numerical method in finite element or finite difference computer programs
16 Types of tests
The drainage conditions in the field must be duplicated as well as possible in the laboratory tests This may be done by appropriate drainage facilities or preventions as discussed above for the triaxial test In most cases the field drainage conditions can be approximated by one of the following three types of tests
1 Consolidated‐drained test called a CD‐test or just a drained test
2 Consolidated‐undrained test or a CU‐test3 Unconsolidated‐undrained test or a UU‐test
Additionalload
Excavation
ΔσV asymp 0
ΔσV asymp 0
ΔσV gt 0
ΔσV lt 0
Δσh lt 0
Δσh gt 0
Δσh lt ΔσV
Δσh
Figure 14 Examples of stress changes leading to failure in the field
6 Triaxial Testing of Soils
These tests are described in ASTM Standards D7181 (2014) D4767 (2014) and D2850 (2014) respectively
Which condition of drainage in the laboratory test logically corresponds to each case in the field depends on a comparison of loading rate with the rate at which the water can escape or be sucked into the ground Thus the permeability of the soil and the drainage boundary conditions in the field together with the loading rate play key roles in determination of the type of analysis and the type of test drained or undrained that are appropriate for each case Field cases with partial drainage can be correctly duplicated in laboratory tests if the effective stress path is determined for the design condition However the idea of the CD‐ CU‐ and UU‐tests is to make it relatively simple for the design engineer to analyze a condition that will render a sufficient factor of safety under the actual drainage condishytion without trying to estimate and experimenshytally replicate the actual stress path
It has been determined through experience and common sense that the extreme conditions are drained and undrained with and without consolidation As a practical matter in a commershycial laboratory it is easier to run an undrained test than a drained test because it is easier and faster to measure pore pressures than volume change Therefore even drained parameters are more likely to be estimated from a CU‐test than from a CD‐test
161 Simulation of field conditions
Presented below is a brief review of the three types of tests together with examples of field cases for which the tests are appropriate and with typishycal strength results shown on Mohr diagrams
Drained tests
Isotropic consolidation is most often used in the first stage of the triaxial test However anisoshytropic consolidation with any stress ratio is also possible
The shearing stage of a drained test is pershyformed so slowly the soil is so permeable and the drainage facilities are such that no excess
pore pressure (positive or negative) can exist in the specimen at any stage of the test that is
∆u = 0 (15)
It follows then from the effective stress principle
prime = minusσ σ u (16)
that the effective stress changes are always the same as the total stress changes
A soil specimen always changes volume during shearing in a drained test If it contracts in volume it expels pore fluid (usually water or air) and if it expands in volume (dilates) then it sucks water or air into the pores If a non‐zero pore pressure is generated during the test (eg by performing the shearing too fast so the water does not have sufficient time to escape) then the specimen will expel or suck water such that the pore pressure goes towards zero to try to achieve equilibrium between externally applied stresses and internal effective stresses Thus there will always be volume changes in a drained test Consequently the water content the void ratio and the dry density of the specimen at the end of the test are most often not the same as at the beginning
The following field conditions can be simushylated with acceptable accuracy in the drained test
1 Almost all cases involving coarse sands and gravel whether saturated or not (except if confined in eg a lens andor exposed to rapid loading as in eg an earthquake)
2 Many cases involving fine sand and someshytimes silt if the field loads are applied reashysonable slowly
3 Long term loading of any soil as for examplea) Cut slopes several years after excavationb) Embankment constructed very slowly in
layers over a soft clay depositc) Earth dam with steady seepaged) Foundation on clay a long time after
construction
These cases are illustrated in Fig 15The strength results obtained from drained
tests are illustrated schematically on the Mohr diagram in Fig 16 The shear strength of soils increases with increasing confining pressure
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
This edition first published 2016copy 2016 by John Wiley amp Sons Ltd
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Disclaimer All reasonable attempts have been made to contact the owners of copyrighted material used in this book [Figures 112 338 341 450 451 455ab Table 71] However if you are the copyright owner of any source used in this book which is not credited please notify the Publisher and this will be corrected in any subsequent reprints or new editions
Library of Congress Cataloging‐in‐Publication data applied for
ISBN 9781119106623
A catalogue record for this book is available from the British Library
Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic books
Set in 1012pt Palatino by SPi Global Pondicherry India
1 2016
Contents
Preface xiiiAbout the Author xvii
1 Principles of Triaxial Testing 111 Purpose of triaxial tests 112 Concept of testing 113 The triaxial test 214 Advantages and limitations 315 Test stages ndash consolidation and shearing 4
151 Consolidation 5152 Shearing 5
16 Types of tests 5161 Simulation of field conditions 6162 Selection of test type 12
2 Computations and Presentation of Test Results 1321 Data reduction 13
211 Sign rule ndash 2D 13212 Strains 13213 Cross‐sectional area 23214 Stresses 24215 Corrections 25216 The effective stress principle 25217 Stress analysis in two dimensions ndash Mohrrsquos circle 25218 Strain analysis in two dimensions ndash Mohrrsquos circle 27
22 Stressndashstrain diagrams 28221 Basic diagrams 28222 Modulus evaluation 37223 Derived diagrams 41224 Normalized stressndashstrain behavior 48225 Patterns of soil behavior ndash error recognition 49
23 Strength diagrams 51231 Definition of effective and total strengths 51232 MohrndashCoulomb failure concept 51233 MohrndashCoulomb for triaxial compression 54234 Curved failure envelope 55235 MIT pndashq diagram 57236 Cambridge pndashq diagram 59237 Determination of best‐fit soil strength parameters 60238 Characterization of total strength 60
24 Stress paths 61241 Drained stress paths 61242 Total stress paths in undrained tests 61243 Effective stress paths in undrained tests 61244 Normalized pndashq diagrams 66245 Vector curves 68
vi Contents
25 Linear regression analysis 72251 MIT pndashq diagram 72252 Cambridge pndashq diagram 74253 Correct and incorrect linear regression analyses 75
26 Three‐dimensional stress states 76261 General 3D stress states 76262 Stress invariants 76263 Stress deviator invariants 80264 Magnitudes and directions of principal stresses 81
27 Principal stress space 83271 Octahedral stresses 83272 Triaxial plane 84273 Octahedral plane 86274 Characterization of 3D stress conditions 87275 Shapes of stress invariants in principal stress space 89276 Procedures for projecting stress points onto a common
octahedral plane 90277 Procedure for plotting stress points on an octahedral plane 96278 Representation of test results with principal stress rotation 97
3 Triaxial Equipment 9931 Triaxial setup 99
311 Specimen cap and base 99312 Membrane 103313 O‐rings 105314 Drainage system 106315 Leakage of triaxial setup 112316 Volume change devices 113317 Cell fluid 113318 Lubricated ends 120
32 Triaxial cell 125321 Cell types 125322 Cell wall 127323 Hoek cell 128
33 Piston 128331 Piston friction 129332 Connections between piston cap and specimen 132
34 Pressure supply 133341 Water column 133342 Mercury pot system 134343 Compressed gas 135344 Mechanically compressed fluids 136345 Pressure intensifiers 137346 Pressure transfer to triaxial cell 137347 Vacuum to supply effective confining pressure 138
35 Vertical loading equipment 139351 Deformation or strain control 139352 Load control 140353 Stress control 141354 Combination of load control and deformation control 141355 Stiffness requirements 143
Contents vii
356 Strain control versus load control 14336 Triaxial cell with integrated loading system 143
4 Instrumentation Measurements and Control 14541 Purpose of instrumentation 14542 Principle of measurements 14543 Instrument characteristics 14744 Electrical instrument operation principles 149
441 Strain gage 149442 Linear variable differential transformer 151443 Proximity gage 153444 Reluctance gage 153445 Electrolytic liquid level 154446 Hall effect technique 154447 Elastomer gage 154448 Capacitance technique 155
45 Instrument measurement uncertainty 155451 Accuracy precision and resolution 156452 Measurement uncertainty in triaxial tests 156
46 Instrument performance characteristics 158461 Excitation 158462 Zero shift 159463 Sensitivity 159464 Thermal effects on zero shift and sensitivity 159465 Natural frequency 159466 Nonlinearity 159467 Hysteresis 159468 Repeatability 159469 Range 1594610 Overload capacity 1604611 Overload protection 1604612 Volumetric flexibility of pressure transducers 160
47 Measurement of linear deformations 160471 Inside and outside measurements 160472 Recommended gage length 162473 Operational requirements 162474 Electric wires 163475 Clip gages 163476 Linear variable differential transformer setup 167477 Proximity gage setup 168478 Inclinometer gages 170479 Hall effect gage 1714710 X‐ray technique 1714711 Video tracking and high‐speed photography 1714712 Optical deformation measurements 1724713 Characteristics of linear deformation measurement devices 174
48 Measurement of volume changes 178481 Requirements for volume change devices 178482 Measurements from saturated specimens 180483 Measurements from a triaxial cell 189484 Measurements from dry and partly saturated specimens 192
viii Contents
49 Measurement of axial load 195491 Mechanical force transducers 195492 Operating principle of strain gage load cells 197493 Primary sensors 197494 Fabrication of diaphragm load cells 198495 Load capacity and overload protection 198
410 Measurement of pressure 1994101 Measurement of cell pressure 1994102 Measurement of pore pressure 1994103 Operating principles of pressure transducers 2014104 Fabrication of pressure transducers 2014105 Pressure capacity and overpressure protection 201
411 Specifications for instruments 201412 Factors in the selection of instruments 202413 Measurement redundancy 202414 Calibration of instruments 203
4141 Calibration of linear deformation devices 2034142 Calibration of volume change devices 2044143 Calibration of axial load devices 2044144 Calibration of pressure gages and transducers 204
415 Data acquisition 2064151 Manual datalogging 2064152 Computer datalogging 206
416 Test control 2064161 Control of load pressure and deformations 2064162 Principles of control systems 207
5 Preparation of Triaxial Specimens 21151 Intact specimens 211
511 Storage of samples 211512 Sample inspection and documentation 212513 Ejection of specimens 214514 Trimming of specimens 215515 Freezing technique to produce intact samples of granular materials 217
52 Laboratory preparation of specimens 217521 Slurry consolidation of clay 217522 Air pluviation of sand 219523 Depositional techniques for silty sand 222524 Undercompaction 227525 Compaction of clayey soils 232526 Compaction of soils with oversize particles 234527 Extrusion and storage 235528 Effects of specimen aging 235
53 Measurement of specimen dimensions 235531 Compacted specimens 235
54 Specimen installation 235541 Fully saturated clay specimen 236542 Unsaturated clayey soil specimen 237
6 Specimen Saturation 23961 Reasons for saturation 23962 Reasons for lack of full saturation 239
Contents ix
63 Effects of lack of full saturation 24064 B‐value test 241
641 Effects of primary factors on B‐value 241642 Effects of secondary factors on B‐value 243643 Performance of B‐value test 246
65 Determination of degree of saturation 24966 Methods of saturating triaxial specimens 250
661 Percolation with water 250662 CO2‐method 251663 Application of back pressure 252664 Vacuum procedure 258
67 Range of application of saturation methods 262
7 Testing Stage I Consolidation 26371 Objective of consolidation 26372 Selection of consolidation stresses 263
721 Anisotropic consolidation 264722 Isotropic consolidation 267723 Effects of sampling 268724 SHANSEP for soft clay 268725 Very sensitive clay 272
73 Coefficient of consolidation 272731 Effects of boundary drainage conditions 272732 Determination of time for 100 consolidation 272
8 Testing Stage II Shearing 27781 Introduction 27782 Selection of vertical strain rate 277
821 UU‐tests on clay soils 277822 CD‐ and CU‐tests on granular materials 277823 CD‐ and CU‐tests on clayey soils 277824 Effects of lubricated ends in undrained tests 282
83 Effects of lubricated ends and specimen shape 282831 Strain uniformity and stability of test configuration 282832 Modes of instability in soils 284833 Triaxial tests on sand 284834 Triaxial tests on clay 290
84 Selection of specimen size 29285 Effects of membrane penetration 293
851 Drained tests 293852 Undrained tests 293
86 Post test inspection of specimen 293
9 Corrections to Measurements 29591 Principles of measurements 29592 Types of corrections 29593 Importance of corrections ndash strong and weak specimens 29594 Tests on very short specimens 29695 Vertical load 296
951 Piston uplift 296952 Piston friction 296953 Side drains 298954 Membrane 301
x Contents
955 Buoyancy effects 308956 Techniques to avoid corrections to vertical load 309
96 Vertical deformation 309961 Compression of interfaces 309962 Bedding errors 309963 Techniques to avoid corrections to vertical deformations 311
97 Volume change 312971 Membrane penetration 312972 Volume change due to bedding errors 317973 Leaking membrane 317974 Techniques to avoid corrections to volume change 319
98 Cell and pore pressures 319981 Membrane tension 319982 Fluid self‐weight pressures 319983 Sand penetration into lubricated ends 319984 Membrane penetration 319985 Techniques to avoid corrections to cell and pore pressures 320
10 Special Tests and Test Considerations 321101 Introduction 321
1011 Low confining pressure tests on clays 3211012 Conventional low pressure tests on any soil 3211013 High pressure tests 3221014 Peats and organic soils 322
102 K0‐tests 322103 Extension tests 322
1031 Problems with the conventional triaxial extension test 3231032 Enforcing uniform strains in extension tests 324
104 Tests on unsaturated soils 3261041 Soil water retention curve 3261042 Hydraulic conductivity function 3271043 Low matric suction 3271044 High matric suction 3291045 Modeling 3301046 Triaxial testing 331
105 Frozen soils 331106 Time effects tests 333
1061 Creep tests 3331062 Stress relaxation tests 333
107 Determination of hydraulic conductivity 335108 Bender element tests 335
1081 Fabrication of bender elements 3361082 Shear modulus 3371083 Signal interpretation 3381084 First arrival time 3381085 Specimen size and geometry 3401086 Ray path analysis 3401087 Surface mounted elements 3401088 Effects of specimen material 3411089 Effects of cross‐anisotropy 341
Contents xi
11 Tests with Three Unequal Principal Stresses 343111 Introduction 343112 Tests with constant principal stress directions 344
1121 Plane strain equipment 3441122 True triaxial equipment 3451123 Results from true triaxial tests 3481124 Strength characteristics 3531125 Failure criteria for soils 355
113 Tests with rotating principal stress directions 3601131 Simple shear equipment 3601132 Directional shear cell 3621133 Torsion shear apparatus 3641134 Summary and conclusion 370
Appendix A Manufacturing of Latex Rubber Membranes 373A1 The process 373A2 Products for membrane fabrication 373A3 Create an aluminum mold 374A4 Two tanks 374A5 Mold preparation 374A6 Dipping processes 374A7 Post production 375A8 Storage 375A9 Membrane repair 375
Appendix B Design of Diaphragm Load Cells 377B1 Load cells with uniform diaphragm 377B2 Load cells with tapered diaphragm 378B3 Example Design of 5 kN beryllium copper load cell 378 B31 Punching failure 379
References 381Index 397
Preface
The triaxial test is almost always chosen for studies of new phenomena because it is rela-tively simple and versatile The triaxial test is the most suitable for such studies and it is required in geotechnical engineering for the purposes of design of specific projects and for studying and understanding the behavior of soils
The first triaxial compression test apparatus shown in Fig P1 was designed by von Kārmān (1910 1911) for testing of rock cores The scale may be deduced from the fact that the specimen is 4 cm in diameter (Vaacutesaacuterhelyi 2010) However his paper was not noticed or it was forgotten by 1930 when Casagrande at Harvard University wrote a letter to Terzaghi at the Technical University in Vienna in which he describes his visit to the hydraulics laboratory in Berlin Here he saw an apparatus for measuring the permea-bility of soil Casagrande suggested that the cylindrical specimen in this apparatus could be loaded in the vertical (axial) direction to indi-cate its strength Therefore he was going to build a prototype and Terzaghi proposed that he build one for him too This appears to be the begin-ning of triaxial testing of soils in geotechnical engineering The apparatus was immediately employed by Rendulic (Terzaghi and Rendulic 1934) for tests with and without membranes the results of which played an important role in understanding the effective stress principle as well as the role of pore water pressure and consolidation on shear strength at a time when the effective stress principle was still being questioned (Skempton 1960 de Boer 2005)
Previous books on the developments of tech-niques for triaxial testing have been written by Bishop and Henkel (1957 1962) and by Head (1986) The proceedings from a conference on Advanced Triaxial Testing of Soil and Rock (Donaghe et al 1988) was published to summa-
rize advances in this area Other books have not appeared since then To understand the present book the reader is required to have a background in basic soil mechanics some experience in soil mechanics laboratory testing and perhaps in foundation engineering
In addition to triaxial testing of soils the contents of the book may in part apply to more advanced tests and to the testing of hard soils ndash soft rocks It is written for research workers soil testing laboratories and consulting engineers The emphasis is placed on what the soil speci-men is exposed to and experiences rather than the esthetic appearance of the equipment There will be considerable use of physics and mathe-matics to illustrate the arguments and discus-sions With a few exceptions references are made to easily accessible articles in the literature Much of the book centers on how to obtain high quality experimental results and the guiding concepts for this purpose have been expressed by the car industry in their slogans ldquoQuality is Job Onerdquo (Ford Motor Company) and ldquoQuality is never an accident it is always the result of excellent workmanshiprdquo (Mercedes)
The book is organized in a logical sequence beginning with the principles of triaxial testing in Chapter 1 and the computations and presen-tations of test results in Chapter 2 The triaxial equipment is explained in Chapter 3 and instrumentation measurements and control is reviewed in Chapter 4 Preparation of triaxial specimens is presented in Chapter 5 and satu-ration of specimens is described in Chapter 6 The two testing stages in an experiment are made clear in Chapter 7 Consolidation and in Chapter 8 Shearing Chapter 9 accounts for the corrections to the measurements Chapter 10 informs about special tests and test conditions and Chapter 11 puts the results from triaxial tests in perspective by reviewing results from
xiv Preface
tests with three unequal principal stresses Appendices are provided to explain special experimental techniques Information on ven-dors for the various types of equipment may be obtained from the internet
The authorrsquos background for writing this book consists of a career in laboratory experi-mentation at university level to study and model the behavior of soils More specifically he received an MS degree in 1967 from the Technical University of Denmark for which he wrote a thesis on the influence of the intermedi-ate principal stress on the strength of sand and in retrospect ended up with the wrong conclu-sion on the basis of perfectly correct results He received a PhD from the University of California at Berkeley in 1972 with a dissertation on ldquoThe StressndashStrain and Strength Characteristics of Cohesionless Soilsrdquo which included results
from triaxial compression tests true triaxial tests and torsion shear tests to indicate the effects of the intermediate principal stress on sand behavior as well as a three‐dimensional elasto‐plastic constitutive model for the behavior of soils
With his students the author developed testing equipment performed experiments and built constitutive models for the observed soil behavior while a professor at the University of California at Los Angeles (UCLA) (1972ndash1993) Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015) Many of the experimental techniques developed over this range of years are explained in the present book
Great appreciation is expressed to John F Peters of the US Army Engineer Research and Development Center in Vicksburg MS for his careful review of the manuscript and for his many comments Special thanks go to Afshin Nabili for his invaluable assistance with drafting a large number of the figures and for modifica-tion of other diagrams for the book
Poul V Lade October 2015
References
Bishop AW and Henkel DJ (1957) Measurement of Soil Properties in Triaxial Test Edward Arnold London
Bishop AW and Henkel DJ (1962) The Measurement of Soil Properties in the Triaxial Test 2nd edn St Martinrsquos Press New York NY
de Boer R (2005) The Engineer and the Scandal Springer Berlin
Donaghe RT Chaney RC and Silver ML (eds) (1988) Advanced Triaxial Testing of Soil and Rock ASTM STP 977 ASTM Philadelphia PA
Head KH (1986) Manual of Soil Laboratory Testing ndash Volume 3 Effective Stress Tests Pentech Press London
von Kārmān T (1910) Magyar Meacuternoumlk eacutes Ėpiteacuteszegylet Koumlzloumlnye 10 212ndash226
B
b
c
aD1
D2
Figure P1 Triaxial apparatus designed and con-structed for testing of rock cores by von Kārmān (1910 1911)
Preface xv
von Kārmān T (1911) Verhandlungen Deutsche Ingenieur 55 1749ndash1757
Skempton AW (1960) Terzaghirsquos discovery of effec-tive stress In From Theory to Practice in Soil Mechanics (eds L Bjerrum A Casagrande RB Peck and AW Skempton) pp 42ndash53 John Wiley and Sons Ltd London
Terzaghi K and Rendulic L (1934) Die wirksame Flaumlchenporositaumlt des Betons Zeitschrift des Ōsterreichischen Ingenieur‐ und Architekten Vereines 86 1ndash9
Vaacutesaacuterhelyi B (2010) Tribute to the first triaxial test performed in 1910 Acta Geology and Geophysics of Hungary 45(2) 227ndash230
About the Author
Poul V Lade received his MS degree from the Technical University of Denmark in 1967 and he continued his studies at the University of California at Berkeley where he received his PhD in 1972 Subsequently his academic career began at the University of California at Los Angeles (UCLA) and he continued at Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015)
His research interests include application of appropriate experimental methods to determine the three‐dimensional stressndashstrain and strength behavior of soils and the development of consti-tutive models for frictional materials such as soils concrete and rock He developed laboratory experimental apparatus to investigate monotonic loading and large three‐dimensional stress rever-
sals in plane strain true triaxial and torsion shear equipment This also included studies of effects of principal stress rotation stability instability and liquefaction of granular materials and time effects The constitutive models are based on elasticity and work‐hardening isotropic and kinematic plasticity theories
He has written nearly 300 publications based on research performed with support from the National Science Foundation (NSF) and from the Air Force Office of Scientific Research (AFOSR) He was elected member of the Danish Academy of Technical Sciences (2001) and he was awarded Professor Ostenfeldrsquos Gold Medal from the Technical University of Denmark (2001) He was inaugural editor of Geomechanics and Engineering and he has served on the editorial boards of eight international journals on geotechnical engineering
Triaxial Testing of Soils First Edition Poul V Lade copy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd
Principles of Triaxial Testing1
11 Purpose of triaxial tests
The purpose of performing triaxial tests is to determine the mechanical properties of the soil It is assumed that the soil specimens to be tested are homogeneous and representative of the material in the field and that the desired soil properties can in fact be obtained from the triaxial tests either directly or by interpretation through some theory
The mechanical properties most often sought from triaxial tests are stressndashstrain relations volshyume change or pore pressure behavior and shear strength of the soil Included in the stressndashstrain behavior are also the compressibility and the value of the coefficient of earth pressure at rest K0 Other properties that may be obtained from the triaxial tests which include time as a component are the permeability the coefficient of consolidation and properties relating to time dependent behavior such as rate effects creep and stress relaxation
It is important that the natural soil deposit or the fill from which soil samples have been taken in the field are sufficiently uniform that the soil samples possess the properties which are approshypriate and representative of the soil mass in the field It is therefore paramount that the geology at the site is well‐known and understood Even then samples from uniform deposits may not
ldquocontainrdquo properties that are representative of the field deposit This may happen either (a) due to the change in effective stress state which is always associated with the sampling process or (b) due to mechanical disturbance from sampling transshyportation or handling in the laboratory The stressndashstrain and strength properties of very senshysitive clays which have been disturbed cannot be regenerated in the lab oratory or otherwise obtained by interpretation of tests performed on inadequate specimens The effects of sampling will briefly be discussed below in connection with choice of consolidation pressure in the trishyaxial test The topic of sampling is otherwise outshyside the scope of the present treatment
12 Concept of testing
The concept to be pursued in testing of soils is to simulate as closely as possible the process that goes on in the field Because there is a large number of variables (eg density water content degree of saturation overconsolidation ratio loading conditions stress paths) that influence the resulting soil behavior the simplest and most direct way of obtaining information pertinent to the field conditions is to duplicate these as closely as possible
2 Triaxial Testing of Soils
However because of limitations in equipment and because of practical limitations on the amount of testing that can be performed for each project it is essential that
1 The true field loading conditions (including the drainage conditions) are known
2 The laboratory equipment can reproduce these conditions to a required degree of accuracy
3 A reasonable estimate can be made of the sigshynificance of the differences between the field loading conditions and those that can be proshyduced in the laboratory equipment
It is clear that the triaxial test in many resshypects is incapable of simulating several imporshytant aspects of field loading conditions For example the effects of the intermediate princishypal stress the effects of rotation of principal stresses and the effects of partial drainage durshying loading in the field cannot be investigated on the basis of the triaxial test The effects of such conditions require studies involving other types of equipment or analyses of boundary value problems either by closed form solutions or solutions obtained by numerical techniques
To provide some background for evaluation of the results of triaxial tests other types of laboratory shear tests and typical results from such tests are presented in Chapter 11 The relashytions between the different types of tests are reviewed and their advantages and limitations are discussed
13 The triaxial test
The triaxial test is most often performed on a cylindrical specimen as shown in Fig 11(a) Principal stresses are applied to the specimen as indicated in Fig 11(b) First a confining pressure σ3 is applied to the specimen This pressure acts all around and therefore on all planes in the specimen Then an additional stress difference σd is applied in the axial direction The stress applied externally to the specimen in the axial direction is
σ σ σ1 3= +d (11)
and therefore
σ σ σd = minus1 3 (12)
In the general case three principal stresses σ1 σ2 and σ3 may act on a soil element in the field However only two different principal stresses can be applied to the specimen in the convenshytional triaxial test The intermediate principal stress σ2 can only have values as follows
σ σ2 3= Triaxial compression (13)
σ σ2 1= Triaxial extension (14)
The condition of triaxial extension can be achieved by applying negative stress differshyences to the specimen This merely produces a reduction in compression in the extension direcshytion but no tension occurs in the specimen The state of stress applied to the specimen is in both cases axisymmetric The triaxial compression test will be discussed in the following while the triaxial extension test is discussed in Chapter 10
The test is performed using triaxial apparashytus as seen in the schematic illustration in Fig 12 The specimen is surrounded by a cap and a base and a membrane This unit is placed in a triaxial cell in which the cell pressure can be applied The cell pressure acts as a hydrostatic confinement for the specimen and the pressure is therefore the same in all directions In addition
σ1
(a) (b)
σ1 = σd + σ3
σ2 = σ3
σd = σ1 ndash σ3σ3
σ3σ3
σ3
σd
Figure 11 (a) Cylindrical specimen for triaxial testing and (b) stresses applied to a triaxial specimen
Principles of Triaxial Testing 3
a deviator load can be applied through a piston that goes through the top of the cell and loads the specimen in the axial direction
The vertical deformation of the specimen may be measured by a dial gage attached to the piston which travels the same vertical distance as the cap sitting on top of the specimen Drainage lines are connected to the water saturated specishymen through the base (or both the cap and the base) and connected to a burette outside the trishyaxial cell This allows for measurements of the volume changes of the specimen during the test
Alternatively the connection to the burette can be shut off thereby preventing the specimen from changing volume Instead the pore water pressure can be measured on a transducer conshynected to the drainage line
The following quantities are measured in a typical triaxial test
1 Confining pressure2 Deviator load3 Vertical (or axial) deformation4 Volume change or pore water pressure
These measurements constitute the data base from which other quantities can be derived
[eg stress difference (σ1 ndash σ3) axial strain ε1 and volumetric strain εv]
14 Advantages and limitations
Whereas the triaxial test potentially can proshyvide a substantial proportion of the mechanical properties required for a project it has limitashytions especially when special conditions are encountered and necessitates clarification based on experimentation
The advantages of the triaxial test are
1 Drainage can be controlled (onndashoff)2 Volume change or pore pressure can be
measured3 Suction can be controlled in partially satushy
rated soils4 Measured deformations allow calculation of
strains and moduli5 A larger variety of stress and strain paths
that occur in the field can be applied in the triaxial apparatus than in any other testing apparatus (eg initial anisotropic consolidashytion at any stress ratio including K0 extension active and passive shear)
The limitations of the triaxial test are
1 Stress concentrations due to friction between specimen and end plates (cap and base) cause nonuniform strains and stresses and therefore nonuniform stressndashstrain volume change or pore pressure response
2 Only axisymmetric stress conditions can be applied to the specimen whereas most field problems involve plane strain or general three‐dimensional conditions with rotation of principal stresses
3 Triaxial tests cannot provide all necessary data required to characterize the behavior of an anisotropic or a cross‐anisotropic soil deposit as illustrated in Fig 13
4 Although the axisymmetric principal stress condition is limited it is more difficult to apply proper shear stresses or tension to soil in relatively simple tests
The first limitation listed above can be overcome by applying lubricated ends on the
Pore pressure transducer
On-Off valve
Burette
Piston
Dial gage
Triaxial cell
P = σd middot A
Aprime
σcell
σ3
σ3 σ3= σcell
Figure 12 Schematic diagram of triaxial apparatus
4 Triaxial Testing of Soils
specimen such that uniform strains and stresses and therefore correct soil response can be proshyduced This is discussed in Chapter 3 In addishytion to the limitations listed above it should be mentioned that it may be easier to reproduce certain stress paths in other specialty equipment than in the triaxial apparatus (eg K0‐test)
Although the triaxial test is limited as explained under points 2 and 3 above it does combine versatility with relative simplicity in concept and performance Other equipment in which three unequal principal stresses can be applied or in which the principal stress direcshytions can be rotated do not have the versatility or is more com plicated to operate Thus other types of equipment have their own advantages and limitations These other equipment types
include plane strain true triaxial simple shear directional shear and torsion shear apparatus All these pieces of equipment are with the excepshytion of the simple shear apparatus employed mainly for research purposes Their operational modes capabilities and results are reviewed in Chapter 11
15 Test stages ndash consolidation and shearing
Laboratory tests are made to simulate field loadshying conditions as close as possible Most field conditions and the corresponding tests can be simplified to consist of two stages consolidation and shearing
Axis of symmetry
1Eh
1Eh
1Ghv
1Ev
ndashmicrohvEh
ndashmicrohvEn
2(1 + microhh)En
ndashmicrohhEn
ndashmicrohvEh
ndashmicrohvEh
ndashmicrohhEh
0
h
h
v
0 0
σh
σh
σv
τhv
τhv
τvh
τvh
σh
σv
σh
τhv
τvh
τhh
τhh τhh
ϵh
ϵv
ϵh
γhv
γvh
γhh
0
Require tests withapplication of
shear stresses
0 0
0
0 0 0 00
1Ghv0 0 0 00
0 0 0 0 0
0 0
bull =
Figure 13 Cross‐anisotropic soil requiring results from more than triaxial tests for full characterization
Principles of Triaxial Testing 5
151 Consolidation
In the first stage the initial condition of the soil is established in terms of effective stresses and stress history (including overconsolidation if applicable) Thus stresses are applied correshysponding to those acting on the element of soil in the field due to weight of the overlying soil strata and other materials or structures that exist at the time the mechanical properties (stressndashstrain strength etc) are sought Sufficient time is allowed for complete consolidation to occur under the applied stresses The condition in the field element has now been established in the triaxial specimen
152 Shearing
In the second stage of the triaxial test an addishytional stress is applied to reach peak failure and beyond under relevant drainage conditions The additional stress applied to the specimen should correspond as closely as possible to the change in stress on the field element due to some new change in the overall field loading situashytion This change may consist of a vertical stress increase or decrease (eg due to addition of a structure or excavation of overlying soil strata) or of a horizontal stress increase or decrease (eg due to the same constructions causing the vertical stress changes) Any combination of vertical and horizontal stress changes may be simulated in the triaxial test Examples of vertishycal and horizontal stress changes in the field are shown in Fig 14
Usually it is desirable to know how much change in load the soil can sustain without failshying and how much deformation will occur under normal working conditions The test is therefore usually continued to find the strength of the soil under the appropriate loading condishytions The results are used with an appropriate factor of safety so that normal working stresses are always somewhat below the peak strength
The stressndashstrain relations obtained from the triaxial tests provide the basis for determinashytion of deformations in the field This may be done in a simplified manner by closed‐form
solutions or it may be done by employing the results of the triaxial tests for calibration of a constitutive model used with a numerical method in finite element or finite difference computer programs
16 Types of tests
The drainage conditions in the field must be duplicated as well as possible in the laboratory tests This may be done by appropriate drainage facilities or preventions as discussed above for the triaxial test In most cases the field drainage conditions can be approximated by one of the following three types of tests
1 Consolidated‐drained test called a CD‐test or just a drained test
2 Consolidated‐undrained test or a CU‐test3 Unconsolidated‐undrained test or a UU‐test
Additionalload
Excavation
ΔσV asymp 0
ΔσV asymp 0
ΔσV gt 0
ΔσV lt 0
Δσh lt 0
Δσh gt 0
Δσh lt ΔσV
Δσh
Figure 14 Examples of stress changes leading to failure in the field
6 Triaxial Testing of Soils
These tests are described in ASTM Standards D7181 (2014) D4767 (2014) and D2850 (2014) respectively
Which condition of drainage in the laboratory test logically corresponds to each case in the field depends on a comparison of loading rate with the rate at which the water can escape or be sucked into the ground Thus the permeability of the soil and the drainage boundary conditions in the field together with the loading rate play key roles in determination of the type of analysis and the type of test drained or undrained that are appropriate for each case Field cases with partial drainage can be correctly duplicated in laboratory tests if the effective stress path is determined for the design condition However the idea of the CD‐ CU‐ and UU‐tests is to make it relatively simple for the design engineer to analyze a condition that will render a sufficient factor of safety under the actual drainage condishytion without trying to estimate and experimenshytally replicate the actual stress path
It has been determined through experience and common sense that the extreme conditions are drained and undrained with and without consolidation As a practical matter in a commershycial laboratory it is easier to run an undrained test than a drained test because it is easier and faster to measure pore pressures than volume change Therefore even drained parameters are more likely to be estimated from a CU‐test than from a CD‐test
161 Simulation of field conditions
Presented below is a brief review of the three types of tests together with examples of field cases for which the tests are appropriate and with typishycal strength results shown on Mohr diagrams
Drained tests
Isotropic consolidation is most often used in the first stage of the triaxial test However anisoshytropic consolidation with any stress ratio is also possible
The shearing stage of a drained test is pershyformed so slowly the soil is so permeable and the drainage facilities are such that no excess
pore pressure (positive or negative) can exist in the specimen at any stage of the test that is
∆u = 0 (15)
It follows then from the effective stress principle
prime = minusσ σ u (16)
that the effective stress changes are always the same as the total stress changes
A soil specimen always changes volume during shearing in a drained test If it contracts in volume it expels pore fluid (usually water or air) and if it expands in volume (dilates) then it sucks water or air into the pores If a non‐zero pore pressure is generated during the test (eg by performing the shearing too fast so the water does not have sufficient time to escape) then the specimen will expel or suck water such that the pore pressure goes towards zero to try to achieve equilibrium between externally applied stresses and internal effective stresses Thus there will always be volume changes in a drained test Consequently the water content the void ratio and the dry density of the specimen at the end of the test are most often not the same as at the beginning
The following field conditions can be simushylated with acceptable accuracy in the drained test
1 Almost all cases involving coarse sands and gravel whether saturated or not (except if confined in eg a lens andor exposed to rapid loading as in eg an earthquake)
2 Many cases involving fine sand and someshytimes silt if the field loads are applied reashysonable slowly
3 Long term loading of any soil as for examplea) Cut slopes several years after excavationb) Embankment constructed very slowly in
layers over a soft clay depositc) Earth dam with steady seepaged) Foundation on clay a long time after
construction
These cases are illustrated in Fig 15The strength results obtained from drained
tests are illustrated schematically on the Mohr diagram in Fig 16 The shear strength of soils increases with increasing confining pressure
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
Contents
Preface xiiiAbout the Author xvii
1 Principles of Triaxial Testing 111 Purpose of triaxial tests 112 Concept of testing 113 The triaxial test 214 Advantages and limitations 315 Test stages ndash consolidation and shearing 4
151 Consolidation 5152 Shearing 5
16 Types of tests 5161 Simulation of field conditions 6162 Selection of test type 12
2 Computations and Presentation of Test Results 1321 Data reduction 13
211 Sign rule ndash 2D 13212 Strains 13213 Cross‐sectional area 23214 Stresses 24215 Corrections 25216 The effective stress principle 25217 Stress analysis in two dimensions ndash Mohrrsquos circle 25218 Strain analysis in two dimensions ndash Mohrrsquos circle 27
22 Stressndashstrain diagrams 28221 Basic diagrams 28222 Modulus evaluation 37223 Derived diagrams 41224 Normalized stressndashstrain behavior 48225 Patterns of soil behavior ndash error recognition 49
23 Strength diagrams 51231 Definition of effective and total strengths 51232 MohrndashCoulomb failure concept 51233 MohrndashCoulomb for triaxial compression 54234 Curved failure envelope 55235 MIT pndashq diagram 57236 Cambridge pndashq diagram 59237 Determination of best‐fit soil strength parameters 60238 Characterization of total strength 60
24 Stress paths 61241 Drained stress paths 61242 Total stress paths in undrained tests 61243 Effective stress paths in undrained tests 61244 Normalized pndashq diagrams 66245 Vector curves 68
vi Contents
25 Linear regression analysis 72251 MIT pndashq diagram 72252 Cambridge pndashq diagram 74253 Correct and incorrect linear regression analyses 75
26 Three‐dimensional stress states 76261 General 3D stress states 76262 Stress invariants 76263 Stress deviator invariants 80264 Magnitudes and directions of principal stresses 81
27 Principal stress space 83271 Octahedral stresses 83272 Triaxial plane 84273 Octahedral plane 86274 Characterization of 3D stress conditions 87275 Shapes of stress invariants in principal stress space 89276 Procedures for projecting stress points onto a common
octahedral plane 90277 Procedure for plotting stress points on an octahedral plane 96278 Representation of test results with principal stress rotation 97
3 Triaxial Equipment 9931 Triaxial setup 99
311 Specimen cap and base 99312 Membrane 103313 O‐rings 105314 Drainage system 106315 Leakage of triaxial setup 112316 Volume change devices 113317 Cell fluid 113318 Lubricated ends 120
32 Triaxial cell 125321 Cell types 125322 Cell wall 127323 Hoek cell 128
33 Piston 128331 Piston friction 129332 Connections between piston cap and specimen 132
34 Pressure supply 133341 Water column 133342 Mercury pot system 134343 Compressed gas 135344 Mechanically compressed fluids 136345 Pressure intensifiers 137346 Pressure transfer to triaxial cell 137347 Vacuum to supply effective confining pressure 138
35 Vertical loading equipment 139351 Deformation or strain control 139352 Load control 140353 Stress control 141354 Combination of load control and deformation control 141355 Stiffness requirements 143
Contents vii
356 Strain control versus load control 14336 Triaxial cell with integrated loading system 143
4 Instrumentation Measurements and Control 14541 Purpose of instrumentation 14542 Principle of measurements 14543 Instrument characteristics 14744 Electrical instrument operation principles 149
441 Strain gage 149442 Linear variable differential transformer 151443 Proximity gage 153444 Reluctance gage 153445 Electrolytic liquid level 154446 Hall effect technique 154447 Elastomer gage 154448 Capacitance technique 155
45 Instrument measurement uncertainty 155451 Accuracy precision and resolution 156452 Measurement uncertainty in triaxial tests 156
46 Instrument performance characteristics 158461 Excitation 158462 Zero shift 159463 Sensitivity 159464 Thermal effects on zero shift and sensitivity 159465 Natural frequency 159466 Nonlinearity 159467 Hysteresis 159468 Repeatability 159469 Range 1594610 Overload capacity 1604611 Overload protection 1604612 Volumetric flexibility of pressure transducers 160
47 Measurement of linear deformations 160471 Inside and outside measurements 160472 Recommended gage length 162473 Operational requirements 162474 Electric wires 163475 Clip gages 163476 Linear variable differential transformer setup 167477 Proximity gage setup 168478 Inclinometer gages 170479 Hall effect gage 1714710 X‐ray technique 1714711 Video tracking and high‐speed photography 1714712 Optical deformation measurements 1724713 Characteristics of linear deformation measurement devices 174
48 Measurement of volume changes 178481 Requirements for volume change devices 178482 Measurements from saturated specimens 180483 Measurements from a triaxial cell 189484 Measurements from dry and partly saturated specimens 192
viii Contents
49 Measurement of axial load 195491 Mechanical force transducers 195492 Operating principle of strain gage load cells 197493 Primary sensors 197494 Fabrication of diaphragm load cells 198495 Load capacity and overload protection 198
410 Measurement of pressure 1994101 Measurement of cell pressure 1994102 Measurement of pore pressure 1994103 Operating principles of pressure transducers 2014104 Fabrication of pressure transducers 2014105 Pressure capacity and overpressure protection 201
411 Specifications for instruments 201412 Factors in the selection of instruments 202413 Measurement redundancy 202414 Calibration of instruments 203
4141 Calibration of linear deformation devices 2034142 Calibration of volume change devices 2044143 Calibration of axial load devices 2044144 Calibration of pressure gages and transducers 204
415 Data acquisition 2064151 Manual datalogging 2064152 Computer datalogging 206
416 Test control 2064161 Control of load pressure and deformations 2064162 Principles of control systems 207
5 Preparation of Triaxial Specimens 21151 Intact specimens 211
511 Storage of samples 211512 Sample inspection and documentation 212513 Ejection of specimens 214514 Trimming of specimens 215515 Freezing technique to produce intact samples of granular materials 217
52 Laboratory preparation of specimens 217521 Slurry consolidation of clay 217522 Air pluviation of sand 219523 Depositional techniques for silty sand 222524 Undercompaction 227525 Compaction of clayey soils 232526 Compaction of soils with oversize particles 234527 Extrusion and storage 235528 Effects of specimen aging 235
53 Measurement of specimen dimensions 235531 Compacted specimens 235
54 Specimen installation 235541 Fully saturated clay specimen 236542 Unsaturated clayey soil specimen 237
6 Specimen Saturation 23961 Reasons for saturation 23962 Reasons for lack of full saturation 239
Contents ix
63 Effects of lack of full saturation 24064 B‐value test 241
641 Effects of primary factors on B‐value 241642 Effects of secondary factors on B‐value 243643 Performance of B‐value test 246
65 Determination of degree of saturation 24966 Methods of saturating triaxial specimens 250
661 Percolation with water 250662 CO2‐method 251663 Application of back pressure 252664 Vacuum procedure 258
67 Range of application of saturation methods 262
7 Testing Stage I Consolidation 26371 Objective of consolidation 26372 Selection of consolidation stresses 263
721 Anisotropic consolidation 264722 Isotropic consolidation 267723 Effects of sampling 268724 SHANSEP for soft clay 268725 Very sensitive clay 272
73 Coefficient of consolidation 272731 Effects of boundary drainage conditions 272732 Determination of time for 100 consolidation 272
8 Testing Stage II Shearing 27781 Introduction 27782 Selection of vertical strain rate 277
821 UU‐tests on clay soils 277822 CD‐ and CU‐tests on granular materials 277823 CD‐ and CU‐tests on clayey soils 277824 Effects of lubricated ends in undrained tests 282
83 Effects of lubricated ends and specimen shape 282831 Strain uniformity and stability of test configuration 282832 Modes of instability in soils 284833 Triaxial tests on sand 284834 Triaxial tests on clay 290
84 Selection of specimen size 29285 Effects of membrane penetration 293
851 Drained tests 293852 Undrained tests 293
86 Post test inspection of specimen 293
9 Corrections to Measurements 29591 Principles of measurements 29592 Types of corrections 29593 Importance of corrections ndash strong and weak specimens 29594 Tests on very short specimens 29695 Vertical load 296
951 Piston uplift 296952 Piston friction 296953 Side drains 298954 Membrane 301
x Contents
955 Buoyancy effects 308956 Techniques to avoid corrections to vertical load 309
96 Vertical deformation 309961 Compression of interfaces 309962 Bedding errors 309963 Techniques to avoid corrections to vertical deformations 311
97 Volume change 312971 Membrane penetration 312972 Volume change due to bedding errors 317973 Leaking membrane 317974 Techniques to avoid corrections to volume change 319
98 Cell and pore pressures 319981 Membrane tension 319982 Fluid self‐weight pressures 319983 Sand penetration into lubricated ends 319984 Membrane penetration 319985 Techniques to avoid corrections to cell and pore pressures 320
10 Special Tests and Test Considerations 321101 Introduction 321
1011 Low confining pressure tests on clays 3211012 Conventional low pressure tests on any soil 3211013 High pressure tests 3221014 Peats and organic soils 322
102 K0‐tests 322103 Extension tests 322
1031 Problems with the conventional triaxial extension test 3231032 Enforcing uniform strains in extension tests 324
104 Tests on unsaturated soils 3261041 Soil water retention curve 3261042 Hydraulic conductivity function 3271043 Low matric suction 3271044 High matric suction 3291045 Modeling 3301046 Triaxial testing 331
105 Frozen soils 331106 Time effects tests 333
1061 Creep tests 3331062 Stress relaxation tests 333
107 Determination of hydraulic conductivity 335108 Bender element tests 335
1081 Fabrication of bender elements 3361082 Shear modulus 3371083 Signal interpretation 3381084 First arrival time 3381085 Specimen size and geometry 3401086 Ray path analysis 3401087 Surface mounted elements 3401088 Effects of specimen material 3411089 Effects of cross‐anisotropy 341
Contents xi
11 Tests with Three Unequal Principal Stresses 343111 Introduction 343112 Tests with constant principal stress directions 344
1121 Plane strain equipment 3441122 True triaxial equipment 3451123 Results from true triaxial tests 3481124 Strength characteristics 3531125 Failure criteria for soils 355
113 Tests with rotating principal stress directions 3601131 Simple shear equipment 3601132 Directional shear cell 3621133 Torsion shear apparatus 3641134 Summary and conclusion 370
Appendix A Manufacturing of Latex Rubber Membranes 373A1 The process 373A2 Products for membrane fabrication 373A3 Create an aluminum mold 374A4 Two tanks 374A5 Mold preparation 374A6 Dipping processes 374A7 Post production 375A8 Storage 375A9 Membrane repair 375
Appendix B Design of Diaphragm Load Cells 377B1 Load cells with uniform diaphragm 377B2 Load cells with tapered diaphragm 378B3 Example Design of 5 kN beryllium copper load cell 378 B31 Punching failure 379
References 381Index 397
Preface
The triaxial test is almost always chosen for studies of new phenomena because it is rela-tively simple and versatile The triaxial test is the most suitable for such studies and it is required in geotechnical engineering for the purposes of design of specific projects and for studying and understanding the behavior of soils
The first triaxial compression test apparatus shown in Fig P1 was designed by von Kārmān (1910 1911) for testing of rock cores The scale may be deduced from the fact that the specimen is 4 cm in diameter (Vaacutesaacuterhelyi 2010) However his paper was not noticed or it was forgotten by 1930 when Casagrande at Harvard University wrote a letter to Terzaghi at the Technical University in Vienna in which he describes his visit to the hydraulics laboratory in Berlin Here he saw an apparatus for measuring the permea-bility of soil Casagrande suggested that the cylindrical specimen in this apparatus could be loaded in the vertical (axial) direction to indi-cate its strength Therefore he was going to build a prototype and Terzaghi proposed that he build one for him too This appears to be the begin-ning of triaxial testing of soils in geotechnical engineering The apparatus was immediately employed by Rendulic (Terzaghi and Rendulic 1934) for tests with and without membranes the results of which played an important role in understanding the effective stress principle as well as the role of pore water pressure and consolidation on shear strength at a time when the effective stress principle was still being questioned (Skempton 1960 de Boer 2005)
Previous books on the developments of tech-niques for triaxial testing have been written by Bishop and Henkel (1957 1962) and by Head (1986) The proceedings from a conference on Advanced Triaxial Testing of Soil and Rock (Donaghe et al 1988) was published to summa-
rize advances in this area Other books have not appeared since then To understand the present book the reader is required to have a background in basic soil mechanics some experience in soil mechanics laboratory testing and perhaps in foundation engineering
In addition to triaxial testing of soils the contents of the book may in part apply to more advanced tests and to the testing of hard soils ndash soft rocks It is written for research workers soil testing laboratories and consulting engineers The emphasis is placed on what the soil speci-men is exposed to and experiences rather than the esthetic appearance of the equipment There will be considerable use of physics and mathe-matics to illustrate the arguments and discus-sions With a few exceptions references are made to easily accessible articles in the literature Much of the book centers on how to obtain high quality experimental results and the guiding concepts for this purpose have been expressed by the car industry in their slogans ldquoQuality is Job Onerdquo (Ford Motor Company) and ldquoQuality is never an accident it is always the result of excellent workmanshiprdquo (Mercedes)
The book is organized in a logical sequence beginning with the principles of triaxial testing in Chapter 1 and the computations and presen-tations of test results in Chapter 2 The triaxial equipment is explained in Chapter 3 and instrumentation measurements and control is reviewed in Chapter 4 Preparation of triaxial specimens is presented in Chapter 5 and satu-ration of specimens is described in Chapter 6 The two testing stages in an experiment are made clear in Chapter 7 Consolidation and in Chapter 8 Shearing Chapter 9 accounts for the corrections to the measurements Chapter 10 informs about special tests and test conditions and Chapter 11 puts the results from triaxial tests in perspective by reviewing results from
xiv Preface
tests with three unequal principal stresses Appendices are provided to explain special experimental techniques Information on ven-dors for the various types of equipment may be obtained from the internet
The authorrsquos background for writing this book consists of a career in laboratory experi-mentation at university level to study and model the behavior of soils More specifically he received an MS degree in 1967 from the Technical University of Denmark for which he wrote a thesis on the influence of the intermedi-ate principal stress on the strength of sand and in retrospect ended up with the wrong conclu-sion on the basis of perfectly correct results He received a PhD from the University of California at Berkeley in 1972 with a dissertation on ldquoThe StressndashStrain and Strength Characteristics of Cohesionless Soilsrdquo which included results
from triaxial compression tests true triaxial tests and torsion shear tests to indicate the effects of the intermediate principal stress on sand behavior as well as a three‐dimensional elasto‐plastic constitutive model for the behavior of soils
With his students the author developed testing equipment performed experiments and built constitutive models for the observed soil behavior while a professor at the University of California at Los Angeles (UCLA) (1972ndash1993) Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015) Many of the experimental techniques developed over this range of years are explained in the present book
Great appreciation is expressed to John F Peters of the US Army Engineer Research and Development Center in Vicksburg MS for his careful review of the manuscript and for his many comments Special thanks go to Afshin Nabili for his invaluable assistance with drafting a large number of the figures and for modifica-tion of other diagrams for the book
Poul V Lade October 2015
References
Bishop AW and Henkel DJ (1957) Measurement of Soil Properties in Triaxial Test Edward Arnold London
Bishop AW and Henkel DJ (1962) The Measurement of Soil Properties in the Triaxial Test 2nd edn St Martinrsquos Press New York NY
de Boer R (2005) The Engineer and the Scandal Springer Berlin
Donaghe RT Chaney RC and Silver ML (eds) (1988) Advanced Triaxial Testing of Soil and Rock ASTM STP 977 ASTM Philadelphia PA
Head KH (1986) Manual of Soil Laboratory Testing ndash Volume 3 Effective Stress Tests Pentech Press London
von Kārmān T (1910) Magyar Meacuternoumlk eacutes Ėpiteacuteszegylet Koumlzloumlnye 10 212ndash226
B
b
c
aD1
D2
Figure P1 Triaxial apparatus designed and con-structed for testing of rock cores by von Kārmān (1910 1911)
Preface xv
von Kārmān T (1911) Verhandlungen Deutsche Ingenieur 55 1749ndash1757
Skempton AW (1960) Terzaghirsquos discovery of effec-tive stress In From Theory to Practice in Soil Mechanics (eds L Bjerrum A Casagrande RB Peck and AW Skempton) pp 42ndash53 John Wiley and Sons Ltd London
Terzaghi K and Rendulic L (1934) Die wirksame Flaumlchenporositaumlt des Betons Zeitschrift des Ōsterreichischen Ingenieur‐ und Architekten Vereines 86 1ndash9
Vaacutesaacuterhelyi B (2010) Tribute to the first triaxial test performed in 1910 Acta Geology and Geophysics of Hungary 45(2) 227ndash230
About the Author
Poul V Lade received his MS degree from the Technical University of Denmark in 1967 and he continued his studies at the University of California at Berkeley where he received his PhD in 1972 Subsequently his academic career began at the University of California at Los Angeles (UCLA) and he continued at Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015)
His research interests include application of appropriate experimental methods to determine the three‐dimensional stressndashstrain and strength behavior of soils and the development of consti-tutive models for frictional materials such as soils concrete and rock He developed laboratory experimental apparatus to investigate monotonic loading and large three‐dimensional stress rever-
sals in plane strain true triaxial and torsion shear equipment This also included studies of effects of principal stress rotation stability instability and liquefaction of granular materials and time effects The constitutive models are based on elasticity and work‐hardening isotropic and kinematic plasticity theories
He has written nearly 300 publications based on research performed with support from the National Science Foundation (NSF) and from the Air Force Office of Scientific Research (AFOSR) He was elected member of the Danish Academy of Technical Sciences (2001) and he was awarded Professor Ostenfeldrsquos Gold Medal from the Technical University of Denmark (2001) He was inaugural editor of Geomechanics and Engineering and he has served on the editorial boards of eight international journals on geotechnical engineering
Triaxial Testing of Soils First Edition Poul V Lade copy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd
Principles of Triaxial Testing1
11 Purpose of triaxial tests
The purpose of performing triaxial tests is to determine the mechanical properties of the soil It is assumed that the soil specimens to be tested are homogeneous and representative of the material in the field and that the desired soil properties can in fact be obtained from the triaxial tests either directly or by interpretation through some theory
The mechanical properties most often sought from triaxial tests are stressndashstrain relations volshyume change or pore pressure behavior and shear strength of the soil Included in the stressndashstrain behavior are also the compressibility and the value of the coefficient of earth pressure at rest K0 Other properties that may be obtained from the triaxial tests which include time as a component are the permeability the coefficient of consolidation and properties relating to time dependent behavior such as rate effects creep and stress relaxation
It is important that the natural soil deposit or the fill from which soil samples have been taken in the field are sufficiently uniform that the soil samples possess the properties which are approshypriate and representative of the soil mass in the field It is therefore paramount that the geology at the site is well‐known and understood Even then samples from uniform deposits may not
ldquocontainrdquo properties that are representative of the field deposit This may happen either (a) due to the change in effective stress state which is always associated with the sampling process or (b) due to mechanical disturbance from sampling transshyportation or handling in the laboratory The stressndashstrain and strength properties of very senshysitive clays which have been disturbed cannot be regenerated in the lab oratory or otherwise obtained by interpretation of tests performed on inadequate specimens The effects of sampling will briefly be discussed below in connection with choice of consolidation pressure in the trishyaxial test The topic of sampling is otherwise outshyside the scope of the present treatment
12 Concept of testing
The concept to be pursued in testing of soils is to simulate as closely as possible the process that goes on in the field Because there is a large number of variables (eg density water content degree of saturation overconsolidation ratio loading conditions stress paths) that influence the resulting soil behavior the simplest and most direct way of obtaining information pertinent to the field conditions is to duplicate these as closely as possible
2 Triaxial Testing of Soils
However because of limitations in equipment and because of practical limitations on the amount of testing that can be performed for each project it is essential that
1 The true field loading conditions (including the drainage conditions) are known
2 The laboratory equipment can reproduce these conditions to a required degree of accuracy
3 A reasonable estimate can be made of the sigshynificance of the differences between the field loading conditions and those that can be proshyduced in the laboratory equipment
It is clear that the triaxial test in many resshypects is incapable of simulating several imporshytant aspects of field loading conditions For example the effects of the intermediate princishypal stress the effects of rotation of principal stresses and the effects of partial drainage durshying loading in the field cannot be investigated on the basis of the triaxial test The effects of such conditions require studies involving other types of equipment or analyses of boundary value problems either by closed form solutions or solutions obtained by numerical techniques
To provide some background for evaluation of the results of triaxial tests other types of laboratory shear tests and typical results from such tests are presented in Chapter 11 The relashytions between the different types of tests are reviewed and their advantages and limitations are discussed
13 The triaxial test
The triaxial test is most often performed on a cylindrical specimen as shown in Fig 11(a) Principal stresses are applied to the specimen as indicated in Fig 11(b) First a confining pressure σ3 is applied to the specimen This pressure acts all around and therefore on all planes in the specimen Then an additional stress difference σd is applied in the axial direction The stress applied externally to the specimen in the axial direction is
σ σ σ1 3= +d (11)
and therefore
σ σ σd = minus1 3 (12)
In the general case three principal stresses σ1 σ2 and σ3 may act on a soil element in the field However only two different principal stresses can be applied to the specimen in the convenshytional triaxial test The intermediate principal stress σ2 can only have values as follows
σ σ2 3= Triaxial compression (13)
σ σ2 1= Triaxial extension (14)
The condition of triaxial extension can be achieved by applying negative stress differshyences to the specimen This merely produces a reduction in compression in the extension direcshytion but no tension occurs in the specimen The state of stress applied to the specimen is in both cases axisymmetric The triaxial compression test will be discussed in the following while the triaxial extension test is discussed in Chapter 10
The test is performed using triaxial apparashytus as seen in the schematic illustration in Fig 12 The specimen is surrounded by a cap and a base and a membrane This unit is placed in a triaxial cell in which the cell pressure can be applied The cell pressure acts as a hydrostatic confinement for the specimen and the pressure is therefore the same in all directions In addition
σ1
(a) (b)
σ1 = σd + σ3
σ2 = σ3
σd = σ1 ndash σ3σ3
σ3σ3
σ3
σd
Figure 11 (a) Cylindrical specimen for triaxial testing and (b) stresses applied to a triaxial specimen
Principles of Triaxial Testing 3
a deviator load can be applied through a piston that goes through the top of the cell and loads the specimen in the axial direction
The vertical deformation of the specimen may be measured by a dial gage attached to the piston which travels the same vertical distance as the cap sitting on top of the specimen Drainage lines are connected to the water saturated specishymen through the base (or both the cap and the base) and connected to a burette outside the trishyaxial cell This allows for measurements of the volume changes of the specimen during the test
Alternatively the connection to the burette can be shut off thereby preventing the specimen from changing volume Instead the pore water pressure can be measured on a transducer conshynected to the drainage line
The following quantities are measured in a typical triaxial test
1 Confining pressure2 Deviator load3 Vertical (or axial) deformation4 Volume change or pore water pressure
These measurements constitute the data base from which other quantities can be derived
[eg stress difference (σ1 ndash σ3) axial strain ε1 and volumetric strain εv]
14 Advantages and limitations
Whereas the triaxial test potentially can proshyvide a substantial proportion of the mechanical properties required for a project it has limitashytions especially when special conditions are encountered and necessitates clarification based on experimentation
The advantages of the triaxial test are
1 Drainage can be controlled (onndashoff)2 Volume change or pore pressure can be
measured3 Suction can be controlled in partially satushy
rated soils4 Measured deformations allow calculation of
strains and moduli5 A larger variety of stress and strain paths
that occur in the field can be applied in the triaxial apparatus than in any other testing apparatus (eg initial anisotropic consolidashytion at any stress ratio including K0 extension active and passive shear)
The limitations of the triaxial test are
1 Stress concentrations due to friction between specimen and end plates (cap and base) cause nonuniform strains and stresses and therefore nonuniform stressndashstrain volume change or pore pressure response
2 Only axisymmetric stress conditions can be applied to the specimen whereas most field problems involve plane strain or general three‐dimensional conditions with rotation of principal stresses
3 Triaxial tests cannot provide all necessary data required to characterize the behavior of an anisotropic or a cross‐anisotropic soil deposit as illustrated in Fig 13
4 Although the axisymmetric principal stress condition is limited it is more difficult to apply proper shear stresses or tension to soil in relatively simple tests
The first limitation listed above can be overcome by applying lubricated ends on the
Pore pressure transducer
On-Off valve
Burette
Piston
Dial gage
Triaxial cell
P = σd middot A
Aprime
σcell
σ3
σ3 σ3= σcell
Figure 12 Schematic diagram of triaxial apparatus
4 Triaxial Testing of Soils
specimen such that uniform strains and stresses and therefore correct soil response can be proshyduced This is discussed in Chapter 3 In addishytion to the limitations listed above it should be mentioned that it may be easier to reproduce certain stress paths in other specialty equipment than in the triaxial apparatus (eg K0‐test)
Although the triaxial test is limited as explained under points 2 and 3 above it does combine versatility with relative simplicity in concept and performance Other equipment in which three unequal principal stresses can be applied or in which the principal stress direcshytions can be rotated do not have the versatility or is more com plicated to operate Thus other types of equipment have their own advantages and limitations These other equipment types
include plane strain true triaxial simple shear directional shear and torsion shear apparatus All these pieces of equipment are with the excepshytion of the simple shear apparatus employed mainly for research purposes Their operational modes capabilities and results are reviewed in Chapter 11
15 Test stages ndash consolidation and shearing
Laboratory tests are made to simulate field loadshying conditions as close as possible Most field conditions and the corresponding tests can be simplified to consist of two stages consolidation and shearing
Axis of symmetry
1Eh
1Eh
1Ghv
1Ev
ndashmicrohvEh
ndashmicrohvEn
2(1 + microhh)En
ndashmicrohhEn
ndashmicrohvEh
ndashmicrohvEh
ndashmicrohhEh
0
h
h
v
0 0
σh
σh
σv
τhv
τhv
τvh
τvh
σh
σv
σh
τhv
τvh
τhh
τhh τhh
ϵh
ϵv
ϵh
γhv
γvh
γhh
0
Require tests withapplication of
shear stresses
0 0
0
0 0 0 00
1Ghv0 0 0 00
0 0 0 0 0
0 0
bull =
Figure 13 Cross‐anisotropic soil requiring results from more than triaxial tests for full characterization
Principles of Triaxial Testing 5
151 Consolidation
In the first stage the initial condition of the soil is established in terms of effective stresses and stress history (including overconsolidation if applicable) Thus stresses are applied correshysponding to those acting on the element of soil in the field due to weight of the overlying soil strata and other materials or structures that exist at the time the mechanical properties (stressndashstrain strength etc) are sought Sufficient time is allowed for complete consolidation to occur under the applied stresses The condition in the field element has now been established in the triaxial specimen
152 Shearing
In the second stage of the triaxial test an addishytional stress is applied to reach peak failure and beyond under relevant drainage conditions The additional stress applied to the specimen should correspond as closely as possible to the change in stress on the field element due to some new change in the overall field loading situashytion This change may consist of a vertical stress increase or decrease (eg due to addition of a structure or excavation of overlying soil strata) or of a horizontal stress increase or decrease (eg due to the same constructions causing the vertical stress changes) Any combination of vertical and horizontal stress changes may be simulated in the triaxial test Examples of vertishycal and horizontal stress changes in the field are shown in Fig 14
Usually it is desirable to know how much change in load the soil can sustain without failshying and how much deformation will occur under normal working conditions The test is therefore usually continued to find the strength of the soil under the appropriate loading condishytions The results are used with an appropriate factor of safety so that normal working stresses are always somewhat below the peak strength
The stressndashstrain relations obtained from the triaxial tests provide the basis for determinashytion of deformations in the field This may be done in a simplified manner by closed‐form
solutions or it may be done by employing the results of the triaxial tests for calibration of a constitutive model used with a numerical method in finite element or finite difference computer programs
16 Types of tests
The drainage conditions in the field must be duplicated as well as possible in the laboratory tests This may be done by appropriate drainage facilities or preventions as discussed above for the triaxial test In most cases the field drainage conditions can be approximated by one of the following three types of tests
1 Consolidated‐drained test called a CD‐test or just a drained test
2 Consolidated‐undrained test or a CU‐test3 Unconsolidated‐undrained test or a UU‐test
Additionalload
Excavation
ΔσV asymp 0
ΔσV asymp 0
ΔσV gt 0
ΔσV lt 0
Δσh lt 0
Δσh gt 0
Δσh lt ΔσV
Δσh
Figure 14 Examples of stress changes leading to failure in the field
6 Triaxial Testing of Soils
These tests are described in ASTM Standards D7181 (2014) D4767 (2014) and D2850 (2014) respectively
Which condition of drainage in the laboratory test logically corresponds to each case in the field depends on a comparison of loading rate with the rate at which the water can escape or be sucked into the ground Thus the permeability of the soil and the drainage boundary conditions in the field together with the loading rate play key roles in determination of the type of analysis and the type of test drained or undrained that are appropriate for each case Field cases with partial drainage can be correctly duplicated in laboratory tests if the effective stress path is determined for the design condition However the idea of the CD‐ CU‐ and UU‐tests is to make it relatively simple for the design engineer to analyze a condition that will render a sufficient factor of safety under the actual drainage condishytion without trying to estimate and experimenshytally replicate the actual stress path
It has been determined through experience and common sense that the extreme conditions are drained and undrained with and without consolidation As a practical matter in a commershycial laboratory it is easier to run an undrained test than a drained test because it is easier and faster to measure pore pressures than volume change Therefore even drained parameters are more likely to be estimated from a CU‐test than from a CD‐test
161 Simulation of field conditions
Presented below is a brief review of the three types of tests together with examples of field cases for which the tests are appropriate and with typishycal strength results shown on Mohr diagrams
Drained tests
Isotropic consolidation is most often used in the first stage of the triaxial test However anisoshytropic consolidation with any stress ratio is also possible
The shearing stage of a drained test is pershyformed so slowly the soil is so permeable and the drainage facilities are such that no excess
pore pressure (positive or negative) can exist in the specimen at any stage of the test that is
∆u = 0 (15)
It follows then from the effective stress principle
prime = minusσ σ u (16)
that the effective stress changes are always the same as the total stress changes
A soil specimen always changes volume during shearing in a drained test If it contracts in volume it expels pore fluid (usually water or air) and if it expands in volume (dilates) then it sucks water or air into the pores If a non‐zero pore pressure is generated during the test (eg by performing the shearing too fast so the water does not have sufficient time to escape) then the specimen will expel or suck water such that the pore pressure goes towards zero to try to achieve equilibrium between externally applied stresses and internal effective stresses Thus there will always be volume changes in a drained test Consequently the water content the void ratio and the dry density of the specimen at the end of the test are most often not the same as at the beginning
The following field conditions can be simushylated with acceptable accuracy in the drained test
1 Almost all cases involving coarse sands and gravel whether saturated or not (except if confined in eg a lens andor exposed to rapid loading as in eg an earthquake)
2 Many cases involving fine sand and someshytimes silt if the field loads are applied reashysonable slowly
3 Long term loading of any soil as for examplea) Cut slopes several years after excavationb) Embankment constructed very slowly in
layers over a soft clay depositc) Earth dam with steady seepaged) Foundation on clay a long time after
construction
These cases are illustrated in Fig 15The strength results obtained from drained
tests are illustrated schematically on the Mohr diagram in Fig 16 The shear strength of soils increases with increasing confining pressure
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
vi Contents
25 Linear regression analysis 72251 MIT pndashq diagram 72252 Cambridge pndashq diagram 74253 Correct and incorrect linear regression analyses 75
26 Three‐dimensional stress states 76261 General 3D stress states 76262 Stress invariants 76263 Stress deviator invariants 80264 Magnitudes and directions of principal stresses 81
27 Principal stress space 83271 Octahedral stresses 83272 Triaxial plane 84273 Octahedral plane 86274 Characterization of 3D stress conditions 87275 Shapes of stress invariants in principal stress space 89276 Procedures for projecting stress points onto a common
octahedral plane 90277 Procedure for plotting stress points on an octahedral plane 96278 Representation of test results with principal stress rotation 97
3 Triaxial Equipment 9931 Triaxial setup 99
311 Specimen cap and base 99312 Membrane 103313 O‐rings 105314 Drainage system 106315 Leakage of triaxial setup 112316 Volume change devices 113317 Cell fluid 113318 Lubricated ends 120
32 Triaxial cell 125321 Cell types 125322 Cell wall 127323 Hoek cell 128
33 Piston 128331 Piston friction 129332 Connections between piston cap and specimen 132
34 Pressure supply 133341 Water column 133342 Mercury pot system 134343 Compressed gas 135344 Mechanically compressed fluids 136345 Pressure intensifiers 137346 Pressure transfer to triaxial cell 137347 Vacuum to supply effective confining pressure 138
35 Vertical loading equipment 139351 Deformation or strain control 139352 Load control 140353 Stress control 141354 Combination of load control and deformation control 141355 Stiffness requirements 143
Contents vii
356 Strain control versus load control 14336 Triaxial cell with integrated loading system 143
4 Instrumentation Measurements and Control 14541 Purpose of instrumentation 14542 Principle of measurements 14543 Instrument characteristics 14744 Electrical instrument operation principles 149
441 Strain gage 149442 Linear variable differential transformer 151443 Proximity gage 153444 Reluctance gage 153445 Electrolytic liquid level 154446 Hall effect technique 154447 Elastomer gage 154448 Capacitance technique 155
45 Instrument measurement uncertainty 155451 Accuracy precision and resolution 156452 Measurement uncertainty in triaxial tests 156
46 Instrument performance characteristics 158461 Excitation 158462 Zero shift 159463 Sensitivity 159464 Thermal effects on zero shift and sensitivity 159465 Natural frequency 159466 Nonlinearity 159467 Hysteresis 159468 Repeatability 159469 Range 1594610 Overload capacity 1604611 Overload protection 1604612 Volumetric flexibility of pressure transducers 160
47 Measurement of linear deformations 160471 Inside and outside measurements 160472 Recommended gage length 162473 Operational requirements 162474 Electric wires 163475 Clip gages 163476 Linear variable differential transformer setup 167477 Proximity gage setup 168478 Inclinometer gages 170479 Hall effect gage 1714710 X‐ray technique 1714711 Video tracking and high‐speed photography 1714712 Optical deformation measurements 1724713 Characteristics of linear deformation measurement devices 174
48 Measurement of volume changes 178481 Requirements for volume change devices 178482 Measurements from saturated specimens 180483 Measurements from a triaxial cell 189484 Measurements from dry and partly saturated specimens 192
viii Contents
49 Measurement of axial load 195491 Mechanical force transducers 195492 Operating principle of strain gage load cells 197493 Primary sensors 197494 Fabrication of diaphragm load cells 198495 Load capacity and overload protection 198
410 Measurement of pressure 1994101 Measurement of cell pressure 1994102 Measurement of pore pressure 1994103 Operating principles of pressure transducers 2014104 Fabrication of pressure transducers 2014105 Pressure capacity and overpressure protection 201
411 Specifications for instruments 201412 Factors in the selection of instruments 202413 Measurement redundancy 202414 Calibration of instruments 203
4141 Calibration of linear deformation devices 2034142 Calibration of volume change devices 2044143 Calibration of axial load devices 2044144 Calibration of pressure gages and transducers 204
415 Data acquisition 2064151 Manual datalogging 2064152 Computer datalogging 206
416 Test control 2064161 Control of load pressure and deformations 2064162 Principles of control systems 207
5 Preparation of Triaxial Specimens 21151 Intact specimens 211
511 Storage of samples 211512 Sample inspection and documentation 212513 Ejection of specimens 214514 Trimming of specimens 215515 Freezing technique to produce intact samples of granular materials 217
52 Laboratory preparation of specimens 217521 Slurry consolidation of clay 217522 Air pluviation of sand 219523 Depositional techniques for silty sand 222524 Undercompaction 227525 Compaction of clayey soils 232526 Compaction of soils with oversize particles 234527 Extrusion and storage 235528 Effects of specimen aging 235
53 Measurement of specimen dimensions 235531 Compacted specimens 235
54 Specimen installation 235541 Fully saturated clay specimen 236542 Unsaturated clayey soil specimen 237
6 Specimen Saturation 23961 Reasons for saturation 23962 Reasons for lack of full saturation 239
Contents ix
63 Effects of lack of full saturation 24064 B‐value test 241
641 Effects of primary factors on B‐value 241642 Effects of secondary factors on B‐value 243643 Performance of B‐value test 246
65 Determination of degree of saturation 24966 Methods of saturating triaxial specimens 250
661 Percolation with water 250662 CO2‐method 251663 Application of back pressure 252664 Vacuum procedure 258
67 Range of application of saturation methods 262
7 Testing Stage I Consolidation 26371 Objective of consolidation 26372 Selection of consolidation stresses 263
721 Anisotropic consolidation 264722 Isotropic consolidation 267723 Effects of sampling 268724 SHANSEP for soft clay 268725 Very sensitive clay 272
73 Coefficient of consolidation 272731 Effects of boundary drainage conditions 272732 Determination of time for 100 consolidation 272
8 Testing Stage II Shearing 27781 Introduction 27782 Selection of vertical strain rate 277
821 UU‐tests on clay soils 277822 CD‐ and CU‐tests on granular materials 277823 CD‐ and CU‐tests on clayey soils 277824 Effects of lubricated ends in undrained tests 282
83 Effects of lubricated ends and specimen shape 282831 Strain uniformity and stability of test configuration 282832 Modes of instability in soils 284833 Triaxial tests on sand 284834 Triaxial tests on clay 290
84 Selection of specimen size 29285 Effects of membrane penetration 293
851 Drained tests 293852 Undrained tests 293
86 Post test inspection of specimen 293
9 Corrections to Measurements 29591 Principles of measurements 29592 Types of corrections 29593 Importance of corrections ndash strong and weak specimens 29594 Tests on very short specimens 29695 Vertical load 296
951 Piston uplift 296952 Piston friction 296953 Side drains 298954 Membrane 301
x Contents
955 Buoyancy effects 308956 Techniques to avoid corrections to vertical load 309
96 Vertical deformation 309961 Compression of interfaces 309962 Bedding errors 309963 Techniques to avoid corrections to vertical deformations 311
97 Volume change 312971 Membrane penetration 312972 Volume change due to bedding errors 317973 Leaking membrane 317974 Techniques to avoid corrections to volume change 319
98 Cell and pore pressures 319981 Membrane tension 319982 Fluid self‐weight pressures 319983 Sand penetration into lubricated ends 319984 Membrane penetration 319985 Techniques to avoid corrections to cell and pore pressures 320
10 Special Tests and Test Considerations 321101 Introduction 321
1011 Low confining pressure tests on clays 3211012 Conventional low pressure tests on any soil 3211013 High pressure tests 3221014 Peats and organic soils 322
102 K0‐tests 322103 Extension tests 322
1031 Problems with the conventional triaxial extension test 3231032 Enforcing uniform strains in extension tests 324
104 Tests on unsaturated soils 3261041 Soil water retention curve 3261042 Hydraulic conductivity function 3271043 Low matric suction 3271044 High matric suction 3291045 Modeling 3301046 Triaxial testing 331
105 Frozen soils 331106 Time effects tests 333
1061 Creep tests 3331062 Stress relaxation tests 333
107 Determination of hydraulic conductivity 335108 Bender element tests 335
1081 Fabrication of bender elements 3361082 Shear modulus 3371083 Signal interpretation 3381084 First arrival time 3381085 Specimen size and geometry 3401086 Ray path analysis 3401087 Surface mounted elements 3401088 Effects of specimen material 3411089 Effects of cross‐anisotropy 341
Contents xi
11 Tests with Three Unequal Principal Stresses 343111 Introduction 343112 Tests with constant principal stress directions 344
1121 Plane strain equipment 3441122 True triaxial equipment 3451123 Results from true triaxial tests 3481124 Strength characteristics 3531125 Failure criteria for soils 355
113 Tests with rotating principal stress directions 3601131 Simple shear equipment 3601132 Directional shear cell 3621133 Torsion shear apparatus 3641134 Summary and conclusion 370
Appendix A Manufacturing of Latex Rubber Membranes 373A1 The process 373A2 Products for membrane fabrication 373A3 Create an aluminum mold 374A4 Two tanks 374A5 Mold preparation 374A6 Dipping processes 374A7 Post production 375A8 Storage 375A9 Membrane repair 375
Appendix B Design of Diaphragm Load Cells 377B1 Load cells with uniform diaphragm 377B2 Load cells with tapered diaphragm 378B3 Example Design of 5 kN beryllium copper load cell 378 B31 Punching failure 379
References 381Index 397
Preface
The triaxial test is almost always chosen for studies of new phenomena because it is rela-tively simple and versatile The triaxial test is the most suitable for such studies and it is required in geotechnical engineering for the purposes of design of specific projects and for studying and understanding the behavior of soils
The first triaxial compression test apparatus shown in Fig P1 was designed by von Kārmān (1910 1911) for testing of rock cores The scale may be deduced from the fact that the specimen is 4 cm in diameter (Vaacutesaacuterhelyi 2010) However his paper was not noticed or it was forgotten by 1930 when Casagrande at Harvard University wrote a letter to Terzaghi at the Technical University in Vienna in which he describes his visit to the hydraulics laboratory in Berlin Here he saw an apparatus for measuring the permea-bility of soil Casagrande suggested that the cylindrical specimen in this apparatus could be loaded in the vertical (axial) direction to indi-cate its strength Therefore he was going to build a prototype and Terzaghi proposed that he build one for him too This appears to be the begin-ning of triaxial testing of soils in geotechnical engineering The apparatus was immediately employed by Rendulic (Terzaghi and Rendulic 1934) for tests with and without membranes the results of which played an important role in understanding the effective stress principle as well as the role of pore water pressure and consolidation on shear strength at a time when the effective stress principle was still being questioned (Skempton 1960 de Boer 2005)
Previous books on the developments of tech-niques for triaxial testing have been written by Bishop and Henkel (1957 1962) and by Head (1986) The proceedings from a conference on Advanced Triaxial Testing of Soil and Rock (Donaghe et al 1988) was published to summa-
rize advances in this area Other books have not appeared since then To understand the present book the reader is required to have a background in basic soil mechanics some experience in soil mechanics laboratory testing and perhaps in foundation engineering
In addition to triaxial testing of soils the contents of the book may in part apply to more advanced tests and to the testing of hard soils ndash soft rocks It is written for research workers soil testing laboratories and consulting engineers The emphasis is placed on what the soil speci-men is exposed to and experiences rather than the esthetic appearance of the equipment There will be considerable use of physics and mathe-matics to illustrate the arguments and discus-sions With a few exceptions references are made to easily accessible articles in the literature Much of the book centers on how to obtain high quality experimental results and the guiding concepts for this purpose have been expressed by the car industry in their slogans ldquoQuality is Job Onerdquo (Ford Motor Company) and ldquoQuality is never an accident it is always the result of excellent workmanshiprdquo (Mercedes)
The book is organized in a logical sequence beginning with the principles of triaxial testing in Chapter 1 and the computations and presen-tations of test results in Chapter 2 The triaxial equipment is explained in Chapter 3 and instrumentation measurements and control is reviewed in Chapter 4 Preparation of triaxial specimens is presented in Chapter 5 and satu-ration of specimens is described in Chapter 6 The two testing stages in an experiment are made clear in Chapter 7 Consolidation and in Chapter 8 Shearing Chapter 9 accounts for the corrections to the measurements Chapter 10 informs about special tests and test conditions and Chapter 11 puts the results from triaxial tests in perspective by reviewing results from
xiv Preface
tests with three unequal principal stresses Appendices are provided to explain special experimental techniques Information on ven-dors for the various types of equipment may be obtained from the internet
The authorrsquos background for writing this book consists of a career in laboratory experi-mentation at university level to study and model the behavior of soils More specifically he received an MS degree in 1967 from the Technical University of Denmark for which he wrote a thesis on the influence of the intermedi-ate principal stress on the strength of sand and in retrospect ended up with the wrong conclu-sion on the basis of perfectly correct results He received a PhD from the University of California at Berkeley in 1972 with a dissertation on ldquoThe StressndashStrain and Strength Characteristics of Cohesionless Soilsrdquo which included results
from triaxial compression tests true triaxial tests and torsion shear tests to indicate the effects of the intermediate principal stress on sand behavior as well as a three‐dimensional elasto‐plastic constitutive model for the behavior of soils
With his students the author developed testing equipment performed experiments and built constitutive models for the observed soil behavior while a professor at the University of California at Los Angeles (UCLA) (1972ndash1993) Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015) Many of the experimental techniques developed over this range of years are explained in the present book
Great appreciation is expressed to John F Peters of the US Army Engineer Research and Development Center in Vicksburg MS for his careful review of the manuscript and for his many comments Special thanks go to Afshin Nabili for his invaluable assistance with drafting a large number of the figures and for modifica-tion of other diagrams for the book
Poul V Lade October 2015
References
Bishop AW and Henkel DJ (1957) Measurement of Soil Properties in Triaxial Test Edward Arnold London
Bishop AW and Henkel DJ (1962) The Measurement of Soil Properties in the Triaxial Test 2nd edn St Martinrsquos Press New York NY
de Boer R (2005) The Engineer and the Scandal Springer Berlin
Donaghe RT Chaney RC and Silver ML (eds) (1988) Advanced Triaxial Testing of Soil and Rock ASTM STP 977 ASTM Philadelphia PA
Head KH (1986) Manual of Soil Laboratory Testing ndash Volume 3 Effective Stress Tests Pentech Press London
von Kārmān T (1910) Magyar Meacuternoumlk eacutes Ėpiteacuteszegylet Koumlzloumlnye 10 212ndash226
B
b
c
aD1
D2
Figure P1 Triaxial apparatus designed and con-structed for testing of rock cores by von Kārmān (1910 1911)
Preface xv
von Kārmān T (1911) Verhandlungen Deutsche Ingenieur 55 1749ndash1757
Skempton AW (1960) Terzaghirsquos discovery of effec-tive stress In From Theory to Practice in Soil Mechanics (eds L Bjerrum A Casagrande RB Peck and AW Skempton) pp 42ndash53 John Wiley and Sons Ltd London
Terzaghi K and Rendulic L (1934) Die wirksame Flaumlchenporositaumlt des Betons Zeitschrift des Ōsterreichischen Ingenieur‐ und Architekten Vereines 86 1ndash9
Vaacutesaacuterhelyi B (2010) Tribute to the first triaxial test performed in 1910 Acta Geology and Geophysics of Hungary 45(2) 227ndash230
About the Author
Poul V Lade received his MS degree from the Technical University of Denmark in 1967 and he continued his studies at the University of California at Berkeley where he received his PhD in 1972 Subsequently his academic career began at the University of California at Los Angeles (UCLA) and he continued at Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015)
His research interests include application of appropriate experimental methods to determine the three‐dimensional stressndashstrain and strength behavior of soils and the development of consti-tutive models for frictional materials such as soils concrete and rock He developed laboratory experimental apparatus to investigate monotonic loading and large three‐dimensional stress rever-
sals in plane strain true triaxial and torsion shear equipment This also included studies of effects of principal stress rotation stability instability and liquefaction of granular materials and time effects The constitutive models are based on elasticity and work‐hardening isotropic and kinematic plasticity theories
He has written nearly 300 publications based on research performed with support from the National Science Foundation (NSF) and from the Air Force Office of Scientific Research (AFOSR) He was elected member of the Danish Academy of Technical Sciences (2001) and he was awarded Professor Ostenfeldrsquos Gold Medal from the Technical University of Denmark (2001) He was inaugural editor of Geomechanics and Engineering and he has served on the editorial boards of eight international journals on geotechnical engineering
Triaxial Testing of Soils First Edition Poul V Lade copy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd
Principles of Triaxial Testing1
11 Purpose of triaxial tests
The purpose of performing triaxial tests is to determine the mechanical properties of the soil It is assumed that the soil specimens to be tested are homogeneous and representative of the material in the field and that the desired soil properties can in fact be obtained from the triaxial tests either directly or by interpretation through some theory
The mechanical properties most often sought from triaxial tests are stressndashstrain relations volshyume change or pore pressure behavior and shear strength of the soil Included in the stressndashstrain behavior are also the compressibility and the value of the coefficient of earth pressure at rest K0 Other properties that may be obtained from the triaxial tests which include time as a component are the permeability the coefficient of consolidation and properties relating to time dependent behavior such as rate effects creep and stress relaxation
It is important that the natural soil deposit or the fill from which soil samples have been taken in the field are sufficiently uniform that the soil samples possess the properties which are approshypriate and representative of the soil mass in the field It is therefore paramount that the geology at the site is well‐known and understood Even then samples from uniform deposits may not
ldquocontainrdquo properties that are representative of the field deposit This may happen either (a) due to the change in effective stress state which is always associated with the sampling process or (b) due to mechanical disturbance from sampling transshyportation or handling in the laboratory The stressndashstrain and strength properties of very senshysitive clays which have been disturbed cannot be regenerated in the lab oratory or otherwise obtained by interpretation of tests performed on inadequate specimens The effects of sampling will briefly be discussed below in connection with choice of consolidation pressure in the trishyaxial test The topic of sampling is otherwise outshyside the scope of the present treatment
12 Concept of testing
The concept to be pursued in testing of soils is to simulate as closely as possible the process that goes on in the field Because there is a large number of variables (eg density water content degree of saturation overconsolidation ratio loading conditions stress paths) that influence the resulting soil behavior the simplest and most direct way of obtaining information pertinent to the field conditions is to duplicate these as closely as possible
2 Triaxial Testing of Soils
However because of limitations in equipment and because of practical limitations on the amount of testing that can be performed for each project it is essential that
1 The true field loading conditions (including the drainage conditions) are known
2 The laboratory equipment can reproduce these conditions to a required degree of accuracy
3 A reasonable estimate can be made of the sigshynificance of the differences between the field loading conditions and those that can be proshyduced in the laboratory equipment
It is clear that the triaxial test in many resshypects is incapable of simulating several imporshytant aspects of field loading conditions For example the effects of the intermediate princishypal stress the effects of rotation of principal stresses and the effects of partial drainage durshying loading in the field cannot be investigated on the basis of the triaxial test The effects of such conditions require studies involving other types of equipment or analyses of boundary value problems either by closed form solutions or solutions obtained by numerical techniques
To provide some background for evaluation of the results of triaxial tests other types of laboratory shear tests and typical results from such tests are presented in Chapter 11 The relashytions between the different types of tests are reviewed and their advantages and limitations are discussed
13 The triaxial test
The triaxial test is most often performed on a cylindrical specimen as shown in Fig 11(a) Principal stresses are applied to the specimen as indicated in Fig 11(b) First a confining pressure σ3 is applied to the specimen This pressure acts all around and therefore on all planes in the specimen Then an additional stress difference σd is applied in the axial direction The stress applied externally to the specimen in the axial direction is
σ σ σ1 3= +d (11)
and therefore
σ σ σd = minus1 3 (12)
In the general case three principal stresses σ1 σ2 and σ3 may act on a soil element in the field However only two different principal stresses can be applied to the specimen in the convenshytional triaxial test The intermediate principal stress σ2 can only have values as follows
σ σ2 3= Triaxial compression (13)
σ σ2 1= Triaxial extension (14)
The condition of triaxial extension can be achieved by applying negative stress differshyences to the specimen This merely produces a reduction in compression in the extension direcshytion but no tension occurs in the specimen The state of stress applied to the specimen is in both cases axisymmetric The triaxial compression test will be discussed in the following while the triaxial extension test is discussed in Chapter 10
The test is performed using triaxial apparashytus as seen in the schematic illustration in Fig 12 The specimen is surrounded by a cap and a base and a membrane This unit is placed in a triaxial cell in which the cell pressure can be applied The cell pressure acts as a hydrostatic confinement for the specimen and the pressure is therefore the same in all directions In addition
σ1
(a) (b)
σ1 = σd + σ3
σ2 = σ3
σd = σ1 ndash σ3σ3
σ3σ3
σ3
σd
Figure 11 (a) Cylindrical specimen for triaxial testing and (b) stresses applied to a triaxial specimen
Principles of Triaxial Testing 3
a deviator load can be applied through a piston that goes through the top of the cell and loads the specimen in the axial direction
The vertical deformation of the specimen may be measured by a dial gage attached to the piston which travels the same vertical distance as the cap sitting on top of the specimen Drainage lines are connected to the water saturated specishymen through the base (or both the cap and the base) and connected to a burette outside the trishyaxial cell This allows for measurements of the volume changes of the specimen during the test
Alternatively the connection to the burette can be shut off thereby preventing the specimen from changing volume Instead the pore water pressure can be measured on a transducer conshynected to the drainage line
The following quantities are measured in a typical triaxial test
1 Confining pressure2 Deviator load3 Vertical (or axial) deformation4 Volume change or pore water pressure
These measurements constitute the data base from which other quantities can be derived
[eg stress difference (σ1 ndash σ3) axial strain ε1 and volumetric strain εv]
14 Advantages and limitations
Whereas the triaxial test potentially can proshyvide a substantial proportion of the mechanical properties required for a project it has limitashytions especially when special conditions are encountered and necessitates clarification based on experimentation
The advantages of the triaxial test are
1 Drainage can be controlled (onndashoff)2 Volume change or pore pressure can be
measured3 Suction can be controlled in partially satushy
rated soils4 Measured deformations allow calculation of
strains and moduli5 A larger variety of stress and strain paths
that occur in the field can be applied in the triaxial apparatus than in any other testing apparatus (eg initial anisotropic consolidashytion at any stress ratio including K0 extension active and passive shear)
The limitations of the triaxial test are
1 Stress concentrations due to friction between specimen and end plates (cap and base) cause nonuniform strains and stresses and therefore nonuniform stressndashstrain volume change or pore pressure response
2 Only axisymmetric stress conditions can be applied to the specimen whereas most field problems involve plane strain or general three‐dimensional conditions with rotation of principal stresses
3 Triaxial tests cannot provide all necessary data required to characterize the behavior of an anisotropic or a cross‐anisotropic soil deposit as illustrated in Fig 13
4 Although the axisymmetric principal stress condition is limited it is more difficult to apply proper shear stresses or tension to soil in relatively simple tests
The first limitation listed above can be overcome by applying lubricated ends on the
Pore pressure transducer
On-Off valve
Burette
Piston
Dial gage
Triaxial cell
P = σd middot A
Aprime
σcell
σ3
σ3 σ3= σcell
Figure 12 Schematic diagram of triaxial apparatus
4 Triaxial Testing of Soils
specimen such that uniform strains and stresses and therefore correct soil response can be proshyduced This is discussed in Chapter 3 In addishytion to the limitations listed above it should be mentioned that it may be easier to reproduce certain stress paths in other specialty equipment than in the triaxial apparatus (eg K0‐test)
Although the triaxial test is limited as explained under points 2 and 3 above it does combine versatility with relative simplicity in concept and performance Other equipment in which three unequal principal stresses can be applied or in which the principal stress direcshytions can be rotated do not have the versatility or is more com plicated to operate Thus other types of equipment have their own advantages and limitations These other equipment types
include plane strain true triaxial simple shear directional shear and torsion shear apparatus All these pieces of equipment are with the excepshytion of the simple shear apparatus employed mainly for research purposes Their operational modes capabilities and results are reviewed in Chapter 11
15 Test stages ndash consolidation and shearing
Laboratory tests are made to simulate field loadshying conditions as close as possible Most field conditions and the corresponding tests can be simplified to consist of two stages consolidation and shearing
Axis of symmetry
1Eh
1Eh
1Ghv
1Ev
ndashmicrohvEh
ndashmicrohvEn
2(1 + microhh)En
ndashmicrohhEn
ndashmicrohvEh
ndashmicrohvEh
ndashmicrohhEh
0
h
h
v
0 0
σh
σh
σv
τhv
τhv
τvh
τvh
σh
σv
σh
τhv
τvh
τhh
τhh τhh
ϵh
ϵv
ϵh
γhv
γvh
γhh
0
Require tests withapplication of
shear stresses
0 0
0
0 0 0 00
1Ghv0 0 0 00
0 0 0 0 0
0 0
bull =
Figure 13 Cross‐anisotropic soil requiring results from more than triaxial tests for full characterization
Principles of Triaxial Testing 5
151 Consolidation
In the first stage the initial condition of the soil is established in terms of effective stresses and stress history (including overconsolidation if applicable) Thus stresses are applied correshysponding to those acting on the element of soil in the field due to weight of the overlying soil strata and other materials or structures that exist at the time the mechanical properties (stressndashstrain strength etc) are sought Sufficient time is allowed for complete consolidation to occur under the applied stresses The condition in the field element has now been established in the triaxial specimen
152 Shearing
In the second stage of the triaxial test an addishytional stress is applied to reach peak failure and beyond under relevant drainage conditions The additional stress applied to the specimen should correspond as closely as possible to the change in stress on the field element due to some new change in the overall field loading situashytion This change may consist of a vertical stress increase or decrease (eg due to addition of a structure or excavation of overlying soil strata) or of a horizontal stress increase or decrease (eg due to the same constructions causing the vertical stress changes) Any combination of vertical and horizontal stress changes may be simulated in the triaxial test Examples of vertishycal and horizontal stress changes in the field are shown in Fig 14
Usually it is desirable to know how much change in load the soil can sustain without failshying and how much deformation will occur under normal working conditions The test is therefore usually continued to find the strength of the soil under the appropriate loading condishytions The results are used with an appropriate factor of safety so that normal working stresses are always somewhat below the peak strength
The stressndashstrain relations obtained from the triaxial tests provide the basis for determinashytion of deformations in the field This may be done in a simplified manner by closed‐form
solutions or it may be done by employing the results of the triaxial tests for calibration of a constitutive model used with a numerical method in finite element or finite difference computer programs
16 Types of tests
The drainage conditions in the field must be duplicated as well as possible in the laboratory tests This may be done by appropriate drainage facilities or preventions as discussed above for the triaxial test In most cases the field drainage conditions can be approximated by one of the following three types of tests
1 Consolidated‐drained test called a CD‐test or just a drained test
2 Consolidated‐undrained test or a CU‐test3 Unconsolidated‐undrained test or a UU‐test
Additionalload
Excavation
ΔσV asymp 0
ΔσV asymp 0
ΔσV gt 0
ΔσV lt 0
Δσh lt 0
Δσh gt 0
Δσh lt ΔσV
Δσh
Figure 14 Examples of stress changes leading to failure in the field
6 Triaxial Testing of Soils
These tests are described in ASTM Standards D7181 (2014) D4767 (2014) and D2850 (2014) respectively
Which condition of drainage in the laboratory test logically corresponds to each case in the field depends on a comparison of loading rate with the rate at which the water can escape or be sucked into the ground Thus the permeability of the soil and the drainage boundary conditions in the field together with the loading rate play key roles in determination of the type of analysis and the type of test drained or undrained that are appropriate for each case Field cases with partial drainage can be correctly duplicated in laboratory tests if the effective stress path is determined for the design condition However the idea of the CD‐ CU‐ and UU‐tests is to make it relatively simple for the design engineer to analyze a condition that will render a sufficient factor of safety under the actual drainage condishytion without trying to estimate and experimenshytally replicate the actual stress path
It has been determined through experience and common sense that the extreme conditions are drained and undrained with and without consolidation As a practical matter in a commershycial laboratory it is easier to run an undrained test than a drained test because it is easier and faster to measure pore pressures than volume change Therefore even drained parameters are more likely to be estimated from a CU‐test than from a CD‐test
161 Simulation of field conditions
Presented below is a brief review of the three types of tests together with examples of field cases for which the tests are appropriate and with typishycal strength results shown on Mohr diagrams
Drained tests
Isotropic consolidation is most often used in the first stage of the triaxial test However anisoshytropic consolidation with any stress ratio is also possible
The shearing stage of a drained test is pershyformed so slowly the soil is so permeable and the drainage facilities are such that no excess
pore pressure (positive or negative) can exist in the specimen at any stage of the test that is
∆u = 0 (15)
It follows then from the effective stress principle
prime = minusσ σ u (16)
that the effective stress changes are always the same as the total stress changes
A soil specimen always changes volume during shearing in a drained test If it contracts in volume it expels pore fluid (usually water or air) and if it expands in volume (dilates) then it sucks water or air into the pores If a non‐zero pore pressure is generated during the test (eg by performing the shearing too fast so the water does not have sufficient time to escape) then the specimen will expel or suck water such that the pore pressure goes towards zero to try to achieve equilibrium between externally applied stresses and internal effective stresses Thus there will always be volume changes in a drained test Consequently the water content the void ratio and the dry density of the specimen at the end of the test are most often not the same as at the beginning
The following field conditions can be simushylated with acceptable accuracy in the drained test
1 Almost all cases involving coarse sands and gravel whether saturated or not (except if confined in eg a lens andor exposed to rapid loading as in eg an earthquake)
2 Many cases involving fine sand and someshytimes silt if the field loads are applied reashysonable slowly
3 Long term loading of any soil as for examplea) Cut slopes several years after excavationb) Embankment constructed very slowly in
layers over a soft clay depositc) Earth dam with steady seepaged) Foundation on clay a long time after
construction
These cases are illustrated in Fig 15The strength results obtained from drained
tests are illustrated schematically on the Mohr diagram in Fig 16 The shear strength of soils increases with increasing confining pressure
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
Contents vii
356 Strain control versus load control 14336 Triaxial cell with integrated loading system 143
4 Instrumentation Measurements and Control 14541 Purpose of instrumentation 14542 Principle of measurements 14543 Instrument characteristics 14744 Electrical instrument operation principles 149
441 Strain gage 149442 Linear variable differential transformer 151443 Proximity gage 153444 Reluctance gage 153445 Electrolytic liquid level 154446 Hall effect technique 154447 Elastomer gage 154448 Capacitance technique 155
45 Instrument measurement uncertainty 155451 Accuracy precision and resolution 156452 Measurement uncertainty in triaxial tests 156
46 Instrument performance characteristics 158461 Excitation 158462 Zero shift 159463 Sensitivity 159464 Thermal effects on zero shift and sensitivity 159465 Natural frequency 159466 Nonlinearity 159467 Hysteresis 159468 Repeatability 159469 Range 1594610 Overload capacity 1604611 Overload protection 1604612 Volumetric flexibility of pressure transducers 160
47 Measurement of linear deformations 160471 Inside and outside measurements 160472 Recommended gage length 162473 Operational requirements 162474 Electric wires 163475 Clip gages 163476 Linear variable differential transformer setup 167477 Proximity gage setup 168478 Inclinometer gages 170479 Hall effect gage 1714710 X‐ray technique 1714711 Video tracking and high‐speed photography 1714712 Optical deformation measurements 1724713 Characteristics of linear deformation measurement devices 174
48 Measurement of volume changes 178481 Requirements for volume change devices 178482 Measurements from saturated specimens 180483 Measurements from a triaxial cell 189484 Measurements from dry and partly saturated specimens 192
viii Contents
49 Measurement of axial load 195491 Mechanical force transducers 195492 Operating principle of strain gage load cells 197493 Primary sensors 197494 Fabrication of diaphragm load cells 198495 Load capacity and overload protection 198
410 Measurement of pressure 1994101 Measurement of cell pressure 1994102 Measurement of pore pressure 1994103 Operating principles of pressure transducers 2014104 Fabrication of pressure transducers 2014105 Pressure capacity and overpressure protection 201
411 Specifications for instruments 201412 Factors in the selection of instruments 202413 Measurement redundancy 202414 Calibration of instruments 203
4141 Calibration of linear deformation devices 2034142 Calibration of volume change devices 2044143 Calibration of axial load devices 2044144 Calibration of pressure gages and transducers 204
415 Data acquisition 2064151 Manual datalogging 2064152 Computer datalogging 206
416 Test control 2064161 Control of load pressure and deformations 2064162 Principles of control systems 207
5 Preparation of Triaxial Specimens 21151 Intact specimens 211
511 Storage of samples 211512 Sample inspection and documentation 212513 Ejection of specimens 214514 Trimming of specimens 215515 Freezing technique to produce intact samples of granular materials 217
52 Laboratory preparation of specimens 217521 Slurry consolidation of clay 217522 Air pluviation of sand 219523 Depositional techniques for silty sand 222524 Undercompaction 227525 Compaction of clayey soils 232526 Compaction of soils with oversize particles 234527 Extrusion and storage 235528 Effects of specimen aging 235
53 Measurement of specimen dimensions 235531 Compacted specimens 235
54 Specimen installation 235541 Fully saturated clay specimen 236542 Unsaturated clayey soil specimen 237
6 Specimen Saturation 23961 Reasons for saturation 23962 Reasons for lack of full saturation 239
Contents ix
63 Effects of lack of full saturation 24064 B‐value test 241
641 Effects of primary factors on B‐value 241642 Effects of secondary factors on B‐value 243643 Performance of B‐value test 246
65 Determination of degree of saturation 24966 Methods of saturating triaxial specimens 250
661 Percolation with water 250662 CO2‐method 251663 Application of back pressure 252664 Vacuum procedure 258
67 Range of application of saturation methods 262
7 Testing Stage I Consolidation 26371 Objective of consolidation 26372 Selection of consolidation stresses 263
721 Anisotropic consolidation 264722 Isotropic consolidation 267723 Effects of sampling 268724 SHANSEP for soft clay 268725 Very sensitive clay 272
73 Coefficient of consolidation 272731 Effects of boundary drainage conditions 272732 Determination of time for 100 consolidation 272
8 Testing Stage II Shearing 27781 Introduction 27782 Selection of vertical strain rate 277
821 UU‐tests on clay soils 277822 CD‐ and CU‐tests on granular materials 277823 CD‐ and CU‐tests on clayey soils 277824 Effects of lubricated ends in undrained tests 282
83 Effects of lubricated ends and specimen shape 282831 Strain uniformity and stability of test configuration 282832 Modes of instability in soils 284833 Triaxial tests on sand 284834 Triaxial tests on clay 290
84 Selection of specimen size 29285 Effects of membrane penetration 293
851 Drained tests 293852 Undrained tests 293
86 Post test inspection of specimen 293
9 Corrections to Measurements 29591 Principles of measurements 29592 Types of corrections 29593 Importance of corrections ndash strong and weak specimens 29594 Tests on very short specimens 29695 Vertical load 296
951 Piston uplift 296952 Piston friction 296953 Side drains 298954 Membrane 301
x Contents
955 Buoyancy effects 308956 Techniques to avoid corrections to vertical load 309
96 Vertical deformation 309961 Compression of interfaces 309962 Bedding errors 309963 Techniques to avoid corrections to vertical deformations 311
97 Volume change 312971 Membrane penetration 312972 Volume change due to bedding errors 317973 Leaking membrane 317974 Techniques to avoid corrections to volume change 319
98 Cell and pore pressures 319981 Membrane tension 319982 Fluid self‐weight pressures 319983 Sand penetration into lubricated ends 319984 Membrane penetration 319985 Techniques to avoid corrections to cell and pore pressures 320
10 Special Tests and Test Considerations 321101 Introduction 321
1011 Low confining pressure tests on clays 3211012 Conventional low pressure tests on any soil 3211013 High pressure tests 3221014 Peats and organic soils 322
102 K0‐tests 322103 Extension tests 322
1031 Problems with the conventional triaxial extension test 3231032 Enforcing uniform strains in extension tests 324
104 Tests on unsaturated soils 3261041 Soil water retention curve 3261042 Hydraulic conductivity function 3271043 Low matric suction 3271044 High matric suction 3291045 Modeling 3301046 Triaxial testing 331
105 Frozen soils 331106 Time effects tests 333
1061 Creep tests 3331062 Stress relaxation tests 333
107 Determination of hydraulic conductivity 335108 Bender element tests 335
1081 Fabrication of bender elements 3361082 Shear modulus 3371083 Signal interpretation 3381084 First arrival time 3381085 Specimen size and geometry 3401086 Ray path analysis 3401087 Surface mounted elements 3401088 Effects of specimen material 3411089 Effects of cross‐anisotropy 341
Contents xi
11 Tests with Three Unequal Principal Stresses 343111 Introduction 343112 Tests with constant principal stress directions 344
1121 Plane strain equipment 3441122 True triaxial equipment 3451123 Results from true triaxial tests 3481124 Strength characteristics 3531125 Failure criteria for soils 355
113 Tests with rotating principal stress directions 3601131 Simple shear equipment 3601132 Directional shear cell 3621133 Torsion shear apparatus 3641134 Summary and conclusion 370
Appendix A Manufacturing of Latex Rubber Membranes 373A1 The process 373A2 Products for membrane fabrication 373A3 Create an aluminum mold 374A4 Two tanks 374A5 Mold preparation 374A6 Dipping processes 374A7 Post production 375A8 Storage 375A9 Membrane repair 375
Appendix B Design of Diaphragm Load Cells 377B1 Load cells with uniform diaphragm 377B2 Load cells with tapered diaphragm 378B3 Example Design of 5 kN beryllium copper load cell 378 B31 Punching failure 379
References 381Index 397
Preface
The triaxial test is almost always chosen for studies of new phenomena because it is rela-tively simple and versatile The triaxial test is the most suitable for such studies and it is required in geotechnical engineering for the purposes of design of specific projects and for studying and understanding the behavior of soils
The first triaxial compression test apparatus shown in Fig P1 was designed by von Kārmān (1910 1911) for testing of rock cores The scale may be deduced from the fact that the specimen is 4 cm in diameter (Vaacutesaacuterhelyi 2010) However his paper was not noticed or it was forgotten by 1930 when Casagrande at Harvard University wrote a letter to Terzaghi at the Technical University in Vienna in which he describes his visit to the hydraulics laboratory in Berlin Here he saw an apparatus for measuring the permea-bility of soil Casagrande suggested that the cylindrical specimen in this apparatus could be loaded in the vertical (axial) direction to indi-cate its strength Therefore he was going to build a prototype and Terzaghi proposed that he build one for him too This appears to be the begin-ning of triaxial testing of soils in geotechnical engineering The apparatus was immediately employed by Rendulic (Terzaghi and Rendulic 1934) for tests with and without membranes the results of which played an important role in understanding the effective stress principle as well as the role of pore water pressure and consolidation on shear strength at a time when the effective stress principle was still being questioned (Skempton 1960 de Boer 2005)
Previous books on the developments of tech-niques for triaxial testing have been written by Bishop and Henkel (1957 1962) and by Head (1986) The proceedings from a conference on Advanced Triaxial Testing of Soil and Rock (Donaghe et al 1988) was published to summa-
rize advances in this area Other books have not appeared since then To understand the present book the reader is required to have a background in basic soil mechanics some experience in soil mechanics laboratory testing and perhaps in foundation engineering
In addition to triaxial testing of soils the contents of the book may in part apply to more advanced tests and to the testing of hard soils ndash soft rocks It is written for research workers soil testing laboratories and consulting engineers The emphasis is placed on what the soil speci-men is exposed to and experiences rather than the esthetic appearance of the equipment There will be considerable use of physics and mathe-matics to illustrate the arguments and discus-sions With a few exceptions references are made to easily accessible articles in the literature Much of the book centers on how to obtain high quality experimental results and the guiding concepts for this purpose have been expressed by the car industry in their slogans ldquoQuality is Job Onerdquo (Ford Motor Company) and ldquoQuality is never an accident it is always the result of excellent workmanshiprdquo (Mercedes)
The book is organized in a logical sequence beginning with the principles of triaxial testing in Chapter 1 and the computations and presen-tations of test results in Chapter 2 The triaxial equipment is explained in Chapter 3 and instrumentation measurements and control is reviewed in Chapter 4 Preparation of triaxial specimens is presented in Chapter 5 and satu-ration of specimens is described in Chapter 6 The two testing stages in an experiment are made clear in Chapter 7 Consolidation and in Chapter 8 Shearing Chapter 9 accounts for the corrections to the measurements Chapter 10 informs about special tests and test conditions and Chapter 11 puts the results from triaxial tests in perspective by reviewing results from
xiv Preface
tests with three unequal principal stresses Appendices are provided to explain special experimental techniques Information on ven-dors for the various types of equipment may be obtained from the internet
The authorrsquos background for writing this book consists of a career in laboratory experi-mentation at university level to study and model the behavior of soils More specifically he received an MS degree in 1967 from the Technical University of Denmark for which he wrote a thesis on the influence of the intermedi-ate principal stress on the strength of sand and in retrospect ended up with the wrong conclu-sion on the basis of perfectly correct results He received a PhD from the University of California at Berkeley in 1972 with a dissertation on ldquoThe StressndashStrain and Strength Characteristics of Cohesionless Soilsrdquo which included results
from triaxial compression tests true triaxial tests and torsion shear tests to indicate the effects of the intermediate principal stress on sand behavior as well as a three‐dimensional elasto‐plastic constitutive model for the behavior of soils
With his students the author developed testing equipment performed experiments and built constitutive models for the observed soil behavior while a professor at the University of California at Los Angeles (UCLA) (1972ndash1993) Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015) Many of the experimental techniques developed over this range of years are explained in the present book
Great appreciation is expressed to John F Peters of the US Army Engineer Research and Development Center in Vicksburg MS for his careful review of the manuscript and for his many comments Special thanks go to Afshin Nabili for his invaluable assistance with drafting a large number of the figures and for modifica-tion of other diagrams for the book
Poul V Lade October 2015
References
Bishop AW and Henkel DJ (1957) Measurement of Soil Properties in Triaxial Test Edward Arnold London
Bishop AW and Henkel DJ (1962) The Measurement of Soil Properties in the Triaxial Test 2nd edn St Martinrsquos Press New York NY
de Boer R (2005) The Engineer and the Scandal Springer Berlin
Donaghe RT Chaney RC and Silver ML (eds) (1988) Advanced Triaxial Testing of Soil and Rock ASTM STP 977 ASTM Philadelphia PA
Head KH (1986) Manual of Soil Laboratory Testing ndash Volume 3 Effective Stress Tests Pentech Press London
von Kārmān T (1910) Magyar Meacuternoumlk eacutes Ėpiteacuteszegylet Koumlzloumlnye 10 212ndash226
B
b
c
aD1
D2
Figure P1 Triaxial apparatus designed and con-structed for testing of rock cores by von Kārmān (1910 1911)
Preface xv
von Kārmān T (1911) Verhandlungen Deutsche Ingenieur 55 1749ndash1757
Skempton AW (1960) Terzaghirsquos discovery of effec-tive stress In From Theory to Practice in Soil Mechanics (eds L Bjerrum A Casagrande RB Peck and AW Skempton) pp 42ndash53 John Wiley and Sons Ltd London
Terzaghi K and Rendulic L (1934) Die wirksame Flaumlchenporositaumlt des Betons Zeitschrift des Ōsterreichischen Ingenieur‐ und Architekten Vereines 86 1ndash9
Vaacutesaacuterhelyi B (2010) Tribute to the first triaxial test performed in 1910 Acta Geology and Geophysics of Hungary 45(2) 227ndash230
About the Author
Poul V Lade received his MS degree from the Technical University of Denmark in 1967 and he continued his studies at the University of California at Berkeley where he received his PhD in 1972 Subsequently his academic career began at the University of California at Los Angeles (UCLA) and he continued at Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015)
His research interests include application of appropriate experimental methods to determine the three‐dimensional stressndashstrain and strength behavior of soils and the development of consti-tutive models for frictional materials such as soils concrete and rock He developed laboratory experimental apparatus to investigate monotonic loading and large three‐dimensional stress rever-
sals in plane strain true triaxial and torsion shear equipment This also included studies of effects of principal stress rotation stability instability and liquefaction of granular materials and time effects The constitutive models are based on elasticity and work‐hardening isotropic and kinematic plasticity theories
He has written nearly 300 publications based on research performed with support from the National Science Foundation (NSF) and from the Air Force Office of Scientific Research (AFOSR) He was elected member of the Danish Academy of Technical Sciences (2001) and he was awarded Professor Ostenfeldrsquos Gold Medal from the Technical University of Denmark (2001) He was inaugural editor of Geomechanics and Engineering and he has served on the editorial boards of eight international journals on geotechnical engineering
Triaxial Testing of Soils First Edition Poul V Lade copy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd
Principles of Triaxial Testing1
11 Purpose of triaxial tests
The purpose of performing triaxial tests is to determine the mechanical properties of the soil It is assumed that the soil specimens to be tested are homogeneous and representative of the material in the field and that the desired soil properties can in fact be obtained from the triaxial tests either directly or by interpretation through some theory
The mechanical properties most often sought from triaxial tests are stressndashstrain relations volshyume change or pore pressure behavior and shear strength of the soil Included in the stressndashstrain behavior are also the compressibility and the value of the coefficient of earth pressure at rest K0 Other properties that may be obtained from the triaxial tests which include time as a component are the permeability the coefficient of consolidation and properties relating to time dependent behavior such as rate effects creep and stress relaxation
It is important that the natural soil deposit or the fill from which soil samples have been taken in the field are sufficiently uniform that the soil samples possess the properties which are approshypriate and representative of the soil mass in the field It is therefore paramount that the geology at the site is well‐known and understood Even then samples from uniform deposits may not
ldquocontainrdquo properties that are representative of the field deposit This may happen either (a) due to the change in effective stress state which is always associated with the sampling process or (b) due to mechanical disturbance from sampling transshyportation or handling in the laboratory The stressndashstrain and strength properties of very senshysitive clays which have been disturbed cannot be regenerated in the lab oratory or otherwise obtained by interpretation of tests performed on inadequate specimens The effects of sampling will briefly be discussed below in connection with choice of consolidation pressure in the trishyaxial test The topic of sampling is otherwise outshyside the scope of the present treatment
12 Concept of testing
The concept to be pursued in testing of soils is to simulate as closely as possible the process that goes on in the field Because there is a large number of variables (eg density water content degree of saturation overconsolidation ratio loading conditions stress paths) that influence the resulting soil behavior the simplest and most direct way of obtaining information pertinent to the field conditions is to duplicate these as closely as possible
2 Triaxial Testing of Soils
However because of limitations in equipment and because of practical limitations on the amount of testing that can be performed for each project it is essential that
1 The true field loading conditions (including the drainage conditions) are known
2 The laboratory equipment can reproduce these conditions to a required degree of accuracy
3 A reasonable estimate can be made of the sigshynificance of the differences between the field loading conditions and those that can be proshyduced in the laboratory equipment
It is clear that the triaxial test in many resshypects is incapable of simulating several imporshytant aspects of field loading conditions For example the effects of the intermediate princishypal stress the effects of rotation of principal stresses and the effects of partial drainage durshying loading in the field cannot be investigated on the basis of the triaxial test The effects of such conditions require studies involving other types of equipment or analyses of boundary value problems either by closed form solutions or solutions obtained by numerical techniques
To provide some background for evaluation of the results of triaxial tests other types of laboratory shear tests and typical results from such tests are presented in Chapter 11 The relashytions between the different types of tests are reviewed and their advantages and limitations are discussed
13 The triaxial test
The triaxial test is most often performed on a cylindrical specimen as shown in Fig 11(a) Principal stresses are applied to the specimen as indicated in Fig 11(b) First a confining pressure σ3 is applied to the specimen This pressure acts all around and therefore on all planes in the specimen Then an additional stress difference σd is applied in the axial direction The stress applied externally to the specimen in the axial direction is
σ σ σ1 3= +d (11)
and therefore
σ σ σd = minus1 3 (12)
In the general case three principal stresses σ1 σ2 and σ3 may act on a soil element in the field However only two different principal stresses can be applied to the specimen in the convenshytional triaxial test The intermediate principal stress σ2 can only have values as follows
σ σ2 3= Triaxial compression (13)
σ σ2 1= Triaxial extension (14)
The condition of triaxial extension can be achieved by applying negative stress differshyences to the specimen This merely produces a reduction in compression in the extension direcshytion but no tension occurs in the specimen The state of stress applied to the specimen is in both cases axisymmetric The triaxial compression test will be discussed in the following while the triaxial extension test is discussed in Chapter 10
The test is performed using triaxial apparashytus as seen in the schematic illustration in Fig 12 The specimen is surrounded by a cap and a base and a membrane This unit is placed in a triaxial cell in which the cell pressure can be applied The cell pressure acts as a hydrostatic confinement for the specimen and the pressure is therefore the same in all directions In addition
σ1
(a) (b)
σ1 = σd + σ3
σ2 = σ3
σd = σ1 ndash σ3σ3
σ3σ3
σ3
σd
Figure 11 (a) Cylindrical specimen for triaxial testing and (b) stresses applied to a triaxial specimen
Principles of Triaxial Testing 3
a deviator load can be applied through a piston that goes through the top of the cell and loads the specimen in the axial direction
The vertical deformation of the specimen may be measured by a dial gage attached to the piston which travels the same vertical distance as the cap sitting on top of the specimen Drainage lines are connected to the water saturated specishymen through the base (or both the cap and the base) and connected to a burette outside the trishyaxial cell This allows for measurements of the volume changes of the specimen during the test
Alternatively the connection to the burette can be shut off thereby preventing the specimen from changing volume Instead the pore water pressure can be measured on a transducer conshynected to the drainage line
The following quantities are measured in a typical triaxial test
1 Confining pressure2 Deviator load3 Vertical (or axial) deformation4 Volume change or pore water pressure
These measurements constitute the data base from which other quantities can be derived
[eg stress difference (σ1 ndash σ3) axial strain ε1 and volumetric strain εv]
14 Advantages and limitations
Whereas the triaxial test potentially can proshyvide a substantial proportion of the mechanical properties required for a project it has limitashytions especially when special conditions are encountered and necessitates clarification based on experimentation
The advantages of the triaxial test are
1 Drainage can be controlled (onndashoff)2 Volume change or pore pressure can be
measured3 Suction can be controlled in partially satushy
rated soils4 Measured deformations allow calculation of
strains and moduli5 A larger variety of stress and strain paths
that occur in the field can be applied in the triaxial apparatus than in any other testing apparatus (eg initial anisotropic consolidashytion at any stress ratio including K0 extension active and passive shear)
The limitations of the triaxial test are
1 Stress concentrations due to friction between specimen and end plates (cap and base) cause nonuniform strains and stresses and therefore nonuniform stressndashstrain volume change or pore pressure response
2 Only axisymmetric stress conditions can be applied to the specimen whereas most field problems involve plane strain or general three‐dimensional conditions with rotation of principal stresses
3 Triaxial tests cannot provide all necessary data required to characterize the behavior of an anisotropic or a cross‐anisotropic soil deposit as illustrated in Fig 13
4 Although the axisymmetric principal stress condition is limited it is more difficult to apply proper shear stresses or tension to soil in relatively simple tests
The first limitation listed above can be overcome by applying lubricated ends on the
Pore pressure transducer
On-Off valve
Burette
Piston
Dial gage
Triaxial cell
P = σd middot A
Aprime
σcell
σ3
σ3 σ3= σcell
Figure 12 Schematic diagram of triaxial apparatus
4 Triaxial Testing of Soils
specimen such that uniform strains and stresses and therefore correct soil response can be proshyduced This is discussed in Chapter 3 In addishytion to the limitations listed above it should be mentioned that it may be easier to reproduce certain stress paths in other specialty equipment than in the triaxial apparatus (eg K0‐test)
Although the triaxial test is limited as explained under points 2 and 3 above it does combine versatility with relative simplicity in concept and performance Other equipment in which three unequal principal stresses can be applied or in which the principal stress direcshytions can be rotated do not have the versatility or is more com plicated to operate Thus other types of equipment have their own advantages and limitations These other equipment types
include plane strain true triaxial simple shear directional shear and torsion shear apparatus All these pieces of equipment are with the excepshytion of the simple shear apparatus employed mainly for research purposes Their operational modes capabilities and results are reviewed in Chapter 11
15 Test stages ndash consolidation and shearing
Laboratory tests are made to simulate field loadshying conditions as close as possible Most field conditions and the corresponding tests can be simplified to consist of two stages consolidation and shearing
Axis of symmetry
1Eh
1Eh
1Ghv
1Ev
ndashmicrohvEh
ndashmicrohvEn
2(1 + microhh)En
ndashmicrohhEn
ndashmicrohvEh
ndashmicrohvEh
ndashmicrohhEh
0
h
h
v
0 0
σh
σh
σv
τhv
τhv
τvh
τvh
σh
σv
σh
τhv
τvh
τhh
τhh τhh
ϵh
ϵv
ϵh
γhv
γvh
γhh
0
Require tests withapplication of
shear stresses
0 0
0
0 0 0 00
1Ghv0 0 0 00
0 0 0 0 0
0 0
bull =
Figure 13 Cross‐anisotropic soil requiring results from more than triaxial tests for full characterization
Principles of Triaxial Testing 5
151 Consolidation
In the first stage the initial condition of the soil is established in terms of effective stresses and stress history (including overconsolidation if applicable) Thus stresses are applied correshysponding to those acting on the element of soil in the field due to weight of the overlying soil strata and other materials or structures that exist at the time the mechanical properties (stressndashstrain strength etc) are sought Sufficient time is allowed for complete consolidation to occur under the applied stresses The condition in the field element has now been established in the triaxial specimen
152 Shearing
In the second stage of the triaxial test an addishytional stress is applied to reach peak failure and beyond under relevant drainage conditions The additional stress applied to the specimen should correspond as closely as possible to the change in stress on the field element due to some new change in the overall field loading situashytion This change may consist of a vertical stress increase or decrease (eg due to addition of a structure or excavation of overlying soil strata) or of a horizontal stress increase or decrease (eg due to the same constructions causing the vertical stress changes) Any combination of vertical and horizontal stress changes may be simulated in the triaxial test Examples of vertishycal and horizontal stress changes in the field are shown in Fig 14
Usually it is desirable to know how much change in load the soil can sustain without failshying and how much deformation will occur under normal working conditions The test is therefore usually continued to find the strength of the soil under the appropriate loading condishytions The results are used with an appropriate factor of safety so that normal working stresses are always somewhat below the peak strength
The stressndashstrain relations obtained from the triaxial tests provide the basis for determinashytion of deformations in the field This may be done in a simplified manner by closed‐form
solutions or it may be done by employing the results of the triaxial tests for calibration of a constitutive model used with a numerical method in finite element or finite difference computer programs
16 Types of tests
The drainage conditions in the field must be duplicated as well as possible in the laboratory tests This may be done by appropriate drainage facilities or preventions as discussed above for the triaxial test In most cases the field drainage conditions can be approximated by one of the following three types of tests
1 Consolidated‐drained test called a CD‐test or just a drained test
2 Consolidated‐undrained test or a CU‐test3 Unconsolidated‐undrained test or a UU‐test
Additionalload
Excavation
ΔσV asymp 0
ΔσV asymp 0
ΔσV gt 0
ΔσV lt 0
Δσh lt 0
Δσh gt 0
Δσh lt ΔσV
Δσh
Figure 14 Examples of stress changes leading to failure in the field
6 Triaxial Testing of Soils
These tests are described in ASTM Standards D7181 (2014) D4767 (2014) and D2850 (2014) respectively
Which condition of drainage in the laboratory test logically corresponds to each case in the field depends on a comparison of loading rate with the rate at which the water can escape or be sucked into the ground Thus the permeability of the soil and the drainage boundary conditions in the field together with the loading rate play key roles in determination of the type of analysis and the type of test drained or undrained that are appropriate for each case Field cases with partial drainage can be correctly duplicated in laboratory tests if the effective stress path is determined for the design condition However the idea of the CD‐ CU‐ and UU‐tests is to make it relatively simple for the design engineer to analyze a condition that will render a sufficient factor of safety under the actual drainage condishytion without trying to estimate and experimenshytally replicate the actual stress path
It has been determined through experience and common sense that the extreme conditions are drained and undrained with and without consolidation As a practical matter in a commershycial laboratory it is easier to run an undrained test than a drained test because it is easier and faster to measure pore pressures than volume change Therefore even drained parameters are more likely to be estimated from a CU‐test than from a CD‐test
161 Simulation of field conditions
Presented below is a brief review of the three types of tests together with examples of field cases for which the tests are appropriate and with typishycal strength results shown on Mohr diagrams
Drained tests
Isotropic consolidation is most often used in the first stage of the triaxial test However anisoshytropic consolidation with any stress ratio is also possible
The shearing stage of a drained test is pershyformed so slowly the soil is so permeable and the drainage facilities are such that no excess
pore pressure (positive or negative) can exist in the specimen at any stage of the test that is
∆u = 0 (15)
It follows then from the effective stress principle
prime = minusσ σ u (16)
that the effective stress changes are always the same as the total stress changes
A soil specimen always changes volume during shearing in a drained test If it contracts in volume it expels pore fluid (usually water or air) and if it expands in volume (dilates) then it sucks water or air into the pores If a non‐zero pore pressure is generated during the test (eg by performing the shearing too fast so the water does not have sufficient time to escape) then the specimen will expel or suck water such that the pore pressure goes towards zero to try to achieve equilibrium between externally applied stresses and internal effective stresses Thus there will always be volume changes in a drained test Consequently the water content the void ratio and the dry density of the specimen at the end of the test are most often not the same as at the beginning
The following field conditions can be simushylated with acceptable accuracy in the drained test
1 Almost all cases involving coarse sands and gravel whether saturated or not (except if confined in eg a lens andor exposed to rapid loading as in eg an earthquake)
2 Many cases involving fine sand and someshytimes silt if the field loads are applied reashysonable slowly
3 Long term loading of any soil as for examplea) Cut slopes several years after excavationb) Embankment constructed very slowly in
layers over a soft clay depositc) Earth dam with steady seepaged) Foundation on clay a long time after
construction
These cases are illustrated in Fig 15The strength results obtained from drained
tests are illustrated schematically on the Mohr diagram in Fig 16 The shear strength of soils increases with increasing confining pressure
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
viii Contents
49 Measurement of axial load 195491 Mechanical force transducers 195492 Operating principle of strain gage load cells 197493 Primary sensors 197494 Fabrication of diaphragm load cells 198495 Load capacity and overload protection 198
410 Measurement of pressure 1994101 Measurement of cell pressure 1994102 Measurement of pore pressure 1994103 Operating principles of pressure transducers 2014104 Fabrication of pressure transducers 2014105 Pressure capacity and overpressure protection 201
411 Specifications for instruments 201412 Factors in the selection of instruments 202413 Measurement redundancy 202414 Calibration of instruments 203
4141 Calibration of linear deformation devices 2034142 Calibration of volume change devices 2044143 Calibration of axial load devices 2044144 Calibration of pressure gages and transducers 204
415 Data acquisition 2064151 Manual datalogging 2064152 Computer datalogging 206
416 Test control 2064161 Control of load pressure and deformations 2064162 Principles of control systems 207
5 Preparation of Triaxial Specimens 21151 Intact specimens 211
511 Storage of samples 211512 Sample inspection and documentation 212513 Ejection of specimens 214514 Trimming of specimens 215515 Freezing technique to produce intact samples of granular materials 217
52 Laboratory preparation of specimens 217521 Slurry consolidation of clay 217522 Air pluviation of sand 219523 Depositional techniques for silty sand 222524 Undercompaction 227525 Compaction of clayey soils 232526 Compaction of soils with oversize particles 234527 Extrusion and storage 235528 Effects of specimen aging 235
53 Measurement of specimen dimensions 235531 Compacted specimens 235
54 Specimen installation 235541 Fully saturated clay specimen 236542 Unsaturated clayey soil specimen 237
6 Specimen Saturation 23961 Reasons for saturation 23962 Reasons for lack of full saturation 239
Contents ix
63 Effects of lack of full saturation 24064 B‐value test 241
641 Effects of primary factors on B‐value 241642 Effects of secondary factors on B‐value 243643 Performance of B‐value test 246
65 Determination of degree of saturation 24966 Methods of saturating triaxial specimens 250
661 Percolation with water 250662 CO2‐method 251663 Application of back pressure 252664 Vacuum procedure 258
67 Range of application of saturation methods 262
7 Testing Stage I Consolidation 26371 Objective of consolidation 26372 Selection of consolidation stresses 263
721 Anisotropic consolidation 264722 Isotropic consolidation 267723 Effects of sampling 268724 SHANSEP for soft clay 268725 Very sensitive clay 272
73 Coefficient of consolidation 272731 Effects of boundary drainage conditions 272732 Determination of time for 100 consolidation 272
8 Testing Stage II Shearing 27781 Introduction 27782 Selection of vertical strain rate 277
821 UU‐tests on clay soils 277822 CD‐ and CU‐tests on granular materials 277823 CD‐ and CU‐tests on clayey soils 277824 Effects of lubricated ends in undrained tests 282
83 Effects of lubricated ends and specimen shape 282831 Strain uniformity and stability of test configuration 282832 Modes of instability in soils 284833 Triaxial tests on sand 284834 Triaxial tests on clay 290
84 Selection of specimen size 29285 Effects of membrane penetration 293
851 Drained tests 293852 Undrained tests 293
86 Post test inspection of specimen 293
9 Corrections to Measurements 29591 Principles of measurements 29592 Types of corrections 29593 Importance of corrections ndash strong and weak specimens 29594 Tests on very short specimens 29695 Vertical load 296
951 Piston uplift 296952 Piston friction 296953 Side drains 298954 Membrane 301
x Contents
955 Buoyancy effects 308956 Techniques to avoid corrections to vertical load 309
96 Vertical deformation 309961 Compression of interfaces 309962 Bedding errors 309963 Techniques to avoid corrections to vertical deformations 311
97 Volume change 312971 Membrane penetration 312972 Volume change due to bedding errors 317973 Leaking membrane 317974 Techniques to avoid corrections to volume change 319
98 Cell and pore pressures 319981 Membrane tension 319982 Fluid self‐weight pressures 319983 Sand penetration into lubricated ends 319984 Membrane penetration 319985 Techniques to avoid corrections to cell and pore pressures 320
10 Special Tests and Test Considerations 321101 Introduction 321
1011 Low confining pressure tests on clays 3211012 Conventional low pressure tests on any soil 3211013 High pressure tests 3221014 Peats and organic soils 322
102 K0‐tests 322103 Extension tests 322
1031 Problems with the conventional triaxial extension test 3231032 Enforcing uniform strains in extension tests 324
104 Tests on unsaturated soils 3261041 Soil water retention curve 3261042 Hydraulic conductivity function 3271043 Low matric suction 3271044 High matric suction 3291045 Modeling 3301046 Triaxial testing 331
105 Frozen soils 331106 Time effects tests 333
1061 Creep tests 3331062 Stress relaxation tests 333
107 Determination of hydraulic conductivity 335108 Bender element tests 335
1081 Fabrication of bender elements 3361082 Shear modulus 3371083 Signal interpretation 3381084 First arrival time 3381085 Specimen size and geometry 3401086 Ray path analysis 3401087 Surface mounted elements 3401088 Effects of specimen material 3411089 Effects of cross‐anisotropy 341
Contents xi
11 Tests with Three Unequal Principal Stresses 343111 Introduction 343112 Tests with constant principal stress directions 344
1121 Plane strain equipment 3441122 True triaxial equipment 3451123 Results from true triaxial tests 3481124 Strength characteristics 3531125 Failure criteria for soils 355
113 Tests with rotating principal stress directions 3601131 Simple shear equipment 3601132 Directional shear cell 3621133 Torsion shear apparatus 3641134 Summary and conclusion 370
Appendix A Manufacturing of Latex Rubber Membranes 373A1 The process 373A2 Products for membrane fabrication 373A3 Create an aluminum mold 374A4 Two tanks 374A5 Mold preparation 374A6 Dipping processes 374A7 Post production 375A8 Storage 375A9 Membrane repair 375
Appendix B Design of Diaphragm Load Cells 377B1 Load cells with uniform diaphragm 377B2 Load cells with tapered diaphragm 378B3 Example Design of 5 kN beryllium copper load cell 378 B31 Punching failure 379
References 381Index 397
Preface
The triaxial test is almost always chosen for studies of new phenomena because it is rela-tively simple and versatile The triaxial test is the most suitable for such studies and it is required in geotechnical engineering for the purposes of design of specific projects and for studying and understanding the behavior of soils
The first triaxial compression test apparatus shown in Fig P1 was designed by von Kārmān (1910 1911) for testing of rock cores The scale may be deduced from the fact that the specimen is 4 cm in diameter (Vaacutesaacuterhelyi 2010) However his paper was not noticed or it was forgotten by 1930 when Casagrande at Harvard University wrote a letter to Terzaghi at the Technical University in Vienna in which he describes his visit to the hydraulics laboratory in Berlin Here he saw an apparatus for measuring the permea-bility of soil Casagrande suggested that the cylindrical specimen in this apparatus could be loaded in the vertical (axial) direction to indi-cate its strength Therefore he was going to build a prototype and Terzaghi proposed that he build one for him too This appears to be the begin-ning of triaxial testing of soils in geotechnical engineering The apparatus was immediately employed by Rendulic (Terzaghi and Rendulic 1934) for tests with and without membranes the results of which played an important role in understanding the effective stress principle as well as the role of pore water pressure and consolidation on shear strength at a time when the effective stress principle was still being questioned (Skempton 1960 de Boer 2005)
Previous books on the developments of tech-niques for triaxial testing have been written by Bishop and Henkel (1957 1962) and by Head (1986) The proceedings from a conference on Advanced Triaxial Testing of Soil and Rock (Donaghe et al 1988) was published to summa-
rize advances in this area Other books have not appeared since then To understand the present book the reader is required to have a background in basic soil mechanics some experience in soil mechanics laboratory testing and perhaps in foundation engineering
In addition to triaxial testing of soils the contents of the book may in part apply to more advanced tests and to the testing of hard soils ndash soft rocks It is written for research workers soil testing laboratories and consulting engineers The emphasis is placed on what the soil speci-men is exposed to and experiences rather than the esthetic appearance of the equipment There will be considerable use of physics and mathe-matics to illustrate the arguments and discus-sions With a few exceptions references are made to easily accessible articles in the literature Much of the book centers on how to obtain high quality experimental results and the guiding concepts for this purpose have been expressed by the car industry in their slogans ldquoQuality is Job Onerdquo (Ford Motor Company) and ldquoQuality is never an accident it is always the result of excellent workmanshiprdquo (Mercedes)
The book is organized in a logical sequence beginning with the principles of triaxial testing in Chapter 1 and the computations and presen-tations of test results in Chapter 2 The triaxial equipment is explained in Chapter 3 and instrumentation measurements and control is reviewed in Chapter 4 Preparation of triaxial specimens is presented in Chapter 5 and satu-ration of specimens is described in Chapter 6 The two testing stages in an experiment are made clear in Chapter 7 Consolidation and in Chapter 8 Shearing Chapter 9 accounts for the corrections to the measurements Chapter 10 informs about special tests and test conditions and Chapter 11 puts the results from triaxial tests in perspective by reviewing results from
xiv Preface
tests with three unequal principal stresses Appendices are provided to explain special experimental techniques Information on ven-dors for the various types of equipment may be obtained from the internet
The authorrsquos background for writing this book consists of a career in laboratory experi-mentation at university level to study and model the behavior of soils More specifically he received an MS degree in 1967 from the Technical University of Denmark for which he wrote a thesis on the influence of the intermedi-ate principal stress on the strength of sand and in retrospect ended up with the wrong conclu-sion on the basis of perfectly correct results He received a PhD from the University of California at Berkeley in 1972 with a dissertation on ldquoThe StressndashStrain and Strength Characteristics of Cohesionless Soilsrdquo which included results
from triaxial compression tests true triaxial tests and torsion shear tests to indicate the effects of the intermediate principal stress on sand behavior as well as a three‐dimensional elasto‐plastic constitutive model for the behavior of soils
With his students the author developed testing equipment performed experiments and built constitutive models for the observed soil behavior while a professor at the University of California at Los Angeles (UCLA) (1972ndash1993) Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015) Many of the experimental techniques developed over this range of years are explained in the present book
Great appreciation is expressed to John F Peters of the US Army Engineer Research and Development Center in Vicksburg MS for his careful review of the manuscript and for his many comments Special thanks go to Afshin Nabili for his invaluable assistance with drafting a large number of the figures and for modifica-tion of other diagrams for the book
Poul V Lade October 2015
References
Bishop AW and Henkel DJ (1957) Measurement of Soil Properties in Triaxial Test Edward Arnold London
Bishop AW and Henkel DJ (1962) The Measurement of Soil Properties in the Triaxial Test 2nd edn St Martinrsquos Press New York NY
de Boer R (2005) The Engineer and the Scandal Springer Berlin
Donaghe RT Chaney RC and Silver ML (eds) (1988) Advanced Triaxial Testing of Soil and Rock ASTM STP 977 ASTM Philadelphia PA
Head KH (1986) Manual of Soil Laboratory Testing ndash Volume 3 Effective Stress Tests Pentech Press London
von Kārmān T (1910) Magyar Meacuternoumlk eacutes Ėpiteacuteszegylet Koumlzloumlnye 10 212ndash226
B
b
c
aD1
D2
Figure P1 Triaxial apparatus designed and con-structed for testing of rock cores by von Kārmān (1910 1911)
Preface xv
von Kārmān T (1911) Verhandlungen Deutsche Ingenieur 55 1749ndash1757
Skempton AW (1960) Terzaghirsquos discovery of effec-tive stress In From Theory to Practice in Soil Mechanics (eds L Bjerrum A Casagrande RB Peck and AW Skempton) pp 42ndash53 John Wiley and Sons Ltd London
Terzaghi K and Rendulic L (1934) Die wirksame Flaumlchenporositaumlt des Betons Zeitschrift des Ōsterreichischen Ingenieur‐ und Architekten Vereines 86 1ndash9
Vaacutesaacuterhelyi B (2010) Tribute to the first triaxial test performed in 1910 Acta Geology and Geophysics of Hungary 45(2) 227ndash230
About the Author
Poul V Lade received his MS degree from the Technical University of Denmark in 1967 and he continued his studies at the University of California at Berkeley where he received his PhD in 1972 Subsequently his academic career began at the University of California at Los Angeles (UCLA) and he continued at Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015)
His research interests include application of appropriate experimental methods to determine the three‐dimensional stressndashstrain and strength behavior of soils and the development of consti-tutive models for frictional materials such as soils concrete and rock He developed laboratory experimental apparatus to investigate monotonic loading and large three‐dimensional stress rever-
sals in plane strain true triaxial and torsion shear equipment This also included studies of effects of principal stress rotation stability instability and liquefaction of granular materials and time effects The constitutive models are based on elasticity and work‐hardening isotropic and kinematic plasticity theories
He has written nearly 300 publications based on research performed with support from the National Science Foundation (NSF) and from the Air Force Office of Scientific Research (AFOSR) He was elected member of the Danish Academy of Technical Sciences (2001) and he was awarded Professor Ostenfeldrsquos Gold Medal from the Technical University of Denmark (2001) He was inaugural editor of Geomechanics and Engineering and he has served on the editorial boards of eight international journals on geotechnical engineering
Triaxial Testing of Soils First Edition Poul V Lade copy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd
Principles of Triaxial Testing1
11 Purpose of triaxial tests
The purpose of performing triaxial tests is to determine the mechanical properties of the soil It is assumed that the soil specimens to be tested are homogeneous and representative of the material in the field and that the desired soil properties can in fact be obtained from the triaxial tests either directly or by interpretation through some theory
The mechanical properties most often sought from triaxial tests are stressndashstrain relations volshyume change or pore pressure behavior and shear strength of the soil Included in the stressndashstrain behavior are also the compressibility and the value of the coefficient of earth pressure at rest K0 Other properties that may be obtained from the triaxial tests which include time as a component are the permeability the coefficient of consolidation and properties relating to time dependent behavior such as rate effects creep and stress relaxation
It is important that the natural soil deposit or the fill from which soil samples have been taken in the field are sufficiently uniform that the soil samples possess the properties which are approshypriate and representative of the soil mass in the field It is therefore paramount that the geology at the site is well‐known and understood Even then samples from uniform deposits may not
ldquocontainrdquo properties that are representative of the field deposit This may happen either (a) due to the change in effective stress state which is always associated with the sampling process or (b) due to mechanical disturbance from sampling transshyportation or handling in the laboratory The stressndashstrain and strength properties of very senshysitive clays which have been disturbed cannot be regenerated in the lab oratory or otherwise obtained by interpretation of tests performed on inadequate specimens The effects of sampling will briefly be discussed below in connection with choice of consolidation pressure in the trishyaxial test The topic of sampling is otherwise outshyside the scope of the present treatment
12 Concept of testing
The concept to be pursued in testing of soils is to simulate as closely as possible the process that goes on in the field Because there is a large number of variables (eg density water content degree of saturation overconsolidation ratio loading conditions stress paths) that influence the resulting soil behavior the simplest and most direct way of obtaining information pertinent to the field conditions is to duplicate these as closely as possible
2 Triaxial Testing of Soils
However because of limitations in equipment and because of practical limitations on the amount of testing that can be performed for each project it is essential that
1 The true field loading conditions (including the drainage conditions) are known
2 The laboratory equipment can reproduce these conditions to a required degree of accuracy
3 A reasonable estimate can be made of the sigshynificance of the differences between the field loading conditions and those that can be proshyduced in the laboratory equipment
It is clear that the triaxial test in many resshypects is incapable of simulating several imporshytant aspects of field loading conditions For example the effects of the intermediate princishypal stress the effects of rotation of principal stresses and the effects of partial drainage durshying loading in the field cannot be investigated on the basis of the triaxial test The effects of such conditions require studies involving other types of equipment or analyses of boundary value problems either by closed form solutions or solutions obtained by numerical techniques
To provide some background for evaluation of the results of triaxial tests other types of laboratory shear tests and typical results from such tests are presented in Chapter 11 The relashytions between the different types of tests are reviewed and their advantages and limitations are discussed
13 The triaxial test
The triaxial test is most often performed on a cylindrical specimen as shown in Fig 11(a) Principal stresses are applied to the specimen as indicated in Fig 11(b) First a confining pressure σ3 is applied to the specimen This pressure acts all around and therefore on all planes in the specimen Then an additional stress difference σd is applied in the axial direction The stress applied externally to the specimen in the axial direction is
σ σ σ1 3= +d (11)
and therefore
σ σ σd = minus1 3 (12)
In the general case three principal stresses σ1 σ2 and σ3 may act on a soil element in the field However only two different principal stresses can be applied to the specimen in the convenshytional triaxial test The intermediate principal stress σ2 can only have values as follows
σ σ2 3= Triaxial compression (13)
σ σ2 1= Triaxial extension (14)
The condition of triaxial extension can be achieved by applying negative stress differshyences to the specimen This merely produces a reduction in compression in the extension direcshytion but no tension occurs in the specimen The state of stress applied to the specimen is in both cases axisymmetric The triaxial compression test will be discussed in the following while the triaxial extension test is discussed in Chapter 10
The test is performed using triaxial apparashytus as seen in the schematic illustration in Fig 12 The specimen is surrounded by a cap and a base and a membrane This unit is placed in a triaxial cell in which the cell pressure can be applied The cell pressure acts as a hydrostatic confinement for the specimen and the pressure is therefore the same in all directions In addition
σ1
(a) (b)
σ1 = σd + σ3
σ2 = σ3
σd = σ1 ndash σ3σ3
σ3σ3
σ3
σd
Figure 11 (a) Cylindrical specimen for triaxial testing and (b) stresses applied to a triaxial specimen
Principles of Triaxial Testing 3
a deviator load can be applied through a piston that goes through the top of the cell and loads the specimen in the axial direction
The vertical deformation of the specimen may be measured by a dial gage attached to the piston which travels the same vertical distance as the cap sitting on top of the specimen Drainage lines are connected to the water saturated specishymen through the base (or both the cap and the base) and connected to a burette outside the trishyaxial cell This allows for measurements of the volume changes of the specimen during the test
Alternatively the connection to the burette can be shut off thereby preventing the specimen from changing volume Instead the pore water pressure can be measured on a transducer conshynected to the drainage line
The following quantities are measured in a typical triaxial test
1 Confining pressure2 Deviator load3 Vertical (or axial) deformation4 Volume change or pore water pressure
These measurements constitute the data base from which other quantities can be derived
[eg stress difference (σ1 ndash σ3) axial strain ε1 and volumetric strain εv]
14 Advantages and limitations
Whereas the triaxial test potentially can proshyvide a substantial proportion of the mechanical properties required for a project it has limitashytions especially when special conditions are encountered and necessitates clarification based on experimentation
The advantages of the triaxial test are
1 Drainage can be controlled (onndashoff)2 Volume change or pore pressure can be
measured3 Suction can be controlled in partially satushy
rated soils4 Measured deformations allow calculation of
strains and moduli5 A larger variety of stress and strain paths
that occur in the field can be applied in the triaxial apparatus than in any other testing apparatus (eg initial anisotropic consolidashytion at any stress ratio including K0 extension active and passive shear)
The limitations of the triaxial test are
1 Stress concentrations due to friction between specimen and end plates (cap and base) cause nonuniform strains and stresses and therefore nonuniform stressndashstrain volume change or pore pressure response
2 Only axisymmetric stress conditions can be applied to the specimen whereas most field problems involve plane strain or general three‐dimensional conditions with rotation of principal stresses
3 Triaxial tests cannot provide all necessary data required to characterize the behavior of an anisotropic or a cross‐anisotropic soil deposit as illustrated in Fig 13
4 Although the axisymmetric principal stress condition is limited it is more difficult to apply proper shear stresses or tension to soil in relatively simple tests
The first limitation listed above can be overcome by applying lubricated ends on the
Pore pressure transducer
On-Off valve
Burette
Piston
Dial gage
Triaxial cell
P = σd middot A
Aprime
σcell
σ3
σ3 σ3= σcell
Figure 12 Schematic diagram of triaxial apparatus
4 Triaxial Testing of Soils
specimen such that uniform strains and stresses and therefore correct soil response can be proshyduced This is discussed in Chapter 3 In addishytion to the limitations listed above it should be mentioned that it may be easier to reproduce certain stress paths in other specialty equipment than in the triaxial apparatus (eg K0‐test)
Although the triaxial test is limited as explained under points 2 and 3 above it does combine versatility with relative simplicity in concept and performance Other equipment in which three unequal principal stresses can be applied or in which the principal stress direcshytions can be rotated do not have the versatility or is more com plicated to operate Thus other types of equipment have their own advantages and limitations These other equipment types
include plane strain true triaxial simple shear directional shear and torsion shear apparatus All these pieces of equipment are with the excepshytion of the simple shear apparatus employed mainly for research purposes Their operational modes capabilities and results are reviewed in Chapter 11
15 Test stages ndash consolidation and shearing
Laboratory tests are made to simulate field loadshying conditions as close as possible Most field conditions and the corresponding tests can be simplified to consist of two stages consolidation and shearing
Axis of symmetry
1Eh
1Eh
1Ghv
1Ev
ndashmicrohvEh
ndashmicrohvEn
2(1 + microhh)En
ndashmicrohhEn
ndashmicrohvEh
ndashmicrohvEh
ndashmicrohhEh
0
h
h
v
0 0
σh
σh
σv
τhv
τhv
τvh
τvh
σh
σv
σh
τhv
τvh
τhh
τhh τhh
ϵh
ϵv
ϵh
γhv
γvh
γhh
0
Require tests withapplication of
shear stresses
0 0
0
0 0 0 00
1Ghv0 0 0 00
0 0 0 0 0
0 0
bull =
Figure 13 Cross‐anisotropic soil requiring results from more than triaxial tests for full characterization
Principles of Triaxial Testing 5
151 Consolidation
In the first stage the initial condition of the soil is established in terms of effective stresses and stress history (including overconsolidation if applicable) Thus stresses are applied correshysponding to those acting on the element of soil in the field due to weight of the overlying soil strata and other materials or structures that exist at the time the mechanical properties (stressndashstrain strength etc) are sought Sufficient time is allowed for complete consolidation to occur under the applied stresses The condition in the field element has now been established in the triaxial specimen
152 Shearing
In the second stage of the triaxial test an addishytional stress is applied to reach peak failure and beyond under relevant drainage conditions The additional stress applied to the specimen should correspond as closely as possible to the change in stress on the field element due to some new change in the overall field loading situashytion This change may consist of a vertical stress increase or decrease (eg due to addition of a structure or excavation of overlying soil strata) or of a horizontal stress increase or decrease (eg due to the same constructions causing the vertical stress changes) Any combination of vertical and horizontal stress changes may be simulated in the triaxial test Examples of vertishycal and horizontal stress changes in the field are shown in Fig 14
Usually it is desirable to know how much change in load the soil can sustain without failshying and how much deformation will occur under normal working conditions The test is therefore usually continued to find the strength of the soil under the appropriate loading condishytions The results are used with an appropriate factor of safety so that normal working stresses are always somewhat below the peak strength
The stressndashstrain relations obtained from the triaxial tests provide the basis for determinashytion of deformations in the field This may be done in a simplified manner by closed‐form
solutions or it may be done by employing the results of the triaxial tests for calibration of a constitutive model used with a numerical method in finite element or finite difference computer programs
16 Types of tests
The drainage conditions in the field must be duplicated as well as possible in the laboratory tests This may be done by appropriate drainage facilities or preventions as discussed above for the triaxial test In most cases the field drainage conditions can be approximated by one of the following three types of tests
1 Consolidated‐drained test called a CD‐test or just a drained test
2 Consolidated‐undrained test or a CU‐test3 Unconsolidated‐undrained test or a UU‐test
Additionalload
Excavation
ΔσV asymp 0
ΔσV asymp 0
ΔσV gt 0
ΔσV lt 0
Δσh lt 0
Δσh gt 0
Δσh lt ΔσV
Δσh
Figure 14 Examples of stress changes leading to failure in the field
6 Triaxial Testing of Soils
These tests are described in ASTM Standards D7181 (2014) D4767 (2014) and D2850 (2014) respectively
Which condition of drainage in the laboratory test logically corresponds to each case in the field depends on a comparison of loading rate with the rate at which the water can escape or be sucked into the ground Thus the permeability of the soil and the drainage boundary conditions in the field together with the loading rate play key roles in determination of the type of analysis and the type of test drained or undrained that are appropriate for each case Field cases with partial drainage can be correctly duplicated in laboratory tests if the effective stress path is determined for the design condition However the idea of the CD‐ CU‐ and UU‐tests is to make it relatively simple for the design engineer to analyze a condition that will render a sufficient factor of safety under the actual drainage condishytion without trying to estimate and experimenshytally replicate the actual stress path
It has been determined through experience and common sense that the extreme conditions are drained and undrained with and without consolidation As a practical matter in a commershycial laboratory it is easier to run an undrained test than a drained test because it is easier and faster to measure pore pressures than volume change Therefore even drained parameters are more likely to be estimated from a CU‐test than from a CD‐test
161 Simulation of field conditions
Presented below is a brief review of the three types of tests together with examples of field cases for which the tests are appropriate and with typishycal strength results shown on Mohr diagrams
Drained tests
Isotropic consolidation is most often used in the first stage of the triaxial test However anisoshytropic consolidation with any stress ratio is also possible
The shearing stage of a drained test is pershyformed so slowly the soil is so permeable and the drainage facilities are such that no excess
pore pressure (positive or negative) can exist in the specimen at any stage of the test that is
∆u = 0 (15)
It follows then from the effective stress principle
prime = minusσ σ u (16)
that the effective stress changes are always the same as the total stress changes
A soil specimen always changes volume during shearing in a drained test If it contracts in volume it expels pore fluid (usually water or air) and if it expands in volume (dilates) then it sucks water or air into the pores If a non‐zero pore pressure is generated during the test (eg by performing the shearing too fast so the water does not have sufficient time to escape) then the specimen will expel or suck water such that the pore pressure goes towards zero to try to achieve equilibrium between externally applied stresses and internal effective stresses Thus there will always be volume changes in a drained test Consequently the water content the void ratio and the dry density of the specimen at the end of the test are most often not the same as at the beginning
The following field conditions can be simushylated with acceptable accuracy in the drained test
1 Almost all cases involving coarse sands and gravel whether saturated or not (except if confined in eg a lens andor exposed to rapid loading as in eg an earthquake)
2 Many cases involving fine sand and someshytimes silt if the field loads are applied reashysonable slowly
3 Long term loading of any soil as for examplea) Cut slopes several years after excavationb) Embankment constructed very slowly in
layers over a soft clay depositc) Earth dam with steady seepaged) Foundation on clay a long time after
construction
These cases are illustrated in Fig 15The strength results obtained from drained
tests are illustrated schematically on the Mohr diagram in Fig 16 The shear strength of soils increases with increasing confining pressure
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
Contents ix
63 Effects of lack of full saturation 24064 B‐value test 241
641 Effects of primary factors on B‐value 241642 Effects of secondary factors on B‐value 243643 Performance of B‐value test 246
65 Determination of degree of saturation 24966 Methods of saturating triaxial specimens 250
661 Percolation with water 250662 CO2‐method 251663 Application of back pressure 252664 Vacuum procedure 258
67 Range of application of saturation methods 262
7 Testing Stage I Consolidation 26371 Objective of consolidation 26372 Selection of consolidation stresses 263
721 Anisotropic consolidation 264722 Isotropic consolidation 267723 Effects of sampling 268724 SHANSEP for soft clay 268725 Very sensitive clay 272
73 Coefficient of consolidation 272731 Effects of boundary drainage conditions 272732 Determination of time for 100 consolidation 272
8 Testing Stage II Shearing 27781 Introduction 27782 Selection of vertical strain rate 277
821 UU‐tests on clay soils 277822 CD‐ and CU‐tests on granular materials 277823 CD‐ and CU‐tests on clayey soils 277824 Effects of lubricated ends in undrained tests 282
83 Effects of lubricated ends and specimen shape 282831 Strain uniformity and stability of test configuration 282832 Modes of instability in soils 284833 Triaxial tests on sand 284834 Triaxial tests on clay 290
84 Selection of specimen size 29285 Effects of membrane penetration 293
851 Drained tests 293852 Undrained tests 293
86 Post test inspection of specimen 293
9 Corrections to Measurements 29591 Principles of measurements 29592 Types of corrections 29593 Importance of corrections ndash strong and weak specimens 29594 Tests on very short specimens 29695 Vertical load 296
951 Piston uplift 296952 Piston friction 296953 Side drains 298954 Membrane 301
x Contents
955 Buoyancy effects 308956 Techniques to avoid corrections to vertical load 309
96 Vertical deformation 309961 Compression of interfaces 309962 Bedding errors 309963 Techniques to avoid corrections to vertical deformations 311
97 Volume change 312971 Membrane penetration 312972 Volume change due to bedding errors 317973 Leaking membrane 317974 Techniques to avoid corrections to volume change 319
98 Cell and pore pressures 319981 Membrane tension 319982 Fluid self‐weight pressures 319983 Sand penetration into lubricated ends 319984 Membrane penetration 319985 Techniques to avoid corrections to cell and pore pressures 320
10 Special Tests and Test Considerations 321101 Introduction 321
1011 Low confining pressure tests on clays 3211012 Conventional low pressure tests on any soil 3211013 High pressure tests 3221014 Peats and organic soils 322
102 K0‐tests 322103 Extension tests 322
1031 Problems with the conventional triaxial extension test 3231032 Enforcing uniform strains in extension tests 324
104 Tests on unsaturated soils 3261041 Soil water retention curve 3261042 Hydraulic conductivity function 3271043 Low matric suction 3271044 High matric suction 3291045 Modeling 3301046 Triaxial testing 331
105 Frozen soils 331106 Time effects tests 333
1061 Creep tests 3331062 Stress relaxation tests 333
107 Determination of hydraulic conductivity 335108 Bender element tests 335
1081 Fabrication of bender elements 3361082 Shear modulus 3371083 Signal interpretation 3381084 First arrival time 3381085 Specimen size and geometry 3401086 Ray path analysis 3401087 Surface mounted elements 3401088 Effects of specimen material 3411089 Effects of cross‐anisotropy 341
Contents xi
11 Tests with Three Unequal Principal Stresses 343111 Introduction 343112 Tests with constant principal stress directions 344
1121 Plane strain equipment 3441122 True triaxial equipment 3451123 Results from true triaxial tests 3481124 Strength characteristics 3531125 Failure criteria for soils 355
113 Tests with rotating principal stress directions 3601131 Simple shear equipment 3601132 Directional shear cell 3621133 Torsion shear apparatus 3641134 Summary and conclusion 370
Appendix A Manufacturing of Latex Rubber Membranes 373A1 The process 373A2 Products for membrane fabrication 373A3 Create an aluminum mold 374A4 Two tanks 374A5 Mold preparation 374A6 Dipping processes 374A7 Post production 375A8 Storage 375A9 Membrane repair 375
Appendix B Design of Diaphragm Load Cells 377B1 Load cells with uniform diaphragm 377B2 Load cells with tapered diaphragm 378B3 Example Design of 5 kN beryllium copper load cell 378 B31 Punching failure 379
References 381Index 397
Preface
The triaxial test is almost always chosen for studies of new phenomena because it is rela-tively simple and versatile The triaxial test is the most suitable for such studies and it is required in geotechnical engineering for the purposes of design of specific projects and for studying and understanding the behavior of soils
The first triaxial compression test apparatus shown in Fig P1 was designed by von Kārmān (1910 1911) for testing of rock cores The scale may be deduced from the fact that the specimen is 4 cm in diameter (Vaacutesaacuterhelyi 2010) However his paper was not noticed or it was forgotten by 1930 when Casagrande at Harvard University wrote a letter to Terzaghi at the Technical University in Vienna in which he describes his visit to the hydraulics laboratory in Berlin Here he saw an apparatus for measuring the permea-bility of soil Casagrande suggested that the cylindrical specimen in this apparatus could be loaded in the vertical (axial) direction to indi-cate its strength Therefore he was going to build a prototype and Terzaghi proposed that he build one for him too This appears to be the begin-ning of triaxial testing of soils in geotechnical engineering The apparatus was immediately employed by Rendulic (Terzaghi and Rendulic 1934) for tests with and without membranes the results of which played an important role in understanding the effective stress principle as well as the role of pore water pressure and consolidation on shear strength at a time when the effective stress principle was still being questioned (Skempton 1960 de Boer 2005)
Previous books on the developments of tech-niques for triaxial testing have been written by Bishop and Henkel (1957 1962) and by Head (1986) The proceedings from a conference on Advanced Triaxial Testing of Soil and Rock (Donaghe et al 1988) was published to summa-
rize advances in this area Other books have not appeared since then To understand the present book the reader is required to have a background in basic soil mechanics some experience in soil mechanics laboratory testing and perhaps in foundation engineering
In addition to triaxial testing of soils the contents of the book may in part apply to more advanced tests and to the testing of hard soils ndash soft rocks It is written for research workers soil testing laboratories and consulting engineers The emphasis is placed on what the soil speci-men is exposed to and experiences rather than the esthetic appearance of the equipment There will be considerable use of physics and mathe-matics to illustrate the arguments and discus-sions With a few exceptions references are made to easily accessible articles in the literature Much of the book centers on how to obtain high quality experimental results and the guiding concepts for this purpose have been expressed by the car industry in their slogans ldquoQuality is Job Onerdquo (Ford Motor Company) and ldquoQuality is never an accident it is always the result of excellent workmanshiprdquo (Mercedes)
The book is organized in a logical sequence beginning with the principles of triaxial testing in Chapter 1 and the computations and presen-tations of test results in Chapter 2 The triaxial equipment is explained in Chapter 3 and instrumentation measurements and control is reviewed in Chapter 4 Preparation of triaxial specimens is presented in Chapter 5 and satu-ration of specimens is described in Chapter 6 The two testing stages in an experiment are made clear in Chapter 7 Consolidation and in Chapter 8 Shearing Chapter 9 accounts for the corrections to the measurements Chapter 10 informs about special tests and test conditions and Chapter 11 puts the results from triaxial tests in perspective by reviewing results from
xiv Preface
tests with three unequal principal stresses Appendices are provided to explain special experimental techniques Information on ven-dors for the various types of equipment may be obtained from the internet
The authorrsquos background for writing this book consists of a career in laboratory experi-mentation at university level to study and model the behavior of soils More specifically he received an MS degree in 1967 from the Technical University of Denmark for which he wrote a thesis on the influence of the intermedi-ate principal stress on the strength of sand and in retrospect ended up with the wrong conclu-sion on the basis of perfectly correct results He received a PhD from the University of California at Berkeley in 1972 with a dissertation on ldquoThe StressndashStrain and Strength Characteristics of Cohesionless Soilsrdquo which included results
from triaxial compression tests true triaxial tests and torsion shear tests to indicate the effects of the intermediate principal stress on sand behavior as well as a three‐dimensional elasto‐plastic constitutive model for the behavior of soils
With his students the author developed testing equipment performed experiments and built constitutive models for the observed soil behavior while a professor at the University of California at Los Angeles (UCLA) (1972ndash1993) Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015) Many of the experimental techniques developed over this range of years are explained in the present book
Great appreciation is expressed to John F Peters of the US Army Engineer Research and Development Center in Vicksburg MS for his careful review of the manuscript and for his many comments Special thanks go to Afshin Nabili for his invaluable assistance with drafting a large number of the figures and for modifica-tion of other diagrams for the book
Poul V Lade October 2015
References
Bishop AW and Henkel DJ (1957) Measurement of Soil Properties in Triaxial Test Edward Arnold London
Bishop AW and Henkel DJ (1962) The Measurement of Soil Properties in the Triaxial Test 2nd edn St Martinrsquos Press New York NY
de Boer R (2005) The Engineer and the Scandal Springer Berlin
Donaghe RT Chaney RC and Silver ML (eds) (1988) Advanced Triaxial Testing of Soil and Rock ASTM STP 977 ASTM Philadelphia PA
Head KH (1986) Manual of Soil Laboratory Testing ndash Volume 3 Effective Stress Tests Pentech Press London
von Kārmān T (1910) Magyar Meacuternoumlk eacutes Ėpiteacuteszegylet Koumlzloumlnye 10 212ndash226
B
b
c
aD1
D2
Figure P1 Triaxial apparatus designed and con-structed for testing of rock cores by von Kārmān (1910 1911)
Preface xv
von Kārmān T (1911) Verhandlungen Deutsche Ingenieur 55 1749ndash1757
Skempton AW (1960) Terzaghirsquos discovery of effec-tive stress In From Theory to Practice in Soil Mechanics (eds L Bjerrum A Casagrande RB Peck and AW Skempton) pp 42ndash53 John Wiley and Sons Ltd London
Terzaghi K and Rendulic L (1934) Die wirksame Flaumlchenporositaumlt des Betons Zeitschrift des Ōsterreichischen Ingenieur‐ und Architekten Vereines 86 1ndash9
Vaacutesaacuterhelyi B (2010) Tribute to the first triaxial test performed in 1910 Acta Geology and Geophysics of Hungary 45(2) 227ndash230
About the Author
Poul V Lade received his MS degree from the Technical University of Denmark in 1967 and he continued his studies at the University of California at Berkeley where he received his PhD in 1972 Subsequently his academic career began at the University of California at Los Angeles (UCLA) and he continued at Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015)
His research interests include application of appropriate experimental methods to determine the three‐dimensional stressndashstrain and strength behavior of soils and the development of consti-tutive models for frictional materials such as soils concrete and rock He developed laboratory experimental apparatus to investigate monotonic loading and large three‐dimensional stress rever-
sals in plane strain true triaxial and torsion shear equipment This also included studies of effects of principal stress rotation stability instability and liquefaction of granular materials and time effects The constitutive models are based on elasticity and work‐hardening isotropic and kinematic plasticity theories
He has written nearly 300 publications based on research performed with support from the National Science Foundation (NSF) and from the Air Force Office of Scientific Research (AFOSR) He was elected member of the Danish Academy of Technical Sciences (2001) and he was awarded Professor Ostenfeldrsquos Gold Medal from the Technical University of Denmark (2001) He was inaugural editor of Geomechanics and Engineering and he has served on the editorial boards of eight international journals on geotechnical engineering
Triaxial Testing of Soils First Edition Poul V Lade copy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd
Principles of Triaxial Testing1
11 Purpose of triaxial tests
The purpose of performing triaxial tests is to determine the mechanical properties of the soil It is assumed that the soil specimens to be tested are homogeneous and representative of the material in the field and that the desired soil properties can in fact be obtained from the triaxial tests either directly or by interpretation through some theory
The mechanical properties most often sought from triaxial tests are stressndashstrain relations volshyume change or pore pressure behavior and shear strength of the soil Included in the stressndashstrain behavior are also the compressibility and the value of the coefficient of earth pressure at rest K0 Other properties that may be obtained from the triaxial tests which include time as a component are the permeability the coefficient of consolidation and properties relating to time dependent behavior such as rate effects creep and stress relaxation
It is important that the natural soil deposit or the fill from which soil samples have been taken in the field are sufficiently uniform that the soil samples possess the properties which are approshypriate and representative of the soil mass in the field It is therefore paramount that the geology at the site is well‐known and understood Even then samples from uniform deposits may not
ldquocontainrdquo properties that are representative of the field deposit This may happen either (a) due to the change in effective stress state which is always associated with the sampling process or (b) due to mechanical disturbance from sampling transshyportation or handling in the laboratory The stressndashstrain and strength properties of very senshysitive clays which have been disturbed cannot be regenerated in the lab oratory or otherwise obtained by interpretation of tests performed on inadequate specimens The effects of sampling will briefly be discussed below in connection with choice of consolidation pressure in the trishyaxial test The topic of sampling is otherwise outshyside the scope of the present treatment
12 Concept of testing
The concept to be pursued in testing of soils is to simulate as closely as possible the process that goes on in the field Because there is a large number of variables (eg density water content degree of saturation overconsolidation ratio loading conditions stress paths) that influence the resulting soil behavior the simplest and most direct way of obtaining information pertinent to the field conditions is to duplicate these as closely as possible
2 Triaxial Testing of Soils
However because of limitations in equipment and because of practical limitations on the amount of testing that can be performed for each project it is essential that
1 The true field loading conditions (including the drainage conditions) are known
2 The laboratory equipment can reproduce these conditions to a required degree of accuracy
3 A reasonable estimate can be made of the sigshynificance of the differences between the field loading conditions and those that can be proshyduced in the laboratory equipment
It is clear that the triaxial test in many resshypects is incapable of simulating several imporshytant aspects of field loading conditions For example the effects of the intermediate princishypal stress the effects of rotation of principal stresses and the effects of partial drainage durshying loading in the field cannot be investigated on the basis of the triaxial test The effects of such conditions require studies involving other types of equipment or analyses of boundary value problems either by closed form solutions or solutions obtained by numerical techniques
To provide some background for evaluation of the results of triaxial tests other types of laboratory shear tests and typical results from such tests are presented in Chapter 11 The relashytions between the different types of tests are reviewed and their advantages and limitations are discussed
13 The triaxial test
The triaxial test is most often performed on a cylindrical specimen as shown in Fig 11(a) Principal stresses are applied to the specimen as indicated in Fig 11(b) First a confining pressure σ3 is applied to the specimen This pressure acts all around and therefore on all planes in the specimen Then an additional stress difference σd is applied in the axial direction The stress applied externally to the specimen in the axial direction is
σ σ σ1 3= +d (11)
and therefore
σ σ σd = minus1 3 (12)
In the general case three principal stresses σ1 σ2 and σ3 may act on a soil element in the field However only two different principal stresses can be applied to the specimen in the convenshytional triaxial test The intermediate principal stress σ2 can only have values as follows
σ σ2 3= Triaxial compression (13)
σ σ2 1= Triaxial extension (14)
The condition of triaxial extension can be achieved by applying negative stress differshyences to the specimen This merely produces a reduction in compression in the extension direcshytion but no tension occurs in the specimen The state of stress applied to the specimen is in both cases axisymmetric The triaxial compression test will be discussed in the following while the triaxial extension test is discussed in Chapter 10
The test is performed using triaxial apparashytus as seen in the schematic illustration in Fig 12 The specimen is surrounded by a cap and a base and a membrane This unit is placed in a triaxial cell in which the cell pressure can be applied The cell pressure acts as a hydrostatic confinement for the specimen and the pressure is therefore the same in all directions In addition
σ1
(a) (b)
σ1 = σd + σ3
σ2 = σ3
σd = σ1 ndash σ3σ3
σ3σ3
σ3
σd
Figure 11 (a) Cylindrical specimen for triaxial testing and (b) stresses applied to a triaxial specimen
Principles of Triaxial Testing 3
a deviator load can be applied through a piston that goes through the top of the cell and loads the specimen in the axial direction
The vertical deformation of the specimen may be measured by a dial gage attached to the piston which travels the same vertical distance as the cap sitting on top of the specimen Drainage lines are connected to the water saturated specishymen through the base (or both the cap and the base) and connected to a burette outside the trishyaxial cell This allows for measurements of the volume changes of the specimen during the test
Alternatively the connection to the burette can be shut off thereby preventing the specimen from changing volume Instead the pore water pressure can be measured on a transducer conshynected to the drainage line
The following quantities are measured in a typical triaxial test
1 Confining pressure2 Deviator load3 Vertical (or axial) deformation4 Volume change or pore water pressure
These measurements constitute the data base from which other quantities can be derived
[eg stress difference (σ1 ndash σ3) axial strain ε1 and volumetric strain εv]
14 Advantages and limitations
Whereas the triaxial test potentially can proshyvide a substantial proportion of the mechanical properties required for a project it has limitashytions especially when special conditions are encountered and necessitates clarification based on experimentation
The advantages of the triaxial test are
1 Drainage can be controlled (onndashoff)2 Volume change or pore pressure can be
measured3 Suction can be controlled in partially satushy
rated soils4 Measured deformations allow calculation of
strains and moduli5 A larger variety of stress and strain paths
that occur in the field can be applied in the triaxial apparatus than in any other testing apparatus (eg initial anisotropic consolidashytion at any stress ratio including K0 extension active and passive shear)
The limitations of the triaxial test are
1 Stress concentrations due to friction between specimen and end plates (cap and base) cause nonuniform strains and stresses and therefore nonuniform stressndashstrain volume change or pore pressure response
2 Only axisymmetric stress conditions can be applied to the specimen whereas most field problems involve plane strain or general three‐dimensional conditions with rotation of principal stresses
3 Triaxial tests cannot provide all necessary data required to characterize the behavior of an anisotropic or a cross‐anisotropic soil deposit as illustrated in Fig 13
4 Although the axisymmetric principal stress condition is limited it is more difficult to apply proper shear stresses or tension to soil in relatively simple tests
The first limitation listed above can be overcome by applying lubricated ends on the
Pore pressure transducer
On-Off valve
Burette
Piston
Dial gage
Triaxial cell
P = σd middot A
Aprime
σcell
σ3
σ3 σ3= σcell
Figure 12 Schematic diagram of triaxial apparatus
4 Triaxial Testing of Soils
specimen such that uniform strains and stresses and therefore correct soil response can be proshyduced This is discussed in Chapter 3 In addishytion to the limitations listed above it should be mentioned that it may be easier to reproduce certain stress paths in other specialty equipment than in the triaxial apparatus (eg K0‐test)
Although the triaxial test is limited as explained under points 2 and 3 above it does combine versatility with relative simplicity in concept and performance Other equipment in which three unequal principal stresses can be applied or in which the principal stress direcshytions can be rotated do not have the versatility or is more com plicated to operate Thus other types of equipment have their own advantages and limitations These other equipment types
include plane strain true triaxial simple shear directional shear and torsion shear apparatus All these pieces of equipment are with the excepshytion of the simple shear apparatus employed mainly for research purposes Their operational modes capabilities and results are reviewed in Chapter 11
15 Test stages ndash consolidation and shearing
Laboratory tests are made to simulate field loadshying conditions as close as possible Most field conditions and the corresponding tests can be simplified to consist of two stages consolidation and shearing
Axis of symmetry
1Eh
1Eh
1Ghv
1Ev
ndashmicrohvEh
ndashmicrohvEn
2(1 + microhh)En
ndashmicrohhEn
ndashmicrohvEh
ndashmicrohvEh
ndashmicrohhEh
0
h
h
v
0 0
σh
σh
σv
τhv
τhv
τvh
τvh
σh
σv
σh
τhv
τvh
τhh
τhh τhh
ϵh
ϵv
ϵh
γhv
γvh
γhh
0
Require tests withapplication of
shear stresses
0 0
0
0 0 0 00
1Ghv0 0 0 00
0 0 0 0 0
0 0
bull =
Figure 13 Cross‐anisotropic soil requiring results from more than triaxial tests for full characterization
Principles of Triaxial Testing 5
151 Consolidation
In the first stage the initial condition of the soil is established in terms of effective stresses and stress history (including overconsolidation if applicable) Thus stresses are applied correshysponding to those acting on the element of soil in the field due to weight of the overlying soil strata and other materials or structures that exist at the time the mechanical properties (stressndashstrain strength etc) are sought Sufficient time is allowed for complete consolidation to occur under the applied stresses The condition in the field element has now been established in the triaxial specimen
152 Shearing
In the second stage of the triaxial test an addishytional stress is applied to reach peak failure and beyond under relevant drainage conditions The additional stress applied to the specimen should correspond as closely as possible to the change in stress on the field element due to some new change in the overall field loading situashytion This change may consist of a vertical stress increase or decrease (eg due to addition of a structure or excavation of overlying soil strata) or of a horizontal stress increase or decrease (eg due to the same constructions causing the vertical stress changes) Any combination of vertical and horizontal stress changes may be simulated in the triaxial test Examples of vertishycal and horizontal stress changes in the field are shown in Fig 14
Usually it is desirable to know how much change in load the soil can sustain without failshying and how much deformation will occur under normal working conditions The test is therefore usually continued to find the strength of the soil under the appropriate loading condishytions The results are used with an appropriate factor of safety so that normal working stresses are always somewhat below the peak strength
The stressndashstrain relations obtained from the triaxial tests provide the basis for determinashytion of deformations in the field This may be done in a simplified manner by closed‐form
solutions or it may be done by employing the results of the triaxial tests for calibration of a constitutive model used with a numerical method in finite element or finite difference computer programs
16 Types of tests
The drainage conditions in the field must be duplicated as well as possible in the laboratory tests This may be done by appropriate drainage facilities or preventions as discussed above for the triaxial test In most cases the field drainage conditions can be approximated by one of the following three types of tests
1 Consolidated‐drained test called a CD‐test or just a drained test
2 Consolidated‐undrained test or a CU‐test3 Unconsolidated‐undrained test or a UU‐test
Additionalload
Excavation
ΔσV asymp 0
ΔσV asymp 0
ΔσV gt 0
ΔσV lt 0
Δσh lt 0
Δσh gt 0
Δσh lt ΔσV
Δσh
Figure 14 Examples of stress changes leading to failure in the field
6 Triaxial Testing of Soils
These tests are described in ASTM Standards D7181 (2014) D4767 (2014) and D2850 (2014) respectively
Which condition of drainage in the laboratory test logically corresponds to each case in the field depends on a comparison of loading rate with the rate at which the water can escape or be sucked into the ground Thus the permeability of the soil and the drainage boundary conditions in the field together with the loading rate play key roles in determination of the type of analysis and the type of test drained or undrained that are appropriate for each case Field cases with partial drainage can be correctly duplicated in laboratory tests if the effective stress path is determined for the design condition However the idea of the CD‐ CU‐ and UU‐tests is to make it relatively simple for the design engineer to analyze a condition that will render a sufficient factor of safety under the actual drainage condishytion without trying to estimate and experimenshytally replicate the actual stress path
It has been determined through experience and common sense that the extreme conditions are drained and undrained with and without consolidation As a practical matter in a commershycial laboratory it is easier to run an undrained test than a drained test because it is easier and faster to measure pore pressures than volume change Therefore even drained parameters are more likely to be estimated from a CU‐test than from a CD‐test
161 Simulation of field conditions
Presented below is a brief review of the three types of tests together with examples of field cases for which the tests are appropriate and with typishycal strength results shown on Mohr diagrams
Drained tests
Isotropic consolidation is most often used in the first stage of the triaxial test However anisoshytropic consolidation with any stress ratio is also possible
The shearing stage of a drained test is pershyformed so slowly the soil is so permeable and the drainage facilities are such that no excess
pore pressure (positive or negative) can exist in the specimen at any stage of the test that is
∆u = 0 (15)
It follows then from the effective stress principle
prime = minusσ σ u (16)
that the effective stress changes are always the same as the total stress changes
A soil specimen always changes volume during shearing in a drained test If it contracts in volume it expels pore fluid (usually water or air) and if it expands in volume (dilates) then it sucks water or air into the pores If a non‐zero pore pressure is generated during the test (eg by performing the shearing too fast so the water does not have sufficient time to escape) then the specimen will expel or suck water such that the pore pressure goes towards zero to try to achieve equilibrium between externally applied stresses and internal effective stresses Thus there will always be volume changes in a drained test Consequently the water content the void ratio and the dry density of the specimen at the end of the test are most often not the same as at the beginning
The following field conditions can be simushylated with acceptable accuracy in the drained test
1 Almost all cases involving coarse sands and gravel whether saturated or not (except if confined in eg a lens andor exposed to rapid loading as in eg an earthquake)
2 Many cases involving fine sand and someshytimes silt if the field loads are applied reashysonable slowly
3 Long term loading of any soil as for examplea) Cut slopes several years after excavationb) Embankment constructed very slowly in
layers over a soft clay depositc) Earth dam with steady seepaged) Foundation on clay a long time after
construction
These cases are illustrated in Fig 15The strength results obtained from drained
tests are illustrated schematically on the Mohr diagram in Fig 16 The shear strength of soils increases with increasing confining pressure
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
x Contents
955 Buoyancy effects 308956 Techniques to avoid corrections to vertical load 309
96 Vertical deformation 309961 Compression of interfaces 309962 Bedding errors 309963 Techniques to avoid corrections to vertical deformations 311
97 Volume change 312971 Membrane penetration 312972 Volume change due to bedding errors 317973 Leaking membrane 317974 Techniques to avoid corrections to volume change 319
98 Cell and pore pressures 319981 Membrane tension 319982 Fluid self‐weight pressures 319983 Sand penetration into lubricated ends 319984 Membrane penetration 319985 Techniques to avoid corrections to cell and pore pressures 320
10 Special Tests and Test Considerations 321101 Introduction 321
1011 Low confining pressure tests on clays 3211012 Conventional low pressure tests on any soil 3211013 High pressure tests 3221014 Peats and organic soils 322
102 K0‐tests 322103 Extension tests 322
1031 Problems with the conventional triaxial extension test 3231032 Enforcing uniform strains in extension tests 324
104 Tests on unsaturated soils 3261041 Soil water retention curve 3261042 Hydraulic conductivity function 3271043 Low matric suction 3271044 High matric suction 3291045 Modeling 3301046 Triaxial testing 331
105 Frozen soils 331106 Time effects tests 333
1061 Creep tests 3331062 Stress relaxation tests 333
107 Determination of hydraulic conductivity 335108 Bender element tests 335
1081 Fabrication of bender elements 3361082 Shear modulus 3371083 Signal interpretation 3381084 First arrival time 3381085 Specimen size and geometry 3401086 Ray path analysis 3401087 Surface mounted elements 3401088 Effects of specimen material 3411089 Effects of cross‐anisotropy 341
Contents xi
11 Tests with Three Unequal Principal Stresses 343111 Introduction 343112 Tests with constant principal stress directions 344
1121 Plane strain equipment 3441122 True triaxial equipment 3451123 Results from true triaxial tests 3481124 Strength characteristics 3531125 Failure criteria for soils 355
113 Tests with rotating principal stress directions 3601131 Simple shear equipment 3601132 Directional shear cell 3621133 Torsion shear apparatus 3641134 Summary and conclusion 370
Appendix A Manufacturing of Latex Rubber Membranes 373A1 The process 373A2 Products for membrane fabrication 373A3 Create an aluminum mold 374A4 Two tanks 374A5 Mold preparation 374A6 Dipping processes 374A7 Post production 375A8 Storage 375A9 Membrane repair 375
Appendix B Design of Diaphragm Load Cells 377B1 Load cells with uniform diaphragm 377B2 Load cells with tapered diaphragm 378B3 Example Design of 5 kN beryllium copper load cell 378 B31 Punching failure 379
References 381Index 397
Preface
The triaxial test is almost always chosen for studies of new phenomena because it is rela-tively simple and versatile The triaxial test is the most suitable for such studies and it is required in geotechnical engineering for the purposes of design of specific projects and for studying and understanding the behavior of soils
The first triaxial compression test apparatus shown in Fig P1 was designed by von Kārmān (1910 1911) for testing of rock cores The scale may be deduced from the fact that the specimen is 4 cm in diameter (Vaacutesaacuterhelyi 2010) However his paper was not noticed or it was forgotten by 1930 when Casagrande at Harvard University wrote a letter to Terzaghi at the Technical University in Vienna in which he describes his visit to the hydraulics laboratory in Berlin Here he saw an apparatus for measuring the permea-bility of soil Casagrande suggested that the cylindrical specimen in this apparatus could be loaded in the vertical (axial) direction to indi-cate its strength Therefore he was going to build a prototype and Terzaghi proposed that he build one for him too This appears to be the begin-ning of triaxial testing of soils in geotechnical engineering The apparatus was immediately employed by Rendulic (Terzaghi and Rendulic 1934) for tests with and without membranes the results of which played an important role in understanding the effective stress principle as well as the role of pore water pressure and consolidation on shear strength at a time when the effective stress principle was still being questioned (Skempton 1960 de Boer 2005)
Previous books on the developments of tech-niques for triaxial testing have been written by Bishop and Henkel (1957 1962) and by Head (1986) The proceedings from a conference on Advanced Triaxial Testing of Soil and Rock (Donaghe et al 1988) was published to summa-
rize advances in this area Other books have not appeared since then To understand the present book the reader is required to have a background in basic soil mechanics some experience in soil mechanics laboratory testing and perhaps in foundation engineering
In addition to triaxial testing of soils the contents of the book may in part apply to more advanced tests and to the testing of hard soils ndash soft rocks It is written for research workers soil testing laboratories and consulting engineers The emphasis is placed on what the soil speci-men is exposed to and experiences rather than the esthetic appearance of the equipment There will be considerable use of physics and mathe-matics to illustrate the arguments and discus-sions With a few exceptions references are made to easily accessible articles in the literature Much of the book centers on how to obtain high quality experimental results and the guiding concepts for this purpose have been expressed by the car industry in their slogans ldquoQuality is Job Onerdquo (Ford Motor Company) and ldquoQuality is never an accident it is always the result of excellent workmanshiprdquo (Mercedes)
The book is organized in a logical sequence beginning with the principles of triaxial testing in Chapter 1 and the computations and presen-tations of test results in Chapter 2 The triaxial equipment is explained in Chapter 3 and instrumentation measurements and control is reviewed in Chapter 4 Preparation of triaxial specimens is presented in Chapter 5 and satu-ration of specimens is described in Chapter 6 The two testing stages in an experiment are made clear in Chapter 7 Consolidation and in Chapter 8 Shearing Chapter 9 accounts for the corrections to the measurements Chapter 10 informs about special tests and test conditions and Chapter 11 puts the results from triaxial tests in perspective by reviewing results from
xiv Preface
tests with three unequal principal stresses Appendices are provided to explain special experimental techniques Information on ven-dors for the various types of equipment may be obtained from the internet
The authorrsquos background for writing this book consists of a career in laboratory experi-mentation at university level to study and model the behavior of soils More specifically he received an MS degree in 1967 from the Technical University of Denmark for which he wrote a thesis on the influence of the intermedi-ate principal stress on the strength of sand and in retrospect ended up with the wrong conclu-sion on the basis of perfectly correct results He received a PhD from the University of California at Berkeley in 1972 with a dissertation on ldquoThe StressndashStrain and Strength Characteristics of Cohesionless Soilsrdquo which included results
from triaxial compression tests true triaxial tests and torsion shear tests to indicate the effects of the intermediate principal stress on sand behavior as well as a three‐dimensional elasto‐plastic constitutive model for the behavior of soils
With his students the author developed testing equipment performed experiments and built constitutive models for the observed soil behavior while a professor at the University of California at Los Angeles (UCLA) (1972ndash1993) Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015) Many of the experimental techniques developed over this range of years are explained in the present book
Great appreciation is expressed to John F Peters of the US Army Engineer Research and Development Center in Vicksburg MS for his careful review of the manuscript and for his many comments Special thanks go to Afshin Nabili for his invaluable assistance with drafting a large number of the figures and for modifica-tion of other diagrams for the book
Poul V Lade October 2015
References
Bishop AW and Henkel DJ (1957) Measurement of Soil Properties in Triaxial Test Edward Arnold London
Bishop AW and Henkel DJ (1962) The Measurement of Soil Properties in the Triaxial Test 2nd edn St Martinrsquos Press New York NY
de Boer R (2005) The Engineer and the Scandal Springer Berlin
Donaghe RT Chaney RC and Silver ML (eds) (1988) Advanced Triaxial Testing of Soil and Rock ASTM STP 977 ASTM Philadelphia PA
Head KH (1986) Manual of Soil Laboratory Testing ndash Volume 3 Effective Stress Tests Pentech Press London
von Kārmān T (1910) Magyar Meacuternoumlk eacutes Ėpiteacuteszegylet Koumlzloumlnye 10 212ndash226
B
b
c
aD1
D2
Figure P1 Triaxial apparatus designed and con-structed for testing of rock cores by von Kārmān (1910 1911)
Preface xv
von Kārmān T (1911) Verhandlungen Deutsche Ingenieur 55 1749ndash1757
Skempton AW (1960) Terzaghirsquos discovery of effec-tive stress In From Theory to Practice in Soil Mechanics (eds L Bjerrum A Casagrande RB Peck and AW Skempton) pp 42ndash53 John Wiley and Sons Ltd London
Terzaghi K and Rendulic L (1934) Die wirksame Flaumlchenporositaumlt des Betons Zeitschrift des Ōsterreichischen Ingenieur‐ und Architekten Vereines 86 1ndash9
Vaacutesaacuterhelyi B (2010) Tribute to the first triaxial test performed in 1910 Acta Geology and Geophysics of Hungary 45(2) 227ndash230
About the Author
Poul V Lade received his MS degree from the Technical University of Denmark in 1967 and he continued his studies at the University of California at Berkeley where he received his PhD in 1972 Subsequently his academic career began at the University of California at Los Angeles (UCLA) and he continued at Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015)
His research interests include application of appropriate experimental methods to determine the three‐dimensional stressndashstrain and strength behavior of soils and the development of consti-tutive models for frictional materials such as soils concrete and rock He developed laboratory experimental apparatus to investigate monotonic loading and large three‐dimensional stress rever-
sals in plane strain true triaxial and torsion shear equipment This also included studies of effects of principal stress rotation stability instability and liquefaction of granular materials and time effects The constitutive models are based on elasticity and work‐hardening isotropic and kinematic plasticity theories
He has written nearly 300 publications based on research performed with support from the National Science Foundation (NSF) and from the Air Force Office of Scientific Research (AFOSR) He was elected member of the Danish Academy of Technical Sciences (2001) and he was awarded Professor Ostenfeldrsquos Gold Medal from the Technical University of Denmark (2001) He was inaugural editor of Geomechanics and Engineering and he has served on the editorial boards of eight international journals on geotechnical engineering
Triaxial Testing of Soils First Edition Poul V Lade copy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd
Principles of Triaxial Testing1
11 Purpose of triaxial tests
The purpose of performing triaxial tests is to determine the mechanical properties of the soil It is assumed that the soil specimens to be tested are homogeneous and representative of the material in the field and that the desired soil properties can in fact be obtained from the triaxial tests either directly or by interpretation through some theory
The mechanical properties most often sought from triaxial tests are stressndashstrain relations volshyume change or pore pressure behavior and shear strength of the soil Included in the stressndashstrain behavior are also the compressibility and the value of the coefficient of earth pressure at rest K0 Other properties that may be obtained from the triaxial tests which include time as a component are the permeability the coefficient of consolidation and properties relating to time dependent behavior such as rate effects creep and stress relaxation
It is important that the natural soil deposit or the fill from which soil samples have been taken in the field are sufficiently uniform that the soil samples possess the properties which are approshypriate and representative of the soil mass in the field It is therefore paramount that the geology at the site is well‐known and understood Even then samples from uniform deposits may not
ldquocontainrdquo properties that are representative of the field deposit This may happen either (a) due to the change in effective stress state which is always associated with the sampling process or (b) due to mechanical disturbance from sampling transshyportation or handling in the laboratory The stressndashstrain and strength properties of very senshysitive clays which have been disturbed cannot be regenerated in the lab oratory or otherwise obtained by interpretation of tests performed on inadequate specimens The effects of sampling will briefly be discussed below in connection with choice of consolidation pressure in the trishyaxial test The topic of sampling is otherwise outshyside the scope of the present treatment
12 Concept of testing
The concept to be pursued in testing of soils is to simulate as closely as possible the process that goes on in the field Because there is a large number of variables (eg density water content degree of saturation overconsolidation ratio loading conditions stress paths) that influence the resulting soil behavior the simplest and most direct way of obtaining information pertinent to the field conditions is to duplicate these as closely as possible
2 Triaxial Testing of Soils
However because of limitations in equipment and because of practical limitations on the amount of testing that can be performed for each project it is essential that
1 The true field loading conditions (including the drainage conditions) are known
2 The laboratory equipment can reproduce these conditions to a required degree of accuracy
3 A reasonable estimate can be made of the sigshynificance of the differences between the field loading conditions and those that can be proshyduced in the laboratory equipment
It is clear that the triaxial test in many resshypects is incapable of simulating several imporshytant aspects of field loading conditions For example the effects of the intermediate princishypal stress the effects of rotation of principal stresses and the effects of partial drainage durshying loading in the field cannot be investigated on the basis of the triaxial test The effects of such conditions require studies involving other types of equipment or analyses of boundary value problems either by closed form solutions or solutions obtained by numerical techniques
To provide some background for evaluation of the results of triaxial tests other types of laboratory shear tests and typical results from such tests are presented in Chapter 11 The relashytions between the different types of tests are reviewed and their advantages and limitations are discussed
13 The triaxial test
The triaxial test is most often performed on a cylindrical specimen as shown in Fig 11(a) Principal stresses are applied to the specimen as indicated in Fig 11(b) First a confining pressure σ3 is applied to the specimen This pressure acts all around and therefore on all planes in the specimen Then an additional stress difference σd is applied in the axial direction The stress applied externally to the specimen in the axial direction is
σ σ σ1 3= +d (11)
and therefore
σ σ σd = minus1 3 (12)
In the general case three principal stresses σ1 σ2 and σ3 may act on a soil element in the field However only two different principal stresses can be applied to the specimen in the convenshytional triaxial test The intermediate principal stress σ2 can only have values as follows
σ σ2 3= Triaxial compression (13)
σ σ2 1= Triaxial extension (14)
The condition of triaxial extension can be achieved by applying negative stress differshyences to the specimen This merely produces a reduction in compression in the extension direcshytion but no tension occurs in the specimen The state of stress applied to the specimen is in both cases axisymmetric The triaxial compression test will be discussed in the following while the triaxial extension test is discussed in Chapter 10
The test is performed using triaxial apparashytus as seen in the schematic illustration in Fig 12 The specimen is surrounded by a cap and a base and a membrane This unit is placed in a triaxial cell in which the cell pressure can be applied The cell pressure acts as a hydrostatic confinement for the specimen and the pressure is therefore the same in all directions In addition
σ1
(a) (b)
σ1 = σd + σ3
σ2 = σ3
σd = σ1 ndash σ3σ3
σ3σ3
σ3
σd
Figure 11 (a) Cylindrical specimen for triaxial testing and (b) stresses applied to a triaxial specimen
Principles of Triaxial Testing 3
a deviator load can be applied through a piston that goes through the top of the cell and loads the specimen in the axial direction
The vertical deformation of the specimen may be measured by a dial gage attached to the piston which travels the same vertical distance as the cap sitting on top of the specimen Drainage lines are connected to the water saturated specishymen through the base (or both the cap and the base) and connected to a burette outside the trishyaxial cell This allows for measurements of the volume changes of the specimen during the test
Alternatively the connection to the burette can be shut off thereby preventing the specimen from changing volume Instead the pore water pressure can be measured on a transducer conshynected to the drainage line
The following quantities are measured in a typical triaxial test
1 Confining pressure2 Deviator load3 Vertical (or axial) deformation4 Volume change or pore water pressure
These measurements constitute the data base from which other quantities can be derived
[eg stress difference (σ1 ndash σ3) axial strain ε1 and volumetric strain εv]
14 Advantages and limitations
Whereas the triaxial test potentially can proshyvide a substantial proportion of the mechanical properties required for a project it has limitashytions especially when special conditions are encountered and necessitates clarification based on experimentation
The advantages of the triaxial test are
1 Drainage can be controlled (onndashoff)2 Volume change or pore pressure can be
measured3 Suction can be controlled in partially satushy
rated soils4 Measured deformations allow calculation of
strains and moduli5 A larger variety of stress and strain paths
that occur in the field can be applied in the triaxial apparatus than in any other testing apparatus (eg initial anisotropic consolidashytion at any stress ratio including K0 extension active and passive shear)
The limitations of the triaxial test are
1 Stress concentrations due to friction between specimen and end plates (cap and base) cause nonuniform strains and stresses and therefore nonuniform stressndashstrain volume change or pore pressure response
2 Only axisymmetric stress conditions can be applied to the specimen whereas most field problems involve plane strain or general three‐dimensional conditions with rotation of principal stresses
3 Triaxial tests cannot provide all necessary data required to characterize the behavior of an anisotropic or a cross‐anisotropic soil deposit as illustrated in Fig 13
4 Although the axisymmetric principal stress condition is limited it is more difficult to apply proper shear stresses or tension to soil in relatively simple tests
The first limitation listed above can be overcome by applying lubricated ends on the
Pore pressure transducer
On-Off valve
Burette
Piston
Dial gage
Triaxial cell
P = σd middot A
Aprime
σcell
σ3
σ3 σ3= σcell
Figure 12 Schematic diagram of triaxial apparatus
4 Triaxial Testing of Soils
specimen such that uniform strains and stresses and therefore correct soil response can be proshyduced This is discussed in Chapter 3 In addishytion to the limitations listed above it should be mentioned that it may be easier to reproduce certain stress paths in other specialty equipment than in the triaxial apparatus (eg K0‐test)
Although the triaxial test is limited as explained under points 2 and 3 above it does combine versatility with relative simplicity in concept and performance Other equipment in which three unequal principal stresses can be applied or in which the principal stress direcshytions can be rotated do not have the versatility or is more com plicated to operate Thus other types of equipment have their own advantages and limitations These other equipment types
include plane strain true triaxial simple shear directional shear and torsion shear apparatus All these pieces of equipment are with the excepshytion of the simple shear apparatus employed mainly for research purposes Their operational modes capabilities and results are reviewed in Chapter 11
15 Test stages ndash consolidation and shearing
Laboratory tests are made to simulate field loadshying conditions as close as possible Most field conditions and the corresponding tests can be simplified to consist of two stages consolidation and shearing
Axis of symmetry
1Eh
1Eh
1Ghv
1Ev
ndashmicrohvEh
ndashmicrohvEn
2(1 + microhh)En
ndashmicrohhEn
ndashmicrohvEh
ndashmicrohvEh
ndashmicrohhEh
0
h
h
v
0 0
σh
σh
σv
τhv
τhv
τvh
τvh
σh
σv
σh
τhv
τvh
τhh
τhh τhh
ϵh
ϵv
ϵh
γhv
γvh
γhh
0
Require tests withapplication of
shear stresses
0 0
0
0 0 0 00
1Ghv0 0 0 00
0 0 0 0 0
0 0
bull =
Figure 13 Cross‐anisotropic soil requiring results from more than triaxial tests for full characterization
Principles of Triaxial Testing 5
151 Consolidation
In the first stage the initial condition of the soil is established in terms of effective stresses and stress history (including overconsolidation if applicable) Thus stresses are applied correshysponding to those acting on the element of soil in the field due to weight of the overlying soil strata and other materials or structures that exist at the time the mechanical properties (stressndashstrain strength etc) are sought Sufficient time is allowed for complete consolidation to occur under the applied stresses The condition in the field element has now been established in the triaxial specimen
152 Shearing
In the second stage of the triaxial test an addishytional stress is applied to reach peak failure and beyond under relevant drainage conditions The additional stress applied to the specimen should correspond as closely as possible to the change in stress on the field element due to some new change in the overall field loading situashytion This change may consist of a vertical stress increase or decrease (eg due to addition of a structure or excavation of overlying soil strata) or of a horizontal stress increase or decrease (eg due to the same constructions causing the vertical stress changes) Any combination of vertical and horizontal stress changes may be simulated in the triaxial test Examples of vertishycal and horizontal stress changes in the field are shown in Fig 14
Usually it is desirable to know how much change in load the soil can sustain without failshying and how much deformation will occur under normal working conditions The test is therefore usually continued to find the strength of the soil under the appropriate loading condishytions The results are used with an appropriate factor of safety so that normal working stresses are always somewhat below the peak strength
The stressndashstrain relations obtained from the triaxial tests provide the basis for determinashytion of deformations in the field This may be done in a simplified manner by closed‐form
solutions or it may be done by employing the results of the triaxial tests for calibration of a constitutive model used with a numerical method in finite element or finite difference computer programs
16 Types of tests
The drainage conditions in the field must be duplicated as well as possible in the laboratory tests This may be done by appropriate drainage facilities or preventions as discussed above for the triaxial test In most cases the field drainage conditions can be approximated by one of the following three types of tests
1 Consolidated‐drained test called a CD‐test or just a drained test
2 Consolidated‐undrained test or a CU‐test3 Unconsolidated‐undrained test or a UU‐test
Additionalload
Excavation
ΔσV asymp 0
ΔσV asymp 0
ΔσV gt 0
ΔσV lt 0
Δσh lt 0
Δσh gt 0
Δσh lt ΔσV
Δσh
Figure 14 Examples of stress changes leading to failure in the field
6 Triaxial Testing of Soils
These tests are described in ASTM Standards D7181 (2014) D4767 (2014) and D2850 (2014) respectively
Which condition of drainage in the laboratory test logically corresponds to each case in the field depends on a comparison of loading rate with the rate at which the water can escape or be sucked into the ground Thus the permeability of the soil and the drainage boundary conditions in the field together with the loading rate play key roles in determination of the type of analysis and the type of test drained or undrained that are appropriate for each case Field cases with partial drainage can be correctly duplicated in laboratory tests if the effective stress path is determined for the design condition However the idea of the CD‐ CU‐ and UU‐tests is to make it relatively simple for the design engineer to analyze a condition that will render a sufficient factor of safety under the actual drainage condishytion without trying to estimate and experimenshytally replicate the actual stress path
It has been determined through experience and common sense that the extreme conditions are drained and undrained with and without consolidation As a practical matter in a commershycial laboratory it is easier to run an undrained test than a drained test because it is easier and faster to measure pore pressures than volume change Therefore even drained parameters are more likely to be estimated from a CU‐test than from a CD‐test
161 Simulation of field conditions
Presented below is a brief review of the three types of tests together with examples of field cases for which the tests are appropriate and with typishycal strength results shown on Mohr diagrams
Drained tests
Isotropic consolidation is most often used in the first stage of the triaxial test However anisoshytropic consolidation with any stress ratio is also possible
The shearing stage of a drained test is pershyformed so slowly the soil is so permeable and the drainage facilities are such that no excess
pore pressure (positive or negative) can exist in the specimen at any stage of the test that is
∆u = 0 (15)
It follows then from the effective stress principle
prime = minusσ σ u (16)
that the effective stress changes are always the same as the total stress changes
A soil specimen always changes volume during shearing in a drained test If it contracts in volume it expels pore fluid (usually water or air) and if it expands in volume (dilates) then it sucks water or air into the pores If a non‐zero pore pressure is generated during the test (eg by performing the shearing too fast so the water does not have sufficient time to escape) then the specimen will expel or suck water such that the pore pressure goes towards zero to try to achieve equilibrium between externally applied stresses and internal effective stresses Thus there will always be volume changes in a drained test Consequently the water content the void ratio and the dry density of the specimen at the end of the test are most often not the same as at the beginning
The following field conditions can be simushylated with acceptable accuracy in the drained test
1 Almost all cases involving coarse sands and gravel whether saturated or not (except if confined in eg a lens andor exposed to rapid loading as in eg an earthquake)
2 Many cases involving fine sand and someshytimes silt if the field loads are applied reashysonable slowly
3 Long term loading of any soil as for examplea) Cut slopes several years after excavationb) Embankment constructed very slowly in
layers over a soft clay depositc) Earth dam with steady seepaged) Foundation on clay a long time after
construction
These cases are illustrated in Fig 15The strength results obtained from drained
tests are illustrated schematically on the Mohr diagram in Fig 16 The shear strength of soils increases with increasing confining pressure
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
Contents xi
11 Tests with Three Unequal Principal Stresses 343111 Introduction 343112 Tests with constant principal stress directions 344
1121 Plane strain equipment 3441122 True triaxial equipment 3451123 Results from true triaxial tests 3481124 Strength characteristics 3531125 Failure criteria for soils 355
113 Tests with rotating principal stress directions 3601131 Simple shear equipment 3601132 Directional shear cell 3621133 Torsion shear apparatus 3641134 Summary and conclusion 370
Appendix A Manufacturing of Latex Rubber Membranes 373A1 The process 373A2 Products for membrane fabrication 373A3 Create an aluminum mold 374A4 Two tanks 374A5 Mold preparation 374A6 Dipping processes 374A7 Post production 375A8 Storage 375A9 Membrane repair 375
Appendix B Design of Diaphragm Load Cells 377B1 Load cells with uniform diaphragm 377B2 Load cells with tapered diaphragm 378B3 Example Design of 5 kN beryllium copper load cell 378 B31 Punching failure 379
References 381Index 397
Preface
The triaxial test is almost always chosen for studies of new phenomena because it is rela-tively simple and versatile The triaxial test is the most suitable for such studies and it is required in geotechnical engineering for the purposes of design of specific projects and for studying and understanding the behavior of soils
The first triaxial compression test apparatus shown in Fig P1 was designed by von Kārmān (1910 1911) for testing of rock cores The scale may be deduced from the fact that the specimen is 4 cm in diameter (Vaacutesaacuterhelyi 2010) However his paper was not noticed or it was forgotten by 1930 when Casagrande at Harvard University wrote a letter to Terzaghi at the Technical University in Vienna in which he describes his visit to the hydraulics laboratory in Berlin Here he saw an apparatus for measuring the permea-bility of soil Casagrande suggested that the cylindrical specimen in this apparatus could be loaded in the vertical (axial) direction to indi-cate its strength Therefore he was going to build a prototype and Terzaghi proposed that he build one for him too This appears to be the begin-ning of triaxial testing of soils in geotechnical engineering The apparatus was immediately employed by Rendulic (Terzaghi and Rendulic 1934) for tests with and without membranes the results of which played an important role in understanding the effective stress principle as well as the role of pore water pressure and consolidation on shear strength at a time when the effective stress principle was still being questioned (Skempton 1960 de Boer 2005)
Previous books on the developments of tech-niques for triaxial testing have been written by Bishop and Henkel (1957 1962) and by Head (1986) The proceedings from a conference on Advanced Triaxial Testing of Soil and Rock (Donaghe et al 1988) was published to summa-
rize advances in this area Other books have not appeared since then To understand the present book the reader is required to have a background in basic soil mechanics some experience in soil mechanics laboratory testing and perhaps in foundation engineering
In addition to triaxial testing of soils the contents of the book may in part apply to more advanced tests and to the testing of hard soils ndash soft rocks It is written for research workers soil testing laboratories and consulting engineers The emphasis is placed on what the soil speci-men is exposed to and experiences rather than the esthetic appearance of the equipment There will be considerable use of physics and mathe-matics to illustrate the arguments and discus-sions With a few exceptions references are made to easily accessible articles in the literature Much of the book centers on how to obtain high quality experimental results and the guiding concepts for this purpose have been expressed by the car industry in their slogans ldquoQuality is Job Onerdquo (Ford Motor Company) and ldquoQuality is never an accident it is always the result of excellent workmanshiprdquo (Mercedes)
The book is organized in a logical sequence beginning with the principles of triaxial testing in Chapter 1 and the computations and presen-tations of test results in Chapter 2 The triaxial equipment is explained in Chapter 3 and instrumentation measurements and control is reviewed in Chapter 4 Preparation of triaxial specimens is presented in Chapter 5 and satu-ration of specimens is described in Chapter 6 The two testing stages in an experiment are made clear in Chapter 7 Consolidation and in Chapter 8 Shearing Chapter 9 accounts for the corrections to the measurements Chapter 10 informs about special tests and test conditions and Chapter 11 puts the results from triaxial tests in perspective by reviewing results from
xiv Preface
tests with three unequal principal stresses Appendices are provided to explain special experimental techniques Information on ven-dors for the various types of equipment may be obtained from the internet
The authorrsquos background for writing this book consists of a career in laboratory experi-mentation at university level to study and model the behavior of soils More specifically he received an MS degree in 1967 from the Technical University of Denmark for which he wrote a thesis on the influence of the intermedi-ate principal stress on the strength of sand and in retrospect ended up with the wrong conclu-sion on the basis of perfectly correct results He received a PhD from the University of California at Berkeley in 1972 with a dissertation on ldquoThe StressndashStrain and Strength Characteristics of Cohesionless Soilsrdquo which included results
from triaxial compression tests true triaxial tests and torsion shear tests to indicate the effects of the intermediate principal stress on sand behavior as well as a three‐dimensional elasto‐plastic constitutive model for the behavior of soils
With his students the author developed testing equipment performed experiments and built constitutive models for the observed soil behavior while a professor at the University of California at Los Angeles (UCLA) (1972ndash1993) Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015) Many of the experimental techniques developed over this range of years are explained in the present book
Great appreciation is expressed to John F Peters of the US Army Engineer Research and Development Center in Vicksburg MS for his careful review of the manuscript and for his many comments Special thanks go to Afshin Nabili for his invaluable assistance with drafting a large number of the figures and for modifica-tion of other diagrams for the book
Poul V Lade October 2015
References
Bishop AW and Henkel DJ (1957) Measurement of Soil Properties in Triaxial Test Edward Arnold London
Bishop AW and Henkel DJ (1962) The Measurement of Soil Properties in the Triaxial Test 2nd edn St Martinrsquos Press New York NY
de Boer R (2005) The Engineer and the Scandal Springer Berlin
Donaghe RT Chaney RC and Silver ML (eds) (1988) Advanced Triaxial Testing of Soil and Rock ASTM STP 977 ASTM Philadelphia PA
Head KH (1986) Manual of Soil Laboratory Testing ndash Volume 3 Effective Stress Tests Pentech Press London
von Kārmān T (1910) Magyar Meacuternoumlk eacutes Ėpiteacuteszegylet Koumlzloumlnye 10 212ndash226
B
b
c
aD1
D2
Figure P1 Triaxial apparatus designed and con-structed for testing of rock cores by von Kārmān (1910 1911)
Preface xv
von Kārmān T (1911) Verhandlungen Deutsche Ingenieur 55 1749ndash1757
Skempton AW (1960) Terzaghirsquos discovery of effec-tive stress In From Theory to Practice in Soil Mechanics (eds L Bjerrum A Casagrande RB Peck and AW Skempton) pp 42ndash53 John Wiley and Sons Ltd London
Terzaghi K and Rendulic L (1934) Die wirksame Flaumlchenporositaumlt des Betons Zeitschrift des Ōsterreichischen Ingenieur‐ und Architekten Vereines 86 1ndash9
Vaacutesaacuterhelyi B (2010) Tribute to the first triaxial test performed in 1910 Acta Geology and Geophysics of Hungary 45(2) 227ndash230
About the Author
Poul V Lade received his MS degree from the Technical University of Denmark in 1967 and he continued his studies at the University of California at Berkeley where he received his PhD in 1972 Subsequently his academic career began at the University of California at Los Angeles (UCLA) and he continued at Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015)
His research interests include application of appropriate experimental methods to determine the three‐dimensional stressndashstrain and strength behavior of soils and the development of consti-tutive models for frictional materials such as soils concrete and rock He developed laboratory experimental apparatus to investigate monotonic loading and large three‐dimensional stress rever-
sals in plane strain true triaxial and torsion shear equipment This also included studies of effects of principal stress rotation stability instability and liquefaction of granular materials and time effects The constitutive models are based on elasticity and work‐hardening isotropic and kinematic plasticity theories
He has written nearly 300 publications based on research performed with support from the National Science Foundation (NSF) and from the Air Force Office of Scientific Research (AFOSR) He was elected member of the Danish Academy of Technical Sciences (2001) and he was awarded Professor Ostenfeldrsquos Gold Medal from the Technical University of Denmark (2001) He was inaugural editor of Geomechanics and Engineering and he has served on the editorial boards of eight international journals on geotechnical engineering
Triaxial Testing of Soils First Edition Poul V Lade copy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd
Principles of Triaxial Testing1
11 Purpose of triaxial tests
The purpose of performing triaxial tests is to determine the mechanical properties of the soil It is assumed that the soil specimens to be tested are homogeneous and representative of the material in the field and that the desired soil properties can in fact be obtained from the triaxial tests either directly or by interpretation through some theory
The mechanical properties most often sought from triaxial tests are stressndashstrain relations volshyume change or pore pressure behavior and shear strength of the soil Included in the stressndashstrain behavior are also the compressibility and the value of the coefficient of earth pressure at rest K0 Other properties that may be obtained from the triaxial tests which include time as a component are the permeability the coefficient of consolidation and properties relating to time dependent behavior such as rate effects creep and stress relaxation
It is important that the natural soil deposit or the fill from which soil samples have been taken in the field are sufficiently uniform that the soil samples possess the properties which are approshypriate and representative of the soil mass in the field It is therefore paramount that the geology at the site is well‐known and understood Even then samples from uniform deposits may not
ldquocontainrdquo properties that are representative of the field deposit This may happen either (a) due to the change in effective stress state which is always associated with the sampling process or (b) due to mechanical disturbance from sampling transshyportation or handling in the laboratory The stressndashstrain and strength properties of very senshysitive clays which have been disturbed cannot be regenerated in the lab oratory or otherwise obtained by interpretation of tests performed on inadequate specimens The effects of sampling will briefly be discussed below in connection with choice of consolidation pressure in the trishyaxial test The topic of sampling is otherwise outshyside the scope of the present treatment
12 Concept of testing
The concept to be pursued in testing of soils is to simulate as closely as possible the process that goes on in the field Because there is a large number of variables (eg density water content degree of saturation overconsolidation ratio loading conditions stress paths) that influence the resulting soil behavior the simplest and most direct way of obtaining information pertinent to the field conditions is to duplicate these as closely as possible
2 Triaxial Testing of Soils
However because of limitations in equipment and because of practical limitations on the amount of testing that can be performed for each project it is essential that
1 The true field loading conditions (including the drainage conditions) are known
2 The laboratory equipment can reproduce these conditions to a required degree of accuracy
3 A reasonable estimate can be made of the sigshynificance of the differences between the field loading conditions and those that can be proshyduced in the laboratory equipment
It is clear that the triaxial test in many resshypects is incapable of simulating several imporshytant aspects of field loading conditions For example the effects of the intermediate princishypal stress the effects of rotation of principal stresses and the effects of partial drainage durshying loading in the field cannot be investigated on the basis of the triaxial test The effects of such conditions require studies involving other types of equipment or analyses of boundary value problems either by closed form solutions or solutions obtained by numerical techniques
To provide some background for evaluation of the results of triaxial tests other types of laboratory shear tests and typical results from such tests are presented in Chapter 11 The relashytions between the different types of tests are reviewed and their advantages and limitations are discussed
13 The triaxial test
The triaxial test is most often performed on a cylindrical specimen as shown in Fig 11(a) Principal stresses are applied to the specimen as indicated in Fig 11(b) First a confining pressure σ3 is applied to the specimen This pressure acts all around and therefore on all planes in the specimen Then an additional stress difference σd is applied in the axial direction The stress applied externally to the specimen in the axial direction is
σ σ σ1 3= +d (11)
and therefore
σ σ σd = minus1 3 (12)
In the general case three principal stresses σ1 σ2 and σ3 may act on a soil element in the field However only two different principal stresses can be applied to the specimen in the convenshytional triaxial test The intermediate principal stress σ2 can only have values as follows
σ σ2 3= Triaxial compression (13)
σ σ2 1= Triaxial extension (14)
The condition of triaxial extension can be achieved by applying negative stress differshyences to the specimen This merely produces a reduction in compression in the extension direcshytion but no tension occurs in the specimen The state of stress applied to the specimen is in both cases axisymmetric The triaxial compression test will be discussed in the following while the triaxial extension test is discussed in Chapter 10
The test is performed using triaxial apparashytus as seen in the schematic illustration in Fig 12 The specimen is surrounded by a cap and a base and a membrane This unit is placed in a triaxial cell in which the cell pressure can be applied The cell pressure acts as a hydrostatic confinement for the specimen and the pressure is therefore the same in all directions In addition
σ1
(a) (b)
σ1 = σd + σ3
σ2 = σ3
σd = σ1 ndash σ3σ3
σ3σ3
σ3
σd
Figure 11 (a) Cylindrical specimen for triaxial testing and (b) stresses applied to a triaxial specimen
Principles of Triaxial Testing 3
a deviator load can be applied through a piston that goes through the top of the cell and loads the specimen in the axial direction
The vertical deformation of the specimen may be measured by a dial gage attached to the piston which travels the same vertical distance as the cap sitting on top of the specimen Drainage lines are connected to the water saturated specishymen through the base (or both the cap and the base) and connected to a burette outside the trishyaxial cell This allows for measurements of the volume changes of the specimen during the test
Alternatively the connection to the burette can be shut off thereby preventing the specimen from changing volume Instead the pore water pressure can be measured on a transducer conshynected to the drainage line
The following quantities are measured in a typical triaxial test
1 Confining pressure2 Deviator load3 Vertical (or axial) deformation4 Volume change or pore water pressure
These measurements constitute the data base from which other quantities can be derived
[eg stress difference (σ1 ndash σ3) axial strain ε1 and volumetric strain εv]
14 Advantages and limitations
Whereas the triaxial test potentially can proshyvide a substantial proportion of the mechanical properties required for a project it has limitashytions especially when special conditions are encountered and necessitates clarification based on experimentation
The advantages of the triaxial test are
1 Drainage can be controlled (onndashoff)2 Volume change or pore pressure can be
measured3 Suction can be controlled in partially satushy
rated soils4 Measured deformations allow calculation of
strains and moduli5 A larger variety of stress and strain paths
that occur in the field can be applied in the triaxial apparatus than in any other testing apparatus (eg initial anisotropic consolidashytion at any stress ratio including K0 extension active and passive shear)
The limitations of the triaxial test are
1 Stress concentrations due to friction between specimen and end plates (cap and base) cause nonuniform strains and stresses and therefore nonuniform stressndashstrain volume change or pore pressure response
2 Only axisymmetric stress conditions can be applied to the specimen whereas most field problems involve plane strain or general three‐dimensional conditions with rotation of principal stresses
3 Triaxial tests cannot provide all necessary data required to characterize the behavior of an anisotropic or a cross‐anisotropic soil deposit as illustrated in Fig 13
4 Although the axisymmetric principal stress condition is limited it is more difficult to apply proper shear stresses or tension to soil in relatively simple tests
The first limitation listed above can be overcome by applying lubricated ends on the
Pore pressure transducer
On-Off valve
Burette
Piston
Dial gage
Triaxial cell
P = σd middot A
Aprime
σcell
σ3
σ3 σ3= σcell
Figure 12 Schematic diagram of triaxial apparatus
4 Triaxial Testing of Soils
specimen such that uniform strains and stresses and therefore correct soil response can be proshyduced This is discussed in Chapter 3 In addishytion to the limitations listed above it should be mentioned that it may be easier to reproduce certain stress paths in other specialty equipment than in the triaxial apparatus (eg K0‐test)
Although the triaxial test is limited as explained under points 2 and 3 above it does combine versatility with relative simplicity in concept and performance Other equipment in which three unequal principal stresses can be applied or in which the principal stress direcshytions can be rotated do not have the versatility or is more com plicated to operate Thus other types of equipment have their own advantages and limitations These other equipment types
include plane strain true triaxial simple shear directional shear and torsion shear apparatus All these pieces of equipment are with the excepshytion of the simple shear apparatus employed mainly for research purposes Their operational modes capabilities and results are reviewed in Chapter 11
15 Test stages ndash consolidation and shearing
Laboratory tests are made to simulate field loadshying conditions as close as possible Most field conditions and the corresponding tests can be simplified to consist of two stages consolidation and shearing
Axis of symmetry
1Eh
1Eh
1Ghv
1Ev
ndashmicrohvEh
ndashmicrohvEn
2(1 + microhh)En
ndashmicrohhEn
ndashmicrohvEh
ndashmicrohvEh
ndashmicrohhEh
0
h
h
v
0 0
σh
σh
σv
τhv
τhv
τvh
τvh
σh
σv
σh
τhv
τvh
τhh
τhh τhh
ϵh
ϵv
ϵh
γhv
γvh
γhh
0
Require tests withapplication of
shear stresses
0 0
0
0 0 0 00
1Ghv0 0 0 00
0 0 0 0 0
0 0
bull =
Figure 13 Cross‐anisotropic soil requiring results from more than triaxial tests for full characterization
Principles of Triaxial Testing 5
151 Consolidation
In the first stage the initial condition of the soil is established in terms of effective stresses and stress history (including overconsolidation if applicable) Thus stresses are applied correshysponding to those acting on the element of soil in the field due to weight of the overlying soil strata and other materials or structures that exist at the time the mechanical properties (stressndashstrain strength etc) are sought Sufficient time is allowed for complete consolidation to occur under the applied stresses The condition in the field element has now been established in the triaxial specimen
152 Shearing
In the second stage of the triaxial test an addishytional stress is applied to reach peak failure and beyond under relevant drainage conditions The additional stress applied to the specimen should correspond as closely as possible to the change in stress on the field element due to some new change in the overall field loading situashytion This change may consist of a vertical stress increase or decrease (eg due to addition of a structure or excavation of overlying soil strata) or of a horizontal stress increase or decrease (eg due to the same constructions causing the vertical stress changes) Any combination of vertical and horizontal stress changes may be simulated in the triaxial test Examples of vertishycal and horizontal stress changes in the field are shown in Fig 14
Usually it is desirable to know how much change in load the soil can sustain without failshying and how much deformation will occur under normal working conditions The test is therefore usually continued to find the strength of the soil under the appropriate loading condishytions The results are used with an appropriate factor of safety so that normal working stresses are always somewhat below the peak strength
The stressndashstrain relations obtained from the triaxial tests provide the basis for determinashytion of deformations in the field This may be done in a simplified manner by closed‐form
solutions or it may be done by employing the results of the triaxial tests for calibration of a constitutive model used with a numerical method in finite element or finite difference computer programs
16 Types of tests
The drainage conditions in the field must be duplicated as well as possible in the laboratory tests This may be done by appropriate drainage facilities or preventions as discussed above for the triaxial test In most cases the field drainage conditions can be approximated by one of the following three types of tests
1 Consolidated‐drained test called a CD‐test or just a drained test
2 Consolidated‐undrained test or a CU‐test3 Unconsolidated‐undrained test or a UU‐test
Additionalload
Excavation
ΔσV asymp 0
ΔσV asymp 0
ΔσV gt 0
ΔσV lt 0
Δσh lt 0
Δσh gt 0
Δσh lt ΔσV
Δσh
Figure 14 Examples of stress changes leading to failure in the field
6 Triaxial Testing of Soils
These tests are described in ASTM Standards D7181 (2014) D4767 (2014) and D2850 (2014) respectively
Which condition of drainage in the laboratory test logically corresponds to each case in the field depends on a comparison of loading rate with the rate at which the water can escape or be sucked into the ground Thus the permeability of the soil and the drainage boundary conditions in the field together with the loading rate play key roles in determination of the type of analysis and the type of test drained or undrained that are appropriate for each case Field cases with partial drainage can be correctly duplicated in laboratory tests if the effective stress path is determined for the design condition However the idea of the CD‐ CU‐ and UU‐tests is to make it relatively simple for the design engineer to analyze a condition that will render a sufficient factor of safety under the actual drainage condishytion without trying to estimate and experimenshytally replicate the actual stress path
It has been determined through experience and common sense that the extreme conditions are drained and undrained with and without consolidation As a practical matter in a commershycial laboratory it is easier to run an undrained test than a drained test because it is easier and faster to measure pore pressures than volume change Therefore even drained parameters are more likely to be estimated from a CU‐test than from a CD‐test
161 Simulation of field conditions
Presented below is a brief review of the three types of tests together with examples of field cases for which the tests are appropriate and with typishycal strength results shown on Mohr diagrams
Drained tests
Isotropic consolidation is most often used in the first stage of the triaxial test However anisoshytropic consolidation with any stress ratio is also possible
The shearing stage of a drained test is pershyformed so slowly the soil is so permeable and the drainage facilities are such that no excess
pore pressure (positive or negative) can exist in the specimen at any stage of the test that is
∆u = 0 (15)
It follows then from the effective stress principle
prime = minusσ σ u (16)
that the effective stress changes are always the same as the total stress changes
A soil specimen always changes volume during shearing in a drained test If it contracts in volume it expels pore fluid (usually water or air) and if it expands in volume (dilates) then it sucks water or air into the pores If a non‐zero pore pressure is generated during the test (eg by performing the shearing too fast so the water does not have sufficient time to escape) then the specimen will expel or suck water such that the pore pressure goes towards zero to try to achieve equilibrium between externally applied stresses and internal effective stresses Thus there will always be volume changes in a drained test Consequently the water content the void ratio and the dry density of the specimen at the end of the test are most often not the same as at the beginning
The following field conditions can be simushylated with acceptable accuracy in the drained test
1 Almost all cases involving coarse sands and gravel whether saturated or not (except if confined in eg a lens andor exposed to rapid loading as in eg an earthquake)
2 Many cases involving fine sand and someshytimes silt if the field loads are applied reashysonable slowly
3 Long term loading of any soil as for examplea) Cut slopes several years after excavationb) Embankment constructed very slowly in
layers over a soft clay depositc) Earth dam with steady seepaged) Foundation on clay a long time after
construction
These cases are illustrated in Fig 15The strength results obtained from drained
tests are illustrated schematically on the Mohr diagram in Fig 16 The shear strength of soils increases with increasing confining pressure
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
Preface
The triaxial test is almost always chosen for studies of new phenomena because it is rela-tively simple and versatile The triaxial test is the most suitable for such studies and it is required in geotechnical engineering for the purposes of design of specific projects and for studying and understanding the behavior of soils
The first triaxial compression test apparatus shown in Fig P1 was designed by von Kārmān (1910 1911) for testing of rock cores The scale may be deduced from the fact that the specimen is 4 cm in diameter (Vaacutesaacuterhelyi 2010) However his paper was not noticed or it was forgotten by 1930 when Casagrande at Harvard University wrote a letter to Terzaghi at the Technical University in Vienna in which he describes his visit to the hydraulics laboratory in Berlin Here he saw an apparatus for measuring the permea-bility of soil Casagrande suggested that the cylindrical specimen in this apparatus could be loaded in the vertical (axial) direction to indi-cate its strength Therefore he was going to build a prototype and Terzaghi proposed that he build one for him too This appears to be the begin-ning of triaxial testing of soils in geotechnical engineering The apparatus was immediately employed by Rendulic (Terzaghi and Rendulic 1934) for tests with and without membranes the results of which played an important role in understanding the effective stress principle as well as the role of pore water pressure and consolidation on shear strength at a time when the effective stress principle was still being questioned (Skempton 1960 de Boer 2005)
Previous books on the developments of tech-niques for triaxial testing have been written by Bishop and Henkel (1957 1962) and by Head (1986) The proceedings from a conference on Advanced Triaxial Testing of Soil and Rock (Donaghe et al 1988) was published to summa-
rize advances in this area Other books have not appeared since then To understand the present book the reader is required to have a background in basic soil mechanics some experience in soil mechanics laboratory testing and perhaps in foundation engineering
In addition to triaxial testing of soils the contents of the book may in part apply to more advanced tests and to the testing of hard soils ndash soft rocks It is written for research workers soil testing laboratories and consulting engineers The emphasis is placed on what the soil speci-men is exposed to and experiences rather than the esthetic appearance of the equipment There will be considerable use of physics and mathe-matics to illustrate the arguments and discus-sions With a few exceptions references are made to easily accessible articles in the literature Much of the book centers on how to obtain high quality experimental results and the guiding concepts for this purpose have been expressed by the car industry in their slogans ldquoQuality is Job Onerdquo (Ford Motor Company) and ldquoQuality is never an accident it is always the result of excellent workmanshiprdquo (Mercedes)
The book is organized in a logical sequence beginning with the principles of triaxial testing in Chapter 1 and the computations and presen-tations of test results in Chapter 2 The triaxial equipment is explained in Chapter 3 and instrumentation measurements and control is reviewed in Chapter 4 Preparation of triaxial specimens is presented in Chapter 5 and satu-ration of specimens is described in Chapter 6 The two testing stages in an experiment are made clear in Chapter 7 Consolidation and in Chapter 8 Shearing Chapter 9 accounts for the corrections to the measurements Chapter 10 informs about special tests and test conditions and Chapter 11 puts the results from triaxial tests in perspective by reviewing results from
xiv Preface
tests with three unequal principal stresses Appendices are provided to explain special experimental techniques Information on ven-dors for the various types of equipment may be obtained from the internet
The authorrsquos background for writing this book consists of a career in laboratory experi-mentation at university level to study and model the behavior of soils More specifically he received an MS degree in 1967 from the Technical University of Denmark for which he wrote a thesis on the influence of the intermedi-ate principal stress on the strength of sand and in retrospect ended up with the wrong conclu-sion on the basis of perfectly correct results He received a PhD from the University of California at Berkeley in 1972 with a dissertation on ldquoThe StressndashStrain and Strength Characteristics of Cohesionless Soilsrdquo which included results
from triaxial compression tests true triaxial tests and torsion shear tests to indicate the effects of the intermediate principal stress on sand behavior as well as a three‐dimensional elasto‐plastic constitutive model for the behavior of soils
With his students the author developed testing equipment performed experiments and built constitutive models for the observed soil behavior while a professor at the University of California at Los Angeles (UCLA) (1972ndash1993) Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015) Many of the experimental techniques developed over this range of years are explained in the present book
Great appreciation is expressed to John F Peters of the US Army Engineer Research and Development Center in Vicksburg MS for his careful review of the manuscript and for his many comments Special thanks go to Afshin Nabili for his invaluable assistance with drafting a large number of the figures and for modifica-tion of other diagrams for the book
Poul V Lade October 2015
References
Bishop AW and Henkel DJ (1957) Measurement of Soil Properties in Triaxial Test Edward Arnold London
Bishop AW and Henkel DJ (1962) The Measurement of Soil Properties in the Triaxial Test 2nd edn St Martinrsquos Press New York NY
de Boer R (2005) The Engineer and the Scandal Springer Berlin
Donaghe RT Chaney RC and Silver ML (eds) (1988) Advanced Triaxial Testing of Soil and Rock ASTM STP 977 ASTM Philadelphia PA
Head KH (1986) Manual of Soil Laboratory Testing ndash Volume 3 Effective Stress Tests Pentech Press London
von Kārmān T (1910) Magyar Meacuternoumlk eacutes Ėpiteacuteszegylet Koumlzloumlnye 10 212ndash226
B
b
c
aD1
D2
Figure P1 Triaxial apparatus designed and con-structed for testing of rock cores by von Kārmān (1910 1911)
Preface xv
von Kārmān T (1911) Verhandlungen Deutsche Ingenieur 55 1749ndash1757
Skempton AW (1960) Terzaghirsquos discovery of effec-tive stress In From Theory to Practice in Soil Mechanics (eds L Bjerrum A Casagrande RB Peck and AW Skempton) pp 42ndash53 John Wiley and Sons Ltd London
Terzaghi K and Rendulic L (1934) Die wirksame Flaumlchenporositaumlt des Betons Zeitschrift des Ōsterreichischen Ingenieur‐ und Architekten Vereines 86 1ndash9
Vaacutesaacuterhelyi B (2010) Tribute to the first triaxial test performed in 1910 Acta Geology and Geophysics of Hungary 45(2) 227ndash230
About the Author
Poul V Lade received his MS degree from the Technical University of Denmark in 1967 and he continued his studies at the University of California at Berkeley where he received his PhD in 1972 Subsequently his academic career began at the University of California at Los Angeles (UCLA) and he continued at Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015)
His research interests include application of appropriate experimental methods to determine the three‐dimensional stressndashstrain and strength behavior of soils and the development of consti-tutive models for frictional materials such as soils concrete and rock He developed laboratory experimental apparatus to investigate monotonic loading and large three‐dimensional stress rever-
sals in plane strain true triaxial and torsion shear equipment This also included studies of effects of principal stress rotation stability instability and liquefaction of granular materials and time effects The constitutive models are based on elasticity and work‐hardening isotropic and kinematic plasticity theories
He has written nearly 300 publications based on research performed with support from the National Science Foundation (NSF) and from the Air Force Office of Scientific Research (AFOSR) He was elected member of the Danish Academy of Technical Sciences (2001) and he was awarded Professor Ostenfeldrsquos Gold Medal from the Technical University of Denmark (2001) He was inaugural editor of Geomechanics and Engineering and he has served on the editorial boards of eight international journals on geotechnical engineering
Triaxial Testing of Soils First Edition Poul V Lade copy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd
Principles of Triaxial Testing1
11 Purpose of triaxial tests
The purpose of performing triaxial tests is to determine the mechanical properties of the soil It is assumed that the soil specimens to be tested are homogeneous and representative of the material in the field and that the desired soil properties can in fact be obtained from the triaxial tests either directly or by interpretation through some theory
The mechanical properties most often sought from triaxial tests are stressndashstrain relations volshyume change or pore pressure behavior and shear strength of the soil Included in the stressndashstrain behavior are also the compressibility and the value of the coefficient of earth pressure at rest K0 Other properties that may be obtained from the triaxial tests which include time as a component are the permeability the coefficient of consolidation and properties relating to time dependent behavior such as rate effects creep and stress relaxation
It is important that the natural soil deposit or the fill from which soil samples have been taken in the field are sufficiently uniform that the soil samples possess the properties which are approshypriate and representative of the soil mass in the field It is therefore paramount that the geology at the site is well‐known and understood Even then samples from uniform deposits may not
ldquocontainrdquo properties that are representative of the field deposit This may happen either (a) due to the change in effective stress state which is always associated with the sampling process or (b) due to mechanical disturbance from sampling transshyportation or handling in the laboratory The stressndashstrain and strength properties of very senshysitive clays which have been disturbed cannot be regenerated in the lab oratory or otherwise obtained by interpretation of tests performed on inadequate specimens The effects of sampling will briefly be discussed below in connection with choice of consolidation pressure in the trishyaxial test The topic of sampling is otherwise outshyside the scope of the present treatment
12 Concept of testing
The concept to be pursued in testing of soils is to simulate as closely as possible the process that goes on in the field Because there is a large number of variables (eg density water content degree of saturation overconsolidation ratio loading conditions stress paths) that influence the resulting soil behavior the simplest and most direct way of obtaining information pertinent to the field conditions is to duplicate these as closely as possible
2 Triaxial Testing of Soils
However because of limitations in equipment and because of practical limitations on the amount of testing that can be performed for each project it is essential that
1 The true field loading conditions (including the drainage conditions) are known
2 The laboratory equipment can reproduce these conditions to a required degree of accuracy
3 A reasonable estimate can be made of the sigshynificance of the differences between the field loading conditions and those that can be proshyduced in the laboratory equipment
It is clear that the triaxial test in many resshypects is incapable of simulating several imporshytant aspects of field loading conditions For example the effects of the intermediate princishypal stress the effects of rotation of principal stresses and the effects of partial drainage durshying loading in the field cannot be investigated on the basis of the triaxial test The effects of such conditions require studies involving other types of equipment or analyses of boundary value problems either by closed form solutions or solutions obtained by numerical techniques
To provide some background for evaluation of the results of triaxial tests other types of laboratory shear tests and typical results from such tests are presented in Chapter 11 The relashytions between the different types of tests are reviewed and their advantages and limitations are discussed
13 The triaxial test
The triaxial test is most often performed on a cylindrical specimen as shown in Fig 11(a) Principal stresses are applied to the specimen as indicated in Fig 11(b) First a confining pressure σ3 is applied to the specimen This pressure acts all around and therefore on all planes in the specimen Then an additional stress difference σd is applied in the axial direction The stress applied externally to the specimen in the axial direction is
σ σ σ1 3= +d (11)
and therefore
σ σ σd = minus1 3 (12)
In the general case three principal stresses σ1 σ2 and σ3 may act on a soil element in the field However only two different principal stresses can be applied to the specimen in the convenshytional triaxial test The intermediate principal stress σ2 can only have values as follows
σ σ2 3= Triaxial compression (13)
σ σ2 1= Triaxial extension (14)
The condition of triaxial extension can be achieved by applying negative stress differshyences to the specimen This merely produces a reduction in compression in the extension direcshytion but no tension occurs in the specimen The state of stress applied to the specimen is in both cases axisymmetric The triaxial compression test will be discussed in the following while the triaxial extension test is discussed in Chapter 10
The test is performed using triaxial apparashytus as seen in the schematic illustration in Fig 12 The specimen is surrounded by a cap and a base and a membrane This unit is placed in a triaxial cell in which the cell pressure can be applied The cell pressure acts as a hydrostatic confinement for the specimen and the pressure is therefore the same in all directions In addition
σ1
(a) (b)
σ1 = σd + σ3
σ2 = σ3
σd = σ1 ndash σ3σ3
σ3σ3
σ3
σd
Figure 11 (a) Cylindrical specimen for triaxial testing and (b) stresses applied to a triaxial specimen
Principles of Triaxial Testing 3
a deviator load can be applied through a piston that goes through the top of the cell and loads the specimen in the axial direction
The vertical deformation of the specimen may be measured by a dial gage attached to the piston which travels the same vertical distance as the cap sitting on top of the specimen Drainage lines are connected to the water saturated specishymen through the base (or both the cap and the base) and connected to a burette outside the trishyaxial cell This allows for measurements of the volume changes of the specimen during the test
Alternatively the connection to the burette can be shut off thereby preventing the specimen from changing volume Instead the pore water pressure can be measured on a transducer conshynected to the drainage line
The following quantities are measured in a typical triaxial test
1 Confining pressure2 Deviator load3 Vertical (or axial) deformation4 Volume change or pore water pressure
These measurements constitute the data base from which other quantities can be derived
[eg stress difference (σ1 ndash σ3) axial strain ε1 and volumetric strain εv]
14 Advantages and limitations
Whereas the triaxial test potentially can proshyvide a substantial proportion of the mechanical properties required for a project it has limitashytions especially when special conditions are encountered and necessitates clarification based on experimentation
The advantages of the triaxial test are
1 Drainage can be controlled (onndashoff)2 Volume change or pore pressure can be
measured3 Suction can be controlled in partially satushy
rated soils4 Measured deformations allow calculation of
strains and moduli5 A larger variety of stress and strain paths
that occur in the field can be applied in the triaxial apparatus than in any other testing apparatus (eg initial anisotropic consolidashytion at any stress ratio including K0 extension active and passive shear)
The limitations of the triaxial test are
1 Stress concentrations due to friction between specimen and end plates (cap and base) cause nonuniform strains and stresses and therefore nonuniform stressndashstrain volume change or pore pressure response
2 Only axisymmetric stress conditions can be applied to the specimen whereas most field problems involve plane strain or general three‐dimensional conditions with rotation of principal stresses
3 Triaxial tests cannot provide all necessary data required to characterize the behavior of an anisotropic or a cross‐anisotropic soil deposit as illustrated in Fig 13
4 Although the axisymmetric principal stress condition is limited it is more difficult to apply proper shear stresses or tension to soil in relatively simple tests
The first limitation listed above can be overcome by applying lubricated ends on the
Pore pressure transducer
On-Off valve
Burette
Piston
Dial gage
Triaxial cell
P = σd middot A
Aprime
σcell
σ3
σ3 σ3= σcell
Figure 12 Schematic diagram of triaxial apparatus
4 Triaxial Testing of Soils
specimen such that uniform strains and stresses and therefore correct soil response can be proshyduced This is discussed in Chapter 3 In addishytion to the limitations listed above it should be mentioned that it may be easier to reproduce certain stress paths in other specialty equipment than in the triaxial apparatus (eg K0‐test)
Although the triaxial test is limited as explained under points 2 and 3 above it does combine versatility with relative simplicity in concept and performance Other equipment in which three unequal principal stresses can be applied or in which the principal stress direcshytions can be rotated do not have the versatility or is more com plicated to operate Thus other types of equipment have their own advantages and limitations These other equipment types
include plane strain true triaxial simple shear directional shear and torsion shear apparatus All these pieces of equipment are with the excepshytion of the simple shear apparatus employed mainly for research purposes Their operational modes capabilities and results are reviewed in Chapter 11
15 Test stages ndash consolidation and shearing
Laboratory tests are made to simulate field loadshying conditions as close as possible Most field conditions and the corresponding tests can be simplified to consist of two stages consolidation and shearing
Axis of symmetry
1Eh
1Eh
1Ghv
1Ev
ndashmicrohvEh
ndashmicrohvEn
2(1 + microhh)En
ndashmicrohhEn
ndashmicrohvEh
ndashmicrohvEh
ndashmicrohhEh
0
h
h
v
0 0
σh
σh
σv
τhv
τhv
τvh
τvh
σh
σv
σh
τhv
τvh
τhh
τhh τhh
ϵh
ϵv
ϵh
γhv
γvh
γhh
0
Require tests withapplication of
shear stresses
0 0
0
0 0 0 00
1Ghv0 0 0 00
0 0 0 0 0
0 0
bull =
Figure 13 Cross‐anisotropic soil requiring results from more than triaxial tests for full characterization
Principles of Triaxial Testing 5
151 Consolidation
In the first stage the initial condition of the soil is established in terms of effective stresses and stress history (including overconsolidation if applicable) Thus stresses are applied correshysponding to those acting on the element of soil in the field due to weight of the overlying soil strata and other materials or structures that exist at the time the mechanical properties (stressndashstrain strength etc) are sought Sufficient time is allowed for complete consolidation to occur under the applied stresses The condition in the field element has now been established in the triaxial specimen
152 Shearing
In the second stage of the triaxial test an addishytional stress is applied to reach peak failure and beyond under relevant drainage conditions The additional stress applied to the specimen should correspond as closely as possible to the change in stress on the field element due to some new change in the overall field loading situashytion This change may consist of a vertical stress increase or decrease (eg due to addition of a structure or excavation of overlying soil strata) or of a horizontal stress increase or decrease (eg due to the same constructions causing the vertical stress changes) Any combination of vertical and horizontal stress changes may be simulated in the triaxial test Examples of vertishycal and horizontal stress changes in the field are shown in Fig 14
Usually it is desirable to know how much change in load the soil can sustain without failshying and how much deformation will occur under normal working conditions The test is therefore usually continued to find the strength of the soil under the appropriate loading condishytions The results are used with an appropriate factor of safety so that normal working stresses are always somewhat below the peak strength
The stressndashstrain relations obtained from the triaxial tests provide the basis for determinashytion of deformations in the field This may be done in a simplified manner by closed‐form
solutions or it may be done by employing the results of the triaxial tests for calibration of a constitutive model used with a numerical method in finite element or finite difference computer programs
16 Types of tests
The drainage conditions in the field must be duplicated as well as possible in the laboratory tests This may be done by appropriate drainage facilities or preventions as discussed above for the triaxial test In most cases the field drainage conditions can be approximated by one of the following three types of tests
1 Consolidated‐drained test called a CD‐test or just a drained test
2 Consolidated‐undrained test or a CU‐test3 Unconsolidated‐undrained test or a UU‐test
Additionalload
Excavation
ΔσV asymp 0
ΔσV asymp 0
ΔσV gt 0
ΔσV lt 0
Δσh lt 0
Δσh gt 0
Δσh lt ΔσV
Δσh
Figure 14 Examples of stress changes leading to failure in the field
6 Triaxial Testing of Soils
These tests are described in ASTM Standards D7181 (2014) D4767 (2014) and D2850 (2014) respectively
Which condition of drainage in the laboratory test logically corresponds to each case in the field depends on a comparison of loading rate with the rate at which the water can escape or be sucked into the ground Thus the permeability of the soil and the drainage boundary conditions in the field together with the loading rate play key roles in determination of the type of analysis and the type of test drained or undrained that are appropriate for each case Field cases with partial drainage can be correctly duplicated in laboratory tests if the effective stress path is determined for the design condition However the idea of the CD‐ CU‐ and UU‐tests is to make it relatively simple for the design engineer to analyze a condition that will render a sufficient factor of safety under the actual drainage condishytion without trying to estimate and experimenshytally replicate the actual stress path
It has been determined through experience and common sense that the extreme conditions are drained and undrained with and without consolidation As a practical matter in a commershycial laboratory it is easier to run an undrained test than a drained test because it is easier and faster to measure pore pressures than volume change Therefore even drained parameters are more likely to be estimated from a CU‐test than from a CD‐test
161 Simulation of field conditions
Presented below is a brief review of the three types of tests together with examples of field cases for which the tests are appropriate and with typishycal strength results shown on Mohr diagrams
Drained tests
Isotropic consolidation is most often used in the first stage of the triaxial test However anisoshytropic consolidation with any stress ratio is also possible
The shearing stage of a drained test is pershyformed so slowly the soil is so permeable and the drainage facilities are such that no excess
pore pressure (positive or negative) can exist in the specimen at any stage of the test that is
∆u = 0 (15)
It follows then from the effective stress principle
prime = minusσ σ u (16)
that the effective stress changes are always the same as the total stress changes
A soil specimen always changes volume during shearing in a drained test If it contracts in volume it expels pore fluid (usually water or air) and if it expands in volume (dilates) then it sucks water or air into the pores If a non‐zero pore pressure is generated during the test (eg by performing the shearing too fast so the water does not have sufficient time to escape) then the specimen will expel or suck water such that the pore pressure goes towards zero to try to achieve equilibrium between externally applied stresses and internal effective stresses Thus there will always be volume changes in a drained test Consequently the water content the void ratio and the dry density of the specimen at the end of the test are most often not the same as at the beginning
The following field conditions can be simushylated with acceptable accuracy in the drained test
1 Almost all cases involving coarse sands and gravel whether saturated or not (except if confined in eg a lens andor exposed to rapid loading as in eg an earthquake)
2 Many cases involving fine sand and someshytimes silt if the field loads are applied reashysonable slowly
3 Long term loading of any soil as for examplea) Cut slopes several years after excavationb) Embankment constructed very slowly in
layers over a soft clay depositc) Earth dam with steady seepaged) Foundation on clay a long time after
construction
These cases are illustrated in Fig 15The strength results obtained from drained
tests are illustrated schematically on the Mohr diagram in Fig 16 The shear strength of soils increases with increasing confining pressure
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
xiv Preface
tests with three unequal principal stresses Appendices are provided to explain special experimental techniques Information on ven-dors for the various types of equipment may be obtained from the internet
The authorrsquos background for writing this book consists of a career in laboratory experi-mentation at university level to study and model the behavior of soils More specifically he received an MS degree in 1967 from the Technical University of Denmark for which he wrote a thesis on the influence of the intermedi-ate principal stress on the strength of sand and in retrospect ended up with the wrong conclu-sion on the basis of perfectly correct results He received a PhD from the University of California at Berkeley in 1972 with a dissertation on ldquoThe StressndashStrain and Strength Characteristics of Cohesionless Soilsrdquo which included results
from triaxial compression tests true triaxial tests and torsion shear tests to indicate the effects of the intermediate principal stress on sand behavior as well as a three‐dimensional elasto‐plastic constitutive model for the behavior of soils
With his students the author developed testing equipment performed experiments and built constitutive models for the observed soil behavior while a professor at the University of California at Los Angeles (UCLA) (1972ndash1993) Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015) Many of the experimental techniques developed over this range of years are explained in the present book
Great appreciation is expressed to John F Peters of the US Army Engineer Research and Development Center in Vicksburg MS for his careful review of the manuscript and for his many comments Special thanks go to Afshin Nabili for his invaluable assistance with drafting a large number of the figures and for modifica-tion of other diagrams for the book
Poul V Lade October 2015
References
Bishop AW and Henkel DJ (1957) Measurement of Soil Properties in Triaxial Test Edward Arnold London
Bishop AW and Henkel DJ (1962) The Measurement of Soil Properties in the Triaxial Test 2nd edn St Martinrsquos Press New York NY
de Boer R (2005) The Engineer and the Scandal Springer Berlin
Donaghe RT Chaney RC and Silver ML (eds) (1988) Advanced Triaxial Testing of Soil and Rock ASTM STP 977 ASTM Philadelphia PA
Head KH (1986) Manual of Soil Laboratory Testing ndash Volume 3 Effective Stress Tests Pentech Press London
von Kārmān T (1910) Magyar Meacuternoumlk eacutes Ėpiteacuteszegylet Koumlzloumlnye 10 212ndash226
B
b
c
aD1
D2
Figure P1 Triaxial apparatus designed and con-structed for testing of rock cores by von Kārmān (1910 1911)
Preface xv
von Kārmān T (1911) Verhandlungen Deutsche Ingenieur 55 1749ndash1757
Skempton AW (1960) Terzaghirsquos discovery of effec-tive stress In From Theory to Practice in Soil Mechanics (eds L Bjerrum A Casagrande RB Peck and AW Skempton) pp 42ndash53 John Wiley and Sons Ltd London
Terzaghi K and Rendulic L (1934) Die wirksame Flaumlchenporositaumlt des Betons Zeitschrift des Ōsterreichischen Ingenieur‐ und Architekten Vereines 86 1ndash9
Vaacutesaacuterhelyi B (2010) Tribute to the first triaxial test performed in 1910 Acta Geology and Geophysics of Hungary 45(2) 227ndash230
About the Author
Poul V Lade received his MS degree from the Technical University of Denmark in 1967 and he continued his studies at the University of California at Berkeley where he received his PhD in 1972 Subsequently his academic career began at the University of California at Los Angeles (UCLA) and he continued at Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015)
His research interests include application of appropriate experimental methods to determine the three‐dimensional stressndashstrain and strength behavior of soils and the development of consti-tutive models for frictional materials such as soils concrete and rock He developed laboratory experimental apparatus to investigate monotonic loading and large three‐dimensional stress rever-
sals in plane strain true triaxial and torsion shear equipment This also included studies of effects of principal stress rotation stability instability and liquefaction of granular materials and time effects The constitutive models are based on elasticity and work‐hardening isotropic and kinematic plasticity theories
He has written nearly 300 publications based on research performed with support from the National Science Foundation (NSF) and from the Air Force Office of Scientific Research (AFOSR) He was elected member of the Danish Academy of Technical Sciences (2001) and he was awarded Professor Ostenfeldrsquos Gold Medal from the Technical University of Denmark (2001) He was inaugural editor of Geomechanics and Engineering and he has served on the editorial boards of eight international journals on geotechnical engineering
Triaxial Testing of Soils First Edition Poul V Lade copy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd
Principles of Triaxial Testing1
11 Purpose of triaxial tests
The purpose of performing triaxial tests is to determine the mechanical properties of the soil It is assumed that the soil specimens to be tested are homogeneous and representative of the material in the field and that the desired soil properties can in fact be obtained from the triaxial tests either directly or by interpretation through some theory
The mechanical properties most often sought from triaxial tests are stressndashstrain relations volshyume change or pore pressure behavior and shear strength of the soil Included in the stressndashstrain behavior are also the compressibility and the value of the coefficient of earth pressure at rest K0 Other properties that may be obtained from the triaxial tests which include time as a component are the permeability the coefficient of consolidation and properties relating to time dependent behavior such as rate effects creep and stress relaxation
It is important that the natural soil deposit or the fill from which soil samples have been taken in the field are sufficiently uniform that the soil samples possess the properties which are approshypriate and representative of the soil mass in the field It is therefore paramount that the geology at the site is well‐known and understood Even then samples from uniform deposits may not
ldquocontainrdquo properties that are representative of the field deposit This may happen either (a) due to the change in effective stress state which is always associated with the sampling process or (b) due to mechanical disturbance from sampling transshyportation or handling in the laboratory The stressndashstrain and strength properties of very senshysitive clays which have been disturbed cannot be regenerated in the lab oratory or otherwise obtained by interpretation of tests performed on inadequate specimens The effects of sampling will briefly be discussed below in connection with choice of consolidation pressure in the trishyaxial test The topic of sampling is otherwise outshyside the scope of the present treatment
12 Concept of testing
The concept to be pursued in testing of soils is to simulate as closely as possible the process that goes on in the field Because there is a large number of variables (eg density water content degree of saturation overconsolidation ratio loading conditions stress paths) that influence the resulting soil behavior the simplest and most direct way of obtaining information pertinent to the field conditions is to duplicate these as closely as possible
2 Triaxial Testing of Soils
However because of limitations in equipment and because of practical limitations on the amount of testing that can be performed for each project it is essential that
1 The true field loading conditions (including the drainage conditions) are known
2 The laboratory equipment can reproduce these conditions to a required degree of accuracy
3 A reasonable estimate can be made of the sigshynificance of the differences between the field loading conditions and those that can be proshyduced in the laboratory equipment
It is clear that the triaxial test in many resshypects is incapable of simulating several imporshytant aspects of field loading conditions For example the effects of the intermediate princishypal stress the effects of rotation of principal stresses and the effects of partial drainage durshying loading in the field cannot be investigated on the basis of the triaxial test The effects of such conditions require studies involving other types of equipment or analyses of boundary value problems either by closed form solutions or solutions obtained by numerical techniques
To provide some background for evaluation of the results of triaxial tests other types of laboratory shear tests and typical results from such tests are presented in Chapter 11 The relashytions between the different types of tests are reviewed and their advantages and limitations are discussed
13 The triaxial test
The triaxial test is most often performed on a cylindrical specimen as shown in Fig 11(a) Principal stresses are applied to the specimen as indicated in Fig 11(b) First a confining pressure σ3 is applied to the specimen This pressure acts all around and therefore on all planes in the specimen Then an additional stress difference σd is applied in the axial direction The stress applied externally to the specimen in the axial direction is
σ σ σ1 3= +d (11)
and therefore
σ σ σd = minus1 3 (12)
In the general case three principal stresses σ1 σ2 and σ3 may act on a soil element in the field However only two different principal stresses can be applied to the specimen in the convenshytional triaxial test The intermediate principal stress σ2 can only have values as follows
σ σ2 3= Triaxial compression (13)
σ σ2 1= Triaxial extension (14)
The condition of triaxial extension can be achieved by applying negative stress differshyences to the specimen This merely produces a reduction in compression in the extension direcshytion but no tension occurs in the specimen The state of stress applied to the specimen is in both cases axisymmetric The triaxial compression test will be discussed in the following while the triaxial extension test is discussed in Chapter 10
The test is performed using triaxial apparashytus as seen in the schematic illustration in Fig 12 The specimen is surrounded by a cap and a base and a membrane This unit is placed in a triaxial cell in which the cell pressure can be applied The cell pressure acts as a hydrostatic confinement for the specimen and the pressure is therefore the same in all directions In addition
σ1
(a) (b)
σ1 = σd + σ3
σ2 = σ3
σd = σ1 ndash σ3σ3
σ3σ3
σ3
σd
Figure 11 (a) Cylindrical specimen for triaxial testing and (b) stresses applied to a triaxial specimen
Principles of Triaxial Testing 3
a deviator load can be applied through a piston that goes through the top of the cell and loads the specimen in the axial direction
The vertical deformation of the specimen may be measured by a dial gage attached to the piston which travels the same vertical distance as the cap sitting on top of the specimen Drainage lines are connected to the water saturated specishymen through the base (or both the cap and the base) and connected to a burette outside the trishyaxial cell This allows for measurements of the volume changes of the specimen during the test
Alternatively the connection to the burette can be shut off thereby preventing the specimen from changing volume Instead the pore water pressure can be measured on a transducer conshynected to the drainage line
The following quantities are measured in a typical triaxial test
1 Confining pressure2 Deviator load3 Vertical (or axial) deformation4 Volume change or pore water pressure
These measurements constitute the data base from which other quantities can be derived
[eg stress difference (σ1 ndash σ3) axial strain ε1 and volumetric strain εv]
14 Advantages and limitations
Whereas the triaxial test potentially can proshyvide a substantial proportion of the mechanical properties required for a project it has limitashytions especially when special conditions are encountered and necessitates clarification based on experimentation
The advantages of the triaxial test are
1 Drainage can be controlled (onndashoff)2 Volume change or pore pressure can be
measured3 Suction can be controlled in partially satushy
rated soils4 Measured deformations allow calculation of
strains and moduli5 A larger variety of stress and strain paths
that occur in the field can be applied in the triaxial apparatus than in any other testing apparatus (eg initial anisotropic consolidashytion at any stress ratio including K0 extension active and passive shear)
The limitations of the triaxial test are
1 Stress concentrations due to friction between specimen and end plates (cap and base) cause nonuniform strains and stresses and therefore nonuniform stressndashstrain volume change or pore pressure response
2 Only axisymmetric stress conditions can be applied to the specimen whereas most field problems involve plane strain or general three‐dimensional conditions with rotation of principal stresses
3 Triaxial tests cannot provide all necessary data required to characterize the behavior of an anisotropic or a cross‐anisotropic soil deposit as illustrated in Fig 13
4 Although the axisymmetric principal stress condition is limited it is more difficult to apply proper shear stresses or tension to soil in relatively simple tests
The first limitation listed above can be overcome by applying lubricated ends on the
Pore pressure transducer
On-Off valve
Burette
Piston
Dial gage
Triaxial cell
P = σd middot A
Aprime
σcell
σ3
σ3 σ3= σcell
Figure 12 Schematic diagram of triaxial apparatus
4 Triaxial Testing of Soils
specimen such that uniform strains and stresses and therefore correct soil response can be proshyduced This is discussed in Chapter 3 In addishytion to the limitations listed above it should be mentioned that it may be easier to reproduce certain stress paths in other specialty equipment than in the triaxial apparatus (eg K0‐test)
Although the triaxial test is limited as explained under points 2 and 3 above it does combine versatility with relative simplicity in concept and performance Other equipment in which three unequal principal stresses can be applied or in which the principal stress direcshytions can be rotated do not have the versatility or is more com plicated to operate Thus other types of equipment have their own advantages and limitations These other equipment types
include plane strain true triaxial simple shear directional shear and torsion shear apparatus All these pieces of equipment are with the excepshytion of the simple shear apparatus employed mainly for research purposes Their operational modes capabilities and results are reviewed in Chapter 11
15 Test stages ndash consolidation and shearing
Laboratory tests are made to simulate field loadshying conditions as close as possible Most field conditions and the corresponding tests can be simplified to consist of two stages consolidation and shearing
Axis of symmetry
1Eh
1Eh
1Ghv
1Ev
ndashmicrohvEh
ndashmicrohvEn
2(1 + microhh)En
ndashmicrohhEn
ndashmicrohvEh
ndashmicrohvEh
ndashmicrohhEh
0
h
h
v
0 0
σh
σh
σv
τhv
τhv
τvh
τvh
σh
σv
σh
τhv
τvh
τhh
τhh τhh
ϵh
ϵv
ϵh
γhv
γvh
γhh
0
Require tests withapplication of
shear stresses
0 0
0
0 0 0 00
1Ghv0 0 0 00
0 0 0 0 0
0 0
bull =
Figure 13 Cross‐anisotropic soil requiring results from more than triaxial tests for full characterization
Principles of Triaxial Testing 5
151 Consolidation
In the first stage the initial condition of the soil is established in terms of effective stresses and stress history (including overconsolidation if applicable) Thus stresses are applied correshysponding to those acting on the element of soil in the field due to weight of the overlying soil strata and other materials or structures that exist at the time the mechanical properties (stressndashstrain strength etc) are sought Sufficient time is allowed for complete consolidation to occur under the applied stresses The condition in the field element has now been established in the triaxial specimen
152 Shearing
In the second stage of the triaxial test an addishytional stress is applied to reach peak failure and beyond under relevant drainage conditions The additional stress applied to the specimen should correspond as closely as possible to the change in stress on the field element due to some new change in the overall field loading situashytion This change may consist of a vertical stress increase or decrease (eg due to addition of a structure or excavation of overlying soil strata) or of a horizontal stress increase or decrease (eg due to the same constructions causing the vertical stress changes) Any combination of vertical and horizontal stress changes may be simulated in the triaxial test Examples of vertishycal and horizontal stress changes in the field are shown in Fig 14
Usually it is desirable to know how much change in load the soil can sustain without failshying and how much deformation will occur under normal working conditions The test is therefore usually continued to find the strength of the soil under the appropriate loading condishytions The results are used with an appropriate factor of safety so that normal working stresses are always somewhat below the peak strength
The stressndashstrain relations obtained from the triaxial tests provide the basis for determinashytion of deformations in the field This may be done in a simplified manner by closed‐form
solutions or it may be done by employing the results of the triaxial tests for calibration of a constitutive model used with a numerical method in finite element or finite difference computer programs
16 Types of tests
The drainage conditions in the field must be duplicated as well as possible in the laboratory tests This may be done by appropriate drainage facilities or preventions as discussed above for the triaxial test In most cases the field drainage conditions can be approximated by one of the following three types of tests
1 Consolidated‐drained test called a CD‐test or just a drained test
2 Consolidated‐undrained test or a CU‐test3 Unconsolidated‐undrained test or a UU‐test
Additionalload
Excavation
ΔσV asymp 0
ΔσV asymp 0
ΔσV gt 0
ΔσV lt 0
Δσh lt 0
Δσh gt 0
Δσh lt ΔσV
Δσh
Figure 14 Examples of stress changes leading to failure in the field
6 Triaxial Testing of Soils
These tests are described in ASTM Standards D7181 (2014) D4767 (2014) and D2850 (2014) respectively
Which condition of drainage in the laboratory test logically corresponds to each case in the field depends on a comparison of loading rate with the rate at which the water can escape or be sucked into the ground Thus the permeability of the soil and the drainage boundary conditions in the field together with the loading rate play key roles in determination of the type of analysis and the type of test drained or undrained that are appropriate for each case Field cases with partial drainage can be correctly duplicated in laboratory tests if the effective stress path is determined for the design condition However the idea of the CD‐ CU‐ and UU‐tests is to make it relatively simple for the design engineer to analyze a condition that will render a sufficient factor of safety under the actual drainage condishytion without trying to estimate and experimenshytally replicate the actual stress path
It has been determined through experience and common sense that the extreme conditions are drained and undrained with and without consolidation As a practical matter in a commershycial laboratory it is easier to run an undrained test than a drained test because it is easier and faster to measure pore pressures than volume change Therefore even drained parameters are more likely to be estimated from a CU‐test than from a CD‐test
161 Simulation of field conditions
Presented below is a brief review of the three types of tests together with examples of field cases for which the tests are appropriate and with typishycal strength results shown on Mohr diagrams
Drained tests
Isotropic consolidation is most often used in the first stage of the triaxial test However anisoshytropic consolidation with any stress ratio is also possible
The shearing stage of a drained test is pershyformed so slowly the soil is so permeable and the drainage facilities are such that no excess
pore pressure (positive or negative) can exist in the specimen at any stage of the test that is
∆u = 0 (15)
It follows then from the effective stress principle
prime = minusσ σ u (16)
that the effective stress changes are always the same as the total stress changes
A soil specimen always changes volume during shearing in a drained test If it contracts in volume it expels pore fluid (usually water or air) and if it expands in volume (dilates) then it sucks water or air into the pores If a non‐zero pore pressure is generated during the test (eg by performing the shearing too fast so the water does not have sufficient time to escape) then the specimen will expel or suck water such that the pore pressure goes towards zero to try to achieve equilibrium between externally applied stresses and internal effective stresses Thus there will always be volume changes in a drained test Consequently the water content the void ratio and the dry density of the specimen at the end of the test are most often not the same as at the beginning
The following field conditions can be simushylated with acceptable accuracy in the drained test
1 Almost all cases involving coarse sands and gravel whether saturated or not (except if confined in eg a lens andor exposed to rapid loading as in eg an earthquake)
2 Many cases involving fine sand and someshytimes silt if the field loads are applied reashysonable slowly
3 Long term loading of any soil as for examplea) Cut slopes several years after excavationb) Embankment constructed very slowly in
layers over a soft clay depositc) Earth dam with steady seepaged) Foundation on clay a long time after
construction
These cases are illustrated in Fig 15The strength results obtained from drained
tests are illustrated schematically on the Mohr diagram in Fig 16 The shear strength of soils increases with increasing confining pressure
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
Preface xv
von Kārmān T (1911) Verhandlungen Deutsche Ingenieur 55 1749ndash1757
Skempton AW (1960) Terzaghirsquos discovery of effec-tive stress In From Theory to Practice in Soil Mechanics (eds L Bjerrum A Casagrande RB Peck and AW Skempton) pp 42ndash53 John Wiley and Sons Ltd London
Terzaghi K and Rendulic L (1934) Die wirksame Flaumlchenporositaumlt des Betons Zeitschrift des Ōsterreichischen Ingenieur‐ und Architekten Vereines 86 1ndash9
Vaacutesaacuterhelyi B (2010) Tribute to the first triaxial test performed in 1910 Acta Geology and Geophysics of Hungary 45(2) 227ndash230
About the Author
Poul V Lade received his MS degree from the Technical University of Denmark in 1967 and he continued his studies at the University of California at Berkeley where he received his PhD in 1972 Subsequently his academic career began at the University of California at Los Angeles (UCLA) and he continued at Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015)
His research interests include application of appropriate experimental methods to determine the three‐dimensional stressndashstrain and strength behavior of soils and the development of consti-tutive models for frictional materials such as soils concrete and rock He developed laboratory experimental apparatus to investigate monotonic loading and large three‐dimensional stress rever-
sals in plane strain true triaxial and torsion shear equipment This also included studies of effects of principal stress rotation stability instability and liquefaction of granular materials and time effects The constitutive models are based on elasticity and work‐hardening isotropic and kinematic plasticity theories
He has written nearly 300 publications based on research performed with support from the National Science Foundation (NSF) and from the Air Force Office of Scientific Research (AFOSR) He was elected member of the Danish Academy of Technical Sciences (2001) and he was awarded Professor Ostenfeldrsquos Gold Medal from the Technical University of Denmark (2001) He was inaugural editor of Geomechanics and Engineering and he has served on the editorial boards of eight international journals on geotechnical engineering
Triaxial Testing of Soils First Edition Poul V Lade copy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd
Principles of Triaxial Testing1
11 Purpose of triaxial tests
The purpose of performing triaxial tests is to determine the mechanical properties of the soil It is assumed that the soil specimens to be tested are homogeneous and representative of the material in the field and that the desired soil properties can in fact be obtained from the triaxial tests either directly or by interpretation through some theory
The mechanical properties most often sought from triaxial tests are stressndashstrain relations volshyume change or pore pressure behavior and shear strength of the soil Included in the stressndashstrain behavior are also the compressibility and the value of the coefficient of earth pressure at rest K0 Other properties that may be obtained from the triaxial tests which include time as a component are the permeability the coefficient of consolidation and properties relating to time dependent behavior such as rate effects creep and stress relaxation
It is important that the natural soil deposit or the fill from which soil samples have been taken in the field are sufficiently uniform that the soil samples possess the properties which are approshypriate and representative of the soil mass in the field It is therefore paramount that the geology at the site is well‐known and understood Even then samples from uniform deposits may not
ldquocontainrdquo properties that are representative of the field deposit This may happen either (a) due to the change in effective stress state which is always associated with the sampling process or (b) due to mechanical disturbance from sampling transshyportation or handling in the laboratory The stressndashstrain and strength properties of very senshysitive clays which have been disturbed cannot be regenerated in the lab oratory or otherwise obtained by interpretation of tests performed on inadequate specimens The effects of sampling will briefly be discussed below in connection with choice of consolidation pressure in the trishyaxial test The topic of sampling is otherwise outshyside the scope of the present treatment
12 Concept of testing
The concept to be pursued in testing of soils is to simulate as closely as possible the process that goes on in the field Because there is a large number of variables (eg density water content degree of saturation overconsolidation ratio loading conditions stress paths) that influence the resulting soil behavior the simplest and most direct way of obtaining information pertinent to the field conditions is to duplicate these as closely as possible
2 Triaxial Testing of Soils
However because of limitations in equipment and because of practical limitations on the amount of testing that can be performed for each project it is essential that
1 The true field loading conditions (including the drainage conditions) are known
2 The laboratory equipment can reproduce these conditions to a required degree of accuracy
3 A reasonable estimate can be made of the sigshynificance of the differences between the field loading conditions and those that can be proshyduced in the laboratory equipment
It is clear that the triaxial test in many resshypects is incapable of simulating several imporshytant aspects of field loading conditions For example the effects of the intermediate princishypal stress the effects of rotation of principal stresses and the effects of partial drainage durshying loading in the field cannot be investigated on the basis of the triaxial test The effects of such conditions require studies involving other types of equipment or analyses of boundary value problems either by closed form solutions or solutions obtained by numerical techniques
To provide some background for evaluation of the results of triaxial tests other types of laboratory shear tests and typical results from such tests are presented in Chapter 11 The relashytions between the different types of tests are reviewed and their advantages and limitations are discussed
13 The triaxial test
The triaxial test is most often performed on a cylindrical specimen as shown in Fig 11(a) Principal stresses are applied to the specimen as indicated in Fig 11(b) First a confining pressure σ3 is applied to the specimen This pressure acts all around and therefore on all planes in the specimen Then an additional stress difference σd is applied in the axial direction The stress applied externally to the specimen in the axial direction is
σ σ σ1 3= +d (11)
and therefore
σ σ σd = minus1 3 (12)
In the general case three principal stresses σ1 σ2 and σ3 may act on a soil element in the field However only two different principal stresses can be applied to the specimen in the convenshytional triaxial test The intermediate principal stress σ2 can only have values as follows
σ σ2 3= Triaxial compression (13)
σ σ2 1= Triaxial extension (14)
The condition of triaxial extension can be achieved by applying negative stress differshyences to the specimen This merely produces a reduction in compression in the extension direcshytion but no tension occurs in the specimen The state of stress applied to the specimen is in both cases axisymmetric The triaxial compression test will be discussed in the following while the triaxial extension test is discussed in Chapter 10
The test is performed using triaxial apparashytus as seen in the schematic illustration in Fig 12 The specimen is surrounded by a cap and a base and a membrane This unit is placed in a triaxial cell in which the cell pressure can be applied The cell pressure acts as a hydrostatic confinement for the specimen and the pressure is therefore the same in all directions In addition
σ1
(a) (b)
σ1 = σd + σ3
σ2 = σ3
σd = σ1 ndash σ3σ3
σ3σ3
σ3
σd
Figure 11 (a) Cylindrical specimen for triaxial testing and (b) stresses applied to a triaxial specimen
Principles of Triaxial Testing 3
a deviator load can be applied through a piston that goes through the top of the cell and loads the specimen in the axial direction
The vertical deformation of the specimen may be measured by a dial gage attached to the piston which travels the same vertical distance as the cap sitting on top of the specimen Drainage lines are connected to the water saturated specishymen through the base (or both the cap and the base) and connected to a burette outside the trishyaxial cell This allows for measurements of the volume changes of the specimen during the test
Alternatively the connection to the burette can be shut off thereby preventing the specimen from changing volume Instead the pore water pressure can be measured on a transducer conshynected to the drainage line
The following quantities are measured in a typical triaxial test
1 Confining pressure2 Deviator load3 Vertical (or axial) deformation4 Volume change or pore water pressure
These measurements constitute the data base from which other quantities can be derived
[eg stress difference (σ1 ndash σ3) axial strain ε1 and volumetric strain εv]
14 Advantages and limitations
Whereas the triaxial test potentially can proshyvide a substantial proportion of the mechanical properties required for a project it has limitashytions especially when special conditions are encountered and necessitates clarification based on experimentation
The advantages of the triaxial test are
1 Drainage can be controlled (onndashoff)2 Volume change or pore pressure can be
measured3 Suction can be controlled in partially satushy
rated soils4 Measured deformations allow calculation of
strains and moduli5 A larger variety of stress and strain paths
that occur in the field can be applied in the triaxial apparatus than in any other testing apparatus (eg initial anisotropic consolidashytion at any stress ratio including K0 extension active and passive shear)
The limitations of the triaxial test are
1 Stress concentrations due to friction between specimen and end plates (cap and base) cause nonuniform strains and stresses and therefore nonuniform stressndashstrain volume change or pore pressure response
2 Only axisymmetric stress conditions can be applied to the specimen whereas most field problems involve plane strain or general three‐dimensional conditions with rotation of principal stresses
3 Triaxial tests cannot provide all necessary data required to characterize the behavior of an anisotropic or a cross‐anisotropic soil deposit as illustrated in Fig 13
4 Although the axisymmetric principal stress condition is limited it is more difficult to apply proper shear stresses or tension to soil in relatively simple tests
The first limitation listed above can be overcome by applying lubricated ends on the
Pore pressure transducer
On-Off valve
Burette
Piston
Dial gage
Triaxial cell
P = σd middot A
Aprime
σcell
σ3
σ3 σ3= σcell
Figure 12 Schematic diagram of triaxial apparatus
4 Triaxial Testing of Soils
specimen such that uniform strains and stresses and therefore correct soil response can be proshyduced This is discussed in Chapter 3 In addishytion to the limitations listed above it should be mentioned that it may be easier to reproduce certain stress paths in other specialty equipment than in the triaxial apparatus (eg K0‐test)
Although the triaxial test is limited as explained under points 2 and 3 above it does combine versatility with relative simplicity in concept and performance Other equipment in which three unequal principal stresses can be applied or in which the principal stress direcshytions can be rotated do not have the versatility or is more com plicated to operate Thus other types of equipment have their own advantages and limitations These other equipment types
include plane strain true triaxial simple shear directional shear and torsion shear apparatus All these pieces of equipment are with the excepshytion of the simple shear apparatus employed mainly for research purposes Their operational modes capabilities and results are reviewed in Chapter 11
15 Test stages ndash consolidation and shearing
Laboratory tests are made to simulate field loadshying conditions as close as possible Most field conditions and the corresponding tests can be simplified to consist of two stages consolidation and shearing
Axis of symmetry
1Eh
1Eh
1Ghv
1Ev
ndashmicrohvEh
ndashmicrohvEn
2(1 + microhh)En
ndashmicrohhEn
ndashmicrohvEh
ndashmicrohvEh
ndashmicrohhEh
0
h
h
v
0 0
σh
σh
σv
τhv
τhv
τvh
τvh
σh
σv
σh
τhv
τvh
τhh
τhh τhh
ϵh
ϵv
ϵh
γhv
γvh
γhh
0
Require tests withapplication of
shear stresses
0 0
0
0 0 0 00
1Ghv0 0 0 00
0 0 0 0 0
0 0
bull =
Figure 13 Cross‐anisotropic soil requiring results from more than triaxial tests for full characterization
Principles of Triaxial Testing 5
151 Consolidation
In the first stage the initial condition of the soil is established in terms of effective stresses and stress history (including overconsolidation if applicable) Thus stresses are applied correshysponding to those acting on the element of soil in the field due to weight of the overlying soil strata and other materials or structures that exist at the time the mechanical properties (stressndashstrain strength etc) are sought Sufficient time is allowed for complete consolidation to occur under the applied stresses The condition in the field element has now been established in the triaxial specimen
152 Shearing
In the second stage of the triaxial test an addishytional stress is applied to reach peak failure and beyond under relevant drainage conditions The additional stress applied to the specimen should correspond as closely as possible to the change in stress on the field element due to some new change in the overall field loading situashytion This change may consist of a vertical stress increase or decrease (eg due to addition of a structure or excavation of overlying soil strata) or of a horizontal stress increase or decrease (eg due to the same constructions causing the vertical stress changes) Any combination of vertical and horizontal stress changes may be simulated in the triaxial test Examples of vertishycal and horizontal stress changes in the field are shown in Fig 14
Usually it is desirable to know how much change in load the soil can sustain without failshying and how much deformation will occur under normal working conditions The test is therefore usually continued to find the strength of the soil under the appropriate loading condishytions The results are used with an appropriate factor of safety so that normal working stresses are always somewhat below the peak strength
The stressndashstrain relations obtained from the triaxial tests provide the basis for determinashytion of deformations in the field This may be done in a simplified manner by closed‐form
solutions or it may be done by employing the results of the triaxial tests for calibration of a constitutive model used with a numerical method in finite element or finite difference computer programs
16 Types of tests
The drainage conditions in the field must be duplicated as well as possible in the laboratory tests This may be done by appropriate drainage facilities or preventions as discussed above for the triaxial test In most cases the field drainage conditions can be approximated by one of the following three types of tests
1 Consolidated‐drained test called a CD‐test or just a drained test
2 Consolidated‐undrained test or a CU‐test3 Unconsolidated‐undrained test or a UU‐test
Additionalload
Excavation
ΔσV asymp 0
ΔσV asymp 0
ΔσV gt 0
ΔσV lt 0
Δσh lt 0
Δσh gt 0
Δσh lt ΔσV
Δσh
Figure 14 Examples of stress changes leading to failure in the field
6 Triaxial Testing of Soils
These tests are described in ASTM Standards D7181 (2014) D4767 (2014) and D2850 (2014) respectively
Which condition of drainage in the laboratory test logically corresponds to each case in the field depends on a comparison of loading rate with the rate at which the water can escape or be sucked into the ground Thus the permeability of the soil and the drainage boundary conditions in the field together with the loading rate play key roles in determination of the type of analysis and the type of test drained or undrained that are appropriate for each case Field cases with partial drainage can be correctly duplicated in laboratory tests if the effective stress path is determined for the design condition However the idea of the CD‐ CU‐ and UU‐tests is to make it relatively simple for the design engineer to analyze a condition that will render a sufficient factor of safety under the actual drainage condishytion without trying to estimate and experimenshytally replicate the actual stress path
It has been determined through experience and common sense that the extreme conditions are drained and undrained with and without consolidation As a practical matter in a commershycial laboratory it is easier to run an undrained test than a drained test because it is easier and faster to measure pore pressures than volume change Therefore even drained parameters are more likely to be estimated from a CU‐test than from a CD‐test
161 Simulation of field conditions
Presented below is a brief review of the three types of tests together with examples of field cases for which the tests are appropriate and with typishycal strength results shown on Mohr diagrams
Drained tests
Isotropic consolidation is most often used in the first stage of the triaxial test However anisoshytropic consolidation with any stress ratio is also possible
The shearing stage of a drained test is pershyformed so slowly the soil is so permeable and the drainage facilities are such that no excess
pore pressure (positive or negative) can exist in the specimen at any stage of the test that is
∆u = 0 (15)
It follows then from the effective stress principle
prime = minusσ σ u (16)
that the effective stress changes are always the same as the total stress changes
A soil specimen always changes volume during shearing in a drained test If it contracts in volume it expels pore fluid (usually water or air) and if it expands in volume (dilates) then it sucks water or air into the pores If a non‐zero pore pressure is generated during the test (eg by performing the shearing too fast so the water does not have sufficient time to escape) then the specimen will expel or suck water such that the pore pressure goes towards zero to try to achieve equilibrium between externally applied stresses and internal effective stresses Thus there will always be volume changes in a drained test Consequently the water content the void ratio and the dry density of the specimen at the end of the test are most often not the same as at the beginning
The following field conditions can be simushylated with acceptable accuracy in the drained test
1 Almost all cases involving coarse sands and gravel whether saturated or not (except if confined in eg a lens andor exposed to rapid loading as in eg an earthquake)
2 Many cases involving fine sand and someshytimes silt if the field loads are applied reashysonable slowly
3 Long term loading of any soil as for examplea) Cut slopes several years after excavationb) Embankment constructed very slowly in
layers over a soft clay depositc) Earth dam with steady seepaged) Foundation on clay a long time after
construction
These cases are illustrated in Fig 15The strength results obtained from drained
tests are illustrated schematically on the Mohr diagram in Fig 16 The shear strength of soils increases with increasing confining pressure
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
About the Author
Poul V Lade received his MS degree from the Technical University of Denmark in 1967 and he continued his studies at the University of California at Berkeley where he received his PhD in 1972 Subsequently his academic career began at the University of California at Los Angeles (UCLA) and he continued at Johns Hopkins University (1993ndash1999) Aalborg University in Denmark (1999ndash2003) and the Catholic University of America in Washington DC (2003ndash2015)
His research interests include application of appropriate experimental methods to determine the three‐dimensional stressndashstrain and strength behavior of soils and the development of consti-tutive models for frictional materials such as soils concrete and rock He developed laboratory experimental apparatus to investigate monotonic loading and large three‐dimensional stress rever-
sals in plane strain true triaxial and torsion shear equipment This also included studies of effects of principal stress rotation stability instability and liquefaction of granular materials and time effects The constitutive models are based on elasticity and work‐hardening isotropic and kinematic plasticity theories
He has written nearly 300 publications based on research performed with support from the National Science Foundation (NSF) and from the Air Force Office of Scientific Research (AFOSR) He was elected member of the Danish Academy of Technical Sciences (2001) and he was awarded Professor Ostenfeldrsquos Gold Medal from the Technical University of Denmark (2001) He was inaugural editor of Geomechanics and Engineering and he has served on the editorial boards of eight international journals on geotechnical engineering
Triaxial Testing of Soils First Edition Poul V Lade copy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd
Principles of Triaxial Testing1
11 Purpose of triaxial tests
The purpose of performing triaxial tests is to determine the mechanical properties of the soil It is assumed that the soil specimens to be tested are homogeneous and representative of the material in the field and that the desired soil properties can in fact be obtained from the triaxial tests either directly or by interpretation through some theory
The mechanical properties most often sought from triaxial tests are stressndashstrain relations volshyume change or pore pressure behavior and shear strength of the soil Included in the stressndashstrain behavior are also the compressibility and the value of the coefficient of earth pressure at rest K0 Other properties that may be obtained from the triaxial tests which include time as a component are the permeability the coefficient of consolidation and properties relating to time dependent behavior such as rate effects creep and stress relaxation
It is important that the natural soil deposit or the fill from which soil samples have been taken in the field are sufficiently uniform that the soil samples possess the properties which are approshypriate and representative of the soil mass in the field It is therefore paramount that the geology at the site is well‐known and understood Even then samples from uniform deposits may not
ldquocontainrdquo properties that are representative of the field deposit This may happen either (a) due to the change in effective stress state which is always associated with the sampling process or (b) due to mechanical disturbance from sampling transshyportation or handling in the laboratory The stressndashstrain and strength properties of very senshysitive clays which have been disturbed cannot be regenerated in the lab oratory or otherwise obtained by interpretation of tests performed on inadequate specimens The effects of sampling will briefly be discussed below in connection with choice of consolidation pressure in the trishyaxial test The topic of sampling is otherwise outshyside the scope of the present treatment
12 Concept of testing
The concept to be pursued in testing of soils is to simulate as closely as possible the process that goes on in the field Because there is a large number of variables (eg density water content degree of saturation overconsolidation ratio loading conditions stress paths) that influence the resulting soil behavior the simplest and most direct way of obtaining information pertinent to the field conditions is to duplicate these as closely as possible
2 Triaxial Testing of Soils
However because of limitations in equipment and because of practical limitations on the amount of testing that can be performed for each project it is essential that
1 The true field loading conditions (including the drainage conditions) are known
2 The laboratory equipment can reproduce these conditions to a required degree of accuracy
3 A reasonable estimate can be made of the sigshynificance of the differences between the field loading conditions and those that can be proshyduced in the laboratory equipment
It is clear that the triaxial test in many resshypects is incapable of simulating several imporshytant aspects of field loading conditions For example the effects of the intermediate princishypal stress the effects of rotation of principal stresses and the effects of partial drainage durshying loading in the field cannot be investigated on the basis of the triaxial test The effects of such conditions require studies involving other types of equipment or analyses of boundary value problems either by closed form solutions or solutions obtained by numerical techniques
To provide some background for evaluation of the results of triaxial tests other types of laboratory shear tests and typical results from such tests are presented in Chapter 11 The relashytions between the different types of tests are reviewed and their advantages and limitations are discussed
13 The triaxial test
The triaxial test is most often performed on a cylindrical specimen as shown in Fig 11(a) Principal stresses are applied to the specimen as indicated in Fig 11(b) First a confining pressure σ3 is applied to the specimen This pressure acts all around and therefore on all planes in the specimen Then an additional stress difference σd is applied in the axial direction The stress applied externally to the specimen in the axial direction is
σ σ σ1 3= +d (11)
and therefore
σ σ σd = minus1 3 (12)
In the general case three principal stresses σ1 σ2 and σ3 may act on a soil element in the field However only two different principal stresses can be applied to the specimen in the convenshytional triaxial test The intermediate principal stress σ2 can only have values as follows
σ σ2 3= Triaxial compression (13)
σ σ2 1= Triaxial extension (14)
The condition of triaxial extension can be achieved by applying negative stress differshyences to the specimen This merely produces a reduction in compression in the extension direcshytion but no tension occurs in the specimen The state of stress applied to the specimen is in both cases axisymmetric The triaxial compression test will be discussed in the following while the triaxial extension test is discussed in Chapter 10
The test is performed using triaxial apparashytus as seen in the schematic illustration in Fig 12 The specimen is surrounded by a cap and a base and a membrane This unit is placed in a triaxial cell in which the cell pressure can be applied The cell pressure acts as a hydrostatic confinement for the specimen and the pressure is therefore the same in all directions In addition
σ1
(a) (b)
σ1 = σd + σ3
σ2 = σ3
σd = σ1 ndash σ3σ3
σ3σ3
σ3
σd
Figure 11 (a) Cylindrical specimen for triaxial testing and (b) stresses applied to a triaxial specimen
Principles of Triaxial Testing 3
a deviator load can be applied through a piston that goes through the top of the cell and loads the specimen in the axial direction
The vertical deformation of the specimen may be measured by a dial gage attached to the piston which travels the same vertical distance as the cap sitting on top of the specimen Drainage lines are connected to the water saturated specishymen through the base (or both the cap and the base) and connected to a burette outside the trishyaxial cell This allows for measurements of the volume changes of the specimen during the test
Alternatively the connection to the burette can be shut off thereby preventing the specimen from changing volume Instead the pore water pressure can be measured on a transducer conshynected to the drainage line
The following quantities are measured in a typical triaxial test
1 Confining pressure2 Deviator load3 Vertical (or axial) deformation4 Volume change or pore water pressure
These measurements constitute the data base from which other quantities can be derived
[eg stress difference (σ1 ndash σ3) axial strain ε1 and volumetric strain εv]
14 Advantages and limitations
Whereas the triaxial test potentially can proshyvide a substantial proportion of the mechanical properties required for a project it has limitashytions especially when special conditions are encountered and necessitates clarification based on experimentation
The advantages of the triaxial test are
1 Drainage can be controlled (onndashoff)2 Volume change or pore pressure can be
measured3 Suction can be controlled in partially satushy
rated soils4 Measured deformations allow calculation of
strains and moduli5 A larger variety of stress and strain paths
that occur in the field can be applied in the triaxial apparatus than in any other testing apparatus (eg initial anisotropic consolidashytion at any stress ratio including K0 extension active and passive shear)
The limitations of the triaxial test are
1 Stress concentrations due to friction between specimen and end plates (cap and base) cause nonuniform strains and stresses and therefore nonuniform stressndashstrain volume change or pore pressure response
2 Only axisymmetric stress conditions can be applied to the specimen whereas most field problems involve plane strain or general three‐dimensional conditions with rotation of principal stresses
3 Triaxial tests cannot provide all necessary data required to characterize the behavior of an anisotropic or a cross‐anisotropic soil deposit as illustrated in Fig 13
4 Although the axisymmetric principal stress condition is limited it is more difficult to apply proper shear stresses or tension to soil in relatively simple tests
The first limitation listed above can be overcome by applying lubricated ends on the
Pore pressure transducer
On-Off valve
Burette
Piston
Dial gage
Triaxial cell
P = σd middot A
Aprime
σcell
σ3
σ3 σ3= σcell
Figure 12 Schematic diagram of triaxial apparatus
4 Triaxial Testing of Soils
specimen such that uniform strains and stresses and therefore correct soil response can be proshyduced This is discussed in Chapter 3 In addishytion to the limitations listed above it should be mentioned that it may be easier to reproduce certain stress paths in other specialty equipment than in the triaxial apparatus (eg K0‐test)
Although the triaxial test is limited as explained under points 2 and 3 above it does combine versatility with relative simplicity in concept and performance Other equipment in which three unequal principal stresses can be applied or in which the principal stress direcshytions can be rotated do not have the versatility or is more com plicated to operate Thus other types of equipment have their own advantages and limitations These other equipment types
include plane strain true triaxial simple shear directional shear and torsion shear apparatus All these pieces of equipment are with the excepshytion of the simple shear apparatus employed mainly for research purposes Their operational modes capabilities and results are reviewed in Chapter 11
15 Test stages ndash consolidation and shearing
Laboratory tests are made to simulate field loadshying conditions as close as possible Most field conditions and the corresponding tests can be simplified to consist of two stages consolidation and shearing
Axis of symmetry
1Eh
1Eh
1Ghv
1Ev
ndashmicrohvEh
ndashmicrohvEn
2(1 + microhh)En
ndashmicrohhEn
ndashmicrohvEh
ndashmicrohvEh
ndashmicrohhEh
0
h
h
v
0 0
σh
σh
σv
τhv
τhv
τvh
τvh
σh
σv
σh
τhv
τvh
τhh
τhh τhh
ϵh
ϵv
ϵh
γhv
γvh
γhh
0
Require tests withapplication of
shear stresses
0 0
0
0 0 0 00
1Ghv0 0 0 00
0 0 0 0 0
0 0
bull =
Figure 13 Cross‐anisotropic soil requiring results from more than triaxial tests for full characterization
Principles of Triaxial Testing 5
151 Consolidation
In the first stage the initial condition of the soil is established in terms of effective stresses and stress history (including overconsolidation if applicable) Thus stresses are applied correshysponding to those acting on the element of soil in the field due to weight of the overlying soil strata and other materials or structures that exist at the time the mechanical properties (stressndashstrain strength etc) are sought Sufficient time is allowed for complete consolidation to occur under the applied stresses The condition in the field element has now been established in the triaxial specimen
152 Shearing
In the second stage of the triaxial test an addishytional stress is applied to reach peak failure and beyond under relevant drainage conditions The additional stress applied to the specimen should correspond as closely as possible to the change in stress on the field element due to some new change in the overall field loading situashytion This change may consist of a vertical stress increase or decrease (eg due to addition of a structure or excavation of overlying soil strata) or of a horizontal stress increase or decrease (eg due to the same constructions causing the vertical stress changes) Any combination of vertical and horizontal stress changes may be simulated in the triaxial test Examples of vertishycal and horizontal stress changes in the field are shown in Fig 14
Usually it is desirable to know how much change in load the soil can sustain without failshying and how much deformation will occur under normal working conditions The test is therefore usually continued to find the strength of the soil under the appropriate loading condishytions The results are used with an appropriate factor of safety so that normal working stresses are always somewhat below the peak strength
The stressndashstrain relations obtained from the triaxial tests provide the basis for determinashytion of deformations in the field This may be done in a simplified manner by closed‐form
solutions or it may be done by employing the results of the triaxial tests for calibration of a constitutive model used with a numerical method in finite element or finite difference computer programs
16 Types of tests
The drainage conditions in the field must be duplicated as well as possible in the laboratory tests This may be done by appropriate drainage facilities or preventions as discussed above for the triaxial test In most cases the field drainage conditions can be approximated by one of the following three types of tests
1 Consolidated‐drained test called a CD‐test or just a drained test
2 Consolidated‐undrained test or a CU‐test3 Unconsolidated‐undrained test or a UU‐test
Additionalload
Excavation
ΔσV asymp 0
ΔσV asymp 0
ΔσV gt 0
ΔσV lt 0
Δσh lt 0
Δσh gt 0
Δσh lt ΔσV
Δσh
Figure 14 Examples of stress changes leading to failure in the field
6 Triaxial Testing of Soils
These tests are described in ASTM Standards D7181 (2014) D4767 (2014) and D2850 (2014) respectively
Which condition of drainage in the laboratory test logically corresponds to each case in the field depends on a comparison of loading rate with the rate at which the water can escape or be sucked into the ground Thus the permeability of the soil and the drainage boundary conditions in the field together with the loading rate play key roles in determination of the type of analysis and the type of test drained or undrained that are appropriate for each case Field cases with partial drainage can be correctly duplicated in laboratory tests if the effective stress path is determined for the design condition However the idea of the CD‐ CU‐ and UU‐tests is to make it relatively simple for the design engineer to analyze a condition that will render a sufficient factor of safety under the actual drainage condishytion without trying to estimate and experimenshytally replicate the actual stress path
It has been determined through experience and common sense that the extreme conditions are drained and undrained with and without consolidation As a practical matter in a commershycial laboratory it is easier to run an undrained test than a drained test because it is easier and faster to measure pore pressures than volume change Therefore even drained parameters are more likely to be estimated from a CU‐test than from a CD‐test
161 Simulation of field conditions
Presented below is a brief review of the three types of tests together with examples of field cases for which the tests are appropriate and with typishycal strength results shown on Mohr diagrams
Drained tests
Isotropic consolidation is most often used in the first stage of the triaxial test However anisoshytropic consolidation with any stress ratio is also possible
The shearing stage of a drained test is pershyformed so slowly the soil is so permeable and the drainage facilities are such that no excess
pore pressure (positive or negative) can exist in the specimen at any stage of the test that is
∆u = 0 (15)
It follows then from the effective stress principle
prime = minusσ σ u (16)
that the effective stress changes are always the same as the total stress changes
A soil specimen always changes volume during shearing in a drained test If it contracts in volume it expels pore fluid (usually water or air) and if it expands in volume (dilates) then it sucks water or air into the pores If a non‐zero pore pressure is generated during the test (eg by performing the shearing too fast so the water does not have sufficient time to escape) then the specimen will expel or suck water such that the pore pressure goes towards zero to try to achieve equilibrium between externally applied stresses and internal effective stresses Thus there will always be volume changes in a drained test Consequently the water content the void ratio and the dry density of the specimen at the end of the test are most often not the same as at the beginning
The following field conditions can be simushylated with acceptable accuracy in the drained test
1 Almost all cases involving coarse sands and gravel whether saturated or not (except if confined in eg a lens andor exposed to rapid loading as in eg an earthquake)
2 Many cases involving fine sand and someshytimes silt if the field loads are applied reashysonable slowly
3 Long term loading of any soil as for examplea) Cut slopes several years after excavationb) Embankment constructed very slowly in
layers over a soft clay depositc) Earth dam with steady seepaged) Foundation on clay a long time after
construction
These cases are illustrated in Fig 15The strength results obtained from drained
tests are illustrated schematically on the Mohr diagram in Fig 16 The shear strength of soils increases with increasing confining pressure
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
Triaxial Testing of Soils First Edition Poul V Lade copy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd
Principles of Triaxial Testing1
11 Purpose of triaxial tests
The purpose of performing triaxial tests is to determine the mechanical properties of the soil It is assumed that the soil specimens to be tested are homogeneous and representative of the material in the field and that the desired soil properties can in fact be obtained from the triaxial tests either directly or by interpretation through some theory
The mechanical properties most often sought from triaxial tests are stressndashstrain relations volshyume change or pore pressure behavior and shear strength of the soil Included in the stressndashstrain behavior are also the compressibility and the value of the coefficient of earth pressure at rest K0 Other properties that may be obtained from the triaxial tests which include time as a component are the permeability the coefficient of consolidation and properties relating to time dependent behavior such as rate effects creep and stress relaxation
It is important that the natural soil deposit or the fill from which soil samples have been taken in the field are sufficiently uniform that the soil samples possess the properties which are approshypriate and representative of the soil mass in the field It is therefore paramount that the geology at the site is well‐known and understood Even then samples from uniform deposits may not
ldquocontainrdquo properties that are representative of the field deposit This may happen either (a) due to the change in effective stress state which is always associated with the sampling process or (b) due to mechanical disturbance from sampling transshyportation or handling in the laboratory The stressndashstrain and strength properties of very senshysitive clays which have been disturbed cannot be regenerated in the lab oratory or otherwise obtained by interpretation of tests performed on inadequate specimens The effects of sampling will briefly be discussed below in connection with choice of consolidation pressure in the trishyaxial test The topic of sampling is otherwise outshyside the scope of the present treatment
12 Concept of testing
The concept to be pursued in testing of soils is to simulate as closely as possible the process that goes on in the field Because there is a large number of variables (eg density water content degree of saturation overconsolidation ratio loading conditions stress paths) that influence the resulting soil behavior the simplest and most direct way of obtaining information pertinent to the field conditions is to duplicate these as closely as possible
2 Triaxial Testing of Soils
However because of limitations in equipment and because of practical limitations on the amount of testing that can be performed for each project it is essential that
1 The true field loading conditions (including the drainage conditions) are known
2 The laboratory equipment can reproduce these conditions to a required degree of accuracy
3 A reasonable estimate can be made of the sigshynificance of the differences between the field loading conditions and those that can be proshyduced in the laboratory equipment
It is clear that the triaxial test in many resshypects is incapable of simulating several imporshytant aspects of field loading conditions For example the effects of the intermediate princishypal stress the effects of rotation of principal stresses and the effects of partial drainage durshying loading in the field cannot be investigated on the basis of the triaxial test The effects of such conditions require studies involving other types of equipment or analyses of boundary value problems either by closed form solutions or solutions obtained by numerical techniques
To provide some background for evaluation of the results of triaxial tests other types of laboratory shear tests and typical results from such tests are presented in Chapter 11 The relashytions between the different types of tests are reviewed and their advantages and limitations are discussed
13 The triaxial test
The triaxial test is most often performed on a cylindrical specimen as shown in Fig 11(a) Principal stresses are applied to the specimen as indicated in Fig 11(b) First a confining pressure σ3 is applied to the specimen This pressure acts all around and therefore on all planes in the specimen Then an additional stress difference σd is applied in the axial direction The stress applied externally to the specimen in the axial direction is
σ σ σ1 3= +d (11)
and therefore
σ σ σd = minus1 3 (12)
In the general case three principal stresses σ1 σ2 and σ3 may act on a soil element in the field However only two different principal stresses can be applied to the specimen in the convenshytional triaxial test The intermediate principal stress σ2 can only have values as follows
σ σ2 3= Triaxial compression (13)
σ σ2 1= Triaxial extension (14)
The condition of triaxial extension can be achieved by applying negative stress differshyences to the specimen This merely produces a reduction in compression in the extension direcshytion but no tension occurs in the specimen The state of stress applied to the specimen is in both cases axisymmetric The triaxial compression test will be discussed in the following while the triaxial extension test is discussed in Chapter 10
The test is performed using triaxial apparashytus as seen in the schematic illustration in Fig 12 The specimen is surrounded by a cap and a base and a membrane This unit is placed in a triaxial cell in which the cell pressure can be applied The cell pressure acts as a hydrostatic confinement for the specimen and the pressure is therefore the same in all directions In addition
σ1
(a) (b)
σ1 = σd + σ3
σ2 = σ3
σd = σ1 ndash σ3σ3
σ3σ3
σ3
σd
Figure 11 (a) Cylindrical specimen for triaxial testing and (b) stresses applied to a triaxial specimen
Principles of Triaxial Testing 3
a deviator load can be applied through a piston that goes through the top of the cell and loads the specimen in the axial direction
The vertical deformation of the specimen may be measured by a dial gage attached to the piston which travels the same vertical distance as the cap sitting on top of the specimen Drainage lines are connected to the water saturated specishymen through the base (or both the cap and the base) and connected to a burette outside the trishyaxial cell This allows for measurements of the volume changes of the specimen during the test
Alternatively the connection to the burette can be shut off thereby preventing the specimen from changing volume Instead the pore water pressure can be measured on a transducer conshynected to the drainage line
The following quantities are measured in a typical triaxial test
1 Confining pressure2 Deviator load3 Vertical (or axial) deformation4 Volume change or pore water pressure
These measurements constitute the data base from which other quantities can be derived
[eg stress difference (σ1 ndash σ3) axial strain ε1 and volumetric strain εv]
14 Advantages and limitations
Whereas the triaxial test potentially can proshyvide a substantial proportion of the mechanical properties required for a project it has limitashytions especially when special conditions are encountered and necessitates clarification based on experimentation
The advantages of the triaxial test are
1 Drainage can be controlled (onndashoff)2 Volume change or pore pressure can be
measured3 Suction can be controlled in partially satushy
rated soils4 Measured deformations allow calculation of
strains and moduli5 A larger variety of stress and strain paths
that occur in the field can be applied in the triaxial apparatus than in any other testing apparatus (eg initial anisotropic consolidashytion at any stress ratio including K0 extension active and passive shear)
The limitations of the triaxial test are
1 Stress concentrations due to friction between specimen and end plates (cap and base) cause nonuniform strains and stresses and therefore nonuniform stressndashstrain volume change or pore pressure response
2 Only axisymmetric stress conditions can be applied to the specimen whereas most field problems involve plane strain or general three‐dimensional conditions with rotation of principal stresses
3 Triaxial tests cannot provide all necessary data required to characterize the behavior of an anisotropic or a cross‐anisotropic soil deposit as illustrated in Fig 13
4 Although the axisymmetric principal stress condition is limited it is more difficult to apply proper shear stresses or tension to soil in relatively simple tests
The first limitation listed above can be overcome by applying lubricated ends on the
Pore pressure transducer
On-Off valve
Burette
Piston
Dial gage
Triaxial cell
P = σd middot A
Aprime
σcell
σ3
σ3 σ3= σcell
Figure 12 Schematic diagram of triaxial apparatus
4 Triaxial Testing of Soils
specimen such that uniform strains and stresses and therefore correct soil response can be proshyduced This is discussed in Chapter 3 In addishytion to the limitations listed above it should be mentioned that it may be easier to reproduce certain stress paths in other specialty equipment than in the triaxial apparatus (eg K0‐test)
Although the triaxial test is limited as explained under points 2 and 3 above it does combine versatility with relative simplicity in concept and performance Other equipment in which three unequal principal stresses can be applied or in which the principal stress direcshytions can be rotated do not have the versatility or is more com plicated to operate Thus other types of equipment have their own advantages and limitations These other equipment types
include plane strain true triaxial simple shear directional shear and torsion shear apparatus All these pieces of equipment are with the excepshytion of the simple shear apparatus employed mainly for research purposes Their operational modes capabilities and results are reviewed in Chapter 11
15 Test stages ndash consolidation and shearing
Laboratory tests are made to simulate field loadshying conditions as close as possible Most field conditions and the corresponding tests can be simplified to consist of two stages consolidation and shearing
Axis of symmetry
1Eh
1Eh
1Ghv
1Ev
ndashmicrohvEh
ndashmicrohvEn
2(1 + microhh)En
ndashmicrohhEn
ndashmicrohvEh
ndashmicrohvEh
ndashmicrohhEh
0
h
h
v
0 0
σh
σh
σv
τhv
τhv
τvh
τvh
σh
σv
σh
τhv
τvh
τhh
τhh τhh
ϵh
ϵv
ϵh
γhv
γvh
γhh
0
Require tests withapplication of
shear stresses
0 0
0
0 0 0 00
1Ghv0 0 0 00
0 0 0 0 0
0 0
bull =
Figure 13 Cross‐anisotropic soil requiring results from more than triaxial tests for full characterization
Principles of Triaxial Testing 5
151 Consolidation
In the first stage the initial condition of the soil is established in terms of effective stresses and stress history (including overconsolidation if applicable) Thus stresses are applied correshysponding to those acting on the element of soil in the field due to weight of the overlying soil strata and other materials or structures that exist at the time the mechanical properties (stressndashstrain strength etc) are sought Sufficient time is allowed for complete consolidation to occur under the applied stresses The condition in the field element has now been established in the triaxial specimen
152 Shearing
In the second stage of the triaxial test an addishytional stress is applied to reach peak failure and beyond under relevant drainage conditions The additional stress applied to the specimen should correspond as closely as possible to the change in stress on the field element due to some new change in the overall field loading situashytion This change may consist of a vertical stress increase or decrease (eg due to addition of a structure or excavation of overlying soil strata) or of a horizontal stress increase or decrease (eg due to the same constructions causing the vertical stress changes) Any combination of vertical and horizontal stress changes may be simulated in the triaxial test Examples of vertishycal and horizontal stress changes in the field are shown in Fig 14
Usually it is desirable to know how much change in load the soil can sustain without failshying and how much deformation will occur under normal working conditions The test is therefore usually continued to find the strength of the soil under the appropriate loading condishytions The results are used with an appropriate factor of safety so that normal working stresses are always somewhat below the peak strength
The stressndashstrain relations obtained from the triaxial tests provide the basis for determinashytion of deformations in the field This may be done in a simplified manner by closed‐form
solutions or it may be done by employing the results of the triaxial tests for calibration of a constitutive model used with a numerical method in finite element or finite difference computer programs
16 Types of tests
The drainage conditions in the field must be duplicated as well as possible in the laboratory tests This may be done by appropriate drainage facilities or preventions as discussed above for the triaxial test In most cases the field drainage conditions can be approximated by one of the following three types of tests
1 Consolidated‐drained test called a CD‐test or just a drained test
2 Consolidated‐undrained test or a CU‐test3 Unconsolidated‐undrained test or a UU‐test
Additionalload
Excavation
ΔσV asymp 0
ΔσV asymp 0
ΔσV gt 0
ΔσV lt 0
Δσh lt 0
Δσh gt 0
Δσh lt ΔσV
Δσh
Figure 14 Examples of stress changes leading to failure in the field
6 Triaxial Testing of Soils
These tests are described in ASTM Standards D7181 (2014) D4767 (2014) and D2850 (2014) respectively
Which condition of drainage in the laboratory test logically corresponds to each case in the field depends on a comparison of loading rate with the rate at which the water can escape or be sucked into the ground Thus the permeability of the soil and the drainage boundary conditions in the field together with the loading rate play key roles in determination of the type of analysis and the type of test drained or undrained that are appropriate for each case Field cases with partial drainage can be correctly duplicated in laboratory tests if the effective stress path is determined for the design condition However the idea of the CD‐ CU‐ and UU‐tests is to make it relatively simple for the design engineer to analyze a condition that will render a sufficient factor of safety under the actual drainage condishytion without trying to estimate and experimenshytally replicate the actual stress path
It has been determined through experience and common sense that the extreme conditions are drained and undrained with and without consolidation As a practical matter in a commershycial laboratory it is easier to run an undrained test than a drained test because it is easier and faster to measure pore pressures than volume change Therefore even drained parameters are more likely to be estimated from a CU‐test than from a CD‐test
161 Simulation of field conditions
Presented below is a brief review of the three types of tests together with examples of field cases for which the tests are appropriate and with typishycal strength results shown on Mohr diagrams
Drained tests
Isotropic consolidation is most often used in the first stage of the triaxial test However anisoshytropic consolidation with any stress ratio is also possible
The shearing stage of a drained test is pershyformed so slowly the soil is so permeable and the drainage facilities are such that no excess
pore pressure (positive or negative) can exist in the specimen at any stage of the test that is
∆u = 0 (15)
It follows then from the effective stress principle
prime = minusσ σ u (16)
that the effective stress changes are always the same as the total stress changes
A soil specimen always changes volume during shearing in a drained test If it contracts in volume it expels pore fluid (usually water or air) and if it expands in volume (dilates) then it sucks water or air into the pores If a non‐zero pore pressure is generated during the test (eg by performing the shearing too fast so the water does not have sufficient time to escape) then the specimen will expel or suck water such that the pore pressure goes towards zero to try to achieve equilibrium between externally applied stresses and internal effective stresses Thus there will always be volume changes in a drained test Consequently the water content the void ratio and the dry density of the specimen at the end of the test are most often not the same as at the beginning
The following field conditions can be simushylated with acceptable accuracy in the drained test
1 Almost all cases involving coarse sands and gravel whether saturated or not (except if confined in eg a lens andor exposed to rapid loading as in eg an earthquake)
2 Many cases involving fine sand and someshytimes silt if the field loads are applied reashysonable slowly
3 Long term loading of any soil as for examplea) Cut slopes several years after excavationb) Embankment constructed very slowly in
layers over a soft clay depositc) Earth dam with steady seepaged) Foundation on clay a long time after
construction
These cases are illustrated in Fig 15The strength results obtained from drained
tests are illustrated schematically on the Mohr diagram in Fig 16 The shear strength of soils increases with increasing confining pressure
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
2 Triaxial Testing of Soils
However because of limitations in equipment and because of practical limitations on the amount of testing that can be performed for each project it is essential that
1 The true field loading conditions (including the drainage conditions) are known
2 The laboratory equipment can reproduce these conditions to a required degree of accuracy
3 A reasonable estimate can be made of the sigshynificance of the differences between the field loading conditions and those that can be proshyduced in the laboratory equipment
It is clear that the triaxial test in many resshypects is incapable of simulating several imporshytant aspects of field loading conditions For example the effects of the intermediate princishypal stress the effects of rotation of principal stresses and the effects of partial drainage durshying loading in the field cannot be investigated on the basis of the triaxial test The effects of such conditions require studies involving other types of equipment or analyses of boundary value problems either by closed form solutions or solutions obtained by numerical techniques
To provide some background for evaluation of the results of triaxial tests other types of laboratory shear tests and typical results from such tests are presented in Chapter 11 The relashytions between the different types of tests are reviewed and their advantages and limitations are discussed
13 The triaxial test
The triaxial test is most often performed on a cylindrical specimen as shown in Fig 11(a) Principal stresses are applied to the specimen as indicated in Fig 11(b) First a confining pressure σ3 is applied to the specimen This pressure acts all around and therefore on all planes in the specimen Then an additional stress difference σd is applied in the axial direction The stress applied externally to the specimen in the axial direction is
σ σ σ1 3= +d (11)
and therefore
σ σ σd = minus1 3 (12)
In the general case three principal stresses σ1 σ2 and σ3 may act on a soil element in the field However only two different principal stresses can be applied to the specimen in the convenshytional triaxial test The intermediate principal stress σ2 can only have values as follows
σ σ2 3= Triaxial compression (13)
σ σ2 1= Triaxial extension (14)
The condition of triaxial extension can be achieved by applying negative stress differshyences to the specimen This merely produces a reduction in compression in the extension direcshytion but no tension occurs in the specimen The state of stress applied to the specimen is in both cases axisymmetric The triaxial compression test will be discussed in the following while the triaxial extension test is discussed in Chapter 10
The test is performed using triaxial apparashytus as seen in the schematic illustration in Fig 12 The specimen is surrounded by a cap and a base and a membrane This unit is placed in a triaxial cell in which the cell pressure can be applied The cell pressure acts as a hydrostatic confinement for the specimen and the pressure is therefore the same in all directions In addition
σ1
(a) (b)
σ1 = σd + σ3
σ2 = σ3
σd = σ1 ndash σ3σ3
σ3σ3
σ3
σd
Figure 11 (a) Cylindrical specimen for triaxial testing and (b) stresses applied to a triaxial specimen
Principles of Triaxial Testing 3
a deviator load can be applied through a piston that goes through the top of the cell and loads the specimen in the axial direction
The vertical deformation of the specimen may be measured by a dial gage attached to the piston which travels the same vertical distance as the cap sitting on top of the specimen Drainage lines are connected to the water saturated specishymen through the base (or both the cap and the base) and connected to a burette outside the trishyaxial cell This allows for measurements of the volume changes of the specimen during the test
Alternatively the connection to the burette can be shut off thereby preventing the specimen from changing volume Instead the pore water pressure can be measured on a transducer conshynected to the drainage line
The following quantities are measured in a typical triaxial test
1 Confining pressure2 Deviator load3 Vertical (or axial) deformation4 Volume change or pore water pressure
These measurements constitute the data base from which other quantities can be derived
[eg stress difference (σ1 ndash σ3) axial strain ε1 and volumetric strain εv]
14 Advantages and limitations
Whereas the triaxial test potentially can proshyvide a substantial proportion of the mechanical properties required for a project it has limitashytions especially when special conditions are encountered and necessitates clarification based on experimentation
The advantages of the triaxial test are
1 Drainage can be controlled (onndashoff)2 Volume change or pore pressure can be
measured3 Suction can be controlled in partially satushy
rated soils4 Measured deformations allow calculation of
strains and moduli5 A larger variety of stress and strain paths
that occur in the field can be applied in the triaxial apparatus than in any other testing apparatus (eg initial anisotropic consolidashytion at any stress ratio including K0 extension active and passive shear)
The limitations of the triaxial test are
1 Stress concentrations due to friction between specimen and end plates (cap and base) cause nonuniform strains and stresses and therefore nonuniform stressndashstrain volume change or pore pressure response
2 Only axisymmetric stress conditions can be applied to the specimen whereas most field problems involve plane strain or general three‐dimensional conditions with rotation of principal stresses
3 Triaxial tests cannot provide all necessary data required to characterize the behavior of an anisotropic or a cross‐anisotropic soil deposit as illustrated in Fig 13
4 Although the axisymmetric principal stress condition is limited it is more difficult to apply proper shear stresses or tension to soil in relatively simple tests
The first limitation listed above can be overcome by applying lubricated ends on the
Pore pressure transducer
On-Off valve
Burette
Piston
Dial gage
Triaxial cell
P = σd middot A
Aprime
σcell
σ3
σ3 σ3= σcell
Figure 12 Schematic diagram of triaxial apparatus
4 Triaxial Testing of Soils
specimen such that uniform strains and stresses and therefore correct soil response can be proshyduced This is discussed in Chapter 3 In addishytion to the limitations listed above it should be mentioned that it may be easier to reproduce certain stress paths in other specialty equipment than in the triaxial apparatus (eg K0‐test)
Although the triaxial test is limited as explained under points 2 and 3 above it does combine versatility with relative simplicity in concept and performance Other equipment in which three unequal principal stresses can be applied or in which the principal stress direcshytions can be rotated do not have the versatility or is more com plicated to operate Thus other types of equipment have their own advantages and limitations These other equipment types
include plane strain true triaxial simple shear directional shear and torsion shear apparatus All these pieces of equipment are with the excepshytion of the simple shear apparatus employed mainly for research purposes Their operational modes capabilities and results are reviewed in Chapter 11
15 Test stages ndash consolidation and shearing
Laboratory tests are made to simulate field loadshying conditions as close as possible Most field conditions and the corresponding tests can be simplified to consist of two stages consolidation and shearing
Axis of symmetry
1Eh
1Eh
1Ghv
1Ev
ndashmicrohvEh
ndashmicrohvEn
2(1 + microhh)En
ndashmicrohhEn
ndashmicrohvEh
ndashmicrohvEh
ndashmicrohhEh
0
h
h
v
0 0
σh
σh
σv
τhv
τhv
τvh
τvh
σh
σv
σh
τhv
τvh
τhh
τhh τhh
ϵh
ϵv
ϵh
γhv
γvh
γhh
0
Require tests withapplication of
shear stresses
0 0
0
0 0 0 00
1Ghv0 0 0 00
0 0 0 0 0
0 0
bull =
Figure 13 Cross‐anisotropic soil requiring results from more than triaxial tests for full characterization
Principles of Triaxial Testing 5
151 Consolidation
In the first stage the initial condition of the soil is established in terms of effective stresses and stress history (including overconsolidation if applicable) Thus stresses are applied correshysponding to those acting on the element of soil in the field due to weight of the overlying soil strata and other materials or structures that exist at the time the mechanical properties (stressndashstrain strength etc) are sought Sufficient time is allowed for complete consolidation to occur under the applied stresses The condition in the field element has now been established in the triaxial specimen
152 Shearing
In the second stage of the triaxial test an addishytional stress is applied to reach peak failure and beyond under relevant drainage conditions The additional stress applied to the specimen should correspond as closely as possible to the change in stress on the field element due to some new change in the overall field loading situashytion This change may consist of a vertical stress increase or decrease (eg due to addition of a structure or excavation of overlying soil strata) or of a horizontal stress increase or decrease (eg due to the same constructions causing the vertical stress changes) Any combination of vertical and horizontal stress changes may be simulated in the triaxial test Examples of vertishycal and horizontal stress changes in the field are shown in Fig 14
Usually it is desirable to know how much change in load the soil can sustain without failshying and how much deformation will occur under normal working conditions The test is therefore usually continued to find the strength of the soil under the appropriate loading condishytions The results are used with an appropriate factor of safety so that normal working stresses are always somewhat below the peak strength
The stressndashstrain relations obtained from the triaxial tests provide the basis for determinashytion of deformations in the field This may be done in a simplified manner by closed‐form
solutions or it may be done by employing the results of the triaxial tests for calibration of a constitutive model used with a numerical method in finite element or finite difference computer programs
16 Types of tests
The drainage conditions in the field must be duplicated as well as possible in the laboratory tests This may be done by appropriate drainage facilities or preventions as discussed above for the triaxial test In most cases the field drainage conditions can be approximated by one of the following three types of tests
1 Consolidated‐drained test called a CD‐test or just a drained test
2 Consolidated‐undrained test or a CU‐test3 Unconsolidated‐undrained test or a UU‐test
Additionalload
Excavation
ΔσV asymp 0
ΔσV asymp 0
ΔσV gt 0
ΔσV lt 0
Δσh lt 0
Δσh gt 0
Δσh lt ΔσV
Δσh
Figure 14 Examples of stress changes leading to failure in the field
6 Triaxial Testing of Soils
These tests are described in ASTM Standards D7181 (2014) D4767 (2014) and D2850 (2014) respectively
Which condition of drainage in the laboratory test logically corresponds to each case in the field depends on a comparison of loading rate with the rate at which the water can escape or be sucked into the ground Thus the permeability of the soil and the drainage boundary conditions in the field together with the loading rate play key roles in determination of the type of analysis and the type of test drained or undrained that are appropriate for each case Field cases with partial drainage can be correctly duplicated in laboratory tests if the effective stress path is determined for the design condition However the idea of the CD‐ CU‐ and UU‐tests is to make it relatively simple for the design engineer to analyze a condition that will render a sufficient factor of safety under the actual drainage condishytion without trying to estimate and experimenshytally replicate the actual stress path
It has been determined through experience and common sense that the extreme conditions are drained and undrained with and without consolidation As a practical matter in a commershycial laboratory it is easier to run an undrained test than a drained test because it is easier and faster to measure pore pressures than volume change Therefore even drained parameters are more likely to be estimated from a CU‐test than from a CD‐test
161 Simulation of field conditions
Presented below is a brief review of the three types of tests together with examples of field cases for which the tests are appropriate and with typishycal strength results shown on Mohr diagrams
Drained tests
Isotropic consolidation is most often used in the first stage of the triaxial test However anisoshytropic consolidation with any stress ratio is also possible
The shearing stage of a drained test is pershyformed so slowly the soil is so permeable and the drainage facilities are such that no excess
pore pressure (positive or negative) can exist in the specimen at any stage of the test that is
∆u = 0 (15)
It follows then from the effective stress principle
prime = minusσ σ u (16)
that the effective stress changes are always the same as the total stress changes
A soil specimen always changes volume during shearing in a drained test If it contracts in volume it expels pore fluid (usually water or air) and if it expands in volume (dilates) then it sucks water or air into the pores If a non‐zero pore pressure is generated during the test (eg by performing the shearing too fast so the water does not have sufficient time to escape) then the specimen will expel or suck water such that the pore pressure goes towards zero to try to achieve equilibrium between externally applied stresses and internal effective stresses Thus there will always be volume changes in a drained test Consequently the water content the void ratio and the dry density of the specimen at the end of the test are most often not the same as at the beginning
The following field conditions can be simushylated with acceptable accuracy in the drained test
1 Almost all cases involving coarse sands and gravel whether saturated or not (except if confined in eg a lens andor exposed to rapid loading as in eg an earthquake)
2 Many cases involving fine sand and someshytimes silt if the field loads are applied reashysonable slowly
3 Long term loading of any soil as for examplea) Cut slopes several years after excavationb) Embankment constructed very slowly in
layers over a soft clay depositc) Earth dam with steady seepaged) Foundation on clay a long time after
construction
These cases are illustrated in Fig 15The strength results obtained from drained
tests are illustrated schematically on the Mohr diagram in Fig 16 The shear strength of soils increases with increasing confining pressure
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
Principles of Triaxial Testing 3
a deviator load can be applied through a piston that goes through the top of the cell and loads the specimen in the axial direction
The vertical deformation of the specimen may be measured by a dial gage attached to the piston which travels the same vertical distance as the cap sitting on top of the specimen Drainage lines are connected to the water saturated specishymen through the base (or both the cap and the base) and connected to a burette outside the trishyaxial cell This allows for measurements of the volume changes of the specimen during the test
Alternatively the connection to the burette can be shut off thereby preventing the specimen from changing volume Instead the pore water pressure can be measured on a transducer conshynected to the drainage line
The following quantities are measured in a typical triaxial test
1 Confining pressure2 Deviator load3 Vertical (or axial) deformation4 Volume change or pore water pressure
These measurements constitute the data base from which other quantities can be derived
[eg stress difference (σ1 ndash σ3) axial strain ε1 and volumetric strain εv]
14 Advantages and limitations
Whereas the triaxial test potentially can proshyvide a substantial proportion of the mechanical properties required for a project it has limitashytions especially when special conditions are encountered and necessitates clarification based on experimentation
The advantages of the triaxial test are
1 Drainage can be controlled (onndashoff)2 Volume change or pore pressure can be
measured3 Suction can be controlled in partially satushy
rated soils4 Measured deformations allow calculation of
strains and moduli5 A larger variety of stress and strain paths
that occur in the field can be applied in the triaxial apparatus than in any other testing apparatus (eg initial anisotropic consolidashytion at any stress ratio including K0 extension active and passive shear)
The limitations of the triaxial test are
1 Stress concentrations due to friction between specimen and end plates (cap and base) cause nonuniform strains and stresses and therefore nonuniform stressndashstrain volume change or pore pressure response
2 Only axisymmetric stress conditions can be applied to the specimen whereas most field problems involve plane strain or general three‐dimensional conditions with rotation of principal stresses
3 Triaxial tests cannot provide all necessary data required to characterize the behavior of an anisotropic or a cross‐anisotropic soil deposit as illustrated in Fig 13
4 Although the axisymmetric principal stress condition is limited it is more difficult to apply proper shear stresses or tension to soil in relatively simple tests
The first limitation listed above can be overcome by applying lubricated ends on the
Pore pressure transducer
On-Off valve
Burette
Piston
Dial gage
Triaxial cell
P = σd middot A
Aprime
σcell
σ3
σ3 σ3= σcell
Figure 12 Schematic diagram of triaxial apparatus
4 Triaxial Testing of Soils
specimen such that uniform strains and stresses and therefore correct soil response can be proshyduced This is discussed in Chapter 3 In addishytion to the limitations listed above it should be mentioned that it may be easier to reproduce certain stress paths in other specialty equipment than in the triaxial apparatus (eg K0‐test)
Although the triaxial test is limited as explained under points 2 and 3 above it does combine versatility with relative simplicity in concept and performance Other equipment in which three unequal principal stresses can be applied or in which the principal stress direcshytions can be rotated do not have the versatility or is more com plicated to operate Thus other types of equipment have their own advantages and limitations These other equipment types
include plane strain true triaxial simple shear directional shear and torsion shear apparatus All these pieces of equipment are with the excepshytion of the simple shear apparatus employed mainly for research purposes Their operational modes capabilities and results are reviewed in Chapter 11
15 Test stages ndash consolidation and shearing
Laboratory tests are made to simulate field loadshying conditions as close as possible Most field conditions and the corresponding tests can be simplified to consist of two stages consolidation and shearing
Axis of symmetry
1Eh
1Eh
1Ghv
1Ev
ndashmicrohvEh
ndashmicrohvEn
2(1 + microhh)En
ndashmicrohhEn
ndashmicrohvEh
ndashmicrohvEh
ndashmicrohhEh
0
h
h
v
0 0
σh
σh
σv
τhv
τhv
τvh
τvh
σh
σv
σh
τhv
τvh
τhh
τhh τhh
ϵh
ϵv
ϵh
γhv
γvh
γhh
0
Require tests withapplication of
shear stresses
0 0
0
0 0 0 00
1Ghv0 0 0 00
0 0 0 0 0
0 0
bull =
Figure 13 Cross‐anisotropic soil requiring results from more than triaxial tests for full characterization
Principles of Triaxial Testing 5
151 Consolidation
In the first stage the initial condition of the soil is established in terms of effective stresses and stress history (including overconsolidation if applicable) Thus stresses are applied correshysponding to those acting on the element of soil in the field due to weight of the overlying soil strata and other materials or structures that exist at the time the mechanical properties (stressndashstrain strength etc) are sought Sufficient time is allowed for complete consolidation to occur under the applied stresses The condition in the field element has now been established in the triaxial specimen
152 Shearing
In the second stage of the triaxial test an addishytional stress is applied to reach peak failure and beyond under relevant drainage conditions The additional stress applied to the specimen should correspond as closely as possible to the change in stress on the field element due to some new change in the overall field loading situashytion This change may consist of a vertical stress increase or decrease (eg due to addition of a structure or excavation of overlying soil strata) or of a horizontal stress increase or decrease (eg due to the same constructions causing the vertical stress changes) Any combination of vertical and horizontal stress changes may be simulated in the triaxial test Examples of vertishycal and horizontal stress changes in the field are shown in Fig 14
Usually it is desirable to know how much change in load the soil can sustain without failshying and how much deformation will occur under normal working conditions The test is therefore usually continued to find the strength of the soil under the appropriate loading condishytions The results are used with an appropriate factor of safety so that normal working stresses are always somewhat below the peak strength
The stressndashstrain relations obtained from the triaxial tests provide the basis for determinashytion of deformations in the field This may be done in a simplified manner by closed‐form
solutions or it may be done by employing the results of the triaxial tests for calibration of a constitutive model used with a numerical method in finite element or finite difference computer programs
16 Types of tests
The drainage conditions in the field must be duplicated as well as possible in the laboratory tests This may be done by appropriate drainage facilities or preventions as discussed above for the triaxial test In most cases the field drainage conditions can be approximated by one of the following three types of tests
1 Consolidated‐drained test called a CD‐test or just a drained test
2 Consolidated‐undrained test or a CU‐test3 Unconsolidated‐undrained test or a UU‐test
Additionalload
Excavation
ΔσV asymp 0
ΔσV asymp 0
ΔσV gt 0
ΔσV lt 0
Δσh lt 0
Δσh gt 0
Δσh lt ΔσV
Δσh
Figure 14 Examples of stress changes leading to failure in the field
6 Triaxial Testing of Soils
These tests are described in ASTM Standards D7181 (2014) D4767 (2014) and D2850 (2014) respectively
Which condition of drainage in the laboratory test logically corresponds to each case in the field depends on a comparison of loading rate with the rate at which the water can escape or be sucked into the ground Thus the permeability of the soil and the drainage boundary conditions in the field together with the loading rate play key roles in determination of the type of analysis and the type of test drained or undrained that are appropriate for each case Field cases with partial drainage can be correctly duplicated in laboratory tests if the effective stress path is determined for the design condition However the idea of the CD‐ CU‐ and UU‐tests is to make it relatively simple for the design engineer to analyze a condition that will render a sufficient factor of safety under the actual drainage condishytion without trying to estimate and experimenshytally replicate the actual stress path
It has been determined through experience and common sense that the extreme conditions are drained and undrained with and without consolidation As a practical matter in a commershycial laboratory it is easier to run an undrained test than a drained test because it is easier and faster to measure pore pressures than volume change Therefore even drained parameters are more likely to be estimated from a CU‐test than from a CD‐test
161 Simulation of field conditions
Presented below is a brief review of the three types of tests together with examples of field cases for which the tests are appropriate and with typishycal strength results shown on Mohr diagrams
Drained tests
Isotropic consolidation is most often used in the first stage of the triaxial test However anisoshytropic consolidation with any stress ratio is also possible
The shearing stage of a drained test is pershyformed so slowly the soil is so permeable and the drainage facilities are such that no excess
pore pressure (positive or negative) can exist in the specimen at any stage of the test that is
∆u = 0 (15)
It follows then from the effective stress principle
prime = minusσ σ u (16)
that the effective stress changes are always the same as the total stress changes
A soil specimen always changes volume during shearing in a drained test If it contracts in volume it expels pore fluid (usually water or air) and if it expands in volume (dilates) then it sucks water or air into the pores If a non‐zero pore pressure is generated during the test (eg by performing the shearing too fast so the water does not have sufficient time to escape) then the specimen will expel or suck water such that the pore pressure goes towards zero to try to achieve equilibrium between externally applied stresses and internal effective stresses Thus there will always be volume changes in a drained test Consequently the water content the void ratio and the dry density of the specimen at the end of the test are most often not the same as at the beginning
The following field conditions can be simushylated with acceptable accuracy in the drained test
1 Almost all cases involving coarse sands and gravel whether saturated or not (except if confined in eg a lens andor exposed to rapid loading as in eg an earthquake)
2 Many cases involving fine sand and someshytimes silt if the field loads are applied reashysonable slowly
3 Long term loading of any soil as for examplea) Cut slopes several years after excavationb) Embankment constructed very slowly in
layers over a soft clay depositc) Earth dam with steady seepaged) Foundation on clay a long time after
construction
These cases are illustrated in Fig 15The strength results obtained from drained
tests are illustrated schematically on the Mohr diagram in Fig 16 The shear strength of soils increases with increasing confining pressure
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
4 Triaxial Testing of Soils
specimen such that uniform strains and stresses and therefore correct soil response can be proshyduced This is discussed in Chapter 3 In addishytion to the limitations listed above it should be mentioned that it may be easier to reproduce certain stress paths in other specialty equipment than in the triaxial apparatus (eg K0‐test)
Although the triaxial test is limited as explained under points 2 and 3 above it does combine versatility with relative simplicity in concept and performance Other equipment in which three unequal principal stresses can be applied or in which the principal stress direcshytions can be rotated do not have the versatility or is more com plicated to operate Thus other types of equipment have their own advantages and limitations These other equipment types
include plane strain true triaxial simple shear directional shear and torsion shear apparatus All these pieces of equipment are with the excepshytion of the simple shear apparatus employed mainly for research purposes Their operational modes capabilities and results are reviewed in Chapter 11
15 Test stages ndash consolidation and shearing
Laboratory tests are made to simulate field loadshying conditions as close as possible Most field conditions and the corresponding tests can be simplified to consist of two stages consolidation and shearing
Axis of symmetry
1Eh
1Eh
1Ghv
1Ev
ndashmicrohvEh
ndashmicrohvEn
2(1 + microhh)En
ndashmicrohhEn
ndashmicrohvEh
ndashmicrohvEh
ndashmicrohhEh
0
h
h
v
0 0
σh
σh
σv
τhv
τhv
τvh
τvh
σh
σv
σh
τhv
τvh
τhh
τhh τhh
ϵh
ϵv
ϵh
γhv
γvh
γhh
0
Require tests withapplication of
shear stresses
0 0
0
0 0 0 00
1Ghv0 0 0 00
0 0 0 0 0
0 0
bull =
Figure 13 Cross‐anisotropic soil requiring results from more than triaxial tests for full characterization
Principles of Triaxial Testing 5
151 Consolidation
In the first stage the initial condition of the soil is established in terms of effective stresses and stress history (including overconsolidation if applicable) Thus stresses are applied correshysponding to those acting on the element of soil in the field due to weight of the overlying soil strata and other materials or structures that exist at the time the mechanical properties (stressndashstrain strength etc) are sought Sufficient time is allowed for complete consolidation to occur under the applied stresses The condition in the field element has now been established in the triaxial specimen
152 Shearing
In the second stage of the triaxial test an addishytional stress is applied to reach peak failure and beyond under relevant drainage conditions The additional stress applied to the specimen should correspond as closely as possible to the change in stress on the field element due to some new change in the overall field loading situashytion This change may consist of a vertical stress increase or decrease (eg due to addition of a structure or excavation of overlying soil strata) or of a horizontal stress increase or decrease (eg due to the same constructions causing the vertical stress changes) Any combination of vertical and horizontal stress changes may be simulated in the triaxial test Examples of vertishycal and horizontal stress changes in the field are shown in Fig 14
Usually it is desirable to know how much change in load the soil can sustain without failshying and how much deformation will occur under normal working conditions The test is therefore usually continued to find the strength of the soil under the appropriate loading condishytions The results are used with an appropriate factor of safety so that normal working stresses are always somewhat below the peak strength
The stressndashstrain relations obtained from the triaxial tests provide the basis for determinashytion of deformations in the field This may be done in a simplified manner by closed‐form
solutions or it may be done by employing the results of the triaxial tests for calibration of a constitutive model used with a numerical method in finite element or finite difference computer programs
16 Types of tests
The drainage conditions in the field must be duplicated as well as possible in the laboratory tests This may be done by appropriate drainage facilities or preventions as discussed above for the triaxial test In most cases the field drainage conditions can be approximated by one of the following three types of tests
1 Consolidated‐drained test called a CD‐test or just a drained test
2 Consolidated‐undrained test or a CU‐test3 Unconsolidated‐undrained test or a UU‐test
Additionalload
Excavation
ΔσV asymp 0
ΔσV asymp 0
ΔσV gt 0
ΔσV lt 0
Δσh lt 0
Δσh gt 0
Δσh lt ΔσV
Δσh
Figure 14 Examples of stress changes leading to failure in the field
6 Triaxial Testing of Soils
These tests are described in ASTM Standards D7181 (2014) D4767 (2014) and D2850 (2014) respectively
Which condition of drainage in the laboratory test logically corresponds to each case in the field depends on a comparison of loading rate with the rate at which the water can escape or be sucked into the ground Thus the permeability of the soil and the drainage boundary conditions in the field together with the loading rate play key roles in determination of the type of analysis and the type of test drained or undrained that are appropriate for each case Field cases with partial drainage can be correctly duplicated in laboratory tests if the effective stress path is determined for the design condition However the idea of the CD‐ CU‐ and UU‐tests is to make it relatively simple for the design engineer to analyze a condition that will render a sufficient factor of safety under the actual drainage condishytion without trying to estimate and experimenshytally replicate the actual stress path
It has been determined through experience and common sense that the extreme conditions are drained and undrained with and without consolidation As a practical matter in a commershycial laboratory it is easier to run an undrained test than a drained test because it is easier and faster to measure pore pressures than volume change Therefore even drained parameters are more likely to be estimated from a CU‐test than from a CD‐test
161 Simulation of field conditions
Presented below is a brief review of the three types of tests together with examples of field cases for which the tests are appropriate and with typishycal strength results shown on Mohr diagrams
Drained tests
Isotropic consolidation is most often used in the first stage of the triaxial test However anisoshytropic consolidation with any stress ratio is also possible
The shearing stage of a drained test is pershyformed so slowly the soil is so permeable and the drainage facilities are such that no excess
pore pressure (positive or negative) can exist in the specimen at any stage of the test that is
∆u = 0 (15)
It follows then from the effective stress principle
prime = minusσ σ u (16)
that the effective stress changes are always the same as the total stress changes
A soil specimen always changes volume during shearing in a drained test If it contracts in volume it expels pore fluid (usually water or air) and if it expands in volume (dilates) then it sucks water or air into the pores If a non‐zero pore pressure is generated during the test (eg by performing the shearing too fast so the water does not have sufficient time to escape) then the specimen will expel or suck water such that the pore pressure goes towards zero to try to achieve equilibrium between externally applied stresses and internal effective stresses Thus there will always be volume changes in a drained test Consequently the water content the void ratio and the dry density of the specimen at the end of the test are most often not the same as at the beginning
The following field conditions can be simushylated with acceptable accuracy in the drained test
1 Almost all cases involving coarse sands and gravel whether saturated or not (except if confined in eg a lens andor exposed to rapid loading as in eg an earthquake)
2 Many cases involving fine sand and someshytimes silt if the field loads are applied reashysonable slowly
3 Long term loading of any soil as for examplea) Cut slopes several years after excavationb) Embankment constructed very slowly in
layers over a soft clay depositc) Earth dam with steady seepaged) Foundation on clay a long time after
construction
These cases are illustrated in Fig 15The strength results obtained from drained
tests are illustrated schematically on the Mohr diagram in Fig 16 The shear strength of soils increases with increasing confining pressure
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
Principles of Triaxial Testing 5
151 Consolidation
In the first stage the initial condition of the soil is established in terms of effective stresses and stress history (including overconsolidation if applicable) Thus stresses are applied correshysponding to those acting on the element of soil in the field due to weight of the overlying soil strata and other materials or structures that exist at the time the mechanical properties (stressndashstrain strength etc) are sought Sufficient time is allowed for complete consolidation to occur under the applied stresses The condition in the field element has now been established in the triaxial specimen
152 Shearing
In the second stage of the triaxial test an addishytional stress is applied to reach peak failure and beyond under relevant drainage conditions The additional stress applied to the specimen should correspond as closely as possible to the change in stress on the field element due to some new change in the overall field loading situashytion This change may consist of a vertical stress increase or decrease (eg due to addition of a structure or excavation of overlying soil strata) or of a horizontal stress increase or decrease (eg due to the same constructions causing the vertical stress changes) Any combination of vertical and horizontal stress changes may be simulated in the triaxial test Examples of vertishycal and horizontal stress changes in the field are shown in Fig 14
Usually it is desirable to know how much change in load the soil can sustain without failshying and how much deformation will occur under normal working conditions The test is therefore usually continued to find the strength of the soil under the appropriate loading condishytions The results are used with an appropriate factor of safety so that normal working stresses are always somewhat below the peak strength
The stressndashstrain relations obtained from the triaxial tests provide the basis for determinashytion of deformations in the field This may be done in a simplified manner by closed‐form
solutions or it may be done by employing the results of the triaxial tests for calibration of a constitutive model used with a numerical method in finite element or finite difference computer programs
16 Types of tests
The drainage conditions in the field must be duplicated as well as possible in the laboratory tests This may be done by appropriate drainage facilities or preventions as discussed above for the triaxial test In most cases the field drainage conditions can be approximated by one of the following three types of tests
1 Consolidated‐drained test called a CD‐test or just a drained test
2 Consolidated‐undrained test or a CU‐test3 Unconsolidated‐undrained test or a UU‐test
Additionalload
Excavation
ΔσV asymp 0
ΔσV asymp 0
ΔσV gt 0
ΔσV lt 0
Δσh lt 0
Δσh gt 0
Δσh lt ΔσV
Δσh
Figure 14 Examples of stress changes leading to failure in the field
6 Triaxial Testing of Soils
These tests are described in ASTM Standards D7181 (2014) D4767 (2014) and D2850 (2014) respectively
Which condition of drainage in the laboratory test logically corresponds to each case in the field depends on a comparison of loading rate with the rate at which the water can escape or be sucked into the ground Thus the permeability of the soil and the drainage boundary conditions in the field together with the loading rate play key roles in determination of the type of analysis and the type of test drained or undrained that are appropriate for each case Field cases with partial drainage can be correctly duplicated in laboratory tests if the effective stress path is determined for the design condition However the idea of the CD‐ CU‐ and UU‐tests is to make it relatively simple for the design engineer to analyze a condition that will render a sufficient factor of safety under the actual drainage condishytion without trying to estimate and experimenshytally replicate the actual stress path
It has been determined through experience and common sense that the extreme conditions are drained and undrained with and without consolidation As a practical matter in a commershycial laboratory it is easier to run an undrained test than a drained test because it is easier and faster to measure pore pressures than volume change Therefore even drained parameters are more likely to be estimated from a CU‐test than from a CD‐test
161 Simulation of field conditions
Presented below is a brief review of the three types of tests together with examples of field cases for which the tests are appropriate and with typishycal strength results shown on Mohr diagrams
Drained tests
Isotropic consolidation is most often used in the first stage of the triaxial test However anisoshytropic consolidation with any stress ratio is also possible
The shearing stage of a drained test is pershyformed so slowly the soil is so permeable and the drainage facilities are such that no excess
pore pressure (positive or negative) can exist in the specimen at any stage of the test that is
∆u = 0 (15)
It follows then from the effective stress principle
prime = minusσ σ u (16)
that the effective stress changes are always the same as the total stress changes
A soil specimen always changes volume during shearing in a drained test If it contracts in volume it expels pore fluid (usually water or air) and if it expands in volume (dilates) then it sucks water or air into the pores If a non‐zero pore pressure is generated during the test (eg by performing the shearing too fast so the water does not have sufficient time to escape) then the specimen will expel or suck water such that the pore pressure goes towards zero to try to achieve equilibrium between externally applied stresses and internal effective stresses Thus there will always be volume changes in a drained test Consequently the water content the void ratio and the dry density of the specimen at the end of the test are most often not the same as at the beginning
The following field conditions can be simushylated with acceptable accuracy in the drained test
1 Almost all cases involving coarse sands and gravel whether saturated or not (except if confined in eg a lens andor exposed to rapid loading as in eg an earthquake)
2 Many cases involving fine sand and someshytimes silt if the field loads are applied reashysonable slowly
3 Long term loading of any soil as for examplea) Cut slopes several years after excavationb) Embankment constructed very slowly in
layers over a soft clay depositc) Earth dam with steady seepaged) Foundation on clay a long time after
construction
These cases are illustrated in Fig 15The strength results obtained from drained
tests are illustrated schematically on the Mohr diagram in Fig 16 The shear strength of soils increases with increasing confining pressure
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
6 Triaxial Testing of Soils
These tests are described in ASTM Standards D7181 (2014) D4767 (2014) and D2850 (2014) respectively
Which condition of drainage in the laboratory test logically corresponds to each case in the field depends on a comparison of loading rate with the rate at which the water can escape or be sucked into the ground Thus the permeability of the soil and the drainage boundary conditions in the field together with the loading rate play key roles in determination of the type of analysis and the type of test drained or undrained that are appropriate for each case Field cases with partial drainage can be correctly duplicated in laboratory tests if the effective stress path is determined for the design condition However the idea of the CD‐ CU‐ and UU‐tests is to make it relatively simple for the design engineer to analyze a condition that will render a sufficient factor of safety under the actual drainage condishytion without trying to estimate and experimenshytally replicate the actual stress path
It has been determined through experience and common sense that the extreme conditions are drained and undrained with and without consolidation As a practical matter in a commershycial laboratory it is easier to run an undrained test than a drained test because it is easier and faster to measure pore pressures than volume change Therefore even drained parameters are more likely to be estimated from a CU‐test than from a CD‐test
161 Simulation of field conditions
Presented below is a brief review of the three types of tests together with examples of field cases for which the tests are appropriate and with typishycal strength results shown on Mohr diagrams
Drained tests
Isotropic consolidation is most often used in the first stage of the triaxial test However anisoshytropic consolidation with any stress ratio is also possible
The shearing stage of a drained test is pershyformed so slowly the soil is so permeable and the drainage facilities are such that no excess
pore pressure (positive or negative) can exist in the specimen at any stage of the test that is
∆u = 0 (15)
It follows then from the effective stress principle
prime = minusσ σ u (16)
that the effective stress changes are always the same as the total stress changes
A soil specimen always changes volume during shearing in a drained test If it contracts in volume it expels pore fluid (usually water or air) and if it expands in volume (dilates) then it sucks water or air into the pores If a non‐zero pore pressure is generated during the test (eg by performing the shearing too fast so the water does not have sufficient time to escape) then the specimen will expel or suck water such that the pore pressure goes towards zero to try to achieve equilibrium between externally applied stresses and internal effective stresses Thus there will always be volume changes in a drained test Consequently the water content the void ratio and the dry density of the specimen at the end of the test are most often not the same as at the beginning
The following field conditions can be simushylated with acceptable accuracy in the drained test
1 Almost all cases involving coarse sands and gravel whether saturated or not (except if confined in eg a lens andor exposed to rapid loading as in eg an earthquake)
2 Many cases involving fine sand and someshytimes silt if the field loads are applied reashysonable slowly
3 Long term loading of any soil as for examplea) Cut slopes several years after excavationb) Embankment constructed very slowly in
layers over a soft clay depositc) Earth dam with steady seepaged) Foundation on clay a long time after
construction
These cases are illustrated in Fig 15The strength results obtained from drained
tests are illustrated schematically on the Mohr diagram in Fig 16 The shear strength of soils increases with increasing confining pressure
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
Principles of Triaxial Testing 7
In the diagram in Fig 16 the total stresses are equal to the effective stresses since there are no changes in pore pressures [Eqs (15) and (16)]
The effective friction angle φprime decreases for all soils with increasing confining pressure and the
failure envelope is therefore curved as indishycated in Fig 16 The effective cohesion cprime is zero or very small even for overconsolidated clays Effective or true cohesion of any signifishycant magnitude is only present in cemented soils
Steady seepage Building foundation
Clay
Soft clay
Cut slope
(c)
(a) (b)
(d)
Slow construction of embankment
Figure 15 Examples of field cases for which long term stability may be determined on the basis of results from drained tests
1200
1200 1600 2000
800
800
Mohr enve
lope
400
4000
0
σ (kNm2)
τ (k
Nm
2 )
Figure 16 Schematic illustration of a Mohr diagram with failure envelope for drained tests on soil
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
8 Triaxial Testing of Soils
The effective stress failure envelope then defines the boundary between states of stress that can be reached in a soil element and states of stress that cannot be reached by the soil at its given dry density and water content
Consolidated‐undrained tests
As in drained tests isotropic consolidation is most often used in CU‐tests However anisoshytropic consolidation can also be applied and it may have greater influence on the results from CU‐tests than those from drained tests The specimen is allowed to fully consolidate such that equilibrium has been obtained under the applied stresses and no excess pore pressure exists in the specimen
The undrained shearing stage is begun by closing the drainage valve before shear loading is initiated Thus no drainage is permitted and the tendency for volume change is reflected by a change in pore pressure which may be measshyured by the transducer (see Fig 12) Therefore the second stage of the CU‐test on a saturated specimen is characterized by
∆V = 0 (17)
and
∆u ne 0 (18)
According to the effective stress principle in Eq (16) the effective stresses are therefore difshyferent from the total stresses applied in a CU‐test
The pore pressure response is directly related to the tendency of the soil to change volume This is illustrated in Fig 17 Thus there will always be pore pressure changes in an undrained test However since there are no volume changes of the fully saturated specimen the water conshytent the void ratio and the dry density at the end of the test will be the same as at the end of the consolidation stage
The following field conditions can be simushylated with good accuracy in the CU‐test
1 Most cases involving short term strength that is strength of relatively impervious soil deposits (clays and clayey soils) that are to be loaded over periods ranging from several
days to several weeks (sometimes even years for very fat clays in massive deposits) followshying initial consolidation under existing stresses before loading Examples of field cases in which short term stability considerations are appropriatea) Building foundationsb) Highway embankments dams highway
foundationsc) Earth dams during rapid drawdown
(special considerations are required here see Duncan and Wright 2005)These cases are illustrated in Fig 18
2 Prediction of strength variation with depth in a uniform soil deposit from which samples can only be retrieved near the ground surface This is illustrated in Fig 19
The strength results obtained from CU‐tests are illustrated schematically on the Mohr diagram in Fig 110 Since pore pressures develop in CU‐tests two types of strengths can be derived from undrained tests total strength and effecshytive strength The Mohr circles corresponding to
In undrained tests εV = 0
τ τσ σ
Loose andor high σ3
Effective conningpressure σ3 = σ3 ndash u
(contraction) (dilation)
Volume changetendency
Pore waterpressure change Δu
Dense andor low σ3εV gt 0 εV lt 0
Pore waterpressureu = ΔuΣ
Simple models for drained tests
Figure 17 Schematic illustration of changes in pore water pressure in undrained tests
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
Principles of Triaxial Testing 9
these two strengths will always have the same diameter but they are displaced by Δu from each other
Both the total and effective stress envelopes from CU‐tests on clays and clayey soils indicate increasing strength with increasing confining pressure As for the drained tests the effective friction angle φprime decreases with increasing conshyfining pressure and the curvature of the failure envelope is sometimes more pronounced than for sands In fact the effective strength envelope obtained from CU‐tests is very similar to that obtained from drained tests Thus the effective cohesion cprime is zero except for cemented soils In particular the effective cohesion is zero for remolded or compacted soils
The total stress friction angle φ is much lower than the effective stress friction angle φprime whereas the total stress cohesion c can have
a substantial magnitude The total stress friction angle is not a friction angle in the same sense as the effective stress friction angle In the latter case φprime is a measure of the strength derived from the applied normal stress while φ is a measure of the strength gained from the consoli-dation stress only If for example the total stress parameters are applied in a slope stability calcushylation in which a surcharge is suddenly added then the surcharge will contribute to the shear resistance in the analysis (which is incorrect) as well as to the driving force because there is no distinction between the normal forces derived from consolidation stresses and those caused by the surcharge A better approach would be to assign undrained shear strengths (su) based on the consolidation stress state by using an approach that involves suσvprime
Unconsolidated‐undrained tests
In the UU‐test a confining pressure is first applied to the specimen and no drainage is allowed In fact UU‐tests are most often pershyformed in triaxial equipment without facilities for drainage The soil has already been consolishydated in the field and the specimen is therefore considered to ldquocontainrdquo the mechanical propshyerties that are present at the location in the ground where the sample was taken Altershynatively the soil may consist of compacted fill whose undrained strength is required for stashybility analysis before any consolidation has occurred in the field
The undrained shearing stage follows immedishyately after application of the confining pressure The shear load is usually increased relatively fast until failure occurs No drainage is permitshyted during shear Thus the volume change is zero for a saturated specimen and the pore presshysure is different from zero as indicated in Eqs (17) and (18) The pore pressure is not measshyured and only the total strength is obtained from this test
Since there are no volume changes in a satushyrated specimen the void ratio the water content and the dry density at the end of the test will be the same as those in the ground
(a)
Building foundation
Embankment foundation
Rapid drawdown
(b)
(c)
Figure 18 Examples of field cases for which short term stability may be determined on the basis of results of CU‐tests
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
10 Triaxial Testing of Soils
The following field conditions may be simushylated in the UU‐test
1 Most cohesive soils of relatively poor drainshyage where the field loads would be applied sufficiently rapidly that drainage does not occur Examples of field cases for which results of UU‐tests may be useda) Compacted fill in an earth dam that is
being constructed rapidlyb) Strength of a foundation soil that will be
loaded rapidly
Descriptionof soil
Silty clayweathered
Silty clayhomogeneous
0
5
10
20
25
Depth (m)wl = liquid limit
wl
wp = plastic limit
wmin wmax
wav
w = 377
wl = 377 wp = 174cp = 0165St = 7
+ Vane tests
+
+
+
+
+
+
+
+
+
++
+
+
γ = 167 (kNm3)
wp15
10 1020 2030 3040 40 70 90
Average values
8050 60
Water content () Shear strength (kNm2)
Figure 19 Strength variation with depth in uniform soil deposit of Norwegian marine clay Reproduced from Bjerrum 1954 by permission of Geotechnique
ϕʹ
ϕ
Totalstresses
Effective stresses
σ3 σ1 σ1σ3 σu
τ
Figure 110 Schematic illustration of a Mohr diagram with total stress and effective stress failure envelopes from CU‐tests on soil (after Bishop and Henkel 1962)
![CTD 第2 部 · 2016. 12. 2. · 2.7 臨床概要 2.7.5 参考文献 2.7.5 参考文献 - 1 - 2.7.5 参考文献 添付資料番号 タイトル 著者 掲載紙 [資料4.3: 19] A](https://img.dokumen.tips/doc/110x75/609eac189e0ad348a403c3f5/ctd-c2-ef-2016-12-2-27-ee-275-efcoe-275-efcoe.jpg)
