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Department of Civil Engineering

Monash University

Compaction Behaviourof Soils

by

Nurses Kurucuk

Thesis submitted to Monash University

in partial fulfilment of of the requirements for the degree of

Doctor of Philosophy

January, 2011

c©Nurses Kurucuk

Copyright Notices Notice 1 Under the Copyright Act 1968, this thesis must be used only under the normal conditions of scholarly fair dealing. In particular no results or conclusions should be extracted from it, nor should it be copied or closely paraphrased in whole or in part without the written consent of the author. Proper written acknowledgement should be made for any assistance obtained from this thesis. Notice 2 I certify that I have made all reasonable efforts to secure copyright permissions for third-party content included in this thesis and have not knowingly added copyright content to my work without the owner's permission.

Declaration

This thesis contains no material which has been accepted for the award of any other degree or

diploma in any University or other institution. To the best of my knowledge, the thesis contains

no material previously published or written by another person, except where due reference has

been made in the text of the thesis.

Nurses Kurucuk

January 2011

Abstract

Soil compaction is widely applied in geotechnical engineering practice. It is used to maximise

the dry density of soils to reduce subsequent settlement under working loads or to reduce the

permeability of soils. The durability and stability of structures are highly related to the appro-

priate compaction achievement. The structural failure of roads and airfields, and the damage

caused by foundation settlement can often be traced back to the failure in achieving adequate

compaction. For that reason, soil compaction is important for engineering activities involving

earthworks.

Compacted soils are unsaturated by nature, which includes both air and water within their

voids. Thus, unsaturated soil mechanics principles are crucial in understanding the compaction

behaviour of soils. There are several qualitative studies, which attempt to explain the compaction

behaviour of soils and there is a vast body of literature covering the behaviour of compacted

soils. Still, fundamental research on the compaction process is limited. In addition, the current

constitutive models available for unsaturated soils assume that the soil state after compaction is

the initial state of the soil. However, compacted soils undergo a stress history which influences

the post compaction behaviour. Considering these facts, it still remains that the compaction

of soil is a complex phenomenon, which is not well explained, particularly from a quantitative

sense. Further understanding of the compaction behaviour during the compaction process will

provide important insights on the behaviour of compacted soils.

The main aim of this research project is to extend the current understanding of the com-

paction process of soils. The research focuses on three different areas: investigating the experi-

mental behaviour of soils during the static compaction process and obtaining data for compaction

modelling; developing a compaction model using the existing constitutive models for unsaturated

soils; and evaluating the performance of this model in predicting the compaction behaviour of

soils.

In the experimental part, static compaction tests were conducted on two different granular

soils, sand with 2% and 5% bentonite content by weight. The tests were undertaken on samples

with different water contents in order to observe the effect of matric suction on the compaction

behaviour. The initial matric suction of the specimens was measured using the null type axis

translation technique and the matric suction variations were monitored during the compaction

process. It was found that the unsaturated samples were always more compressible than the

saturated sample. This finding is contrary to the assumption made in most constitutive models,

and thus modelling the compaction behaviour using these models may result in some deficiencies.

In addition, in granular soils with low water content the axis translation technique was found to

vii

viii

be very time consuming for the suction measurements. This was attributed to the discontinuous

water phase within the samples.

To develop a compaction model, a volume change constitutive relationship for unsaturated

soils, defined in terms of two independent stress variables, was incorporated with pore pressure

predictions. The model was developed for undrained, semi-drained and drained loading condi-

tions. Initially, compressibility coefficients in the volume change relationship were considered

as constant parameters, i.e., the compressibility of a soil element does not change with increas-

ing vertical stress. Using constant compressibility coefficients, the compaction curve can be

predicted only for the wet side of the curve, not the dry side. Thus, variable compressibility

coefficients were derived from constitutive models proposed in the literature, and using these

coefficients, the well-known shape of the compaction curve was predicted on both dry and wet

side of the compaction curve. It was found that the shape of the compaction curve can be the-

oretically predicted using unsaturated soil mechanics principles. The main insight gained from

the model development was that the influence of matric suction on the material compressibility

with respect to net stress is the governing factor determining the inverted parabolic shape of the

compaction curve.

The performance of the compaction models were examined on their ability to predict the

compaction behaviour of soils. Data for four different soils, two sand-bentonite mixtures tested

in this study, and Boom clay and Speswhite kaolin data from literature, were used for mod-

els evaluation. Two different constitutive modelling approaches were analysed, which are the

separate stress state variables approach and combined stress state approach. It was concluded

that the samples prepared from initially slurry soils and from initially dry soils could not be

treated the same and would require the use of different sets of soil parameters. In addition, the

compaction behaviour of soils, prepared from initially dry samples, could only be modelled over

a narrow range of water contents using a single set of soil parameters. Minimum two sets of soil

parameters are required to model the compaction behaviour over a wide range of water contents

with the current constitutive models.

Acknowledgements

I would like to thank my supervisor Dr. Jayantha Kodikara for his ongoing patience and support

throughout the research project. I am grateful to Dr. Del Fredlund for his encouragement and

the valuable feedback he provided me. I should also mention Dr. Chaminda Galage’s help in

building my experimental setup.

I gratefully acknowledge the financial support received from both the Faculty of Engineering

and the Civil Engineering Department of Monash University. In addition, I acknowledge the

Monash Graduate School for providing me a scholarship in the first three and half years of my

study.

Further thanks are extended to the staff of the Civil Engineering Department. In particular

to Jenny, who was always there whenever I needed advice and support. Long and Mike were

always very helpful in the laboratory. I also appreciate Jane Moody’s meticulous work in editing

parts of my thesis.

I would like to thank Daghan for encouraging me to come to Melbourne, for the great

conversations we had together and helping me a lot in the beginning of my PhD journey. Thanks

Seb for always being very patient with me, for the great holidays we had together and for teaching

me to be a calmer person. I should also mention the contributions of my friends Chris, Scott,

Burcu, and David to my thesis in the review and editing processes. In fact, I am thankful to all

my friends for reminding me that there is life outside university.

I run out of words to express my gratitude to Cintia. She has been not only a dearest friend

but also a mother, sister and editor for me during the whole process. Finally, I would like to

thank my parents for simply being who they are and I am grateful to them for everything they

have done for me.

ix

Contents

Abstract vii

1 Introduction 1

1.1 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Research aim and scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Overview of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Literature review 5

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Qualitative studies for compaction theory . . . . . . . . . . . . . . . . . . . . . . 5

2.2.1 Proctor’s theory (1933) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2.2 Hogentogler’s theory (1936) . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2.3 Hilf’s theory (1956) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.4 Lambe’s theory (1959) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.5 Olson’s theory (1963) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.6 Barden and Sides’s theory (1970) . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.7 Summary of the compaction theories . . . . . . . . . . . . . . . . . . . . . 9

2.3 Suction measurement techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3.1 Direct measurement techniques . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.2 Indirect measurement techniques . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.3 Summary of the suction measurement techniques . . . . . . . . . . . . . . 16

2.4 Volume change behaviour of unsaturated soils . . . . . . . . . . . . . . . . . . . . 16

2.4.1 Stress variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.4.2 Volume change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4.3 Pore pressure development . . . . . . . . . . . . . . . . . . . . . . . . . . 18

xi

xii CONTENTS

2.4.4 Constitutive models for unsaturated soils . . . . . . . . . . . . . . . . . . 20

2.4.5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3 Selected materials for the research 25

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 Physical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2.1 Particle size distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2.2 Atterberg limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2.3 Linear shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2.4 Specific gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.3 Compaction characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.4 Soil water retention curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.4.1 Axis translation technique . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.4.2 Tensiometer measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.5 Consolidation characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.5.1 Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.5.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.6 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4 Testing equipment and experimental procedure 45

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.2 Testing Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.2.1 Compaction device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.2.2 Accessories for the compaction device . . . . . . . . . . . . . . . . . . . . 50

4.3 Experimental procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.3.1 Material preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.3.2 Static compaction test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.3.3 Test difficulties and problems . . . . . . . . . . . . . . . . . . . . . . . . . 61


5 Experimental results 65

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

CONTENTS xiii

5.2 Initial suction measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.3 Evolution of suction during the test . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.4 Volume change characteristics of soils . . . . . . . . . . . . . . . . . . . . . . . . 77


6 Modelling the compaction process 87

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.2 Formulation of the compaction process . . . . . . . . . . . . . . . . . . . . . . . . 87

6.2.1 Volume change calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.2.2 Pore pressure development . . . . . . . . . . . . . . . . . . . . . . . . . . 88

6.2.3 Compressibility coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . 92

6.3 Generation of the compaction curve . . . . . . . . . . . . . . . . . . . . . . . . . 96

6.3.1 Modelling of the compaction curve using constant compressibility coefficients 97

6.3.2 Modelling of the compaction curve using variable compressibility coefficients104


7 Performance of the model on predicting the static compaction curves 117

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

7.2 Experimental data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

7.2.1 Sand bentonite mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

7.2.2 Boom clay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

7.2.3 Speswhite kaolin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

7.3 Separate stress state variables approach . . . . . . . . . . . . . . . . . . . . . . . 121


7.3.2 Boom clay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134


7.3.4 Discussion on the BBM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

7.3.5 Other models developed with separate stress variables approach . . . . . . 145

7.4 Combined stress variables approach . . . . . . . . . . . . . . . . . . . . . . . . . . 146


7.4.2 Boom clay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155


7.4.4 Discussion on the SFG model . . . . . . . . . . . . . . . . . . . . . . . . . 163

xiv CONTENTS

7.4.5 Other models developed with combined stress variables approach . . . . . 164

7.5 Overall discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166


8 Conclusions and suggestions for future research 171

8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

8.1.1 Soil behaviour during the compaction process . . . . . . . . . . . . . . . . 171

8.1.2 Modelling the compaction process . . . . . . . . . . . . . . . . . . . . . . 172

8.1.3 Evaluation of the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

8.2 Suggestions for future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

References 176

Appendices

A Matlab Codes 187

A.1 Undrained modelling using the BBM . . . . . . . . . . . . . . . . . . . . . . . . . 187

A.2 Semi-drained modelling using the BBM . . . . . . . . . . . . . . . . . . . . . . . 190

A.3 Undrained modelling using the SFG model . . . . . . . . . . . . . . . . . . . . . 193

A.4 Semi-drained modelling using the SFG model . . . . . . . . . . . . . . . . . . . . 196

B Publications 199

B.1 Prediction of compaction curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

B.2 Theoretical modelling of the compaction curve . . . . . . . . . . . . . . . . . . . . 206

B.3 Evolution of the compaction process: Experimental study - preliminary results . . 211

List of Tables

3.1 Atterberg limits of ActiveGel 150 bentonite adopted from Shannon (2008) . . . . 28

3.2 Specific gravity of the materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.3 Summary of the compaction characteristics for S2B and S5B . . . . . . . . . . . 32

4.1 Loading steps for S2B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.2 Loading steps for S5B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.1 Water content of S2B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.2 Water content of S5B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.3 Matric suction change with loading for S2B . . . . . . . . . . . . . . . . . . . . . 75

5.4 Matric suction change with loading for S5B . . . . . . . . . . . . . . . . . . . . . 76

6.1 Comparison of Hilf and Hasan & Fredlund’s method for pore pressure generations 88

6.2 Parameter values for the pore pressure generations for Hilf’s and Hasan & Fred-

lund’s methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

6.3 Parameters used for the compaction curve modelling using constant compressibil-

ity coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

6.4 Parameters used for the compaction curve modelling using variable compressibility

coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

6.5 Matric suction values used for the corresponding water contents . . . . . . . . . . 105

7.1 Model parameters for S2B (BBM) . . . . . . . . . . . . . . . . . . . . . . . . . . 125

7.2 Modified model parameters for S2B . . . . . . . . . . . . . . . . . . . . . . . . . . 125

7.3 Model parameters for S5B (BBM) . . . . . . . . . . . . . . . . . . . . . . . . . . 129

7.4 Modified model parameters for S5B . . . . . . . . . . . . . . . . . . . . . . . . . . 130

7.5 Model parameters for Boom clay (BBM) . . . . . . . . . . . . . . . . . . . . . . . 135

xv

xvi LIST OF TABLES

7.6 Modified model parameters for Boom clay . . . . . . . . . . . . . . . . . . . . . . 135

7.7 Model parameters for Speswhite kaolin (BBM) . . . . . . . . . . . . . . . . . . . 138

7.8 Modified model parameters for Speswhite kaolin . . . . . . . . . . . . . . . . . . 138

7.9 Model parameters for S2B (SFG model) . . . . . . . . . . . . . . . . . . . . . . . 147

7.10 Model parameters for S5B (SFG model) . . . . . . . . . . . . . . . . . . . . . . . 149

7.11 Model parameters for Boom clay (SFG model) . . . . . . . . . . . . . . . . . . . 155

7.12 Model parameters for Speswhite kaolin (SFG model) . . . . . . . . . . . . . . . . 158

List of Figures

3.1 Particle size distribution of sand . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2 Particle size distributions of S2B and S5B . . . . . . . . . . . . . . . . . . . . . . 28

3.3 Standard and modified compaction curves of S2B . . . . . . . . . . . . . . . . . . 30

3.4 Standard and modified compaction curves of S5B . . . . . . . . . . . . . . . . . . 31

3.5 Schematic of the experimental setup for axis translation technique . . . . . . . . 33

3.6 Experimental setup of axis translation technique . . . . . . . . . . . . . . . . . . 34

3.7 Water volume discharge with time under 20 kPa applied air pressure . . . . . . . 35

3.8 Evaporation of water from the outflow container . . . . . . . . . . . . . . . . . . 36

3.9 Tensiometer used for matric suction measurements . . . . . . . . . . . . . . . . . 37

3.10 Matric suction measurements of S2B with tensiometer . . . . . . . . . . . . . . . 39

3.11 Matric suction measurements of S5B with tensiometer . . . . . . . . . . . . . . . 39

3.12 SWRC of S2B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.13 SWRC of S5B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.14 Load Track III used for oedometer tests . . . . . . . . . . . . . . . . . . . . . . . 41

3.15 Slope of the normal compression line for saturated S2B . . . . . . . . . . . . . . 42

3.16 Slope of the normal compression line for saturated S5B . . . . . . . . . . . . . . 43

4.1 Schematic of the compaction device setup . . . . . . . . . . . . . . . . . . . . . . 47

4.2 Compaction device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.3 Base of the pressure cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.4 Pressure transducer mounted on a steel block . . . . . . . . . . . . . . . . . . . . 49

4.5 Water volume discharge with time under 20 kPa, 50 kPa and 100 kPa applied air

pressures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.6 Average permeability of 1 bar ceramic disk . . . . . . . . . . . . . . . . . . . . . 51

xvii

xviii LIST OF FIGURES

4.7 Calibration curve of the pressure transducer . . . . . . . . . . . . . . . . . . . . . 53

4.8 Calibration curve of the LVDT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.9 GCTS pressure booster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.10 Experimental procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.11 Sample preparation by tamping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.12 Test stress path (matric suction change is exaggerated) . . . . . . . . . . . . . . . 59

5.1 Initial matric suction measurements for S2B . . . . . . . . . . . . . . . . . . . . . 67

5.2 Initial matric suction measurements for S5B . . . . . . . . . . . . . . . . . . . . . 69

5.3 Comparison of initial matric suction measurements using different techniques for

S2B, [a]Variation of degree of saturation with matric suction, [b]Variation of water

content with matric suction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.4 Comparison of initial matric suction measurements using different techniques for

S5B, [a]Variation of degree of saturation with matric suction, [b]Variation of water

content with matric suction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.5 Evolution of matric suction with time for S2B . . . . . . . . . . . . . . . . . . . . 73

5.6 Evolution of matric suction with time for S5B . . . . . . . . . . . . . . . . . . . . 74

5.7 Long equilibration time for S5B with 2.9% water content . . . . . . . . . . . . . 76

5.8 Variation of specific volume during the tests for S2B . . . . . . . . . . . . . . . . 78

5.9 Variation of specific volume during the tests for S5B . . . . . . . . . . . . . . . . 79

5.10 Variation of dry density during the tests for S2B . . . . . . . . . . . . . . . . . . 80

5.11 Variation of dry density during the tests for S5B . . . . . . . . . . . . . . . . . . 81

5.12 Variation of degree of saturation during the tests for S2B . . . . . . . . . . . . . 82

5.13 Variation of degree of saturation during the tests for S5B . . . . . . . . . . . . . 82

5.14 Variation of degree of the coefficient of compressibility due to net stress (ms1) for

S2B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

5.15 Variation of degree of the coefficient of compressibility due to net stress (ms1) for

S5B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

5.16 Variation of the coefficient of compressibility due to net stress (ms1) with degree

of saturation for S2B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.17 Variation of the coefficient of compressibility due to net stress (ms1) with degree

of saturation for S5B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.18 Compaction curves of S2B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

LIST OF FIGURES xix

5.19 Compaction curves of S5B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

6.1 Pore air and pore water pressure generation using Hilf’s approach . . . . . . . . . 90

6.2 Pore air and pore water pressure generation using Hasan & Fredlund’s approach 91

6.3 Comparison of Hasan & Fredlund’s and Hilf’s approach for pore air pressure

generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

6.4 Approach followed for the compaction curve generation . . . . . . . . . . . . . . 98

6.5 Modelling of the compaction curves using constant compressibility coefficients for

undrained loading [a] Hilf’s method [b] Hasan & Fredlund’s method [c] Compari-

son of Hilf’s and Hasan & Fredlund’s methods at σy = 700 kPa . . . . . . . . . . 99


semi-drained loading[a] Hilf’s method [b] Hasan & Fredlund’s method [c] Com-

parison of Hilf’s and Hasan & Fredlund’s methods at σy = 700 kPa . . . . . . . . 101


drained loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

6.8 Comparison of the modelled compaction curves using constant compressibility

coefficients for undrained, semi-drained and drained loading conditions (σy = 700

kPa lower curves and σy = 2000 kPa upper curves) . . . . . . . . . . . . . . . . . 103

6.9 Modelling of the compaction curves using variable compressibility coefficient for

undrained loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

6.10 Variation of the coefficient of compressibility (ms1) due to net stress during undrained

loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

6.11 Variation of the coefficient of compressibility (ms1) and the net stress with water

content during undrained loading . . . . . . . . . . . . . . . . . . . . . . . . . . . 107


semi-drained loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

6.13 Variation of the coefficient of compressibility (ms1) due to net stress during semi-

drained loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109


content during semi-drained loading . . . . . . . . . . . . . . . . . . . . . . . . . 110


drained loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

xx LIST OF FIGURES

6.16 Variation of the coefficient of compressibility (ms1) due to net stress during drained

loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112


content during drained loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

6.18 Comparison of the modelled compaction curves using variable compressibility co-

efficients for undrained, semi-drained and drained loading (σy = 700 kPa lower

curves and σy = 2000 kPa upper curves) . . . . . . . . . . . . . . . . . . . . . . . 113

7.1 Normal compression line of Boom clay . . . . . . . . . . . . . . . . . . . . . . . . 120

7.2 Normal compression lines of Boom clay under constant suctions . . . . . . . . . . 121

7.3 Normal compression line of Speswhite kaolin . . . . . . . . . . . . . . . . . . . . . 122

7.4 Normal compression lines of Speswhite kaolin for constant suctions . . . . . . . . 122

7.5 λ(s) of S2B for varying suctions (BBM) . . . . . . . . . . . . . . . . . . . . . . . 124

7.6 N(s) for S2B for varying matric suctions (BBM) . . . . . . . . . . . . . . . . . . 126

7.7 BBM predictions of the variation of dry density with applied vertical stress for

S2B [a] Comparison of the undrained (U) and semi-drained (S) predictions [b]

Comparison of the experimental data (E) and model (M) predictions (semi-drained)127

7.8 Compaction curves for S2B predicted by BBM [a] Comparison of undrained (U)

and semi-drained (S) predictions [b] Comparison of the experimental data (E) and

model (M) predictions (semi-drained) . . . . . . . . . . . . . . . . . . . . . . . . 128

7.9 λ(s) of S5B for varying matric suctions (BBM) . . . . . . . . . . . . . . . . . . . 129

7.10 N(s) for S5B for varying matric suctions (BBM) . . . . . . . . . . . . . . . . . . 130


S5B [a] Comparison of the undrained (U) and semi-drained (S) predictions [b]


7.12 Compaction curves for S5B predicted by BBM [a] Comparison of undrained (U)

and semi-drained (S) predictions [b] Comparison of the experimental data (E) and

model (M) predictions (semi-drained) . . . . . . . . . . . . . . . . . . . . . . . . 133

7.13 λ(s) of Boom clay for varying suctions (BBM) . . . . . . . . . . . . . . . . . . . . 134

7.14 N(s) for Boom clay for varying suctions (BBM) . . . . . . . . . . . . . . . . . . . 136

LIST OF FIGURES xxi


Boom clay [a] Comparison of the undrained (U) and semi-drained (S) predictions

[b] Comparison of the experimental data (E) and model (M) predictions (semi-

drained) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

7.16 Compaction curves for Boom clay predicted by BBM [a] Comparison of undrained

(U) and semi-drained (S) predictions [b] Comparison of the experimental data (E)

and model (M) predictions (semi-drained) . . . . . . . . . . . . . . . . . . . . . . 139

7.17 λ(s) of Speswhite kaolin for varying suctions (BBM) . . . . . . . . . . . . . . . . 140

7.18 N(s) for Speswhite kaolin for varying suctions (BBM) . . . . . . . . . . . . . . . 141

7.19 BBM predictions of the variation of void ratio with applied vertical stress for

Speswhite kaolin [a] Comparison of the undrained (U) and semi-drained (S) pre-

dictions [b] Comparison of the experimental data (E) and model (M) predictions

(semi-drained) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

7.20 Compaction curves for Speswhite kaolin predicted by BBM [a] Comparison of

undrained (U) and semi-drained (S) predictions [b] Comparison of the experi-

mental data (E) and model (M) predictions (semi-drained) . . . . . . . . . . . . 143

7.21 N(s) for S2B for varying matric suctions (SFG model) . . . . . . . . . . . . . . . 148

7.22 SFG model predictions of the variation of dry density with applied vertical stress

for S2B [a] Comparison of the undrained (U) and semi-drained (S) predictions [b]


7.23 Compaction curves for S2B predicted by SFG model [a] Comparison of undrained



7.24 N(s) for S5B for varying matric suctions (SFG model) . . . . . . . . . . . . . . . 152


for S5B [a] Comparison of the undrained (U) and semi-drained (S) predictions [b]


7.26 Compaction curves for S5B predicted by SFG model [a] Comparison of undrained



7.27 N(s) for Boom clay for varying suctions (SFG model) . . . . . . . . . . . . . . . 155

xxii LIST OF FIGURES


for Boom clay [a] Comparison of the undrained (U) and semi-drained (S) pre-

dictions [b] Comparison of the experimental data (E) and model (M) predictions

(semi-drained) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

7.29 Compaction curves for Boom clay predicted by SFG model [a] Comparison of



7.30 N(s) for Speswhite kaolin for varying suctions (SFG model) . . . . . . . . . . . . 160


for Speswhite kaolin [a] Comparison of the undrained (U) and semi-drained (S)

predictions [b] Comparison of the experimental data (E) and model (M) predic-

tions (semi-drained) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

7.32 Compaction curves for Speswhite predicted by SFG model [a] Comparison of



7.33 Stress paths for attaining samples with similar suctions . . . . . . . . . . . . . . 167

7.34 Volume change behaviour of samples with similar suction but developed under

different stress paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

7.35 Variation of the soil compressibility with suction . . . . . . . . . . . . . . . . . . 168

Chapter 1

Introduction

1.1 Problem statement

Soil compaction is widely used in geotechnical engineering and is important for the construction

of roads, dams, landfills, airfields, foundations and for engineered barriers which include landfill

liners and barriers for underground nuclear waste disposal. The main purpose of compaction is to

maximise the dry density of soils and therefore, to achieve favorable “strength and deformation”

behaviour for geotechnical applications.

Since Proctors’ pioneering work in 1933, researchers have tried to explain the governing

mechanisms in the densification stages of soils mainly in terms of capillarity and lubrication,

viscous water and physico-chemical interactions in soil. It was not until 1956 that the compaction

process was explained by Hilf using unsaturated soil mechanics principles. However, all of these

studies were predominantly qualitative due to the limited knowledge in the unsaturated soils

mechanics at the time. In addition, there is a vast body of literature covering the behaviour

of compacted soils. However, it is the the compaction process that brings the soil to its final

compacted stage. In this respect, examination of the compaction process is crucial to extend

the current understanding of the behaviour of compacted soils and to provide a link between

compaction process and the behaviour of compacted soils.

Since the late 1950s, the mechanical behaviour of unsaturated soils has been an extensive

research topic and significant advances have been made both in experimentation techniques

and constitutive modelling of unsaturated soils. The experimental techniques have reached a

stage where the compaction process can be carefully monitored. Furthermore, in the last few

1

2 CHAPTER 1. INTRODUCTION

decades, there has been an attempt to develop constitutive models for the mechanical behaviour

of unsaturated soils. Alonso et al. (1990) proposed the first elasto-plastic constitutive model to

couple strength and volumetric behaviour of unsaturated soils. Currently, there are numerous

constitutive models available in literature (Wheeler and Sivakumar, 1995; Bolzon et al., 1996;

Gallipoli et al., 2003a; Sheng et al., 2008) which can be used to model the compaction process.

Even though the constitutive models advanced significantly, there still remains a controversy

regarding the approaches used for models’ development. Thus, modelling the compaction process

will not only provide better understanding on the behaviour of the compacted soils but will also

give insights on the applicability of the current constitutive models.

1.2 Research aim and scope

The aim of this research project is to extend the current understanding of the compaction be-

haviour of soil during the compaction process in the light of unsaturated soil mechanics principles

and constitutive models. The scope of the thesis is limited to model and investigate the com-

paction process using the constitutive models that were developed with separate stress state

variables and also with combined stress variables. Constitutive models based on a single effec-

tive stress approach are excluded from the study due to the fact that the former ones are more

widely accepted in the literature.

The overall aim can be broken into the following main objectives:

1. Examining the behaviour of soil during the static compaction process and obtaining ex-

perimental data in order to use in the evaluation of the compaction process modelling;

2. Modelling the compaction process using the existing constitutive models to extend the

current understanding of the behaviour of the compacted soils; and,

3. Evaluating the performance of the compaction process models developed with different

approaches to gain insights on the applicability of the current constitutive models.

1.3 Overview of the thesis

Chapter 2 summarises the main features of the compacted soils. Qualitative studies on the

shape of the compaction curve are reviewed. The chapter provides a detailed description of the

constitutive models employed in the modelling part of this study. Since compaction is regarded

3

as a fabrication process of soils, the experimental studies on the fabric of compacted soils are

also detailed. Key challenges in modelling the compaction process are identified.

Soils that are investigated in the research project and their selection criteria are presented

in Chapter 3. The physical and geotechnical properties of the soils and their determination

techniques are described. These material properties will be used in Chapters 5 and 7 for the

analysis of the experimental results and evaluating the performance of the compaction models

developed with different approaches.

The testing equipments used and the experimental procedure followed to achieve the ob-

jectives of the targeted experiments are presented in Chapter 4. These are important for the

interpretation of the experimental results. Test difficulties and problems encountered during the

experiments are also presented in the chapter.

Chapter 5 presents the experimental results of the constant water content static compaction

tests. The experimental behaviour of soils during the compaction process is examined. The

influence of the initial matric suction on the volume change behaviour and the variation of

the matric suction during the compaction are monitored. The challenges of conducting such

experiments are discussed. The results obtained in this chapter are used for the evaluation of

the compaction model in Chapter 7.

The formulation of modelling the compaction process is presented in Chapter 6. One dimen-

sional static compaction process is modelled for undrained, semi drained and drained loading

conditions on the basis of unsaturated soil mechanics fundamentals and constitutive models. The

main parameters governing the shape of the compaction curve are identified. The formulations

are used in Chapter 7 to obtain the modelling predictions for the evaluation of the compaction

model.

In Chapter 7 the performance of the models developed with two different approaches are

examined on their ability to predict the compaction behaviour of soils. The models are evaluated

on four different soil types which include granular and fine soils. Insights are attained on the

applicability of the current constitutive models.

Chapter 8 presents the main conclusions derived from the work presented in this thesis.

Finally, the recommendations for future works are discussed.

Chapter 2

Literature review

2.1 Introduction

This chapter provides a brief review on experimental methods and theories required for the

examination of the compaction process in soils. Particular emphasis is given to the suction

measurement techniques and volume change behaviour of unsaturated soils because they are

required for monitoring and modelling the compaction process.

In Section 2.2, the theories proposed for the explanation of the inverted parabolic shape of

the compaction curves are summarised. The experimental methods for suction measurements

during the are summarised in Section 2.3. Finally, the volume change behaviour of unsaturated

soils is presented in Section 2.4.

2.2 Qualitative studies for compaction theory

Since Proctor’s pioneering work in 1933, many researchers have attempted to explain the leading

mechanisms in the densification stages, mainly on the dry side of the optimum water content

(OWC). The compaction curve was explained in terms of capillarity and lubrication (Proctor,

1933), viscous water (Hogentogler, 1936), pore pressure theory in unsaturated soils (Hilf, 1956),

physico-chemical interactions (Lambe, 1958), and the effective stress theory (Olson, 1963). In

addition, Barden and Sides (1970) undertook an experimental study on the relation between

the engineering performance of compacted unsaturated clay and microscopic observations of the

clay structure. These studies provide predominantly qualitative explanations of the shape of

5

6 CHAPTER 2. LITERATURE REVIEW

the compaction curve. The current section focuses on these theories and summarises them in a

chronological order.

2.2.1 Proctor’s theory (1933)

Proctor assumes that water has a dual effect on the soil: capillarity and lubrication. It is

contended that a thin film of water covers the soil particles due to surface tension. When the

films come together, they join the soil particles close to each other and cause high frictional

resistance between soil particles. On the other hand, he stated that sufficient amount of water

lubricates soil particles and reduces inter-particle forces. Therefore, in relatively dry soils the

dry density is low due to capillarity effect, whereas adding more water reduces shearing strength

and increases dry density due to lubrication.

Most of Proctor’s research on the compaction curve was based on lubrication and he placed

more emphasis on the concept of lubrication than on the concept of capillarity. However, obser-

vations by Horn (1960) showed that water acts as a lubricant for some but not for all soils. It

is found that water reduces the friction by approximately two times for sheet silicates, whereas

the friction coefficient for the submerged three-dimensional network silicates (i.e., quartz and

feldspar) is five times greater than the oven dry value of three-dimensional network silicates

(Horn, 1960). Therefore, if the lubrication theory is valid, sand should have its maximum dry

density in the dry stage. However, sand has a similar bell shaped compaction curve as other

soils.

2.2.2 Hogentogler’s theory (1936)

Hogentogler (1936) advanced the theory of viscous water to the soil compaction and proposed

that the compaction of soil goes through four stages of wetting. These stages are hydration,

lubrication, swelling and saturation.

The hydration stage involves adsorption of water within the soil particles and formation of

thin films on the particles surfaces. The first layer of the absorbed water is highly cohesive

and the high viscosity of water gives the soil a high shearing strength and results in a low dry

density. Adding more water to the soil results in absorbed water grading into free water, which

is the lubrication stage. When the water layers become thicker, viscosity of the water decreases.

Therefore, the shearing strength of the soil decreases too. As a result of decreasing shearing

strength in the lubrication stage, the dry density of the soil increases. The maximum amount of

7

lubrication occurs in the OWC. Hogentogler asserted that adding more water beyond the OWC

would result in displacement of soil particles and thus, the decrease of the dry density. Through

this stage, the soil swells without any change in air volume. During the saturation stage, he

stated that all the air is displaced and the saturation line joins the zero air voids line.

At present, it is known that the compaction of soils does not result in complete saturation,

and therefore the compaction curve cannot intersect with the zero air voids line. Moreover,

research carried out by Foster et al. (1955), Rowland et al. (1956), Walker (1956) and Martin

(1959) revealed that the thickness of the absorbed water on the surface of most clays is not more

than few molecular layers.

2.2.3 Hilf’s theory (1956)

Hilf (1956) introduced the first modern type of compaction theory, which is based on the theory

of pore-water and pore-air pressure in unsaturated soils. Instead of using the common water

content-dry density curve, he used a plot based on the void ratio-water void ratio. The minimum

void ratio corresponds to the maximum dry density in the Hilf’s curve, and the shape of the

compaction curve is similar to the usual Proctor’s curve.

Hilf explained the shape of the compaction curve by the concepts of pore air pressure and

capillarity. The capillary bridges in dry soils resist the compaction pressure and therefore, the

dry density is low. However, when the water content increases the menisci flattens and cannot

resist the compaction pressure, hence the dry density increases. When the soil reaches its OWC,

the air is trapped and cannot escape. The trapped air builds up high air pressure, and therefore

reduces the effectiveness of the compaction.

The research conducted by Gilbert (1959) and Langfelder et al. (1968) support the Hilf’s pore

pressure explanation on the shape of the compaction curve that the air permeability is zero close

to the OWC. Hilf believed that the negative pressures in the moisture films are interconnected

for the water content used in the field compaction. In addition, he assumed that these pressures

result in an all-round effective compressive stress on the soil skeleton which is equal in magnitude

to the negative pressure. However, subsequent investigations conducted by Bishop (1959) and

Bishop et al. (1960) designate that the capillary pressure act as an effective stress by a factor of

χ. The value of χ is difficult to determine and direct measurements cannot be done. Therefore,

this subject is still divisive (Hilf, 1975).


2.2.4 Lambe’s theory (1959)

Lambe (1958) attempted to explain the shape of the compaction curve with the help of surface

chemical theories. The electrolyte concentration in the pore water is high at low water content.

Therefore, the inter-particle repulsion between the soil particles is reduced. The reduced inter-

particle forces allow flocculation to occur at low water contents and result in low dry-densities.

On the other hand, adding more water to the soil reduces pore water electrolyte concentration

and allows double layers to develop; hence, the soil results in a more disperse structure. Higher

dry densities can be obtained as a result of more dispersed structure.

Olson (1963) stated that Lambe’s explanation of the shape of the compaction curve is based

on the double layer theory and this theory could be used to predict the shape of the swelling

curve for sodium illite. However, he stated that it does not apply to calcium illite which has a

compaction curve of the same shape of other soils. Therefore, Olson (1963) concluded that this

theory does not have general applicability.

2.2.5 Olson’s theory (1963)

Olson (1963) explained the shape of the compaction curve using the effective stress concept. For

compaction on the dry side of the OWC, the increase in the water content increases the degree of

saturation and results in higher pore pressure. Therefore, the effective stress reduces for higher

water contents. As a result of reduced effective stress, the shearing stress of the soil decreases

and allows the soil to densify more than for low water content soil.

He also stated that the lubrication theory of Proctor (1933) and the viscous water theory of

Hogentogler (1936) appear to apply to the low water content-moisture density curve. At very

low water content, the electrical forces which attract the first layer of the water to the mineral

surfaces are stronger than the forces between water molecules. Therefore, the menisci are not

formed at this stage and water act as a lubricant between soil particles. Menisci start to form

by adding more water and this is the peak of the low water content-moisture density curve. The

compacted dry density starts to reduce again by adding more water due to the development of

menisci. Olson (1963) concluded that the low water content-moisture density curve can be seen

only in soils containing high percentage of plate shaped particles.

In his analysis, Olson (1963) assumed that the shearing strength of the inter-particle contact

surfaces is a purely frictional phenomenon and he did not include the cohesion component.

However, for clays of very high plasticity the strength of the inter-particle contacts may be

9

purely cohesional. Therefore, the theory may not be fully applicable for high plasticity soils.

2.2.6 Barden and Sides’s theory (1970)

Barden and Sides (1970) undertook an experimental investigation of the engineering behaviour

of compacted clay and intended to relate this to the microscopic observations of unsaturated clay

structure. Their results indicate that at low water contents, the low dry density is caused by the

presence of large air filled macro pores which have high strength and can resist to compaction

pressure without much distortion. When the water content of the soil is increased, the air filled

macro pores become wetter and weaker. Hence, during compaction it is easier to distort them

and the dry density of the soil increases. If more water above the OWC is added to the soil, the

water layers between the soil particles become thicker and the dry density of the soil decreases.

2.2.7 Summary of the compaction theories

In summary, Proctor’s capillarity and lubrication theory, Hogentogler’s viscous water theory,

and Lambe’s physico-chemical theory were reasonably consistent with the existing knowledge

at the time the theories were developed. However, the advances of knowledge have applied

limitations to these theories (Olson, 1963). Moreover, none of these theories have been subjected

to diagnostic laboratory experiments. As a result, these theories are rather speculative. The

effective stress explanation of the shape of the compaction curve which was carried out by Hilf

(1956), Olson (1963), and Barden and Sides (1970) appears more reasonable than the explanation

of the lubrication, the viscous water and the physico-chemical theories (Hilf, 1975).

In conclusion, these works provide predominantly qualitative explanations of the shape of

the compaction curve. Further research based on new measurement techniques are needed to

explain the shape of the compaction curve and the behaviour of compacted soils.

2.3 Suction measurement techniques

Suction is an important state variable to be monitored in order to better understand the funda-

mentals of the compaction process. There are numerous methods for suction measurements and

they can be divided in to two major groups: direct and indirect suction measurement techniques.

These methods are briefly summarised and evaluated in this section to find the most appropriate

technique to be used in the current study.


2.3.1 Direct measurement techniques

In direct methods, the pore pressure or the water potential of soil is directly measured. This

measurement techniques include the null type axis translation technique and tensiometers.

Axis translation technique

The axis translation technique is the most widely used method for controlling the matric suctions

(Delage et al., 2008), defined as the difference between the pore air pressure (ua) and the pore

water pressure (uw), in soil. It can also be used for matric suction measurements, where it is

referred as the null type axis translation technique.

The working principle of this method is based on the capillary phenomenon. When a capillary

tube is placed in water under atmospheric conditions, the water will rise within the tube due to

the water pressure being smaller in reference to the atmospheric pressure. The angle between

the water and the air interface will determine the magnitude of the matric suction. In a closed

system, if this capillary tube is exposed to elevated air pressures, the increase in the air pressure

will be equally transferred to the water, assuming that the water is incompressible. Thus, the

angle between the air and the water interface would not change, but the water pressure within

the tube will now be positive.

The equipment for measuring the matric suction of soils using this method was first intro-

duced by Hilf (1956). A high air entry ceramic disk is used as an interface to separate the

water and air phases. A ceramic disk is a porous disk with fine pores. The capacity of the disk

determines the maximum air pressure that can be applied to the disk without allowing the free

air to pass through the fine pores. The ceramic disk is placed on a water compartment, which

is connected to a pressure transducer. As soon as an unsaturated soil sample is placed onto the

disk, it will start absorbing water from the ceramic disk and the tension in the water phase will

be directly transferred to the pressure transducer. However, if air pressures, which are higher

than the matric suction of the sample, are applied to the system this will be transferred to the

water phase and thus to the transducer. Now the transducer will be reading positive water

pressures. The matric suction of the sample will be equal to the difference between the applied

air pressure (ua) and the water pressure (uw) readings by the transducer. This hypothesis has

been validated by Hilf (1956) and Bishop and Donald (1961).

This method can be used to measure matric suctions up to 1500 kPa. This is due to the

maximum capacity of the ceramic disks that are currently being manufactured.

11

There are some limitations and difficulties associated with this technique. This limitations

are summarised below:

• The matric suctions measured by the axis translation technique are found to be slightly

lower when compared to the measurement with tensiometers (Chahal and Yong, 1965).

This is attributed to the formation of air nucleation within the water, which will result in

a smaller contact angle between the interface of the air and water phases, when elevated

air pressures are applied.

• At high saturations, when the air phase becomes occluded within the water phase, the

application of air pressure to the system, which is transferred to the water phase, will

compress the occluded air. Thus, the angle between the water and air interface will be

altered and the correct measurements of matric suction will not be possible. This method

was experimentally evaluated by Fredlund and Morgenstern (1977) for degrees of saturation

between 76% and 95%, and by Tarantino et al. (2000) for degrees of saturation between

56% and 77%. In addition, Bocking and Fredlund (1980) conducted a theoretical study

and concluded that the matric suctions are overestimated if the soil has a compressible

structure. It was suggested by Romero (2001) that the air pressure should be changed at

a very slow rate to maintain the continuous air channels.

• Some air can diffuse under the ceramic disk when tests take long time. This can alter the

measurements of the matric suction. In addition, the diffused air will accumulate under

the ceramic disk and may result in the loss of the continuity between the pore water of

the sample and the water in the compartment under the ceramic disk. The diffused air

needs to be regularly flushed to avoid this problem. Vanapalli et al. (2008) suggested a

flushing system to periodically remove the dissolved air accumulated under the ceramic

disk. However, it should be taken into account that, flushing the system too often will

extend the testing durations as it will be described in Chapter 5.

• Condensation of vapour in the pressure chamber walls due to the temperature variations

was reported by Oliveira and Marinho (2006), which will lead to the relative humidity

changes within the chamber. The changes in the relative humidity around the soil specimen

will result in the erroneous measurements at low suctions (Marinho et al., 2009). Moreover,

the compressed air is generally applied to the pressure chamber and a moisture loss through

compressed air lines was reported by Romero (2001). In addition, Romero (2001) have


conducted a study on numerical calculations for the moisture loss through compressed air

lines. Numerical analysis was also carried out by Romero (1999) to simulate the evaporative

fluxes and the corresponding matric suction changes. It was concluded that no important

suction changes are expected with evaporative fluxes lower than 9.4x10−7 (mm3/s)/mm2.

• The test durations can be long due to the matric suction equilibration time once the air

pressure is applied. The time depends on the sample size and type due to the permeability

of the soil sample (Marinho et al., 2009). Kunze and Kirkham (1962) proposed an analytical

equation to estimate the equalisation time, which considers the impedance of the ceramic

disk and the permeability of the soil sample. The equilibration time for the initial matric

suction measurements using null method was reported to be less than a day for fine grained

and residual soils (Vanapalli et al., 1999; Fredlund and Vanapalli, 2002; Rahardjo and

Leong, 2006) and around three days for gneissic soils Oliveira and Marinho (2006).

• Recently, Baker and Frydman (2009) criticised the use of axis translation technique in

suction measurements. They have stated that, in field, high suctions cannot develop with-

out the cavitation of water and the axis translation technique alters the soil behaviour

by preventing the cavitation. Thus, it should not be used to examine the behaviour of

unsaturated soils.

In summary, there are some challenges in using the axis translation technique for suction

measurements. However, when the problems are carefully considered, the axis translation tech-

nique is a reliable and efficient method for soil matric suction measurements. It also provides

some advantages over other techniques which will be pointed out in the reminder of this section.

Tensiometers

Tensiometers are devices that directly measure the pore water pressure of soils. Tensiometers

consist of a water reservoir, a ceramic disk which acts as an interface between the air and water

phases, and a pressure gauge (e.g., strain gauge diaphragm, pressure transducer).

The capacity of the standard tensiometers are recorded to be around -80 kPa pressure. This

value was attributed to the inability of water to sustain negative pressures. This supposition was

incorrect as it was experimentally shown by numerous researchers (Henderson and Speedy, 1980;

Zheng et al., 1991). It was noticed that its not the water that cannot sustain tension beyond that

values but the occurrence of heterogenous cavitation within the water that determines this limit.

13

The cavitation occurs in the boundary between the water reservoir wall and the water, and/or

between the contact of the small particles within the water reservoir and the water. The reasons

of heterogenous cavitation is well explained in Marinho and Chandler (1995) and Marinho et al.

(2009). Ridley and Burland (1993) introduced the first tensiometer which can go beyond that

pressures and it is referred as a high capacity tensiometer. The main difference from standard

tensiometers is the use of a much smaller water reservoir in order to delay cavitation.

The high capacity tensiometers are designed either by using strain gauge diaphragm or fitting

a ceramic disk to a commercial pressure transducer. The ceramic disk is fitted to the transducer

by means of O-ring (Ridley and Burland, 1993; Guan and Fredlund, 1997; He et al., 2006),

araldite (Meilani et al., 2002; Take and Bolton, 2003; Lourenco et al., 2006) or copper gasket

(Toker et al., 2004), which are also a source of air presence within the tensiometer and therefore

a source of cavitation. It is shown that a significant improvement can be done when O-ring is re-

placed by araldite or copper gasket (Toker et al., 2004). In addition, tensiometers designed using

a strain gauge diaphragm (Ridley and Burland, 1995; Marinho and Chandler, 1995; Tarantino

and Mongiovı, 2002; Cui et al., 2008; Rojas et al., 2008b) are found to have higher capacity and

longer measurement duration, compared to the ones that use pressure transducers.

Another source of cavitation is the presence of air babbles within the pores of the ceramic

disk. Full saturation should be attained in order to delay cavitation. This is generally achieved

by initially saturating the transducer under vacuum and subsequently pre-pressurising it. Pre-

pressurisation is required in order to dissolve the pore air trapped in the ceramic disk or on the

walls of the water reservoir. The effects of saturating the tensiometer under vacuum is presented

elaborately by Take and Bolton (2003). The effect of pre-pressurisation on the cavitation and

the procedures for pre-pressurisation has been extensively studied in literature by Ridley and

Burland (1995); Guan and Fredlund (1997); Tarantino and Mongiovı (2002); Meilani et al. (2002);

Take and Bolton (2003); Lourenco et al. (2006); He et al. (2006); Mahler and Diene (2007); Cui

et al. (2008). In addition, cycles of cavitation, which is induced by placing the tensiometer

in contact with a dry sample, and pre-pressurisation was also found to improve the maximum

measurement durations of the test (Tarantino and Mongiovi, 2001; Tarantino and Mongiovı,

2002; Toker, 2002; Take and Bolton, 2003).

Time to reach equilibration during tensiometer measurements was reported to depend on

the good contact between the tensiometer and the soil sample (Boso et al., 2004; Oliveira and

Marinho, 2008). It was suggested by Oliveira and Marinho (2008) to use a soil paste, which has


a water content between its plastic and liquid limits, to maintain a better contact between the

porous disk and the soil. Boso et al. (2004) also showed that the use of soil sample at its liquid

limit would extend the equilibration time. In addition, as it would be expected the equilibration

time will depend on the permeability of the soil. Moreover, for tests at constant water contents

the equilibration time was reported to be about couple of hours (Tarantino and Tombolato, 2005;

Delage et al., 2007). This is a great advantage compared to the equilibration time required in

the axis translation technique.

One drawback of tensiometers compared to the other methods is the maximum measurement

duration. Although, a great care is taken for the preparation of the tensiometers, the cavitation

will eventually occur. Maximum eight days of measurement is reported by Cunningham et al.

(2003) at 800 kPa matric suction. The tensiometer has to be replaced for tests that take long

durations. An important advantage of tensiometers over axis translation technique is that they

can be used for matric suction measurements in the field.

2.3.2 Indirect measurement techniques

Indirect measurements do not measure the soil suction directly, but parameters such as water

content or relative humidity are measured and, later related to suction through a calibration

with a known values of suctions. These methods include the use of psychrometers and filter

paper.

Psychrometers

There are three types of psychrometers based on different working principles. These types in-

clude thermocouple psychrometers, transistor psychrometers and chilled-mirror dew-point psy-

chrometers. These methods can be used to measure the total suction of the soil. Each of these

psychrometers will be explained in the current section.

Thermocouple psychrometers work based on the temperature difference between two refer-

ence points, which are the reference junction and the measurement junction. This method was

used by Spanner (1951); Richards and Ogata (1958); Meeuwig (1972); Campbell (1979); Brown

and Robert (1980); Brown and James (1976) for ranges between 0.3 MPa and 8 MPa. The

equilibration time depends on the volume and initial relative humidity of the chamber, and also

the soil suction of the sample. The time required for equilibrium varies from several hours to

several days (Brown and Robert, 1980; Campbell, 1979). In order to measure the suctions with

15

an accuracy of 10 kPa, the temperature variation should be kept within a range of 0.001 ◦C

(Edil and Motan, 1984).

Transistor psychrometers are developed as an alternative to thermocouple psychrometers

to extend the suction range. The working principle is similar to thermocouple psychrometers.

There are two main difference from the previous method; the application of water, which is

manually applied by dropping water, and the measurement of the current, which is conducted

by means of a transistor. The method was used by Dimos (1991); Woodburn et al. (1993) and

Truong and Holden (1995) with an upper limit to 15 MPa. The equilibration time in general is

about 1 hour. This method was compared with tensiometer measurements (osmotic effect was

subtracted) by Boso et al. (2003) and a good agreement was observed in the range of 1 MPa

and 3 MPa.

Chilled-mirror dew-point psychrometers are also developed as an alternate to the thermocou-

ple psychrometers. This method measures the temperature in which the condensation happens.

The soil sample is placed in a housing chamber which contains a mirror and a photoelectric de-

tector of condensation on the mirror. The mirror temperature is controlled by a thermoelectric

cooler. The relative humidity is estimated from the difference between the first condensation

temperature and the temperature of the soil sample. The method was successfully used by

Gee et al. (1992); Brye (2003); Leong et al. (2003); Tang and Cui (2005); Thakur and Singh

(2005) and Agus and Schanz (2005) up to maximum suctions of 60 MPa. The time required for

equilibration using this method can be as low as 5 minutes. In addition, Cardoso et al. (2007)

compared the measurements between this method and the transistor psychrometers. A good

agreement was observed in the range from 1 MPa to 7 MPa.

In summary, psyhcrometers are used to measure the total suctions at ranges from 0.3 MPa to

70 MPa. The method is not reliable in low suctions because a small change in relative humidity

results in a high suction change and thus, accuracy level is low.

Filter paper

The filter method can be used to measure both the total suction and matric suction of soils. It

is a relatively cheap method compared to the other methods described above.

It works with the principles of either vapour equilibration or water content equilibration.

When the filter paper comes to equilibrium through vapour, total suction is measured. On the

contrary, when it is placed in contact with the soil sample, it comes to equilibrium through


water flow and matric suction is measured. In order to maintain the contact, filter paper can be

either placed on top (Bulut et al., 2001) or buried Houston et al. (1994) within the soil sample.

After equilibrium is reached, the water content of the filter paper is measured and it is related

to suction through calibration curves, which are developed through measurement techniques.

Whatman #42, Schleicher and Schuell #589 White Ribbon, and Fisher 9-790A are commonly

used filter papers commercially available.

The method requires approximately a week for equilibration. It is applicable to ranges from

1 MPa to 500 MPa. At lower suction ranges the relationship between total suctions and relative

humidity is very steep, thus the accuracy becomes very low (Sibley et al., 1990). In addition,

since slight temperature variations can cause significant changes in the relative humidity, the

method is also very sensitive to temperature variations.

2.3.3 Summary of the suction measurement techniques

In this section, direct and indirect suction measurement methods were briefly described. It was

shown that the indirect measurement techniques are better for the high suction ranges and not

reliable at suctions lower that 0.3 MPa (for the thermocouple psychrometer). In addition, the

filter paper method cannot be used for continuous suction measurements, which is the main aim

of the experimental part of this project. Considering these facts, the axis translation technique

and tensiometers are adopted to be used in the current study.

2.4 Volume change behaviour of unsaturated soils

The volume change behaviour of soil needs to be predicted in order to model the compaction

process. This section presents the basic concepts for the volume change calculations. Since the

compaction process is modelled for one dimensional compression, only the volume change calcu-

lations are presented and shear behaviour of soils is beyond the scope of this study. Initially, the

stress variables for unsaturated soils are summarised. As it is shown later in this section, the

pore pressure development during the compaction process is crucial for the modelling the com-

paction behaviour. A brief summary is provided on the pore pressure development approaches

available in literature. In addition, constitutive models are required for the calculations of the

compressibility coefficients. Thus, constitutive models developed for unsaturated soils are also

summarised in this section. The volume change formulations of the models, that are examined

17

in detail in the current study, are also described.

2.4.1 Stress variables

The principal of effective stress (Terzaghi, 1936) provided the key for analysing the mechanical

behaviour of unsaturated soils. For that reason, early researchers attempted to extend the

concept of the effective stress and relate it to the behaviour of unsaturated soils. The most

widely used relationship was proposed by Bishop (1959) in the following form:

σ′ = σ − ua + χ(ua − uw) (2.1)

where σ′ is the effective stress, σ is the total stress, χ is a factor varying with degree of saturation,

ua is the pore air pressure and uw is the pore water pressure.

The important assumption of defining a single effective stress is to relate all the measurable

changes in stress, compression and shearing to the changes in the effective stress. However,

early experimental studies failed to find a single χ parameter which could be used to predict

the volumetric and shearing strengths of soils (Coleman, 1962; Bishop and Blight, 1963; Blight,

1967). Jennings and Burland (1962) were the first to challenge the validity of Equation 2.1 and

whether it was correct to combine the total stress (σ), pore air pressure (ua) and pore water

pressure (uw) in a single equation. However, it became clear that the volumetric strain is not

controlled by a single parameter.

Due to the difficulties in determining the χ parameter, experimental results pushed towards

the adoption of two independent stress state variables. Matyas and Radhakrishna (1968) devel-

oped state surfaces for the void ratio (e) and degree of saturation (Sr), based on two separate

stress state approach. Fredlund and Morgenstern (1977) argued that the use of any two of the

three stress variables σ− ua, σ− uw and ua − uw would be sufficient to fully describe the stress

state of unsaturated soils. This approach is adopted widely in literature and has formed the

basis of the most of the constitutive models for unsaturated soils.

There are also models developed using the effective stress principal for unsaturated soils

in literature (Loret and Khalili, 2002; Laloui and Nuth, 2009). However, this approach is not

considered in this study due to the time restrains and the former approach being more widely

accepted. The topic is very controversial and requires meticulous separate examination; and

thus, is out of the scope of this study.


2.4.2 Volume change

The description of volume change in terms of two independent stress variables was proposed by

Fredlund & Morgenstern (1976). For one dimensional loading, the equation is in the following

form:

εv =∆VvV0

= ms1∆(σy − ua) +ms

2∆(ua − uw) (2.2)

where εv is the volumetric strain, ∆Vv is the overall volume change, V0 is the initial volume,

∆(σy − ua) is the change in the vertical net stress, ∆(ua − uw) is the change in matric suction,

ms1 is the compressibility of a soil element with respect to vertical net stress (σy − ua) and ms

2

is the compressibility of a soil element due to matric suction (ua − uw).

2.4.3 Pore pressure development

One of the primary aspects associated to model the compaction process is the calculations

of the pore pressure development as it can be seen from Equation 2.2. There are two different

approaches available in the literature that can be adopted for pore pressure developments, which

are Hilf’s (1948) and Hasan & Fredlund’s (1980) approaches. These two methods are summarised

in this section.

Hilf’s approach (1948)

Hilf (1948) developed a relationship between pore pressure and applied stress, which is based on

one-dimensional soil compression, Boyle’s law and Henry’s law, and is expressed as follows:

∆ua =

1

1 +(1 − Sr0 + hSr0)n0

(ua0 + ∆ua)mv

∆σy (2.3)

where ∆ua is the change in the pore air pressure, Sr0 is the initial degree of saturation, h is

the solubility coefficient of air in water, n0 is the initial porosity, ua0 is the initial absolute pore

air pressure, mv is the coefficient of volume change in saturated soil, and ∆σy is the change in

applied vertical stress.

Hilf (1948) developed this equation assuming that both air and water phases are undrained,

and volume reduction is due to air dissolving in water and compression of free air. Both liquid

and solid phases were considered to be incompressible. In this approach, it is also assumed that

19

the changes in pore air pressure are equal to the changes in pore water pressure, which makes

the change in matric suction (∆(ua − uw)) insignificant.

Hasan & Fredlund’s approach (1980)

Hasan & Fredlund & (1980), on the other hand, developed an equation for pore pressure (ua

and uw) predictions during undrained loading using pore pressure parameters. They used pore

pressure parameters in the following form:

dua = Badσy (2.4)

duw = Bwdσy (2.5)

where Ba is the pore air pressure parameter and Bw is the pore water pressure parameter. The

pore pressure parameters are defined as:

Ba =R2R3 −R4

1 −R1R3(2.6)

Bw =R2 −R1R4

1 −R1R3. (2.7)

In Equations (2.6) and (2.7) parameters R1, R2, R3 and R4 are expressed as following:

R1 =(ms

2/ms1 − 1 − (1 − Sr + hSr)n/(uam

s1)

ms2/m

s1 + SrnCw/ms

1

(2.8)

R2 =1

ms2/m

s1 + SrnCw/ms

1

(2.9)

R3 =ma

2/ma1

ma2/m

a1 − 1 − (1 − Sr + hSr)n/(uams

1)(2.10)

R4 =1

ma2/m

a1 − 1 − (1 − Sr + hSr)n/(uams

1)(2.11)

where Sr is degree of saturation, n is the porosity, Cw is the compressibility of water, ma1 is

the compressibility of the air phase with respect to vertical net stress (σy − ua) and ma2 is the

compressibility of the air phase with respect to matric suction (ua − uw).


In this method, it is assumed that the soil particles are incompressible, but the fluid phase is

compressible (air and water). Therefore, the volume reduction of a soil element is considered to

be due to the compression of free and dissolved air as well as water. In contrast to the approach

proposed by Hilf (1948), the matric suction changes were taken into account. It was accepted

that the air and water pressures become equal at saturation. Therefore, matric suction will

decrease from the initial value to zero at saturation.

2.4.4 Constitutive models for unsaturated soils

Constitutive models can be used to estimate the variations in the compressibility coefficients,

which are defined in Equation 2.2. In this study, the constitutive models developed with separate

stress and combined stress state variables approach are shortly summarised. The mathematical

formulations for the models that were analysed in detail are presented in this section. These

equations will be later used to model the compaction process.

Separate stress state variables approaches

Alonso et al. (1987) introduced an elasto-plastic critical state framework, which form the basis

for the first constitutive model for unsaturated soils. The mathematical formulation of this

model was later presented in Alonso et al. (1990) and is commonly know as the Barcelona Basic

Model (BBM). The model considers the net stress (σ− ua) and matric suction (s = ua− uw) as

independent stress state variables.

The volumetric strain (εv) for one dimensional loading can be written in the following form

when derived from the BBM:

εv =dν

ν=λ(s)

ν

d(σy − ua)

(σy − ua)+κsν

d(ua − uw)

(ua − uw) + uatm(2.12)

where ν is the specific volume of the soil element, λ(s) is the slope of the NCL at matric suctions

defined in semi logarithmic plot, d(σy − ua) is the change in vertical net stress, d(ua − uw) is

the change in matric suction and κs is the slope of the volume change vs. matric suction curve

defined in semi logarithmic plot.

In Equation 2.12, λ(s) is defined as:

λ(s) = λ(0)[(1 − r)e−βs + r] (2.13)

21

where λ(0) is the slope of the NCL for saturated soil, r is a constant parameter related to the

maximum stiffness of the soil, and β is a constant parameter which controls the rate of increase

of soil stiffness with matric suction.

Integrating Equation 2.12 for vertical net stress changes (σy − ua) under a constant matric

suction leads to:

ν = N(s) − λ(s)ln(σy − ua)

(σy − ua)c(2.14)

where N(s) is the specific volume at an initial stress state, (σy − ua)c) and (σy − ua)c is a

reference stress in which changes of matric suction causes only elastic deformation.

In the BBM, N(s) is defined as:

N(s) = N(0) − (λ(0) − λ(s))ln(σy − ua)c − κsln

(s+ uatmuatm

)(2.15)

where N(0) is the specific volume, at a reference stress state,(σy − ua)c, for saturated soil.

The BBM was later modified by Wheeler and Sivakumar (1995). They abandoned the use

of a reference stress (pc) at which the change of matric suction only produces elastic volume

deformations (a yield curve is a straight vertical line in matric suction and stress plot). Atmo-

spheric pressure was taken as a reference pressure in their volume change equation. In addition,

they used the empirical values for the slope of the NCLs (λ(s)) and the initial specific volumes

(N(s)) of unsaturated soil samples rather than introducing an equation for the variation of the

slope of the NCLs with the change in matric suction. Wheeler and Sivakumar (1995) noticed in

their experimental results that the change in the slope of the NCLs (λ(s)) and the initial specific

volume (N(s)) vary differently (the slope of the NCLs increases with increasing matric suction)

than it was proposed in the BBM; however, they did not developed a complete mathematical

model for this behaviour.

Vaunat et al. (2000) and Thu et al. (2007) slightly modified the BBM and incorporated

SWRC into the model. The same assumption for the slope of the NCLs (λ(s)) as proposed in

the BBM was used.

In addition, Chiu and Ng (2003) incorporated SWRC into the framework proposed by

Wheeler and Sivakumar (1995). For the variation of the slope of the NCLs (λ(s)), they used

a similar approach proposed in the BBM (see Equation 2.13). Different from the BBM, they

considered that the “r” parameter is bigger than one to fit their experimental data better. This


modification was also proposed by Wheeler et al. (2002) in order to capture the increase in

compressibility with the increase in matric suction. This is a reasonable modification and well

captured the behaviour of tested soil in their studies because the soil compressibility increases

with the increase in matric suction.

In summary, the BBM is the first and most widely accepted elasto-plastic model for unsatu-

rated soils. The other models based on two stress state variables approach are mainly derived in

a similar manner or further improved by adding other important behaviour of unsaturated soils

which was not covered in the BBM (e.g., incorporation of SWRC). Thus, the BBM is chosen for

thorough examination in this study.

Combined stress state variables approaches

The combined stress variables approach models differ from the separate stress variables approach

models by combining the net stress and matric suction in their model formulations. These models

are briefly discussed in this section.

The combined stress state approach proposed by Bolzon et al. (1996), modified the BBM

by using average skeleton stress (σ − ua + Sr(ua − uw)) and matric suction (ua − uw) as stress

variables instead of net stress (σ − ua) and matric suction (ua − uw). This modification gives

advantages over the BBM when the transition zone between unsaturated and saturated soils is

considered. This model uses a similar function to the one proposed in the BBM for the variation

of soil compressibility with matric suction (λ(s)).

Santagiuliana and Schrefler (2006) included hydraulic hysteresis to the model proposed by

Bolzon et al. (1996). However, during the compaction process only wetting path is followed and

there is no need to consider the hysteretic nature of the soil. Thus, this modification would not

improve the compaction process predictions and will give similar results to the BBM.

Gallipoli et al. (2003a) proposed an elasto-plastic constitutive model incorporating the effect

of soil fabric into the model. They used average skeleton stress (σ − ua + Sr(ua − uw)) as

a stress variable and introduced a new stress variable as a second stress variable which is a

function of matric suction and degree of saturation (ξ = f(s)(1 − Sr)). In their model, they

proposed two soil parameters which can be found by calibrating the model with the experimental

results. Therefore, the initial specific volume (N(s)) and the slope of the NCLs (λ(s)) do not

necessarily reduce with increasing matric suction but depend on the experimental results and

are incorporated into the model with the proposed soil parameters.

23

Tarantino and De Col (2008) developed a compaction model where they used different work

conjugates than the ones used in the BBM as suggested by Houlsby (1997). The work conjugates

they adopted are the average skeleton stress (σ−ua+Sr(ua−uw)) and modified suction (s∗ = ns).

In addition, Tarantino and De Col (2008) considered the change in matric suction with loading

by incorporating the model proposed by Gallipoli et al. (2003b). Their model is similar to the

model developed by Gallipoli et al. (2003a) and only uses different stress state variables.

The model proposed by Sheng et al. (2008), referred as the SFG model in this study, is de-

veloped in a different way than the models presented above. They developed their mathematical

formulations, extending the volume change equation for saturated soil to unsaturated soil by

adding a suction parameter into it. The volumetric strain (εv) of the SFG model is suggested in

the following form:

εv =dν

ν= λvp

d(σy − ua)

(σy − ua) + s+ λvs

d(ua − uw)

(σy − ua) + s(2.16)

where ν is the specific volume of the soil element, λvp is the slope of the normal compression line

(NCL) for saturated soil when both axes are plot in logarithmic scale, d(σy − ua) is the change

in vertical net stress, d(ua − uw) is the change in matric suction, s is matric suction and λvs is

the slope of the volume change vs. matric suction curve when both axes are plot in logarithmic

scale.

Integrating Equation 2.16 for vertical net stress changes (σy − ua) under a constant matric

suction or for matric suction (s) changes under a constant vertical net stress(σy − ua) lead to:

lnν = lnN(s) − λvpln(σy − ua) + s

(σy − ua)0 + s(2.17)

where N(s) is the specific volume at an initial stress state ((σy − ua)0,s).

N(s), which is the specific volume at an initial stress state ((σy − ua)0,s) for matric suctions

smaller than the saturation suction (ssa), s < ssa is defined as

lnN(s) = lnN0 − λvpln(σy − ua)0 + s

(σy − ua)0(2.18)

and; when N(s) is under net vertical stress (σy −ua)0 equal to unity and matric suctions bigger

than the saturation suction (ssa), s≥ssa, it is defined as


lnN(s) = lnN0 − λvpln(σy − ua)0 + ssa

(σy − ua)0− λvp

(1 − ssa + 1

s+ 1

)(2.19)

where N0 is the specific volume at initial stress state for saturated soil when both axes are plot

in logarithmic scale.

To conclude, the models developed with combined stress variables approach use the BBM

or models with similar approach (Wheeler and Sivakumar, 1995) in their mechanical modelling

formulations but use different stress state variables instead of net stress and matric suction

except for the SFG model. For that reason, the SFG model is also selected in this study for

detailed evaluation.

2.4.5 Concluding remarks

In the first section of this chapter, it is shown that the compaction process of soils is not well

examined particularly from a quantitative sense. Compaction process can be analysed by both

examining the variation of the stress variable during the compaction process and by modelling

the compaction process.

Experimental methods that are required to monitor suction during the compression process

were summarised in this section. The axis translation technique and tensiometers were found

to be applicable for the experimental part of this study. The psychrometers were disregarded

because they are more reliable at high suction ranges. In the current study, the compression

behaviour of sand-bentonite mixtures, which have relatively low suctions, was monitored. In

addition, filter paper cannot be used for continuous suction measurements, which is the main

aim of the experimental part in this study.

In addition, in order to model the compaction process, the volume change theories for un-

saturated soils are also presented. Initially, the stress variables for unsaturated soils are briefly

summarised. Subsequently, the approaches available in literature for pore pressure development

are explained. Finally, the unsaturated constitutive models that can be used for the calculations

of the compressibility coefficients are presented. Two models, the BBM developed by two sepa-

rate stress variables approach and the SFG model based on combined stress variables approach

were selected to be incorporated in the compaction model.

Chapter 3

Selected materials for the

research

3.1 Introduction

The aim of this research project is to fundamentally understand the governing parameters of the

shape of the compaction curve and the volume change characteristics of soils. For that reason,

materials that have complex chemical properties (e.g., clays) and are hard to work with during

experimental procedure were avoided. Initially sand was chosen as a primary material to be

investigated. However, it was difficult to monitor the low suction of the sand with the available

equipment. The suction within the material was increased by introducing a small percentage of

fines to the sand. This resulted in an improved investigation into the effect of matric suction

on the overall shape of the compaction curve. Bentonite was selected as the fine material to

be mixed with sand, considering that the results might be useful for the researchers who study

engineered barriers and clay liners.

Sand bentonite mixtures with 2% and 5% bentonite content by weight were considered for

investigation. The sand with 2% bentonite content had the lowest measurable suction with the

available equipment, therefore it was selected as a material to be studied. In addition, bentonite

in the amount of 5% by weight was mixed with poorly graded sand to produce a material with

higher suctions and was determined as the second material to be tested. Moreover, considering

the research conducted by Mollins et al. (1996) and Montanez (2002) where they found that

sand particles are in contact even for high water contents for similar sand bentonite mixtures;

25

26 CHAPTER 3. SELECTED MATERIALS

the amount of bentonite mixed with sand (2% and 5%) is unlikely to produce any swelling in

the selected materials. Therefore, conditions for experiments are favourable.

This chapter describes the characteristics of the materials investigated in this study cover-

ing physical and geotechnical properties and techniques of their determination. These material

properties will be used in other chapters for analysis and modelling. Firstly, the physical prop-

erties of the selected soils are summarised and this is followed by the compaction characteristics

of the materials. Finally, the soil water characteristic curves and the consolidation curves of the

materials and their determination methods are described.

3.2 Physical properties

This research project has been carried out on two types of soils. Sand and bentonite were mixed

in the amount of 2% and 5% bentonite content by weight. These soils hereafter will be referred

to as S2B for the 2% sand-bentonite mixture and S5B for the 5% sand-bentonite mixture.

The sand selected for the study was the finest sand commercially available during this research

work and was provided by Unimin Australia. It contains 99% of quartz minerals and 1% of

respirable free crystalline silica in the form of quartz.

Bentonite, named as ActiveGel 150, was obtained from the same supplier. It is specified

by the supplier (Unimin Australia, 2002) to contain more than 87% of smectite, less than 2%

of albite and less than 11% of crystalline silica. As characterised by the supplier, its swelling

volume is 35 ml/2g, cation exchange capacity is 95 meq/100g and bulk density 1 Mg/m3. The

water content as received from the supplier was 10% (Shannon, 2008). All the physical properties

of bentonite are adopted from Shannon (2008) who worked on the water flow in unsaturated

reactive soils with the same soil.

The index properties of the individual soils (sand, bentonite) and the mixtures (S2B, S5B)

are summarised in the following part of this section. These include the particle size distribution,

Atterberg limits, linear shrinkage and the specific gravity of the materials where applicable.

3.2.1 Particle size distribution

Two methods were employed to determine the particle size distribution of the materials. Siev-

ing method was used for the determination of the particle size distribution of sand and laser

diffractometer was used for bentonite.

27

10−2

10−1

100

0

10

20

30

40

50

60

70

80

90

100

Diameter (mm)

Per

cent

age

finer

by

wei

ght (

%)

Cu = 1.71Cc = 1.07

Figure 3.1: Particle size distribution of sand

The particle size distribution of the sand was determined using standard method of analysis

by sieving according to the Australian Standards (AS1289.3.3.1-1995) . The particle size dis-

tribution of sand is shown in Figure 3.1. The sand has 100% particles finer than 0.6 mm and

20% particles of finer than 0.2 mm. The uniformity coefficient (Cu = D60/D10) of the sand is

determined to be 1.71 and the coefficient of curvature (Cc = (D30)2/(D10D60)) is 1.07. The

sand used in the investigation is classified as poorly graded sand (SP) according to the Unified

Soil Classification System (USCS).

The particle size distributions of sand bentonite mixture with 2% and 5% content of bentonite

by weight are shown in Figure 3.2. Although the particle size distributions of the two soils are

quite similar, the small difference in the bentonite content changes the suction of the material

enough to serve the experimental purpose (see Chapter 5 and 7).

3.2.2 Atterberg limits

The Atterberg limits of the bentonite ActiveGel 150 were determined according to the Australian

Standards (AS 1289.3.1.1 1995 and AS 1289.3.2.1 1995) . The Casagrande method was performed

for the liquid limit determination. Plastic limit of the soil was found by the standard thread-

rolling method. Table 3.1 shows the Atterberg limits of this soil and the results are in agreement

with the values specified by the soil provider (Unimin, 2002). ActiveGel 150 bentonite has 80%


10−4

10−3

10−2

10−1

100

0

10

20

30

40

50

60

70

80

90

100

Diameter (mm)

Per

cent

age

finer

by

wei

ght (

%)

S2BS5B

Figure 3.2: Particle size distributions of S2B and S5B

fraction finer than 2 µm and a Plasticity index of 514%, resulting in an activity (A = PI/(%

finer than 2 µm)) of 6.425 which is a highly active soil. Bentonite is classified as high plasticity

clay (CH) according to the USCS.

Table 3.1: Atterberg limits of ActiveGel 150 bentonite adopted from Shannon (2008)

Liquid limit (LL) 550%

Plastic limit (PL) 36%

Plasticity index (PI) 514%

3.2.3 Linear shrinkage

A linear shrinkage test was performed according to the AS 1289.3.4.1 . The mould was lubricated

using hydraulic oil and the bentonite was placed in the mould with the water content at the

liquid limit of 550%. The mould was left in a constant temperature environment (22 ◦C) until

shrinkage had stopped. The linear shrinkage was found to be 50.4%.

3.2.4 Specific gravity

The specific gravities (Gs) of the sand, bentonite and the mixtures (2% and 5% bentonite) were

found using a pycnometer (Micro-meritics AccuPyc 1330). Before the measurements, soils were

29

dried in the oven of 105 ◦C overnight and were subsequently placed in a desiccator for a day

to avoid any surface moisture while cooling down. In addition, the instrument purges soils in

dry helium and vacuums ten times in the test chamber to remove any residual surface moisture.

The average values of the specific gravity after eight consecutive measurements are presented in

Table 3.2.

Table 3.2: Specific gravity of the materials

Soil type Gs

Sand 2.65

Bentonite 2.69

Sand-bentonite (2%) 2.65

Sand-bentonite (5%) 2.65

3.3 Compaction characteristics

The compaction characteristics of sand-bentonite mixtures, S2B and S5B, were determined and

are described in this section. Dynamic compaction tests for both standard and modified com-

pactive efforts were conducted according to the procedures described in the Australian Standards

(AS 1289.5.1.1-2003 and AS 1289.5.2.1-2003 ). The applied energy for standard compaction

test is 596 kJ/m3 and for modified compaction test is 2703 kJ/m3 in Australian Standards.

Figure 3.3 shows the compaction curves of S2B for standard and modified compactive efforts.

At a standard compactive effort, the maximum dry density of S2B was found to be about 1.72

Mg/m3 at an optimum water content of 11.5% and at a degree of saturation of about 50%.

In addition, at a modified compactive effort, the maximum dry density was found to be 1.78

Mg/m3 at an optimum water content of 10% and at a degree of saturation of about 50%.

For a standard compactive effort and 2% bentonite content, Ameta and Wayal (2008) attained

a maximum dry density of 1.71 Mg/m3 at 15% optimum water content. The maximum dry

density is similar but the optimum water content is higher compared to the results obtained

in this study. The compaction characteristics of bentonite used in this project was studied by

Shannon (2008), who obtained a maximum dry density of 1.20 Mg/m3 at an optimum water

content of 20% for the ActiveGel 150 bentonite. Bentonite used in both studies have similar

maximum dry densities of about 1.20 Mg/m3, whereas different optimum water contents of


0 5 10 15 201.6

1.65

1.7

1.75

1.8

1.85

1.9

Water content, w (%)

Dry

den

sity

, γd (

Mg/

m3 )

StandardModified

Sr = 70%Sr = 50%

Figure 3.3: Standard and modified compaction curves of S2B

20% and 47%, the lower being the optimum water content of the bentonite used in the current

study. Therefore, this results in a lower overall optimum water content in the mixture of the

sand bentonite used in the current study.

Chalermyanont and Arrykul (2005), however, attained a maximum dry density of 1.97

Mg/m3 at an optimum water content of 10%, at a standard compactive effort. They used

a finer sand with a coefficient of uniformity (Cu) of 11.7 and coefficient of curvature (Cc) of 1.0,

which was classified as well graded silty sand (SW-SM) according to the USCS. Therefore, they

obtained a higher maximum dry density than the one obtained in this study.

In addition, Cavalcante Rocha and Didier (1993) have found a maximum dry density of 1.69

Mg/m3 at an optimum water content of about 10.5%. They have used a uniform sand and their

results are pretty close to the ones attained in this study. Therefore, it can be concluded that

the compaction characteristics of sand containing 2% bentonite by weight (S2B) are within a

range that is comparable with the results found in the literature.

Figure 3.4 shows the compaction curves of S5B for standard and modified compactive efforts.

At a standard compactive effort, the maximum dry density of S5B was found to be about 1.75

Mg/m3 at an optimum water content of 13% and at a degree of saturation of about 63%. In

addition, at a modified compactive effort, the maximum dry density was found to be 1.81 Mg/m3

at an optimum water content of 13% and at a degree of saturation of about 65%. The usual

31

0 5 10 15 201.6

1.65

1.7

1.75

1.8

1.85


Dry

den

sity

, γd (

Mg/

m3 )

StandardModified

Sr = 60% Sr = 80% Sr = 100%

Figure 3.4: Standard and modified compaction curves of S5B

decrease of the optimum water content with the increasing compactive effort has not been seen

for this soil type.

For a standard compactive effort and 5% bentonite content, Cavalcante Rocha and Didier

(1993) attained similar results with a maximum dry density of 1.73 Mg/m3 at an optimum water

content of 11%. Chalermyanont and Arrykul (2005), however, attained a maximum dry density

of 1.94 Mg/m3 at an optimum water content of 10.5%. They used a finer sand, classified as well

graded silty sand (SW-SM) according to the USCS. Therefore, they obtained a higher maximum

dry density than the one obtained in this study. Komine and Ogata (1999), on the other hand,

found a maximum dry density of 1.61 Mg/m3 at an optimum water content of 19.4%. The

maximum dry density attained by Komine and Ogata (1999) is quite low compared to the other

results found in the literature. The comparison of the results of current study and the ones

found in literature for 5% bentonite content shows that the results attained in this study are

within expected range.

The compaction test results for both soil types used in the current study are also presented

in Table 3.3. Comparison of the compaction curves for two soils shows that when the bentonite

content increases the maximum dry density and the optimum water content of the soil also

increases for both compactive efforts. Since the sand used was poorly graded, an increase in

bentonite content resulted in voids being filled with more fines instead of an increase in the


Table 3.3: Summary of the compaction characteristics for S2B and S5B

SoilStandard Modified

γdmax OWC γdmax OWC(Mg/m3) (%) (Mg/m3) (%)

S2B 1.72 11.5 1.78 10S5B 1.75 13 1.81 10

volume of soil. The results of Komine and Ogata (1999) and Cavalcante Rocha and Didier

(1993), who used uniform sand in their research, also show an increase in the maximum dry

density with an increase in bentonite content. Chalermyanont and Arrykul (2005), on the other

hand, observed a decrease in the maximum dry density with an increasing bentonite content.

However, they used a well graded fine sand, which lead to a lower void ratio within the soil.

Bentonite has a higher optimum water content than the optimum water content of sand.

Therefore, this results in increase of optimum water content with increasing bentonite content.

3.4 Soil water retention curve

The soil water retention curve (SWRC), which is also referred to as the soil water characteristic

curve or moisture retention curve is a relationship between suction and water content (gravi-

metric or volumetric) or degree of saturation. Several ways of suction measurements in order to

determine the SWRC of the soil were described in Section 2.3.

The SWRCs for the soils used in this study, S2B and S5B, are presented in this section

together with the type of equipments and methods used for their determination. Two differ-

ent methods for matric suction measurements were employed, axis translation technique and

tensiometer measurements. Tensiometer measurements were conducted for comparison of the

results obtained by axis translation technique.

Both of the techniques used for matric suction measurements are described in detail below.

Firstly, the equipments and methods used to determine the SWRCs will be summarised and

that will be followed by the results of both techniques.

3.4.1 Axis translation technique

The drying curves for the samples S2B and S5B were determined using axis translation technique.

Due to the high sand content in both of the specimens (S2B and S5B), the drying curves were

measured within a range of 0-60 kPa matric suction.

33

Pressure gauge panel

Sample

Valve Scale

Outflowcontainer

Air supply

PC

Tempe cell

Figure 3.5: Schematic of the experimental setup for axis translation technique

Equipment

The schematic diagram and the photo of the experimental setup for axis translation technique

are given in Figures 3.5 and 3.6. The setup consist of three main components: a pressure cell

assembly (tempe cell), a pressure panel and data acquisition system. The tempe cell was designed

and developed by previous researchers at Monash University workshop. A high air entry ceramic

disk was fitted inside the tempe cell for matric suction measurements.

Method

The permeability of the high air entry ceramic disk was checked before the test was commenced

in order to find out if there were any cracks on the disk or any leakage around the disk. In

addition, the capacity of the ceramic disk was unknown and thus, it was necessary to check

whether it was enough to serve within the experimental range which was about 60 kPa. To

calculate the permeability of the ceramic disk the tempe cell was filled with deaired water and

a pressure of 20 kPa was applied in the tempe cell to create a hydraulic head. The thickness

and the diameter of the high-air entry ceramic disk was 10 mm and 70 mm respectively. The

permeability of the disk was calculated using Darcy’s law (Darcy, 1856) given with the following

equation:

k =VwAt

h

H(3.1)


Figure 3.6: Experimental setup of axis translation technique

where; k is the permeability of the ceramic disk in m/s, Vw is the water volume discharge in

m3, A is the cross sectional area of the ceramic disk in m2, t is the time in s, h is the thickness

of the ceramic disk in m and H is the hydraulic head in m.

The water volume discharge with time under 20 kPa applied air pressure is shown in Figure

3.7. The permeability of the ceramic disk is calculated by multiplying the slope of the curve by

h/(AH) and is found to be 1.34x10−10 m/s. The permeability of the disk was compared with

the ones produced by Soil Moisture Equipment Corporation and it was found that it can serve

well above the experimental range which was about 60 kPa. In addition, the permeability of the

disk was compared with the ones used by Padilla et al. (2006); and based on those values, the

ceramic disk has a permeability value equivalent to the permeability of between 5 and 15 bar

high-air entry ceramic disks.

The soil mixed with water at optimum water content was placed in the metal ring with a

desired dry density (all the specimens were matured for 28 days after mixed with water for

hydration and equal distribution of moisture within the soil, see Section 4.3.1). The diameter of

the ring used was 64 mm and the height was 18 mm. The dry density chosen for this study was

1.58 Mg/m3. The choice for the initial void ratio value will be described in Section 4.3.1.

Once the soil samples were prepared with a desired dry density, they were placed on a porous

stone covered with a filter paper and were subsequently placed in a container. The container was

35

0 1 2 3 4 5 6 7

x 104

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

−6

Time, t (s)

Wat

er v

olum

e di

scha

rge,

Vw (

m3 )

y = 5.1e−011*x + 9.5e−007

Figure 3.7: Water volume discharge with time under 20 kPa applied air pressure

filled with deaired water until the water level was slightly below the top of the specimens. This

allowed the saturation of the specimens from bottom up and therefore, release of the entrapped

air from the soil. The soil samples were left overnight for saturation.

To saturate the ceramic disk, it was placed in a vacuum flask and submerged in deaired

water. The vacuum flask was connected to a vacuum pump for 15 minutes and the high air

entry ceramic disk was left for 24 hours under vacuum to ensure the complete removal of air

bubbles trapped in it. The ceramic disk was then placed in the base of the tempe cell ensuring

that no air was trapped under the disk. The tubing connection between the base of the tempe

cell and outflow container was carefully checked for air bubbles assuring that no air bubbles were

left in the tube.

In order to accurately measure water volume changes, it was necessary to account for water

mass or volume losses due to evaporation from the outflow container. As can be seen from Figure

3.6 the lid of the outflow container was placed on the container and only a small hole was drilled

to open it to atmosphere. Figure 3.8 shows the amount of water evaporated from the container

with time. The evaporation rate was found to be 0.0002 ml/min. This amount was taken into

account for the water content or degree of saturation calculations.

After saturating the soil samples, they were removed from water and placed on the ceramic

disk without the porous stone and filter papers. A thin layer of kaolin paste was placed between


0 500 1000 1500 2000 2500 30000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Time (min)

Eva

pora

tion

(ml)

y = 0.000183*x + 0.104

Figure 3.8: Evaporation of water from the outflow container

the sample and the ceramic disk in order to ensure a good contact between them. The tempe

cell was after mounted and was checked for air leakage. The outflow container was placed onto

the scale and the scale was connected to a data acquisition system which took readings every

4 minutes. The level of the scale was arranged so that the water level in the outflow container

would be slightly above the top level of the soil sample. The soil sample was also saturated

within the tempe cell until the system came to equilibrium.

The targeted air pressures were applied after the saturation and the system was left to equi-

librate. The drainage of the water from the specimen continued until it reached the equilibrium

condition with applied air pressure or matric suction. The air pressure was increased by 1 kPa

from 0 to 10 kPa, 2 kPa from 10 kPa to 16 kPa, 5 kPa from 16 kPa to 30 kPa and 10 kPa from

30 kPa to 60 kPa for S2B. For S5B the pressure was increased by 1 kPa from 0 to 6 kPa, 2 kPa

from 6 kPa to 20 kPa, 5 kPa from 20 kPa to 30 kPa and 10 kPa from 30 kPa to 60 kPa. The

same procedure was repeated for every air pressure increment.

After the last pressure increment the pressure within the tempe cell was released, the tempe

cell was dismantled and the soil sample was taken out as quickly as possible to avoid the water

intake into the soil sample from the ceramic disk. The moist soil samples were weighted and

then placed in an oven of 105 ◦C for 24 hours to find the final water content. The water content

for each of the applied air pressure was then back calculated based on the final water content

37

CERAMICDISK

PLASTICBODY TUBE

TRANSDUCER

Figure 3.9: Tensiometer used for matric suction measurements

and the drying SWRCs were plotted. The results are shown in Section 3.4.3.

3.4.2 Tensiometer measurements

Matric suction measurements were also conducted with tensiometers in order to compare the

results obtained by the axis translation technique. Measurements with tensiometers took less

time than the measurements conducted with the axis translation technique. 3 tensiometers were

available in the laboratory and therefore 3 samples with different water contents could be tested

at the same time. This corresponds to 3 points on the SWRC.

Equipment

Tensiometers with a capacity of 100 kPa were used for matric suction measurements. Tensiome-

ters were provided by ICT Australia. The tensiometer consists of a ceramic disk with a capacity

of 100 kPa air entry value, a plastic body tube assembly that connects to the ceramic disk, a

transducer and a data acquisition system. A photo of the tensiometer is shown in Figure 3.9.

Method

The soil samples prepared with the predetermined water content were placed in small containers

with a dry density equivalent to 1.58 Mg/m3 (same as the dry density in the axis translation

technique). Tensiometers were inserted subsequently into the soil samples carefully from the

top to avoid soil disturbance, and therefore, the density of the soil samples. Samples were then


covered with multiple layers of cling wrap and aluminium foil to avoid any evaporation of water

from the specimens. Tensiometers were left to equilibrate to the matric suction level of the

specimens. Experiments were repeated until the measurements were accomplished, in case there

was a breakage in tensiometers before the equilibration. The water content of the specimens

were measured both before and after the test to ensure that no evaporation occurred during

equilibration since the experiment took considerable time to complete.

3.4.3 Results

Matric suction measurements conducted with tensiometers are shown in Figures 3.10 and 3.11.

It took longer time for dryer samples to equilibrate compared to relatively saturated samples for

both soils (S2B and S5B). Since samples prepared with different water content would result in

different microstructure and therefore in different unsaturated permeability, this was an expected

outcome evident from the work of Oliveira and Marinho (2008). The samples prepared at

dry of optimum water content will have an aggregate microstructure, compared to the matrix

microstructure when prepared at the wet of optimum water content (Delage et al., 1996; Romero

et al., 1999). The equilibration time depends on the transfer rate of water between the sample

and the ceramic disk or the tensiometer. As stated by Delage et al. (2008), when the soil sample

has an aggregate microstructure the water transfer is through the inter-aggregates contacts and

inside the inter-aggregates smaller pores; thus, it would take longer time for drier samples to

equilibrate. It was also noted that, S5B has relatively shorter equilibration time compared to

S2B. This is attributed to its finer nature compared to S2B. The presence of higher amount

of fines in soil will result in a better contact between the sample and the ceramic disk, and

eventually this would lead to a shorter equilibration time.

The SWRCs for S2B and S5B are shown in Figures 3.12 and 3.13. Matric suction measure-

ments obtained by both axis translation technique and tensiometer are shown on the figures.

The matric suction measurements obtained by axis translation technique are higher than the

tensiometer measurements. This is due to the different methods used in sample preparation.

The measurements conducted using axis translation technique present the drying path, whereas

the tensiometer results lie on the wetting path of the SWRCs. It should also be noted that

the drying path was obtained from one sample, which had the same pore size distribution for

every measured matric suction or degree of saturation. On the other hand, different samples

with varying water contents were prepared for tensiometer measurements. Sample preparation

39

0 10 20 30 40 5010

−1

100

101

102

Time, t (hours)

Mat

ric s

uctio

n, s

(kP

a)

w = 2.6%w = 3.8%w = 5.2%w = 7.3%w = 9.6%w = 12%

Figure 3.10: Matric suction measurements of S2B with tensiometer

0 10 20 30 4010

0

101

102

Time, t (hours)

Mat

ric s

uctio

n, s

(kP

a)

wc = 3%wc = 3.6%wc = 6.3%wc = 7.7%wc = 9.4%wc = 14%

Figure 3.11: Matric suction measurements of S5B with tensiometer


with different water contents and same density results in different pore size distribution of the

material. Therefore, the drying curve results were obtained from a unique pore size distributed

sample. Whereas, the wetting curves were obtained from a varying pore size distributed samples.

100

101

102

0

10

20

30

40

50

60

70

80

90

100

Matric suction, s (kPa)

Deg

ree

of s

atur

atio

n, S

r (%

)

Axis translationTensiometer

Figure 3.12: SWRC of S2B

100

101

102

10

20

30

40

50

60

70

80

90

100


Deg

ree

of s

atur

atio

n, S

r (%

)

Axis translationTensiometer

Figure 3.13: SWRC of S5B

41

The air entry values obtained from the drying curves are about 3 kPa and 4 kPa for S2B and

S5B respectively (Figures 3.12 and 3.13). The matric suctions for S5B are slightly higher than

the matric suctions obtained for S2B due to the finer nature of S5B.

3.5 Consolidation characteristics

Oedometer tests were performed in order to find the saturated normal compression lines for both

soils (S2B and S5B). The slope of the normal compression line (λvp) for saturated samples is

required for the modelling part of this study and will be used in Chapter 7.

3.5.1 Equipment

Load Track III was used for oedometer tests and was supplied by Geocomp Corporation. Load

Track III consists of a loading frame, consolidation cell and a computer for data acquisition.

The equipment is shown in Figure 3.14. The load frame contains an embedded control system

that generates a desired force on a soil sample and measures the displacement. In addition, it

communicates with the transducers to provide a real-time control of the loading frame.

Figure 3.14: Load Track III used for oedometer tests


100

101

102

103

104

1.6

1.62

1.64

1.66

1.68

1.7

Vertical effective stress, σy − u

w (kPa)

Spe

cific

vol

ume,

ν

Experimental data

λ = 0.013

κ = 0.006

Figure 3.15: Slope of the normal compression line for saturated S2B

3.5.2 Method

Soil samples were compacted at an optimum water content to a desired density (γdry = 1.58Mg/m3)

in a consolidation ring. Subsequently, the ring was placed in a consolidation cell and the cell was

filled with deaired water to achieve complete saturation of the samples. The samples were satu-

rated for 12 hours before the consolidation commenced. After the saturation the consolidation

cell was placed on the loading frame and loading specifications were installed to the computer

software that controls the frame.

3.5.3 Results

The consolidation results for both soils are presented in Figures 3.15 and 3.16. The slopes of

the normal compression lines and the slopes of the unloading curves are calculated from the

experimental results and are shown on the graphs.

The slope of the normal compression line (λ) for soil sample S2B is 0.013 and the slope

of the unloading curve (κ) is calculated as 0.006. (Figure 3.15). For sample S5B, the slope

of the normal compression line (λ) is 0.021 and the slope of the unloading curve (κ) is 0.008

(Figure 3.16). Sample S5B has a higher loading and unloading slope than S2B due to the higher

bentonite content in it.

Evans and Ryan (2005) attained a slope of 0.032 for the normal compression line where the

43

100

101

102

103

104

1.45

1.5

1.55

1.6

1.65

Vertical effective stress, σy − u

w (kPa)

Spe

cific

vol

ume,

ν

Experimental data

λ = 0.021

κ = 0.008

Figure 3.16: Slope of the normal compression line for saturated S5B

soil had 5% bentonite content by weight. They used a sand that was classified as sandy clay

(SC) according to the USCS. This result is slightly higher than the result found in this study

due to the different nature of the sand used in both projects. The sand used by Evans and

Ryan (2005) was a finer sand (SC) than the one used in the current work (SP). Therefore, it is

expected to deform more under the applied vertical stress and have a higher slope of the normal

compression line. In addition, the slope of the unloading curve was found to be 0.002 by Evans

and Ryan (2005), which is lower than the one found in the current study. This might be due to

the finer nature of the sand used by Evans and Ryan (2005). Since the plastic deformation in

clayey soil is higher compared to sandy soils, it is acceptable for the clayey soil to have a lower

unloading slope, which relate to elastic recovery of deformation.

3.6 Concluding remarks

A bentonite content of 2% and 5% has been selected to be mixed with poorly graded sand to

be investigated in this study. Both of the selected materials have a suction range that could be

measured with the equipment available in the laboratory.

The physical properties and compaction characteristics of the selected materials were deter-

mined according to Australian Standards. The sand used is classified as SP and the bentonite


is classified as CH according to the USCS. The maximum dry density of S2B was found to be

1.72 Mg/m3 at an optimum water content of about 11.5% at a standard compactive effort. In

addition, the maximum dry density of the same soil for modified compactive effort was found

to be 1.78 Mg/m3 at an optimum water content of 10%. The maximum dry density of S5B

was found to be 1.75 Mg/m3 at an optimum water content of 13%, at standard compactive

effort, and 1.81 Mg/m3 at an optimum water content of 13% for modified compactive effort.

An increase in maximum dry density and water content was observed with increase in bentonite

content.

The water retention behaviour of the materials was determined using two different methods,

axis translation technique and tensiometer measurements. The air entry value of S2B was

calculated as 3 kPa and the air entry value of S5B was calculated to be 4 kPa. In the overall

water retention curve S5B had slightly higher matric suctions than S2B owing it to its finer

fraction. In addition, the matric suctions measured with axis translation technique were on the

drying path and the matric suctions measured with tensiometer were on the wetting path of

the SWRCs. For that reason, tensiometer measurements for the same water content or degree

of saturation had lower matric suction values than the measurements using axis translation

technique.

Consolidation tests were performed to determine the slope of the normal compression line.

The slopes of the normal compression lines for S2B and S5B were measured to be 0.013 and

0.021. The S5B has a higher slope of the normal compression line than the slope of the S2B due

to the higher clay content. In addition, the slopes of the unloading curves for S2B and S5B are

0.06 and 0.08, respectively.

Chapter 4

Testing equipment and

experimental procedure

4.1 Introduction

Compaction characteristics of soils can be better understood through carefully monitored ex-

periments. Therefore, the testing instruments and their working techniques are crucial in the

interpretation of the results. Another key parameter that leads to a successful outcome of a

research project is the choice of the experimental methods. This chapter is devoted to the both

instrumentation and experimental procedure followed throughout this research project.

The primary objective of the proposed experimental procedure was to conduct constant

water content static compaction tests to represent the compaction process in man made fills or

hydraulic barriers. In addition, the experimental methods were chosen to best represent the

compaction models so that the models could be verified.

The targets of the experiments can be summarised as follows:

1. To measure the initial matric suction of the soil samples;

2. To measure the matric suction changes of the soil specimens during the constant water

static compaction test; and,

3. To measure the volume change of the soil specimens during the constant water static

compaction test.

45

46 CHAPTER 4. TESTING EQUIPMENT AND EXPERIMENTAL PROCEDURE

This chapter describes the equipments used and the experimental procedures followed to

achieve the objective and the targets of the experiments. The first part details the equipments

and accessories used during the testing. The second part describes the paths and methods

of the experimental procedure. Finally, the problems and difficulties encountered during the

experiments are presented.

4.2 Testing Equipment

The soil samples were statically compacted with a device that can be used to measure the initial

matric suction and the matric suction changes during the compaction. The device measures

matric suction with the axis translation technique. The compaction devices and its working

principles are briefly described in this section. In addition, the accessories used in the setup of

the compaction device are summarised.

4.2.1 Compaction device

Static compaction experiments were conducted with SWC-150 Fredlund Device manufactured

by Geotechnical Consulting and Testing Systems (GCTS). The device was modified by adding

a pressure transducer to the bottom of the plate (below the ceramic disk) in order to monitor

the pore water pressure during the static compaction test. This modification also helped to

measure the initial matric suction values of the specimens prepared with predetermined water

content based on the null-type axis translation technique proposed by Hilf (1956). In addition,

a linear variable differential transformer (LVDT) was used in order to track volume changes of

the samples during compaction. The pressure transducer and LVDT were connected to the data

taker. The schematic of the modified equipment setup is shown in Figure 4.1. The setup consists

of a pressure cell assembly, a pressure panel with dual gauges, a loading frame, a pressure booster

and a data acquisition system. The entire setup, excluding the pressure booster and the data

acquisition system, is shown in Figure 4.2.

The SWC-150 Device was originally designed to replace pressure plate devices. Different from

the pressure plate device, changes in the water volume can be continuously monitored without

dismantling the device (Perera et al., 2005). In addition, the device has a loading frame as shown

in Figure 4.2, which helps applying vertical loads to simulate the field overburden pressure. In

this study the loading frame was used to apply a load to the soil sample in order to implement

47

Air SupplyPressurebooster

Pneumaticloader

Loadingframe

LVDT

Releasevalve

Data taker

Pressuretransducer

Steelblock

Computer

B A

Opening L Opening R

Airpressureopening

Water volumechange tube

C

Pressuregauge

Valve

Valves

High

pressureLow

pressure

Low

High

Air

Water

Figure 4.1: Schematic of the compaction device setup

Loading frame

Pneumatic loader

Pressure transducer

Top plate

Bottom plate

Water volume change tube

LVDT

Figure 4.2: Compaction device


To pressure transducer

To water volume tube

Three way valve

To water volume tube

Figure 4.3: Base of the pressure cell

the static compaction test. The system can be flushed with an air pump to remove the diffused

air accumulated beneath the high air entry ceramic disk.

The base of the pressure cell is shown in Figure 4.3. The ceramic disk is embedded into the

groove of the base cell. There is an O-ring between the ceramic disk and the base to create a

sealing interface. However, Zhang et al. (2009) have experienced air leakage problem from this

interface. Therefore, the system was checked for air leakage while measuring the permeability of

the ceramic disk and the results are given in Section 4.2.2.

The base of the pressure cell was connected to the calibrated water volume tubes which were

placed on the pressure panel (see Figure 4.2) via plastic tubes. A three way valve (see Figure

4.3) was added in one of the plastic tubes to connect the base with the pressure transducer which

monitors the water pressure below the ceramic disk (valve C in Figure 4.1). This modification

was done in order to measure the initial matric suction using the null-type axis translation

technique and monitor the pore water pressure, or matric suction, in a constant water content

test. The pressure transducer was mounted on a steel block, which is connected to the base of

the pressure cell, as shown in Figure 4.4. A release valve was also mounted on the steel block to

remove the air bubbles from the plastic tube that connects the base of the pressure cell and the

pressure transducer.

49

Pressure transducer

Release valve

To the base of the pressure cell

Figure 4.4: Pressure transducer mounted on a steel block

The pressure cell is connected to the pressure panel via a plastic tube from the upper part

of the pressure cell. The device can apply air pressures between 0 and 2000 kPa.

The pressure cell was placed under a loading frame which can apply 10 kN load. Considering

the diameter of the specimen used in the experiment (75 mm for S2B and 64 mm for S5B) this

corresponds to about 2250 kPa and/or 3200 kPa applicable pressure to S2B and S5B samples,

respectively. A LVDT was placed between the specimen and the cell in order to monitor the

vertical displacement, or the volume change, of the specimen. The sample was placed in a steel

ring of 1.5 mm thickness.

The original device had been previously used for SWRC measurements by Mavroulidou et al.

(2009) and Chao (2007) for clay, by Li and Zhang (2007) for five types of decomposed granite

- all classified as coarse grained soils, by Chakraborty (2009) for soil bentonite mixtures with

soil being mainly sand, by Perera (2003) for both disturbed granular and undisturbed fine

grained samples and by Zapata et al. (2009) for granular material. In the current study, the

device was modified and used for the null-type initial matric suction measurements and for the

measurements of the matric suction changes during compaction for the first time according to

literature.


4.2.2 Accessories for the compaction device

The compaction device was used with auxiliary devices in order to conduct the desired exper-

iments (constant water content static compaction tests). A pressure transducer was used to

measure the pore water pressure below the ceramic disk, a LVDT was used to monitor the de-

formation of the samples, an air booster was used to increase the air pressure available by the

university central source and a data taker was used to measure and record the parameters of the

pressure transducer and the LVDT. These devices are briefly summarised in this section.

High air entry value ceramic disk

The ceramic disk was purchased glued to a metal ring by an epoxy glue from GCTS. The

diameter and the height of the ceramic disk are 75 mm and 10 mm respectively. A ceramic disk

with an air entry value of 1 bar was selected to use throughout the experimental program.

The ceramic disk was placed in a vacuum flask and submerged in deaired water for saturation.

The vacuum was applied to the vacuum flask to remove any air bubbles left within the ceramic

disk. The ceramic disk was left under vacuum overnight for saturation.

The saturated ceramic disk was placed in its groove (see Figure 4.3) to check for any possible

cracks and leakage within the system. An air pressure was applied gradually within the cell and

the bubbling pressure of the ceramic disk was found to be about 200 kPa. This value is within

a given range for the same disk by the manufacturer. Therefore, the ceramic disk was found to

have no major cracks and the sealing interface between the ceramic disk and the base of the cell

seems to have no leakage problems.

To check the permeability of the disk, the pressure cell was filled with deaired water and an

air pressures of 20 kPa, 50 kPa and 100 kPa were applied inside the pressure cell to create a

hydraulic head. The permeability of the ceramic disk was calculated based on the Darcy’s law

(Darcy, 1856) from the Equation 3.1. The water volume discharge (Vw) from the ceramic disk

with time (t) under 20 kPa, 50 kPa and 100 kPa applied air pressures are shown in Figure 4.5.

The water volume discharge through the ceramic disk within a ceratin time is also presented,

under 20 kPa, 50 kPa and 100 kPa, in Figure 4.6. The slopes of these curves give the average

permeability of the ceramic disk, which is calculated as 4x10−8m/s. The permeability of the

ceramic disk is within an expected range as indicated by Padilla et al. (2006). The leakage

problem that was experienced by Zhang et al. (2009) at the interface of the base cell and the

ceramic disk might be due to damage of the O-ring,

51

0 500 1000 15000

1

2

3

4

5

6

7x 10

−6

Time (s)

Wat

er v

olum

e di

scha

rge

(m3 )

20 kPa50 kPa100 kPa

y = 2.8e−008

y = 1.1e−008

y = 4.13e−009

Figure 4.5: Water volume discharge with time under 20 kPa, 50 kPa and 100 kPa applied airpressures

0 20 40 60 80 1000

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

−6

Hydraulic head (kPa)

Wat

er v

olum

e di

scha

rge

(m3 )

y = 4e−008R2 = 0.9713

Figure 4.6: Average permeability of 1 bar ceramic disk


Garga and Zhang (1997) studied the rate of air dissolution in deaired water and have found

that the deaired water exposed to atmosphere for 10 hours had the same oxygen content of

that of tap water. Therefore, a test was conducted to study the amount of air, passing through

ceramic disk in the form of dissolved air or free air (from the interface of base cell and ceramic

disk). To do that, the saturated ceramic disk was placed on the based of the pressure cell and an

air pressure of 10 kPa was applied for a period of 5 days. At the end of the experiment (after 5

days) the water volume tubes were flushed by an air pump and the changes of the water volume

at the each tube were recorded. It was found that 0.6 ml of air was diffused from the ceramic

disk in 5 days. Therefore, during the static compaction test the water under the ceramic disk

was flushed regularly (once a day) to avoid the accumulation of diffused air under the disc which

might lead to loss of the continuous water connection between the ceramic disk and the water

under the ceramic disk (Vanapalli et al., 2008).

Pressure transducer

Druck PDCR 4011 pressure transducer was used to measure the pore water pressure of the

system under the ceramic disk. The pressure transducer was selected according to two main

reasons. First, the pressure transducer required to be in a range of being able to measure

the matric suction change during the static compaction tests. Second, it needed to be sensitive

enough to detect the small matric suction changes during the compaction tests which was hard to

detect with high capacity transducers due to their lower accuracy level. The Druck PDCR 4011

transducer has an operating pressure range of 0 - 70 kPa and the accuracy of the transducer is

0.04% full scale best fit straight line (FSB). It can successfully operate between -20◦ and +80◦C.

The transducer was calibrated with known pressures of the SWC-150 Device. The calibration

curve is shown on Figure 4.7.

Linear variable differential transformer

Volume changes in the soil samples were tracked using a KYOWA DTH-A-10 LVDT. The LVDT

has a capacity of 10 mm and an accuracy of 0.1% rated output (RO). The instrument can

operate from 0◦ to 60◦C successfully.

The LVDT was calibrated using an LVDT calibrator. The calibration curve is shown in

Figure 4.8.

53

−50 0 50 100 1500

10

20

30

40

50

60

70

80

Pressure transducer reading

App

lied

air

pres

sure

, ua (

kPa)

y = 0.4618*x + 10.37

Figure 4.7: Calibration curve of the pressure transducer

−3000 −2000 −1000 0 1000 2000 30000

1

2

3

4

5

6

7

8

9

10

LVDT reading

Dis

plac

emen

t (m

m)

y = 0.002*x + 5.5

Figure 4.8: Calibration curve of the LVDT


Figure 4.9: GCTS pressure booster

Pressure booster

Air pressure source at laboratory was limited to 700 kPa and PCP-PBOOST pressure booster

manufactured by GCTS was used to increase the available pressure. The pressure booster can

increase the output pressure to 2000 kPa. A photo of the pressure booster is shown in Figure

4.9.

Data taker

The data of the pressure transducer and the LVDT were measured by DT500 data taker. The

data taker was programmed and the data was archived by DeTransfer software. The data taker

was connected to a computer running Windows XP.

4.3 Experimental procedure

The flow chart of the experimental procedure is given in Figure 4.10. Initially, the sand bentonite

samples were prepared and left for hydration. Hydrated samples were then placed into the

metal ring by the procedure described in Section 4.3.1 and the initial matric suctions of the

samples were measured. The device measures the matric suction using null type axis translation

technique. Axis translation technique cannot be used when the air phase in the specimens

becomes discontinuous (Bocking and Fredlund, 1980). In addition, Olson and Langfelder (1965)

55

Experimental Procedure

Suction

measurements

Static compaction

test

Sample preparation

and curing

Compaction device

(modified SWC-150)

Null type axis translation technique

Continuous suction measurement

during compaction test

Figure 4.10: Experimental procedure

and Langfelder et al. (1968) showed that the air phase becomes occluded at about optimum

water content. However, the axis translation technique was experimentally evaluated for soils

having a degree of saturation between 76% and 95% by Fredlund and Morgenstern (1977) and

for soils having a degree of saturation between 56% and 77% by Tarantino et al. (2000). Dynamic

compaction test results (Figures 3.3 and 3.4) for both soils used in the current study shows that

at the end of the compaction test the final degree of saturation of the soil samples will be less

than 95%. Therefore, the matric suction of the samples were measured and monitored in the

compaction device using null type axis translation technique. The experimental procedure is

described in detail in the following sections.

4.3.1 Material preparation

The selection of appropriate material preparation techniques in granular soils is crucial, since the

behaviour of the soils can be affected by the method of preparation (Mulilis et al., 1977). There


are several material preparation techniques for granular soils found in literature which could

be categorised according to their moisture condition, soil placement method and the medium

through soil is placed. The most common ones that are used in the preparation of sandy soils are

air pluviation, water pluviation and moist tamping methods. In addition, the slurry deposition

method developed by Kuerbis and Vaid (1988) for the preparation of well graded and silty sands

is also considered in this study.

The samples prepared by air pluviation represent the natural deposition of wind blown aeolian

deposits (Kuerbis and Vaid, 1988) and water pluviated samples simulate the natural deposition

of sand through water in many natural environments (Vaid and Negussey, 1984). The driving

forces for both of these methods is gravimetry and therefore leads to a segregation of the fine

particles during preparation procedure. Moist tamping method, on the other hand, best models

the soil fabric of construction fills (Lambe, 1951). In addition, the slurry deposition method best

simulates the soil fabric found within a natural fluvial deposit (Kuerbis and Vaid, 1988). For

uniformly graded soils, air and water pluviated samples are more homogenous than the moist

tamped samples (Vaid et al., 1999; Frost and Park, 2003); whereas, the slurry deposition method

produces the most homogenous samples for sand with fines.

Most of these methods were used in the preparation of soil samples for saturated soil me-

chanics problems. There is not much information available in literature on the applicability of

these methods for the preparation of unsaturated soil samples. There are two important criteria

for the selection of material reconstitution method in this study:

1. the sample should be well mixed and have a uniform void ratio throughout; and,

2. the sample preparation technique should simulate the soil fabric found in soil fills.

Air pluviation, water pluviation, and slurry deposition method cannot be used in this study,

since the initial water content of the samples can not be controlled. In these methods, the initial

water content can only be controlled by saturating or drying the initially prepared samples which

would lead to a different soil fabric properties than the desired initial ones. By the moist tamping

method, on the other hand this issue could be easily overcome. In addition, the moist tamping

method is originally found by Lambe (1951) for the construction of fills. Although the moist

tamping method results in less uniform soil fabric compared to the other noted methods, the

study conducted by Frost and Park (2003) shows that the change in void ratio with height of

the sample is not that significant. Therefore, moist tamping by layers is chosen as a material

57

Figure 4.11: Sample preparation by tamping

preparation technique in this study. This method was also selected by Rojas et al. (2008a) and

Lauer (2005) for the preparation of unsaturated soil samples.

Initially, sand and bentonite were mixed in an air dry state by hand for 15 minutes. The

desired amount of water was then added and mixed for another 20 minutes to evenly distribute

the moisture. The samples were first attempted to be mixed in a mixer; however, due to the

uneven mix of the fine and coarse particles the use of mixer was abandoned. The major difficulty

of using a mixer during the soil mixing procedure was the separation of fine and coarse particles

while the blade of the mixer was rotating. The fine particles were accumulating on the inner

wall while the coarse particles were staying in the centre of the mixer container.

The mixture was then wrapped with several layers of plastic wrap and aluminum foil. All

the samples were placed in air tight plastic zip bags and stored in plastic containers in the high

humidity room for a minimum of 28 days. Montanez (2002) conducted a study to investigate

the influence of the hydration time on the soil specimens. He stated that it is necessary to allow

a minimum period of 28 days for hydration in order to establish an equal distribution of suction

within the material.

Hydrated soil samples were placed in a metal ring in 5 thin equal layers by softly tamping

the specimen with a metal disk (or hammer) as shown in Figure 4.11. The diameter of the metal

disc was slightly less than the diameter of the steel ring so that it can freely move within the

ring.

The dry density was desired to be the lowest dry density attainable since one of the purposes

of this study was to observe not only the final soil properties of the compacted soils but also the

evolution of the compression properties during the compaction process. There were two concerns

for deciding the initial dry density. The first aim was to attain the lowest density possible.

Therefore, while soil was saturating under zero applied total or net vertical stress it should not


collapse. The second aim was to stop the swelling of the sample while saturating. Prepared soil

samples contain only 2% and 5% bentonite content by weight and therefore, swelling was not

considered to be an issue (Montanez, 2002). Taking into account these concerns, the initial dry

density of the samples was chosen to be 1.43 Mg/m3 initially. However, after testing the samples

with 2% bentonite content, it was noticed that as water content was increasing it was harder to

maintain such low density. Therefore, the dry density of the samples with 5% bentonite content

was changed to 1.58 Mg/m3. The tests for the samples with lower initial density (γd = 1.43

Mg/m3) were not repeated and are presented in Chapter 5 due to long duration of the tests. The

diameter and height of S2B samples were 75 mm and 25 mm respectively. The sample diameter

was reduced to 64 mm when testing S5B samples in order to shorten the long equilibration time

observed during the initial tests (S2B samples).

4.3.2 Static compaction test

Hydrated soil samples were statically compacted in order to produce the static compaction curves

of the soils and to compare them with the proposed compaction model. The stress path followed

during the test and the loading rate, the preparation of the compaction device for the test,

measurement during the test and the dismantling of the device are explained in this section.

Test stress path and loading rate

Figure 4.12 shows the stress path followed during the compaction experiment. Due to the

reduction in volume during the constant water content tests, there was a decrease in matric

suction with increasing net vertical stress or applied vertical stress (since air phase is considered

to be drained applied vertical stress is equal to the net vertical stress).

There are two main types of loading rates found in literature; time dependent loading rate

and equilibration or stabilisation dependent loading rate. It was shown in numerous studies

that the time dependent rate of loading has an influence on the volume change characteristics of

unsaturated soils (Huat et al., 2006; Rojas et al., 2008a). Huat et al. (2006) conducted an exper-

imental study on the influence of loading rate to the volume change behaviour of unsaturated

granitic residual soil. They found that the higher the rate of loading is, the bigger the volume

change of the soil is. This was explained with the higher pore water pressure development or the

sudden matric suction reduction during the higher loading rates (Fredlund, 1979). Contrary to

the findings of Huat et al. (2006), Rojas et al. (2008a) found that the higher the rate of loading

59

σy - ua

u a-

u w

Figure 4.12: Test stress path (matric suction change is exaggerated)

is, the smaller the volume change of the pyroclastic silty sand is. This was explained by the creep

phenomena in soil, as time passed the creep also increased, resulting in bigger volume changes of

the soil specimens. Therefore, the effect of a time dependent loading rate on the volume change

characteristics of soils seems to be not only dependent on loading rate but also soil type and the

experimental techniques used.

In this study, suction equilibration loading rate was chosen so that the matric suction change

could be monitored in each loading step. The duration of the loading time was changed according

to the time required at each step for stabilisation of the matric suction and volume change. There

are similar loading rate approaches presented in the literature (Tang et al., 2008). The loading

steps applied to the soil specimens during the tests are shown in Tables 4.1 and 4.2. The loading

increment was initially chosen to be 80 kPa for S2B and 110 kPa for S5B, differing due to the

change in sample diameters (the lower rates were harder to maintain with the equipment). Later

in the test it was observed that the matric suction and volume change of the sample were low

and therefore the loading increment was increased.

Table 4.1: Loading steps for S2B

Vertical stress Number of Increment

(kPa) increments (kPa)

0 - 640 8 80

640 - 1280 4 160

1280 - 2250 3 320


Table 4.2: Loading steps for S5B

Vertical stress Number of Increment

(kPa) increments (kPa)

0 - 880 8 110

880 - 1760 4 220

1760 - 3080 3 440

Equipment preparation and test setup

Before placing the saturated ceramic disk into the groove on the base cell, valve C was turned

to the direction of the water volume change tubes and valves A and B were left open (Figure

4.1) . The groove was filled with deaired water and the ceramic disk was then placed and gently

pushed into the groove. This made some amount of water under the ceramic disk (replacing

the volume of the ceramic disk) to move into the water volume tubes. Water was then flushed

with the help of an air pump from the opening L and R until the trapped air bubbles under the

ceramic disk were completely removed. Subsequently, valve C was turned to the direction of the

pressure transducer and the release valve on the block was opened for water to flow. The release

valve was then closed ensuring that no air bubbles were left in the plastic tube that connects

the base of the pressure cell and the transducer. A back pressure of about 20 kPa was applied

to the transducer to avoid air cavitation due to the long time of the test and valve C was turned

again to the direction of the water volume tube. Ensuring that air bubbles were removed from

the entire setup a thin layer of kaolin paste was spreaded on the ceramic disk and the steel

ring with the soil sample was placed onto the kaolin paste. Kaolin paste was placed to ensure

a good connection between the ceramic disk and the granular soil sample. Kaolin paste was

used for similar purpose (to ensure good conductivity between the soil and the ceramic disk)

in tensiometers by Tarantino et al. (2000) and Boso et al. (2004), and in thermal conductivity

suction sensors by Zhan et al. (2007). The pressure cell was quickly mounted to start the test

in order to avoid any water intake of the specimen from the ceramic disk. The valves A and

B were then closed, the valve C was turned to the direction of the pressure transducer and the

experiment was ready for initial matric suction measurements using null-type axis translation

technique.

61

Measurements during the test

An air pressure higher than the back pressure was applied inside the cell from the top of the

specimen and the water pressure below the ceramic disk was monitored by the help of the pressure

transducer. The applied air pressure was gradually changed after equilibrium was reached (i.e.,

there was no changes in water pressure below the ceramic disk). Final water pressure values are

plotted against the applied air pressures. The function of this curve needed to be a 45◦line when

the applied air pressure was greater than the initial matric suction of the specimen(taking into

account the Hilf’s approach for undrained systems). The initial matric suction of the specimen

was determined from the intersection of the curve with the abscissa of the graph (Hilf, 1956).

After initial matric suction was measured, the air pressure inside the cell was left as it was

and a vertical load was applied by the loading cell. The soil samples were statically compacted

using the loading steps shown on Tables 4.1 and 4.2. The duration of the loading time was

changed according to the time required at each step for stabilisation of the matric suction and

volume change. At the end of the last loading increment, the air pressure within the pressure

cell was reduced to zero, the valve C was turned to the direction of water volume tube and the

valves A and B were opened to allow saturation of the specimen under constant applied vertical

stress. This was conducted in order to see the volume change of the samples when the matric

suction was reduced (collapse).

Dismantling the compaction device

At the end of the saturation procedure the valves A and B were closed. The sample was quickly

taken out from the pressure cell. The samples were left in the oven overnight to find the final

water content of the samples.

4.3.3 Test difficulties and problems

Some difficulties and problems were experienced during the experimental procedure. These

problems are summarised below:

1. Matric suction readings for samples with different water contents, in the initial experiments,

were not going beyond 1 to 2 kPa, which probably was the matric suction of the ceramic

disk. This problem was attributed to the poor contact between the sample and the ceramic

disk due to the granular nature of the soil used in the experiments. Therefore, a thin layer


of kaolin paste was spreaded on the ceramic disk and the soil sample was placed on it to

ensure a better connection. This resolution is also suggested by other researchers (e.g.,

Tarantino et al. (2000); Boso et al. (2004); Zhan et al. (2007)).

2. Some tests, particularly the ones with lower water contents or higher suctions, failed to be

successfully completed. This problem was thought to rise due to the cavitation of the water

in the tube which connects the pressure transducer and the bottom plate (tube between

pressure transducer and valve C). Thus, back pressure was applied to the water within this

tube. Still occasionally using this method was not successful and some tests needed to be

ceased; however, it was found more efficient.

3. During the initial matric suction measurement, after the application of air pressure to the

sample, the water pressure or suction equilibration took longer time than it was expected

(see Section 5.3). This lead to very long duration of the tests (in lower water contents

reaching up to 3 months). However, in literature, the equilibration time for the initial

matric suction measurements using null method was reported to be less than a day for fine

grained and residual soils (Vanapalli et al., 1999; Fredlund and Vanapalli, 2002; Rahardjo

and Leong, 2006).

4. Due to the long duration of the tests the device required to be flushed regularly in order

to stop the accumulation of the defused air beneath the ceramic disk. However, after this

procedure an additional time was required for the pressure transducer to equilibrate, which

extended the testing time further. This problem was raised more in S5B samples and in

the samples with a relatively lower water content (see Chapter 5 ).

5. It was very hard to maintain initially identical sample size for granular soils used in the

tests. Since the deformation of the granular soils is already very small, it was important to

know precisely the initial sizes of the samples. This lead to some difficulties in the inter-

pretation of the trial test. Therefore, extra care needed to be taken during the preparation

of the samples.


In this chapter the equipments used in the experimental part of the current study and the

experimental procedure were presented. SWC-150 Fredlund Device that is originally designed to

63

control matric suction was modified to measure matric suction. A pressure transducer was added

to the bottom plate of the pressure cell to measure the pore water pressure under the ceramic disk.

This modification was done in order to measure initial matric suctions and the matric suction

changes during the constant water static compaction tests. The equipment measures matric

suctions based on null-type axis translation technique. In addition, a LVDT was mounted to the

device to monitor volume changes of the sample during static compaction. The equipment was

checked for any possible leakage and it was found out that it can operate successfully. However,

it was decided to flush the equipment regularly due to the air diffusion within the water.

An experimental procedure was developed to conduct constant water content (undrained

water) static compaction tests. Soil specimens were prepared using moist tamping method. The

stress path followed was also described. Each loading increment was applied after the matric

suction from previous loading increment reached equilibrium. Loading increments were also

increased gradually, the sample was initially loaded slow and the rate was increased later on due

to the reduction in the total volume change.

The difficulties experienced during the experimental measurements were also summarised in

the last section. Since granular soil was used in experimentation, a thin layer of kaolin paste was

spreaded on the ceramic disk to maintain good contact between the disk and the soil sample.

Furthermore, after experimentation, the application of back pressure to the pressure transducer

was found to be beneficial to prevent water cavitation due to the long duration of the tests.

Chapter 5

Experimental results

5.1 Introduction

Static undrained (water) compaction tests (constant water content) were conducted on two

different granular soils, sand with 2% (S2B) and 5% (S5B) bentonite, with varying water contents

in order to cover a wide range in the compaction curve and thus to observe the effect of suction on

the compaction behaviour. Soil samples were compacted with vertical stresses ranging between

80 kPa and 2250 kPa for S2B and 110 kPa and 3100 kPa for S5B. Initial matric suctions of

the specimens were measured using the null type axis translation technique. Matric suction

variation was also monitored during the compaction process and its influence on the overall

volume change behaviour was observed. The physical properties of tested materials and the

experimental procedure were described in detail in Chapters 3 and 4.

This chapter presents the experimental results of the static compaction tests conducted in

the current study. Firstly, the initial matric suction measurements are summarised and this is

followed by the evolution of the matric suction during the tests. Finally, the volume change

behaviour of tested soils were discussed in detail. The results from this chapter will be used in

Chapter 7 where experimental results were compared with the modelling predictions.

5.2 Initial suction measurement

The initial matric suction of soil specimens was measured using the null type axis translation

technique (Hilf, 1956) before the compaction commenced. Matric suction measurements and

65

66 CHAPTER 5. EXPERIMENTAL RESULTS

Table 5.1: Water content of S2B

Test Water content (%) Dry densitybefore after Mg/m3

2b6.9wc 5.6 6.9 1.432b8.4wc 7.6 8.4 1.462b8.6wc 7.7 8.6 1.462b10.2wc 6.0 10.2 1.442b10.7wc 9.8 10.7 1.46

compaction tests were conducted within the same device (Figure 4.2), which allowed continuous

matric suction measurements during the tests.

The water contents of tested samples and their initial dry densities (γd) are given in Tables

5.1 and 5.2. Tests are named according to their bentonite and water contents. For both soils,

five compaction tests with different water contents were successfully performed and their results

are presented here. More tests were conducted; however, as it will be explained later in this

chapter, there were difficulties in finalising the tests and thus, these tests were disregarded. The

water content of the samples were measured before and at the end of the each test. It can be

seen from Tables 5.1 and 5.2 that there was a slight increase in the water content of the samples.

The increase in water content is unlikely to happen during the compaction process and/or after

the application of air pressure on the samples, because the applied air pressure to the samples

was higher than the matric suction of the samples. Eliminating the time spend during loading,

it seems that the water content increased either during the preparation stage of the test (before

the application of pore air pressure (ua)) or during the dismantling of the equipment. The time

spent during equipment preparation was much longer than the time spent when dismantling

the equipment. It took a considerable time, ranging from five to twenty minutes, to remove air

bubbles from the system after the placement of the sample onto the ceramic disk. During this

time, some water may have been imbibed from the ceramic disk. Thus, the final water content

of the samples was considered to be the water content during the compaction tests. In addition

to that, these values are in agreement with matric suction values measured using tensiometer as

shown in Figures 5.3 and 5.4. Initial dry density (γd) of the samples were chosen to be about

1.43Mg/m3 at first. However, it was hard to maintain that low dry density with increasing water

content because samples tend to collapse to a higher dry density (γd). Therefore, the initial dry

density for samples with 5% bentonite content was changed to 1.58Mg/m3 (see Section 4.3.1 for

more details).

Initial matric suction measurements for both soil types (S2B and S5B) and different water

67

Table 5.2: Water content of S5B

Test Water content (%) Dry densitybefore after Mg/m3

5b6.5wc 6.2 6.5 1.595b7.5wc 7.0 7.5 1.585b10.3wc 9.7 10.3 1.585b10.9wc 10.3 10.9 1.585b12.7wc 11.8 12.6 1.58

0 20 40

0

20

40

0 20 40

0

20

40

0 20 40

0

20

40

0 20 40

0

20

40

0 20 40

0

20

40

Pore air pressure, ua (kPa)

Por

e w

ater

pre

ssur

e, u

w (

kPa)

y = 1.0474x − 7.7773 y = 1.0207x − 5.198

y = 1.0007x − 4.8872

y = 1.0452x − 4.131y = 1.025x − 5.6921

wc = 6.9% wc = 8.4%

wc = 10.7%

wc = 8.6% wc = 10.2%

Figure 5.1: Initial matric suction measurements for S2B


content are shown in Figures 5.1 and 5.2. The applied air pressures (ua) and the final pore water

pressures (uw), values after equilibration, are plotted against each other. Taking into account

Hilf’s approach (Hilf, 1956) for undrained loading condition, after applied air pressure was greater

than the initial matric suction of the specimens, the increase in pore air pressure (∆ua) would be

equal to the increase in pore water pressure (∆uw). This leads to a linear relationship between

pore air (ua) and pore water pressure (uw), with a slope equal to unity. Thus, the initial pore

water pressure (uw) of the specimen would be the intersection of the line with the ordinate of the

graph. Equations of the relationship between pore air (ua) and pore water pressure (uw), which

have the information of the initial matric suction, are also shown on the graphs for every water

content. As it was expected, the matric suction reduced with increasing water content, except

for the slight inconsistency between the samples 2b8.4wc and 2b8.6wc, and between 2b10.2wc

and 2b10.7wc. The difference, however, is very small. In addition, there is a discrepancy in the

water content of the sample 2b10.2wc, which showed higher variation than rest of the tested

samples. Therefore, this anomaly was ignored and accepted to result due to experimental errors.

The water retention curves obtained by different methods for both soil types are presented

in Figures 5.3 and 5.4. The matric suction measurements using the null type axis translation

technique are also plotted on the graphs. The null type measurements are close to the matric

suction measured with tensiometer. The matric suction measurement conducted using the axis

translation technique differ from the other two methods. While using axis translation technique,

the drying curve was measured. On the contrary, the measurements recorded by tensiometer

and null method lie on the wetting path of the water retention curve. In addition to that,

the soil specimens were prepared at an optimum water content for the measurements of drying

water retention curves. On the other hand, the soil specimens were prepared with different

water contents for the suction measurements using the null-type axis translation technique and

tensiometers. Specimens prepared with different water contents have different soil structure

which influence the water retention behaviour of the soils (Vanapalli et al., 1999; Catana, 2006).

The specimens compacted with an initial water content on the dry of optimum conditions have

relatively large pore spaces compared to the specimens compacted on the optimum or wet of

optimum conditions. Therefore, the specimens compacted with water contents on the optimum

or wet of optimum have higher storage capacity (Cui and Delage, 1996; Vanapalli et al., 2004).

The effect of structure on water retention behaviour, however, is not as big for coarse grained

soils compared to fine soils due to its relatively homogenous structure. Thus, the discrepancy in

69

60 80 100 1200

40

80 y = 0.9753x − 49.63

40 60 80 1000

50

100 y = 1.156x − 34.57

40 60 80 10020

60

100 y = 0.9587x − 15.34

20 40 60 8020

40

60

80 y = 0.999x − 10.88

40 60 80 10020

60

100

Pore air pressure, ua (kPa)

Por

e w

ater

pre

ssur

e, u

w (

kPa)

y = 0.9539x − 7.51

wc = 6.5% wc = 7.5%

wc = 10.3% wc = 10.9%

wc = 12.6%

Figure 5.2: Initial matric suction measurements for S5B


suction measurements between axis translation technique and the other two methods resulted

mainly due to the measurement of wetting and drying paths in the water retention curve; and

the differences within the soil fabric of the samples prepared with different initial water contents.

It should also be noted that, the samples measured with tensiometer had higher dry densities

(γd = 1.58Mg/m3) than the samples measured by the null method (γd = 1.43 to 1.46 Mg/m3)

for S2B. However, it is not expected to have noticeable suction differences due to the variation

in density for granular soils which already have low suctions. Considering these arguments, the

results obtained by tensiometer and null method are in good agreement. Moreover, S2B has a

bigger hysteresis compared to S5B (Figures 5.3 and 5.4). S2B seems to be more sensitive to the

structure compared to S5B.

5.3 Evolution of suction during the test

Figures 5.5 and 5.6 present the evolution of matric suction during the tests (initial matric suction

measurement and loading). The applied air pressures (ua) and measured pore water pressures

(uw) are also shown on the figures. Matric suction values are calculated by subtracting the pore

water pressure (uw) from the applied air pressure (ua). In the initial part of the experiments,

the pore air pressures (ua) were increased to greater values than the initial matric suctions of

the samples (the initial matric suction of the specimens was approximated from the tensiometer

measurements conducted before). After exceeding the initial matric suction values, a minimum

of three air pressure increments (∆ua) were applied in order to obtain three points on pore

air pressure (ua) and pore water pressure (uw) graphs (see Figures 5.1 and 5.2). Following the

calculation of the initial matric suction values, the air pressure was kept constant and the loading

of the specimens was commenced.

During the initial matric suction measurement part of the tests, it can be seen that the

increase of air pressure (ua) resulted in a sudden increase of pore water pressure (uw). Initially,

the increase in the pore water pressure (∆uw) was slightly lower than the increase in the air

pressure (∆ua), thus resulting in a sudden matric suction increase. This is due to the time

taken of the pore air pressure and therefore, pore water pressure (uw) to evenly distribute

within the samples. Thereafter the pore water pressure gradually (uw) increased until it reached

equilibration.

The equilibration time for the initial part of the tests (matric suction measurements) was

71

[a]10

−110

010

110

20

10

20

30

40

50

60

70

80

90

100


Deg

ree

of s

atur

atio

n, S

r (%

)

Axis translationTensiometerNull method

[b]10

−110

010

110

20

5

10

15

20

25

Gra

vim

etric

wat

er c

onte

nt, w

c (%

)



Figure 5.3: Comparison of initial matric suction measurements using different techniques forS2B, [a]Variation of degree of saturation with matric suction, [b]Variation of water content withmatric suction


[a]10

010

110

210

20

30

40

50

60

70

80

90

100


Deg

ree

of s

atur

atio

n, S

r (%

)


[b]10

010

110

20

5

10

15

20

25

30


Gra

vim

etric

wat

er c

onte

nt, w

c (%

)


Figure 5.4: Comparison of initial matric suction measurements using different techniques forS5B, [a]Variation of degree of saturation with matric suction, [b]Variation of water content withmatric suction

73

0 100 200−50

0

50

100

0 50 100 150−50

0

50

100

0 20 40 60−50

0

50

100

0 100 200−50

0

50

100

0 20 40 60−50

0

50

100

Time, t (hours)

Por

e pr

essu

re, u

a, uw a

nd m

atric

suc

tion,

s (

kPa)

ua

uw

matric suction

wc = 6.9%

wc = 10.7%

wc = 10.2%wc = 8.6%

wc = 8.4%

Figure 5.5: Evolution of matric suction with time for S2B

very long for the samples with low water content or low degree of saturation. An example for this

is shown for S5B with 2.9% water content in Figure 5.7 (also see Figure 5.5 for wc = 6.5%). In

some cases experiments were ceased due to the accumulation of dissolved air under the ceramic

disk. The device was regularly flushed, however, it took a long time after flushing for the system

to re-equilibrate in low water content tests, which further extended the testing period. This

can be seen in Figure 5.7 where after 350 hours the device was flushed. There was a sudden

reduction in pore water pressure with flushing and it took about five days for the system to

reach the previous pore water pressure (uw). Therefore, many tests with low water contents

were stopped and due to the time taken tests were not repeated.

In the literature, the equilibration time for the initial matric suction measurements using null

method was reported to be less than a day for fine grained and residual soils (Vanapalli et al.,

1999; Fredlund and Vanapalli, 2002; Rahardjo and Leong, 2006). However, during this project,

the equilibration time for the samples with low water content was found to be much longer. In


0 500 10000

50

100

150

0 100 200−100

0

100

200

0 200 400−50

0

50

100

0 50 100−50

0

50

100

0 200 400−50

0

50

100

Time, t (hours)

Por

e pr

essu

re, u

a, uw a

nd m

atric

suc

tion,

s (

kPa)

ua

uw

matric suction

wc = 6.5%

wc = 7.5%

wc = 10.3%

wc = 12.6%

wc = 10.9%

Figure 5.6: Evolution of matric suction with time for S5B

the example shown here the equilibration time was about two and half months (Figure 5.7). This

might be due to the problems in applicability of the axis translation technique to the samples

with low degrees of saturation (Sr = 3− 10%). Most of the soils tested in literature were clayey

soils which had high suction values and it is well known that with this method matric suctions

up to 1500 kPa can be measured. Therefore, clayey soils with low water contents, which would

have matric suction values beyond 1500 kPa, were not measured before. This is the first time

in literature where suctions of granular samples with low water contents were tested using the

null method. The long equilibration time can be attributed to the low water content which in

some cases would result in discontinuous water phase. Most likely vapour equilibration took

place within the sample which lasted for a very long time. Another question that might rise

out of this study is whether the axis translation technique can be used to measure correctly

the matric suction of soils that have discontinuous water phase. Even though, the difficulties in

the applicability of the axis translation technique to the soils with occluded air phase (i.e., with

75

Table 5.3: Matric suction change with loading for S2B

Test ∆(ua − uw)(kPa)

2b6.9wc 1.12b8.4wc 0.82b8.6wc 0.62b10.2wc 02b10.7wc 0.2

high degrees of saturation) was extensively studied (Olson and Langfelder, 1965; Bocking and

Fredlund, 1980; Romero, 2001), there is not any previous work conducted on the applicability

of this technique to soils with a discontinuous water phase. However, in this study, it is found

that the matric suction values measured using null method are close to the values measured

with tensiometer (Figures 5.3 and 5.4). This is a promising result on the applicability of the

axis translation technique to dry granular soils. However, the method seems to be very time

consuming and therefore, not practical. Another reason for long equilibration time could be the

low permeability of the granular soils with low water content. Thus, further studies should be

undertaken before coming to a general conclusion.

After the initial matric suction measurements, samples were loaded incrementally as it was

described in Section 4.3.2. There was an instantaneous suction decrease when samples were

loaded in each loading step (Figures 5.5 and 5.6). Similar behaviour of sudden matric suction

decrease with loading was observed with a tensiometer by Delage et al. (2007). This resulted

due to a sudden increase in pore air pressure (ua) and therefore, pore water pressure (uw) with

loading. The increase in pore water pressure (uw) due to loading reduced at higher stresses due

to relative reduction in deformation. The excess pore air pressure (ua) dissipated in a short time

after loading, because air phase was drained. However, suction equilibration took a longer time

due to rearrangement of water. Water rearrangement occurred because of soil deformation which

resulted in a different pore size distribution within the sample. Equilibration time for suction or

pore water pressure (uw) was longer for samples with 5% bentonite content than samples having

2% bentonite content. This was due to the lower permeability of the samples with 5% bentonite

content. In general, the equilibration after loading took a longer time for samples that had lower

water contents in both types of soils. As it was discussed previously in this section this might

be due to the discontinuity of the water phase within the samples.

Tables 5.3 and 5.4 show the matric suction change with loading for samples with different


0 500 1000 1500 20000

50

100

150

200

250

300

Time, t (hours)

Por

e pr

essu

re, u

a, uw a

nd m

atric

suc

tion,

s (

kPa)

ua

uw

matric suction

wc = 2.9%

Figure 5.7: Long equilibration time for S5B with 2.9% water content

Table 5.4: Matric suction change with loading for S5B

Test ∆(ua − uw)(kPa)

5b6.5wc 105b7.5wc 125b10.3wc 65b10.9wc 55b12.6wc 3.9

77

water contents. There was a matric suction reduction for both soil types at all tested water

contents. Most of the matric suction reduction took place at the first loading step. There was

no or very little matric suction reduction during the following loading steps. Matric suction

changes with loading gradually reduced with increasing water content for both soils. Similar

behaviour was observed by Tarantino and De Col (2008) for kaolin and by Olson and Langfelder

(1965) for Champaign till and Fayalite clay. At first sight the results seems to be unexpected,

because there is a common belief that suction reduces with loading on the wet side of the

optimum water content and stays almost constant in the dry side of the optimum water content.

Examining the previous studies carried on by Li (1995); Romero (1999); Montanez (2002), it is

expected an increasing suction change with increasing water content which is opposite to the

results obtained from this study. It should be noted, however, that post compaction suctions

were measured in those studies. When samples were unloaded, it resulted in an elastic volume

increase of the samples and samples moved from a loading wetting curve to an unloading drying

curve. This phenomena is well explained in Tarantino and Tombolato (2005) and Tarantino and

De Col (2008). Therefore, the past studies, where post compaction suctions were measured, may

not be directly comparable to suctions measured during the compaction process.

5.4 Volume change characteristics of soils

The change in specific volume (ν) with applied vertical stress (σy) is presented in Figure 5.8

for S2B and in Figure 5.9 for S5B. The results are also plotted in semi logarithmic graphs and

the normal compression lines (NCLs) for saturated soil samples are included in the figures for

comparison. It should be noted that the compression curves are for constant water content tests

and are not for constant suction tests except for the results of saturated soils, which are specified

on the figures. However, since the suction reduction with loading is low they can be regarded as

constant suction tests (see Section 5.3). Even though, the deformation of the samples were quite

low due to high sand proportion within the samples, a clear trend of deformation increase with

increase in water content can be noticed. In Figure 5.8, the sample with 10.2% water content

experienced an unexpected deformation. Moreover, the water content change during this test

was recorded to be much higher than the other tests (Table 5.1). Therefore, this experiment is

disregarded in the interpretation of the overall results and it will not be presented hereafter.

The slope of the normal compression lines (λ(s)) for unsaturated soil samples are higher


[a]

0 500 1000 1500 2000 25001.3

1.4

1.5

1.6

1.7

1.8

1.9

Net vertical stress, σy − u

a (kPa)

Spe

cific

vol

ume,

ν

wc = 6.9%wc = 8.4%wc = 8.6%wc = 10.2%wc = 10.7%s = 0

[b]

10−2

100

102

104

1.6

1.7

1.8

1.9


a (kPa)

Spe

cific

vol

ume,

ν

wc = 6.9%wc = 8.4%wc = 8.6%wc = 10.7%s = 0

Figure 5.8: Variation of specific volume during the tests for S2B

79

[a]

[b]

Figure 5.9: Variation of specific volume during the tests for S5B


0 500 1000 1500 2000 25001.4

1.45

1.5

1.55

1.6

1.65


a (kPa)

Dry

den

sity

, γd (

t/m3 )

wc = 6.9wc = 8.4wc = 8.6wc = 10.7

Figure 5.10: Variation of dry density during the tests for S2B

than the slope of the saturated soils in both type of soils. An increase in the slope of the

NCL with increase in matric suction was also observed by Estabragh et al. (2004),Cuisinier and

Masrouri (2005) and Monroy et al. (2008). Moreover, this can be also observed in Tarantino

and De Col (2008), where kaolin samples were initially prepared with different water contents

and later saturated before loading. The samples initially prepared with less water contents had

higher slopes of the NCLs (λ(s)) than the slope of the NCL for initially slurry soils (λ(0)). These

results contradict with the assumption taken in most of the constitutive models (Alonso et al.,

1990; Bolzon et al., 1996; Sheng et al., 2008), which state a decreasing slope with increasing

suction. Due to this discrepancy, these models may fail to successfully simulate the compaction

process. This will be examined in Chapter 7.

Figures 5.10 and 5.11 show the changes in dry density with increasing applied net vertical

stress (σy − ua). The dry density increased exponentially with loading. In addition, as it would

be expected from the compaction curve, the samples with higher water content have higher dry

density.

Changes in degree of saturation with loading are given in Figures 5.12 and 5.13. The variation

of degree of saturation with loading have a similar trend with dry density. It can be seen that

at the end of the loading none of the samples reached saturation. Saturation in these samples

could be only reached at high stresses if particles were compressible. It is important to notice

that the granular soils have very low degrees of saturation even at high applied stresses. In

81

Figure 5.11: Variation of dry density during the tests for S5B

addition, tested soils (S2B and S5B) reached saturation at low water contents in the wetting

path of their water retention curves (Figures 5.3 and 5.4). S2B had a degree of saturation about

50% at 1 kPa matric suction and S5B about 55% at 6 kPa matric suction. Probably, the pores

were already filled with water where the radius between the air and the water interface was at

its minimum angle. Therefore, addition of more water would only resulted in an increase of the

degrees of saturation but not in a reduction of the suctions. There is a common observation

that the water contents at saturation are lower in the wetting path than the drying path due

to the air being trapped within the sample during wetting. However, at such low degrees of

saturation, it is very unlikely for the air to be trapped. Moreover, these values are very close to

the degrees of saturation at their optimum water content. In the wetting path at zero suctions, as

the degrees of saturation increases when soils get finer, the optimum water content of these soils

also increases. However, further research needs to be conducted to find the direct correlation

between the optimum water content and the degree of saturation at zero suction for the wetting

path to assure this finding.

The variation of the coefficient of compressibility (ms1) with applied vertical net stress (σy −

ua) is shown in Figures 5.14 and 5.15. The compressibility coefficient (ms1) decreases with

increasing applied net vertical stress (ms1) up to 500 kPa for S2B and up to 1000 kPa for S5B,

and later remains almost constant for higher applied stresses. In general, the compressibility


0 500 1000 1500 2000 250015

20

25

30

35

40

45

50


a (kPa)

Deg

ree

of s

atur

atio

n, S

r (%

)

wc = 6.9wc = 8.4wc = 8.6wc = 10.7

Figure 5.12: Variation of degree of saturation during the tests for S2B

Figure 5.13: Variation of degree of saturation during the tests for S5B

coefficient (ms1) also decreases with decreasing water content at a particular stress. However,

since the deformation differences between samples are very small; this is not very obvious in the

current results.

The variation of the coefficient of compressibility (ms1) with degree of saturation is shown

in Figures 5.16 and 5.17. The compressibility coefficient (ms1) reduces with increasing degree of

83

0 500 1000 1500 2000 25000

1

2

3

4

5

6x 10

−4


a (kPa)

Coe

ffici

ent o

f com

pres

sibi

lity,

m1s (

1/kP

a) wc = 6.9wc = 8.4wc = 8.6wc = 10.7

Figure 5.14: Variation of degree of the coefficient of compressibility due to net stress (ms1) for

S2B

0 1000 2000 3000 40000

1

2

3x 10

−4


a (kPa)

Coe

ffici

ent o

f com

pres

sibi

lity,

m1s (

1/kP

a) wc = 6.5%wc = 7.5%wc = 10.3%wc = 10.9%wc = 12.6%

Figure 5.15: Variation of degree of the coefficient of compressibility due to net stress (ms1) for

S5B

saturation during the compaction process.

Finally, Figures 5.18 and 5.19 show the static and dynamic compaction curves for S2B and

S5B. Even though, the deformations of the samples were low, there is still a clear trend of

a density increase with an increase in water content for both soils. In addition, the static


20 25 30 35 40 45 500

1

2

3

4

5

6x 10

−4

Degree of saturation, Sr (%)

Coe

ffici

ent o

f com

pres

sibi

lity,

m1s , (

1/kP

a) wc = 6.9wc = 8.4wc = 8.6wc = 10.7

Figure 5.16: Variation of the coefficient of compressibility due to net stress (ms1) with degree of

saturation for S2B

20 30 40 50 600

1

2

3x 10

−4

Degree of saturation, Sr (%)

Coe

ffici

ent o

f com

pres

sibi

lity,

m1s (

1/kP

a) wc = 6.5%wc = 7.5%wc = 10.3%wc = 10.9%wc = 12.6%

Figure 5.17: Variation of the coefficient of compressibility due to net stress (ms1) with degree of

saturation for S5B

compaction curves have a similar trend to dynamic compaction curves. The energy applied

with dynamic compaction for the Standard tests was 596kJ/m3 and for Modified tests was

2703kJ/m3. On the other hand, the stresses applied for static compaction curves were 560kPa

and 2250kPa for S2B and 560kPa and 2650kPa for S5B.

85

0 5 10 15 201.5

1.55

1.6

1.65

1.7

1.75

1.8

1.85

1.9

1.95

2


Dry

den

sity

, γd (

Mg/

m3 )

Standard (596 kJ)Modified (2703 kJ)560 kPa2250 kPa

Sr = 70%Sr = 50%

Figure 5.18: Compaction curves of S2B

0 5 10 15 201.6

1.65

1.7

1.75

1.8

1.85

1.9

1.95

2


Dry

den

sity

, γd (

Mg/

m3 )

Standard (596 kJ)Modified (2703 kJ)560 kPa2650 kPa Sr = 100%

Sr = 80%

Figure 5.19: Compaction curves of S5B


This chapter presented the experimental results of the constant water content static compaction

tests conducted during this study. Before compaction, the initial matric suction of the specimens

was measured using null type axis translation technique. Matric suction measurements were

conducted in the same device with compaction tests. This allowed continuous matric suction


measurements during loading.

Initial matric suction measurements took a long time for the low water content samples.

This was attributed to the discontinuous water phase within the samples. There was a good

agreement between the matric suction measurements with null method and tensiometers. Post

loading equilibration time was also found to be very long for samples with low water content

compared to the time reported in the literature. Matric suction reduction was observed during

loading for all tested samples with varying water contents. The matric suction change decreased

with increasing water content and decreasing clay content.

The slopes of the normal compression lines for the constant water content tests were found

to be higher than the slopes of the saturated samples for both samples. This finding is different

from the assumption taken in most of the constitutive models which states a decrease in the

slopes of the normal compression line with increasing suctions. This might result in deficiencies

to model the compaction behaviour with existing soil constitutive models and will be further

examined in Chapter 7.

Full saturation was never reached at the end of the compaction tests. On the contrary, the

degrees of saturation attained at the end of the compaction process were very low and were

close to the values of their water retention curves at zero suction in the wetting paths. This

strengthens the idea of direct correlation between the degree of saturation at optimum water

content and the maximum degree of saturation in the wetting path of the water retention curve.

Further investigation needs to be undertaken to validate the correlation observed in this study.

The coefficient of compressibility (ms1) of the soils decreased with both increasing vertical

net stress (σy−ua) and degree of saturation during the test. In addition, the compaction curves

obtained with static loading had similar shapes to the dynamic compaction curves.

In conclusion, the matric suction of granular soils were measured using null type axis transla-

tion technique for the first time in the literature. Even though, the experiments were very time

consuming, they gave insights to the possibilities in matric suction measurement techniques for

granular soils with low water content.

Chapter 6

Modelling the compaction process

6.1 Introduction

Compacted soils undergo a compaction process which influences the post compaction behaviour.

However, information on the evolution of the compaction process is limited particularly from a

quantitative sense. Thus, examination of the compaction process is a crucial topic in order to

extend the current knowledge on the behaviour of compacted soils.

One way of accomplishing this aim is to model the compaction process. Modelling the

compaction process will help to understand the evolution of the stress and phase variables during

compaction and the fundamental reasons for the inverted parabolic shape of the compaction

curve.

6.2 Formulation of the compaction process

The main parameters required to be predicted to model the compaction process are the volume

change, the pore pressure development, and the compressibility coefficients. Theoretical concepts

used to predict these parameters were presented in Section 2.4 and are briefly summarised here

for clarity.

6.2.1 Volume change calculation

The constitutive relationship proposed by Fredlund & Morgenstern (1976) was used for the

volume change and thus, dry density calculations (see Equation 2.2). The volume change consti-

87

88 CHAPTER 6. MODELLING THE COMPACTION PROCESS

Table 6.1: Comparison of Hilf and Hasan & Fredlund’s method for pore pressure generations

Hilf (1948) Hasan & Fredlund (1980)compressibility free air 4 4

dissolved air 4 4water x 4

soil x xmatric suction ∆ua = ∆uw 4 x

∆(ua − uw) = 0 4 x

tutive relationship is defined in terms of two independent stress variables (σy−ua and ua−uw).

As applicable to one dimensional loading, the constitutive relationship can be expressed as fol-

lows:

εv =∆VvV0

= ms1∆(σy − ua) +ms

2∆(ua − uw) (2.2)

where εv is the volumetric strain, ∆Vv is the overall volume change, V0 is the initial volume,

∆(σy − ua) is the change in the vertical net stress, ∆(ua − uw) is the change in matric suction,

ms1 is the compressibility of a soil element with respect to vertical net stress (σy − ua) and ms

2

is the compressibility of a soil element due to matric suction (ua − uw).

The volume changes (∆Vv) were incrementally calculated by multiplying the right hand side

of the Equation 2.2 with the initial volume (V0). The corresponding dry density (γd) was then

calculated once the final total volume of the soil element is known.

Examination of the Equation 2.2 clearly indicates that in order to calculate the volume change

(∆Vv) with the applied vertical stress (σy), the pore pressures (ua, uw) and the compressibility

coefficients (ms1, ms

2) need to be predicted at each stress state.

6.2.2 Pore pressure development

One of the primary aspects associated to model the compaction process is the pore pressure

development. Two different approaches were identified in literature, namely the Hilf’s (1948)

and the Hasan & Fredlund’s (1980) approaches. The major differences between two methods

are summarised in Table 6.1 and their mathematical formulations were presented in Chapter 2.

In this section, both approaches are analysed for undrained loading conditions in detail. The

assumptions taken for the undrained, semi-drained and drained loading calculations are also

explained.

For the analysis of Hilf’s approach, the compressibility coefficient for saturated soil sample

89

Table 6.2: Parameter values for the pore pressure generations for Hilf’s and Hasan & Fredlund’smethods

mv = ms1 ms

2 ma1 ma

2 Cw ua0 h Sr0 n0(kPa−1) (kPa−1) (kPa−1) (kPa−1) (kPa−1) (kPa)

Hilf 1.45E-04 - - - - 101.3 0.02 0.85 0.50Hasan & Fredlund 1.45E-04 1.02E-04 1.15E-04 0.00 4.00E-07 101.30 0.02 0.85 0.50

(mv) was replaced with the unsaturated compressibility coefficient (ms1) (see Equation 2.3). This

modification was adopted considering that the soil being compressed is unsaturated and thus,

will better represent the real situation. If compressibility coefficient for saturated soil (mv)

is used higher deformations would be expected and this will lead to higher pore air pressure

generation within the soil sample.

∆ua =

1

1 +(1 − Sr0 + hSr0)n0

(ua0 + ∆ua)ms1

∆σy (2.3)

where ∆ua is the change in the pore air pressure, Sr0 is the initial degree of saturation, h is the

solubility coefficient of air in water, n0 is the initial porosity, ua0 is the initial absolute pore air

pressure, ms1 is the coefficient of volume change in unsaturated soil, and ∆σy is the change in


Undrained loading

During undrained loading, both the air and water phases were considered to be undrained.

An example of pore pressure development during compression, using Hilf’s approach is shown

in Figure 6.1. The soil parameters used for the predictions are given in Table 6.2 and were

obtained from Fredlund and Rahardjo (1993). It was assumed by Hilf (1948) that the changes

in the pore water pressures (∆uw) will be equal to the changes in the pore air pressures (∆ua).

Thus, matric suction changes (∆(ua − uw)) will remain constant. For that reason, when Hilf’s

approach is adopted for pore pressure calculations, the second part or the matric suction part

of the volume change equation (see Equation 2.2) can be neglected.

During the pore water pressure (uw) calculations, the initial matric suction (s = ua − uw)

values were obtained from the calculations of Hasan & Fredlund’s method. They assume that

the pore water pressure (uw) will be equal to the atmospheric pressure when the soil sample

reaches saturation (Sr = 100%). Therefore, even the initial matric suction (s0 = ua0 −uw0) was

unknown it could be back calculated.


0 500 1000 1500 2000−200

0

200

400

600

800

1000

1200

Vertical stress, σy (kPa)

Por

e ai

r an

d w

ater

pre

ssur

es u

a, uw (

kPa)

ua

uw

Figure 6.1: Pore air and pore water pressure generation using Hilf’s approach

An example of pore pressure development using Hasan & Fredlund’s approach is shown in

Figure 6.2 and the parameter values used to generate the curves are given in Table 6.2. Different

than the Hilf’s approach, Hasan and Fredlund (1980) assumed that the suction becomes zero at

full saturation. Thus, the suction is progressively reducing with loading.

The pore air (ua) predictions for both approaches are presented in Figure 6.3. Constant

soil coefficients are used for both methods. Although, the results of the two methods are quite

close, it can be seen from the figure that Hilf’s method generates higher pore air pressures (ua)

than Hasan & Fredlund’s method for the same applied vertical stress. This difference could be

explained by two arguments:

1. Hasan & Fredlund (1980) take into consideration matric suction changes (∆(ua−uw)) with

applied vertical stress (σy), whereas Hilf’s method assumes a constant matric suction with

the increasing vertical stress. Taking matric suction changes (∆(ua − uw)) into account

(second part of the Equation 2.2) reduces the compressibility and therefore results in lower

density of the soil element. It should be noted that at the end of the compression the

two samples have different densities; Hilf’s approach has higher and Hasan & Fredlund’s

approach has lower density, thus they develop different pore air pressures at the same


2. The compressibility of water is considered in Hasan & Fredlund’s approach and this results

91

0 500 1000 1500 2000−200

0

200

400

600

800

1000

1200

1400

1600


Por

e ai

r an

d w

ater

pre

ssur

es u

a, uw (

kPa)

ua

uw

Sr = 1

Figure 6.2: Pore air and pore water pressure generation using Hasan & Fredlund’s approach

in a slightly different pore air pressure development. However, since the compressibility of

water is very low (Cw = 4.00E − 07kPa−1) the effect of this is only minor.

Semi-drained loading

In semi-drained loading, it was accepted that pore pressures (ua and uw) develop in every loading

step, and after the pore air pressure (ua) and therefore, the pore water pressure (uw) dissipate.

Therefore, each loading step started with the atmospheric air pressure (ua0 = 101.3kPa). This

results in different porosity (n) and degree of saturation (Sr) of the soil element than undrained

and drained loading types.

This type of loading was implemented in order to better capture the experimental method.

As it was explained in Chapters 4 and 5, air phase is drained during the experiments but it

requires some time for the buildup air pressure to dissipate after each loading increment. Thus,

it is expected that air pressure builds up in every load increment and later dissipates.

Drained loading

During drained loading, it was considered that the air is continuous throughout the soil element

and can drain freely, thus, keeping the pore air pressure (ua) constant and equal to atmospheric

air pressure. However, water was considered to be undrained. It is well known that in un-


0 500 1000 1500 20000

200

400

600

800

1000

1200


Por

e ai

r pr

essu

re, u

a (kP

a)

Hilf (1948)Hasan & Fredlund (1980)

Figure 6.3: Comparison of Hasan & Fredlund’s and Hilf’s approach for pore air pressure gener-ation

saturated soils, due to the presence of suction, water cannot drain until it reaches the OWC

where air becomes discontinues and is trapped within water (Langfelder et al., 1968; Hilf, 1956).

Moreover, it could be argued that by a sudden increase in vertical stress (σy), there would be

a temporary increase in the pore water pressure (uw) due to the increase in pore air pressure

(ua) and this might result in water drainage (which might be the case in dynamic compaction).

However, this study concentrates on static compaction and the loading rate is considered to be

rather small.

In practice, this loading type could be the case in coarse grained soils where the pores are

large and the pore air pressure could quickly dissipate. In addition, the compaction behaviour

for drained loading is modelled in order to compare with undrained loading results and illustrate

the effect of pore pressure on the overall shape of the compaction curve.

6.2.3 Compressibility coefficients

Compressibility coefficients (ms1,m

s2) are vital for compaction behaviour modelling. In this

section the basic assumptions and approaches used for their predictions are explained.

93

Constant compressibility coefficients

Initially, the compressibility coefficients (ms1 and ms

2) were considered as constant parameters,

i.e., compressibility of a soil element does not change with increasing vertical stresses (σy) or

vertical net stresses (σy − ua) and changes in matric suction (∆(ua − uw)). Compaction curves

generated with this assumption are shown and discussed in Section 6.3.1.

Variable compressibility coefficients

An insight for the variation of the compressibility coefficients was gained from the study con-

ducted by Cho & Santamarina (2001) on the variation of the shear wave velocity of granite

powder for different degrees of saturation. They found that the shear wave velocity (Vs), hence

the shear modulus (G = ρVs) increases with decreasing degrees of saturation. This outcome is

confirming that material stiffness is increasing for decreasing saturations and is not a constant

parameter. Therefore, it can be stated that the compressibility of the material is increasing with

increasing degrees of saturation. In addition, Lloret et al. (2003) showed that the coefficient

of compressibility (ms1) decreases with both increasing suctions (s = ua − uw) and vertical net

stresses (σy − ua).

A functional form for the compressibility coefficients (ms1 and ms

2) could be approximated

from the constitutive models available in literature. Two of these models are considered in

this study. Barcelona Basic Model (BBM) proposed by Alonso et al. (1990) and the model,

which will be referred hereafter as SFG model, proposed by Sheng et al. (2008). The BBM

is the first introduced constitutive model for unsaturated soils. It is a separate stress state

variables approach model, which considers the vertical net stress (σy − ua) and matric suction

(s = ua−uw) as independent variables. Other separate stress state variables models in literature

(Wheeler and Sivakumar, 1995; Vaunat et al., 2000; Thu et al., 2007; Chiu and Ng, 2003) are

derived in a similar manner to the BBM and only minor changes were added to adapt the specific

modelling purposes. For that reason, the BBM was selected for detailed examination in the

current study. In contrast to the BBM, the SFG model is a combined stress variables approach

model, which combines the vertical net stress (σy − ua) and matric suction (s = ua − uw) in its

model formulations. There are other combined stress-suction approach models in literature (such

as Bolzon et al. (1996); Santagiuliana and Schrefler (2006); Gallipoli et al. (2003a); Tarantino and

De Col (2008)); however, those models use the BBM or models with similar approach (Wheeler

and Sivakumar, 1995) in their mechanical modelling formulations. Therefore, the SFG model is


the second selected approach for detailed examination in this study.

As applicable to one dimensional loading, volumetric strain (εv) can be written the following

form for the BBM:

εv =dν

ν=λ(s)

ν

d(σy − ua)

(σy − ua)+κsν

d(ua − uw)

(ua − uw) + uatm(2.12)

where ν is the specific volume of the soil element, λ(s) is the slope of the NCL at suctions defined

in semi logarithmic plot, d(σy −ua) is the change in vertical net stress, d(ua−uw) is the change

in suction and κs is the slope of the volume change vs. suction curve defined in semi logarithmic

plot.

In Equation 2.12, λ(s) is defined as:

λ(s) = λ(0)[(1 − r)e−βs + r] (2.13)

where λ(0) is the slope of the NCL for saturated soil defined in semi logarithmic plot, r is a

constant parameter related to the maximum stiffness of the soil, and β is a constant parameter

which controls the rate of increase of soil stiffness with matric suction.

From the BBM, the compressibility coefficients (ms1 and ms

2) can be derived as:

ms1 =

λ(s)

ν(σy − ua)(6.1)

ms2 =

κsν(σy − ua)

(6.2)

.

In addition, volumetric strain (εv) for one dimensional loading is suggested in the following

form in the SFG model:

εv =dν

ν= λvp

d(σy − ua)

(σy − ua) + s+ λvs

d(ua − uw)

(σy − ua) + s(2.16)

where ν is the specific volume of the soil element, λvp is the slope of the normal compression line

(NCL) for saturated soil when both axes are plot in logarithmic scale, d(σy − ua) is the change

in vertical net stress, d(ua − uw) is the change in matric suction, s is matric suction and λvs is

the slope of the volume change vs. matric suction curve when both axes are plot in logarithmic

scale.

95

This gives the compressibility coefficients (ms1 and ms

2) as:

ms1 =

λvp(σy − ua) + s

(6.3)

ms2 =

λvs(σy − ua) + s

(6.4)

.

Equations 2.12 and 2.16 are integrable for vertical net stress changes (σy−ua) under constant

matric suctions (s = ua−uw). Integrating Equations 2.12 and 2.16 for vertical net stress changes

(σy − ua) under a constant matric suction or for matric suction (s) changes under a constant

vertical net stress(σy − ua) lead to:

ν = N(s) − λ(s)ln(σy − ua)

(σy − ua)c(2.14)

lnν = lnN(s) − λvpln(σy − ua) + s

(σy − ua)0 + s(2.17)

where N(s) is the specific volume at an initial stress state ((σy − ua)0,s) and (σy − ua)c is a

reference stress in which changes of matric suction causes only elastic deformation.

In the BBM, N(s) is defined as (in Equation 2.14):

N(s) = N(0) − (λ(0) − λ(s))ln(σy − ua)c − κsln

(s+ uatmuatm

)(2.15)

where N(0) is the specific volume, at a reference stress state ((σy − ua)c), for saturated soil

defined in semi logarithmic plot.

In the SFG model, N(s), which is the specific volume at an initial stress state ((σy − ua)0,s)

for matric suctions smaller than the saturation suction (ssa), s < ssa is defined as:

lnN(s) = lnN0 − λvpln(σy − ua)0 + s

(σy − ua)0(2.18)

and; when N(s) is under net vertical stress (σy −ua)0 equal to unity and matric suctions bigger

than the saturation suction (ssa), s≥ssa, it is defined as

lnN(s) = lnN0 − λvpln(σy − ua)0 + ssa

(σy − ua)0− λvp

(1 − ssa + 1

s+ 1

)(2.19)


where N0 is the specific volume at initial stress state for saturated soil when both axes are plot

in logarithmic scale.

These equations will be used for the compaction curve generation. The variation of the

compressibility coefficients with degree of saturation and their effect on the overall compaction

curve are further discussed in Section 6.3.2 under the light of selected constitutive models.

6.3 Generation of the compaction curve

The compaction curves were generated by using the theories summarised in Chapter 2 and

Section 6.2. First, the pore pressures (ua, uw) were predicted and were used for the calculations

of the volumetric strain (εv = ∆V/V ). Subsequently, the volume change (∆V ) results were

used to find the corresponding dry densities. The computations were performed for a range of

moisture contents (w) which also define the values of the initial degrees of saturation (Sr0).

A summary of the approach that was followed and all the combinations used for the gener-

ation of the compaction curves are illustrated in Figure 6.4. The following combinations were

performed and each combination is described in detail in the following sections:

1. undrained modelling using Hilf’s method for pore pressure development and constant com-

pressibility coefficient (ms1)

2. undrained modelling using Hasan & Fredlund’s approach for pore pressure development

and constant compressibility coefficients (ms1 and ms

2)

3. undrained modelling using Hilf’s method for pore pressure development and variable com-

pressibility coefficient (ms1)

4. semi-drained modelling using Hilf’s method for pore pressure development and constant

compressibility coefficient (ms1)

5. semi-drained modelling using Hasan & Fredlund’s approach for pore pressure development

and constant compressibility coefficients (ms1 and ms

2)

6. semi-drained modelling using Hilf’s method for pore pressure development and variable

compressibility coefficient (ms1)

7. drained modelling using constant compressibility coefficient (ms1)

8. drained modelling using variable compressibility coefficient (ms1)

97

The compaction curves predictions are explained under two different classifications. First,

all the loading types which are developed using constant compressibility coefficients (ms1,m

s2)

are summarised and this is followed by the compaction curves generated using variable com-

pressibility coefficient (ms1). In this chapter, the shape of the compaction curve is qualitatively

examined. According to the model formulations and the assumptions in the both constitutive

models (the SFG model and the BBM) presented in Chapter 2 and Section 6.2.3, the shape of

the compaction curve will be similar and only the quantitative results will differ. For simplicity,

in this chapter, the compaction curves are only generated using the SFG model. In Chapter 7,

however, the performances of the both models are comprehensively examined.

6.3.1 Modelling of the compaction curve using constant compressibil-

ity coefficients

In this section, compaction curves were generated using constant compressibility coefficients

(ms1,m

s2) for undrained, semi-drained and drained loading conditions. During undrained and

semi-drained loading, the pore pressures (ua, uw) were predicted by the two aforementioned

methods (Hilf, 1948 and Hasan & Fredlund, 1980). For modelling purposes, the compressibility of

the soil element is accepted to be equal to the compressibility of water at the time it reaches 100%

saturation (Sr) (soil does not compress further after it reaches full saturation). A comparison of

the results of the three loading types as well as the use of constant compressibility coefficients

in the modelling of the compaction curve is discussed.

Undrained loading

The compaction curves generated assuming constant compressibility coefficients (ms1 and ms

2)

during undrained loading for different energy levels are presented in Figure 6.5. It should be

noted that the first method (Hilf, 1948) does not take into account the changes in suction and

assumes a constant suction during the compression of the soil specimen. Therefore, in the volume

change equation (Equation 2.2) the second component of the equation was neglected, whereas

in the Hasan & Fredlund’s method the second part of the volume change equation is taken into

account. Parameters used for the modelling of the compaction curves are presented in Table 6.3.

Figure 6.5 shows that both methods produced a reasonable shape on the wet side of the

compaction curve, but not on the dry side. In addition, the effect of applied vertical stress

(σy) or applied energy can be seen in the simulations by the both approaches. Moreover, matric


Compaction Curve

Undrained

Compaction

Drained

Compaction

Semi-drained

Compaction

BBM

Constant

Compressibility Coefficients

Variable

Compressibility Coefficients

Fredlund & Rahardjo’s

approach (1993)

Hilf’s approach

(1948)

Pore pressure development

SFG model

Volume change calculations

Figure 6.4: Approach followed for the compaction curve generation

99

[a]0 5 10 15 20 25

1.6

1.8

2

2.2

2.4


Dry

den

sity

, γd (

Mg/

m3 )

σy = 700 kPa

σy = 2000 kPa

Saturation curve

[b]0 5 10 15 20 25

1.6

1.8

2

2.2

2.4


Dry

den

sity

, γd (

Mg/

m3 )

σy = 700 kPa

σy = 2000 kPa

Saturation curve

[c]0 5 10 15 20 25

1.6

1.8

2

2.2

2.4


Dry

den

sity

, γd (

Mg/

m3 )

Hilf (1948)Hasan & Fredlund (1980)Saturation curve

Figure 6.5: Modelling of the compaction curves using constant compressibility coefficients forundrained loading [a] Hilf’s method [b] Hasan & Fredlund’s method [c] Comparison of Hilf’s andHasan & Fredlund’s methods at σy = 700 kPa


Table 6.3: Parameters used for the compaction curve modelling using constant compressibilitycoefficients

mv = ms1 ms

2 ma1 ma

2 Cw ua0 h Gs e0(kPa−1) (kPa−1) (kPa−1) (kPa−1) (kPa−1) (kPa)1.45E-04 1.02E-04 1.15E-04 0.00 4.00E-07 101.30 0.02 2.65 0.68

suction changes (∆(ua−uw)) that were included in Hasan & Fredlund (1980)’s method resulted in

some reduction in the dry density. This was due to the matric suction (s = ua − uw) reduction

in the specimen with compression (see Section 6.2.2). When matric suction (s = ua − uw)

reduced, the change in matric suction (∆(ua − uw)), which is the second part of the volume

change equation (Equation 2.2), became negative; and therefore resulted in lower total volume

changes (∆V ) which led to lower dry densities.


The compaction curves generated during semi-drained loading type and using constant compress-

ibility coefficients (ms1 and ms

2) are illustrated in Figure 6.6. Figure 6.6(a) shows the results of

the compaction curves using the approach of Hilf (1948) for pore pressure (ua, uw) predictions.

The results obtained by using Hasan and Fredlund (1980)’s approach for pore pressure genera-

tion (ua, uw) were shown in Figure 6.6(b) for different energy levels (σy = 700 kPa and σy = 2000

kPa). The comparison of the compaction curves modelled by employing these two methods at

the applied vertical stress of 700 kPa are presented in Figure 6.6(c).

Similar results to undrained loading were obtained while compaction curves were generated

for semi-drained loading conditions. Again, a reasonable shape of the compaction curve was

attained on the wet side of the compaction curve, but not on the dry side.

Drained loading

In this section, the compaction curves modelled for drained loading are analysed. During drained

loading it was assumed that pore air pressure (ua) stayed constant and equal to atmospheric

pressure. Therefore, the pore air pressure (ua) predictions were not required and only the volume

change equation (Equation 2.2) was necessary to use. The use of the second part of the volume

change equation (Equation 2.2) is attainable only if matric suction change (∆(ua − uw)) with

compression can be predicted. Here, the volume change (∆V ) resulted due to the change in

matric suction (∆(ua − uw)) was neglected and the calculated volume change (∆V ) was only

101

[a]0 5 10 15 20 25

1.6

1.8

2

2.2

2.4


Dry

den

sity

, γd (

Mg/

m3 )

σy = 700 kPa

σy = 2000 kPa

Saturation curve

[b]0 5 10 15 20 25

1.6

1.8

2

2.2

2.4


Dry

den

sity

, γd (

Mg/

m3 )

σy = 700 kPa

σy = 2000 kPa

Saturation curve

[c]0 5 10 15 20 25

1.6

1.8

2

2.2

2.4


Dry

den

sity

, γd (

Mg/

m3 )

Hilf (1948)Hasan & Fredlund (1980)Saturation curve

Figure 6.6: Modelling of the compaction curves using constant compressibility coefficients forsemi-drained loading[a] Hilf’s method [b] Hasan & Fredlund’s method [c] Comparison of Hilf’sand Hasan & Fredlund’s methods at σy = 700 kPa


0 5 10 15 20 251.6

1.8

2

2.2

2.4


Dry

den

sity

, γd (

Mg/

m3 )

σy = 700 kPa

σy = 2000 kPa

Saturation curve

Figure 6.7: Modelling of the compaction curves using constant compressibility coefficients fordrained loading

due to the change in the vertical net stress (σy − ua).

The compaction curves generated with the assumption of using constant compressibility

coefficient (ms1) for drained loading are presented in Figure 6.7. In this figure, the compaction

curves were generated for applied vertical stresses of 700 kPa and 2000 kPa. The shape of the

modelled curves on the dry side were similar to the ones modelled for undrained and semi-

drained loading. However,it can be seen that due to the elimination of the pore air pressure (ua)

generation the compaction curves joined the saturation line on the wet side of the curve.

Discussion on using constant compressibility coefficients for the compaction mod-

elling

The comparison of the compaction curves generated using constant coefficients of compressibility

(ms1,m

s2) for undrained, semi-drained and drained loading types are demonstrated in Figure 6.8.

During the modelling of the drained loading type only the first part of the volume change

equation (Equation 2.2) was used. Therefore, for the impartial comparison of the three loading

types the results shown in the figure for undrained and semi-drained loadings are the curves

generated with Hilf’s method (Hilf’s method also uses only the first part of the volume change

equation). In this figure, compaction curves are shown for applied vertical stress (σy) at 700

kPa (the lower curve) and 2000 kPa (the upper curve).

103

0 5 10 15 20 251.6

1.8

2

2.2

2.4


Dry

den

sity

, γd (

Mg/

m3 )

UndrainedSemi−drainedDrainedSaturation curve

Figure 6.8: Comparison of the modelled compaction curves using constant compressibility coef-ficients for undrained, semi-drained and drained loading conditions (σy = 700 kPa lower curvesand σy = 2000 kPa upper curves)

Figure 6.8 shows that the modelling results of drained loading produced the highest densities

and the modelling results of undrained loading generated the lowest densities under the same

applied vertical stresses (σy). It was an expected result as higher pore air pressure (ua) would

make the soil element harder to compress. In addition, another difference could be noticed close

to saturation. The model results attained during drained loading coincided with the saturation

curve. This happened due to the assumption that the air phase is continuous and can drain freely

for all degrees of saturation (Sr). However, it is well known that after the soil specimen reaches

the OWC, air is discontinuous and is trapped into water and thus, cannot drain (Langfelder et al.

(1968)). However, during the modelling of the semi-drained and the undrained loading types

there was high pore air pressure (ua) generation which could be expected to act like trapped air.

Therefore, the results obtained for the wet side of the compaction curves during the semi-drained

and the undrained loading types better represents the real situation. The comparison between

the modelling results of the semi-drained and the undrained loading conditions will be examined

further in Chapter 7 when the models’ performance is evaluated with the experimental results.

It is clear from Figure 6.8 that using constant compressibility coefficients (mv = ms1 and ms

2),

a reasonable shape for the compaction curve can be attained on the wet side of the compaction

curve, but not on the dry side of the curve. Moreover, the matric suction changes (∆(ua − uw))


that were included in Hasan & Fredlund (1980)’s method resulted in some reduction in the dry

density (see Figure 6.5(c) and Figure 6.6(c)), but did not change the shape of the compaction

curve at lower water contents.

In order to examine the likely suction change during compaction, consideration was given to

the experimental results produced by Montanez (2002). Montanez (2002) provided the suction

contours for compacted sand-bentonite mixtures associated with domains defined by compaction

curves at various apparent energy levels. He found that the matric suction (ua − uw) only

decreases marginally with the density increase and in many cases can be considered constant.

Similar results for the suction change (∆(ua−uw)) can be found in literature (Li (1995); Delage

and Graham (1995). In addition, even if there is a small reduction in matric suction (ua − uw)

with compression, the ms2 applicable to the unloading process can be considered smaller than

that applicable to loading process. Therefore, Hilf’s analysis of assuming constant matric suction

during compaction appears to be close to the real situation and requires less soil parameters (no

need for parameters such as ma1 ,m

a2 etc.). Therefore, in the reminder of this thesis pore pressure

(ua and uw) predictions will be calculated using Hilf’s method.

6.3.2 Modelling of the compaction curve using variable compressibility

coefficients

In Section 6.3.1 the reasons for using only the first part of the volume change equation (Equation

2.2) and the discussion on neglecting the compressibility coefficient due to matric suction (ms2)

were presented. In this section, the attention is given to the compressibility coefficient due to net

stress (ms1) and the compaction curves are generated using variable coefficient of compressibility

(ms1) for undrained, semi-drained and drained loading conditions. Equation 6.3 was used for the

compressibility coefficient (ms1) calculations. It was accepted that the suction (s = ua − uw)

stays constant and equal to the initial suction (s0) during compression.

Equations 2.2, 2.3 and 6.3 were used in incremental forms to compute the incremental and

the total volume changes and the corresponding dry densities during undrained and semi-drained

compression. In addition, as it was taken into account in the previous section (see Section 6.3.1)

the compressibility of the soil element was accepted to be equal to the compressibility of water

(Cw) at the time it reaches saturation (Sr = 100%), which is only the case for drained loading.

Subsequently, a comparison of the results of the three loading types modelled using variable

compressibility coefficient (ms1) are discussed.

105

0 5 10 15 20 251.6

1.8

2

2.2

2.4


Dry

den

sity

, γd (

Mg/

m3 )

σy = 700 kPa

σy = 2000 kPa

Saturation curve

Figure 6.9: Modelling of the compaction curves using variable compressibility coefficient forundrained loading

Table 6.4: Parameters used for the compaction curve modelling using variable compressibilitycoefficients

Cw ua0 λvp h Gs e0(kPa−1) (kPa)4.00E-07 101.30 1.45E-01 0.02 2.65 0.68

Undrained loading

In this section, the compaction curves are generated assuming variable compressibility coefficient

(ms1) during undrained loading for different energy levels. The results are given in Figure 6.9.

Parameters used for the modelling of the compaction curves are presented in Table 6.4. The

initial matric suctions (s0 = ua0 − uw0) for varying water contents were calculated with the

assumption explained in Section 6.2.2 and are given in Table 6.5.

Figure 6.9 shows that the inverted parabolic shape of the compaction curve can be predicted

using variable compressibility coefficient (ms1) during undrained loading not only on the wet side

of the compaction curve but also on the dry side of the compaction curve. The effect of applied

stress was also well captured for this type of loading (the OWC shifts to the left).

Table 6.5: Matric suction values used for the corresponding water contents

water content (%) 2 5 10 15 20 25suction (kPa) 1183 1003 721 768 238 27


100

101

102

103

104

0

1

2

3

4

5

6

7

8x 10

−4

Vertical net stress, σy − u

a (kPa)

m1s (

kPa−

1 )

w = 2%w = 5%w = 10%w = 15%w = 20%

Figure 6.10: Variation of the coefficient of compressibility (ms1) due to net stress during undrained

loading

Figure 6.10 shows the variation of the coefficient of compressibility (ms1) with vertical net

stress (σy − ua) and water content (w) during undrained compression. It can be seen that the

coefficient of compressibility due to net stress (ms1) decreases with decreasing water content

(w) or initial degree of saturation (Sr0), as it was assumed in previous published work of this

study (see Appendix B). In addition, coefficient of compressibility (ms1) also decreases with

increasing vertical net stress (σy − ua). However, during the compression process, the degree of

saturation increases from the initial value, but the coefficient of compressibility (ms1) decreases.

This decrease of compressibility happens owing to the increase of net stress as the compression is

progressed. Therefore, it can be argued that the coefficient of compressibility (ms1) increases with

increasing initial degree of saturation (Sr0) but decreases with increasing degree of saturation

(Sr) during compression precess. It is also apparent that much of the compaction takes place in

the early part of the process where the soil compressibility decreases rapidly.

In Figure 6.11, the predicted values of the coefficient of compressibility (ms1) for different

values of water content (w) during undrained loading are shown together with vertical net stress

(σy−ua) development. The predictions of the coefficient of compressibility (ms1) and vertical net

stress (σy − ua) for both σy = 700 kPa and σy = 2000 kPa applied vertical stress are presented

on the figure. The curves shown by dotted lines represent the vertical net stress (σy − ua)

development with varying water content (w) and energy level. The curves shown by continues

107

5 10 15 200

1

2

3

4x 10

−4


m1s (

kPa−

1 )

5 10 15 200

500

1000

1500

2000

Ver

tical

net

str

ess,

σy −

ua (

kPa)

σy − u

a (σ

y = 700 kPa)

σy − u

a (σ

y = 2000 kPa)

m1s (σ

y = 700 kPa)

m1s (σ

y = 2000 kPa)

Figure 6.11: Variation of the coefficient of compressibility (ms1) and the net stress with water

content during undrained loading

lines represent the predicted values of the coefficient of compressibility (ms1) for varying water

content (w) and energy levels.

As can be seen from Equation 2.2, when the volume change due to matric suction change

(∆s = ∆(ua − uw)) is disregarded, the volumetric strain (∆V/V ), and thus the dry density,

becomes a function of the compressibility coefficient (ms1) and the change in vertical net stress

(∆(σy − ua)). It is important to note that in Figure 6.11 while the coefficient of compressibility

(ms1) increases, the vertical net stress (σy − ua) decreases with increasing water content (w).

Therefore, the maximum dry density could be attained at the optimum combination of these

two parameters (ms1 and ∆(σy − ua)).

It can be seen in Figure 6.11 that the vertical net stress (σy−ua) development decreases with

increasing water contents (w). This is due to the increase in pore air pressure (ua) generation

with increasing water content (w). On the other hand, the decrease in vertical net stress (σy−ua)

increases the coefficient of compressibility (ms1) as can be seen from Equation 6.3 and Figure

6.10. In addition, the initial matric suction (s0) decreases with increasing water content (w),

which also gives rise to higher coefficient of compressibility (ms1) (see Equation 6.3). As a result,

coefficient of compressibility (ms1) increases with increasing water content (w).

The optimum combination of the coefficient of compressibility (ms1) and vertical net stress


0 5 10 15 20 251.6

1.8

2

2.2

2.4


Dry

den

sity

, γd (

Mg/

m3 )

σy = 700 kPa

σy = 2000 kPa

Saturation curve

Figure 6.12: Modelling of the compaction curves using variable compressibility coefficient forsemi-drained loading

(σy − ua) happens in lower water contents for the soil samples compacted with higher energy

than the soil samples compacted with lower energy. Figure 6.11 shows that the change in vertical

net stress (σy − ua) is higher than the change in the coefficient of compressibility (ms1) for two

different energy levels. Therefore, the vertical net stress (σy − ua) has higher impact on the

volumetric strain (∆V/V ) than the impact of the coefficient of compressibility (ms1) for the soil

samples compacted with higher energy levels. This results in the shift of the OWC to the left,

where higher net stresses could be attained for increased energy levels.


The compaction curves generated during semi-drained loading and using variable compressibility

coefficient (ms1) are illustrated in Figure 6.12. The parameters used for the modelling are same

as the ones used for undrained loading type (Tables 6.4 and 6.5). Similar results to undrained

loading are obtained while modelling is done for semi-drained loading. A reasonable shape of

the compaction curve is attained on both wet and dry side of the compaction curve.

Figure 6.13 presents the variations of the coefficient of compressibility (ms1) with vertical

net stress (σy − ua) and water content (w) during semi-drained compression. The coefficient

of compressibility due to net stress (ms1) decreases with decreasing water content (w) or initial

degree of saturation (Sr0) and the coefficient of compressibility (ms1) also decreases with increas-

109

100

101

102

103

104

0

1

2

3

4

5

6

7

8x 10

−4


a (kPa)

m1s (

kPa−

1 )

w = 2%w = 5%w = 10%w = 15%w = 20%

Figure 6.13: Variation of the coefficient of compressibility (ms1) due to net stress during semi-

drained loading

ing vertical net stress (σy − ua), which is similar to the undrained loading condition. The main

difference with undrained loading is that during semi drained loading higher vertical net stress

(σy − ua) values could be attained for high water contents due to the low pore air pressure (ua)

generations.

The predicted values of the coefficient of compressibility (ms1) and the vertical net stress

(σy − ua) for different values of water content (w) during semi-drained loading are shown in

Figure 6.14. The predictions of the coefficient of compressibility (ms1) and the vertical net stress

(σy−ua) for both σy = 700 kPa and σy = 2000 kPa applied vertical stresses are presented on this

figure. The curves with dotted lines represent the vertical net stress (σy − ua), while the curves

plot with continues lines represent the predicted values of the coefficient of compressibility (ms1)

for varying water content (w) and energy levels.

Similar to undrained loading, vertical net stress (σy − ua) decreases with increasing water

contents (w) and the coefficient of compressibility (ms1) increases with increasing water contents

(w). The decrease in vertical net stress (σy − ua), however, is less with increasing water content

(w) compared to undrained loading because every loading increment was considered to start

with atmospheric pore air pressure which resulted in lower pore air pressure (ua) generation.


5 10 15 200

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8x 10

−4


m1s (

kPa−

1 )

5 10 15 20400

600

800

1000

1200

1400

1600

1800

2000

2200

Ver

tical

net

str

ess,

σy −

ua (

kPa)

σy − u

a (σ

y = 700 kPa)

σy − u

a (σ

y = 2000 kPa)

m1s (σ

y = 700 kPa)

m1s (σ

y = 2000 kPa)


content during semi-drained loading

Drained loading

The compaction curves generated for drained loading are presented in this section. During

drained loading it was assumed that pore air (ua) pressure stays constant and equal to atmo-

spheric pressure (101.3kPa). Therefore, the pore air pressure (ua) predictions were not nec-

essary. After the predictions of the coefficients of compressibility (ms1) for the different water

contents, which is only a function of initial suction (s0 = ua0−uw0), the volume change equation

(Equation 2.2) was used for the volume change and subsequently dry density calculations. The

compaction curves modelled for this type of loading are shown in Figure 6.15. The shape of the

modelled compaction curves are similar to the ones modelled for undrained and semi-drained

loading. However, it can be seen that, as was the case for the constant compressibility coefficients

(ms1,m

s2) modelling, due to the elimination of pore air pressure (ua) generation the compaction

curves join the saturation line on the wet side of the curve.

Figure 6.16 shows the variations of the coefficient of compressibility (ms1) with vertical net

stress (σy−ua) and water content (w) during drained loading. The coefficient of compressibility

due to net stress (ms1) decreases with decreasing water content (w) and the coefficient of com-

pressibility (ms1) also decreases with increasing vertical net stress (σy − ua). For water contents

of 15% and 20%, the degree of saturation (Sr) reached 100% and therefore, the compressibility

111

0 5 10 15 20 251.6

1.8

2

2.2

2.4


Dry

den

sity

, γd (

Mg/

m3 )

σy = 700 kPa

σy = 2000 kPa

Saturation curve

Figure 6.15: Modelling of the compaction curves using variable compressibility coefficient fordrained loading

coefficient (ms1) dropped to the value of the water compressibility(Cw).

Figure 6.17 shows the predicted values of the coefficient of compressibility (ms1) for different

values of water content (w) during drained loading together with vertical net stress (σy − ua)

development. The predictions of the coefficient of compressibility (ms1) and vertical net stress

(σy − ua) for both σy = 700 kPa and σy = 2000 kPa applied vertical stress are presented on the

figure. The curves shown by dotted lines represent the vertical net stress (σy −ua) development

with varying water content (w) and energy level. The curves shown by continues lines represent

the predicted values of the coefficient of compressibility (ms1) for varying water content (w) and

energy levels.

During drained loading, the vertical net stress (σy−ua) stays constant with increasing water

contents (w). This is due to the disregard of the pore air pressure (ua) generation for drained

loading. The coefficient of compressibility (ms1), on the other hand, first increases and after

starts decreasing with increasing water contents (w), which is different than undrained and semi-

drained loading types. The decrease of the coefficient of compressibility (ms1) starts when the

soil element reaches 100% degree of saturation (Sr). The increasing part of the compressibility

coefficient (ms1) resulted due to the decrease of initial suction (s0) with increasing water content.

In contrast to the undrained and to a certain extent to semi-drained loading, the vertical net

stress (σy−ua) has no effect on the compressibility coefficient (ms1) with changing water content,


100

101

102

103

104

0

1

2

3

4

5

6

7

8x 10

−4


a (kPa)

m1s (

kPa−

1 )

w = 2%w = 5%w = 10%w = 15%w = 20%

Figure 6.16: Variation of the coefficient of compressibility (ms1) due to net stress during drained

loading

2 4 6 8 10 12 14 16 18 20−2

0

2

4

6

8

10

12

14

16x 10

−5

m1s (

kPa−

1 )

2 4 6 8 10 12 14 16 18 20400

600

800

1000

1200

1400

1600

1800

2000

2200

Ver

tical

net

str

ess,

σy −

ua (

kPa)


σy − ua (σy = 700 kPa)

σy − ua (σy = 2000 kPa)

m1s (σy = 700 kPa)

m1s (σy = 2000 kPa)


content during drained loading

113

0 5 10 15 20 251.6

1.8

2

2.2

2.4


Dry

den

sity

, γd (

Mg/

m3 )

UndrainedSemi−drainedDrainedSaturation curve

Figure 6.18: Comparison of the modelled compaction curves using variable compressibility co-efficients for undrained, semi-drained and drained loading (σy = 700 kPa lower curves andσy = 2000 kPa upper curves)

since it stays constant with varying water content (w). Therefore, the compaction curve owns

its shape to the shape of the coefficient of compressibility (ms1) with water content (w).

Discussion on using variable compressibility coefficients for the compaction mod-

elling

The compaction curves generated with the assumption of using variable coefficient of compress-

ibility (ms1) for undrained, semi-drained and drained loading are compared in Figure 6.18. In

this figure, compaction curves were modelled at the applied vertical stresses (σy) of 700 kPa (the

lower curve) and 2000 kPa (the upper curve).

Figure 6.18 shows that the well known inverted parabolic shape of the compaction curve was

predicted using variable compressibility coefficient (ms1) for all three types of loading conditions.

The highest dry density was produced for drained loading condition and the lowest dry density

was attained for undrained loading condition. The same results were obtained for the modelling

with constant coefficients (ms1, ms

2) of compressibility. Moreover, the dependency of the curves

to different stress levels (or energy input) was reasonably well captured, where the OWC shifts

to the left with increasing stress level.

The analysis showed that it is the compressibility coefficient due to net stress (ms1) that


controls the volume changes during the compression. As it can be seen from Equation 6.3 the

main controlling parameters for the coefficient of compressibility due to net stress (ms1) are the

suction (s = ua − uw) and the slope of the NCL for saturated soils (λvp). However, during the

generation of the compaction curve for a specific type of soil, the differences in the coefficient

of compressibility (ms1) between two different water contents (w) were only resulted due to the

difference in suction between these two water contents. Therefore, it can be argued that during

the generation of the compaction curve for a certain type of soil the suction (s = ua−uw) is the

governing parameter.

The coefficient of compressibility (ms1) increases with increasing initial degree of saturation

(Sr0) but decreases with increasing degree of saturation (Sr) during compression process in all

types of loading conditions. In addition, most of the compaction takes place in the early part of

the process where the soil compressibility decreases rapidly.


This chapter presented theoretical concepts for modelling the compaction behaviour for soils,

during one dimensional undrained, semi-drained and drained loading, using unsaturated soil

mechanics principles and constitutive models. The main parameters required to be predicted for

the modelling of the compaction curve are found to be the the pore pressure development and

the compressibility coefficient due to net stress (ms1). The volume changes were estimated by

the volume change constitutive relationship proposed by Fredlund and Morgenstern (1976) for

unsaturated soils. Two approaches, Hilf (1948) and Hasan & Fredlund (1980) for pore pressure

development were examined. The second approach, however, has been subsequently disregarded

in favour of the first one which presents some advantages. The most important advantage is

that it requires less parameters for the predictions of pore pressure with applied vertical stress

(σy). Moreover, it was found that the matric suction component of the volume change equation

(Equation 2.2), which was taken into account in the second approach, does not have a significant

influence on the shape of the compaction curve but the influence of suction on the compressibility

coefficient due to net stress (ms1) is a governing parameter.

It was found that by using constant compressibility coefficients (ms1,m

s2) the shape of the

compaction curve can be only produced on the wet side of the curve but not on the dry side.

On the other hand, the well-known shape of the compaction curve was modelled both on the

115

dry and wet side of the compaction curve using the variable compressibility coefficient (ms1). In

addition, the dependency of the compaction curve to the applied vertical stress (σy) or energy

level is well captured, where the OWC shifts left with the higher applied vertical stress (σy).

It was shown that the dry density is a function of the compressibility coefficient (ms1) and the

change in vertical net stress (∆(σy − ua)). During undrained and semi drained loading, while

the coefficient of compressibility (ms1) increases, the vertical net stress (σy − ua) decreases with

increasing water content (w). This is due to the increase in pore air pressure (ua) generation with

increasing water content (w). During drained loading, while the coefficient of compressibility

(ms1) increases, the vertical net stress (σy − ua) stays constant with increasing water content

(w). Therefore, the maximum dry density could be attained at the optimum combination of the

compressibility coefficient (ms1) and the change in vertical net stress ∆(σy − ua)).

The optimum combination of the coefficient of compressibility (ms1) and vertical net stress

(σy − ua) happens in lower water contents for the soil samples compacted with higher energy

than the soil samples compacted with lower energy. This results in the shift of the OWC to the

left.

It was also shown that the variation in the drainage conditions during compression may

influence the results. The highest dry densities were achieved for drained loading where there

was no pore air pressure (ua) generation and the lowest dry densities were attained for undrained

loading. The influence of the loading types on the modelling of the compaction curve will be

further examined through targeted experiments, where model’s performance is analysed (see

Chapter 7).

In conclusion, this chapter highlights the fact that the inverted parabolic shape of the com-

paction curve can be theoretically predicted using unsaturated soil mechanics principles. The

main insight gained was that the changes in the matric suction (s = ua−uw) are not significantly

important for the evolution of the compaction states, but that the influence of the matric suction

(s = ua − uw) on the material compressibility with respect to net stress (ms1) is the governing

factor determining the compaction density. Therefore, it is argued that the inverted parabolic

shape of the compaction curve is a direct function of the variation of the material compressibility

(ms1) with vertical net stress (σy − ua).

Chapter 7

Performance of the model on

predicting the static compaction

curves

7.1 Introduction

In Chapter 6, it was found that the variable compressibility coefficients must be adopted for

producing the well known shape of the compaction curve and that the variation of the com-

pressibility coefficient due to net stress (ms1) is the governing parameter on the shape of the

compaction curve. The calculation of the compressibility coefficient due to net stress (ms1)

requires the use of soil constitutive models. In literature, there are different approaches for con-

stitutive model development and the topic is still controversial. As it was explained in Chapter

6, two of those approaches were used in the compaction process modelling. This includes the

separate stress variables and the combined stress variables approach. The basis of choosing these

two approaches were discussed in the previous chapter.

In this chapter, the models developed with the two approaches are evaluated on their ability

to predict the static compaction curve. This will not only reveal the quantitative predictions by

the models but more importantly will enlighten the controversial topic in the constitutive model

development from a different perspective.

The compaction curve data of four different soils are used for the evaluation. These include

117

118 CHAPTER 7. PERFORMANCE OF THE MODEL

the data of sand-bentonite mixtures (S2B and S5B) obtained in the experimental part of this

study (see Chapter 5); and, Boom clay and Speswhite kaolin data from the literature.

Firstly, the experimental data used for the analysis is presented. Subsequently, the model

performance developed by adopting separate stress variables approach is examined. This is

followed by the evaluation of the model developed using the combined stress variables approach.

Finally, the effectiveness of the models are compared and their limitations are discussed.

7.2 Experimental data

The experimental data obtained from the current study (S2B and S5B) and data from literature

(for Boom clay and Speswhite kaolin) were used to evaluate the performance of the compaction

models using two different constitutive modelling approaches. The data from literature were

used in order to evaluate the models for a wider range of soil types, thus drawing more gener-

alised conclusions. The experimental data were used first to find the model parameters that are

necessary for implementations and later to compare the model predictions with experimental

results. The model parameters are given on the basis of both semi logarithmic relationship and

when both axes are plot in logarithmic scale as will be noted later in this section because of the

differences taken on the derivation of the constitutive models’ equations with different constitu-

tive models. The physical properties of the materials that were used in the implementations are

also summarised in this section.

7.2.1 Sand bentonite mixtures

Experimental results for sand bentonite mixtures were presented in Chapter 5. Experiments

were conducted on two different types of granular soils (S2B and S5B). Samples with different

water contents were statically compacted and their matric suctions were measured during the

compaction process using axis translation technique. Normal compression lines (NCLs) for the

saturated and unsaturated samples are given in Figures 5.8 for S2B and in Figure 5.9 for S5B.

For these soil types, the NCLs of the unsaturated samples are plotted for constant water content

tests and not for constant suction tests. However, they are considered to be approximately

equivalent to the constant suction NCLs due to the low suction change during the compaction

of these samples (see Figures 5.5 and 5.6, and Tables 5.3 and 5.4).

The specific gravity (Gs) of S2B is 2.65. The slope of the NCL for saturated S2B is 0.0131 and

119

the specific volume (ν) under 1 kPa applied stress was found to be 1.7164 for semi logarithmic

relationship; on the other hand, the slope of the NCL and the specific volume (ν) under 1 kPa

applied stress when both axes are plot in logarithmic scale were found to be 0.0079 and 1.7176,

respectively.

The specific gravity (Gs) of S5B is 2.65. The slope of the NCL of S5B is 0.0207 and its cor-

responding specific volume (ν) under 1 kPa applied vertical stress is 1.6651 for semi logarithmic

relationship. Moreover, the slope of the NCL of S5B is 0.0132 and the specific volume (ν) under

1 kPa applied vertical stress is 1.6678 when both axes are plot in logarithmic scale.

7.2.2 Boom clay

Static compaction curve data for Boom clay were obtained from Romero (1999), where he studied

the thermo-hydro-mechanical behaviour of unsaturated Boom clay. In this study, static com-

paction tests were conducted for five different water contents ranging from 3% to 22.3%. The

samples were compacted to the desired density with their initially determined water content

and later they were removed from the compaction mould for suction measurements. The dry

samples that had high suction values (higher than 1500 kPa) were placed in a psychrometer and

their total suctions were measured using vapour equilibration technique. On the other hand,

the matric suction of the wetter samples were measured using axis translation technique. Post

compaction suction was measured by both methods.

Romero (1999) conducted consolidation test for saturated soil up to the maximum vertical

stress of 1 MPa. However, the maximum vertical stress applied during the static compaction

tests for unsaturated samples was 10 MPa. Thus, other studies were also examined to find out

the behaviour of saturated Boom clay under a wider range of applied vertical stresses as shown

in Figure 7.1. Bouazza et al. (1996) also investigated the consolidation behaviour of saturated

Boom clay up to 1 MPa vertical stress. Deng et al. (2010), however, conducted oedometer test

under wider range of stresses, where the maximum applied vertical stress was 32 MPa. Thus,

the slope of this curve is adopted for implementations in this study.

The specific gravity (Gs) of Boom clay is 2.70 (Romero, 1999). The slope of the NCL is

0.1446 and the specific volume (ν) under 1 kPa applied stress was found to be 2.7703 for semi

logarithmic relationship; on the other hand, the slope of the NCL and the specific volume (ν)

under 1 kPa applied stress when both axes are plot in logarithmic scale were found to be 0.0993

and 3.5744, respectively (Deng et al., 2010). The elastic stiffness parameter for the changes in


101

102

103

104

105

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

2.1

Vertical effective stress, σv − u

w (kPa)

Spe

cific

vol

ume,

ν

Romero (1999)Bouazza et al. (1996)Deng et al. (2010)

ν = −0.1446ln(σv − ua) + 2.7703

Figure 7.1: Normal compression line of Boom clay

suction (κs) is 0.00732 (Vaunat and Gens, 2005).

Slopes of the NCLs for unsaturated samples were determined from the study of Romero

(1999), where the constant suction contours were plotted on the static compaction curves data.

The results are shown in Figure 7.2. It is interesting to note that the slope of the NCL for

saturated sample is lower than the slopes of the NCL for unsaturated clay samples. In addition,

unsaturated samples have higher specific volumes (ν) than the saturated samples under low

stresses. This is most probably due to the aggregation of soil into cloddy structure within the

drier samples.

7.2.3 Speswhite kaolin

Speswhite kaolin data were obtained from Tarantino and De Col (2008). They conducted static

compaction tests for twelve different water contents ranging between 8.5% and 31%. The matric

suction of the samples higher than 18% water content were measured by tensiometer. Suction

measurements of the drier samples were conducted by psychrometer; thus, the total suction of

these samples were measured. Continuous matric suction measurements during compression were

conducted for the relatively wet samples (wc = 22− 31% ) in which a high capacity tensiometer

was used for the matric suction measurements. On the other hand, post compaction suctions

were measured for the samples that had lower water contents (or higher suctions).

121

102

103

104

105

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

2.1

Vertical net stress, σv − u

a (kPa)

Spe

cific

vol

ume,

νs = 0s = 450s = 3000s = 6000s = 8000s = 10000s = 32000s = 102000

Figure 7.2: Normal compression lines of Boom clay under constant suctions

The specific gravity (Gs) of Speswhite kaolin is 2.61 (Chung, 2006). The slope of the NCL

is 0.1537 and the specific volume (ν) under 1 kPa applied stress was found to be 2.851 for semi

logarithmic relationship (see Figure 7.3); on the other hand, the slope of the NCL and the specific

volume (ν) under 1 kPa applied stress when both axes are plot in logarithmic scale were found

to be 0.0748 and 3.0156, respectively. The elastic stiffness parameter for changes in suction (κs)

is 0.00013 (Tarantino and De Col, 2008).

The NCLs for unsaturated samples under constant suction are given in Figure 7.4. These data

were derived from the constant suction contours presented on the compaction curve in Tarantino

and De Col (2008). Similar to the Boom clay data, unsaturated samples have higher slopes than

the saturated sample. In addition, the slope tends to reduce with increasing stresses. The initial

specific volume of the unsaturated samples (N(s)) are higher than the saturated sample (N(0)).

7.3 Separate stress state variables approach

In this section, the models developed with two stress state variables approach are examined on

their ability to predict the static compaction curve. The performance of the Barcelona Basic

Model (BBM) developed by Alonso et al. (1990) is evaluated in detail. The BBM is the first and

most widely used elasto-plastic model for unsaturated soils and other models based on two stress

state variables approach (Wheeler and Sivakumar, 1995; Vaunat et al., 2000; Chiu and Ng, 2003;


101

102

103

1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

Vertical effective stress, σv − u

w (kPa)

Spe

cific

vol

ume,

νν = −0.1537ln(σv − uw) + 2.851

Figure 7.3: Normal compression line of Speswhite kaolin

101

102

103

104

1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

Vertical net stress, σv − u

a (kPa)

Spe

cific

vol

ume,

ν

s = 0s = 400s = 600s = 800s = 1000s = 1200s = 2000s = 3000s = 5000

Figure 7.4: Normal compression lines of Speswhite kaolin for constant suctions

123

Thu et al., 2007) are mainly derived in a similar manner or further improved by adding other

important behaviour of unsaturated soils which was not covered in the BBM (e.g., incorporation

of SWRC). Thus, the BBM is chosen for thorough examination in this study. The application of

the BBM on the development of the compaction process is presented in Chapter 6. Here, only

the results of the implementations are shown and discussed.

Firstly, the BBM is used for predicting the compaction behaviour of four different soils;

orderly, S2B, S5B, Boom clay and Speswhite kaolin. The performance of using the BBM in

compaction model development is assessed for each soil type. Model parameters that are neces-

sary for the implementations were determined using the experimental data and/or when avail-

able the model parameters found in literature. Subsequently, the static compaction curves were

predicted using the model parameters and the modelling results were compared with the experi-

mental results. Although the experiments were conducted using semi-drained loading conditions,

the implementations of undrained loading conditions are also presented for comparison. During

undrained loading both air and water phases were considered to be undrained. Whereas, in

semi-drained loading, the air phase was assumed to be undrained during each loading step but

the buildup air pressure was released before the next loading increment; thus, the air pressure

was set to atmospheric pressure in the beginning of every loading increment. Like in undrained

loading, the water phase was also assumed to be undrained in semi-drained loading simulations

(see Section 6.2.2 for details in the loading conditions). Suction was considered to stay constant

during loading for constant water content tests in both type of simulations. Implications of

assuming constant suction throughout loading are discussed later in this section. To incorporate

other constitutive models, that are developed with separate stress variables approach, in com-

paction model development are also evaluated briefly. Finally, the advantages and shortcomings

of using the current constitutive models in compaction model development are discussed.


The performance of the compaction model which is developed using the BBM is evaluated on

two granular soils; S2B and S5B. Firstly, the results for S2B is presented and this is followed

with the implementations for S5B.

The experimental results on the variation of the slopes of the NCLs (λ(s)) with matric suction

are shown in Figure 7.5 for the S2B. These results were calculated using the experimental data

presented in Figure 5.8. Model estimations for the slope of the NCLs calculated using the


0 2 4 6 80.01

0.015

0.02

0.025

0.03

0.035

0.04


λ(s)

experimentmodel (Eq. 2.13)modified model

Figure 7.5: λ(s) of S2B for varying suctions (BBM)

equation proposed by the BBM (see Equation 2.13) are also presented on the graph and the

parameters used for the predictions are given in Table 7.1. Experimental observations revealed

that the slope of the NCL (λ(s)) first increases and later starts to decrease slightly as matric

suction increased. However, the matric suction range covered in the experiments were very low

due to the difficulties in the measurements of high suctions in granular materials (see Section

5.3). For this reason, the evolution of the slope of the NCLs at higher suctions is not very

certain. Nevertheless, the model estimates are far beyond the experimental data mainly due to

the assumption adopted in the BBM, which states that the slopes of the NCLs decreases with

increasing matric suctions. It can be seen from the experimental results presented in Figure 7.5

that the slopes of the NCLs have their lowest value at saturated state. Thus, the model will not

be able to predict the correct deformations for the S2B samples. The model parameters were

modified in order to fit most of the experimental data and modified parameters are presented in

Table 7.2. The estimates with the modified parameters are also shown in Figure 7.5 and they fit

most of the experimental data better than the original model predictions except at zero suction.

It should be noted that, the slope of the NCL (λ(0)) for the saturated sample was modified but

the soil parameters κs, pc, r and β were kept constant. The consequence of such change is only

a shift of the curve, as shown in Figure 7.5, which is the relationships between the slope of the

NCLs (λ(s)) and the matric suction.

The experimental data for the initial specific volumes (N(s)) under the reference stress (pc)

125

Table 7.1: Model parameters for S2B (BBM)

N(0) λ(0) κs pc r β(kPa) (kPa−1)

1.7164 0.0131 0.00006 10 0.769 0.18985

Table 7.2: Modified model parameters for S2B


1.835 0.036 0.00006 10 0.769 0.18985

are presented in Figure 7.6 for S2B. The initial specific volumes (N(s)) were calculated using the

Equation 2.15. The modelling estimates for the variation of the initial specific volume (N(s))

with matric suction are also shown on the figure. The BBM model estimated a decrease in the

initial specific volume (N(s)) with increasing matric suctions. This is due to the assumption

taken by the model, which states that ”at reference stress (pc) the suction increase leads to an

elastic shrinkage in the soils”. The experimental results in Figure 7.6, however, show that the

initial specific volumes (N(s)) increase with increasing matric suctions. Similar to the slope

of the NCLs (λ(s)), the initial specific volumes (N(s)) have their lowest value at saturation.

The model predictions of N(s) poorly represent the experimental behaviour and therefore were

modified. The modification was done only by increasing the initial specific volume (N(0)) of the

saturated state and keeping the other model parameters constant (κs, pc, r and β). There is a

better agreement between the model predictions with modified parameters (see Table 7.2) and

the experimental results except for the data at saturation.

Using the modified parameters, the model predictions for the variation of dry density with

applied vertical stress are shown in Figure 7.7. Figure 7.7(a) presents the comparison between

the undrained and semi-drained simulations; whereas, Figure 7.7(b) compares the semi-drained

model predictions with the experimental results (experiments were also semi-drained). The

difference between the undrained and semi-drained simulations is not very notable because the

degrees of saturation reached during the compaction are low (at about between 28% and 43%).

Since the pore air volume is high at low degrees of saturation, the development of pore air

pressure is low. This subject was explained in detail in Section 6.2.2.

Figure 7.7(b) demonstrates that the model predictions for the dry densities at the lower

water contents (w = 6.9% and w = 8.4%) fit better the experimental results than the model

predictions at relatively wetter samples (w = 8.6% and w = 10.7%). At 6.9% water content, the

model estimates for both the slope of the NCL (λ(s)) and the initial specific volume (N(s)) are


0 2 4 6 81.7

1.72

1.74

1.76

1.78

1.8

1.82

1.84


N(s

)


Figure 7.6: N(s) for S2B for varying matric suctions (BBM)

in good agreement with the experimental data, which in return resulted in a reasonable match

between the experimental and the predicted values for the dry density. In addition, at 8.4%

water content (5.2kPa matric suction), the model estimated a higher slope of the NCL (λ(s))

and a higher initial specific volume (N(s)) (initially less dense sample) than the experimental

data. These two values (λ(s), N(s)) compensated each other and resulted in a good agreement

between the predicted and experimental dry density. At 8.6% (5.7kPa matric suction) and 10.7%

water contents, the model estimated less compressible (lower λ(s)) and initially looser (higher

N(s)) sample compared to the experimental data, which led to a lower predicted dry density.

Figure 7.8 presents the model predictions of the static compaction curves for S2B. The

comparison between the undrained and semi-drained implementations are shown in Figure 7.8(a).

Figure 7.8(b) illustrates the comparison between the modelled and experimental compaction

curves. There is no much difference between the undrained and semi-drained predictions due to

the low degrees of saturation attained during the compaction process (see Figure 5.12).

At 6.9% and 8.4% water contents, the model predictions are in good agreement with the

experimental results. However, the model underestimates the experimental results at higher

water content as shown in Figure 7.8(b). As discussed earlier, this is due to crude estimates of

the the slope of the NCLs (λ(s)) and the initial specific volumes (N(s)) by the model.

The experimental results for the variation of the slopes of the NCLs (λ(s)) with matric suc-

tion are shown in Figure 7.9 for S5B. The results were obtained from the experimental data

127

[a]

0 500 1000 1500 2000 25001.44

1.46

1.48

1.5

1.52

1.54

1.56

1.58

1.6

1.62

Applied vertical stress (kPa)

Dry

den

sity

(M

g/m

3 )

wc = 6.9% Uwc = 8.4% Uwc = 8.6% Uwc = 10.7% Uwc = 6.9% Swc = 8.4% Swc = 8.6% Swc = 10.7% S

[b]

0 500 1000 1500 2000 25001.44

1.46

1.48

1.5

1.52

1.54

1.56

1.58

1.6

1.62

1.64


Dry

den

sity

(M

g/m

3 )

wc = 6.9% Mwc = 8.4% Mwc = 8.6% Mwc = 10.7% Mwc = 6.9% Ewc = 8.4% Ewc = 8.6% Ewc = 10.7% E

Figure 7.7: BBM predictions of the variation of dry density with applied vertical stress for S2B[a] Comparison of the undrained (U) and semi-drained (S) predictions [b] Comparison of theexperimental data (E) and model (M) predictions (semi-drained)


[a]

6 7 8 9 10 111.55

1.56

1.57

1.58

1.59

1.6

1.61

Water content (%)

Dry

den

sity

(M

g/m

3 )

560 kPa U2250 kPa U560 kPa S2250 kPa S

[b]

6.5 7 7.5 8 8.5 9 9.5 10 10.5 111.55

1.56

1.57

1.58

1.59

1.6

1.61

1.62

1.63

1.64

1.65

Water content (%)

Dry

den

sity

(M

g/m

3 )

560 kPa M2250 kPa M560 kPa E2250 kPa E

Figure 7.8: Compaction curves for S2B predicted by BBM [a] Comparison of undrained (U)and semi-drained (S) predictions [b] Comparison of the experimental data (E) and model (M)predictions (semi-drained)

129

0 10 20 30 40 500.01

0.015

0.02

0.025

0.030.03


λ(s)


Figure 7.9: λ(s) of S5B for varying matric suctions (BBM)

Table 7.3: Model parameters for S5B (BBM)


1.6174 0.021 0.00008 10 0.765 0.451

presented in Figure 5.9. The slope of the NCLs (λ(s)) initially increases with increasing matric

suctions and after reaching a peak at about 35kPa matric suction, it starts to decrease. Model

estimations for the NCLs are also presented in Figure 7.9. These values were calculated using

the equation proposed in the BBM (see Equation 2.13) and the model parameters presented in

Table 7.3. Different than the experimental observation, the BBM predicts decreasing slope of

the NCLs (λ(s)) with increasing matric suctions. The model predicts less compressible soil than

the experimental observations and thus, this will lead to poor predictions of the soil deformation.

Therefore, the model parameters were modified and the predictions with the modified param-

eters are also presented in Figure 7.9. The modified model parameters are given in Table 7.4.

Modification was done by increasing the slope of the NCL (λ(0)) for saturated soil and keeping

the other parameters constant (κs, pc, r and β). This modification resulted only in a shift of

the relationship between the slope of the NCLs (λ(s)) and the matric suction on the ordinate.

The experimental data for the initial specific volumes (N(s)) under the reference stress (pc)

are presented in Figure 7.10 for the S5B. The initial specific volumes (N(s)) increased with

increasing matric suctions. The model estimates for the initial specific volumes (N(s)) are


Table 7.4: Modified model parameters for S5B


1.7 0.028 0.00008 10 0.765 0.451

0 10 20 30 40 501.6

1.65

1.7

1.75


N(s

)


Figure 7.10: N(s) for S5B for varying matric suctions (BBM)

also presented in Figure 7.10 and are far from the experimental results. Model estimates were

obtained from the Equation 2.15. The BBM predicts a decrease in the initial specific volumes

(N(s)) with increasing matric suctions due to the assumption taken by the model. Similar to the

slope of the NCLs (λ(s)), the initial specific volumes (N(s)) have their lowest value at saturated

state. The model parameters were modified in a similar manner to S2B by increasing the initial

specific volume for saturated sample (N(0)) and keeping the other parameters constant (κs, pc,

r and β). The predictions were made in a way that they would fit most of the experimental

data. However, due to the nature of the equation proposed in the model (Equation 2.15), it

was very difficult to fit the model predictions to the entire range of suctions. The modification

was done to fit the values between 10kPa and 20kPa. This selection was made considering the

results of the slope of the NCLs (λ(s)) (Figure 7.9). The model predictions for the slope of the

NCLs (λ(s)) were best capturing the experimental data about that suction range.

Using the modified model parameters, the model predictions for the variation of dry density

with applied vertical stress are shown in Figure 7.11. Figure 7.11(a) presents the comparison

between the undrained and semi-drained simulations; whereas, Figure 7.11(b) compares the semi-

131

drained model predictions with the experimental results which were also conducted under semi-

drained loading conditions. The difference between the undrained and semi-drained simulations

is not very notable due to the low degrees of saturation attained during the compaction process

(between 28% and 59%). It was explained in Section 6.2.2 that the pore air pressure buildup is

crucial at high degrees of saturation.

Figure 7.11(b) shows that the model predictions for the dry densities, at 10.3% and 10.9%

water contents fit better the experimental results than the model predictions at 6.5%, 7.5% and

12.6% water contents. This is purely related to the agreement between the model estimates

and the experimental values on the slope of the NCLs (λ(s)) and the initial specific volumes

(N(s)). At 10.3% and 10.9% water contents, the model estimates are in good agreement with

the experimental data for both the slope of the NCLs (λ(s)) and the initial specific volumes

(N(s)), which led to a reasonable match between the experimental and the predicted values

for dry densities. At 6.5% and 7.5% water content, the model estimated lower values for both

the slope of the NCLs (λ(s)) and initial specific volumes (N(s)) (initially denser soil) than

the experimental data. This resulted in higher dry density predictions. It can be noticed in

Figure 7.11(b) that the difference between the predicted and experimental values increases with

increasing applied vertical stresses. This is the consequence of the model being more sensitive to

the slope of the NCLs (λ(s)) at increased stresses (see Equation 2.14). At 12.6% water content,

the model estimated less compressible (lower λ(s)) and initially looser (higher N(s)) sample

compared to the experimental data, which led to a lower predicted dry density.

Figure 7.12 presents the model predictions of the static compaction curves for S5B. The com-

parison between the undrained and semi-drained implementations are shown in Figure 7.12(a).

In addition, Figure 7.12(b) illustrates the comparison between the modelled and experimen-

tal compaction curves. Due to the low degrees of saturation attained during the compaction

process (see Figure 5.13), there is no much difference between the undrained and semi-drained

predictions.

At 10.3% and 10.9% water contents, the model predictions are in good agreement with the

experimental results. However, at 6.5% and 7.5% water contents, the model over estimates the

experimental results, and at 12.6% water content, the model under estimates the experimental

dry density. As discussed earlier, this is due to crude estimates of the the slope of the NCLs

(λ(s)) and the initial specific volumes (N(s)) by the model.


[a]

0 500 1000 1500 2000 2500 3000 35001.56

1.58

1.6

1.62

1.64

1.66

1.68

1.7

1.72


Dry

den

sity

(M

g/m

3 )

wc = 6.5% Uwc = 7.5% Uwc = 10.3% Uwc = 10.9% Uwc = 12.6% Uwc = 6.5% Swc = 7.5% Swc = 10.3% Swc = 10.9% Swc = 12.6% S

[b]

0 500 1000 1500 2000 2500 3000 35001.56

1.58

1.6

1.62

1.64

1.66

1.68

1.7

1.72

1.74


Dry

den

sity

(M

g/m

3 )

wc = 6.5% Mwc = 7.5% Mwc = 10.3% Mwc = 10.9% Mwc = 12.6% Mwc = 6.5% Ewc = 7.5% Ewc = 10.3% Ewc = 10.9% Ewc = 12.6% E

Figure 7.11: BBM predictions of the variation of dry density with applied vertical stress for S5B[a] Comparison of the undrained (U) and semi-drained (S) predictions [b] Comparison of theexperimental data (E) and model (M) predictions (semi-drained)

133

[a]

6 7 8 9 10 11 12 131.655

1.66

1.665

1.67

1.675

1.68

1.685

1.69

1.695

1.7

Water content (%)

Dry

den

sity

(M

g/m

3 )

560 kPa U2650 kPa U560 kPa M2650 kPa M

[b]

6 7 8 9 10 11 12 131.62

1.64

1.66

1.68

1.7

1.72

1.74

Water content (%)

Dry

den

sity

(M

g/m

3 )


Figure 7.12: Compaction curves for S5B predicted by BBM [a] Comparison of undrained (U)and semi-drained (S) predictions [b] Comparison of the experimental data (E) and model (M)predictions (semi-drained)


0 20 40 60 80 100 1200.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

Suction, s (MPa)

λ(s)


Figure 7.13: λ(s) of Boom clay for varying suctions (BBM)

7.3.2 Boom clay

The experimental results for the slopes of the NCLs (λ(s)) of Boom clay are shown in Figure 7.13.

These results were calculated using the experimental data presented in Figure 7.1. The model

estimations for the NCLs calculated using the equation proposed by BBM (see Equation 2.13)

are also presented in this figure and the parameters used for the predictions are given in Table

7.5. Experimental observations reveal that the slopes of the NCLs (λ(s)) first increases and later,

after a peak value at about 3 MPa suction, start decreasing with increasing suctions. It should be

noted that the slopes of the NCLs for unsaturated Boom clay have greater values than the slope

of the NCL for its saturated state. This observation is contrary to the assumption taken by BBM

(Alonso et al., 1990). Therefore, the modelling predictions for the slope of the NCLs (λ(s)) are

far beyond the experimental results. In order to better implement the experimental behaviour,

the model parameters were modified to fit most of the experimental data and the predictions

with the modified parameters are also presented in the same figure. The modified parameters

are given in Table 7.6 and the values are similar to the ones found in other studies (Vaunat

and Gens, 2005) for the same soil. This time the predictions fit most of the experimental data

reasonably well except for the saturated sample. Similar to the modification done for granular

soils (see Section 7.3.1) only the slope of the NCL (λ(0)) and the initial specific volume for

saturated sample (N(0)) were modified.

135

Table 7.5: Model parameters for Boom clay (BBM)


2.4373 0.1446 0.0732 10 0.564 0.0000544

Table 7.6: Modified model parameters for Boom clay


3.1 0.26 0.0732 10 0.564 0.0000544

The experimental data for the initial specific volumes (N(s)) under reference stress (pc) are

presented in Figure 7.14 for varying suctions. Model predictions using Equation 2.15 and the

initial model parameters (see Table 7.5) are also shown in the figure. The BBM model predicts

a decrease in the initial specific volume (N(s)) with increasing suction. On the other hand,

the experimental results in Figure 7.14 show that the initial specific volume (N(s)) is at its

lowest value for saturated Boom clay. Similar to the model predictions for the slopes of the

NCLs (λ(s)), the model predictions for the initial specific volumes (N(s)) poorly represent the

experimental behaviour, and therefore the model parameters were modified. There is a good

agreement between the model predictions with modified parameters (see Table 7.6) and the

experimental results except for the data at saturation.

Using the modified parameters, the model predictions on the variation of dry density with ap-

plied vertical stress is shown in Figure 7.15 for both undrained and semi-drained simulations. In

semi-drained loading simulations, the loading was ceased when the samples reached saturation.

At low water contents, both type of simulations are predicting similar results (7.15(a)). However,

at high water contents, undrained model simulations produce lower dry densities than the pre-

dictions of the semi-drained simulations. This is due to the high pore air pressure development

at high water contents during undrained loading. Although, the experiments were conducted

under semi-drained loading conditions, undrained loading simulations are also presented here for

comparison, because the well known inverted parabolic shape of the dynamic compaction curve

can be better produced under undrained loading conditions and it better represents practice.

Examination of Figure 7.15(b) shows that the model underestimates the experimental results

at low water contents (3%) and overestimates the results at high water contents (9.8%, 14.7%,

18.7%) except for the sample with 22.3% water content. This is similar to the estimations of

the slopes of the NCLs (λ(s)) (see Figure 7.13) by the model. Therefore, it can be stated that

the model predictions are mainly influenced by the slopes of the NCLs (λ(s)) for Boom clay.


0 20 40 60 80 100 1202.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3

3.1

3.2

Suction, s (MPa)

N(s

)


Figure 7.14: N(s) for Boom clay for varying suctions (BBM)

At 22.3% water content, the model prediction for the slopes of the NCL (λ(s)) is higher than

the experimental value and therefore, the predicted dry densities are expected to be higher than

the experimental values. However, the modelled and experimental results are in good agreement

(Figure 7.15(b)). This is considered to arise due to the suction reduction at high water contents

during loading in the experiments, which was not considered in the current model development

for simplicity.

The modelling predictions for the static compaction curve for Boom clay are presented in

Figure 7.16 for undrained and semi-drained simulations. As before, there is not much difference

between undrained and semi-drained simulations at low water contents. However, considerable

difference is observed after 9.8% water content (Figure 7.16(a)). In addition, at high water

contents, the predicted dry densities start dropping during undrained simulations resulting in a

well known inverted parabolic shape of the compaction curve. Semi-drained simulations do not

produce similar inverted parabolic shape because it is accepted that there is no trapped air at

high water contents, which would normally result in high pore air pressure buildup within the

sample, and the compaction is ceased after reaching the saturation.

Figure 7.16(b) shows the comparison between the model predictions and experimental data

for the compaction curves. The model predictions poorly represent the experimental results at

3% water content. Moreover, at higher water contents, the model overestimates the experimental

results, as it was stated previously, except at 22.3% water content. This is due to the overesti-

137

[a]

0 2000 4000 6000 8000 100000.8

1

1.2

1.4

1.6

1.8

2


Dry

den

sity

(M

g/m

3 )

w = 3% Uw = 9.8% Uw = 14.7% Uw = 18.7 Uw = 22.3 Uw = 3% Sw = 9.8% Sw = 14.7% Sw = 18.7 Sw = 22.3 S

[b]

0 2000 4000 6000 8000 100000.8

1

1.2

1.4

1.6

1.8

2


Dry

den

sity

(M

g/m

3 )

w = 3% Mw = 9.8% Mw = 14.7% Mw = 18.7% Mw = 22.3% Mw = 3% Ew = 9.8% Ew = 14.7% Ew = 18.7% Ew = 22.3% E

Figure 7.15: BBM predictions of the variation of dry density with applied vertical stress for Boomclay [a] Comparison of the undrained (U) and semi-drained (S) predictions [b] Comparison ofthe experimental data (E) and model (M) predictions (semi-drained)


Table 7.7: Model parameters for Speswhite kaolin (BBM)


2.4971 0.1537 0.00013 10 0.74 0.0018

Table 7.8: Modified model parameters for Speswhite kaolin


4.12 0.49 0.00013 10 0.74 0.0018

mation of the slopes of the NCLs (λ(s)) by the model. The influence of the slope of the NCL

(λ(s)) on the specific volume or the dry density increases as the applied stress increases. In other

words, as stress increases the model becomes more sensitive to the slope of the NCL (λ(s)) than

to the initial specific volume (N(s)). This can be clearly seen from Equation 2.14. Therefore,

the differences between experimental and predicted values increase as the applied vertical stress

increases (Figure 7.15(b) and 7.16(b)).


Figure 7.17 presents the experimental and modelling results for the variation of the slopes of the

NCLs (λ(s)) with suction for Speswhite kaoline. Experimental points were calculated from the

data presented in Figure 7.4. Modelling predictions for the slope of the NCLs were calculated

using the equation proposed by the BBM (see Equation 2.13). Similar to sand-bentonite mixtures

and Boom clay, again the experimental observations are far beyond the model estimations;

therefore, the model parameters were modified and the modified model predictions are also

presented in Figure 7.17. Model parameters and modified model parameters are given in Tables

7.7 and 7.8, respectively. Again, the modification is done only to the slope of the NCL (λ(0))

and the initial specific volume for saturated sample (N(0)). Both parameters were increased

which makes the soil sample more compressible than the model predictions.

The experimental data for the initial specific volume (N(s)) under reference stress (pc) are

presented in Figure 7.18 for varying suctions. The model estimates using Equation 2.15 are

shown in the figure together with the modified modelling estimations. Similar to the estimations

observed in sand-bentonite mixtures and Boom clay, BBM predicts a decrease in the initial

specific volume (N(s)) with increasing suction. On the other hand, experimental data in Figure

7.18 illustrate that the initial specific volume (N(s)) is at its lowest value for saturated sample.

139

[a]

0 5 10 15 20 25

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

Water content (%)

Dry

den

sity

(M

g/m

3 )

1 MPa U2 MPa U3 MPa U4 MPa U5 MPa U6 MPa U8 MPa U10 MPa U1 MPa S2 MPa S3 MPa S4 MPa S5 MPa S6 MPa S8 MPa S10 MPa S

[b]

0 5 10 15 20 25

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

Water content (%)

Dry

den

sity

(M

g/m

3 )

1 MPa M2 MPa M3 MPa M4 MPa M5 MPa M6 MPa M8 MPa M10 MPa M1 MPa E2 MPa E3 MPa E4 MPa E5 MPa E6 MPa E8 MPa E10 MPa E

Figure 7.16: Compaction curves for Boom clay predicted by BBM [a] Comparison of undrained(U) and semi-drained (S) predictions [b] Comparison of the experimental data (E) and model(M) predictions (semi-drained)


0 1000 2000 3000 4000 50000.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Suction, s (kPa)

λ(s)


Figure 7.17: λ(s) of Speswhite kaolin for varying suctions (BBM)

Similar to the model predictions of the slope of the NCL (λ(s)), the model predictions of the

initial specific volume (N(s)) poorly represent the experimental behaviour and therefore were

modified. There is a better agreement between the model predictions with modified parameters

(see Table 7.8) and the experimental results except for the data at zero suction.

Figure 7.19 shows the variation in void ratio with applied vertical stress for Speswhite kaolin.

Both undrained and semi-drained simulations are shown in Figure 7.19(a). Undrained simula-

tions have lower deformations than the semi-drained ones due to the higher pore air pressure

buildup within the undrained samples. Figure 7.19(b) illustrates the comparison between the

model predictions and experimental results for the samples with 24%, 25% and 28% water con-

tent. In overall, there is a good agreement between the experimental and predicted values, with

only a slight underestimation of the predicted values at 28% water content. This discrepancy is

most likely to happen due to suction reduction with loading which was not taken into account

in the model simulations.

Figure 7.20 shows the predicted static compaction curve of Speswhite kaolin for both undrained

and drained loading types. Firstly, in Figure 7.20(a) the comparison between undrained and

semi-drained simulations are given and later, in Figure 7.20(b) experimental data are compared

with the model predictions. Dry density stays almost constant until 18% water content for both

type of simulations and later slightly decreases with increasing water content in undrained sim-

ulations; whereas, it increases in semi-drained simulations. The slope of the NCL (λ(s)) and

141

0 1000 2000 3000 4000 5000

2.6

2.8

3

3.2

3.4

3.6

3.8

4

4.2

Suction, s (kPa)

N(s

) experimentmodel (Eq. 2.15)modified model

Figure 7.18: N(s) for Speswhite kaolin for varying suctions (BBM)

the initial specific volume (N(s)), which are the parameters that influence the deformation, stay

constant until 18% water content (that corresponds to 2000 kPa suction), as shown in Figures

7.17 and 7.18. Therefore, the dry densities also stay almost constant for both type of simulations

(undrained and semi-drained). After 18% water content (less suction than 2000 kPa), both the

slope of the NCL (λ(s)) and the initial specific volume (N(s)) start to increase, which means

the soil is more compressible and initially in a looser state. Therefore, as it is stated that the

initial specific volume (N(s)) is more dominant at low applied stresses and the slope of the NCL

(λ(s)) at high applied stresses. It can be seen that at higher applied stresses the dry density

reduction is much less or even dry density stays almost constant due to the higher influence of

the the slope of the NCL (λ(s)) on the model. In addition, the development of pore air pressure

within the samples resulted in slight reduction of the dry density in undrained simulations.

The comparison of the experimental data and model predictions shown in Figure 7.16(b)

reveals that the model can predict the compaction curve at mid water contents reasonably

well but model underestimates the dry densities at higher water contents. Nevertheless, if

the reduction of suction with loading was included in the model, reasonable predictions could

probably be attained at higher water contents as it was shown by Tarantino and De Col (2008).

On the other hand, at low water contents (up to 18%) model overestimates the experimental

data and inclusion of suction reduction with loading would not help to attain better predictions.

Firstly, because inclusion of suction reduction would result in higher predicted dry densities


[a]

0 200 400 600 800 1000 12000.5

1

1.5

2

2.5

3


Voi

d ra

tio (

e) w = 24% Uw = 25% Uw = 28% Uw = 24% Sw = 25% Sw = 28% S

[b]

0 200 400 600 800 1000 12000.5

1

1.5

2

2.5

3


Voi

d ra

tio (

e) w = 24% Mw = 25% Mw = 28% Mw = 24% Ew = 25% Ew = 28% E

Figure 7.19: BBM predictions of the variation of void ratio with applied vertical stress forSpeswhite kaolin [a] Comparison of the undrained (U) and semi-drained (S) predictions [b]Comparison of the experimental data (E) and model (M) predictions (semi-drained)

143

[a]

5 10 15 20 25 30 350.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

Water content (%)

Dry

den

sity

(M

g/m

3 )

300 kPa U600 kPa U900 kPa U1200 kPa U300 kPa S600 kPa S900 kPa S1200 MPa S

[b]

5 10 15 20 25 30 350.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

Water content (%)

Dry

den

sity

(M

g/m

3 )

300 kPa M600 kPa M900 kPa M1200 kPa M300 kPa E600 kPa E900 kPa E1200 MPa E

Figure 7.20: Compaction curves for Speswhite kaolin predicted by BBM [a] Comparison ofundrained (U) and semi-drained (S) predictions [b] Comparison of the experimental data (E)and model (M) predictions (semi-drained)


than the current ones, which would increase the error. Secondly, at low water contents suction

reduction with loading is not an expected phenomena and generally evident from experimental

results (Li, 1995; Tarantino and De Col, 2008).

7.3.4 Discussion on the BBM

The BBM was evaluated on its ability to predict the static compaction curve of four different

type of soils. The following conclusions about the model are gained:

• The model assumes that the slope of the NCLs (λ(s)) decreases with increasing suction.

However, experimental observations revealed that the slope of the NCLs (λ(s)) initially

increases and after reaching a peak starts to decrease. In addition, the slope of the NCLs

(λ(s)) for the unsaturated specimens is higher than the saturated sample, which is contra-

dictory to the assumption made in the BBM.

• The model predicted decreasing initial specific volumes (N(s)) with increasing suctions.

The initial specific volumes of the unsaturated samples were predicted to be lower than

the saturated samples. However, similar to the slope of the NCLs (λ(s)), the experimental

measurements revealed that the initial specific volumes (N(s)) of the unsaturated samples

are higher than the saturated one.

• To overcome the model deficiencies stated above, the modelling parameters for the slope

of the NCL (λ(0)) and the initial specific volume (N(0)) for the saturated soil sample were

increased. This led to a more compressible soil, which is consistent with the experimen-

tal results. After introducing these modifications, the model predictions are in a better

agreement with the experimental results.

• In the compaction process modelling, the suction change inclusion with loading was not

considered for simplicity. The inclusion of the suction change with loading into the model

would result in better model predictions after the mid water contents. However, it would

not change the results in the dry part of the compaction curve because of the low suction

change in relatively dry soil samples with loading. The inclusion of suction into the BBM

could be done by incorporating a SWRC relationship as suggested by Gallipoli et al.

(2003b). In addition, for a wide range of water contents, it is hard to determine the model

parameters for the SWRC with the change in void ratio with the same accuracy level.

Gallipoli et al. (2003b) evaluated the model for Speswhite kaolin where the maximum

145

applied matric suction was only 300 kPa. This model was also used by Tarantino and

De Col (2008) for the same soil, but wider range of water contents. They determined the

model parameters for matric suctions up to 1200 kPa. However, it can be clearly noticed

that if the suction range is further increased the same model parameters cannot be used.

• After the modification, the BBM can predict the compaction curves for granular and

fine soils in a narrow range of water contents with single set of soil parameters. The

correct predictions for the whole compaction curves would require an additional set of soil

parameters to be used.

• As can be seen from the modified predictions of the slope of the NCLs (λ(s)) and the

initial specific volume (N(s)), the transition zone between the saturated and unsaturated

soils cannot be well captured by the BBM.

7.3.5 Other models developed with separate stress variables approach

Other models developed with separate stress variables approach are mainly the modified versions

of the constitutive model proposed by Alonso et al. (1990). These models and their overall effect

on the prediction of the compaction curve is briefly discussed in this section.

Wheeler and Sivakumar (1995) developed an elasto-plastic critical state framework for un-

saturated soils by modifying some of the assumptions in the BBM. They abandoned the use

of a reference stress (pc) at which the change of suction only produces elastic volume deforma-

tions (a yield curve is a straight vertical line in suction and stress plot). Atmospheric pressure

was taken as a reference pressure in their volume change equation. This might result in some

problems when calculating the volume changes at stresses lower than the atmospheric pressure.

In addition, they used the empirical values for the slope of the NCLs (λ(s)) and the initial

specific volumes (N(s)) of unsaturated soil samples rather than introducing an equation for the

variation of the slope of the NCLs with the change in suction (see Equation 2.13). However,

the use of empirical values for these parameters is not practical and very time consuming when

trying to model a soil behaviour for wide range of water contents. In fact, model’s purpose is

to reduce the amount of experiments in order to predict the behaviour of soils. Wheeler and

Sivakumar (1995) noticed in their experimental results that the change in the slope of the NCLs

(λ(s)) and the initial specific volume (N(s)) vary differently (the slope of the NCLs increases

with increasing suction) than it was proposed in the BBM; however, they did not developed a


complete mathematical model for this behaviour.

Vaunat et al. (2000) and Thu et al. (2007) slightly modified the BBM and incorporated SWRC

into the model. However, the same assumption for the slope of the NCLs (λ(s)) as proposed

in the BBM was used. Therefore, this will lead to a similar predictions for the compaction

behaviour as it is in the BBM.

Chiu and Ng (2003) incorporated SWRC into the framework proposed by Wheeler and

Sivakumar (1995). For the variation of the slope of the NCLs (λ(s)), they used a similar approach

proposed in the BBM (see Equation 2.13). Different from the BBM, they considered that the ”r”

parameter is bigger than one in order to fit their experimental data better. This modification

was also proposed by Wheeler et al. (2002) in order to capture the increase in compressibility

with an increase in suction. This is a reasonable modification and well captured the behaviour

of tested soil (Speswhite kaolin) in their studies because the soil compressibility increases with

the increase in suction. However, it should be noted that the examples they presented were in a

narrow range of suctions and do not exceed 300 kPa of suction. When wider range of suctions or

water contents are considered, it was shown that the compressibility initially increases and after

reaching a peak value starts to decrease (see Figures 7.13 and 7.17). Therefore, this is consid-

ered to be a worthwhile modification up to the suctions where the peak in the compressibility is

reached.

7.4 Combined stress variables approach

In this section, the models developed with combined stress variables approach are examined on

their ability to predict the static compaction curve. The performance of the model proposed by

Sheng et al. (2008) and named as SFG model by the developers is evaluated in detail. There

are other combined stress variables approach models proposed in literature (Bolzon et al., 1996;

Gallipoli et al., 2003a; Tarantino and De Col, 2008). However, those models use the BBM or

models with similar approach (Wheeler and Sivakumar, 1995) in their mechanical modelling

formulations and only use different work conjugates as suggested by Houlsby (1997). Therefore,

the SFG model is selected in this study for detailed evaluation. The application of the SFG

model on the development of the compaction process is presented in Chapter 6. In this section,

only the results of the model implementations are presented.

The SFG model is used for predicting the compaction behaviour of four different soils, which

147

Table 7.9: Model parameters for S2B (SFG model)

N0 λvp (σy − ua)0 ssa(kPa) (kPa)

1.6866 0.0079 10 2

are S2B, S5B, Boom clay and Speswhite kaolin. The performance of the SFG model on pre-

dicting the static compaction curves is evaluated for each soil type. Model parameters that are

necessary for implementations were determined using the experimental data. Subsequently, the

static compaction curves were predicted using the model parameters; and the modelling results

were compared with the experimental results. The experiments were conducted using semi-

drained loading condition but the implementations of undrained loading are also presented for

comparison. Suction was considered to stay constant during loading for constant water content

tests in the model implementations. Implications of assuming constant suction throughout load-

ing are discussed later in this section. Other models developed using combined stress variables

approach are also evaluated briefly in this section. Finally, the advantages and shortcomings of

the models are discussed.


The performance of the compaction model developed using the constitutive model proposed by

Sheng et al. (2008) is evaluated in this section for sand-bentonite mixtures. Initially, the results

for S2B are presented and this is followed with the results for S5B.

The model parameters used for the implementations of S2B are given in Table 7.9. These

parameters were calculated from the experimental results given in Figure 5.8. The experimental

results were derived when both axes are plot in logarithmic scale of the specific volume (ν) and

the applied net vertical stress (σy − ua) instead of a semi logarithmic relationship as it was in

the BBM. This is due to the the derivation of the modelling equations for the SFG model (see

Section 6.2.3).

The experimental values and the model estimates for the initial specific volumes (N(s)) are

given in Figure 7.21. The model predicts lower initial specific volumes (N(s)) with increasing

matric suctions. On the contrary, the experimental results revealed that the initial specific

volume (N(s)) for S2B increases with increasing matric suctions. Thus, the model assumes

initially denser samples compared to the experimental values.

Figure 7.22 shows the model predictions for the variation of the dry density with the applied


0 2 4 6 81.68

1.7

1.72

1.74

1.76

1.78

1.8

1.82

1.84


N(s

)

experimentmodel (Eqs. 2.18 and 2.19)

Figure 7.21: N(s) for S2B for varying matric suctions (SFG model)

vertical stress for S2B. Although the experiments were conducted under semi-drained conditions,

the model predictions are presented for both the undrained and semi-drained loading conditions

in Figure 7.22(a). The model predicted slightly lower dry densities under the same applied

vertical stresses for undrained loading condition. This is due to the higher buildup air and

water pressures, which made the compaction harder. The difference is very small due to the low

degrees of saturation attained during the compaction (see Figure 5.12). Figure 7.22(b) shows

the comparison between the experimental values and the model predictions. For all the samples,

the model predicted higher dry densities than the experimental results due to the lower initial

specific volume (N(s)) estimates by the model. In addition, the gradient of the curve predicted

by the model is lower than the gradient of the experimental curve. This means that even if the

model correctly predicted the initial specific volumes (N(s)), it would still fail to predict the

correct dry densities. This model deficiency may result due to two reasons: the underestimation

of the slope of the NCL (λvp) or the over emphasis of the suction in the volume change equation

(Equation 2.17). For S2B, matric suctions are very low due to the granular nature of the soil.

Thus, the lower gradients of the predicted curves are due to the underestimation of the slope of

the NCL for saturated soil sample (λvp). Moreover, the model predicts very similar dry densities

for samples with different water contents, which is different from the experimental observations.

Considering that the matric suctions in S2B samples with different water contents are close to

each other (see Figure 5.1), the model can only depict this experimental observation by adopting

149

Table 7.10: Model parameters for S5B (SFG model)


1.6179 0.0132 10 4

different slopes for the NCLs.

Figure 7.23 presents the model predictions of the compaction curves for S2B. The comparison

of the undrained and semi-drained predictions for different water contents are shown in Figure

7.23(a). The model predictions for undrained loading are slightly lower than the predictions for

semi-drained loading conditions, due to the buildup air and water pressure in undrained loading

condition. As stated earlier, the difference is very small due to the low degrees of saturation in the

tested samples. Figure 7.23(b) shows the comparison of the model predictions and experimental

results for different stress levels. The model overestimated the dry densities. As discussed earlier,

this is due to the underestimation of the initial specific volume (N(s)) by the model.

A conference paper was published before (see Appendix B) for the the comparison of the

experimental results and predictions with the SFG model for S2B. In that paper, the model

predictions better depict the experimental results for the compaction curve. However, the slope

of the NCL for saturated soil sample (λvp) was not measured at the time and was chosen to be

a value which would result in a best model prediction. After the measurement of the slope of

the NCL (λvp) which lead to a poor prediction as shown in Figure 7.23(b), it was noticed that

the experimental value is much lower than the previously adopted one. This fact also reveals

that the model underestimates the compressibility or slope of the NCL for the unsaturated soil

samples.

The model parameters used for the implementations of S5B are given in Table 7.10. These

parameters were calculated from the experimental results given in Figure 5.9. The experimental

results were derived from a double logarithmic relationship (when both axes are plot in logarith-

mic scale) instead of a semi logarithmic relationship due to the approach adopted in the SFG

model.

The experimental values and the model estimates for the initial specific volumes (N(s)) are

given in Figure 7.24. Similar to the BBM, the SFG model predicts lower initial specific volumes

(N(s)) with increasing suctions. On the contrary, the experimental results revealed that the

initial specific volume (N(s)) for S5B increases with increasing matric suctions.

Figure 7.25 presents the model predictions for the variation of the dry density with the applied


[a]

0 500 1000 1500 2000 25001.57

1.58

1.59

1.6

1.61

1.62

1.63

1.64

1.65

1.66


Dry

den

sity

(M

g/m

3 )

wc = 6.9% Uwc = 8.4% Uwc = 8.6% Uwc = 10.7% Uwc = 6.9% Swc = 8.4% Swc = 8.6% Swc = 10.7% S

[b]

0 500 1000 1500 2000 25001.5

1.55

1.6

1.65


Dry

den

sity

(M

g/m

3 )

wc = 6.9% Mwc = 8.4% Mwc = 8.6% Mwc = 10.7% Mwc = 6.9% Ewc = 8.4% Ewc = 8.6% Ewc = 10.7% E

Figure 7.22: SFG model predictions of the variation of dry density with applied vertical stressfor S2B [a] Comparison of the undrained (U) and semi-drained (S) predictions [b] Comparisonof the experimental data (E) and model (M) predictions (semi-drained)

151

[a]

6 7 8 9 10 111.615

1.62

1.625

1.63

1.635

1.64

Water content (%)

Dry

den

sity

(M

g/m

3 )


[b]

6 7 8 9 10 111.55

1.56

1.57

1.58

1.59

1.6

1.61

1.62

1.63

1.64

1.65

Water content (%)

Dry

den

sity

(M

g/m

3 )


Figure 7.23: Compaction curves for S2B predicted by SFG model [a] Comparison of undrained(U) and semi-drained (S) predictions [b] Comparison of the experimental data (E) and model(M) predictions (semi-drained)


0 10 20 30 40 501.6

1.65

1.7

1.75


N(s

)


Figure 7.24: N(s) for S5B for varying matric suctions (SFG model)

vertical stress for S5B. Figure 7.25(a) shows the model predictions for both the undrained and

semi-drained loading conditions. The model predicted slightly lower dry densities under the same

applied vertical stresses due to the higher buildup air and water pressures, for undrained loading

condition. However, the difference is very small because of the low degrees of saturation attained

at the end of the compaction (see Figure 5.13). Figure 7.25(b) shows the comparison between

the experimental values and the model predictions. For all the samples, the model predicted

higher dry densities than the experimental results due to the lower initial specific volume (N(s))

estimates by the model. Different than S2B predictions, the model predicted more disperse dry

densities for S5B samples with different contents. This resulted due to the higher variation in

suction between the samples with different water contents.

Figure 7.26 shows the model predictions of the compaction curves for S5B. The comparison

of the undrained and semi-drained predictions are shown in Figure 7.26(a). The model pre-

dicted slightly lower dry densities for undrained loading due to the higher buildup air and water

pressures. However, the difference is very small due to the low degrees of saturation within the

samples (see Figure 5.13). Figure 7.26(b) shows the comparison of the model predictions and

experimental results for different stress levels. The model overestimated the dry densities due

to the underestimation of the initial specific volume (N(s)).

153

[a]

0 500 1000 1500 2000 2500 3000 35001.64

1.66

1.68

1.7

1.72

1.74

1.76

1.78

1.8


Dry

den

sity

(M

g/m

3 )

wc = 6.5% Uwc = 7.5% Uwc = 10.3% Uwc = 10.9% Uwc = 12.6% Uwc = 6.5% Swc = 7.5% Swc = 10.3%Swc = 10.9% Swc = 12.6% S

[b]

0 500 1000 1500 2000 2500 3000 35001.58

1.6

1.62

1.64

1.66

1.68

1.7

1.72

1.74

1.76

1.78


Dry

den

sity

(M

g/m

3 )

wc = 6.5% Mwc = 7.5% Mwc = 10.3% Mwc = 10.9% Mwc = 12.6% Mwc = 6.5% Ewc = 7.5% Ewc = 10.3% Ewc = 10.9% Ewc = 12.6% E

Figure 7.25: SFG model predictions of the variation of dry density with applied vertical stressfor S5B [a] Comparison of the undrained (U) and semi-drained (S) predictions [b] Comparisonof the experimental data (E) and model (M) predictions (semi-drained)


[a]

6 7 8 9 10 11 12 131.7

1.71

1.72

1.73

1.74

1.75

1.76

1.77

1.78

Water content (%)

Dry

den

sity

(M

g/m

3 )


[b]

6 7 8 9 10 11 12 131.62

1.64

1.66

1.68

1.7

1.72

1.74

1.76

1.78

Water content (%)

Dry

den

sity

(M

g/m

3 )


Figure 7.26: Compaction curves for S5B predicted by SFG model [a] Comparison of undrained(U) and semi-drained (S) predictions [b] Comparison of the experimental data (E) and model(M) predictions (semi-drained)

155

Table 7.11: Model parameters for Boom clay (SFG model)


2.8438 0.0993 10 35

10−6

10−4

10−2

100

102

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8

Suction, s (MPa)

N(s

) experimentmodel (Eqs. 2.18 and 2.19)

Figure 7.27: N(s) for Boom clay for varying suctions (SFG model)

7.4.2 Boom clay

The model parameters used for Boom clay are given in Table 7.11. The parameters are derived

from the experimental results of Deng et al. (2010) which are presented in Figure 7.1. The

tests conducted only on saturated soil samples are adequate for the determination of the model

parameters necessary for the SFG model.

Figure 7.27 shows the variation of the initial specific volume (N(s)) with suction. Both

experimental measurements and model predictions calculated with Equation 2.19 are presented

in the figure. Similar to the sand bentonite mixtures, the SFG model predicts decreasing initial

specific volumes (N(s)) with increasing suction for Boom clay. The experimental measurements,

however, show that the initial specific volume initially increases and after a peak value (at about

3000 kPa suction) starts decreasing with increasing suctions. The experimentally measured

initial specific volumes (N(s)) for unsaturated soil samples have greater values than the saturated

sample.

The model estimates for the variation of dry density with applied vertical stress for Boom


clay are shown in Figure 7.28. Figure 7.28(a) shows the comparison of the undrained and semi

drained modelling predictions. The difference between the two loading conditions is negligible at

low water contents and only starts to be noticed after 18.7% water content. It was also discussed

in Chapter 6 that air pressure and water pressure start to be influential after the OWC under

undrained loading conditions, first due to the high water content and therefore lower space left

for the air within the soil skeleton and second due to the air being trapped within the water.

Figure 7.28(b) shows the comparison of the model predictions and the experimental results

for the variation of dry density with applied vertical stress. Contrary to the predictions for

sand bentonite mixtures, even though the model estimates that the initial specific volumes

(N(s)) are lower than the experimental ones, the model predicts lower dry densities than the

experimentally measured values for Boom clay. This results due to high influence of suction in

the model derivation. This can be clearly observed comparing the model predictions for low

water content and higher water contents (or samples having high suction with samples having

low suctions). The error between the model predictions and experimental results reduces with

increasing water contents or reducing suctions. The evaluation of the model with sand bentonite

mixtures, which had low suctions compared to Boom clay, revealed the deficiency of the model’s

sensitivity to the slope of the NCL. The evaluation of the model with Boom clay, on the other

hand, clearly reveals the deficiency of the model, which highly emphasises the suctions. Even

the sample with 22.3% water content, which had the lowest suction between the tested samples,

failed to reach the experimentally measured dry densities. Therefore, it seems that the influence

of the suction in the model equation needs to be reduced.

Figure 7.29 shows the model estimates of the compaction curve for different stress levels. The

comparison of undrained and semi-drained model predictions are given in Figure 7.29(a). The

effect of buildup air pressure, which causes in lower predicted dry densities, is only noticeable

after 18.7% water content. In addition, the effect of buildup pore air pressure within the samples

becomes higher with increasing applied vertical stresses.

Figure 7.29(b) presents the comparison of the experimental and the modelling results for the

compaction curves with under different applied vertical stresses. The model highly underesti-

mates the experimental results due to the high dependency of the model equation (Equation

2.17) to suction. This can be clearly noticed at higher water contents (due to suction reduction),

when the error rate between the experimentally measured and predicted values reduces. The

effect of suction on volume change behaviour is so strong that in low water contents (at about

157

[a]

0 2000 4000 6000 8000 100001.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8


Dry

den

sity

(M

g/m

3 )

w = 3% Uw = 9.8% Uw = 14.7% Uw = 18.7% Uw = 22.3% Uw = 3% Sw = 9.8% Sw = 14.7% Sw = 18.7% Sw = 22.3% S

[b]

0 2000 4000 6000 8000 100001.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9


Dry

den

sity

(M

g/m

3 )

w = 3% Mw = 9.8% Mw = 14.7% Mw = 18.7% Mw = 22.3% Mw = 3% Ew = 9.8% Ew = 14.7% Ew = 18.7% Ew = 22.3% E

Figure 7.28: SFG model predictions of the variation of dry density with applied vertical stress forBoom clay [a] Comparison of the undrained (U) and semi-drained (S) predictions [b] Comparisonof the experimental data (E) and model (M) predictions (semi-drained)


Table 7.12: Model parameters for Speswhite kaolin (SFG model)


2.5385 0.0748 10 30

3% water content) the effect of applied vertical stress is not noticeable. This is due to the higher

suctions of the sample (102 MPa) than the maximum applied vertical stress (10 MPa). The

effect of applied vertical stress on the volume change of the sample starts to be noticed after

9.8% water content, because at this water content the suction value is about 10 MPa which is

close to the maximum applied vertical stress. Therefore, in the SFG model the ratio between

suction and applied vertical stress is important.


The model parameters for Speswhite kaolin are given in Table 7.12. This parameters are calcu-

lated from the experimental measurements presented in Figure 7.3. The experimental results in

Figure 7.3 are plotted in semi logarithmic graphs. The model parameters for the SFG model,

however, are derived from double logarithmic graphs (when both axes are plot in logarithmic

scale), thus the values differ from the values shown in Figure 7.3.

Figure 7.30 shows the variation of initial specific volumes (N(s)) with suction. Both experi-

mentally measured values and model estimates are presented in the figure. The model predicts

reducing initial specific volumes (N(s)) with increasing suction. Experimentally measured val-

ues, on the other hand, initially increase and after a peak value start to decrease. The model

predicts initially lower specific volumes (N(s)), which means the model assumes that the unsat-

urated samples are initially denser compared to the experimental conditions.

The modelling results for the variation of void ratio with applied vertical stress are shown

in Figure 7.31. Figure 7.31(a) shows the comparison of the undrained and semi-drained model

predictions. Similar to the other soil types examined, the difference between the undrained

and semi-drained loading conditions increases with increasing water content. Figure 7.31(b)

presents the comparison between the experimental results and the model predictions. Since the

model predicted much lower initial void ratios (or initial specific volumes (N(s))), the model

estimates for the void ratio at low applied vertical stresses are much lower than the experimentally

measured values. The difference between the predicted and experimental measurements reduces

with increasing applied vertical stresses. This is explained by the fact that the high influence

159

[a]

0 5 10 15 20 25

1.25

1.3

1.35

1.4

1.45

1.5

1.55

1.6

1.65

1.7

Water content (%)

Dry

den

sity

(M

g/m

3 )

1 MPa U2 MPa U3 MPa U4 MPa U5 MPa U6 MPa U8 MPa U10 MPa U1 MPa S2 MPa S3 MPa S4 MPa S5 MPa S6 MPa S8 MPa S10 MPa S

[b]

0 5 10 15 20 25

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

Water content (%)

Dry

den

sity

(M

g/m

3 )

1 MPa M2 MPa M3 MPa M4 MPa M5 MPa M6 MPa M8 MPa M10 MPa M1 MPa E2 MPa E3 MPa E4 MPa E5 MPa E6 MPa E8 MPa E10 MPa E

Figure 7.29: Compaction curves for Boom clay predicted by SFG model [a] Comparison ofundrained (U) and semi-drained (S) predictions [b] Comparison of the experimental data (E)and model (M) predictions (semi-drained)


0 1000 2000 3000 4000 50002

2.5

3

3.5

4

4.5

5

Suction, s (kPa)

N(s

)


Figure 7.30: N(s) for Speswhite kaolin for varying suctions (SFG model)

of suction in the model derivation starts to be less influential with increasing applied vertical

stresses. The model’s sensitivity to suction reduces after the applied vertical stress exceeds the

suctions of the samples and the model becomes more sensitive to the applied vertical stresses.

The gradient of the curves in Figure 7.31(b) are much lower for the model estimates compared

to the experimentally measured values. As it was stated before, this again reveals that model

places unreasonable emphasis on suction in its derivations and in return underestimates the

compressibility (slope of the NCLs) of the soil.

Figure 7.32 shows the model predictions of the compaction curve for Speswhite kaolin. The

comparison between undrained and semi-drained modelling predictions are presented in Figure

7.32(a). Similar to the other examined soils (sand bentonite mixtures and Boom clay), the

influence of buildup pore pressure is noticeable at high water contents. The comparison between

the modelling predictions and the experimental results of the compaction curve is shown in

Figure 7.32(b) for different stress levels. The model overestimates the dry densities up to 15%

water content at all stress levels due to initially overestimated dry densities (or underestimated

initial specific volumes (N(s))). After 15% water content, the model still overestimates the

experimental results at low applied stresses, however, predicts better at high applied vertical

stresses. As stated before, this is due to the ratio between the suction and applied vertical stress.

After reaching the applied stresses higher than the initial suction value, the model becomes less

sensitive to suction and more sensitive to the slope of the NCL and the applied stresses.

161

[a]

0 200 400 600 800 1000 12000.98

1

1.02

1.04

1.06

1.08

1.1

1.12

1.14

1.16


Voi

d ra

tio (

e) wc = 24% Uwc = 25% Uwc = 28% Uwc = 24% Swc = 25% Swc = 28% S

[b]

0 200 400 600 800 1000 12000.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9


Voi

d ra

tio (

e) wc = 24% Mwc = 25% Mwc = 28% Mwc = 24% Ewc = 25% Ewc = 28% E

Figure 7.31: SFG model predictions of the variation of dry density with applied vertical stressfor Speswhite kaolin [a] Comparison of the undrained (U) and semi-drained (S) predictions [b]Comparison of the experimental data (E) and model (M) predictions (semi-drained)


[a]

5 10 15 20 25 30 351.22

1.24

1.26

1.28

1.3

1.32

1.34

Water content (%)

Dry

den

sity

(M

g/m

3 )

300 kPa U600 kPa U900 kPa U1200 MPa U300 kPa S600 kPa S900 kPa S1200 kPa S

[b]

5 10 15 20 25 30 350.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

Water content (%)

Dry

den

sity

(M

g/m

3 )

300 kPa M600 kPa M900 kPa M1200 MPa M300 kPa E600 kPa E900 kPa E1200 kPa E

Figure 7.32: Compaction curves for Speswhite predicted by SFG model [a] Comparison ofundrained (U) and semi-drained (S) predictions [b] Comparison of the experimental data (E)and model (M) predictions (semi-drained)

163

7.4.4 Discussion on the SFG model

The SFG model was evaluated on its ability to predict the static compaction curve of four

different soils. The following conclusions about the model are gained:

• The model predicts decreasing initial specific volumes (N(s)) with increasing suctions. In

addition, the initial specific volumes for unsaturated samples are predicted to be lower than

the saturated samples. However, the experimental measurements reveal that the initial

specific volumes (N(s)) of unsaturated samples are higher than the saturated samples.

This model deficiency results in overestimation of the dry densities under low applied

vertical stresses.

• Although a direct relationship between the slope of the NCL and suction, similar to the

equation proposed in BBM (see Equation 2.13), is not presented in the model formulation,

the effect of suction in the compressibility of the soil samples is considered in the model.

However, similar to the BBM, in the SFG model, the higher the suction is, the less com-

pressible the soil is (see Equation 2.17). The experimental results, however, reveals the

contrary (see Figures 5.8, 5.9, 7.2 and 7.4).

• The examination of the gradient of the dry density and applied vertical stress relationship

reveals that the model over emphasises the suction effect on the compressibility. The effect

of suction on the compressibility is so high that the samples with high suctions are very

hard to compact, thus the suction effect needs to be reduced. This can be done by adding

a value between zero and one to the power of suction in the model formulation. This is

very similar to multiplying the suction parameter with χ parameter to reduce the effect of

suction as it is adopted in single stress approach models (effective stress models) (Khalili

et al., 2004; Laloui and Nuth, 2009). However, when this is done explicit integration of

the model equation (see Equation 2.16) could not be preformed.

• The examination of the gradient of the dry density and applied vertical stress relationship

also reveals that the slope of the NCL is underestimated. Although, it looks very convenient

to only use the slope of the NCL for saturated soil samples in the model formulations, the

model fails to depict the compressibility of the samples. This was proven in the evaluation

of the sand bentonite mixtures, where the suctions were very low and therefore the low

gradient did not result due to the over emphasis of the suction in the model but only due


to the low values of the compressibility coefficients. In addition, during the evaluation of

the granular soils (S2B and S5B), it was shown that the adoption of a single slope for the

NCL (λvp), which is for saturated samples in the SFG model, is not adequate and results in

very close predicted dry densities for samples with low suction but different water contents.

Therefore, there might be a need for the adoption of different values for the slope of the

NCLs for samples with different water contents, in place of the slope of the NCL (λvp) for

saturated soil sample.

• The ratio between suction and applied vertical stress is important in the model formula-

tions. When suctions are high the effect of applied stresses are almost considered to be

negligible on the volume change of the samples.

Sheng et al. (2008) evaluated the model for compacted bentonite data presented by Lloret

et al. (2003) and found a reasonable fit to the data. At low suctions, the model was shown to

correctly predict the void ratio of the soil with applied net stresses. At high suctions, the model

underestimates the void ratio (the model predicts less dense samples than the experimental

results). At low suctions, the net stress and suction ratio is high; whereas, at high suctions,

the net stress and suction ratio is lower. This leads to reasonable model predictions at low

suctions. In addition, the model parameter, which is the slope of the NCL (λvp), is assumed to

be much higher (λvp−model = 0.085) than the experimentally measured value (λvp−exp = 0.069)

for the same soil (Lloret et al., 2003), when calculated from a double logarithmic relationship

as defined in the model derivations (when both axes are plot in logarithmic scale). The model

places too much emphasis on suction, which would normally lead to a less compressible soil.

Thus, the use of a higher value for the slope of the NCL (λvp) than the experimentally measured

value, substituted the model’s overemphasis on the suction parameter. Therefore, the model

predictions seems to fit the experimental data better than it would normally fit.

7.4.5 Other models developed with combined stress variables approach

Other models developed with combined stress variables approach use the BBM or models with

similar approach (Wheeler and Sivakumar, 1995) in their mechanical modelling formulations

but use different stress state variables instead of net stress and suction. These models and their

overall effect on the prediction of the compaction curve are briefly discussed in this section.

165

Bolzon et al. (1996) modified the BBM by using average skeleton stress (σ−ua+Sr(ua−uw))

and suction (ua−uw) as stress variables instead of net stress (σ−ua) and suction (ua−uw). This

modification gives advantages over the BBM when the transition zone between unsaturated and

saturated soils is considered. However, this model uses a similar function to the one proposed in

the BBM for the variation of the soil compressibility with suction (λ(s)). Therefore, using this

model will give similar results to the BBM.

Santagiuliana and Schrefler (2006) included hydraulic hysteresis to the model proposed by

Bolzon et al. (1996). However, during the compaction process only wetting path is followed and

there is no need to consider the hysteretic nature of the soil. Thus, this modification would not

improve the compaction process predictions and will give similar results to the BBM.

Gallipoli et al. (2003a) proposed an elasto-plastic constitutive model incorporating the effect

of soil fabric into the model. They used average skeleton stress (σ − ua + Sr(ua − uw)) as

a stress variable and introduced a new stress variable as a second stress variable which is a

function of suction and degree of saturation (ξ = f(s)(1 − Sr)). In their model, they proposed

two soil parameters which can be found by calibrating the model with the experimental results.

Therefore, the initial specific volume (N(s)) and the slope of the NCLs (λ(s)) do not necessarily

reduce with increasing suction but depend on the experimental results and are incorporated

into the model with the proposed soil parameters. In fact, this model is very similar to the

modified BBM suggested in Section 7.3 when ”r” parameter is considered to be bigger than one

(see Equation 2.13). However, the model proposed by Gallipoli et al. (2003a) needs less soil

parameters and will produce better results in the transition zone due to the use of the average

skeleton stress as a stress variable. Gallipoli et al. (2003a) validated their model for Speswhite

kaolin for a very narrow range of suctions. Looking at the experimental results of the soils

examined in this study, it is clear that the compressibility first increases and after reaching a

peak starts decreasing. Thus, still the soil behaviour cannot be modelled using a single set of

soil parameters for a wider range of water contents but will require more sets of parameters.

Tarantino and De Col (2008) developed a compaction model where they used different work

conjugates than the ones used in the BBM as suggested by Houlsby (1997). The work conjugates

they adopted are the average skeleton stress (σ−ua+Sr(ua−uw)) and modified suction (s∗ = ns).

In addition, Tarantino and De Col (2008) considered the change in suction with loading by

incorporating the model proposed by Gallipoli et al. (2003b). Their model is similar to the

model developed by Gallipoli et al. (2003a) and expected to predict similar results.


7.5 Overall discussion

The evaluation of the compaction models developed using two different constitutive modelling

approaches revealed that both modelling approaches have significant shortcomings in capturing

the volume change behaviour of the compacted soils, except the models prosed by Gallipoli et al.

(2003a) and Tarantino and De Col (2008). The main shortcomings for both approaches are as

follows:

1. The assumption of a decreasing slope of the NCLs (λ(s)) or decreasing compressibility

with increasing suctions; and,

2. The assumption of a decreasing initial specific volume (N(s)) with increasing suctions.

These assumptions are correct when the suction is applied by drying the initially slurry

soil. Slurry soil have a homogeneous fabric compared to compacted soils and drying the soil

would not change the fabric significantly. However, the same suctions could be attained in soils

by two main different ways which would result in completely different fabric within the soil

structure. The stress paths for both type of conditions are presented in Figure 7.33. First,

initially slurry soil can be dried to certain suctions (path AB) and subsequently compacted to

certain stresses (path BC). Second, initially dry soil can be mixed with ceratin amount of water

(path DB’) and after compacted to desired stresses (path B’C’). Although, this two samples

will have similar suctions, they would have completely different volume change behaviour which

is presented in Figure 7.34. Sivakumar and Wheeler (2000) conducted experiments where they

initially compacted the samples with different initial suctions and later saturated them. They

also showed that those two samples have different compaction behaviour.

It was shown in this study that unsaturated loose samples are more compressible than the

saturated samples at the same stress level. The compressibility or the slope of the NCLs (λ(s))

of the unsaturated samples initially increases up to a certain suction and later starts to decrease

with increasing suctions as shown in Figures 7.5, 7.9, 7.13 and 7.17. Most likely, at high applied

vertical stresses, the NCLs for unsaturated samples will join the NCL for saturated sample. This

was experimentally observed by Tarantino and De Col (2008). They initially prepared samples

with different water contents and compacted them under relatively low stresses. Subsequently,

they saturated the samples and loaded them to higher stresses in order to obtain the NCLs. The

samples which were prepared with lower water contents have higher slopes of the NCLs than

167

Net stress, σ −ua

Suc

tion,

s

A

1

C’B’

B C

2

s1

D

Figure 7.33: Stress paths for attaining samples with similar suctions

ln Net stress, ln(σ−ua)

Spe

cific

vol

ume,

ν

C’

D

B’

s = s1

Initially dry soil

A

B C

s = s0

s = s1 Initially slurry soil

Figure 7.34: Volume change behaviour of samples with similar suction but developed underdifferent stress paths


Suction, s

λ(s)

, N(s

)

2a 2b

set ofparameters set of

parameters

set ofparameters 1

Figure 7.35: Variation of the soil compressibility with suction

the samples prepared with higher water contents. Eventually, all samples joined the NCL for

saturated sample.

The discrepancy observed between the experimental results and the current constitutive

models arises due to the cloddy fabric within the unsaturated samples generalised with initially

dry soils. The current models do not capture the fabric effect of the unsaturated samples

except the models developed by Gallipoli et al. (2003a) and Tarantino and De Col (2008).

However, these models still need to use different sets of soil parameters for the compaction

model development as shown in Figure 7.35. Initially slurry soils require a set of soil parameters

and samples prepared as shown in the stress path 2 (see Figure 7.33) require two different sets of

soil parameters, one for the part where compressibility increases with suction (2a) and another

one for the part where compressibility decreases with increasing suction (2b). Alternatively, the

relationships between the slope of the NCLs (λ(s)) and suction, and between the initial specific

volume (N(s)) and suction need to be captured by a single equation.

In addition, the fabric effect can be easily incorporated to the models formulated using similar

approach to the BBM by adopting the ”r” parameter bigger than one up to the suction level

where the peak value for the slope of the NCL is attained (2a) and after that suction value by

adopting ”r” parameter smaller than one (2b). For initially slurry soils another set of parameters

should be determined by using an ”r” parameter smaller than one (1). This basically highlights

that compacted soils from initially dry soil and initially slurry soil cannot be treated as same.

169


This chapter presented the performance of the compaction models on predicting the static com-

paction behaviour during the compaction process. The models were evaluated with the data of

four different soils. These soils are two sand-bentonite mixtures with different bentonite contents

(S2B and S5B), Boom clay and Speswhite kaolin. The experiments used for the model evalu-

ation were conducted for semi-drained loading conditions. However, the model predictions for

undrained loading conditions were also presented in the chapter to show the comparison between

the two loading conditions. It is found that during undrained loading, lower dry densities were

attained under the same applied vertical stresses. This is due to the higher pore pressure devel-

opment during the undrained loading conditions, which made the compaction process harder (see

Chapter 6). The difference between the predicted dry densities of these two loading conditions

became notable for Boom clay and Speswhite kaolin but not sand-bentonite mixtures. This is

due to the low degrees of saturation attained for S2B and S5B samples during the compaction

process.

Firstly, the performance of using constitutive models developed with separate stress state

variables approach in the compaction process modelling were evaluated. The BBM was chosen for

detailed evaluation and other models developed with a similar approach were briefly examined.

The BBM and the models developed by Vaunat et al. (2000) and Thu et al. (2007) assume

decreasing values with increasing suctions, for the slope of the NCLs (λ(s)) and the initial

specific volumes (N(s)). However, experimental observations revealed that the slope of the

NCLs (λ(s)) initially increases and after reaching a peak value starts to decrease with increasing

suctions, for all the soil types. In addition, the initial specific volumes (N(s)) have a similar

trend to the slope of the NCLs for Boom clay and Speswhite kaolin, and increasing values with

suction for sand-bentonite mixtures. Different than those models, Chiu and Ng (2003) adopted

an increasing slope of the NCLs with increasing suctions by modifying the ”r” parameter to

bigger than one in the BBM. However, this still contradicts with the experimental observations.

Chiu and Ng (2003) would result in reasonable predictions up to the suctions where peak values

for the slope of the NCLs (λ(s)) were attained but would fail to predict the values beyond that

suctions. In the current study, the BBM was modified by increasing the slope of the NCL (λ(0))

and the initial specific volume (N(0)) for saturated soil. This modification led to better model

predictions; however, still the compaction behaviour was not captured using a single set of soil

parameters for a wide range of water contents or suctions.


Secondly, the performance of using constitutive models developed with combined stress state

variables approach in the compaction process modelling was evaluated. The SFG model was

chosen for detailed evaluation and other models developed with a similar approach were briefly

examined. It is found that the SFG model estimates decreasing values for the initial specific

volumes (N(s)) with increasing suctions. This is due to the over emphasis placed on suction

in the model development. In addition, even a direct relationship for the slope of the NCLs

(λ(s)) is not proposed in this model, it indirectly predicts a decreasing compressibility with

increasing suctions. Both of these assumptions contradict with the experimental observations.

Therefore, the predictions using the SFG model fails to depict the experimental behaviour during

the compaction process. The models developed by Bolzon et al. (1996) and Santagiuliana and

Schrefler (2006) estimates decreasing slope with increasing suctions. Thus, those models would

not correctly predict the compaction behaviour either. The models proposed by Gallipoli et al.

(2003a) and Tarantino and De Col (2008) use similar formulations to the BBM with different

work conjugates for their volume change predictions. However, these models do not have restrains

like decreasing or increasing compressibility with changing suctions. Instead, they calibrate their

models according to the experimental results. Therefore, they can capture both decreasing or

increasing compressibility according to the experimental results. In addition, they use average

skeleton stress (σ− ua +Sr(ua− uw)) as a stress variable in their modelling formulations which

would result in a better transition between the unsaturated and saturated soil states. Thus,

the models developed by Gallipoli et al. (2003a) and Tarantino and De Col (2008) are the

most promising ones in predicting the compaction process. However, using a single set of soil

parameters for the prediction of the compaction behaviour over a wide range of water contents

would not be possible.

In conclusion, it is shown that the samples prepared from initially slurry soils and initially

dry soils could not be treated the same. They would require the adoption of different sets

of soil parameters in order to model their compaction behaviour. In addition, compaction

behaviour of the samples prepared form initially dry soils can be predicted using a single set of

soil parameters only for a narrow range of water contents. Minimum of two sets of soil parameters

are required to model the compaction behaviour over a wide range of water contents with the

existing constitutive models.

Chapter 8

Conclusions and suggestions for

future research

8.1 Conclusions

The objective of this research project was to advance the current understanding of the com-

paction process of soils. The research concentrated on the following areas: investigating the

behaviour of soils during the static compaction process; modelling the compaction process using

the unsaturated soil mechanics principles; and evaluating the performance of the model. The

conclusions gained from the study are presented in this chapter.

8.1.1 Soil behaviour during the compaction process

On the experimental side, the main contribution of this work is the observation of the stress

and phase variables during the static compaction process. Constant water content tests were

conducted on two different granular soils, sand with 2% and 5% bentonite content, with varying

water contents to observe the effect of matric suction on the compaction behaviour.

It is found that matric suction decreases with loading for all tested samples in the present

research program. The matric suction change increases with reducing water content and increas-

ing clay content. For the matric suction range tested, the slopes of the NCLs for unsaturated

samples are found to be higher than the saturated samples. The compressibility coefficient (ms1)

decreases with both increasing vertical net stress (σy − ua) and degree of saturation (Sr) during

171

172 CHAPTER 8. CONCLUSIONS AND SUGGESTIONS FOR FUTURE RESEARCH

the tests.

Complete saturation was never attained during the compaction tests for both samples. On

the contrary, the degrees of saturation reached at the end of the compaction process were low

and similar to their values at their saturation matric suctions in the wetting path of the water

retention curves. This is attributed to the correlation between the degree of saturation at

optimum water content and the degree of saturation achieved at zero matric suction in the

wetting path of the water retention curve.

Matric suction was measured using null type axis translation technique for granular soils

for the first time in literature. It is found that this method is not practical for the matric

suction measurements at low degrees of saturation or water contents. This is attributed to the

discontinues water phase within the soil samples.

8.1.2 Modelling the compaction process

On the modelling part, one dimensional static compaction process is modelled for undrained,

semi drained and drained loading conditions. Model is developed by incorporating pore pres-

sure predictions into a volume change constitutive relationship for unsaturated soils. The pore

pressure generation was calculated using two approaches, Hilf (1948) and Hasan & Fredlund

(1980). The first approach is adopted for the pore pressure calculations because it requires less

parameters for the predictions of the pore pressure with applied vertical stress (σy).

It is found that by using constant compressibility coefficients (ms1,m

s2) the shape of the

compaction curve cannot be produced on the the dry side but only on the wet side of the

compaction curve. Thus, variable compressibility coefficients were derived from constitutive

models proposed in the literature, and using these coefficients, the well-known shape of the

compaction curve can be modelled both on the dry and wet side of the compaction curve using

variable compressibility coefficient (ms1). Moreover, it is found that the matric suction component

of the volume change equation (Equation 2.2) does not have a significant influence on the shape

of the compaction curve but the influence of matric suction on the compressibility coefficient

due to net stress (ms1) is a governing parameter.

It is shown that the dry density is a function of the compressibility coefficient (ms1) and the

change in vertical net stress (∆(σy − ua)). During undrained and semi drained loading, while

coefficient of compressibility (ms1) increases, vertical net stress (σy−ua) decreases with increasing

water contents (w). This happens due to the increase in pore-air pressure (ua) development

173

with increasing water contents (w). Therefore, the maximum dry density is attained at the

optimum combination of the compressibility coefficient (ms1) and the change in vertical net

stress ∆(σy − ua)). The optimum combination of the coefficient of compressibility (ms1) and

vertical net stress (σy − ua) takes place in lower water contents for the soil samples compacted

with higher energy than the soil samples compacted with lower energy. This results in the shift of

the OWC to the left. In addition, during drained loading, while the coefficient of compressibility

(ms1) increases, vertical net stress (σy − ua) stays constant with increasing water content (w).

For that reason, during drained loading the OWC is on the full saturation line.

8.1.3 Evaluation of the model

On the model’s performance part, the compaction models developed with two different con-

stitutive modelling approaches, namely separate stress variables and combined stress variables

approaches, are evaluated on their ability to capture the compaction behaviour of soils.

For the models developed with separate stress variables approach the following conclusions

are derived:

• The BBM, and the models developed by Vaunat et al. (2000) and Thu et al. (2007) assumed

decreasing values for the slope of the NCLs (λ(s)) and the initial specific volumes (N(s))

with increasing suctions. However, experimental observations show that the slope of the

NCLs (λ(s)) initially increases and after reaching a peak value starts to decrease with

increasing suctions, for the tested soil types. In addition, the initial specific volumes (N(s))

have a similar trend to the slope of the NCLs for Boom clay and Speswhite kaolin, but

increasing values with increasing matric suction for sand-bentonite mixtures. Therefore,

using these two constitutive models for compaction process modelling would fail to predict

the volume change behaviour of the soils.

• Chiu and Ng (2003) adopted an increasing slope for the NCLs with increasing suctions.

However, this still contradicts with the experimental observations. Chiu and Ng (2003)

would result in reasonable predictions up to the suction values where the slope of the NCLs

(λ(s)) starts decreasing but would fail to predict the values beyond those suctions.

• Those models can be improved by:

1. modifying the ”r” parameter to values bigger than one up to the suction values where

peak compressibility is observed; and,


2. adopting an ”r” parameter smaller than one, and adopting higher values for the slope

of the NCL (λ(0)) and the initial specific volume (N(0)) for saturated soils.

For the models developed with combined stress variables approach the following conclusions

are obtained:

• The SFG model, and the models developed by Bolzon et al. (1996) and Santagiuliana and

Schrefler (2006) estimate decreasing values for the slope of the NCLs (λ(s)) and initial

specific volumes (N(s)) with increasing matric suctions. Therefore, those models would

not predict the compaction behaviour of soils correctly.

• The models developed by Gallipoli et al. (2003a) and Tarantino and De Col (2008) use

similar formulations for their volume change calculations but different stress variables with

the BBM. However, both of these models do not have restrains like decreasing or increasing

compressibility with changing matric suctions but they calibrate their models according to

the experimental data. Therefore, they can have either decreasing or increasing compress-

ibility according to the experimental results. Thus, they are the most promising ones in

predicting the compaction process. However, they would still require more than one set of

soil parameters to model the compaction behaviour for the wide range of water contents.

• The SFG, and the models developed by Bolzon et al. (1996) and Santagiuliana and Schrefler

(2006) can be improved with the modifications suggested below:

1. The SFG model over emphasises the matric suction in the model formulations. The

effect of matric suction can be reduced by adding a value between zero and one to the

power of matric suction in the model formulation. This is very similar to multiplying

the matric suction parameter with χ parameter to reduce the effect of matric suction

as it is adopted in single stress approach models (effective stress models) (Khalili

et al., 2004; Laloui and Nuth, 2009). However, after this modification the explicit

integration of the model equation (see Equation 2.16) could not be preformed.

2. The models developed by Bolzon et al. (1996) and Santagiuliana and Schrefler (2006)

can be modified similar suggestions proposed above for the models developed with a

separate stress variables approach.

In conclusion, it is shown that the samples prepared to different water contents from initially

slurry soils and initially dry soils could not be treated the same. They would require the adoption

175

of different sets of soil parameters in order to model their compaction behaviour for a wide range

of water contents. In addition, compaction behaviour of the samples prepared from initially

dry soils can be predicted using minimum two sets of soil parameters for a wide range of water

contents. In order to model the compaction behaviour using single set of soil parameters for

samples prepared from initially dry soils, the relationships between the slope of the NCLs (λ(s))

and suction, and between the initial specific volume (N(s)) and suction need to be captured by

a single equation.

8.2 Suggestions for future research

The research conducted in this study significantly contributed to the current knowledge on the

compaction process and therefore the compaction behaviour of soils. Future research, however, is

needed to further extend the understanding of the compaction behaviour. This can be achieved

by improving the experimental techniques and the constitutive models suggested for unsaturated

soils.

On the experimental side, the following work is suggested:

1. It is found that for granular soils, there are some difficulties in suction measurements for

the samples with low water contents using the null type axis translation technique. The

validity of this technique for soils with low water content or degrees of saturation should

be further investigated by using different soil types and conducting more tests. The mea-

surements should be compared by the measurements obtained using different techniques.

The fundamental reasons for the long duration of the tests need to be investigated and

clearly identified.

2. It is found that there is a correlation between the saturations at the OWC and the sat-

urations at zero suctions in the wetting path of the soil water retention curve for tested

soils. This evidence should be further investigated for different types of soils in order to

generalise this finding.

3. Modelling the compaction process will provide better understanding of the post compaction

behaviour of soils. Thus, further experiments using different types of soils should be

conducted to provide the link between the compaction process and the post compaction

behaviour of soils.


On the modelling side the following work is suggested:

1. It is shown in this study that the current constitutive models are unable to predict the

compaction behaviour of soils using single set of soil parameters for a wide range of water

contents and a minimum of three sets of parameters are required; one for the samples

prepared at different water contents from initially slurry soil and two for the samples

prepared from initially dry soils. This can be improved by proposing a single equation for

the relationship between the slope of the NCLs (λ(s)) and suction, and incorporating this

equation into the current existing constitutive models.

2. It has been inferred that the compaction process produce the basis for the post compaction

behaviour. Therefore, it is believed that the yield behaviour of soils (e.g., yield curves)

could be correlated to the compaction curves at differen stress levels.

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Appendix A

Matlab Codes

A.1 Undrained modelling using the BBM

clc;

clear all;

%CONSTANT SUCTION WITH LOADING

%UNDRAINED WITH BBM

%air solvability in water

h = [value];

%slope of the NCL in semi log axis

lvp = [value];

%specific gravity of soil

Gs = [value];

%model parameter

r = [value];

%model parameter

B = [value];

%model parameter

pc = [value];

%model parameter

ks = [value];

%initial specific volume for saturated soil

N_0 = [value];

%change in vertical stress

d_sigma = [value];

%final applied vertical stress

sigma_final = [value];

%atmospheric pressure

p_atm = [value];

%wc and suction_0 needs to be the same size vector

%wc of the samples (add as many as you want)

187

188 APPENDIX A. MATLAB CODES

wc = [values];

%initial suction of the samples

suction_0 = [values];

%calculating lvps and Ns using BBM assumptions and equations

for t = [1:length(suction_0)]

lvp_s(t) = lvp*((1 - r)*exp(-B*suction_0(t)) + r);

N_s(t) = N_0 - (lvp - lvp_s(t))*log(pc) - ks*log((suction_0(t) + p_atm)/p_atm);

end

%programming trick to keep the final values all together

sigma_ff = [];

u_a_ff = [];

v_ff = [];

e_ff = [];

S_rff = [];

n_ff = [];

m1s_ff = [];

gamma_d_ff = [];

%loop that is rotating for different wc

for i = 1:length(wc)

%resetting the initial air pressure

u_a0(i,1) = p_atm;

%keep the final values within the next loop together

sigma_f = [];

u_a_f = [];

v_f = [];

e_f = [];

S_rf = [];

n_f = [];

m1s_f = [];

gamma_d_f = [];

%the loop that is rotating for different vertical stress

for sigma = [d_sigma:d_sigma:sigma_final]

%defining the index for the loop

j = sigma/d_sigma;

%net stress

net_stress(i,j) = sigma - u_a0(i,j) + p_atm;

%specific volume

v(i,j) = N_s(i) - lvp_s(i)*log(net_stress(i,j)/pc);;

%void ratio

e(i,j) = v(i,j) - 1;

%degree of saturation

S_r(i,j) = wc(i)*Gs/e(i,j);

%porosity

n(i,j) = e(i,j)/(e(i,j) + 1);

%coefficient of compressibility due to net stress

189

m1s(i,j) = lvp_s(i)/v(i,j)/(net_stress(i,j));

%dry density

gamma_d(i,j) = Gs/(1 + e(i,j));

%changes in air pressure with loading

du_a(i,j+1) = 1/2/m1s(i,j)*(-m1s(i,j)*u_a0(i,j)...

- n(i,j)+ n(i,j)*S_r(i,j) - n(i,j)*h*S_r(i,j)...

+ m1s(i,j)*d_sigma + (-2*n(i,j)*m1s(i,j)*d_sigma...

+ 2*m1s(i,j)*u_a0(i,j)*n(i,j)...

+ n(i,j)^2*h^2*S_r(i,j)^2 ...

+ 2*m1s(i,j)^2*d_sigma*u_a0(i,j)...

+ 2*n(i,j)^2*h*S_r(i,j)...

- 2* n(i,j)^2*S_r(i,j)^2*h...

- 2*m1s(i,j)*u_a0(i,j)*n(i,j)*S_r(i,j)...

+ m1s(i,j)^2*u_a0(i,j)^2...

+ n(i,j)^2-2*n(i,j)^2*S_r(i,j)...

+ n(i,j)^2*S_r(i,j)^2 + m1s(i,j)^2*d_sigma^2 ...

+ 2*m1s(i,j)*u_a0(i,j)*n(i,j)*h*S_r(i,j) ...

+ 2*n(i,j)*S_r(i,j)* m1s(i,j)*d_sigma...

- 2*n(i,j)*h*S_r(i,j)*m1s(i,j)*d_sigma)^(1/2));

%absolute air pressure

u_a0(i,j+1) = u_a0(i,j) + du_a(i,j+1);

%keep the final values within the loop together

sigma_f = [sigma_f,sigma];

u_a_f = [u_a_f, u_a0(i,j)];

v_f = [v_f, v(i,j)];

e_f = [e_f, e(i,j)];

S_rf = [S_rf, S_r(i,j)];

n_f = [n_f, n(i,j)];

m1s_f = [m1s_f, m1s(i,j)];

gamma_d_f = [gamma_d_f, gamma_d(i,j)];

end


sigma_ff = [sigma_ff; sigma_f];

u_a_ff = [u_a_ff; u_a_f];

v_ff = [v_ff; v_f];

e_ff = [e_ff; e_f];

S_rff = [S_rff; S_rf];

n_ff = [n_ff; n_f];

m1s_ff = [m1s_ff; m1s_f];

gamma_d_ff = [gamma_d_ff; gamma_d_f];

end


A.2 Semi-drained modelling using the BBM

clc;

clear all;


%SEMI DRAINED WITH BBM


h = [value];


lvp = [value];


Gs = [value];

%model parameter

r = [value];

%model parameter

B = [value];

%model parameter

pc = [value];

%model parameter

ks = [value];


N_0 = [value];


d_sigma = [value];




p_atm = [value];



wc = [values];



%calculating lvps and Ns using BBM assumptions and equations


lvp_s(t) = lvp*((1 - r)*exp(-B*suction_0(t)) + r);

N_s(t) = N_0 - (lvp - lvp_s(t))*log(pc) - ks*log((suction_0(t) + p_atm)/p_atm);

end


sigma_ff = [];

u_a_ff = [];

v_ff = [];

e_ff = [];

S_rff = [];

n_ff = [];

m1s_ff = [];

gamma_d_ff = [];

191




sigma_f = [];

u_a_f = [];

v_f = [];

e_f = [];

S_rf = [];

n_f = [];

m1s_f = [];

gamma_d_f = [];




j = sigma/d_sigma;


u_a0(i,j) = 101.3;

%net stress

net_stress(i,j) = sigma - u_a0(i,j) + 101.3;

%specific volume


%void ratio

e(i,j) = v(i,j) - 1;



%porosity

n(i,j) = e(i,j)/(e(i,j) + 1);



%dry density


if S_r(i,j) >= 0.98;

net_stress(i,j) = net_stress(i,j-1);

v(i,j) = v(i,j-1);

e(i,j) = e(i,j-1);

S_r(i,j) = S_r(i,j-1);

n(i,j) = n(i,j-1);

m1s(i,j) = m1s(i,j-1);

gamma_d(i,j) = gamma_d(i,j-1);

else






+ 2*m1s(i,j)*u_a0(i,j)*n(i,j)...

+ n(i,j)^2*h^2*S_r(i,j)^2 ...


+ 2*n(i,j)^2*h*S_r(i,j)...

- 2* n(i,j)^2*S_r(i,j)^2*h...


+ m1s(i,j)^2*u_a0(i,j)^2...

+ n(i,j)^2-2*n(i,j)^2*S_r(i,j)...






u_a0(i,j+1) = u_a0(i,j) + du_a(i,j+1);

%net stress


%specific volume

v(i,j) = N_s(i) - lvp_s(i)*log(net_stress(i,j)/pc);

%void ration

e(i,j) = v(i,j) - 1;



%porosity

n(i,j) = e(i,j)/(e(i,j) + 1);



%dry density


end;



u_a_f = [u_a_f, u_a0(i,j)];

v_f = [v_f, v(i,j)];

e_f = [e_f, e(i,j)];


n_f = [n_f, n(i,j)];

m1s_f = [m1s_f, m1s(i,j)];


end




v_ff = [v_ff; v_f];

e_ff = [e_ff; e_f];


n_ff = [n_ff; n_f];



end

193

A.3 Undrained modelling using the SFG model

clc;

clear all;


%UNDRAINED WITH SFG


h = [value];


lvp = [value];


Gs = [value];

%initial net stress where N is calculated

p_0 = [value];


N_0 = [value];

%saturation suction

s_sa = [value];


d_sigma = [value];




p_atm = [value];



wc = [values];



%calculating Ns using SFG assumptions and equations (choose one of them)


%for s > s_sa

N(t) = exp(log(N_0) - lvp*log((p_0 + s_sa)/p_0)...

- lvp*(s_sa +1)/(p_0 - 1)*log((suction_0(t)...

+ 1)*(p_0 + s_sa)/(p_0 + suction_0(t))/(s_sa + 1)));

%for s < s_sa

N(t) = exp(log(N_0) - lvp*log((p_0 + s_sa)/p_0) ...

- lvp*(1 - (s_sa + 1)/(suction_0(t) + 1)));

end


sigma_ff = [];

u_a_ff = [];

v_ff = [];

e_ff = [];

S_rff = [];

n_ff = [];

m1s_ff = [];


gamma_d_ff = [];




u_a0(i,1) = p_atm;

%keep the final values within the next loop together

sigma_f = [];

u_a_f = [];

v_f = [];

e_f = [];

S_rf = [];

n_f = [];

m1s_f = [];

gamma_d_f = [];




j = sigma/d_sigma;

%net stress

net_stress(i,j) = sigma - u_a0(i,j) + p_atm;

%specific volume


%void ratio

e(i,j) = v(i,j) - 1;



%porosity

n(i,j) = e(i,j)/(e(i,j) + 1);



%dry density






+ 2*m1s(i,j)*u_a0(i,j)*n(i,j)...

+ n(i,j)^2*h^2*S_r(i,j)^2 ...


+ 2*n(i,j)^2*h*S_r(i,j)...

- 2* n(i,j)^2*S_r(i,j)^2*h...


+ m1s(i,j)^2*u_a0(i,j)^2...

+ n(i,j)^2-2*n(i,j)^2*S_r(i,j)...




195



u_a0(i,j+1) = u_a0(i,j) + du_a(i,j+1);



u_a_f = [u_a_f, u_a0(i,j)];

v_f = [v_f, v(i,j)];

e_f = [e_f, e(i,j)];


n_f = [n_f, n(i,j)];

m1s_f = [m1s_f, m1s(i,j)];


end




v_ff = [v_ff; v_f];

e_ff = [e_ff; e_f];


n_ff = [n_ff; n_f];



end


A.4 Semi-drained modelling using the SFG model

clc;

clear all;


%SEMI DRAINED WITH SFG


h = [value];


lvp = [value];


Gs = [value];

%initial net stress where N is calculated

p_0 = [value];


N_0 = [value];

%saturation suction

s_sa = [value];


d_sigma = [value];




p_atm = [value];



wc = [values];



%calculating Ns using SFG assumptions and equations (choose one of them)


%for s > s_sa

N(t) = exp(log(N_0) - lvp*log((p_0 + s_sa)/p_0)...

- lvp*(s_sa +1)/(p_0 - 1)*log((suction_0(t)...

+ 1)*(p_0 + s_sa)/(p_0 + suction_0(t))/(s_sa + 1)));

%for s < s_sa

N(t) = exp(log(N_0) - lvp*log((p_0 + s_sa)/p_0) ...

- lvp*(1 - (s_sa + 1)/(suction_0(t) + 1)));

end


sigma_ff = [];

u_a_ff = [];

v_ff = [];

e_ff = [];

S_rff = [];

n_ff = [];

m1s_ff = [];

197

gamma_d_ff = [];




sigma_f = [];

u_a_f = [];

v_f = [];

e_f = [];

S_rf = [];

n_f = [];

m1s_f = [];

gamma_d_f = [];




j = sigma/d_sigma;


u_a0(i,j) = 101.3;

%net stress


%specific volume


%void ratio

e(i,j) = v(i,j) - 1;



%porosity

n(i,j) = e(i,j)/(e(i,j) + 1);



%dry density


if S_r(i,j) >= 0.98;

net_stress(i,j) = net_stress(i,j-1);

v(i,j) = v(i,j-1);

e(i,j) = e(i,j-1);

S_r(i,j) = S_r(i,j-1);

n(i,j) = n(i,j-1);

m1s(i,j) = m1s(i,j-1);

gamma_d(i,j) = gamma_d(i,j-1);

else






+ 2*m1s(i,j)*u_a0(i,j)*n(i,j)...

+ n(i,j)^2*h^2*S_r(i,j)^2 ...


+ 2*n(i,j)^2*h*S_r(i,j)...

- 2* n(i,j)^2*S_r(i,j)^2*h...


+ m1s(i,j)^2*u_a0(i,j)^2...

+ n(i,j)^2-2*n(i,j)^2*S_r(i,j)...






u_a0(i,j+1) = u_a0(i,j) + du_a(i,j+1);

%net stress


%specific volume

v(i,j) = N_s(i) - lvp_s(i)*log(net_stress(i,j)/pc);

%void ration

e(i,j) = v(i,j) - 1;



%porosity

n(i,j) = e(i,j)/(e(i,j) + 1);



%dry density


end;



u_a_f = [u_a_f, u_a0(i,j)];

v_f = [v_f, v(i,j)];

e_f = [e_f, e(i,j)];


n_f = [n_f, n(i,j)];

m1s_f = [m1s_f, m1s(i,j)];


end




v_ff = [v_ff; v_f];

e_ff = [e_ff; e_f];


n_ff = [n_ff; n_f];



end

Appendix B

Publications

Kurucuk, N., Kodikara, J., and Fredlund, D. G., 2009. Evolution of the compaction process:

Experimental study - preliminary results. Unsaturated Soils - Theoretical & Numerical Advances

in Unsaturated Soil Mechanics: Proceedings of the 4th Asia-Pacific Conference on Unsaturated

Soils, pages 887-893, Newcastle, Australia, November 2009.

Kurucuk, N., Kodikara, J., and Fredlund, D. G., 2008. Theoretical modelling of the compaction

curve. Advances in Geo-Engineering: Proceedings of the 1st European Conference, E-UNSAT,

pages 375-379, Durham, United Kingdom, July 2008.

Kurucuk, N., Kodikara, J., and Fredlund, D. G., 2007. Prediction of compaction curves.

Proceedings of the 10th ANZ Conference on Geomechanics, Common Ground, pages 115-119,

Brisbane, Australia, October 2007.

199

200 APPENDIX B. PUBLICATIONS

B.1

114 grouNd improvemeNt

cO

mm

On

gr

Ou

nd

07

Common Ground ProCeedinGs 10th AustrAliA new ZeAlAnd ConferenCe on GeomeChAniCs BrisBAne

cO

mm

On

gr

Ou

nd

07 Prediction of compaction curves

Nurses Kurucuk Faculty of Engineering, Monash University, Clayton, VIC, Australia

Jayantha Kodikara Faculty of Engineering, Monash University, Clayton, VIC, Australia

Delwyn Fredlund Golder Associates, Saskatoon, Saskatchewan, Canada.

Keywords: soil compaction, soil suction, stiffness, unsaturated soil, pore pressure development

ABSTRACT

Compaction of soil is one of the major activities in geotechnical engineering involving earthworks. Compaction curve generally features an inverted parabolic shape and is used to find the optimum water content that maximises dry density. Since its introduction by Proctor in 1933, several researchers have provided qualitative explanations for the general shape of the compaction curve. Furthermore, there is a vast body of literature covering the behaviour of compacted soil. However, fundamental research on the compaction process and the evolution of compaction characteristics are limited. Therefore, in order to understand the driving mechanisms of compaction, this paper investigates the effect of soil suction and stiffness in the shape of the compaction curve, from unsaturated soil mechanics standpoint. On the basis of unsaturated soil mechanics principles, a theoretical prediction of the parabolic shape of the compaction curve is provided.

1 INTRODUCTION

Soil compaction is widely used in geo-engineering and is important for the construction of roads, dams, landfills, airfields, foundations, hydraulic barriers, and ground improvements. Compaction is applied to the soil, with the purpose of finding optimum water content to maximise its dry density, and therefore, to decrease soil’s compressibility, increase its shearing strength, and in some cases, to reduce its permeability. Proper compaction of materials ensures the durability and stability of earthen constructions.

A typical compaction curve presents different densification stages when the soil is compacted with the same apparent energy input but different water contents. The water content at the peak of the curve is called optimum water content (OWC) and represents the water content at which dry density is at its maximum for a given compaction energy.

Since Proctor`s pioneering work in 1933, many researchers have attempted to explain the leading mechanisms in the densification stages, mainly on the dry side of optimum water content. The compaction curve was explained in terms of capillarity and lubrication (Proctor, 1933), viscous water (Hogentogler, 1936), pore pressure theory in unsaturated soils (Hilf, 1956), physico-chemical interactions (Lambe, 1960), and concepts of effective stress theory (Olson, 1963). More recently, Barden & Sides (1970) undertook an experimental research on the relation between the engineering performance of compacted unsaturated clay and microscopic observations of clay structure. In addition, Lee & Suedkamp (1972) conducted research on the shape of the compaction curve for different soils. These works provide predominantly qualitative explanations of the shape of the curve.

Despite this research work, and the importance and high demand for the compaction process in engineering practice, it still remains that the compaction of soil is quite complex and not well explained, particularly from a quantitative sense. Therefore, there is need for research to be undertaken at a fundamental level to understand the compaction characteristics of soil and the inverted parabolic shape of the compaction curve.

This paper presents a theoretical prediction of the compaction curve for sand using unsaturated soil mechanics principles. In order to achieve this aim, approaches developed by Hilf (1948) and Fredlund & Rahardjo (1993) for undrained loading process are simulated. Volume changes of a compacted soil are calculated using the volume change theory from unsaturated soil mechanics, and are used to predict theoretical compaction curves.

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072 MODELLING OF COMPACTION CURVES

2.1 Theoretical background

Theoretical concepts utilized for the development of soil compaction curves are presented in this section. Initially, Hilf’s (1948) and Fredlund & Rahardjo’s (1993) approaches for pore pressure development are presented. This is continued with Fredlund & Morgenstern’s (1976) volume change theory for a compacted soil and the derivation of the dry density of a soil.

2.1.1 Pore pressure development during static compaction

One of the main simulations for the generation of the compaction curve is that of pore pressure development. Hilf (1948) developed a relationship between pore pressure and applied stress, which is based on one-dimensional soil compression, Boyle’s law, and Henry’s law, and is expressed as follows:

0 0 0

0

11

1a y

a a v

uS hS n

u u m

(1)

where; au = change in absolute pore air pressure, 0S = initial degree of saturation, h = coefficient

of solubility, 0n = initial porosity, 0au = initial absolute air pressure, vm = coefficient of volume

change in saturated soil, and y= change in applied vertical stress.

Hilf (1948) developed this equation assuming that air and water phases are undrained, and volume reduction is due to air dissolving in the water and compression of free air. Both liquid and solid parts were considered to be incompressible. He also assumed that the change in pore air pressure is equal to the change in pore water pressure, and therefore, matric suction change was insignificant. These assumptions will be reviewed further in Section 2.2. On the other hand, Fredlund & Rahardjo (1993) developed an equation for undrained loading for pore pressure changes by using pore pressure parameters:

a a yu B (2) w w yu B (3)

where; aB = pore air pressure parameter, wB = pore water pressure parameter, and y= change in


Pore air ( )aB and pore water ( )wB pressure parameters are defined as follows:

2 3 4

1 31aR R RB

R R (4); 2 1 4

1 31wR R RB

R R. (5)

In Equations 4 and 5, 1R , 2R , 3R and 4R are defined as:

2 1 11

2 1 1

/ 1 1 /

/ /

s s sa

s s sw

m m S hS n u mR

m m SnC m (6);

22 1 1

1/ /s s s

w

Rm m SnC m

(7)

2 13

2 1 1

// 1 1 /

a a

a a sa

m mRm m S hS n u m

(8); 4

2 1 1

1/ 1 1 /a a s

a

Rm m S hS n u m

(9)

where; 1sm = compressibility of soil particles with respect to net stress ( )y au , 2

sm =

compressibility of soil particles referenced to suction ( )a wu u , 1am = compressibility of air phase



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am = compressibility of air phase with respect to suction

( )a wu u , au = absolute pore air pressure, S = degree of saturation, h = coefficient of solubility,

n = porosity, and wC = compressibility of water.

This approach assumes that soil particles are incompressible, but the fluid phases are compressible. In contrast to the approach by Hilf (1948), matric suction changes were taken into account. It was accepted that air and water pressures become equal at saturation. Therefore, matric suction will decrease from the initial value to zero at saturation

2.1.2 Computation of volume change and dry density

The volume change constitutive relationship proposed by Fredlund & Morgenstern (1976) for unsaturated soils is used for the calculations of compaction curves, and is expressed as follows:

1 20

( ) ( )s svy a a w

V m u m u uV

(10)

where; vV = overall volume change of a soil element, 0V = initial total volume of the soil element,

1sm = compressibility of soil particles with respect to net stress ( )y au , 2

sm = compressibility of

soil particles referenced to suction ( )a wu u , ( )y au = change in net stress, and ( )a wu u =

change in soil suction.

Since soil particles are incompressible, it is accepted that deformation is primarily due to compression of the pore fluid (i.e., the air and water mixture). The independent stress state variable concept is utilized in the derivation; namely, net stress ( )y au (causes a reduction in

volume with compression), and matric suction stress ( )a wu u (generally results in volume increase with compression). Consequently, overall volume change of the soil sample is calculated by multiplying the right hand side of Equation 10 by the initial volume of the soil sample. Furthermore, the final total volume can be obtained using the volume change of the soil, and this gives the corresponding dry density.

2.2 Estimation of soil compaction curves

Figure 1: Pore air pressure development with applied stress In order to produce compaction curve for a given set of parameters, the pore air pressure development for Hilf`s (1948) and Fredlund & Rahardjo’s (1993) approaches are plotted in Figure 1. The parametric values used in this calculation are given in this figure, and were obtained by

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07consulting graphs given by Fredlund & Rahardjo (1993). It should be noted that Fredlund &

Rahardjo`s (1993) approach takes into consideration the changes in suction with compression, whereas Hilf’s (1948) analysis assumes that the suction change is negligible during compression and suction is equal to the initial matric suction. Therefore, Hilf`s (1948) approach produces larger pore air pressure values than Fredlund & Rahardjo’s (1993) approach for a given applied stress.

Using the volume change equation (Equation 10) and air pressure computed with applied stress (Figure 1), compaction curves are produced for both approaches as shown in Figure 2. In Figure 2 compressibility coefficients are assumed to be constant and their values are given on the figure. It should be noted that compaction curve which is plotted using Hilf’s (1948) approach does not include the suction component of volume change theory (or assumed m2

s is assumed equal to zero in Equation 10).

Figure 2: Compaction curves for constant coefficient of compressibility

It is clear that using constant compressibility coefficients (mv, m1s, m2

s, in fact it can be shown that mv=m1

s) a reasonable shape for the compaction curve can be produced on the wet side of OWC, but not on the dry side of OWC. Moreover, suction change that is included in Fredlund & Rahardjo’s (1993) approach results in some reduction in dry density, but does not change the shape of the compaction curve at lower water contents. In order to examine the likely suction change during compaction, consideration is given to the experimental results produced by Montanez (2002), as shown in Figure 3. Montanez (2002) produced suction contours for compacted sand-bentonite mixtures associated with domains defined by compaction curves at various apparent energy levels. He found that matric suction only decreases marginally with a density increase and in many cases can be considered constant. Therefore, Hilf’s analysis of assuming constant suction during compaction appears to be close to the real situation, but direct data measured during the compaction process may be useful to validate this assumption.

1.90

2 6

Contours of equal suction

Water content (%)

Dry

den

sity

( M

g/m

)

4 8 1210 1614 2018 2422 2826

1.80

1.70

1.60

1.50

1.40

3

Compaction energyHeavyStandard

5153

kPa

1498

kPa

780

kPa

374

kPa

182

kPa

84 k

Pa

Sr = 100%

Figure 3: Data for uniform sand-bentonite (10%) mixture (adopted from Montanez, 2002)



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07 Furthermore, even if there is a small reduction in suction with compaction, m2

s applicable to the unloading process can be considered smaller than that applicable to loading process. Therefore, the effect of the suction component (as in the second component of Equation 10) can be considered not very significant. With this insight, the focus on the compaction process falls on the coefficient of soil compressibility due to net stress, m1

s. In the following part of the paper, the influence of coefficient of compressibility due to net stress (m1

s) on the shape of the compaction curve is presented. Direct data related to the variation of m1

s with saturation are not available. However, some insight can be gained from the shear-wave velocity measured by Cho & Santamarina (2001) in granite powder at various saturations, shown in Figure 4, to explain the relationship between m1

s

and degree of saturation.

Figure 4: Shear-wave velocity data for granite powder (adopted from Cho & Santamarina, 2001)

It is clear from Figure 4 that the shear-wave velocity sV , hence shear modulus 2sG = V of the

soil increases with decreasing saturation (or conversely soil compressibility decreases). Therefore, it can be argued that m1

s will decrease with decreasing saturation in some form. On this basis, a relationship between m1

s and degree of saturation is plotted as shown in Figure 5.

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s values with initial degree of saturation When the variation of m1

s with degree of saturation is taken into account, the resulting compaction curves are shown in Figure 6. Clearly, now the proper shape of the compaction curve can be produced. Moreover, it is clear that the dependency of compaction curves at different stress levels (or energy input) is reasonably well captured, where optimum water content shifts to the right with higher stress levels.

Figure 6: Compaction curves for different energy levels

3 CONCLUSIONS

This paper presents the theoretical concepts related to the prediction of the compaction curve. For the first time, it highlights the fact that shape of the compaction curve can be predicted using unsaturated soil mechanics principles. The main insight gained was that the changes in matric suction is not important for the evolution of the compaction states, but that the influence of matric suction on the material compressibility with respect to net stress is the governing factor determining the compaction density. Therefore, it can be reasoned that the inverted parabolic shape of the compaction curves is a direct function of the variation of the material compressibility with degree of saturation. More research, however, is necessary to reinforce these concepts.

REFERENCES

Barden, L., and Sides, G. R. (1970), Engineering behaviour and structure of compacted clay, Journal Soil Mechanics and Foundations Division, ASCE, 96, No. SM4, 1171. Cho, G. C., and Santamarina, J. C. (2001), Unsaturated particulated materials – Particle level studies, Journal of Geotechnical and Geoenvironmental Engineering, 127(1), 84-96. Fredlund, D. G., and Morgenstern, N. R. (1976), Constitutive relations for volume change in unsaturated soils, Canadian Geotechnical Journal, 14, 3, 261-276. Fredlund, D. G., and Rahardjo, H. (1993), Soil mechanics for unsaturated soils, p. 191-194, John Wiley & Sons. Hilf, J. W. (1956), An Investigation of Pore Water Pressures in Compacted Cohesive Soils, Technical Memorandum 654, U. S. Department of the Interior, Bureau of Reclamation, Denver, Colorado. Hogentogler, C. A. (1936), Essentials of soil compaction, Proceedings Highway Research Board, National Research Council, Washington, D.C., 309-316. Lambe, T. W. (1960), Structure of compacted clay, Transactions, ASCE, 125, 682-705. Lee, D. Y., and Suedkamp, R. J. (1972), Characteristics of irregularly shaped compaction curves of soil, Highway Research Board, 381, 1-9. Montanez, J. E. C. (2002), Suction and volume changes of compacted sand-bentonite mixtures, PhD thesis, University of London, Imperial College of Science, London, England. Olson, R. E. (1963), Effective stress theory of soil compaction, Journal Soil Mechanics and Foundations Division, ASCE, 89, No. SM2, 27-45. Proctor, R. R. (1933), Fundamental Principles of Soil Compaction, Engineering News-Record, 111,286.


B.2

Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds)© 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8

Theoretical modelling of the compaction curve

N. Kurucuk & J. KodikaraDepartment of Civil Engineering, Faculty of Engineering, Monash University, Clayton, VIC, Australia

D.G. FredlundGolder Associates, Saskatoon, Saskatchewan, Canada

ABSTRACT: Soil compaction is one of the major activities in geotechnical engineering involving earthworks.The compaction curve is used to find the optimumwater content thatmaximizes dry density. Since its introductionby Proctor in 1933, several researchers have provided qualitative explanations for the inverted parabolic shapeof the compaction curve. However, fundamental research on the compaction process and the evolution ofcompaction characteristics are limited, particularly from a quantitative sense. In order to understand the drivingmechanisms of soil compaction, this paper investigates the effect of soil suction, stiffness and pore air pressureon the shape of the compaction curve, from an unsaturated soil mechanics standpoint. This paper presents anapproach to predict the soil compaction curve during undrained loading. Particular attention is focused on thederivation of the compressibility coefficient due to net stress. Model predictions of the compaction curve arecompared with some experimental results from the literature.

1 INTRODUCTION

Soil compaction is widely used in geo-engineeringand is important for the construction of roads, dams,landfills, airfields, foundations, hydraulic barriers,and ground improvements. Compaction is applied tothe soil, with the purpose of finding optimum watercontent in order to maximize its dry density, and there-fore, to decrease compressibility, increase shearingstrength, and in some cases, to reduce permeability.Proper compaction of materials ensures the durabilityand stability of earthen constructions.A typical compaction curve presents different den-

sification stages when the soil is compacted with thesame apparent energy input but different water con-tents. The water content at the peak of the curve iscalled the optimum water content (OWC) and repre-sents the water content at which dry density is at itsmaximum for a given compaction energy.Since Proctor’s pioneering work in 1933, many

researchers have attempted to explain qualitativelythe leading mechanisms in the densification stages,mainly on the dry side of optimum water content. Thecompaction curvewas explained in terms of capillarityand lubrication (Proctor, 1933), viscouswater (Hogen-togler, 1936), pore pressure theory in unsaturated soils(Hilf, 1956), physico-chemical interactions (Lambe,1960), and concepts of effective stress theory (Olson,1963). More recently, Barden & Sides (1970) under-took experimental research on the relation between the

engineering performance of compacted unsaturatedclay andmicroscopic observations of clay structure. Inaddition, Lee & Suedkamp (1972) conducted researchon the shape of the compaction curve for differentsoils.Despite this research work, and the importance and

high demand for the compaction process in engineer-ing practice, the compaction of soil is quite complexand notwell explained, particularly from a quantitativesense. Theoretical modelling of the soil compactioncurve will provide a better understanding of the mainparameters that affect the shape of the compactioncurve, and understanding the behaviour of compactedmaterials. Therefore, there is need for research tobe undertaken at a fundamental level to understandthe compaction characteristics of soil and the invertedparabolic shape of the compaction curve.This paper presents a theoretical explanation of the

compaction curve using unsaturated soil mechanicsprinciples. Particular attention is focused on the pre-diction of the compressibility coefficient due to netstress. Likely predictions of the model are comparedwith the experimental results from literature.

2 THEORETICAL BACKGROUNDFOR MODELLING

Theoretical concepts utilized for the development ofsoil compaction curves are presented in this section.

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207

Initially, Hilf’s (1948) approach for pore pressuredevelopment is presented. This is continued withFredlund &Morgenstern’s (1976) volume change the-ory for a compacted soil and the derivation of the drydensity of soil.

2.1 Pore pressure development during staticcompaction

One of the main simulations for the generation of thecompaction curve is that of pore pressure develop-ment. Hilf (1948) developed a relationship betweenpore pressure and applied stress, which is based onone-dimensional K0 soil compression, Boyle’s law,and Henry’s law, and is expressed as follows:

ua =1

1 + (1− S0+ hS0)n0(ua0+ ua)mv

σ y (1)

where; ua = change in absolute pore air pressure,S0 = initial degree of saturation, h = coefficient ofsolubility, n0 = initial porosity, ua0 = initial absoluteair pressure, mv = coefficient of volume change insaturated soil, and σy = change in applied verticalstress.Hilf (1948) developed this equation assuming that

air and water phases are undrained, and volumereduction is due to air dissolving in the water andcompression of free air. Both liquid and solid partswere considered to be volumetrically incompressible.Hilf also assumed that the change in pore air pres-sure is equal to the change in pore water pressure,and therefore, matric suction change was insignifi-cant. Experimental results on suction change duringcompaction can be found in literature (e.g. Li 1995,Montanez 2002). It is shown that matric suction onlydecreases marginally with a density increase and maybe approximated to be constant. Therefore, Hilf’sanalysis assuming constant suction during compactionappears to be close to the real situation. Further justifi-cation for assuming constant matric suction during thecompaction test is presented in Kurucuk et al. (2007).

2.2 Computation of volume change and dry density

The volume change constitutive relationship as appli-cable to K0 loading, which is defined in termsof two independent stress variables as proposed byFredlund &Morgenstern (1976) for unsaturated soils,is used for the calculation of compaction curves:

εv =VvV

= ms1 σy − ua + ms2 (ua − uw) (2)

where; εv = volumetric strain, Vv = overall volumechange of soil element, V = initial total volume of soil

element, ms1 = compressibility of soil particles with

respect to net stress (σy − ua), ms2 = compressibility

of soil particles referenced to matric suction (ua− uw),( σy − ua) = change in net stress, and ( ua − uw) =change in soil suction.Since soil particles are incompressible, it is

accepted that deformation is primarily due to compres-sion of the pore fluid (i.e., the air and air/water mix-ture). The independent stress state variable concept isutilized in the derivation; namely, net stress (σy − ua)(causes a reduction in volume with compression), andmatric suction stress (ua − uw) (generally results involume increase with compression). Once the overallvolume change is computed, the corresponding drydensity can be easily computed.

3 MODELLING ASSUMPTIONS

Kurucuk et al. (2007) showed that the assumptionof constant coefficients of compressibility duringcompaction does not produce a proper shape of thecompaction curve especially on the dry side of theoptimum water content. Their analysis showed that itis ms

1 that controls the volume changes during com-paction because the associated change in suction maybe neglected. The parameter ms

1 was represented as afunction of saturation and decreases with decreasingsaturation. However, the experimental results pre-sented by Loret et al. (2003) showed that ms

1 decreasedwith both suction and net stress. Therefore, followingthe functional form suggested by Sheng et al. (2007),the volumetric strain, ignoring suction change, may bepresented as:

εv =dV

V= λvp

d (σnet − ua)

(σnet − ua) + s0(3)

where; εv = volumetric strain, (σnet− ua) = mean netstress, ua = pore air pressure, s0 = suction, λvp =slope of the normal compression line (NCL) of thesaturated soil, and V = initial total volume of the soilelement.This gives ms

1 as:

ms1 =λvp

σy − ua + s0(4)

This assumption will be used and discussed furtherin the modelling of the compaction curve. It is reason-able to replace mv in Equation 1 by ms

1. A numericalexample of the variation ofms

1 during compaction pro-cess is given in the following section. Equations (1),(3) and (4) were used in incremental forms to com-pute the incremental and total volume change and thecorresponding dry density values during compaction.

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4 NUMERICAL EXAMPLES

The performance of the proposed model is demon-strated by comparing the experimental results pre-sented by Montanez (2002) and Kenai et al. (2006).Figures 1 and 2 show the compaction curves for sand-bentonite mixture with bentonite content of 5% and15% by weight. Montanez’s experimental data presentvalues for theStandardProctorTest (BS, external grossenergy input = 637 kJ/m3 or kPa). In Figures 1 and2, two model predictions are also shown. The curvesshown by dashed lines represent the static compactioncurve predicted by the model for undrained (air/water)loading up to external quasi-static pressure, σy, of637 kPa. The curves shown by solid lines are for equalenergy input, calculated by integrating the appliedstress σy with respect to volumetric strain. The actualenergy input into the soil was computed on the basisof the values applicable at the optimum water con-tent, which were found to be 16 kJ/m3 and 18 kJ/m3

respectively.

Figure 1. Comparison of predicted and experimental com-paction curves for well graded sand with 5% bentonite (afterMontanez, 2002).

Figure 2. Comparison of predicted and experimental com-paction curves for well graded sandwith 15%bentonite (afterMontanez, 2002).

Figure 3 shows an example of compaction curvefor clay sandy soil (liquid limit = 39%, plasticityindex = 15%) adopted from Kenai et al. (2006).Experimental results shown in figure are for static(σy = 2100 kPa) and dynamic (external gross energyinput 3000 kJ/m3) compaction tests. Both predictedcompaction curves are produced from quasi-staticcompaction up to external pressures, σy, of 2100 kPaand 4000 kPa respectively.

Model parameters used for prediction of the abovecompaction curves are shown in Table 1, 2 and 3.Initial pore air pressure (ua0) is taken to be equalto atmospheric pressure (101.3 kPa). For a certainsoil, a lower initial porosity was assumed and thecomputations were performed for a range of mois-ture contents which also define the values of initialdegree of saturation (S0). The water solubility value isadopted from Fredlund & Rahardjo (1993). The val-ues of λvp (slope of the NCL) are selected to best fitthe experimental results and compared with the mea-sured values from literature. These values are foundto be generally in the range of experimentally mea-sured values. Table 2 shows the initial equilibriumsuctions measured for compacted specimens at differ-entmoisture contents given byMontanez (2002). Theyare presented as constant suction contours which are

Figure 3. Comparison of predicted and experimental com-paction curves for clay sandy soil (after Kenai et al., 2006).

Table 1. Parameter values for the proposed model.

Well graded sand with Well graded sand5% bentonite with 15% bentonite

Parameter Value Value

h∗ 0.02 0.02λvp 0.045 0.13n0 34 % 36 %Gs 2.656 2.660

∗Water solubility

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Table 2. Initial matric suction (s0) values.

Well graded sand with Well graded sand with5% bentonite content 15% bentonite content

w (%) s0 (kPa) w (%) s0 (kPa)

3.9 4630 4.9 178005.8 1130 6.4 115007.8 350 8.5 25509.7 130 10.6 126011.7 54 12.7 85013.6 32 14.9 53015.6 26 17.0 29017.5 22 19.1 270

Table 3. Parameter values for the proposed model.

Clay sandy soil

Parameter Value

h∗ 0.02λvp 1.3n0 46 %Gs 2.66

generally perpendicular to the water content axis giv-ing approximately constant suction values for a givencompaction water content. This ignores the curving ofthese contours close to saturation towards the left even-tually becoming almost parallel to the full saturationline.

Figures 1 and 2 show comparisons between exper-imental and predicted values of compaction curvesfor sand-bentonite mixtures. The experiments wereperformed under dynamic conditions (Proctor com-paction), whereas model prediction assumed staticundrained conditions for both air and water. Despitethese differences, it is clear that reasonable predictionsof the shape of the compaction curve can be obtainedwith the proposed approach.

Figure 3 shows comparison between experimen-tal and predicted values of the compaction curve forsandy clay soil. For this example, experiments wereperformed under both dynamic and static conditions.It should be noted that in this example, experimentalresults did not include the initial suction values. There-fore, initial suction values are assumed to be same aswell graded sand with 15% bentonite (Table 2).

Differences in the predicted and experimentalbehaviour can be traced to a number of sources. Onepossibility is the drainage of air, particularly on thedry side of the optimum, which can lead to higherdry densities. This analysis, however, shows that the

Figure 4. Variations of ms1 with initial degree of saturation

(S0) and during compaction for well graded sand with 5%bentonite.

development of air pressure on the dry side is not verysignificant, but will depend on ms

1. It can be seen thatthe predicted and experimental density difference onFigure 1 is higher than that of Figure 2. In additionto the likely influence of the other assumptions madein the analysis, this difference seems to indicate thatthe drainage of air may lead to higher densities in thedry side. It is likely that the pore sizes in well gradedsandwith 5%bentonite content is higher than the samesand with 15% bentonite. These issues will be furtherexamined through future targeted experiments.

Figure 4 shows the variation of ms1 with initial

degree of saturation (S0) and during compaction forthe well graded sand with 5% bentonite content. It canbe seen that coefficient of compressibility due to netstress (ms

1) decreases with decreasing initial degreeof saturation (S0), as assumed previously by Kuru-cuk et al. (2007). However, during the compactionprocess, the degree of saturation increases from the ini-tial value, but the coefficient of compressibility (ms

1)decreases. This decrease of compressibility happensowing to the increase of net stress as the compactionprogresses. It is also apparent that much of the com-paction takes place in the early part of the processwhere the soil compressibility decreases rapidly.

5 CONCLUSION

This paper presents theoretical concepts to predictthe compaction curve for soil during undrained K0or isotropic loading using unsaturated soil mechan-ics principles. It highlights the fact that the well-known inverted parabolic shape of the compactioncurve may be theoretically predicted using unsatu-rated soil mechanics principles, arguably for the firsttime in literature. This was demonstrated using pub-lished experimental results, but it was necessary tomake some assumptions. The controlling parameter

378


governing the compaction process was identified asthe coefficient of compressibility with respect to netstress or ms1. It was also identified that the variationin drainage conditions during compaction may influ-ence the results. Future experiments will be targetedto develop a comprehensive set of data to examinethe modelling assumptions and improve modellingcapability.

ACKNOWLEDGEMENTS

Thanks are rendered to Monash University for pro-viding a Monash Graduate Scholarship and financialassistance to the first author for her PhD candidature.

REFERENCES

Barden, L. & Sides, G.R. 1970. Engineering behaviour andstructure of compacted clay. Journal Soil Mechanics andFoundations Division, ASCE, 96, No. SM4: 1171.

Fredlund, D.G. & Rahardjo, H. 1993. Soil mechanics forunsaturated soils. John Wiley & Sons, Inc.

Fredlund, D.G. & Morgenstern, N.R. 1976. Constitutiverelations for volume change in unsaturated soils. CanadianGeotechnical Journal, 14, 3: 261–276.

Hilf, J.W. 1948. Estimating construction pore pressuresin rolled earth dams. Proceedings of 2nd InternationalConference in Soil Mechanics and Foundation Engineer-ing, 3: 234–240. Rotterdam, The Netherlands.

Hilf, J.W. 1956. An investigation of pore water pressures incompacted cohesive soils. Technical Memorandum 654,U.S. Department of the Interior, Bureau of Reclamation,Denver, Colorado.

Hogentogler, C.A. 1936. Essentials of soil compaction.ProceedingsHighwayResearchBoard, National ResearchCouncil, Washington, D.C., 309–316.

Kenai, S., Bahar, R. & Benazzoug, M. 2006. Experimentalanalysis of the effect of some compaction methods onmechanical properties and durability of cement stabilizedsoil. Journal of Material Science, 41: 6956–6964.

Kurucuk, N., Kodikara, J. & Fredlund, D.G. 2007. Pre-diction of compaction curves. 10th ANZ Conference onGeomechanics, 2: 115–119.

Lambe, T.W. 1960. Structure of compacted clay. Transac-tions, ASCE, 125: 682–705.

Lee, D.Y. & Suedkamp, R.J. 1972. Characteristics of irregu-larly shaped compaction curves of soil. HighwayResearchBoard, 381: 1–9.

Li, Z.M. 1995. Compressibility and collapsibility of com-pacted unsaturated loessial soils. Unsaturated Soils. Proc.1st Int. Conf. on Unsaturated Soils (UNSAT 95), Paris,France (ed. Alonzo, E.E. and Delage, P.), Rotterdam:Balkema, Vol. 1: 139–144.

Lloret, A., Villar, M.V., Sanchez, M., Gens, A., Pintado, X.& Alonso, E.E. 2003. Mechanical behaviour of heav-ily compacted bentonite under high suction changes.Géotechnique, 53(1): 27–40.

Montanez, J.E.C. 2002. Suction and volume changes of com-pacted sand-bentonite mixtures. PhD thesis, University ofLondon, Imperial College of Science, London, England.

Olson, R.E. 1963. Effective stress theory of soil compaction.Journal SoilMechanics and FoundationsDivision, ASCE,89, No. SM2: 27–45.

Proctor, R.R. 1933. Fundamental Principles of Soil Com-paction, Engineering News-Record, 111: 286.

Sheng, D., Fredlund, D.G. & Gens, A. 2007. A new mod-elling approach for unsaturated soils using independentstress state variables. Research Report No. 261.11.06,University of Newcastle, NSW 2308, Australia.

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B.3

Unsaturated Soils – Buzzi, Fityus & Sheng (eds)© 2010 Taylor & Francis Group, London, ISBN 978-0-415-80480-6

Evolution of the compaction process: Experimental study – preliminaryresults

N. Kurucuk & J. KodikaraDepartment of Civil Engineering, Faculty of Engineering, Monash University, Clayton, Australia

D.G. FredlundGolder Associates, Saskatoon, Canada

ABSTRACT: Fundamental research on the compaction characteristics and the evolution of the compactionprocess is limited in literature, particularly froma quantitative standpoint. Improved understanding of unsaturatedsoil mechanics over the last few decades has allowed more detailed study of the driving mechanism of thecompaction process. This paper presents an approach to predict the soil compaction curve during static loadingusing unsaturated soil mechanics principles. Particular attention is given to the effect of suction on the overallcompaction process. The results obtained by the model are compared with the experimental results obtainedusing a special oedometer. Sand-bentonite mixtures were prepared with a range of initial water contents. Thesoils were statically compacted in the special oedometer. Soil samples were compacted with vertical stressesranging between 80 kPa and 1600 kPa. The initial suction was measured and controlled using the axis translationtechnique. A pressure transducer was also installed on the lower part of oedometer and was connected to thewater under the ceramic disk. It was possible to measure pore-water pressure changes (and therefore suctionchanges) during the loading process. Some results are presented and discussed in the paper.

1 INTRODUCTION

Soil compaction is widely used in geo-engineeringand is important for the construction of roads, dams,landfills, airfields, foundations, hydraulic barriers,and ground improvements. Compaction is appliedto the soil with the purpose of finding the optimumwater content corresponding to themaximum dry den-sity. Compaction decreases the soil’s compressibility,increases its shearing strength, and in some cases,reduces its permeability. Proper compaction of mate-rials ensures the durability and stability of earthenstructures.A typical compaction curve presents different den-

sification stages when the soil is compacted withthe same apparent energy input but different ini-tial water contents. The water content at the peakof the curve is called the optimum water content(OWC) and represents the water content at whichdry density is a maximum for a given compactionenergy.Since Proctor’s pioneering work in 1933, many

researchers have attempted to explain qualitativelythe leading mechanisms in the densification stages,mainly on the dry side of optimum water content.The compaction curve has been explained in termsof capillarity and lubrication (Proctor, 1933), vis-cous water (Hogentogler, 1936), pore pressure theory

in unsaturated soils (Hilf, 1956), physico-chemicalinteractions (Lambe, 1960), and the concept of effec-tive stress theory (Olson, 1963). More recently,Barden & Sides (1970) undertook an experimentalstudy on the relationship between engineering perfor-mance of compacted unsaturated clay andmicroscopicobservations of clay structure. Lee&Suedkamp (1972)also conducted research on the shape of the com-paction curve for different soils.Despite this research work, and the importance and

high usage of the compaction process in engineeringpractice, it still remains that the compaction of soilis quite complex and not well explained, particularlyfrom a quantitative standpoint. Theoretical modelingof soil compaction can provide a better understandingof themain parameters that affect the shape of the com-paction curve. It will also provide a better understand-ing of the behavior of compactedmaterials. Therefore,there is need for research to be performed at a funda-mental level in order to understand the compactioncharacteristics of soil and the inverted parabolic shapeof the compaction curve.An approach to predict the soil compaction curve

during static loading was developed and presented inprevious works by the authors (Kurucuk et al., 2007and Kurucuk et al., 2008). The approach was sup-ported by data from the literature. This paper presentsan experimental study conducted in order to compare

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with the proposedmodel. Predictions by the model arecompared with the experimental data presented in thispaper.

2 FORMULATION OF THE MODEL

Theoretical concepts utilized for the development ofsoil compaction curves are presented in this section.Initially, Hilf’s (1948) approach for pore pressuredevelopment is presented and this is followed withthe Fredlund & Morgenstern’s (1976) volume changetheory for a compacted soil.

2.1 Pore pressure development during staticcompaction

One of the primary aspects associated with the gen-eration of the compaction curve is the simulation ofpore pressure development. Hilf (1948) developed arelationship between pore pressure and applied stress,which is based on one-dimensional K0 soil compres-sion, Boyle’s law, and Henry’s law, and is expressed asfollows:

ua =1

1 +(1 − S0 + hS0) n0(ua0 + ua)mv

σ y (1)

where; ua = change in absolute pore air pressure,S0 = initial degree of saturation, h = coefficient ofsolubility, n0 = initial porosity, ua0 = initial absoluteair pressure, mv = coefficient of volume change insaturated soil, and σ y = change in applied verticalstress.Hilf (1948) developed this equation assuming that

air and water phases were undrained, and volumereduction was due to air dissolving in the water andthe compression of free air. Both liquid and solidphases were considered to be volumetrically incom-pressible. It was also assumed that the change in poreair pressure was equal to the change in pore waterpressure, and therefore, matric suction change wasinsignificant. Experimental results on suction changeduring compaction can be found in literature (e.g., Li,1995; Montanez, 2002). It is shown that matric suc-tion only decreases marginally with a density increaseand may be approximated as a constant value. There-fore, Hilf’s assumption that suction remains constantduring compaction appears to be close to the reality.Further justification for assuming that suction remainsconstant during compaction test has been presented inKurucuk et al. (2007).

2.2 Computation of volume change and dry density

The volume change constitutive relationship corre-sponding to K0 loading can be defined in terms of two

independent stress variables as proposed byFredlund &Morgenstern (1976) for unsaturated soils.The relationship will be used for the calculationsassociated with the compaction curves:

εv =VvV

= ms1( σ y − ua) + ms2 (ua − uw) (2)

where; εv = volumetric strain, Vv = overall volumechange of soil element, V = initial total volume of soilelement, ms1 = compressibility of soil particles withrespect to net stress (σy − ua), ms2 = compressibilityof soil particles referenced to matric suction (ua− uw),( σ y − ua) = change in net stress, and ( ua − uw) =change in soil suction.Since soil particles are incompressible, it is accepted

that deformation is primarily due to compression ofthe pore fluid (i.e., the air and air/water mixture). Theindependent stress state variable concept is utilized inthe derivation; namely, net stress (σy − ua) (causes areduction in volume with compression), and matricsuction stress (ua − uw) (generally results in volumeincrease with compression). Once the overall volumechange is computed, the corresponding dry densitycan be computed.

2.3 Modelling assumptions

Kurucuk et al. (2007) showed that the assumptionof a constant coefficient of compressibility duringcompaction does not produce a proper shape of thecompaction curve, particularly on the dry side of opti-mum water content. The analysis showed that it iswas ms1 that controlled volume changes during com-paction because the associated change in suction maybe neglected. The parameter ms1 was represented as afunction of saturation and decreased with decreasingsaturation. However, the experimental results pre-sented byLloret et al. (2003) showed thatms1 decreasedwith both suction and net stress. Therefore, followingthe functional form suggested by Sheng et al. (2008),the volumetric strain, ignoring suction change, can bepresented as:

εv =dV

V= λvp

d (σnet − ua)

(σnet − ua) + s0(3)

where; εv = volumetric strain, (σnet − ua) = meannet stress, ua = pore air pressure, s0 = suction, λvp =slope of the normal compression line (NCL) of thesaturated soil, and V = initial total volume of the soilelement.This gives the following equation for ms1 as:

ms1 =λvp

(σy − ua) + s0(4)

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This assumption will be used and discussed furtherin the modeling of the compaction curve. It is reason-able to replacemv in Equation 1 withms1. A numericalexample of the variation of ms1 during the compactionprocess is given in the following section. Equations(1), (3) and (4) were used in incremental forms to com-pute the incremental and total volume change and thecorresponding dry density values during compaction.

3 EXPERIMENTAL PROGRAM

Experimental tests were performed in a specialoedometer for comparison with the model predictions.Material characteristics, the experimental device,details of the performed tests and the steps followedare explained in the following sections.

3.1 Material characteristics

The material selected for this research is a sand-bentonite mixture. Bentonite in the amount of 2% byweight was mixed with poorly graded sand to producea material with some fines. The fines allow the genera-tion of higher initial suctions. The amount of bentonitemixed with sand is unlikely to produce some swellingin the soil sample (sand particles are in contact evenfor high water contents) (Montanez, 2002). Particlesize distributions (PSD) for the sand and bentonite areshown in Figures 1 and 2.

The bentonite used for the experiments is commer-cially available as ActiveGel 150 bentonite. Atterberglimits of this clay are given in Table 1.

The specific gravity of the sand, bentonite and themixture was measured using a pycnometer (Micro-meritics AccuPyc 1330). Measured values are pre-sented in Table 2.

Dynamic compaction tests were conducted accord-ing to the procedures described in Australian Standards(AS 1289.5.1.1-2003). Figure 3 shows the compactioncurve of sand-bentonite mixture.

0

10

20

30

40

50

60

70

80

90

100

0.010.11

Diameter (mm)

% P

ass

ing Cu = 1.71

Cc = 1.07

Figure 1. PSD for sand.

0

10

20

30

40

50

60

70

80

90

100

1101001000

Particle Size ( m)

%P

assi

ng

Figure 2. PSD for bentonite (adopted from Shannon, 2008).

Table 1. Atterberg limits.

Liquid limit (%) 550Plastic limit (%) 36Plasticity index (%) 514

Table 2. Specific gravity of the soil.

Soil type Gs

Sand (SP) 2.65Bentonite 2.69Mixture 2.65

1.66

1.68

1.70

1.72

1.74

1.76

2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0

Water content (%)

Dry

den

sity

(t/

m3)

Sr = 80%

Figure 3. Standard compaction curve of sand-bentonitemixture.

3.2 Material preparation

Sand and bentonite were mixed in an air dry statewith a mixer for 15 minutes initially. The desiredamount of water was then added and mixed for another20 minutes to evenly distribute the moisture. The mix-ture was then wrapped with several layers of plasticwrap and aluminum foil. All the samples were placedin air tight plastic zip bags and stored in contain-ers in the moisture room for a minimum of 28 days.Montanez (2002) conducted a study to investigate theinfluence of the hydration time on the soil specimens.

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He stated that it is necessary to allow a minimumperiod of 28 days for hydration in order to establish anequal distribution of suction within the material.

3.3 Experimental apparatus

Static compaction experiments were conducted withFredlund’s SWCCDevice (Figure 4). Devicewasmod-ified by adding pressure transducer to the bottom ofthe plate (below the ceramic disk) in order to conductthe desired experiments (i.e., constant water contenttest). A Druck—PDCR 4011 pressure transducer wasused. This modification helped to measure the initialsuction values of the prepared specimens and alsomea-sure changes in suction with loading. Volume changesin the specimen were tracked using a linear variabledifferential transformer (LVDT-KYOWADTH-A-10).

3.4 Methods

Hydrated soil samples were placed in a metal ring byhand tapping (loose) to ensure similar initial void ratiosfor all samples prepared with different water contents.The metal ring with soil was then placed after on theceramic disk inside the experimental device.Before starting the loading process, the initial suc-

tion of the soil specimen was measured. Air pressurewas applied to the specimen and the water pressurebelow the ceramic disk was monitored with the helpof the pressure transducer. The applied air pressurewas gradually changed after equilibrium was reached(i.e., there was no changes in water pressure below theceramic disk). Final water pressure values are plottedagainst the applied air pressure. The function of thiscurve is a 45◦ line (taking into account theHilf’s (1948)approach for undrained systems, ua = uw). Theinitial suction was determened from the intersection ofthe curve with the abscissa of the graph (Fredlund &Rahardjo, 1993).

Figure 4. Experimental SWCC pressure plate device.

Table 3. Loading steps.

Load (kPa) No of increments Increment (kPa)

0− 640 8 80640− 1280 4 1601280− 2250 3 320

uu a-u w

Figure 5. Stress path followed (constant water content test)(small suction change is exaggerated).

Table 4. Suction change in first load-ing step for different water contents.

Water content (%) ( ua − uw) (kPa)

6 1.18 0.810 0.3

Soil samples were statically compacted using ver-tical stresses ranging between 80 kPa and 2250 kPa.Loading steps followed are given in the Table 3. Theduration of the loading time was changed according tothe time required at each step for stabilization of thesuction and volume change. There are similar loadingrate approaches presented in the literature (e.g., Tanget al., 2008).Figure 5 shows the stress path followed during the

compression process. Since the tests conducted areconstant water content tests, there should be a decreasein suction with increasing net stress. However, con-sidering the soil type used and taking into account theexperimental results, it is noted that the change in suc-tion with loading is very small (Table 4). Moreover,suction changes can only be seen in the first loadingstep and suction stays constant during the followingloading steps. Therefore, as stated in Section 2.3, itappears to be acceptable to assume the suction remainsconstant with loading. In addition during loading, the

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soil passes through plastic yielding with the increase ofthe yield stress concurrently with the applied loading.

4 RESULTS AND DISCUSSION

Results from the conducted experiments are presentedin this section. These results are compared with thepredictions produced by the proposed model.

4.1 Conducted experiments

Static undrained (water) compaction tests were con-ducted on 5 samples with different water contents andsimilar initial densities. The properties of the spec-imens prepared for static compaction test are givenin Table 5. The water content of each specimen wasmeasured before and after the test and also presentedin Table 5. It is clear that the water contents remainedalmost constant during the tests (Note: it is a constantwater content test but during the preparation or dis-mantling stage the specimen might take on water fromthe ceramic disk).

Specimens prepared with 6% and 8% water contentwere tested two times in order to ensure the repeatabil-ity of the test. An important point to be noted here isthat every sample was assumed to be identical but therewere slight differences in initial properties (Table 5),which would present some dissimilarity between tests.Taking into account this fact, the results show that thetests were repeatable.

4.2 Test results

Figure 6 shows the changes in specific volume(1 + e) with net stress (σy − ua). It can be seen thatthere is a general trend that specific volume is lowerfor soils with a higher water contents.

The variation of coefficient of compressibility (ms1)

with net stress is shown in the following figure(Figure 7). The compressibility coefficient (ms

1)increases with increasing water content at a particularnet stress. For example, the highest coefficient of com-pressibility at 1000 kPa net stress is for the specimen

Table 5. Specimen properties.

Water contentInitial drydensity Before test After test Suction

Test (t/m3) (%) (%) (kPa)

Test1 (6%) 1.44 5.56 6.93 7.5Test1 (8%) 1.46 7.62 8.37 5.34Test1 (10%) 1.46 9.82 10.67 4.95

1.6

1.65

1.7

1.75

1.8

1.85

1.9

1 10 100 1000 10000

Net Stress + Suction (kPa)

Sp

ecif

ic v

olu

me

test1 (6%)test1 (8%)test1 (10%)

Figure 6. Changes in specific volume with loading andwater content.

0.0E+00

2.0E-05

4.0E-05

6.0E-05

8.0E-05

1.0E-04

1.2E-04

1.4E-04

1.6E-04

1.8E-04

2.0E-04

0 500 1000 1500 2000 2500

Net Stress (kPa)

m1s

-co

eff.

of

com

p. (

1/kP

a) test1 (6%)test1 (8%)test1 (10%)

Figure 7. Changes in ms1 with loading and water content.

prepared with 10% water content and the lowest coef-ficient of compressibility is for the specimen preparedwith 6% water content.

Figure 8 presents the changes in slope of the com-pression curve (λ) with net stress (σy − ua). The slopeof the compression (λ) curve is again higher for higherwater contents. Moreover, the slope has a tendency todecrease with increasing net stress (σy − ua) exceptat higher stresses at which slope tends to increaseagain. The slope of the compression line (λ) is alsodecreasing with an increasing suction (ua −uw) for thesame net stress (σy −ua). This observation is in agree-ment with the model proposed by Alonso et al. (1990),generally referred as Barcelona Basic Model (BBM),and Sheng et al. (2008). Some researchers have indi-cated an increase in slope with increasing suction (e.g.Monroy et al., 2008) and some point out initially anincrease and after decrease with suction (e.g. Wheelerand Sivakumar, 1995, Estabragh et al., 2004, Cuisinerand Masrouri, 2005).

The variation in degree of saturation with compres-sion is shown in Figure 9. As it is expected, there isan increase in degree of saturation with increasingnet stress. However, it should be noted that all threecases are well below saturation and saturation was notreached at the end of compression.

Finally, the change in dry density with compressionand different water contents is shown in Figure 10. Thespecimens compacted with higher water contents are

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0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 500 1000 1500 2000 2500 3000

Net Stress (kPa)

Slo

pe

of

the

com

pre

ssio

n c

urv

e test1 (6%)test1 (8%)test1 (10%)

Figure 8. Changes in the slope of the compression line withloading and water content.

12

17

22

27

32

37

42

47

0 500 1000 1500 2000 2500

Net Stress (kPa)

Sr

(%)

test1 (6%)test1 (8%)test1 (10%)

Figure 9. Changes in degree of saturation with compressionand water content.

1.4

1.45

1.5

1.55

1.6

1.65

1.7

0 500 1000 1500 2000 2500

Net Stress (kPa)

Dry

den

sity

(t/

m3)

test1 (6%)test1 (8%)test1 (10%)

Figure 10. Changes in dry density with compression andwater content.

more compressible and therefore, result in higher finaldensities.

4.3 Discussion

The static compaction curve obtained during the exper-imental program and the predicted compaction curveis presented in Figure 11. All initial parameters areobtained from the conducted experiments except theslope of the normal compression line is for saturated

1.5

1.54

1.58

1.62

1.66

4 5 6 7 8 9 10 11

Water content ( %)

Dry

den

sity

(t/

m3)

Experimental results (560 kPa)Model prediction (560 kPa)

Figure 11. Static compaction curve.

soil (λvp). Further oedometer test needs to be com-pleted to determine this parameter more accurately.In this paper, an approximate value (assuming thatslope of the normal compression line for saturatedsoil is higher than unsaturated soil) from the testsconducted for unsaturated soils is estimated (λvp =0.028).

It can be seen from Figure 11 that the predictedand experimental compaction curves are in reason-able agreement. There are slight differences betweenpredicted and experimental values for the specimensprepared at 6% and 8% water contents. This can beexplained using two different hypotheses.

First, as it can be seen from Equation 3 and 4 that themain controlling parameters for deformation is suc-tion (ua − uw) and the slope of the compaction curvefor saturated soils (λvp). In contrast to Alonso et al.(1990), Sheng et al. (2008) introduced the use of aconstant parameter for the slope of the normal com-pression line which is measured from the saturated soilspecimens (λvp) and the resulting deformation due tonet stress is a function of suction and λvp as shown inEquation 3. In addition to that, during the generationof the compaction curve for a specific type of soil,the differences in deformation between two differentwater contents were only assumed to be a function ofsuction (Equation 4). Taking into account the granularnature of the soil used, it is clear that the suction differ-ences between the two different water contents will bevery small and this leads to negligible density differ-ences. Hence, it may be stated that better results canbe obtained for fine soils than coarse soils. However,the proposed model needs to be modified with differ-ent constitutive soil model assumptions from literature(such as BBM) and compared for clarification.

The second possible explanation could be that suc-tion is assumed to stay constant during loading andit is actually slightly changing as shown in Table 4.The effect of suction (as a second component in Equa-tion 2) on the compaction curve is shown in Kurucuket al. (2007). It was stated there that taking into accountthe changes in suction will result in lower dry densities.Moreover, it can be seen in Table 4 that the changes insuctions are higher for lower water content. Therefore,

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a bigger difference is anticipated between the pre-dicted and experimental results in lower water contentsoils. This difference appears to reducewith increasingwater content.

5 CONCLUSION

This paper presents experimental study conducted inorder to evaluate a proposed theoretical model forthe compaction curve. The proposed model predictsthe compaction curve for soil during undrained K0 orisotropic loading using unsaturated mechanics princi-ples. It suggests that thewell-known inverted parabolicshape of the compaction curve may be theoreticallypredicted using unsaturated soil mechanics princi-ples. Obtained experimental results are comparedwithmodel predictions but it was necessary to make someassumptions. It is shown that the proposed model canpredict the compaction curve reasonably well. Futureexperiments will be targeted to develop a comprehen-sive set of data using different types of soil. Moreover,the model will be modified in the light of several con-stitutive models (e.g. Alonso et al., 1990, Wheeleret al. 2003) and the capability of the models will beexamined.

ACKNOWLEDGEMENTS

Thanks are rendered to Monash University for pro-viding a Monash Graduate Scholarship and financialassistance to the first author for her PhD candidatureand to Dr. Chaminda Gallage for his advice regardingexperimental setup.

REFERENCES

Alonso, E.E., Gens, A. and Josa, A. (1990). A constitutivemodel for partially saturated soils. Geotechnique, 40(3),405–430.

AS 1289.5.1.1 (2003), Soil compaction and density tests—Determination of the dry density/moisture content rela-tion of a soil using standard compactive effort, StandardsAustralia, Sai Global, Sydney.

Barden, L. & Sides, G.R. (1970). Engineering behaviour andstructure of compacted clay. Journal Soil Mechanics andFoundations Division, ASCE, 96, No. SM4: 1171.

Cuisinier, O. and Masrouri, F. (2005). Hydromechanicalbehaviour of a compacted swelling soil over awide suctionrange. Engineering Geology, 81, 204–212.

Estabragh, A.R. Javadi, A.A., and Boot, J.C. (2004). ‘‘Effectof compaction pressure on consolidation behaviour ofunsaturated soil.’’ Canadian Geotechnical Journal, 41,540–550.

Fredlund, D.G. & Rahardjo, H. (1993). Soil mechanics forunsaturated soils. John Wiley & Sons, Inc.

Fredlund, D.G. & Morgenstern, N.R. (1976). Constitutiverelations for volume change in unsaturated soils. Cana-dian Geotechnical Journal, 14, 3: 261–276.

Hilf, J.W. (1948). Estimating construction pore pressures inrolled earth dams. Proceedings of 2nd International Con-ference in Soil Mechanics and Foundation Engineering,3: 234–240. Rotterdam, The Nederlands.

Hilf, J.W. (1956). An investigation of pore water pressures incompacted cohesive soils. Technical Memorandum 654,U.S. Department of the Interior, Bureau of Reclamation,Denver, Colorado.

Hogentogler, C.A. (1936). Essentials of soil compaction.ProceedingsHighwayResearchBoard, NationalResearchCouncil, Washington, D.C., 309–316.

Kurucuk, N., Kodikara, J. & Fredlund, D.G. (2007). Pre-diction of compaction curves. 10th ANZ Conference onGeomechanics, 2: 115–119.

Kurucuk, N., Kodikara, J. & Fredlund, D.G. (2008). The-oretical modelling of the compaction curve1st EuropeanConference onUnsaturated Soils, Durham, UK, 375–379.

Lambe, T.W. (1960). Structure of compacted clay. Transac-tions, ASCE, 125: 682–705.

Lee, D.Y.&Suedkamp, R.J. (1972). Characteristics of irregu-larly shaped compaction curves of soil.HighwayResearchBoard, 381: 1–9.

Li, Z.M. (1995). Compressibility and collapsibility of com-pacted unsaturated loessial soils.Unsaturated Soils. Proc.1st Int. Conf. on Unsaturated Soils (UNSAT 95), Paris,France (ed. Alonzo, E.E. and Delage, P.), Rotterdam:Balkema, Vol. 1: 139–144.

Lloret, A., Villar, M.V., Sanchez, M., Gens, A., Pintado, X.&Alonso, E.E. (2003). Mechanical behaviour of heav-ily compacted bentonite under high suction changes.Geotechnique, 53(1): 27–40.

Monroy, R., Zdravkovic, L. and Ridley, A. (2008) Volumetricbehaviour of compacted London Clay during wetting andloading. 1st European Conference on Unsaturated Soils,Durham, UK, 315–320.

Montanez, J.E.C. (2002). Suction and volume changes ofcompacted sand-bentonite mixtures. PhD thesis, Univer-sity of London, Imperial College of Science, London,England.

Olson, R.E. (1963). Effective stress theory of soil com-paction. Journal Soil Mechanics and Foundations Divi-sion, ASCE, 89, No. SM2: 27–45.

Proctor, R.R. (1933). Fundamental Principles of Soil Com-paction, Engineering News-Record, 111: 286.

Sheng, D., Fredlund, D.G. & Gens, A. (2008). A new mod-elling approach for unsaturated soils using independentstress variables. Canadian Geotechnical Journal, 45,511–534.

Shannon, B. (2008). Laboratory modeling of unsaturatedwater flow and heave in reactive soils. Final Year ProjectReport, Monash University, Australia.

Tang, A.M., Cui, Y.J. and Barnel, N. (2008). Compression-induced suction change in a compacted expansive clay.1st European Conference on Unsaturated Soils, Durham,UK, 369–374.

Wheeler, S.J. and Sivakumar, V. (1995). ‘‘An elasto-plasticcritical state framefork for unsaturated soil.’’ Geotech-nique, 45(1), 35–53.

Wheeler, S.J., Sharma, R.S. and Buisson, S.R. (2003). ‘‘Cou-pling of hydraulic hysteresis and stress—strain behaviourin unsaturated soils.’’ Geotechnique, 53(1), 41–54.

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