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Portland State University Portland State University
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Dissertations and Theses Dissertations and Theses
1987
Hyperbolic soil parameters for granular soils derived Hyperbolic soil parameters for granular soils derived
from pressuremeter tests for finite element from pressuremeter tests for finite element
programs programs
Dieter Neumann Portland State University
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Recommended Citation Recommended Citation Neumann, Dieter, "Hyperbolic soil parameters for granular soils derived from pressuremeter tests for finite element programs" (1987). Dissertations and Theses. Paper 3718. https://doi.org/10.15760/etd.5602
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AN ABSTRACT OF THE THESIS OF Dieter Neumann for the Master
of Arts in Ci vi 1 Engineering presented on December 9, 1967.
Title: Hyperbolic Soi 1 Parameters for Granular Soi ls
Derived from Pressuremeter Tests for Finite Element
Programs.
APPROVED BY MEMBERS OF THE THESIS COMMITTEE:
Trevor D. Smith, Chairman
F
Michael J. Cummings
In the discipline of geotechnical Engineering the
majority of finite element program users is fami 1 iar with
the hyperbolic soil model. The input parameters are
commonly obtained from a series of triaxial tests. For
cohesionless soi ls however, todays sampling techniques fail
2
to provide undisturbed soi I specimen. Furthermore, routine
triaxial tests can not be carried out on soils with grains
exceeding 10 - 15 mm in size.
In situ tests, such as the pressuremeter test, avoid
many of the shortcomings inherent in the conventional soil
investigation methods and are very cost effective.
The initial developments towards a I inK between high
quality pressuremeter tests and the hyperbolic finite
element input are presented. Theoretical and empirical
approaches are used to determine the entire set Of
and parameters from pressuremeter tests. Tri axial
pressuremeter tests are performed on the same soi I. The
proposed method is evaluated using a finite element program
for axisymetric sol ids model I ing pressuremeter tests as wel I
as a model foundation. The computer solutions are compared
to the response of a physical model
application.
foundation under load
Further evaluation of the proposed method is accomp-
I ished using pressuremeter tests performed under field
conditions in a severly cracKed earth retaining structure.
It has been shown that finite element model I ing using pres
suremeter data resulted in simi Jar distress features as
those observed at the real structure.
HYPERBOLIC SOIL PARAMETERS FOR GRANULAR SOILS
DERIVED FROM PRESSUREMETER TESTS
FOR FINITE ELEMENT PROGRAMS
by
Dieter Neumann
A thesis submitted in partial fulfillment of the requirements for the degree of
MASTER OF ARTS in
CIVIL ENGINEERING
Portland State University
1987
i i
TO THE OFFICE OF GRADUATE STUDIES AND RESEARCH:
The members of the committee approve the thesis of
Dieter Neumann presented December 9, 1987.
Dr. Trevor D. Smith, Chairman
Dr. Michael J. Cummings
'
APPROVED:
Dr. of Ci vi I Engineering
Bernard Ross, Dean of Graduate Studies
To:
and,
i i i
DEDICATION
Danuta, my wife and friend for al I her support
and understanding,
to those who fight for the preservation of the
beautiful nature of Australia, the Americas and
the world.
iv
ACKNOWLEDGEMENTS
Gratefully acKnowledged is the constructive and
profound guidance by Prof. Dr. Trevor D. Smith in the
progress of this study, whose professional efficiency and
human composure maKe him an excellent teacher.
Of special importance were the many, most
enjoyable, hours of formal and informal instruction and
discussion of the pressuremeter as well as the applications
of computerized
engineering.
solution techniques in geotechnical
Financially, this study was supported by a scholarship
of the German Fulbright Commission, Bonn, West-Germany and
by an award # 90-050-5801 8TS of the Office of Grants and
Contracts at PSU.
The donation of the Willamette River sand by the Ross
Island Sand & Gravel Company is much appreciated.
Finally, special thanKs are extended to Anne Hotan of
the PSU Computing Services, for her friendly and safe
navigation through the jungle of peculiarities related to
the CMS on the PSU mainframe computer.
TABLE OF CONTENTS
DEDICATION ...
ACKNOWLEDGEMENTS
TABLE OF CONTENTS
LIST OF TABLES .
LIST OF FIGURES
CHAPTER
I I
INTRODUCTION
Problem Description
Research Objective
THEORETICAL BACKGROUND
Triaxial Test - Theory
Pressuremeter Test - Theory
Elastic Range Plastic Range
I I I HYPERBOLIC SOIL MODELLING
Stress-Strain Relationships
Stress-Strain Parameters from Pressuremeter Tests
Volume Change Relationships
Volume Change Parameters from Pressuremeter Tests
PAGE
i ii
iv
v
viii
ix
2
4
4
6
1 7
17
32
CHAPTER
IV
v
VI
Conventional Parameters
Conventional Parameters from Pressuremeter Tests
SOIL TESTING PROGRAM
Selected Soi 1
Triaxial Tests
Sample Preparation Test Results
Pressuremeter Tests
Placement Procedure Test Results
FINITE ELEMENT STUDIES
Introduction
Finite Element Program AXISYM
Volume Changes
Finite Element Analysis -Pressuremeter test
Finite Element Analysis - Foundation
MODEL FOUNDATION STUDY
Model Foundation and Load Application
Foundation Testing Procedure
and Results
v i
PAGE
40
45
45
45
55
61
61
62
66
10
76
76
11
CHAPTER
VI I CASE HISTORY
Sand 'H' Debris Basin
VI I I DISCUSSION OF THE RESULTS
Conclusions and Recommendations
LIST OF REFERENCES
LIST OF NOTATIONS
APPENDIX
Calculations for Hyperbolic Parameters, Triaxial Tests
Calculations for Hyperbolic Parameters, Pressuremeter Tests
vii
PAGE
80
80
83
84
87
92
95
96
99
viii
LIST OF TABLES
TABLE PAGE
correction Factor a . . . . . . . . . . . . . 27
I I Parameters for Sand - Handcalculated . . . . . 53
I I I Parameters for Sand - SP-5 Solutions . . . . . 54
IV Parameters for Sand from Pressuremeter Tests . . 60
v Parameters used for Pressuremeter Analysis . . . 68
VI Parameters used for Foundation Analysis . . . . 72
VI I PMT Results from sand 'H' Debris Basin . . . . 81
VI I I Hyperbolic Parameters Standard vs. PMT . . . . 82
LIST OF FIGURES
FIGURE
1. Soi I Sample in Tri axial Compression
2. Mohr Circles for Triaxial Test
3. PMT and the Surrounding Soil
4. Typical Pressuremeter Curve
5. Mohr Circles for PMT
6. Real Stress-Strain Hyperbola
7. Transformed Stress-strain Hyperbola
8. Mohr-coulomb Failure Envelope
9. Failure Ratio
10. Variation of Ei with Confining Pressure
11. Variation of Tangent Moduli
12. Variation of Eur with Confining Pressure
13. Soil Moduli from Triaxial and Pressuremeter Tests with Increasing confining Pressure
14. Variation of Kb with Confining Pressure
15. BulK Modulus Exponent m
ix
PAGE
6
6
9
10
14
18
18
. . 20
20
. . . 22
22
. 25
.. 26
34
as a Function of Relative Density .... ' .. 36
16. BulK Modulus Number Kb as a Function of Relative Density ....... 38
x
FIGURE PAGE
17. Density Components of Strength t• t t t t t t I I 42
18. Grain Size Distribution Curve for Willamette River Sand •••••• 46
19. Stress-Strain and Volume Change Curves for Willamette River Sand , Dr = 50 :t. . . . . . 49
20. Stress-Strain and Volume Change Curves for Wi 1 lamette River Sand ,Dr = 70 :t. . . . . . 50
21 . Stress-Strain and Volume Change Curves for Willamette River Sand ,Dr = 95.6 :t. . . . . 51
22. Pressuremeter Curve - Chamber Test, Dr = 66 :t. 57
23. Pressuremeter Curve - Drum Test I, Dr= 67 :t. 58
24. Pressuremeter Curve - Drum Test I I, Dr= 68 :t. 59
25. Finite Element Mesh for Analysis of Pressuremeter Test I I I I I I I I I 67
26. Variation of Pressuremeter Moduli with Increasing Depth ............. 69
27. Finite Element Mesh for Analysis of Model Foundation
28. Load-Deflection Response for Model Foundation from AXISYM using Pressuremeter Parameters
29. Failure Generation During AXISYM Analysis
30. Load-Deflection Response
. . . 71
73
. . 75
as Measured for the Model Foundation •••••• 78
CHAPTER I
INTRODUCTION
The widespread use of digital computers and the
development of powerful numerical schemes, such as the
finite difference method or the finite element method, has
increased the re I i ab i I i ty of otherwise lengthy ca I cu I at ions
and has provided the means to solve many problems for the
first time. However, the precision of the computer solutions
in mechanics is dependent upon the accurate determination of
the material properties. This applies in particular to the
discipline of geotechnical engineering, where sti I I a great
deal of empiricism is part of everyday practice.
PROBLEM DESCRIPTION
In the past two decades many formulations of
nonlinear soil behavior have been published. The most
successful being the hyperbolic soi I model proposed by
J.M. Duncan et a I . ( 1980) , and incorporated into numerous
finite element programs solving a wide variety of geotech-
nical problems. Nevertheless, many of the shortcomings of
c 1 ass i ca I so I ut ion procedures is st i I l inherent.
The style and format of this thesis fol lows that used by the Journal of the Geotechnical Engineering Division, American Society of Ci vi I Engineers.
2
The parameters describing the soil behavior are derived from
conventional triaxial tests, where scale effects and dis
turbance of the samples may influence the reliability of the
results significantly.
Today it is widely accepted that in-situ tests are
more applicable for the accurate determination of soil
parameters. This applies especially to granular soils where
it is generally difficult to obtain undisturbed samples for
conventional laboratory tests. Recompaction of disturbed
samples does not necessarily model the in-situ conditions
because the in-situ density is difficult to measure.
Among al 1 available devices testing the soi 1 in place,
the pressuremeter seems to be most superior since it reveals
information about the soi 1 prior to, and at failure. The
fundamental idea of the pressuremeter is very wel 1 expressed
if an "inside-out triaxial test" is considered. In addition
to high quality design parameters, disturbed samples are
obtained allowing visual examination and identification
tests such as water content, Atterberg 1 imits, or grain size
distribution of the encountered soil.
RESEARCH OBJECTIVE
It is relevant to note that so far only very few
attempts have been made to establish a 1 ink between the high
quality soil information obtained from a pressuremeter test
and the sophisticated soi 1 model input for finite element
3
programs used frequently by engineers.
This thesis reports the initial developments towards a
I inK between pressuremeter test results and finite element
input. Theoretical considerations are employed in con
junction with pressuremeter tests, under laboratory con
ditions, to derive the soi I parameters used in the hyper
bolic soil model as input for the AXISYH (D.H. Holloway
1976) finite element program.
A finite element analysis of a simple foundation
problem is performed where the parameters describing the
soi I behavior are based on pressuremeter testing. The
predicted deflections are compared to the response of an
instrumented physical model foundation tested on Willamette
River sand. Reasonable agreement is found between the
computer predicted and measured settlements. Finally, the
derived equations are then applied to pressuremeter tests
performed under field conditions, where good agreement with
standard parameters is found.
CHAPTER I I
THEORETICAL BACKGROUND
The hyperbolic, stress-dependent soi I model proposed
by J.M. Duncan et al. uti 1 izes a total of nine parameters to
describe the stress-strain characteristics of the soi I.
Three parameters, KI Kur• and n, characterize the soi 1
modulus in its elastic-plastic behavior I imited by a fai Jure
ratio, Rf· Additional Jy, two terms, Kb and m, express the
volume change characteristics of the soil medium, wh i I e
three further, more conventional parameters, namely c,
~. and A~. represent the shear and friction fai Jure charac
teristics of the soi I. A detailed description of the entire
set of parameters is presented in Chapter I I I.
According to the recommended procedures,
above parameters are derived from triaxial
al I of the
compression
tests. In order to prepare the theoret i ca I bacKground for
the development of the above parameters derived from
pressuremeter tests, a theoretical study of both soil
investigation methods is presented.
TRIAXIAL TEST - THEORY
The triaxial compression test is a widely used
laboratory test to determine shear strength and friction
5
parameters for soi Is and is certainly the most versatile
laboratory test available. Volume changes and pore water
pressure measurements are possible under a variety of stress
states shown in detai I by the classic worK of A.W. Bishop
and D. J. HenKe I ( 1962) .
It is of special significance to note that, contrary
to what the test name might imply, it is not possible to
induce any arbitrary stress condition to the triaxial
sample. This would be the case in a true triaxial test, as
proposed P.V. Lade (1979) or J.A. Pierce {1971), but no
apparatus has yet been developed which is unquestionable.
A specimen in a conventional triaxial compression test
is schematically displayed in Fig. 1. c 2 and c3 are held
equal and constant, usually by pneumatical means, while c1
is continously increased to failure. Hence measured external
principal stresses are applied to the sample. As the stress
rises, readings of the applied axial load and the sample de
formation are taKen unti I the specimen fails by shearing on
internal planes. The shear strength of the soi 1 is deter-
mined from the applied axial load at failure. The maximum
soi 1 shear strength is given by the Mohr-Coulomb equation:
Tmax = c' + (c - u) ·tan t' (2-1)
where c' is the cohesion intercept, o is the total pressure
normal to the plane in question, u is the pore pressure and
t' is the effective angle of internal friction (Fig. 2).
Sgecimen in Tri axial ComRression
02 C13 Oz
C11
<13
Cf 1
Figure 1. Soi 1 Sample in Tri axial Compression.
l
0'1-0'3)
I -j0'3 01-j d' n
FiQure 2. Mohr Circles for Tri axial Test.
6
of
7
The failure planes (Fig. 1) are inclined at an angle
ef = 45° + t/2 (2-2)
to the maximum principal plane, as can be seen from a
typical plot of Mohr circles for a triaxial test (Fig. 2).
Conventional cohesion and friction parameters are
determined from a series of tests at varying confining
pressures.
PRESSUREMETER TEST - THEORY
The pressuremeter test is an in-situ soil test which
was in principle presented by F. KOgler (1933), while
further development was accomplished by L. M~nard (1957).
Today, with nearly thirty years of sound theoretical and
empirical development in France, the U.K., and Australia,
where it has already found its place in routine soil
investigations, the pressuremeter test is gradually emerging
into geotechnical engineering practice of the U.S ..
The pressuremeter is an inflatable probe which can be
lowered down into a prebored or selfdri 1 led borehole. The
test itself is carried out by applying internal principal
stresses to the cavity by inflating the probe by either
pneumatical or hydraul ical means, or a combination of both.
During expansion of the membrane, measurements of volume
change and pressure are taKen unti 1 the cavity has doubled
8
its initial volume.
Examination of the basic stress conditions in the soil
mass surrounding the probe, given in Fig. 3, reveals the
axisymetric nature of the stress field as opposed to the
cartesian coordinate system conventionally applied to the
triaxial test. Not only are different coordinates used, but
also an entirely different set of parameters is procured,
providing the basis for settlement and bearing capacity
calculations.
For the case of a prebored test, stress relief taKes
place upon borehole dri 11 ing and the first part of a typical
pressure-volume change curve for a pressuremeter test, as
given in Fig. 4, represents the reloading of the soil to its
initial stress condition. Further stress increase exposes a
I inear, elastic response of the soil, from which the pres-
suremeter modulus, E usually is calculated by the elasticity
relationship given by Eq. 2-3.
E : 2 · ( 1 + V) G (2-3)
where poisson's ratio is frequently assumed to be 0.33 and G
is the shear modulus measured during the cavity expansion as
defined by Eq. 2-4.
4.p G : VAv·-;;;- (2-4)
In this expression 4.p is the change in radial pressure, 4.V
is the change in cavity volume and VAv is the average cavity
~ \1 3: -I
Q)
:l a. ..+ :::r (1)
(/)
c: 1 1 0 c: :l a. :l co (/)
0
6
-03 -0 .., rt> .., 0 _.rt>
er rt> "' rt> .., "'
c .., rt>
[:>
CD 0 .., rt> ::r 0
rt>
~ rn -0 rn >< 0 "O 0 0
"' "' - ::i ::!: ;:;· 0. n
::i N N \0 0 0 ::i ::i
-0 rt> rt> .., 0 CT rt>
' V'lo', ::r :::!. ~------------' I \ ~;g ) I
I I \..,a,,, I \ -0 cs· '--.... f I __ \
0 5
......._ ___ L---:J o rt> ;,
"'
en ::i g -..... ...,
9..
0r I ____________________ PL __
=--------------------pl
EPM
initial stress condition
probe cootact to cavity
Figure 4. Typical Pressuremeter Curve.
/j, v Vo
10
1 1
volume.
Finally, upon continued cavity expansion the soil
yields and the plastic range of the soi 1 is reached. While
the soil particles close to the probe have failed already,
more outer particles are just becoming distorted and move
from elastic through plastic response as further expansion
taKes place. For this reason, two different sets of rheo
logical equations need to be considered to represent the
pressuremeter test in its ful I range.
In most current pressuremeter theories the fol lowing
assumptions are made:
1. Distortions occur only in the horizontal plane, that
is plane strain. J.P. Hartman (1974) showed, using
C.J. Tranters (1946) closed form solution, that only
small differences exist between the expansion of a
cavity with finite and infinite length. J.-L. Briaud,
L.M. TucKer and C.A. MaKarim (1985) recommend the use
of probes with a minimum L/D ratio of 6.5.
2. End effects at the membrane ends are negligible,
allowing the assumption of an ideally cylindrical
cavity.
3. The soi 1
mater i a I.
is assumed to be an isotropic, elastic
4. Poisson's ratio is frequently assumed as v = 0.33 and
a Menard modulus EM = 2.66·G is obtained.
12
Pressuremeter Test~ Elastic Range
In the pressuremeter test, only the soil in the
immediate vicinity of the probe is stressed through its full
range of stresses, radial strains decay with the square of
the distance dramatically, F. Baguel in, J.-F. Jezequel and
D.H. Shields (1978), as can be seen from Eq. 2-5.
Er = E0 · r 0 2
r2 (2-5)
in which Er is the radial strain, E0 is the strain at the
cavity wall, r 0 is the initial radius of the cavity and r is
the radial distance to a point in the surrounding soil mass.
In axisymetrical problems, any radial displacement
automatically induces strain in the circumferential di-
rection. Radial and circumferential stresses are principal
stresses by reasons of symmetry. The radial stress, or, is
increasing as the probe expands against the borehole wall,
wh i 1 e the c i rcumferent i a 1 stress, oe, is decreasing about an
equal amount, F. Baguel in, J.-F. Jezequel and D.H. Shields
(1978), (Eq. 2-6).
Aor = -Aoe = 2G · Eo . ro2
r2 (2-6)
So that the radial stress at a point becomes
Or = Po + 2G . E o . ro2
r2
1 3
(2-7)
where Po is the initial horizontal soil pressure. The cir
cumferential stress then becomes
oe = Po - 2G · Eo . ro2
r2 (2-8)
Mohr circles for the stress changes in a particular
element, shown in Fig. 5, demonstrate that the average all
around stress, that is Ooct• is unchanged and hence,
Aooct -Aor + Aoe + Aoz
3 (2-9)
where Oz is the vertical stress. Nevertheless, the principal
stress difference, (o 1-o3 ) , increases.
Failure planes are inclined 450+~/2 to the principal
stress directions where the maximum shear stress occurs as
given by Eq. 2-10.
Tmax -
However,
or - oe
2 (2-10)
it must be clearly recognized that elastic
soi I is only realistic in the range of smal I strains, say up
to 51. and hence, to represent the pressuremeter expansion in
-r
Elastic loading of soil .....
'trnax - .............
//
(
/---
"" \ \
t.ca 0 t:.dr)
\ increase /
\ f / " / ""'-- _./'
L'
}rnE!
'1e po
total
...... UP. to failure.
1 4
dr I C1
LL-..---4------+--~ aet po O'rt I (f
Figure 5. Mohr Circles for PMT.
1 5
its full range, additional factors are to be considered.
Pressuremeter Test ~ Plastic Range
considering a soi I with cohesion and friction,
F. Baguel in J.-F. Jezequel and D.H. Shields (1978) showed
that the well understood Mohr-coulomb failure criterion can
be written for the pressuremeter test as:
ae + c ·cot 4> = Ka· (O'r + c cos 4>) ( 2- 1 1 )
where
Ka = tan2. (lT/4 - 4>/2) (2-12)
and is the active earth pressure coefficient. The theo-
retical I imit pressure at infinite expansion is given by
PL = ( p 0
+ c cot 4>) · ( 1 + sin 4>) · [ 1
] 2·cx
f
1-Ka
2
c cot 4>
(2-13)
as opposed to the practical I imit pressure, Pi• which is
somewhat 1 ower than PL. s i nee p 1 is, by definition, reached
when the initial cavity volume has been doubled and is
expressed by
1-Ka --
+ c cot •l · [ 1
]
2
pl = ( O' - c cot 4> . . . (2-14) f 4·cx
f
The almansi strain, af in Eqs. 2-13 and 2-14 becomes,
Of - Po af =
G
16
(2-15)
and the stress at the onset of failure is expressed by,
Of = P0 +(p0 +c·cot ~)·sin ~ (2-16)
Of = Po. ( 1 + sin ~) +C. cos ~ (2-17)
Most of the above equations simplify considerably for
a purely frictional material because of the absence of
cohesion.
CHAPTER I I I
HYPERBOLIC SOIL MODELLING
STRESS-STRAIN RELATIONSHIPS
R.L. Kondner (1963) showed that a two-constant
hyperbola, represented by Eq. 3-1, was most suitable to fit
to a high degree of precision the stress-strain curves of
many soils (Fig. 6). Noteworthy is that an identical
expression was proposed 110 years earlier by H. cox (1850)
in his hyperbolic law of elasticity for metals. Both
expressions are of the form :
Ea Ca 1 - <73 > = ( 3- 1)
a + bEa
Where a1 is the major principal stress, a3 is the minor
principal stress, and Ea is the axial strain, while a and b
are constants. Transformation of Eq.3-1 into its 1 inear form
yields Eq. 3-2, presented in Fig. 7.
Ea = a + bE a (3-2)
(01 - 03)
Inspection of Fig. 6 and 7 reveals that a and b are
mean i ngfu 1 phys i ca 1 parameters. R. L. Kondner and
S.S. ZelasKo (1963) showed that 'a' represents the reci
procal of the initial tangent modulus, Ei, while b is the
19
reciprocal of the ultimate normal stress difference, Known
as the deviator stress (01-03)u1t and serving as the
asymptote of the hyperbola.
The actual values of a and b are coventional ly derived
by plotting triaxial test data on the transformed plot,
where the best fitting straight line corresponds to the best
fitting hyperbola on the stress-strain plot.
Then (01 - 03lu1t is found to be greater than the
stress difference expressed by the Mohr-Coulomb failure
envelope (Fig. 8) and it can be shown, given by Eq. 3-3,
2 c cos t + 2 03 sin t (01 - 03)f :
1 - sin t (3-3)
in which c is the cohesion and t is the angle of internal
friction. Assuming the above criterion is still val id at
failure, this difference is accounted for by introducing a
parameter called the failure ratio, Rf·
(01 - 03)f Rf : (3-4)
(01 - 03)ult
Graphically the effect of this multiplier on the
modelled stress-strain curve is displayed in Fig. 9.
N. Janbu (1963) recommended the use of an initial
tangent modulus, as defined by Eq. 3-5, as an appropriate
measure of the compressibility of soils ranging from solid
rocK to plastic clays.
20
'"L
(0'1
-d') = 2c'cos~'+za3~ 3 f 1- sin "
' dn
Figure 8. Mohr-Coulomb Failure Envelope.
(<11- <13) ( a1 - 6 3 lu_l_!_ ------
(<11 -<13)f =Rt·(cr1-C13)ult
E.a
Figure 9. Failure Ratio.
2 1
E = KPa [tJ" (3-5)
Where Pa is the atmospheric pressure, K and n are modulus
number and modulus exponent, respectively, relating Ei, the
initial tangent modulus, to the confining pressure, a 3 .
Based on triaxial tests, the actual values of both K and n
are determined by plotting the results for Ei and a 3 of a
series of tests on a log-log scale, as in Fig. 10. From the
best fitting straight I ine, K is found as the intercept on
the vertical axis, while n is the slope of the 1 ine. Both
parameters are dimensionless numbers.
While the initial tangent modulus defines the initial
portion of the stress-strain curve, the remaining part is
represented by a simple tangent modulus as given by Eq. 3-4.
which is graphically displayed in Fig. 11.
Et = aca, - a3)
dEa (3-6)
J.M. Duncan and C.Y. Chang (1970) showed that the
tangent modulus might also be expressed independently of
stress and strain as:
Et= (1 - Rf·S)2·Ei (3-7)
22
log (Ej /P0 }
n
K Ej=KPa· ~~~~n
10 100 log (o3/P0
)
Figure 10. Variation of Ei with Confining Pressure.
(<11-d3)
Ea
Figure 11. Variation of Tangent Moduli.
23
where S, the stress 1eve1, is expressed as:
(<71 - <73)
s = (3-8) (<71 - <73)f
Substituting the expressions for S, (01 - a3)f• and Ei
as given by Eqs. 3-8, 3-3, and 3-5 into Eq. 3-7 yields the
following expression for the tangent modulus at any stress
state.
Et = [ 1 -
R · ( 1 - sin t)' (o - a ) f 1 3
2 c cos t + 2 a sin t 3
]
2
· K·P8
· [~Jn a (3-9)
In the case of an element undergoing shear failure,
i.e. the Mohr-Coulomb strength relationship as expressed in
Eq. 3-3 is exceeded, the value of the tangent modulus is
defaulted to a very small number, being equivalent to a very
soft soil. The element has failed and for a slight increase
in stresses large deflections are observed, not uni iKe
"plastic" behavior.
The fact that the stress-strain relationship of the
soil is model led hyperbolically shows quite readily that
soi 1 is by no means behaving elastically. This imp! ies that
a soil element once deformed wi 11 not recover its initial
shape if the applied load is removed. Furthermore, if the
element is reloaded, possibly beyond the previous stress
level, the unload-reload cycle is steeper than the initial
24
stress-strain response due to the first load application.
This phenomenon is shown in Fig. 12.
The expression for the unload-reload modulus, Eur is
given by Eq. 3-10.
E =K ·P·[~]n ur ur a P
a
(3-10)
It should be noted that the modulus exponent is the
same as the one used in Eq. 3-5. J.M.Duncan et al. ( 1980)
state depending on the soil type, the actual value of Kur
might be in the range of 1.2 times the value for K, as in
the case of a stiff soil, but could climb up to three times
the value of K in the case of very soft soils.
Stress-Strain Parameters from PMT
It is clearly recognized that, especially for granular
soils, the stress-strain response is highly dependent upon
confining pressure, that is to say modulus values in an
isotropic soil increase with depth, as shown in Fig. 13.
A very similar observation was made by L.D. Johnson (1986),
comparing pressuremeter moduli with first load moduli from
undrained triaxial tests on Midway clay. Both were
increasing I inear with depth.
The evidence, however, is that the pressuremeter
modulus cannot be compared directly with a compression
modulus such as the Young's modulus, since the stress paths
, !
SOIL
M
OD
ULI
FR
OM
TRIA
XIA
L AN
D PR
ESSU
REM
ETER
TE
STS
AT
VA
RYIN
G
CO
NFI
NIN
G
PRES
SUR
ES
50
0
45
0 .
o
Tri
ax
ial
tests
,,a
4
00
t x
Pre
ssu
rem
eter
te
sts
co
a..
2:.
3
50
w
a:
30
0
::::>
Cf)
[
0 C
f)
w
25
0
a:
a..
(.')
2
00
z H
z H
15
0
t lL
0
z 0 u 1
00
50
[
o I
)( /x
0 3
00
00
6
00
00
9
00
00
1
20
00
0
15
00
00
FIR
ST
LOAD
M
ODUL
US
[kPa
]
Fig
ure
13
. S
oi
I M
odu
li
from
T
ria
xia
l an
d
Press
urem
ete
r
Test
s w
ith
In
crea
sin
g
Co
nfi
nin
g
Press
ure.
I\)
(J)
27
followed are different in pressuremeter and traditional
compression tests. A comparision of H~nard moduli. EH and
soil moduli. Es (obtained from traditional soil investi-
gat ion methods) indicates that Es might be anywhere from 2
to 10 times higher than EH (r. Baguel in. J.F. Jezequel and
D.H. Shields. 1978).
Investigating the pressuremeter modulus, EH at very
smal 1 strains. L. M~nard (1961) states that the so cal led
modu 1 us of "micro-deformation", Em• is usu a 11 y in the order
of 3 times EM (but for certain soils might be as high as 20
times EM>· Based on the ratio EM/Pi an empirical correction
factor. a has been determined (Centre d~Etudes M~nard. 1975)
to account for the above mentioned differences as given in
Table 1.
TABLE I
CORRECTION FACTOR a
Type of Si It Sand sand and Soi I Gravel
EMIP1 a EMIP1 a EMIP1 a
Overcon- >14 2/3 >12 1/2 > 10 1/3 so 1 i dated
Norma 11 y 8-14 1/2 7-12 t/3 6-to 1/4 conso t i dated
Weathered and 1 /2 1/3 1/4 Remoulded
26
The modified pressuremeter modulus, EpM is then,
EpM = EM I <X ( 3-11)
which is still a secant modulus rather than an initial
tangent modulus as used in the hyperbo l i c soi I model . If the
corrected pressuremeter modulus is used, it seems
intuitively appropriate to use a modified version of Eq. 3-5
as given by the following.
E : K · p . [_::__;___] s PM PM a p
a
(3-12)
Where KpM and s are modulus number and modulus exponent
respectively, based on pressuremeter tests. EpM is the first
loading modulus as obtained from the pseudo-elastic portion
of the pressuremeter curve. Oz' is the effective overburden
pressure and represents a conservative estimate of the
confining pressure. The actual values of both KpM and s are
determined by plotting the results for EpM and Oz' for a
series of tests at increasing depth on a log-log scale,
analogous to the triaxial test procedure. From the best
fitting straight I ine KpM is then found as the intercept on
the vertical axis, whiles is the slope of the line. Both
parameters are, again, dimensionless numbers.
The above expression describes the variation of the
pressuremeter modulus with depth in terms of overburden
29
pressure. A very similar relationship is proposed for the
unload-reload behavior. As in triaxial tests, an increase
of the soi 1 modulus is noticed if an unload-reload cycle is
performed during a pressuremeter test. The variation is
similar in both pressuremeter and triaxial tests, so
Eq. 3-13 is proposed.
[ J
S 0 ,
E : K ·P · _z._ Pur Pur a pa
(3-13)
The modulus exponent, s, remains unchanged from
Eq. 3-12 and the modulus number, Kpur• is obtained in a
similar fashion as for the triaxial test.
In the hyperbolic soil model, the permitted range of
stresses is 1 imited by the failure ratio, Rf. This is for
triaxial tests the ratio of the measured peaK strength to
the theoretical maximum strength using a hyperbo 1 i c
function.
If the Mohr-Coulomb failure criterion, as given by
Eq. 2-9, is assumed val id at failure, the radial stress, or•
becomes the radial stress at the onset of plastic behavior,
Of• This is the point on the pressuremeter curve at which
failure commences, initiated at the wall of the cavity.
Further expansion of the cavity, up to 100 Y. volumetric
strain, marKs the end of the pressuremeter curve where the
practical 1 imit pressure, p 1 (Eq. 2-14). is reached. The
theoretical maximum resistance the soil could mobilize, at
30
infinite cavity expansion, is given by PL (Eq. 2-13).
In direct analogy to the triaxial test, Eq. 3-14 gives
the proposed relationship for a failure ratio based on
pressuremeter tests.
Rpf : Pl
PL
Considering
(3-14)
an entirely frictional material, the
expressions for P1 and PL can be simplified and substitution
of both expressions into Eq. 3-14 gives,
Rpf :
1-Ka
of · C 1 / 4af) 2
1-Ka
Of·(1/2<Xf) 2
(3-15)
In order to determine Ka, the angle of internal
friction has to be Known and might be computed either by
bacKcalculation using Pl (as measured or by interpretation)
or Of·
yields
Substitution of Eq. 2-15 into the above expression
Rpf =
1-Ka
Of· [G/(20f-2P0 )J 2
1-Ka
Of. [G/ (Of-Po)] 2
(3-16)
where the nominator might be taken as the practical 1 imit
31
pressure, p 1 . For a series of tests, as recommended herein,
the actual value of Rpf is determined as the average of the
calculated values from each test.
VOLUME CHANGE RELATIONSHIPS
J.M. Duncan et a 1 . ( 1980) showed that a bu I K modu 1 us
as defined by Eq. 3-17 could express the volume change cha-
racteristics of a soi I with good accuracy.
Ao 1 + Ao2 + A0'3 B = (3-17)
3 ·Evol
Where Evol is the volumetric strain. For the conventional
triaxial test, this expression reduces to
(0'1 - 0'3) B : (3-18)
3·EVO1
because the deviator stress increases while the confining
pressure is held constant and 02 = 03. Hence, B might be
calculated using any point on the stress-strain curve and
its corresponding point of the volume change curve.
Investigating the effect of varying confining pres-
sure, o3 , on the bulK modulus, Duncan and his co-workers
found B to be a function of the confining pressure,
analogous to the initial tangent modulus.
B=K·P·[~]m b a P
a
(3-19)
In which Kb is the bulK modulus number and m is the bulk
33
modulus exponent. The procedure for the determination of
bulK modulus number and exponent is simi Jar as for the
determination of Kand n and can readily be seen in Fig. 14.
For the use of this soi I model in finite element
programs, (this is the prime reason for the development
of such a soil model), the range of the bulK modulus has to
be I imited in order to avoid certain values of poisson's
ratio. This can be visualized by substituting values of
v -> 0.5 into Eq. 3-20, which is the equation for the bulK
modulus assuming elastic behavior.
E B = (3-20)
3· (1-2v)
A further, more detailed discussion on this aspect is
presented in Chapter v.
Volume Change Parameters from PMT
Soil volume changes are not directly measured during a
pressuremeter test because they occur externally, even
indirect measurements by interpretation of pore water
pressure changes during probe expansion, are not taKen on a
routine basis. Therefore, no clear cut solution for the
representation of volume changes can be derived. However,
since volume changes are of significance for granular soils,
compared to clays, they can not be neglected. In fact, a
Wide range of volume
mater i a I) to expansion
changes
(dense
from contraction
material) has
(I oose
to be
34
log (B/ Pa)
Kb B=Kb·Pa·(;~r
10 100 log ( er 3 I P 0 )
Figure 14. Variation of Kb with Confining Pressure.
35
considered. For a cohesionless soil, poisson 1 s ratio might
be expected in the range between 0.3 - 0.4.
The si~nificance of volume changes has been the
subject of many parametric studies by various researchers.
J.P. Hartman 1 s (1974) findings indicate that, for a 1 inear
elastic material as wel I as for a nonlinear material obeying
the hyperbolic relationships, the calculated pressuremeter
moduli are independent of poisson 1 s ratio. Nevertheless, a
significant effect on the 1 imit pressure is found to be
related to a change in v.
Considering the foregoing, a way out of the dilemma
might be the correlation of changes in volume to some other
relevant soil property or parameter. Al 1 indications show
that volume changes are highly dependent on the relative
density of the soil, and to a lesser extent on grain size
and shape. Based on available triaxial test data, correla
tions of relative density to the bulK modulus exponent and
bulK modulus number have been investigated. The incorporated
data was pub! ished by J.M. Duncan et al. (1980) and H. Schad
(1979) and represents only excellent qua! ity information,
i.e. using the hyperbolic parameters the bacKcalculated
stress-strain curves are in very good agreement to those
measured.
A range of butK modulus exponent values for granular
soils, ranging from sandy gravels to silty sands, has been
established and is graphically displayed in Fig. 15 (data
E
I- z w
z 0 n..
x w
(/)
:::i
_J
:::i
0 0 :I:
~
_J
::i
m
1. 0
0.9
0.8
0.7
0.6
0.5
0.
4
0.3
0.2
0.
1
0.0
-0.
1
-0.2
0
VA
RIA
TIO
N
OF
m A
S A
FU
NC
TIO
N
OF
DEN
SITY
-·-
lin
k o
f sa
me
soils
bu
t di
ff.
dens
ities
. El-.
..~
m=
0.01
4+ 5
.08
Dr
~·~ ~.~ ~~
a, '
-----
I ."
>.,
, ~...........
<,
. "' -
·---
·--·
_,..
.c__
,-·-
·~ ... ___ _
--
-....;,.,
__ ..
... ·
.· ..
. ...
......
......
......
......
.. <. ..
......
......
......
.... .
10
2
0
30
4
0
50
6
0
70
8
0
90
1
00
REL
ATI
VE
DEN
SITY
D
r [%
]
Fig
ure
1
5.
Bul
K
Mo
du
lus
Ex
po
nen
t m
as
a F
un
cti
on
o
f R
ela
tiv
e
Den
sity
.
OJ
(J'l
37
points corresponding to identical soils are connected). In
genera 1, it can be stated that the bu 1 k modu 1 us exponent, m,
is decreasing with increasing density. Moreover, in densi-
ties exceeding 70 Y. is practically zero. Hence the bulK
modulus, B, shows a I inear increase at higher densities in
dependently of confining pressures. A multiple regression
analysis of the accumulated data was performed and a cor
relation as given by Eq. 3-21 was obtained.
m = o. o 1 4 + 5. 08 · 1 /Dr (3-21)
where Dr is used in Y.. Fig. 15 also displays the curve
representing the above equation. It should be noted that
only values of Dr > 10 Y. should be used.
M.G. Katona et al. (1981) recommended in the CANOE
manual the use of a standard bulk modulus exponent of
m = 0.2 for granular aggregates with densities ranging from
21.2 - 23.6 KN/m3. Katonas recommendation is based
on an extensive collection of hyperbolic parameters given by
J.M. Duncan et al. (1980). The given range of densities
relates to a relative density of approximately 75 Y. to
100 Y.. A fairly good correlation to the typical value of
m = 0.2 is recognized upon inspection of the graph.
A similar procedure was followed for the bulK modulus
number, Kb, for which the data base and the regression curve
is given in Fig. 16. Even though the scatter of the data
points is larger than for the exponent, it was found that Kb
.D
~
a:
w
m
:I:
::>
z (f)
::>
_J
::>
0 0 l:
~
_J
::>
m
VA
RIA
TIO
N
OF
Kb
AS
A F
UN
CTI
ON
OF
D
ENSI
TY
2500-....-~~~~~~~~~~~~~~~~~~~~~~~~---.
20
00
15
00
10
00
50
0
link
of
sam
e so
ils
but
di ff
. de
nsiti
es. /
/ /
/ /
~
+
/
"'-o
----·--o
O-t-~---it---~--1-~~--~~t---~--1-~~-+-~~t---~-+~~-+-~--1
0 1
0
20
3
0
40
50
6
0
70
8
0
90
1
00
RE
LA
TIV
E
DE
NS
ITY
D
r [%
]
Fig
ure
1
6.
Bul
K
Mo
du
lus
Num
ber
Kb
as
a F
un
cti
on
o
f R
ela
tiv
e
Den
sity
.
()J co
39
in all cases is increasing with density. The relationship is
given by Eq. 3-22.
Kb= 57 + 1.22 . Dr+ 0.09 . Dr2 (3-22)
The relative density is also used in x. BacKcalcula-
tion of the bulK modulus parameters for most cases.
including Willamette River sand. which have not been
included in the correlation procedure gave
results.
reasonable
40
CONVENTIONAL PARAMETERS
The cohesion and friction parameters are the tradi
tional properties presented in Chapter I I. Since this study
is confined to granular soils i.e. sands, silts and gravels,
which rely entirely on friction for the mobilisation of
shear strength, only • and A• are of significance.
Conventional Parameters from PMT
The pressuremeter test is fundamentally different from
conventional soi 1 investigation methods, so the different
set of soil parameters is not surprising. It is apparent
however, that the use of these parameters is most 1 iKely to
yield the best results. Nevertheless, correlations of
pressuremeter data to conventional parameters have been
reported (G.Y. Felio, J.-L. Briaud,
success.
1986) and used with
c.P. Wroth (1982) recommended the use of the following
equations.
sin •' =
sin a =
CKa+1) ·s
CKa-1> · s+2
2Kas - (Ka-1>
CKa+1)
(3-23)
(3-24)
5 = sin 4'' · (1 +sin 0)
(1 + sin 4'')
41
(3-25)
where 4'' is the effective angle of internal friction, e is
the angle of dilation, and Ka is the active earth pressure
coefficient as given by Eq. 3-26.
Ka = tan2 ( n/4 + 4'cv/2 ) (3-26)
and 4'cv is the angle of internal friction at the end of
the pressuremeter test at which the sand has reached its
critical state. C.P. Wroth (1982) states that if 4'cv is un
known it might be approximated by 4'cv = 35°.
Recognizing that the angle of repose for a granular
material is equal to the angle of internal friction at the
critical void ratio (constant volume) D.H. Cornforth (1973)
recommended the use of a diagram (Fig. 17) in which the
increase in 4'' is given as a function of the relative dry
density.
Eq. 3-27.
The actual value for 4''
4'' = 4'cv + 4'dc
is calculated using
(3-27)
An empirical correlation between the practical net
t imit pressure, Pt*• and the angle of internal friction has
been pubt ished (Centre d'Etudes M!nard, 1978).
4'' = 5.77·1n(P1*) - 7.86 (KPa) (3-28)
Ul
w
w
a:
t!>
w
8 u "O
o0o -
'.I:
I- t!>
z w
a:
I- en
LL.
0 en
I- z w
z 0 a..
:I::
0 u >- I- H en
z w
a
COM
PON
ENTS
OF
ST
REN
GTH
AS
A
FU
NC
TIO
N.O
F D
ENSI
TY
f\FTE
A:
O.H
. CO
RNFO
RTH
(197
3)
15
14
13
12
T
rlax
lal
compre~sion ~~-
11
10
P
lane
str
ain
~-·~-
g 8 7 6 5 4 3 2 l 0 0
10
2
0
30
40
so
6
0
70
BO
9
0
10
0
RELA
TIV
E DR
Y D
ENSI
TY
[%)
Fig
ure
17
. D
en
sity
C
om
po
nen
ts
of Strength~·.
~
['\)
43
Finally, it should be noted that, using Eqs. 2-13,
2-14 and others a theoretically correct value for~ could
be calculated if c is Known. It has been shown (F. Baguel in,
J.F. Jezequel and D.H. Shields, 1978) however, that minor
errors in Of, Po and P1 have a significant impact on the
computed angle of internal friction. The accumulation of
those errors might even lead to meaningless results, so that
this approach can not be recommended.
For the calculation of initial stresses due to
gravity, the lateral earth pressure coefficient at rest, K0 ,
and the dry unit weight, Ydry• is also a frequently required
input for finite element programs.
K0 is defined as the ratio of the horizontal effective
stress, oh 1, to the effective vertical stress, Oz 1
•
Oh1
Ko = (3-29) Oz1
Theoretically, PoM as shown in Fig. 4, should give
some indication of the value of K0 , because it indicates the
point on the pressuremeter curve where the soil has been
reloaded to its initial stress state. However, unavoidable
borehole disturbance and membrane resistance have a strong
impact on this early part of the pressuremeter test, so that
K0 and Ydry are usually assumed, based on soil type and con
dition or other soil tests.
T.C. McCormack (1987) showed in a parametric study for
44
a retaining wall that K0 has only negligible effects and
hence, it seems reasonable to base K0 and Ydry on engi
neering judgement. Typical values for various soil types can
be found in virtually any soil mechanics textbooK.
CHAPTER lV
SOIL TESTING PROGRAM
SELECTED SOIL
All tests were conducted using dry Willamette River
sand containing grains of subangular shape. The grain size
distribution curve is given in Fig. 18. According to the
unified system of soil classification, the sand is classi
fied as SP. The specific gravity was determined as 2.70,
the minimum and maximum densities were 1.30 g/cm3 and
1.67 g/cm3, respectively. The angle of repose was found to
be tcv = 31,90,
A total of twelve direct shear tests with normal
stresses ranging from 15.5 KPa to 124 KPa were carried out.
Furthermore, three pressuremeter tests at two different
depths, as wel I as nine triaxia1 compression, tests were
conducted.
TRIAXIAL TESTS
A total of nine consolidated-drained triaxia1
compression tests were carried out at confining pressures of
138 KPa, 276 KPa, and 414 KPa. Failure was approached at a
constant rate of strain. Three test series in relative
densities of 50 X, 70 Y., and 95.6 Y. were conducted. Since
~I
c ·a .... &1
.... c:
QJ t'.I
QJ
a..
Gra
in
Siz
e D
istr
ibut
ion
[mm
}
0
10
20
30
40
so
60
70
80
90
100 0.
001
J .. -_
/ _ ...
0.
005
0.01
0.
05
0.1
' I j I I
Fig
ure
1
8.
Gra
in
Siz
e
Dis
trib
uti
on
C
urv
e fo
r W
i I
lam
ett
e
Riv
er
San
d.
____ ...,..._
, ..... ""~~~·~---·-··~-
--·
~ --
1~1"~ ' ' I 0.5
1.0
5.
0 10
.0
100
90
80
70
60
50
40
~
20
10
0 ~o
100.
0
"C
QJ
Vl 1:3
a.. ... ~
u '- QJ
a..
~
en
47
volume changes are an important aspect of the triaxial tests
a large specimen size of 7.2 cm diameter and 14 cm height
was chosen, thus magnifying poisson 1 s ratio effects. The
specimen ends were not lubricated.
Sample Preparation
It is virtually impossible to obtain undisturbed sand
specimens for triaxial tests, but since the accompanying
pressuremeter tests were conducted in an artificially placed
soi 1 it is now possible to reconstruct samples of equal, or
at least similar, properties.
Two rubber membranes inside each other were mounted
in a membrane jacKet, a slight vacuum was applied and a
porous stone fitted inside the membrane, forming the bottom
of the sample and al lowing for drainage. The membrane jacKet
was arranged on the pedestal and a predetermined amount of
sand, corresponding to the desired density, was placed
uniformly inside the membrane and topped with a second
porous stone.
Whithout releasing the vacuum stretching the mem
branes, the inner membrane was slid over the top cap. The
application of a slight internal negative pressure through a
hole in the pedestal added some strength to the sample, so
that the outer membrane and the o-rings could be slid over
the top cap and the external support by the membrane jacKet
therefore made redundant. From that point on the standard
procedure to assemble the confining chamber and the dial
48
gauges was followed. A confining pressure of 34 KPa was
applied before the internal negative pressure was released.
Hence, the specimen had never been without support or
confinement.
Prior to testing, the specimen was saturated in order
to observe volume changes and the confining pressure was
increased to the test level. After sufficient time for the
sample to consolidate under the all around confining pres
sure (depending on the specimen density and the confining
pressure it tooK from 15 to 30 minutes) the test was
conducted.
Failure to seal the sample effectively would have
resulted in erratic volume change measurements, therefore a
high vacuum grease was used to establish, and maintain, the
best possible contact between the pedestal or top cap and
the membrane. The use of two membranes and two a-rings for
each end added further to the seal quality.
Test Results
Volume change and axial load readings were taKen every
0.051 cm of deformation, corresponding to 0.36 Y. axial
strain. For the first test CDr = 50 Y. and a 3 = 138 KPa)
twice as many data points, as for the remaining tests, were
recorded. The data points given in the following diagrams
represent the genuine material properties. Stress-strain
diagrams with volume change curves of the tests are given in
Fig. 19, 20, and 21. A correction for membrane resistance,
ro Cl. ~
(/) Cf) w a: t(/)
a: 0 t-< H > w 0
~
z H < a: t(/)
u H a: tw :i: :::::> ..J 0 >
TRIAXIAL TESTS - Dr = 50 % STRESS-STRAIN CURVES
2000-r-~~~~~~~~~~~~~~~~~~~~~~
1500 Cl3 = 414 kPa
1000
500
_____ . __ .__....-·
/.~------· ;;~·-·~..--.-~ _0
_3_: 276 kPa
Iv/.--·-// ....-.---·- __ o3 = 138 kPa
. ·-
0 ' 0 l 2 3 4 5 6 7 8 g 10 11 12 13 14 15
AXIAL STRAIN (%]
TRIAXIAL TESTS - Dr = 50 % VOLUME-CHANGE CURVES
s-.-~~~~~~~~~~~~~~~~~~~~~~--.
4
3
2
0
-1
-2
-3
-4
• Data points used for computation of hyper
bolic parameters
~ _,._,._,. ~~.......__ .. ____ ,, ---0
~ 0-0 ----0 --~ ~-0
+'--.... -·-· ·-· .. ------·--·---5-+-~+---+~-+~-+-~+-~1--_,.~-+-~-+-~+-~~-+~-+-~+----<
0 l 2 3 4 5 6 7 8 g 10 11 12 13 14 15
AXIAL STRAIN (%]
Figure 19. Stress-Strain and Volume Change Curves for Wi I Jamette River Sand ,Dr = 50 /..
49
~
t1l a.. 26
UJ UJ w
TRIAXIAL TESTS - Dr = 70 % STRESS-STRAIN CURVES
2000~~~~~~~~~~~~~~~~~~~~~~~~~~~
1500
~--·-·-. /' ___,_.._,, • 414 kPo
.+
~.----o-
g: l 000 UJ
/ o.-_o I -"--<-----"-'-. • 176 kPo
a: 0 I-< H >
__ .., __ ,... ~ 500 o~" - .. ---.. --- .. --2 .. = 138 kPa
§ z H < a: 1-UJ
u H a: 1-w :i::: ::i _J 0 >
O+---t~-+-~+--+~-+-~+---+-~~---il----+-~+---+~-+-~+---1
0 l 2 3 4 5 6 7 8 9 10 11 12 13 14 15
AXIAL STRAIN [%)
TRIAXIAL TESTS - Dr = 70 % VOLUME-CHANGE CURVES
s---~~~~~~~~~~~~~~~~~~~~~~--.
4
3
2
• Data points used for computation of hyper
bolic parameters
o~------------------------------------~...__
-.. ~ .. _ ,, ___ ,, ___ ,, "':::: ---·-· .. 0-'-... o ----o-~o-o-o .. --.. ___ ,,_ .. _ .. __ .. __ ..
-1
-2
-3
-4
-5-1---1~-+-~-+---+~-+-~+--+~-+-~~-+-~+---1~-1-~-t---1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
AXIAL STRAIN [%)
Figure 20. Stress-Strain and Volume Change Curves for Wi 1 Jamette River Sand ,Dr= 70 I..
50
~
IC a.. ~
UJ UJ w
TRIAXIAL TESTS - Dr = 95.6 % STRESS-STRAIN CURVES
·-~ ............ 2000 .,---- ~ ,, " 414 kPo
/ ----------· 1500
~ 1000 UJ
a: a I-< H > w a
§ z H < a: 1-UJ
u H a: 1-w :i: :::i _J a >
--.. --.._ .. _,. 500
o = 138 kPa 3 -- ..
O+---t~-+-~-+---+~-+-~+---+~-+-~t---+~+---t~-+-~+---1
0 l 2 3 4 5 6 7 8 g 10 11 12 13 14 15
AXIAL STRAIN (%]
TRIAXIAL TESTS - Dr = 95.6 % VOLUME-CHANGE CURVES
s~~~~~~~~~~~~~~~~~~~~~~~~
4
3
2
0
-1
-2
-3
-4
____ .. _ .. _ .. _ /" -·
/
,. ___ o __ o_o_
~o C>------O
/" 0,,.,----;;,r,7,c~.:._..----·----·--·-·~ ~.T ---------------. -------------
• Data points used for computation of hyper
bolic parameters
-S+---!~-+-~+---+~-+-~+---+~-+----1---+-~+---+~-+-~+---1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
AXIAL STRAIN [%]
Figure 21. Stress-Strain and Volume Change Curves for Wi I Jamette River Sand ,Dr = 95.6 /..
51
52
drain resistance or ram friction was neglected, and it is
not done on a routine basis with these test rates.
Table I I summarizes the hyperbolic soil parameters
computed in accordance with the soil model by J.M. Duncan
(1980), as presented in Chapter I I I. sample calculations are
given in the Appendix.
The finite element code AXISYM requires poisson's
ratio values prior to, and at, failure as input and avoids
the bulK modulus formulation. Using Eqs. 3-6 and 3-19
values corresponding to the computed bulK modulus parameters
have been determined and are listed for completeness. Since
failure for the higher densities coincides with horizontal
tangent moduli, a value of 0.5 would be appropriate. The
same value is chosen for the lower density because no volume
change taKes place when the critical void ratio is reached.
Due to limitations of the finite element formulation a value
of Vf = 0.49 has been selected.
53
TABLE I I
PARAMETERS FOR SAND - HANDCALCULATED
Parameter Dr = 50 Y. Dr = 10 Y. Dr = 90 Y.
K 540 650 860
n 0.45 0.65 0.95
4' 39.5 40.7 43.7
Rf 0.91 0.78 0.86
Kb 106 315 360
m o. 19 0.05 o.o
v 0.33 0.39 0.30
Vf 0.49 0.49 0.49
The computer program SP-5 written by Kai Wong at the
University of California at BerKeley in 1977 (J.M. Duncan et
al. 1980) , was adopted to evaluate the strength and stress
strain parameter by means of the least squares regression
method. The computer solutions for the conducted triaxial
tests are given in the Appendix.
Comparision of the computed bulK modulus values with
the proposed correlation to relative density, as displayed
in Fig. 15 and 16, reveals only little deviation from the
given curve. So that the incorporation of the Willamette
River sand data would not have changed the correlation
significantly.
54
Good agreement to hand computed values is recognized
upon inspection of Table I I I, which summarizes the parameter
obtained by the computer program. The increased deviation
for the bulK modulus numbers with increasing density is
believed to be a result of the deviator stresses used by the
program to compute the bulK moduli.
TABLE I I I
PARAMETERS FOR SAND - SP-5 SOLUTIONS
Parameter Dr = 50 :t. Dr = 70 ;t, Dr : 90 :t.
K 555 645 872
n 0.43 0.78 0.93
~ 39.8 41. 0 44.0
Rf 0.91 0.78 0.85
Kb 104 298 396
m o. 17 0.04 o.o
v 0.33 0.39 0.30
Vf 0.49 0.49 0.49
55
PRESSUREMETER TESTS
An EX PUP pressuremeter with a monocell probe (32 mm
diameter) and a length to diameter ratio of L/D = 8 was used
for all tests. The control unit was located at an elevation
not requiring any hydrostatic correction at the gauge level.
The pressuremeter was placed in the soil container prior to
deposition to eliminate stability problems from the dry
sand. A total of three pressuremeter tests were carried out.
Placement Procedure
Pressuremeter testing tooK place in a plywood,
cube-shaped chamber 90 cm x 90 cm x 90 cm, and in steel
drums of 57 cm diameter and a height of 86 cm. The sand, air
dried (water content= 1.0 X), was deposited by pluviation
through air from a constant height of fall of 90 cm through
openings of 20.6 mm and 14.3 mm in diameter. resulting in a
uniform, relative density of Dr = 68 X. Density pots were
placed during deposition of the sand and penetration tests
were carried out to confirm the desired uniformity. Further
details of the sample preparation have been described by
J.J. KolbuszewsKi and R.H. Jones (1961) and by T.D. Smith
(1983).
Test Results
Injected volume and radial pressure readings were
taKen every 10.1 cm3 of injected volume corresponding to
56
4.63 Y. of volumetric strain. The first test was performed in
the plywood chamber and the following two in the steel
drums. Equal test results for the chamber test and the first
drum test (both were conducted under equal overburden
pressure) confirm that the different sizes of the testing
container did not influence the test results, but the amount
of sand to be deposited had been reduced considerably.
For volume loss and membrane resistance corrected,
pressuremeter curves are given in Fig. 22 - 24. Their
different appearance from the typical pressuremeter curve,
as given in Fig. 4, is expected considering that the probe
was in place while the sand was deposited. For this reason
no stress relief tooK place in order to drill the hole for
probe insertion and therefore the curves are similar in
shape to those from selfboring pressuremeter tests. The
interpretation of the curves however,
identical.
is essentially
The problem of a critical depth, De, for pressuremeter
tests has been investigated by a number of researchers.
J.-L. Briaud and D.H. Shields (1981) reported critical depth
effects on the 1 imit pressure up to a depth of 20 diameters
or 1.20 m in medium dense to dense sands. Deformation moduli
were not influenced. A finite element study by T.D. Smith
(1983) indicates a critical depth for cavity moduli at ap
proximately 12 times the radius of the probe.
considering the foregoing, the pressuremeter curves
,-, ro
CL
200
~ 150
w a: :::> Cf) Cf) w a: a... _J 100 < H 0 < a:
50
57
PRESSUREMETER TEST - CHAMBER I Dr ~ 66.4 %, Depth ~ 57 crn
i +-+ Calibration curves +
o-o Row data curve
._. Corrected PMT curve
/ /. + //
/ ~·
/ /'/ //1( //'
l. AA I ... I /.Ji
/ .
·---·--· . - r___.-·-·-· Q_._._._ __ ""-+ ____ .._._-+-...__. ......... _.._+--_____ -+-______ ~
0 50 100 150 200 250
INJECTED VOLUME [ccm)
Figure 22. Pressuremeter Curve - Chamber Test, Dr = 66 ~.
PRESSUREMETER TEST - DRUM I 58
Dr ~ 66.9 %, Depth c 57 cm
t +-+ Calibration curves +
o-o Row data curve
-· C or rec t ed PHT curve 200
+ I I .....-,
co CL .::L ..__,
150 w a: ::J CJ) CJ)
w a: a.
~ 100 H a <( a:
...
50
/.
·--·--· / r-~·~-·
0 +-' _____ """-+-__ ...._._.._...,_. ........ _._"""-+-__ ___._,_-+-.__._ __ ~
0 so 100 150 200 250
INJECTED VOLUME [ccm]
Figure 23. Pressuremeter Curve - Drum Test I, Dr = 67 I..
59
PRESSUREMETER TEST - ORUM TI Dr ~ 67.9 %, Depth= 147 cm
t + +--+ Calibration curves 9
o--o Row data curve I ·200 -· Corrected PMT curve //
,....... ro CL y ...._.
w 150 er: :J UJ UJ w er: Q._
..J < 100 H 0 < er:
50
// (
/_,, 1 I ,/______. / }· /+
I A /,/' I !Ji ,
I. /./{;)
1 r· ,, i.--·-·-o·-·-·-·/·
+
Q-+---------+----.i......a..--+-......_._.__._~_.__._~_.____._._~
0 50 100 150 200 250
INJECTED VOLUME [ccm]
Figure 24. Pressuremeter Curve - Drum Test I I, Dr = 68 /..
60
given in Fig. 22 and 23 are probably influenced by critical
depth effects and have to be carefully inspected. Even
though the data reduction for drum test I I (Fig. 24) has
been difficult due to low confining pressures and a high
membrane resistance the given curve most I iKely represents
the genuine material properties.
The following soil parameters are computed according
to the proposed method and are summarized in Table IV based
on the pressuremeter tests illustrated in Fig. 23 and 24.
TABLE IV
PARAMETERS FOR SAND BASED ON PRESSUREMETER TESTS
Parameter
KpM
s
• Rf
Kb
m
v
Vf
Dr = 68 :I.
84 (650)*
0.51 (0.65)*
41. 9 (40.7)*
0. 71 (0.78)*
556 (315)*
0.09 (0.05)*
0.33 (0.39)*
0.49 (0.49)*
•Based on triaxial data (see also Table I I).
CHAPTER V
FINITE ELEMENT STUDIES
INTRODUCTION
The finite element method has, since its development
by M.J. Turner et al. (1956), experienced an enormous
number of app l i cations in many engineering disc i p 1 i nes. In
principle, a continuum is divided into discrete elements
with connecting nodal points and equilibrium equations are
generated for each element with unknowns at each nodal
displacement. These equations are stored in matrix form and
solved for the nodal displacements. Once the joint displace-
ments are Known the strains and subsequently the stresses
within each element can be calculated from elasticity.
The stress-strain relationship for axisymetric sol ids,
expressed in Eq. 5-1, is based on the genera 1 i zed Hooke's
law and applies to each element, the solution is obtained
for the entire continuum.
(] 1-v v v 0 E r r
(] E v 1-v v 0 E z = z
(] (1+v) (1-2v) v 1-V v 0 E e 1-v e
'l' 0 0 0 -- y yz 2 yz
(5-1)
62
It is apparent that this solution procedure is
only practicable in conjunction with high speed computers in
order to solve for the many unKnowns in the large number of
equations. In fact, a fairly simple structure, consisting of
only a few elements, could not be solved by hand.
In the case of most geotechnical finite element codes,
the nonlinear behavior of the material compounds the
complicated process with the difficulty of updating modulus
of elasticity values, depending on the current stress level.
Furthermore, anisotropy, di latancy (granular soi Is), strain
softening (brittle materials) as well as time dependency and
stress history are factors of significant influence on soil
displacements upon load application. This wide variety of
problems illuminates the enormous difficulties to formulate
a general constitutive law for soils.
The implementation of the hyperbolic soil model into
computer programs employing the finite element method was
the next logical step after its initial formulation by
F.H. Kulhawy et al. (1969). Since then this model has been
1 inKed to numerous finite element programs for the solution
of various geotechnical problems.
FINITE ELEMENT PROGRAM "AXISYM"
The finite element program AXISYH developed by
D.M. Holloway (1976) models the nonlinear behavior of the
soil according to a hyperbolic function (described in
Chapter I I I except for the bulK modulus
63
formulation)
incrementally in successive, I inear portions (Fig. 11).
In solving the finite element mesh for its nodal
displacements, a distinct tangent modulus value is assigned
to each of the five node (four external and one internal)
quadrilateral elements depending on the current stress level
in the specific element. In other words, a 1 inearly elastic
program is tricKed into nonlinear model I ing by a piecewise
I inear elastic solution of a nonlinear problem. The
principal advantage of the tangent modulus approach rather
than utilizing the secant modulus is, that a non-zero stress
state can be model led. In addition, a ful I load vs. deflec
tion response is obtained.
In addition to the aforementioned two-dimensional
element, the use of a one-dimensional interface element is
possible to allow relative displacements between two sol io
elements. The problem geometry and loading conditions are
model led in axisymetric coordinates. Loads may be applied in
steps and additional iterations can be specified to improve
convergence. The assigned tangent modulus is updated and
subsequently the mesh is solved again for its nodal dis
placements, strains and stresses.
It should be noted that the stress-strain relationship
given by Eq. 5-1 is accurate only in the range of small
strains and therefore only stresses and strains prior to
failure should be considered.
Volume Chanse·s
In the formulation
the hyperbolic soi I model
64
of AXISYM, the latest version of
is not incorporated, i.e. the bulK
modulus formulation is omitted. Two values of poisson's
ratio are required as part of the material property input,
this is poisson's ratio before failure and at failure,
Vf· Clearly, poisson's ratio is constant regardless of the
stress level up to failure, from whereon the second value is
used.
Problems due to a value of v approaching 0.5 can be
seen by inspection of the term preceeding the elasticity
matrix (Eq. 5-1). The solution of the matrix for radial,
circumferential, axial and shearing strains would cause an
unstable situation. Plane strain and axisymetric problems
encounter in this respect similar difficulties for constant
volume or di latant soils and most geotechnical problems are
frequently grouped into either of these two categories.
For these reasons, both values of v are not to exceed
the specified limits of
0 < v < o. 49 • . . • • • • . • • • • • • • • (5-2)
This implies that dilatant materials l iKe dense sands
or stiff clays with values of v > 0.5 can not be modelled
accurately, which is somewhat less critical since the hyper-
65
bol ic model itself does not account for di latancy.
Noteworthy is the approach L.R. Herrmann (1965) tooK,
in his entirely different stress-strain relationship formu
lated for elastic materials. The problems due to v = 0.5 are
eliminated.
66
FINITE ELEMENT ANALYSIS - PRESSUREMETER TEST
To evaluate the computed hyperbolic soi I parameters
and in order to gain an increased understanding of the soil
behavior during cavity expansion, a pressuremeter test was
simulated analytically using the finite element code AXISYM.
The accuracy of the code was evaluated by a "patch" test as
recommended by R.H. MacNeal and R.L. Harder (1984). A thick
walled cylinder with elastic properties and an internal
pressure condition was analyzed. Good agreement to the close
form solution was observed with a deviation of -8 X to the
handcomputed values if poisson's ratio was taken as 0.49.
The validity of the chosen mesh with 260 elements, as dis
played in Fig. 25, was confirmed using the elastic solution
byM. Livnehet al. (1971).
Two materials were used for the nonlinear AXISYM
analysis. The soil was Willamette River sand with 70 x
relative density for which the hyperbolic parameters have
been determined in Chapter IV. The second material was an
elastic material simulating dri 11 ing fluid, and supported
the cavity during gravity-turn-on prior to pressure
application. Table v summarizes the selected parameters.
J_ 9
·+sa~ ~a+awa~nssa~d JO s1sA1euv ~OJ ~saw +uawa13 a+!U!J '92 a~n6!J
I
, , , , , , 'iE ,9·
,..o-----+---+-+--+--+--+-+t-tttic-1-~
/ 6 /n----+----+-+-+-+.-,1-+~i!++-1~>/ /
Vl 0
/0----+----+--+-+-+-!l-f-H~~~ / /
Vl 0
,A1----+---l-+-+-+-+--+-1~..,_,~ ... ~ /o----+---+--+-+-+-1-f-H~~::·~i.n
~fj N /D----+-~-1--+-+-+-~.......-~-~ ~AJ.----+---+-+-+-+--+--1-t-#t-i"""l:: _ ... ~ /n----+---+--+-+-+-~-H~··· ----- ~ /.n-----+---+-+-+--1-+--+-1-4+++~;;;;;iI _ ... ~ , f ~
~~---+---1--l-+-+-.__.i-+-<~%i==== ~ ::·:·· "'
/..o----+-~-+-+-+-+--1--1--1-+U-~:::8 i.n , }}-~~ /o-----11---+-~-+-+-!-~+"4-~~ , .. ,.. i.n ,1:1-----+---+-+-+-+--+-++-1++1~ -~ ,,. ._,,,.
, ') ~
, [}----+----+--+--+-+--+---<~~ - >-, t ,. , / / 1=: A1---+--+-+-++-l--H-+H-~ ->-~ ::·::ii
~n-~---i.~~--1--1--+-.+-~~i~.g ~ I ~ Q·l ~__.__..__.__........._~,_.....___._
aJOJJflS aOJ:I D!n LI 5U!J1!-0
~
68
TABLE V
TRIAXIAL SP5-PARAHETERS USED FOR ANALYSIS OF PHT
Parameter Wi 11 amette Ori 11 i ng River Sand Fluid
K 645 1. 0
n 0.78 o.o
4' 41. 0 o.o
Rf 0.78 1. 0
v 0.39 0.20
Vf 0.49 0.20
Ko 0.4 t.O
Ydry 15.10 KN/m3 23.70 KN/m3
An increasing hydrostatic pressure was applied from
within the cavity. The computed displacements allowed the
calculation of the corresponding cavity volume. Additional
analysis with the same parameters but a vertically expanded
mesh, allowed the simulation of pressuremeter tests at
varying confining pressures. A plot of the computed soil
moduli with increasing depth (Fig. 26) confirms the rel a-
tionship given in Chapter I I I, proposed for a variation of
pressuremeter moduli with overburden pressure. The absolute
number however, is different from the actually measured
value as dispayed in Fig. 26, indicating a possible
violation of the fundamental plane strain assumption.
......
ltl a.. ~
.......
CJ)
:::l
_J
:::l
0 0 l:
_J
H
0 CJ)
SOIL
M
ODUL
US
AS
A F
UN
CTI
ON
OF
D
EPTH
B
AS
ED
O
N A
XIS
VM
S
OLU
TIO
NS
A
T E
9 •
5 "
2000
0....
.----
----
----
----
----
----
----
----
----
----
----
----
0 P
red
icte
d
Res
pons
e
+
Mea
sure
d
(PM
T)
1600
0 (!
)~
12 0
00 I
0
8 00
0
4000
(i
)
+
+
0-1-
----
----
----
----
----
----
--.--
----
-...--
---..
..,...
----
-1
0 2
4 5
DE
PT
H
[m]
Fig
ure
2
6.
Vari
ati
on
o
f P
ress
ure
mete
r M
od
uli
w
ith
In
cre
asi
ng
D
ep
th.
6 7
°' Ci)
70
FINITE ELEMENT ANALYSIS - FOUNDATION
The first independent use of the hyperbolic parameters
based on pressuremeter testing was made by predicting the
load deflection response of a circular footing, with simi Jar
characteristics as the model foundation in the following
chapter.
The vertical surface displacement for a rigid circular
foundation on elastic material
E.H. Davis 1974) by,
dz = n /2 · ( 1 - v2) Pav a
E
is given (H.G. Poulos and
( 5-3)
where Pav is the average pressure acting on the soil and 'a'
is the radius of the loaded area. Using elastic properties
an AXISYM analysis gave almost identical results compared to
the close form solution (deviation -2 I.).
Modelling the problem analytically, using the finite
element program AXISYM, a center point load of 100 N was
applied in 19 increments. A total of four different
materials was used to simulate the mesh configuration as
presented in Fig. 27. The same soil was used with a relative
density of 70 I., for which the previously calculated
hyperbolic parameters from pressuremeter testing were used.
Average properties for brass were assigned to the elements
representing the foundation. A row of one-dimensional
interface elements has been introduced between the
N 'J .--:
E u
11 ri
"
Point r. load~'t..
I /
l nt er foe e elements
Footing ~Aic etements
---,-- ---1------:------ --- - i= / I I I I~
,,,,. : /; ~ I -IJ"l ..-
IJ"l ..- I
\ /\ Ll1 ...--
Ul ......
0 ,...;
0 ,...;
0 rri
0 -4
0 ..:i
I 1.11 I.Ii
I// // / /// // / / / //// // / / / / / / /.-I • I I • I • I
].6.l.1.5 .. l,.1.5.IP .. 1.2.0.1.2.0.1.2.012.0.1. 3.65 17.75 cm
Figure 27. Finite Element Mesh for Analysis of Model Foundation.
~ r./
~ ~
~ ~ ~ ~ v ~ ~ I / v / ~
~ / /
~ I / ./ / / I ~
/ / I I / / I
~
71
72
foundation base and the soi I surface to permit slip between
the two materials. Finally, elements having the properties
of air have been employed to form a continuum. Table VI
summarizes the selected values.
The mesh containing 142 elements was analyzed in
axisymetry. The introduction of the interface elements did
not yield significant changes in displacements or stresses.
The performance of the foundation in terms of settlements at
the footing center vs. axial load is presented in Fig. 28.
TABLE VI
PRESSUREMETER PARAMETERS USED FOR FOUNDATION ANALYSIS
Parameter
K
n
~
Rf
v
Vf
Ko
Ydry
Wi 11 amette River Sand
84
0.51
41. 9
0.71
0.33
0.49
0.40
15. 10 KN/m3
Foundation (brass)
o.o
0.0
o.o
1. 0
0.30
0.30
o.o
118. 81 KN/m3
Interface Element
1500
0.8
a = 250
0.8
~
z .__,
a <
0 _J
0 w
H
_J
CL
CL <
AN
ALY
TIC
AL
FOU
ND
ATI
ON
R
ESPO
NSE
BA
SED
ON
A
XIS
YN
SO
LUTI
ON
S
15
0
14
0 t
Tri
ax
ial
par
amet
ers
lt
13
0
a PH
T p
aram
eter
s
12
0
11
0
10
0 +
lt
0
90
80
+
lt
0
70
60
+
I+
0
50
+
I+
0
40
I I+
0
lt
0
30
..
a ..
a 2
0
I+
0
....
0
0 10
I+
~
0
0 0
1 2
3 4
5 6
7 8
9 10
11
1
2
13
1
4
15
SETT
LEM
ENT
[mm
]
Fig
ure
2
8.
Lo
ad
-Defl
ecti
on
R
esp
on
se
for
Mod
el
Fo
un
dati
on
fr
om
A
XIS
YM
u
sin
g
Pre
ssu
rem
ete
r P
ara
mete
rs.
-.j w
74
A detailed inspection of the accumulated computer
results revealed a very clear picture of the generated
failure mechanisms. From the first load application of 1 N
failure was noticed in some of the elements. Initiating from
the footing edges failure continuosly extended into the
halfspace upon load increase. Graphically the load failure
relationship for the elements is captured in Fig. 29.
El w
Ln o:j N
I
Failure of elements at load of..... 75
-El
~
l Point load-,, , .If.
u:
C> rri
J I
0' rn
J
Oi rn'
C> -.1
C> -.s
Ln1 tnl
1 N ~ 9 N
4 N n::q 11 N
5 N D 20 N
Footing Free surface
17.75 cm
Figure 29. Failure Generation During AXISYM Analysis.
CHAPTER VI
MODEL FOUNDATION STUDY
In the previous chapter the response of a foundation
was analytically investigated by means of the finite element
code AXISYM. In order to further evaluate the established
I inK between hyperbolic parameters and the pressuremeter
test, the aforementioned footing was bui It, instrumented and
subjected to a concentric point load similar to the
analytical problem.
MODEL FOUNDATION AND LOAD APPLICATION
A consol idometer brass loading cap was employed as a
model foundation measuring 1.2 cm in thicKness and 6.2 cm in
diameter. With a weight of 372.3 g and a Young's modulus of
110000 MPa this may be considered rigid relative to the
soil. From its original design the model footing was
furnished with a hollow sphere on top so that, by insertion
of a metal bal I weighing 66.6 g, a normal load application
was forced. The bearing capacity for the model footing was
determined after G.G. Meyerhof (1955) as being 67 N.
The sand was placed in a cylindrical container with a
diameter of 35.5 cm and a height of 28.5 cm so that the
depth of the container measured more than 4.5 times the
77
footing diameter. The placement procedure for the sand was
similar to the one used for the pressuremeter tests, except
that the sand was sieved into the container from a height of
15 cm. The application of high frequency (175 Hz) vibra
tions by means of a 3.5 cm diameter vibrating concrete
poKer, along the outer wall of the container yielded a
relative density of Dr = 70 1.. The uniformity of the
sand specimen was confirmed using cone penetration tests
and only insignificant changes colud be detected.
FOUNDATION TESTING PROCEDURE AND RESULTS
For this model foundation study the previously used
triaxial test apparatus has been employed as a loading frame
for the model foundation, al lowing a smooth and gradual load
application and settlement readings at the footing center.
The brass footing was placed on the level led sand
surface in the center of the container as shown. After the
dial gauge was mounted and initialized, the load was
gradually applied by the triaxial gear box up to a maximum
force of 225 N (by far exceeding the calculated bearing
capacity) at which a settlement of 2.5 cm was measured.
Applied load measurements were taKen every 0.127 mm of
settlement at the footing center corresponding to 0.02 r. of
the footing diameter. Fig. 30 is a graphical display of the
foundation response as measured in the loading frame.
Repeat tests showed almost identical results and the
z 0 < a _
J
0 w
H
_J a..
a..
<
MOD
EL
FOU
ND
ATI
ON
R
ESPO
NSE
M
EASU
RED
v
s.
PRED
ICTE
D
2sor--:--;;:~-::::--:~::--::--~~~~~~~~~~~~-
+ * 0
Mea
sure
d
resp
on
se
20
0
15
0
10
0
50
Pre
dic
tio
n
(Tri
ax
ial
para
mete
rs)
Pre
dic
tio
n
(PM
T p
ara
mete
rs)
~
~
+++
+• ..
. .-.C
l t
....
..,,
...,
.
.. +• . +
• : +• +
+ . . .
D
D
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24
CEN
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ENT
[mm]
Fig
ure
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ad
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79
addition of dial gauges on the edge of the footing confirmed
that no tilt took place upon load application.
Comparing the
settlements (Fig.
predicted
30) at the
(Fig. 28)
footing
to the measured
surface it is
recognized, that only poor aggreement is achieved, compared
to the measured deflections. The deviation of predicted
(using parameters based on pressuremeter tests) and measured
deflections is explained by the very low modulus number
used. Violation of the plane strain assumption during
pressuremeter testing is a possible source of error. An
additional factor of influence is suspected to be introduced
by the placement procedure for the sand. Grains raining down
in the vicinity of the probe are 1 iKely to contact the probe
prior to final deposition leading to an area of looser
material surrounding the probe.
A second execution of the problem using the parameters
from triaxial tests resulted in much better agreement to the
measured deflections as Fig. 30. shows.
CHAPTER VI I
CASE HISTORY
A final evaluation of the proposed 1 inK between
pressuremeter tests and the hyperbolic soil model is
accomp 1 i shed using results from pressuremeter tests
performed under field conditions as presented in the
fol lowing.
SAND 'H' DEBRIS BASIN
To evaluate the stabi 1 ity of an earth retaining
structure a number of prebored (NX size TEXAM probe) and
driven (slotted tube)
(T.D. Smith and C.E.
pressuremeter
Dea 1, 1988) .
embanKment shows severe longitudinal
moisture sensitive foundation. Built
tests were performed
The investigated
cracKing due to a
on fan debris flow
deposits comprised of stratified gravels, sands, and silts,
conventional soil
economical soi 1
investigation methods fail to provide
information because of the coarse grained
materials (Ydry = 19 KN/m3) involved.
A summary of the results for the conducted pressure
meter tests is presented in Table VI I.
81
TABLE VI I
PMT RESULTS FOR DRY SOIL
Depth <J ' z G EM Of P1 PL [m] [KPa] [KP a] [KP a] [KP a] [KPa] [KPa]
1. 83 34.8 8034 21370 1250 1750 2929
1. 83 34.8 1992 5300 270 570 687
2.74 52. 1 6015 16000 400 1160 1406
3.66 69.5 2519 6700 300 650 826
4.57 86.8 3019 8030 300 550 907
6. 10 115. 9 4154 11050 700 '120 1623
7.62 144.8 4530 12050 900 1450 1935
9.61 182.6 2481 6600 600 880 1214
11. 00 209.0 4549 12100 800 1380 1855
Based on the above tabulated pressuremeter test results the
hyperbo I i c parameters have been calculated using the
proposed set of equations, assuming a cohesionless material.
The computed parameters are presented in Table Vt I I and
compared to the typical values recommended by M.G. Katona
et a I. (1981), where the correct order of magnitude is
found.
82
TABLE VI I I
HYPERBOLIC PARAMETERS - STANDARD vs. PMT
Parameter CANOE Pressuremeter recommendation test
K 200 90
n 0.4 0.6
~ 33.0 35.0
Rf 0.10 0.73
Kb 50 140
m 0.2 o. 12
Finite element modelling using the above parameters
within the finite element program FEADAM (J.M. Duncan,
K.S. Wong and Y. Ozawa, 1980) resulted in similar distress
features as those observed at the real embanKment.
CHAPTER VI I I
DISCUSSION OF THE RESULTS
An investigation has been carried out to explore the
potential of the pressuremeter for the derivation of non-
1 inear, stress-dependent parameters as input for finite
element programs.
From this initial study it is clear that the calcula
tion of parameters for soil models from pressuremeter tests
might be, in general, the right step towards an approxima
tion of the rel iabi 1 ity of soi 1 input to the high standards
of finite element programs. This is also supported by fin
dings of J.L. Kauschinger (1985) who successfully extracted
parameters from pressuremeter data for J.H. Pr!vost's multi
yield surface model.
It is apparent that the accuracy of the proposed
correlation between density and bulK modulus parameters is a
function of the amount of incorporated data. Therefore an
expansion of the data base would be desirable.
However, it must be pointed out that the foregoing
study was 1 imited to granular soi ls, where considerable
volume changes occur due to compression and dilatancy. Those
effects, among others, can not be model led accurately using
64
the hyperbolic soi 1 model. Therefore, if an attempt is made
to model soils exhibiting such behavior, significant error
can be introduced.
In addition, the function of the tangent modulus in
the hyperbolic soi I model is not continous, as a brief
inspection of Fig. 3 reveals. Even though this discontinuity
may seem negligible it might result, incorporated into an
incremental finite element calculation, in additional itera
tions, as H. Schad (1979) stated.
CONCLUSIONS AND RECOMMENDATIONS
During this investigation it became apparent that the
construction material soil displays such a diversity of
conditions that it does seem neither possible, nor
meaningful, to develop a single soil model from which
parameters are easily obtained and which yields correct
descriptions of all possible stress states under every
possible boundary condition. Nevertheless, a number of
conclusions can be drawn from the foregoing:
1. Pressuremeter testing should be employed in the
absence of triaxial data to calculate parameters describing
the soil behavior according to the hyperbolic soil model,
even though it seems more appropriate to use the pressure
meter data directly without the constraints of correlations
to convent i ona 1 soi I investigation methods.
85
2. Noni inear modeling is essential in capturing the
real soil behavior and is best employed in conjunction with
finite element programs.
3. Finite element solutions utilizing the hyperbolic
approach might be very adequate for many "up-to-failure"
problems in geotechnical engineering, even though short
comings are obvious since important factors l iKe stress
history, time dependency and strain softening of the soil
can not be accounted for.
4. A parametric study to investigate the sensitivity
of the hyperbolic soil model, in its various stages of
development, to deviations of the parameters from their
determined values is recommended in order to evaluate the
significance of errors introduced hereby.
5. The step increase of poisson•s ratio at failure is
not a realistic representation of the actual soil behavior.
The bulK modulus formulation eliminates this problem by
use of a hyperbolic function for the volume changes which
have to be compressive, even though the test data may
indicate dilation.
86
6. The development of a generalized constitutive law
for soils represents a formidable tasK for future research.
Volume change effects and failure mechanisms are undoubtly
of prime importance and inhibit many problems to be solved.
7. In the development of new models the derivation of
the coefficients has to be realistically considered.
Clearly, an integration of soil tests and model theory is
absolutely necessary. It could be stated that any soi 1 model
is only as good as the soil test employed to find the
parameters.
8. Laboratory pressuremeter testing turned out to be
difficult to accomplish at small scale since considerable
confining pressures were necessary to satisfy the plane
strain condition. Moreover, adequate demonstration of the
impact of increasing depth on the pressuremeter modulus and
the I imit pressure could not be made. Since chamber testing
is an essential part of research in geotechnical engineering
the avai Jabil ity of such a chamber is very much recommended.
LIST OF REFERENCES
Baguelin, F., Jezequet, J.-F., and Shields, D.H., The Pressuremeter and Foundation Engineering, Trans-Tech Pub! ications, Clausthal, West-Germany, 1978.
Bishop, A.W., and HenKel, D.J., The Measurement Properties JB the Triaxial Test, Second Edward Arnold Publishers, London, United 1962.
of Soi I Edition, Kingdom,
Bowles, J.E., Foundation Analysis and Design, Third Edition, McGraw-Hi I I BooK Company, New YorK, United States, 1982.
Briaud, J.-L., Lytton, R.L., and Hung, J.-T., "Obtaining Moduli from Cyclic Pressuremeter Tests," Journal of the Soil Mechanics and Foundation Division, ASCE, Vol. 109, No. 5, May, 1983, pp. 657-665.
Briaud, J.-L., and Shields, D.H., "Pressuremeter Tests At very Shallow Depth," Journal of the Soi I Mechanics and Foundation Division, ASCE, Vol. 107, No. GT8, August, 1981, pp. 1023-1040.
Briaud, J.-L., TucKer, L.M. and MaKarim, C.A., "Pressuremeter Standard and Pressuremeter Parameters," The Pressuremeter and Its Marine Applications: Second International Symposium, ASTM STP 950, Texas, 1986.
Centre d'Etudes M~nard, "R~gtes d'Uti 1 isation des Techniques Pressiom~triques et d'Exploitation des R~suttats
Obtenus pour le Cal cul des Fondations", Publication D/60/75, France, 1975.
Cornforth, D.H., "Prediction of Drained Strength of Sands from Relative Density Measurements," Special Technical Publication 523, ASTM Evaluation of Relative Density and its role JB Geotechnical Projects Involving Cohesionless Soi ts, 1973, pp. 281-303.
cox, H., "The Deflection of Imperfectly Elastic Beams and the Hyperbolic Law of Elasticity," Transactions of the Cambridge Philosophical Society, Part 2, 9, 1850, pp. 177-190.
Desai, c.s., and Geotechnical USA, 1977.
Christian, T., Numerical Engineering, McGraw-Hil I
Methods JB BooK Company,
88
Dorairaja, R. , "Finite Element Analysis of the Behavior of Noni inear Soil Continua Including Dilatancy," ~ Dissertation submitted to the Graduate Faculty of Texas Tech University, in partial fulfi 1 lment of the requirements for the Degree of Doctor of Philosophy, 1975.
Duncan, J.M., and Chang, C.Y., "Noni inear Analysis and Strain in Soils," Journal of the Soil and Foundation Division, ASCE, Vol. 96, September, 1970, pp. 1629-1653.
of Stress Mechanics
No. SM5,
Duncan, J.M., Byrne, P., Wong, K.S., and Mabry, P., "Strength, Stress-Strain and BulK Modulus Parameters for Finite Element Analyses of Stresses and Movements in Soil Masses," Report No. UCB/GT/80-01, University of California, BerKeley, California, August 1980.
Duncan, J.M., Wong, K.S., and Ozawa, Y., "FEADAM: A Computer Program for Finite Element Analysis of Dams," Report No. UCB/GT/80-02, University of California, BerKeley, California, December 1980.
Felio, G.J., and Briaud, J.-L., "Conventional Parameters from Pressuremeter Test Data: Review of Existing Methods," The Pressuremeter and Its Marine Applications, Second International Symposium, ASTM STP 950, Texas, 1986.
Gallagher, R.H., Finite Element Analysis: Fundamentals, Prentice Hall, Englewood Cliffs, New Jersey, 1975.
Hartman, J.P., "Finite Element Parametric Study of Vertical Strain Influence Factors and the Pressuremeter Test to Estimate the Settlement of Footings in Sand," Thesis presented to the University of F 1 or i da, in part i a 1 fulfillment of the requirements for the Degree of Doctor of Phi 1 osophy, 197 4.
Herrmann, L.R., "Elasticity Equations for Incompressible and Nearly Incompressible Materials by a variational Theorem," AIAA Journal, Vol. 3, No. 10, pp. 1896-1900, October, 1965.
Holloway, D.M .• "User's Manual for Axisym: A Finite Element Program for Axisymmetric or Plane Strain Simulation of Soi I-Structure Interaction," Contract Report S-76-13 U.S. Army .sn.s..: Waterw. Expt. Stn., VicKsburg, Miss. 1976.
89
Janbu, N., "Soi I Compressibility as Determined by Oedometer and Triaxial Tests," European Conference on Soil Mechanics and Foundation Engineering, Wiesbaden, Germany, Vol .1, pp. 19-25, 1963.
Johnson, L.D., "Correlation of Soi 1 Parameters from In Situ and Laboratory Tests for Building 333," Proceedings of the ASCE Specialty Conference on use of .lJJ Situ Tests ..i.!J Geotechnical Engineering, Virginia Polytechnic Institute and State University, June, 1986.
Katona, M.G., Vittes, P.O., Lee, C.H. and Ho, H.T., "CANDE-1980: Box Culverts and Soi 1 Models," Report No. FHWA/RD-80/172, Notre Dame, Indiana, May, 1981.
Kauschinger, J.L., "Interim Report: Extracting Multi-Yield Surface Model Parameters from Pressuremeter Data," ~ Report .Q.D Research sponsored !ll'. the Engineering Foundation of ASCE under Research Contract No. Rl-A-84-2, Medford, Massachusetts, July 1985.
KOgler, F., "BaugrundprQfung im Bohrloch," Der Bauingenieur, Heft 19-20, pp. 266-270, Berl in, Germany, 1933.
KolbuszewsKi, J.J., and Jones, R.H., "The Preparation of Sand samples for Laboratory Testing," Proceedings of the Midland Soil Mechanics and Foundation Engineering Society, Vol. 4., Birmingham, England, 1961.
KolbuszewsKi, J.J., "General Investigation of the Fundamental Factors Control 1 ing Loose PacKing of Sands," Proceedings of the Second International Conference on Soi I Meehan i cs, Vo 1. 7, pp. 4 7-49, Rotherdam, Nether 1 ands, 1948.
KolbuszewsKi, J.J., "An Experimental Study of the Maximum and Minimum Porosities of Sands," Proceedings of the second International Conference .Q.D Soil Mechanics, Vol.1, pp. 158-165, Rotherdam, Netherlands, 1948.
Kondner, R.L., "Hyperbolic Stress-Strain Response: Cohesive Soils," Journal of the Soil Mechanics and Foundation Division, ASCE, Vol. 89, No. SM1, February, 1963, pp. 115-143.
Kondner, R.L., Formulation PanAmerican Foundation 289-324.
ZelasKo, S.S., "A Hyperbolic Stress-strain of Sands," Proceedings of the 2nd Conference on Soil Mechanics and
Engineering , Vo 1 . 1 , Braz i 1 , 1963, pp.
90
Kulhawy, F.H., Duncan, J.M. and Seed, H.B., "Finite Element Analyses of stresses and Movements in EmbanKments During construction," U.S. Army ~ Waterw. Expt. Stn. contract Report 569-8, VicKsburg, Miss., 1969.
Lade, P.V., "Cubical Tri axial Apparatus for Soil Testing," Geotechnical Testing Journal, No. 1, 1979, pp.93-101.
Livneh, M., Gilbert, M., and Uzan, J., "Determination of the Elastic Modulus of Soil by the Pressuremeter TestTheoretical BacKground," Journal of Materials, Vol. 6, No. 2, June 1971.
MacNeal, R.H., and Harder, R.H., "A Proposed set of Problems to Test the Finite Element Accuracy", 25th SOM Finite Element Validation Forum, Palm Springs, 1984.
McCormacK, T.C., "A Finite Difference Soi I-Structure Interaction Study of a Section of the Bonneville Navigation LocK Buttress Diaphragm Wall Uti I izing Pressuremeter Test Results," .!i: Sc. Thesis, submitted in partial fulfi I lment of the requirements for the degree of Master of Science, Portland State University, 1987.
M~nard, L., "An Apparatus Soi Is in PI ace, " 111 inois, 1957.
for .!1:
Measuring the Sc. Thesis,
strength University
Of of
M~nard, L., "Influence de l'ampl itude et de l'histoire d'un champ de contraintes sur le tassement d'un sol de fondation," Proceedings of the Fifth International Conference on Soi I Mechanics and Foundation Engineering, Paris, 1961, Vol. 1, pp. 249-253.
Meyerhof, G.G., "Influence of Roughness Base and Groundwater conditions on the Ultimate Bearing Capacity of Foundations," Geotechnigue, Vol. V, 1955, pp. 227-242.
Mitchell, J.K., and Sample Preparation on
the Soil Mechanics and
Mu I i 1 is, J.P. , Seed, H.B. , Chan, c. K. , Aru 1 anandan, K. , "Effects of Sand Liquefaction," Journal of Foundation Division, ASCE, February, 1977, pp. 91-108.
Vol. 103, No. GT2,
Pierce, J.A., "A New True Triaxial Apparatus," Stress-Strain Behaviour of Soils. Roscoe Memorial Symposium, 1971, pp. 330 - 339.
91
Poulos, H.G., and Davis, E.H., Elastic Solutions for Soi 1 and RocK Mechanics, John Wiley and Sons, New YorK, 1974.
Pr~vost, J.-H., "Anisotropic Undrained Stress-Strain Behaviour of Clays," Journal of the Soil Mechanics and Foundation Division, ASCE, Vol. 104, No. GT8, August, 1978, pp. 1075-1090.
Schad, H., "Nichtl ineare Stoffgleichungen fDr Beden und ihre Verwendung bei der numerischen Analyse von Grundbauaufgaben," Mittei lung Nr. 1Q des Baugrundinstituts Stuttgart, West Germany, 1979.
Smith, T.D., "Pressuremeter Design Method for Single Piles Subjected to Static Lateral Load," Dissertation submitted to the Graduate College of Texas A&M University, in partial fulfi I lment of the requirements for the Degree of Doctor of Philosophy, 1983.
Smith, T.D., and Deal, C.E., "CracKing Studies at Sand H Debris Basin by the Finite Element Method," to be published in Proceedings of the Second International Conference .QD Case Histories .lD Geotechnical Engineering, St. Louis, Missouri, June, 1988.
Spangler, M.G., Handy, R.L., Soi 1 Engineering , Fourth Edition, Harper & Row Publishers, New YorK, 1982.
Tranter, C.J., "On the Elastic Distortion of a Cylindrical Hole by a Localized Hydrostatic Pressure," Quarterly of Applied Mathematics, Vol. 4, No. 3, 1946.
Turner, M.J., Clough, R.W., Martin, H.C., and Topp, L.J., "Stiffness and Deflection Analysis of complex Structures," Journal of the Aeronautical Sciences, Vol. 23, No. 9, September 1956.
Wroth, C.P., and Windle, D., "Analysis of the Pressuremeter Test al lowing for Volume Change," Geotechnigue, Vol. XXV, Number 3, September, 1975, pp, 598-604.
Wroth, C.P., "British Experience with the Selfboring Pressuremeter," Symposium .QD the Pressuremeter and Its Marine Applications, IFP, Paris, Apri 1 1982.
a
b
8
c
Dr
E
Ei
Em
EM
EpM
Es
Et
Eur
G
K
Ko
Ka
Kb
KpM
Kpur
LIST OF NOTATIONS
Initial tangent modulus constant.
Ultimate stress difference constant.
BulK modulus.
Cohesion.
Relative density.
Young's modulus, modulus of elasticity.
Initial tangent modulus.
Pressuremeter modulus of micro-deformation.
Menard modulus based on v = 0.33.
Modified pressuremeter modulus.
Soil modulus.
Tangent modulus.
Unload-reload modulus.
Shear modulus.
Modulus number.
At rest earth pressure coefficient.
Active earth pressure coefficient.
BulK modulus number.
Modulus number from pressuremeter test.
Unload-reload modulus number
from pressuremeter test.
Kur Unload-reload modulus number.
L/D Length to diameter ratio.
m BulK modulus exponent.
n Modulus exponent.
Pa Atmospheric pressure.
PL Theoretical 1 imit pressure.
P1 Practical 1 imit pressure.
P1* Net 1 imit pressure.
Po Total initial horizontal stress.
PoM Pressure at the start of the straight 1 ine portion
of the pressuremeter test curve.
Rf Failure ratio.
Rpf Failure ratio based on pressuremeter test.
r Radial distance.
r 0 Initial cavity radius.
s Modulus exponent from pressuremeter test.
s Stress level.
<XF
a or A
Eo
Ea
Er
Evol
Ez
t
4'cv
Almansi strain at failure.
Change of ....
Cavity strain.
Axial strain.
Radial strain.
Volumetric strain.
Vertical strain.
Angle of internal friction.
Angle of internal friction at constant volume.
tdc Density component for angle of
internal friction.
93
94
A4> Change in angle of internal friction.
Ydry Dry unit weight.
Yyz Shear strain.
v Poisson's ratio.
Vf Poisson's ratio at failure.
01 Major principal stress.
02 Intermediate principal stress.
03 Minor principal stress.
Of Radial stress at failure.
oh I Effective horizontal stress.
On Normal stress.
Or Radial stress.
Oz' Effective vertical stress.
oe Circumferential stress.
Ooct Octahedral stress.
T Shear stress.
Tmax Maximum shear stress.
Tyz Shear stress in axisymetric coordinates.
ef Angle of failure plane.
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Site: Soil: Test No.: Depth: Quality: 1)
'P.5U l,J; l( 1un~ Ht.. 1t~ IJJ .:Pr"'" I (). 5.,.,,, * ,
Measured information:
p : 0 1 K7>« cr' f : '" 1<1'1t. pl = 33 ~'t.
Calculated from curve :
G = 325 ~-- E = Sb5' Kftt l :v = fJ.33)
Remarks: ft bt- mtlf nu tt l (!.~.,.,.. .. e_ol1tf;, f? l I.\ ni.c.s et«.l sit 0. e ~ ·t C.!il.r:i~ f.,t- .t•riJ., J,,.·,,,,,if intere_l'<.:to..h'onJ ;' L:,a.strl •n e~ 3-lb.
Theoretical vclues:
P0 = 2.Blf. t<P4t of = lf.1¥ f<1>ct. pl: J2.5 ~A PL = 35.1 k'Ptt
Remarks: ~ b!~J aa. K ,_ =- o."' d:>~ : 8. bl K'P1t. . t':11YI. 'i
0
1 r
!jy_perbolic Parameters:
p T/'46DTl..l ME~Si.CR~ (). rJ 'I Kb = SE' Rpf = ~ = 0.7~0.15 m=
PL 5000 1111 1111 :.; '!, d: . ~ ~ ; i!i: ,,I I
11:111 .. ' :
B'f Ill ''I •II q: : I I ' ' '
KPM = II :111 II.: I: ·hi:' 1•1 I '
; ii 11;, :.j '1' 1!:i.:! I. l
2000 ~Id ! ! ; ~ ' I ,.
·'.!··:: "I'·:
I''' 1::. .... O.Sf :!!'. •··· :1 :;: .... ,, .. , .. ... .. .. , ..
s : 1000 '" Ei/Po "
/(Plf ' ..s ~ ' I t ''1 ,. ,s,, it 1 :.
500 ,!I. :: ·j .:
t'l.eit. f e.~# £ • ..
11 I '' l, • ,,
I ':, ,1 :, i .. f t\A,.~ c..tcl 2.
,,
J>c J: I: ,I' ·: :1 . ' 200 ;;1 ::.•: .. • I. ·: i
1) I Poor quality, .... .. " ,., '
100 '1' • ' "
only I i1ited value. '" ., ' . .,.
II 6ood qua I j ty I I " ' ,,
I act< i ng in soe areas. 50 1:· ;11'
HI Excellent quality. 0.1 0.2 o.~ I I 2 5 I() 20 50
G"z/Pa
Site: P.su
Soil : 6'6 '°I Test No.: I Depth : ~ill-m(.t~~~ ~r"'m IL 1. '11' m
' Measured in for mat ion:
p 0 : , '+ k'Pr.t. 11t = 2. b.5' KP. pl : t+'t /f'Ptt.
Calculated from curve:
G = '+'I 5 kRt E = I l t '1- k1'1t (v:: o.i3)
Remarks: .see pt(..,; o U.$ pqi"
Theoretical vciues:
p : 0
Re marks:
B. 88 l<1k
f; loa.k,J
~y_perbolic Parameters:
7
1 00
a uality : 1l ~
/IJ(),y ~
Kb= 55 0 p rheor.r. MFiAS\.(ft~
Rpf = ~ = O.l-'tZ0.¥'1 m= IJ.O'i PL r
KPM = &If.
s : o.sr
1) I Poor qHI ity, only ti1ited watue.
11 6ooCI qi111 itr, lackint in SOie n•. H• Excellent qaal itr.
:1ooo 1111 !llilll:li l'Ll'l'1ii!IH11 I I:: i =L:d''I I 111 I 1111 I l IJ tLJ Tlll 1111: m;;T1TI !lttlilJl:FI H:l'•'I'
! 'TiTTfT'P i:.
'!i Ji' '·1 ·1
:1ootTtnj ''.! 'j" :11: ::n ::1 :; iTTITT ~: 'I 1 i
··1 F
i;f•'·li!l.:H1:.i1 · 1!;11· · i I Id I· f I :·ib
200,: ::;11$1 ::.lo;J~I':
• 1 ... .
100
l/e 50
0.1 0.2 0.:1 5 () 20 50 I I 2 <:rz/Pa
10 1
Site: !Soil: Test No.: Depth: Quality: ff
Measured information:
p : 0
Calculated from curve :
G =
Remarks:
Th eor eti ca I values :
p : 0
Re marks:
!::!Y..perbolic Parameters:
R Pf = -.!:.L_ -p -L
KPM =
c1f : pl :
E =
C1f : p : I
p : L
m= Kb =
~000
Ii l l illliil!ii:l:l:!l:ij,H:illl1ii ~ ~ i : L. ! . +m . , .. " . ,, .. ., . rm:f"T'll!):JTn ., '
! illl!liil i11.1:;1q Jiha~rn, ', ,, "T;'1
I''
s = •• ;~~o Iii l1li111l1 il 1~l~l1i1~1~~ i Iii!++ 1:111: 11 I 111 , 111 llli ~ooFTil!Tl:FlTll 11111 111111111111 I I l 1111
·11; I 1!d1 1.•j I, li'.li:
,, l;'F":JffU'l'f 1::1
200r'!r 'I:: liill r,r ::. ::· •c :: . :i:: :;::·.
'"l IT 1) I 1·1·1 . ,, ···l•·l··l·•·•I·"
Poer 11111 ity, .......... ., ... , ....
oely I ilited HI•. 100
II 6ood 11111 ity, ~ 0 l!!! 1 li: 1.·:1:'l·l lY lackint ill s. nas.
0.1 0.2 o.~ I I 2 ~ IQ 20 ~o H~ Excellet1t 11111 ity. (jz/Pa
