a biot formulation for geotechnical earthquake engineering applications

A BIOT FORMULATION FOR
GEOTECHNICAL EARTHQUAKE ENGINEERING APPLICATIONS
by
YU BAO
B.S., Tianjin University, China, 1998
M.S., Tianjin University, China, 2001




A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirement for the degree of
Doctor of Philosophy
Department of Civil, Environmental, and Architectural Engineering
2006




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This thesis entitled:
A Biot Formulation for Geotechnical Earthquake Engineering Applications
written by Yu Bao
has been approved for the Department of Civil, Environmental, and
Architectural Engineering


___________________________________
Stein Sture


___________________________________
Hon-Yim Ko


Date_____________________

The final copy of this thesis has been examined by the signatories, and we find that
both the content and the form meet acceptable presentation standards of scholarly
work in the above mentioned discipline


Bao, Yu (Ph.D., Civil Engineering)
A Biot Formulation for Geotechnical Earthquake Engineering Applications
Thesis directed by Professor Stein Sture


The mechanical behavior of saturated soil is mainly governed by the
interaction between the soil skeleton and the pore fluid, and this interaction may lead
to significant loss of strength known as liquefaction under seismic loadings. The
main objective of this thesis is to develop and implement a cyclic constitutive model
capable of modeling soil skeleton dilatancy during earthquake excitation. The
constitutive model is based on the fuzzy-set plasticity theory and enhancement is
made on the description of dilatancy behavior under cyclic loading. A robust Biot
formulation, in which the governing equations of motion of the soil mixture are
coupled with the global mass balance equations, is developed to describe the realistic
behavior of saturated soil. The finite element discretization is established without
neglecting the convective terms. An unconditionally stable implicit time integration
scheme, Hilber-Hughes-Taylor
α
method is used and an iterative algorithm based on
Newton-Raphson method is developed to solve the nonlinear time-discretized
problem. A numerical study of sand liquefaction is performed and compared with the
centrifuge experimental results to show the capabilities of the proposed formulation

on pore water pressure generation and strength loss occurred in loose granular soil
deposit under cyclic loading. The computed results show good agreement with the
experimental data. The capability of the enhanced fuzzy-set model in simulating
cyclic soil behaviors including liquefaction is validated. It is concluded that the
developed Biot formulation and computational procedure are an effective means to
assess liquefaction potential and liquefaction-related deformations.



iv




Dedication


To My Family
For your love and encouragement

v



Acknowledgments


I would like to express my most sincere appreciation to my advisor Professor
Stein Sture for his invaluable guidance, encouragement and support throughout this
study.
I would like to thank Professor Hon-Yim Ko for his friendship, and his guidance
and support in centrifuge modeling. I am also very grateful to Professor Richard
Regueiro for his sharing of knowledge and support.
I am grateful to Professor Tad Pfeffer and Professor Carlos Felippa for serving as
my defense committee. I would like to thank Professor Ronald Pak, who was my
academic advisor during my first year of Ph.D. study.
My appreciation goes to Dr. Yu-Ning Ge for his help in understanding the fuzzy-
set plasticity constitutive model and Dr. Sung Ryul Kim for his help in the centrifuge
experiments.
My thanks go to my parents, my husband Miao and my son Dylan for their love,

encouragement and support.










vi



CONTENTS

CHAPTER
1 INTRODUCTION……………………………………………………………1
1.1 Motivation……………………………………………………………… 1
1.2 Research Focus………………………………………………………… 4
1.3 Scope of Work and Layout………………………………………………5

2 BACKGROUND AND LITERATURE REVIEW………………………… 7
2.1 Laboratory Tests…………………………………………………………8
2.2 Centrifuge Modeling……………………………………………………15
2.3 Constitutive Modeling………………………………………………….16
2.4 The Theory of Mixtures……………………………………………… 24
2.5 Finite Element Implementation…………………………………………26
2.6 Time Integration Scheme……………………………………………….27

3 ENHANCED FUZZY-SET PLASTICITY CONSTITUTIVE MODEL… 29
3.1 Fuzzy Sets………………………………………………………………30
3.2 Classical Plasticity Theory…………………………………………… 31
3.3 Fuzzy-Set Plasticity Theory…………………………………………….35
3.4 Stress Control Formulation in p-q Space……………………………….38
3.5 Stress Control Formulation in Cartesian Stress Space………………….46
3.6 Strain Control Formulation…………………………………………… 50
3.7 2-D Plane Strain Formulation………………………………………… 52
3.8 Kinematic Mechanism of Deviatoric Membership Function
d
γ
………54


vii

3.9 Kinematic Mechanism of Locking Membership Function
l
γ
…………62
3.10 Model Parameters………………………………………………………67
3.11 Model Capabilities on Cyclic Mobility…………………………………67
3.12 Model Responses……………………………………………………….71
3.13 Dilatancy Parameters………………………………………………… 91
3.14 Model Calibration………………………………………………………93
3.14.1 Unconstrained Numerical Optimization…………………… 93
3.14.2 Numerical Optimization in Constitutive Model Calibration 96

4 THEORY OF MIXTURES FOR FLUID-SATURATED POROUS

MEDIA…………………………………………………………………… 98
4.1 Average Quantities…………………………………………………… 99
4.2 Laws of Balance……………………………………………………….103
4.2.1 Balance of Mass…………………………………………….104
4.2.2 Balance of Linear Momentum…………………………… 107
4.2.3 Balance of Angular Momentum…………………………….110
4.2.4 First Law of Thermodynamics (Balance of Energy)……….113
4.2.5 Second Law of Thermodynamics (Entropy Inequality)…….113
4.3 Field Equations for Saturated Soil…………………………………….114

5 FINITE ELEMENT FORMULATION….……………………………… 119
5.1 The Finite Element Method (FEM)………………………………… 119
5.2 Matrix Form of the Field Equations for Saturated Soil……………….122
5.3 FEM Form of the Balance of Linear Momentum in the Solid Phase…125
5.4 FEM Form of the Balance of Linear Momentum in the Fluid Phase…129
5.5 FEM Form of Conservation of Mass for the Mixture…………………132
5.6 Combination of the Discretized Governing Equations……………… 134


viii


6 COUPLED FINITE ELEMENT – INFINITE ELEMENT MODEL…… 137
6.1 Mixed Displacement – Pore Pressure Element……………………… 138
6.1.1 2-D 9-node Lagrangian Isoparametric Quadrilateral Element…… 139
6.1.2 4-node Lagrangian Isoparametric Quadrilateral Element…………145
6.2 2-D 6-Node Infinite Element…………………………………………147
6.2.1 1-D 2-Node Infinite Element………………………………………148
6.2.2 2-D 6-Node Infinite Element…………………………………… 150
6.3 2-D Coupled Finite Element - Infinite Element Numerical Model… 158

7 TIME INTEGRATION AND NONLINEAR ANALYSIS……………… 159
7.1 Direct Time Integration Techniques………………………………… 160
7.1.1 Newmark Method…………………………………………………161
7.1.2 Hilber-Hughes-Taylor
α
-Method………………………………….163
7.2 Implementation of Hilber-Hughes-Taylor
α
-Method……………… 165
7.3 Newton-Raphson Method: Nonlinear Analysis……………………….167
7.4 Calculation Procedure……………………………………………… 169

8 VERIFICATION OF NUMERICAL SIMULATION…………………… 172
8.1 Centrifuge Modeling of Soil Liquefaction…………………………….173
8.1.1 Centrifuge Model Test on a Layer of Liquefiable Sand Deposit… 173
8.1.2 Experimental Results………………………………………………176
8.2 Fully Coupled FEM Code “DYNSOILS”…………………………… 187
8.2.1 Pre-Processing Module…………………………………………… 187
8.2.2 Post-Processing Module…………………………………………….188
8.2.3 Analysis Module……………………………………………………188
8.3 Case 1: A Liquefiable Layer of Sand Deposit


ix

– Comparison of Numerical Simulation with Centrifuge Experiment 190
8.4 Case 2: A Footing Subject to Vertical Sinusoidal Loading………… 206
8.5 Summary………………………………………………………………215

9 SUMMARY, CONCLUSION AND RECOMMENDATION FOR FUTURE
WORK…………………………………………………………………… 216
9.1 Summary and Conclusions……………………………………………216
9.2 Recommendation for Future Work……………………………………218

BIBLIOGRAPHY………………………………………………………………219



















x



TABLE

Table
2.1 Table of Scaling Relations (Centrifuge Modeling at N*g)…………………… 15
3.1 Fuzzy-Set Model Parameters……………………………………………… …72
3.2 Dilatancy Parameters………………………………………………………… 91





















xi

FIGURES

Figure
2.1 Excess Pore-Water- Pressure Response Behavior and Deviatoric Stress – Strain
Curve during an Undrained Stress-Controlled Cyclic Triaxial Test of Nevada
Sand (Dr = 40%) (Arulmoli et al., 1992)……………………………………….9
2.2 Stress-Strain and Excess Pore Water Pressure Histories during an Undrained
Stress-Controlled Cyclic Triaxial Test of Bonnie Silt (Arulmoli et al., 1992) 10
2.3 Variations of Shear Stress with Axial Strain (Lee and Schofield, 1988)………11
2.4 Stress-strain Curve and Stress-path for Nevada Sand of D
r
= 60% Obtained from
Cyclic Undrained Simple Shear Test (Arulmoli et al., 1992)………………….12
2.5 Recorded Time Histories of Acceleration and Pore Water Pressure (Koga and
Matsuo, 1990)………………………………………………………………….13
2.6 Time Records of Acceleration and Lateral Displacement Responses (Ishihara et
al., 1991)……………………………………………………………………….14
2.7 Iai’s Model Performance (Iai 1991)………………………………………… 17
2.8 Schematic Illustration of Multi-Surface Model……………………………… 19
2.9 Schematic Illustration of the Bounding Surface in Uniaxial Stress-Strain Space
(reproduced from Dafalias and Popov, 1975)………………………………….20
2.10 Schematic Representation of a Loading and a Bounding Surface (reproduced
from Dafalias and Popov, 1975)……………………………………………….21
2.11 Schematic Illustration of Fuzzy-Set Model…………………………………….23
3.1 “Fuzzy” Yield Surface Specified by a Given Constant Value of the Membership
Function (Klisinski, 1987)…………………………………………………… 31
3.2 Lode’s Angle in Deviatoric Plane (William and Warnke, 1973)………………40


xii

3.3 Effective Stress Path under Undrained Cyclic Loading……………………… 42
3.4 Deviatoric Stress – Strain Response Curve of Two Unloading-Reloading
Cycles………………………………………………………………………… 55
3.5 (a) Pictorial Illustration of Kinematic Mechanism of Deviatoric Membership
Function
d
γ
from Point “a” to Point “b”……………………………………….56
(b) Pictorial Illustration of Kinematic Mechanism of Deviatoric Membership
Function
d
γ
from Point “b” to Point “c”……………………………… 57
(c) Pictorial Illustration of Kinematic Mechanism of Deviatoric Membership
Function
d
γ
from Point “c” to Point “d”………………………………….58
(d) Pictorial Illustration of Kinematic Mechanism of Deviatoric Membership
Function
d
γ
from Point “d” to Point “e”………………………………….59
(e) Pictorial Illustration of Kinematic Mechanism of Deviatoric Membership
Function
d
γ
from Point “e” to Point “f”………………………………….60
3.6 Mean Stress – Strain Curve of Two Unloading – Reloading Cycles………….63

3.7 (a) Pictorial Illustration of Kinematic mechanism of locking membership
Function
l
γ
from Point “a” to Point “b”……………………………………….63
(b) Pictorial Illustration of Kinematic mechanism of locking membership
Function
l
γ
from Point “b” to Point “c”…………………………… ….64
(c) Pictorial Illustration of Kinematic mechanism of locking membership
Function
l
γ
from Point “c” to Point “d”…………………………………64
(d) Pictorial Illustration of Kinematic mechanism of locking membership
Function
l
γ
from Point “d” to Point “e”……………………………… 65
(e) Pictorial Illustration of Kinematic mechanism of locking membership
Function
l
γ
from Point “e” to Point “f”…………………………………65
3.8 Schematic Cross section of Sand Particles’ Deformation under Cyclic Loading
(Youd, 1977)…………………………………………………….…………… 68
3.9 Stress – Strain Curve under Cyclic Loading………………………………… 69

xiii

3.10 Pore-Water-Pressure vs. Deviatoric Strain Response under Undrained Cyclic
Loading…………………………………………………………………………70
3.11 Stress Path Showing Cyclic Mobility………………………………………… 71
3.12 Loading History of Deviatoric Stress………………………………………… 73
3.13 (a) Deviatoric Strain History………………………………………………….74
(b) Deviatoric Stress – Deviatoric Strain Curve………………………………75
(c) Pore Water Pressure – Deviatoric Strain Response Curve……………… 76
(d) Pore Water Pressure Buildup History…………………………………… 77
(e) Effective Stress Path Approaching Liquefaction………………………….78
3.14 Loading History of Deviatoric Stress with Increasing Amplitude…………… 79
3.15 (a) Deviatoric Strain History………………………………………………….80
(b) Deviatoric Stress – Deviatoric Strain Curve………………………………81
(c) Pore Water Pressure – Deviatoric Strain Response Curve……………… 82
(d) Pore Water Pressure Buildup History…………………………………… 83
3.15 (e) Effective Stress Path Approaching Liquefaction………………………….84
3.16 Loading History of Deviatoric Stress with Decreasing Amplitude………… 85
3.17 (a) Deviatoric Strain History………………………………………………… 86
(b) Deviatoric Stress – Deviatoric Strain Curve………………………………87
(c) Pore Water Pressure – Deviatoric Strain Response Curve……………… 88
(d) Pore Water Pressure Buildup History…………………………………… 89
(e) Effective Stress Path Approaching Liquefaction………………………….90
3.18 Effect of Change of Dilatancy Parameters on Pore Water Pressure Buildup…92
4.1 Typical Averaging Volume……………………………………………………100
6.1 Mixed Displacement-Pore Pressure Element………………………………….138
6.2 2-D 9-node Isoparametric Quadrilateral Element…………………………… 139
6.3 2-D 4-node Isoparametric Quadrilateral Element…………………………… 145
6.4 1-D infinite element………………………………………………………… 148

xiv

6.5 2-D 6-node infinite element………………………………………………… 150
7.1 Stability of Newmark Time Integration Scheme…………………………… 163
8.1 Cross-Section of the Model and Instrumentation Layout…………………… 175
8.2 Particle Gradation Curve for Nevada Sand #120…………………………… 176
8.3 Base Input Motion: Horizontal Acceleration……………………………… 177
8.4 Measured Horizontal Acceleration at the Surface…………………………….178
8.5 Measured Horizontal Acceleration at the Depth of 2 m…………………… 179
8.6 Measured Horizontal Acceleration at the Depth of 4 m………………………180
8.7 Measured Horizontal Acceleration at the Depth of 6 m………………………181
8.8 Measured Horizontal Acceleration at the Depth of 8 m………………………182
8.9 Measured Excess Pore Water Pressure at Different Depths………………… 183
8.10 Short-Term Excess Pore Water Pressure History…… …………………….184
8.11 Measured Surface Settlement……………………………………………… 185
8.12 Short-Term Settlement Record………………………………………………186
8.13 Flowchart of Computing Procedure………………………………………….189
8.14 Flowchart for Fuzzy-Set Plasticity Constitutive Model…………………… 190
8.15 2-D FEM Mesh………………………………………………………………192
8.16 Base Horizontal Acceleration……………………………………………… 193
8.17 Short-Term Pore Water Pressure at the Depth of 9.6 m………………… 194
8.18 Short-Term Pore Water Pressure at the Depth of 8 m……………………….195
8.19 Short-Term Pore Water Pressure at the Depth of 6 m……………………….196
8.20 Short-Term Pore Water Pressure at the Depth of 4 m……………………….197
8.21 Short-Term Pore Water Pressure at the Depth of 2 m……………………….198
8.22 Short-Term Settlement……………………………………………………….199
8.23 Long-Term Pore Water Pressure at the Depth of 9.6 m…………………… 200
8.24 Long-Term Pore Water Pressure at the Depth of 8 m……………………….201
8.25 Long-Term Pore Water Pressure at the Depth of 6 m……………………….202

xv

8.26 Long-Term Pore Water Pressure at the Depth of 4 m……………………….203
8.27 Long-Term Pore Water Pressure at the Depth of 2 m……………………….204
8.28 Long-Term Settlement……………………………………………………….205
8.29 Finite Element Mesh with Boundary Conditions…………………………….208
8.30 Input Distribution Force…………………………………………………… 209
8.31 Settlement…………………………………………………………………….210
8.32 Excess Pore Water Pressure at 2 m………………………………………… 211
8.33 Excess Water Pressure at 4 m……………………………………………… 212
8.34 Excess Water Pressure at 8 m……………………………………………… 213
8.35 Deformed Mesh…………………………………………………………… 214

CHAPTER 1

INTRODUCTION


1.1 Motivation

Liquefaction is a phenomenon in which the strength and stiffness of a soil is
reduced by strong ground motion or earthquake shaking or other rapid cyclic loading.
Liquefaction has historically been responsible for tremendous amounts of damage
including landslides, differential settlements, lateral spreading, structural and earth
system failures throughout the world. Cyclic mobility is a liquefaction phenomenon,
triggered by cyclic loading, occurring in soil deposits with static shear stresses lower
than the soil strength. Deformations due to cyclic mobility develop incrementally,
because of static and dynamic stresses that develop during an earthquake. Lateral
spreading, a common result of cyclic mobility, can occur on gently sloping and on
relatively flat ground close to rivers and lakes. Liquefaction problems have received
a great deal of attention, and great efforts have been made to understand the basic
mechanism and phenomenon. However, due to the complexity of liquefaction
problems, such as nonlinearity of responses, sudden phase transition from solid to
liquid behavior, material instability, interaction and relative movement between the
porous soil skeleton and interstitial water, limitations on experimental and numerical
techniques, material model formulation and so on, reliable and accurate predictive
methods have yet to be developed.


2

Since 1960’s, significant progress has been made in understanding the
liquefaction phenomena. There are three main approaches: (1) field observations
before, during and/or after earthquakes, (2) laboratory experiments, and (3) numerical
simulations. Among the theoretical studies, three different methods have been
developed: (1) total stress approaches, (2) quasi-effective stress approaches, and (3)
effective stress – based techniques, which are also referred to as fully coupled
methods.
Strong ground motion induces a tendency for volume change and the soil-
skeleton dilation/contraction effects are of great importance to cause a progressive
pore water pressure build-up as well as cyclic pore pressure variations depending on
the drainage condition and soil permeability. Even if liquefaction were not to take
place, the development of excess pore pressures may lead to excessive soil softening,
weakening or to partial loss of stability and even to bearing capacity failures.
Rational analysis of the development of earthquake – induced pore pressures requires
a fundamental description of the soil’s constitutive relations. Therefore, the ability of
the constitutive model to predict permanent volume changes during cyclic loading
becomes a major factor in seismic analysis.
Although some geotechnical engineering problems may be idealized as quasi-
static analysis or dynamic analysis in one-phase media, due to the coupled effects of
the solid and the fluid, it is difficult to predict the soil dynamic behavior by using
simplified procedures. A saturated soil behaves as a two-phase system and any
comprehensive analysis should take into consideration the interaction between the
soil skeleton and the interstitial fluid. The mixture theory, characterized by the
concept of volume fractions, perhaps yields the most consistently developed
framework for the treatment of liquid-saturated porous solids.
The finite element method (FEM) is considered as a powerful numerical
technique in solving geotechnical engineering problems. However, every finite

3

element model has to be terminated at some finite boundary. For wave propagation
problems, the usual finite boundary of the finite element model will cause the seismic
waves to be reflected and superimposed on the progressing waves. Therefore, the
boundary conditions involved in simulating the dynamic behavior of semi-infinite soil
media are a major challenge in FEM. The desired boundary should ideally be
radiating to outgoing waves and transparent to incoming waves. In addition, the
boundary should be located as close to the finite structure as possible for
computational efficiency. The infinite element is a recently developed technique to
deal with the infinite media in the finite element analysis. The basic idea is to place
elements with a special shape function for the geometry at the infinite boundary.
The accuracy of numerical analysis needs to be validated. However, due to
the difficulty of predicting when and where a major earthquake will occur and the
general random nature of these events, most field liquefaction failures have occurred
at sites which were not instrumented. The advent of centrifuge modeling that
incorporates scaled dynamic events brought light on the development of proper
numerical techniques to simulate the consequences of soil liquefaction. Centrifuge
testing creates stress conditions in the model that closely simulate those in the full-
scale prototype, so that the behavior of the model can approximate that of the
prototype. Since 1988, the University of Colorado – Boulder (CU) has operated a
400 g-ton centrifuge, which among the ones having highest capacity in the world. A
servo-controlled electro-hydraulic shake table is mounted on the swing platform of
the centrifuge, which could be operated inflight to produce earthquake-like motions.
The centrifuge is currently used to study the liquefaction mechanisms related to earth
systems, as well as to validate numerical simulations. A large body of knowledge is
related to centrifuge experiments using a wide range of soils and medium-structure
configurations. The Nevada Sand, which was used in the VELACS project, is
specific to this research.

4

1.2 Research Focus

This thesis concentrates on developing and implementing an efficient,
transparent and accurate constitutive model based on the fuzzy set plasticity theory to
describe the nonlinear volume changes for granular soils and Biot field equations
used in overall analysis. Traditional concepts of critical state soil mechanics, state
parameter and phase transformation surface are introduced in the enhanced model.
The new development of a strongly dilative/contractive phase beneath the failure
surface is added and new analytical developments for the dilatancy parameter are
presented. The numerical optimization procedures for model calibration are
investigated.
In this thesis, the governing equations of motion of the soil mixture are coupled
with the global mass balance equations, and necessary assumptions are made to
obtain the equivalent Biot’s equations from the general balance equations. The
)()( fs
xux −−
formulation is used in the finite element spatial discretization, where
)(
s
x
,
u
and
)(
f
x
denote solid skeleton displacement, pore water pressure and fluid

displacement, respectively. The convective terms in the general Biot equations are
not neglected during the discretization and the effect of convective terms on the finite
element formulation is investigated. The three-parameter time integration scheme
Hilber-Hughes-Taylor
α
-method is used to integrate the spatially discrete finite
element equations.
The developed fuzzy set plasticity constitutive model is implemented in the
originally – developed fully coupled finite element code. Several examples will be
analyzed to show the capabilities of the finite element formulation. Centrifuge
experiments on soil liquefaction are conducted. The experimental results are used to
verify the elasto-plastic numerical solutions by comparing the numerical simulation
results with the data obtained from centrifuge modeling tests.


5

1.3

Scope of Work and Layout

The main purposes of the thesis are:
(1) To enhance the performance of the fuzzy-set plasticity model proposed by
Klisinski (1988) and make the model more versatile and perform realistic analysis
under a wider range of cyclic loading conditions during liquefaction.
(2) To develop the dilatancy parameters in the enhanced constitutive model to
simulate the shear-induced soil dilation/contraction along loading, unloading and
reloading cycles.
(3) To use the theory of mixtures to describe the behavior of saturated soil by
using the volume fraction concepts.

(4) To establish the coupled finite element – infinite element numerical model
to realistically simulate the boundary conditions of semi-infinite soil body under
dynamic loadings.
(5) To include the nonlinear convective terms, which in previous formulations
have frequently been excluded for the sake of simplicity, in the finite element
formulation and to develop the corresponding fully coupled FE analysis code.
(6) To use the enhanced fuzzy-set constitutive model and the FE procedure to
study pore water pressure development, the liquefaction phenomenon, and the
consequences of liquefaction.
(7) To conduct centrifuge experiments to validate the numerical procedure and
compare physical and simulated phenomena.
This thesis consists of 9 chapters. A literature review of liquefaction research
related to cyclic mobility is included in Chapter 2. Chapter 3 presents the formulation
and improvement of the fuzzy-set plasticity model, along with the necessary material
parameters calibration and model responses. Chapter 4 addresses the modern theory
of mixtures and its application to modeling two-phase saturated soil. The governing


6

equations of motion of saturated soil are also presented in Chapter 4. In Chapter 5,
the finite element semi-discretization of the governing equations is established
without neglecting the convective terms by means of a
)()(
fs
xux −−
weighted
residual Galerkin method. The coupled finite element – infinite element numerical
model is presented in Chapter 6. Time integration of the semi-discretized governing
equations using the Hilber-Hughes-Taylor

α
-method and its implementation in the
nonlinear problem is presented in Chapter 7. Several numerical examples, which
include various geotechnical structures subjected to sinusoidal loadings, are presented
in Chapter 8. Centrifuge tests on liquefiable soils are also described in Chapter 8.
Some of the numerical solutions are compared with the data obtained from centrifuge
experiments. Finally, Chapter 9 summarizes the thesis work that has been presented,
as well as conclusions and recommendations for future research work.

















7



CHAPTER 2

BACKGRPOUND AND LITERATURE REVIEW


The background and the literature review of liquefaction research related to
cyclic mobility, including cyclic laboratory sample tests, centrifuge experiments,
recent development of soil constitutive modeling, Biot-type fully coupled analysis
and mixture theory, finite element implementation and time integration scheme, are
described in this Chapter. The seismic behaviors of soils have in many instances
been recorded at specific locations and the liquefaction-induced shear-deformation
mechanism has been observed. These ground acceleration records show a strong
influence of soil dilation or contraction at large cyclic shear strain excursions.
Dilation phases can cause significant regain in shear stiffness and strength and lead to
a strong restraining effect on the magnitude of cyclic and accumulated permanent
shear strains, while a contractive soil skeleton typically leads to immediate
liquefaction. Under cyclic loading, a granular soil will show strongly coupled shear-
dilation behavior. In a saturated soil, the volume change caused by dilation or
contraction is achieved by the migration of fluid into or from the pore-space. This
migration process will be retarded by the relatively low permeability of soil or the
relatively fast rate of loading and result in pore water pressure generation and
associated change of effective confinement. Pioneering and traditional liquefaction
studies related to the overall phenomenon and cyclic mobility include the work by
Seed and Lee (1966), Casagrande (1975), Castro (1975), Castro and Poulos (1977)
and Seed (1979).


8

2.1

Laboratory Tests

A thorough review of laboratory tests and case studies of sand liquefaction
was conducted by Ishihara (1993). The triaxial test has been widely used for
laboratory testing granular soils under both monotonic and cyclic loading conditions
to obtain constitutive parameters. The cyclic triaxial test requires that the apparatus
should be capable of applying extensional as well as compression loads to the soil
specimen so that the cyclic stresses can reverse between triaxial compression and
extension state. Fig. 2.1 Shows the result of a typical triaxial test when a cyclically
imposed shear stress is present (Arulmoli et al. 1992). Fig. 2.2 (Arulmoli et al. 1992)
shows the stress-strain and excess pore water pressure response histories during an
undrained stress-controlled cyclic triaxial test of Bonnie silt. Fig. 2.3 (Lee and
Schofield, 1988) shows the sand response during one cycle in triaxial test
investigations.



9



Fig.2.1 Excess Pore-Water- Pressure Response Behavior and Deviatoric Stress –
Strain Curve during an Undrained Stress-Controlled Cyclic Triaxial Test
of Nevada Sand (Dr = 40%) (Arulmoli et al., 1992)