Dr. Malek Smadi, Ph.D. thesis lateral deformation and associated settlement resulting from embankment loading of soft clay and silt deposits

GEOTECHNICAL ENGINEERING
Dr. Malek Smadi
Ph.D. Thesis
LATERAL DEFORMATION AND ASSOCIATED SETTLEMENT
RESUL TING FROM EMBANKMENT LOADING OF SOFT CLAY
AND SILT DEPOSITS
THESIS
Submitted in partial fulfillment of the requirements
for the degree of Doctor of Philosophy in Civil Engineering
in the Graduate College of the
University of Illinois at Urbana-Champaign, 2001
Urbana, Illinois
14074 Trade Center Drive, Suite 102
Fishers, IN 46038
Ph. 317-449-0033 Fax 317- 285-0609 (info@geotill.com)
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RESULTING FROM EMBANKMENT LOADING OF SOFT CLAY
AND SILT DEPOSITS
Volume I ofII
BY
MALEK M. SMADI
B.s., Jordan University of Science and Technology, 1988
M.S., Jordan University of Science and Technology, 1991
THESIS
Submitted in partial fulfillment of the requirements
for the degree of Doctor of Philosophy in Civil Engineering
in the Graduate College of the
University of Illinois at Urbana-Champaign, 2001
Urbana, Illinois

UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
GRADUATE COLLEGE
JANUARY 2001
date
WE HEREBY RECOMMEND THAT THE THESIS BY
MALEK M. SMADI
ENTITLED LATERAL DEFORMATION AND ASSOCIATED SETTLEMENT
RESULTING FROM EMBANKMENT LOADING OF SOFT CLAY AND SILT DEPOSITS
BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR
THE DEGREE OF DOCTOR OF PHILOSOPHY
~~
Director of Thesis Research
Head of Department
tRequired for doctor's degree but not for master's.
0-517

RESULTING FROM EMBANKMENT LOADING OF SOFT CLAY AND
SILT DEPOSITS
Malek M. Smadi, Ph.D.
Department of Civil Engineering
University oflllinois at Urbana Champaign, 2001
Gholamreza Mesri, Advisor
Settlement of structures on soft clay deposits results from flow and
consolidation of soil. In the latter case, water squeezes out from under the
structure, whereas in the former case soil squeezes out. Settlement resulting
from flow of soil depends on the factor of safety against undrained instability.
In construction situations where the factor of safety is small, an accurate
prediction of settlement reSUlting from flow of soil is required. Field
measurements of horizontal deformation of soft clays during and after
construction of embankments and storage facilities have been collected from
throughout the world, covering 180 case histories, to relate lateral deformation
to the factor of safety and to develop a practical procedure for computing
settlements resulting from flow of soil.
The available methods for predicting the undrained settlement and lateral
deformation, including solutions based on elasticity, empirical procedures, and
numerical techniques, were reviewed. The behavior of clay foundations
subjected to embankment loading and empirical methods using lateral
deformation as a measure of undrained stability, were reviewed and discussed.
The 180 case histories of embankments on soft clay and silt deposits with
lateral deformation measurements cover a wide range of subsurface
conditions, including plasticity index Ip from 5 to 340, undrained shear
strength Su from 5 to 80 kPa, Eu/su from 200 to 1000, cr/plcr/vo from 1 to 5,
embankment width B from 8.5 m to 630 m, embankment height h from 1 to
ill

35m, embankment slope width L from 1.35 to 195 m, and depth of foundation
Lo from 7 to 63 m.
An empirical correlation, based on 58 cases was developed between maximum
lateral deformation Dm or area of lateral deformation profile AD and factor of
safety against undrained failure. Parameters such as Eu, L, B/2 were also
included in the correlation.
A procedure, based on 16 cases with three or more inclinometers at several
distances from the centerline, was developed for determining distribution of
maximum lateral deformation and flow settlement across the embankment as a
function of LoIB and UO.5B. The procedure could be used either with one
inclinometer measurement e.g. near the toe of the embankment, or together
with the empirical correlation between Dm and factor of safety.
A procedure was developed for determining settlement trough resulting from
lateral deformation of soil out from under the embankment. The procedure
could be used together with inclinometer measurements at one location, e.g.
near the toe of the embankment or with Dm or AD determined from the
empirical correlation between lateral deformation and factor of safety.
Using the empirical database and the developed procedures, it was possible to
make successful prediction of lateral deformation and associated settlement for
embankments on soft clay and silt deposits.
IV

ACKNOWLEDGMENTS
This thesis is based on theoretical and empirical studies of field observations
conducted at the University of lllinois. It has been prepared under the direct
supervision of Dr. G. Mesri, Ralph B. Peck Professor of Civil Engineering, to
whom the writer is indebted for his constructive criticism, guidance, and
encouragement in the preparation of the manuscript.
During graduate study, the writer was employed part time in the office of
Minority Student Affairs. Special acknowledgement is due Mr. Otis Williams,
Associate Director of Minority Student Affairs at University of lllinois for his
valuable help.
Special thanks are extended to Professors E. J. Cording, J. H. Long, T. D.
Stark, and Dr. G. Fernandez for their encouragement during writer's graduate
study at the University of lllinois.
The writer wishes to thank his office mates Dr. H. Eid and Mr. B
Vardhanabhuti, and Dr. M. Shahain, M. Al-zoubi, M. Ajlouni, V. Schifano,
and M. Maniaci, graduate students at the University of lllinois, for discussions
and constructive criticism during the preparation of this thesis.
The author wishes to express his gratitude to the Department of Civil
Engineering and the National Science Foundation (NSF) for their continued
support during writer's graduate study at the University of lllinois at Urbana
Champaign.
Finally the writer gratefully appreciates the continued encouragement, support
and patience of his parents, brothers, and sisters throughout his education.
v

TABLE OF CONTENTS
Page
CHAPTER 1 INTRODUCTION.................................................................. 1
1.1 Statement of the Problem.................................................... 1
1.2 Objectives of the Study ....................................................... 3
1.3 Scope ..............................................................................".... 4
CHAPTER 2 PREDICTION OF SETTLEMENT AND
LATERAL DEFORMATIONS.......................................... 6
2.1 Introduction ...................................................................... 6
2.2 Prediction of Undrained Settlement and
Lateral Deformation Using Theory of Elasticity.............. 6
2.2.1 Flow Settlement........................................................... 6
2.2.2 Lateral Defolmation .................................................... 9
2.3 Prediction of Settlement and Lateral Deformation
Using Constitutive Models.............................................. 11
2.3.1 Constitutive Models .................................................. 11
2.3.2 Implementing Finite Element Analysis on
Case Histories............................................................ 12
2.3.3 Prediction of Deformations by The
Finite Element Method ............................................. 16
2.4 Predictions of Deformations Using
Empirical procedures....................................................... 17
2.4.1 Undrained Settlement................................................ 17
vi

2.4.2 Lateral Deformation during Construction ................ 20
2.4.3 Long Term Lateral Deformation............................... 22
2.4.4 Lateral Deformation during Stage-construction....... 23
2.4.5 Effect of Vertical Drains on Lateral Deformation.... 24
2.4.6 Field Deformation Analysis (FDA) ......................... 25
2.4.6.1 Loading Stage...................................................... 25
2.4.6.2 Post-Loading Stage ............................................. 30
CHAPTER 3 BILHAVIOR OF CLAY FOUNDATIONS SUBJECTED
TO E:MBANKMENT LOADING ........................................ 67
3.1 Yielding of Clay Foundations Subjected to
Embankment Loading......"................................................. 67
3.1.1 Yielding of Clay Structure............................................ 67
3.1.2 Yielding of Clay Foundation under Embankments ..... 68
3.1.3 Foundation Behavior Described Using Effective
Stress Path ..................................................................... 69
3.2 Parewater Pressures in Clay Foundations
under Embankments ........................................................... 72
3.2.1 Porewater Pressure Predictions during Single
Stage Embankment Construction................................. 72
3.2.2 Porewater Pressure Changes During
Construction.................................................................. 75
3.3 Lateral Deformation with Depth......................................... 81
3.3.1 Effect of Soil Type on the Distribution
of Lateral Deformation ................................................. 81
3.3.2 Effect ofLc/B on the Distribution of
V11

Lateral Deformation ..................................................... 81
3.3.3 Effect of Preconsolidation Pressure on the
Distribution of Lateral Deformation ............................ 81
3.3.4 Effect of Time on the Distribution of
Lateral Deformation ..................................................... 84
3.3.5 Prediction of the Normalized Lateral
Deformation Profile...................................................... 84
3.4 Stability Analysis of Embankments on Soft
Clay Foundations ................................................................ 85
3.4.1 Choosing Values for the Undrained Strength .............. 86
3.4.1.1 Vane Tests............................................................... 86
3.4.1.2 The Mobilized Undrained Shear Strength ............. 87
3.4.2 The Value of Factor of Safety that Triggers
an Abrupt Increase in Rate of Lateral Deformation .... 88
3.5 Shear Stress Level and Undrained Shear Deformations .... 89
3.6 Undrained Modulus of Soft Clay and Silt Deposits........... 92
3.7 Lateral Deformation under Reinforced Embankments ...... 94
CHAPTER 4 CONTROL OF ElfBANKMENTS CONSTRUCTION
BY OBSERVING LATERAL DEFORMATION .......... 131
4.1 Measurement of Dm and St.............................................. 131
4.2 Evaluation of AD and As ................................................. 132
4.3 UsingHorizontal Displacement,
Fill height, and Time....................................................... 133
4.4 Horizontal Displacement at the Surface
and the Factor of Safety .................................................. 133
4.5 Dm/St and St ..................................................................... 134
viii

4.6 Lateral Deformability Factor and
Total Load (~q/M)m and q) ) ......................................... 136
4.7 Other Methods.............................................................·.... 137
4.8 Maximum Lateral Deformation and Factor
of Safety Against Undrained Failure .............................. 139
4.9 Non-dimensional Lateral Deformation Analysis .......... 140
CHAPTER 5 CASE mSTORIES .............................................................. 193
CHAPTER 6 PREDICTING SETTLEMENT RESULTING FROM
LAT~RAL DEFORMATION ...,....................................... 330
6.1 Introduction ..................................................................... 330
6.2 Lateral Deformation Profile............................................ 332
6.3 Lateral Displacement Volume of Soil and Associate
Settlements ...................................................................... 333
6.3.1 Methodology ............................................................. 333
6.3.2 Deformability factor ................................................. 335
6.3.3 Effect of Embankment Width and Foundation
Thickness on Consolidation..................................... 336
6.4 Deformation of Lateral Across Embankment Width ..... 338
6.4.1 Lateral Deformation Distribution Across
Embankment Width.................................................. 338
6.4.2 Prediction of Lateral Deformation Across
Embankment Width .................................................. 339
6.5 Settlement Trough........................................................... 343
6.5.1 Total Settlement Trough ........................................... 343
6.5.2 Undrained Settlement trough.................................... 343
1X

6.6 Prediction of Undrained Settlement ............................... 346
6.7 Undrained Settlement Prediction for Embankment
1-95 Sec 246 Using the Proposed Method...................... 351
6.7.1 The Influence of the Inclinometer Location on
the Predicted Undrained Settlement for Embankment
1-95 Sec 246 Using the Proposed Method................. 352
6.7.2 Undrained Settlement Prediction for Embankment
1-95 Sec 246 Using the Proposed Method
and the Giroud (1973) Method................................. 352
6.7.3 Undrained Settlement Prediction for Embankment
. 1-95 Sec 246 Using the Proposed Method
and Poulos (1972b) Method ..................................... 353
6.7.4 Maximum Lateral Deformation Profile Across
the Embankment Width for 1-95 Sec 246 using
the proposed method and MIT-E3 .......................... 353
6.7.5 Maximum Lateral Deformation Profile Across
the Embankment Width for Rio de Janeiro Trial
Embankment Using the Proposed Method and
CRISP........................................................................ 354
6.8 Total Settlement Prediction forEmbankment 1-95
Sec 246 using ILL1CON for Consolidation Settlement
and the Proposed Method for the Undrained
Settlement........................................................................... 355
6.8.1 Introduction ............................................................... 355
6.8.2 One Dimensional Settlement Analysis for
Embankment 1-95 Sec 246 Using ILLICON............. 356
x

CHAPTER 7 SUMMARY AND CONCLUSIONS................................. 546
7.1 Summary ......................................................................... 546
7.2 Conclusions ..................................................................... 551
REFERENCES ............................................................................................. 557
APPENDIX A ................................................................................................ 593
APPENDIX B ............................................................................................. 595
VITA ............................................................................................................... 602
Xl

A
AD
Af
As
Asu
B
B
cy
D
e
LIST OF SYMBOLS
Porewater-pressure coefficient
Volume of soil per unit length of embankment that displaces
laterally, measured at the toe.
Pore pressure parameter A at (crl - cr3)max
Total volume of soil per unit length of embankment and B/2
that displaces vertically.
Volume of soil per unit length of embankment and B/2
that displaces vertically due to lateral flow of soil = AD
Coefficient of compressibility
Width of the loaded area
The ratio of incremental excess porewater pressure to the
incremental mean effective stress
Compression index
Permeability change index, ile/log k
Swelling index
Secondary compression index
Coefficient of consolidation
Lateral deformation at any depth
Maximum lateral deformation
Largest maximum lateral deformation across the embankment
width
Lateral deformation at ground surface
Undrained Young's modulus
Drained modulus
Void ratio
xii

EOC
EOP
FS
G
IDC
K
Ko
KoUC
KoUE
k
Initial void ratio
End of construction
End of primary consolidation
Factor of safety
Undrained shear modulus
Specific gravity of solids
Height of the embankment
Threshold height or critical height
Influence value, depending on the shape of the loaded area and
the depth of the elastic layer
Isotropic (equal all-round pressure) consolidated drained
compression test
Influence value, depending on the geometry of the problem
Liquidity index
Plasticity index
Isotropic (equal all-round pressure) consolidated undrained
compression test
Lateral stress ratio (dh/ d v)
Coefficient of Earth Pressure at rest
Laterally constrained consolidated undrained compression test
Laterally constrained consolidated undrained extension test
Permeability
Permeability in the vertical direction
Permeability in the horizontal direction
Width of the embankment slope
Thickness of the compressible layer
Non-dimensional Deformation Method
Lateral deformation at certain depth z / Maximum lateral
X111

Nz
NZsum
pi
Su
Su (ruC)
Su (ruE)
Su (KoUC)
Su (KoUE)
Su (mob)
Su (vane)
USSA
UU
deformation (= DlDm)
Depth of certain point at depth z 1Whole depth of the lateral
deformation profile (= z/ZD
Depth of Maximum lateral deformation 1Whole depth of the
lateral deformation profile (= Zrr/ZI = 0.26 ± 0.14)
Depth of minimum undrained shear strength 1Total depth of
the lateral deformation profile
(dl +d3)12, (dy + d h)12
(d1 - d 3)12, (dy - d h)12
Net foundation pressure.
Consolidation settlement
The end-of-primary settlement resulting from compression of
the voids
Shear stress level
Maximum settlement at the center
The undrained shear settlement resulting from lateral
deformation of the foundation soil
Maximum undrained settlement across the embankment width
Undrained shear strength
Undrained strength from ruc test
Undrained strength from ruE test
Undrained strength from KoUC test
Undrained strength from KoUE test
Mobilized undrained shear strength
Undrained vane shear strength
Undrained Strength Stability Analysis
Unconsolidated undrained test
XlV

Wf Water content at failure defined at, (0"1 - 0"3)ma:x/2
w o Natural water content
WI Liquid limit
wp Plastic limit
z Depth of any point in the foundation soil
ZI Depth of influence of lateral deformation
Zm Depth of maximum lateral deformation
a Deformability factor
~ Side slope of the embankment
mm Increment of maximum lateral deformation near the toe per
increment of time
Llu
/'),V
y
Loading Pressure
Increment of maximum settlement at the center per increment
of time
Excess porewater pressure
Shear induced excess porewater pressure
Volume change
Strain
Axial strain
Axial strain at failure, (d1 - d3)ma:x/2
Radial strain
Volumetric strain
Unit weight
In situ effective vertical stress, effective overburden pressure
Final effective vertical stress
xv

d ho
d ve
d p
qY
<j>'m
<j>'d
V
In situ effective horizontal stress
Vertical consolidation stress
Preconsolidation pressure
Friction angle
Mobilized friction angle at (d1 - d 3)max/2
Drained friction angle
Poisson's ratio
XV1

CHAPTER 1
INTRODUCTION
1.1 Statement of the Problem
When an embankment load is rapidly applied to a deposit of saturated clay, the
clay deforms at constant volume to accommodate the imposed shear stresses. The
settlement associated with these deformations, which occurs without significant
dissipation of excess porewater pressures, is called undrained settlement.
Evaluation of the undrained settlement of structures on clay is important for a
number of reasons. First, Undrained settlement may constitute a large portion of the total
final settlement, depending on the nature of the soil, the loading geometry, and the
thickness of the compressible layer. Second, analysis of undrained settlement is an
integral part of the analysis of the overall settlement-time behavior of foundations. Third,
undrained settlement is closely related to the undrained stability of a foundation.
Excessive undrained settlement may be a warning of impending failure.
The two basic components in the theoretical analysis of undrained settlement are:
an analysis to relate settlement to the loading geometry and the soil properties; and the
determination of the appropriate stress-strain and strength properties of the soil to input to
the theoretical solutions.
The finite element method of analysis facilitates the solution of a broad range of
boundary loading problems involving inhomogeneous, anisotropic and nonlinear soil
properties. However, even though improved analytical capabilities have been developed,
accurate determination of stress-strain properties in undrained shear for in situ clay
deposits remains a major obstacle to the successful analytical prediction of undrained
1

settlement. Therefore, the principal aim herein is to present an empirical method for
estimating undrained settlement using the in situ measurements of lateral deformations.
When an embankment, storage facility, or a footing is constructed, that is of
limited size in comparison with the thickness of the compressible ground, there are two
components of deformation; one is the volumetric compression due to consolidation and
the other is the shear distortion. An example of the latter is the immediate lateral
deformation and associated settlement under undrained conditions. Shear deformation or
flow causes horizontal displacement of soil. The undrained shear deformation depends
on soil profile, nature of the soil deposits, type of structure, and rate and method of
construction. Shear deformation can cause large initial and post construction settlements.
Experience with the construction of embankments on soft ground has shown that
there have been many instances of base failure of embankments. However, evaluating
and comparing entire ground deformations may allow a prediction of ground failure
during embankment construction.
The lateral deformation of soft clay due to embankment loading is becoming more
of interest because lateral deformation has detrimental effect on the behavior of adjacent
structures such as pile foundations, movement of bridge abutments, and movement of
water and gas pipelines.
In this study current empirical, numerical, and elastic-theory methods for the
prediction of undrained lateral deformation, and settlement of clay foundations subjected
to embankment loading are reviewed. Field measurements of lateral deformation for 180
embankments on soft clay and silt deposits were used in the present investigation. The
distribution of lateral displacement with depth is used to calculate the settlement resulting
from lateral deformation.
In general, finite element methods have not been very successful in predicting
lateral deformation. Accuracy of predictions however has increased for the finite element
methods which properly model constitutive equations of soil, the loading procedure, and
time dependent creep. Empirical methods for estimating lateral deformation are
2

presented predicting settlement resulting from lateral flow for undrained and drained
conditions.
1.2 Objectives of the Study
The objectives of this research are to develop, using field observation of lateral
deformation, empirical procedures for: (a) determining distribution of lateral deformation
across an embankment, based on a limited number of inclinometers measurements, (b)
predicting settlement resulting from lateral deformation, (c) relating lateral deformation to
factor of safety against undrained failure, (d) using lateral deformation as a measure of
undrained stability, (e) examining time-dependant deformation of soil subjected to
embankment loading and different drainage boundary conditions, (f) superimposing
undrained deformation and drained one-dimensional consolidation settlement.
Field measurements of horizontal deformation of soft clay and silt deposits during
and after construction of embankments and storage facilities have been collected from
throughout the world, covering 180 case histories. These probably represent 95% of
cases with lateral deformation measurements reported in the literature. The undrained
settlement resulting from the lateral deformation of the foundation soil is computed from
an integration of the lateral deformation profile obtained at various locations across the
embankment width.
Lateral deformation of the ground resulting from embankment loading has been
the subject of numerous studies for years. There has been an interest in predicting lateral
deformation because of the observed detrimental effect of lateral deformation on adjacent
structures and also because plastic flow that produces lateral deformation may lead to
ground failure. However, even in the absence of a ground failure and adjacent structures,
lateral deformation is important because it contributes to settlement of the embankments,
storage facilities, and structures on soft ground. In some situations, part of lateral
deformation results from multidimensional consolidation. A procedure has been
3

developed for estimating lateral deformation using an empirical correlation between
lateral deformation and factor of safety against undrained failure. The correlation
includes influence of ground condition as well as the geometry of the embankment.
1.3 Scope
In Chapter 2, the available methods for predicting the undrained settlement and
lateral deformation are reviewed. They are divided into three categories: solutions based
on elasticity, numerical techniques, and empirical procedures.
In Chapter 3, behavior of clay foundations subjected to embankment loading is
reviewed and discussed. The behavior includes, yielding of clay structure, porewater
pressures produced by embankment loading, lateral deformation with depth, stability
analysis and choosing the mobilized undrained shear strength, the value of factor of safety
that triggers an abrupt increase in rate of lateral deformation, shear stress level and
undrained shear deformations, and the undrained modulus of soft clay and silt deposits.
In Chapter 4, methods using lateral deformation as a measure of undrained
stabiltty are reviewed and discussed. In addition, a method to control embankment
construction by observing lateral deformation is developed through relating lateral
deformation to factor of safety against undrained failure. The same empirical correlation
could be used to estimate the maximum lateral deformation at the toe or the area of lateral
deformation profile with depth, given the factor of safety against undrained failure.
In Chapter 5, the collected database covering 180 case histories is presented.
These probably represent 95% of cases with lateral deformation measurements reported
in the literature. All the parameters that are believed to affect the undrained deformations
are identified for the cases and are included in Table 5.1. The references for the cases are
tabulated in Table 5.2. These cases are sorted by case name in Table 5.3 and they are
sorted by case ID in Table 5.4. In addition, the general parameters whenever available for
the case that were used in the present empirical analyses are tabulated in Table 5.5. The
4

behavior of the lateral deformation with depth is strongly dependant on the soil type.
Therefore, normalized lateral deformation measurements are presented together with the
soil profile and soil properties.
In Chapter 6, displacement volume of soil and associate settlements is discussed.
Two types of correlations have been examined for each case history. In the first
correlation, the lateral deformation near the toe has been compared with the total
settlement at the embankment center during and after construction. In the second
correlation, the area of lateral deformation has been compared with the area of total
settlement during and after construction. From these correlations the values of the
deformability factor RDS for different cases have been computed and the averages are
tabulated in Table 6.1 for different periods during and after construction. Two empirical
procedures are presented and discussed: (1) predicting distribution of lateral deformation
across embankment, (2) predicting settlement resulting from lateral deformation. Then
the two proposed methods are verified by implementing them on several case histories.
Finally, in Chapter 7, the summary and conclusions are presented.
5

CHAPTER 2
PREDICTION OF SETTLEMENT AND LATERAL
DEFORMATIONS
2.1 Introduction
Loading the soft clay and silt deposits by embankments or storage facilities
creates vertical settlement and lateral deformation. In some cases, the undrained shear
distortion, which is included in the undrained settlement and lateral deformation, causes
stability problems for the embankment or storage facilities and adjacent structures.
Therefore, a prediction of lateral deformations prior to construction would allow (a) an
estimate of settlements resulting from flow of soil for stable situations and (b) soil
improvement measures and construction procedures to prevent excessive deformations or
unstable conditions.
The available methods for predicting the undrained settlement and lateral
deformation can be divided into three categories: solutions based on elasticity, numerical
techniques (e.g. using FEM), and empirical procedures.
2.2 Prediction of Undrained Settlement and Lateral Deformation Using Theory of
Elasticity
The theory of elasticity has been previously used to predict undrained settlement
and lateral deformation.
2.2.1 Flow Settlement
The settlement resulting from lateral deformation or flow of saturated soils has
6

been previously termed, initial settlement, immediate settlement, elastic settlement, shear
settlement, and undrained settlement. In this thesis settlement resulting from lateral
deformation of soil is termed flow settlement to distinguish it from consolidation
settlement. Flow settlement results from time-independent as well as time-dependent
flow of soil from under the structure, whereas consolidation settlement in saturated soils
results from time-dependent flow of water from under the structure.
Terzaghi (1943), using the solution by Steinbrenner (1934), expressed elastic settlement
for a flexible load on a circular area in terms of values of surface load q, thickness of
elastic layer La, modulus of elasticity of the layer, E, and Poisson's ratio v, Fig. 2.1. In
Figs. 2.1 band 2.1c the base of the elastic layer is rigid and elastic layer adheres perfectly
to the rigid base. Figure 2.1 shows that the ground surface under and outside the loaded
area settle and the magnitude of settlement at the edge of loaded area is about 50 to 70%
of the settlement at the center. In Fig. 2.1 c where the depth ratio LaIR is smaller than 2/3
and Poisson's ratio is close to 0.5, the settlement is maximum at a distance of two third of
the radius from the center of the loaded area, it is near zero at the edge of the loaded area,
and ground surface heaves outside the loaded area.
The settlement of an elastic layer subjected to uniform flexible strip load has been
expressed in different forms. They are summarized in Table 2.1 and Figs. 2.2 to 2.5.
However. It has the general form:
(2. 1)
Where:
q = Net foundation pressure.
B = Width of the loaded area.
v =Poisson's ratio. (v =0.5 for saturated clays).
7

I =Influence value, depending on the shape of the loaded area and the
depth of the elastic layer.
Eu = Undrained young's modulus.
The use of elastic theory to predict undrained deformations ignores the effect of
local yielding that is likely to occur even at very high factors of safety. D'Appolonia et
aI. (1970, 1971) proposed a modified elastic method taking into account the effects of
local yielding. They suggested a correction factor SR based on theoretical considerations
to correct the computed elastic settlement. D'Appolonia and Lambe (1970) proposed a
finite element method taking into consideration variation of modulus with depth and local
yielding.
The undrained elastic settlement of a finite elastic layer subjected to embankment
loading was studied by Giroud (1973). Balasubramaniam and Brenner (1981) presented
the work of Giroud where the influence factors are expressed in term of the geometry of
the embankment and thickness of elastic layer, Fig. 2.6. The value of the undrained
settlement of the ground surface was expressed by Giroud (1973) as:
(2.2)
Where:
Eu = undrained Young's modulus.
bI = half of embankment width at the bottom.
8

b2 =half of embankment width at the top.
rl and r2 = Influence factors.
Analysis has been made using Giroud's method to predict the undrained
settlement trough for an embankment located on a thin and thick deposit. It has been
found as it is shown in Fig. 2.7 that the method can't predict a reasonable trough for a
thick deposit. Figure 2.7 shows that the undrained settlement trough for an embankment
located on a thick deposit becomes zero at an unrealistic distance from the center, that is
10 times the width of the embankment. However, for a thin layer Giroud's method
predicts a realistic near zero settlement at the toe of the embankment.
2.2.2 Lateral Deformation
Theoretical analysis of undrained shear deformation of soils is quite complicated
and there is no widely accepted method for predicting lateral deformation. Prediction of
lateral deformation is difficult partly because consolidation produces inward movement,
whereas undrained and drained deformation including creep produce outward movement.
The most significant part of lateral deformation beneath an embankment generally
occurs during construction when the undrained condition exists. The settlement under
the embankment is produced by time dependent lateral flow of soil. Poulos (l972b)
attempted to predict lateral deformation using the theory of elasticity. The computation
of the lateral deformation based on theory of elasticity mainly used Poisson's ratio v =
0.5 and an undrained modulus of elasticity Eu. Poulos (1972b) expressed lateral
deformation for v = 0.5 as:
9

(2.3)
Where:
Lo = Thickness of the compressible layer.
Ih = Influence value, depending on the geometry of the problem.
Eu = Undrained Young's modulus.
The influence factor Ih is shown in Fig. 2.8c for the horizontal deformation at the surface
at any distance from centerline and Fig. 2.8d for the horizontal deformation at any depth
beneath the edge. Poulos (1972b) concluded that there is a discrepancy between
measured and predicted lateral deformation beneath an embankment for the following
reasons:
1) The difficulty of estimating the soil Poisson's ratio
2) Anisotropy
3) Non-linear stress-strain behavior
4) In-homogeneity
5) Neglect of embankment stiffness and roughness at the bottom of elastic layer.
Poulos (1972b) examined the influence of the five factors on elastic settlement and
horizontal deformation. The results are shown in Table 2.2, and the effects of
inhomogeneity and anisotropy are illustrated Figs. 2.8 and 2.9, respectively. Based on
the comparison of calculated and observed behavior shown in Fig. 2.10 Poulos concluded
10

that the linear elastic models give poor prediction of foundation deformations and there is
a need for detailed evaluation of field observations. Tavenas et al. (1974) and stille et al.
(1976) attempted to resolve the discrepancy between calculations and observed behavior
of natural clays by including nonlinear and anisotropic response. Tavenas et. al. (1974)
used finite element elastic analysis to predict the deformations for Saint-Alban B, C, and
D. The analysis gave lateral deformations much larger than those observed and
distributed differently over the depth of the foundation, even though a value of 0.3 was
assigned for Poisson's ratio which is less than 0.5. Stille et. al. (1976) considered the
anisotropy of the soil in a finite element elastic analysis for Kalix embankment. A close
agreement between calculated and measured values was obtained when a Poisson's ratio
of 0.4 was used in the analysis.
2.3 Prediction of Settlement and Lateral Deformation Using Constitutive Models
The most significant development in lateral deformation calculation started with
the introduction of the finite element method, which permitted calculation of lateral
deformations under the slopes of embankments (Clough and Woodward 1967). The
plane strain state of deformation that exists under some embankments could be modeled
with non-linear constitutive models.
2.3.1 Constitutive Models
Stress-strain relationships, or more generally the constitutive equations used to
describe the soil behavior are the essential elements in the finite element analysis. There
has been a substantial literature describing constitutive models for soils, and they have
been summarized in comprehensive State of the Art reports (e.g. Hashiguchi, 1985;
Sekiguchi, 1985). Duncan (1994) listed most of the models that have been used to
analyze embankments and dams. The wide variety of soils leads one to conclude that no
11

material model will be able to encompass the behavior of all soils under all conditions.
The parameters for any useful constitutive model should be measured directly by simple
laboratory or insitu tests and should have a clear physical meaning.
2.3.2 Implementing Finite Element Analysis on Case Histories
The finite element method has found one of its major uses in geotechnical
engineering in the analysis of embankment deformations. The earliest reported
application was by Clough and Woodward (1967), who also simulated the process of
construction of the embankment by adding elements, representing layers of fill, at
successive stages of construction. Other researchers also adopted the finite element
method for embankment deformation analysis (Hollingshead and Raymond 1971, Shibata
et al 1976, Davis and Poulos 1975, Tavenas et al. 1974, Stille et al. 1976, Wroth and
Simpson 1972, Ladd 1972, Simon et al. 1974, Smith and Hobbs 1974, Smith and Hobbs
1976). Some investigators considered creep deformations (Christian and Watt 1972,
Thoms et al. 1976, Akagi et al. 1976).
Ladd et al. (1994) implemented MIT-E3 model in a finite element analysis for the
1-95 Sec 246 embankment using the ABAQUAS program (HKS 1989) together with
subroutines (user materials) for the effective stress models being used at MIT (Hashash
and Whittle 1993). For comparison purposes the same analysis was carried out using the
Modified cam clay (MCC) model. Figures. 2.11 and 2.12 compare predictions of
horizontal displacements by MIT-E3 and MCC, respectively, with the measurements
from inclinometers 13, 14, 15, and 16 at the end of construction (CD 620 day) and at CD
2000 day corresponding to the end of the field monitoring. The largest lateral movements
are measured in the upper clay by inclinometer 14 located close to the toe of the
embankment. All the inclinometers measured progressive outward displacements at all
elevations in the clay throughout the entire monitoring period (up to CD 2000). There are
large differences in predictions of lateral deflections by the two soil models. There is
12

also a significant difference between measured and computed lateral deformations in the
upper 15 m of clay. The patterns of the measured lateral deformations as they change
with time are different from those of the calculated movements; especially near to the toe
of the embankment. While the measured values show large increase with time near the
fill base, the predictions show significant increases at deeper depths. This is true for both
the Modified Cam clay and the MIT-F3 method.
The MIT-E3 model gives much more realistic predictions of lateral deformation
at the end of construction at all four inclinometer locations. Analyses were made using
upper and lower bound estimates of the preconsolidation pressure, profiles 1 and 2. The
results for profiles 1 and 2 in Fig. 2.11 show the importance of the stress history on the
magnitude of the lateral deformation, but have little effect on the distribution of
deformation. ill general, the model overestimates the lateral deformation in layer F, with
maximum outward displacements occurring in layer D under the embankment. In
contrast, the MIT-E3 shape of the measured data shows maximum movements in layer B.
Ladd et al. (1994), suggested that the results from MIT-E3 are encouraging and show that
lateral deformation during consolidation or post construction can be described by a model
which includes anisotropic yielding and does not include creep effect.
The Modified Cam Clay greatly overestimates the measured lateral deformation at
the end of construction (Fig. 2.12), especially in the bottom half of the deposit.
Ladd et al. (1994) offered several reasons for lack of agreement between the MIT-
E3 model and the measurements. In the MIT-E3 method there is a smooth transition to
normally consolidated behavior. The simplification of this transition during the
formulation of the MIT-E3 model may decrease the overall accuracy of the method. The
MIT-E3 model incorporates fifteen (15) parameters; these parameters must be selected
carefully. It is known that these parameters are somewhat difficult to measure, and that a
small error in several parameters may lead to a large error in the final calculations. The
MIT-E3 also assumes throughout that the soil is a rate independent material (i.e., creep
effects are not considered). However, if tp (time to reach end of primary consolidation) is
13

relatively short and effective vertical stress is near the preconsolidation pressure,
significant secondary settlements may occur. In addition, one of the input parameters,
2GIK is the ratio of the tangential elastic shear modulus to the bulk modulus, which is
related to Poisson's ratio, v, of the soil. Since Poisson's ratio changes with loading and
consolidation, Ladd et al. (1994) used an approximation to estimate 2GIK. There is no
way to verify the validity of the approximation.
Almeida and Ramalho-Ortigao (1982) presented results of finite element analysis
of Rio De Janeiro trial embankment using two programs CRISP and FEECON. Analyses
carried out were: elasto plastic undrained and coupled consolidation using the CRISP
program and the elastic non-linear undrained using FEECON program. The results of
lateral deformations from numerical analyses were compared with observed values
during embankment construction as shown in Fig. 2.13. Computed results and measured
values of lateral deformations at the base of the embankment are presented in Fig.
2.13(a). The main observations by Almeida and Ramalho-Ortigao (1982) from Fig
2.13(a) were that computed deformations are within the range of measured values under
the embankment platform, however, are larger under the slope and outside. In addition,
computed values showed the maximum lateral deformation in front of the embankment
slope whereas the observed maximum values occurred under the slope. Lateral
deformation with depth that would be measured by inclinometers was also predicted.
The computed lateral deformations, shown in Fig. 2.13b, were higher than the measured.
Chai and Bergado (1993) used the modified Cam clay model (Roscoe and
Burland 1967) and a hyperbolic nonlinear constitutive model, for the soft foundation soil
in analyzing the deformations for the Malaysian trial embankment (scheme 6/8). The
analysis was based on applying the embankment load by two methods: 1) increasing the
self weight of all of the embankment elements, and 2) increasing the load by placing a
new layer of elements, while correcting the coordinates of the nodes above of topmost
embankment surface. Method 1 involves modeling the entire embankment as completed,
at the beginning of the analysis. Giving the entire embankment a percentage of its entire
14

completed weight, which simulates the construction procedure. The percentage of weight
corresponds to the actual weight of the fill on the foundation at that time. This method is
referred to as loading by percentage method, which implies that, the stiffness of the
whole embankment elements existed at the beginning of the analysis. Method 2 adds
new nodes to the finite element analysis as the fill is constructed. As a new fill layer is
constructed, placing a new layer of nodes simulates the effect. The location of the nodes
was corrected for the settlement of the fill and foundation prior to placement of the new
layer of fill. This method is referred to as the loading by layer method. The results
suggested that the finite element analysis by loading layer by layer, and correcting the
node location predicted results that were in better agreement with measurements for both
settlements and lateral deformation. The conclusion of Chai and Bergado (1993) was that
the deformation pattern of the soft ground predicted by a finite element analysis not only
depends on the magnitude of the load, but also on the sequence of applying the load.
Russell (1996) calculated the rate of lateral deformation for whitewall creek
embankment using finite element analysis to assist the assessment of failure during
embankment construction. The finite element analyses were carried out using a version
of CRISP program with the modified Cam-clay constitutive model, which allowed a gain
in the undrained shear strength during consolidation. The drains were included in the
analysis using the method developed by Hird et al. (1992). The finite element predictions
and observed behavior are compared for the maximum lateral deformation below the toe
in Fig. 2.14. Russell stated that the comparison of the lateral deformation with the
measurements is encouraging considering the difference between actual construction
schedule and that assumed in the prediction in the duration of the loading and post
loading stages.
Tavenas et al. (1979) summarized from literature comparisons between measured
and computed, by finite element techniques, total settlements at the center and maximum
lateral displacements near the toe for a number of case histories. This comparison is
presented in Fig. 2.15. Tavenas et al. (1979) concluded that the quality of the settlement
15

prediction is apparently remarkable not withstanding the C-l type of predictions (Lambe
1973) with an opportunity to adjust the large number of assumptions and parameters. On
the other hand, the lateral displacement predictions by the same analyses are all much
larger than the observed displacements, which indicate that experience up to 1979 was
not successful in lateral deformation prediction by means of finite element analysis. The
most recent effort on the use of constitutive models together with finite element
techniques has been by Whittle and co-workers (Kavvadas 1982, 1983, Whittle 1987,
1993, Whittle et al. 1994). The latest version of their model has 15 parameters.
2.3.3 Prediction of Deformations by The Finite Element Method
Sekiguchi et al. (1988) developed a chart to assess the effect of partial drainage on
lateral soil movements. The chart was developed from coupled stress- flow analysis using
the finite element method. A plane strain elasto-viscoplastic constitutive model for clays
was implemented for the analysis. Figure 2.16 shows the effect of partial drainage on the
soil movements. The VDand Vs are defined in Fig. 2.17. (Uy)ec is the degree of elasto-
viscoplastic consolidation at the end of construction and can be assessed from Fig. 2.18.
Note that for a 10 m thick clay layer with Cy = 3 m2
/year and draining from top and
bottom, subjected to an embankment loading completed in 1112 of a year, Tc = 0.01
which leads to U =6 %. This means that at the end of construction VDNs =0.66 and
0.28 for BIH of 2 and 6, respectively.
Loganathan et al. (1993) studied the deformation of clay under embankment using
the finite element program CRISP, developed at the University of Cambridge.
Constitutive soil models included in this program are the Cam-Clay (both the original and
the modified version), elastic perfectly plastic (options for the Von Mises, Tresca,
Drucker-Prager, and Mohr-Coulomb models) and elastic isotropic and anisotropic
models. They found that the maximum lateral deformation beneath the toe of the
embankment is approximately 0.28 times the maximum settlement observed below the
16

center of the embankment at the end of loading.
2.4 Predictions of Deformations Using Empirical procedures
There are only a limited number of empirical procedures in the literature for
computing settlement resulting from lateral flow of soil during construction as well as in
the long term.
2.4.1 Undrained Settlement
Assuming that significant undrained shear settlement begins when the yield stress
is exceeded and the soil becomes normally consolidated, Leroueil et al. (1990) pointed
out that this settlement resulting from plastic flow of soil can not be analyzed in terms of
theory of elasticity. On the other hand, the more satisfactory procedure using
elastoplastic constitutive equations together with finite element procedure is too complex
for general use in practice. Tavenas and Leroueil (1980) assumed that the undrained
shear settlement begins to occur when the embankment height reaches what they termed
the threshold height Rne which is the height of the embankment at the moment when the
effective vertical stresses in the foundation exceed the preconsolidation pressure. They
suggested an empirical expression for predicting the undrained shear settlement at the
center of embankment at the end of construction:
(2.4)
Where R is the height of embankment after the Rne has been reached and
exceeded.
Tavenas and Leroueil (1980) concluded that the construction settlement during
the stage where the effective vertical stress in the foundation is less than the
17

preconsolidation pressure is due to recompression. However, field measurements show
that the lateral deformation starts at very early stages of construction when H is less than
Hnc (Tavenas et al. 1979). In addition, Eq. 2.4 provides Su up to the end of construction.
However, the undrained shear settlements continue even after the end of construction as
has been demonstrated by significant lateral deformations observed by inclinometers
especially when the embankment has steep slopes or has been built with a low safety
factor.
The undrained settlement resulting from the lateral deformation of the foundation
soil can be computed from an integration of the lateral deformation profile obtained at the
toe of the embankment slope. Mesri et al. (1994) integrated the lateral deformation
profile and concluded the following relationship:
S =Dm
u 2
Where:
(2.5)
Su =The undrained shear settlement resulting from lateral deformation of
the foundation soil.
Dm = The maximum lateral deformation within the foundation depth.
Mesri et al. (1994) combined an empirical relationship, which relates Dm to
consolidation settlement (Tavenas et al. 1979), and Eq. 2.5 to obtain the following
relationship between Su and the end of primary settlement, Sp, for embankments with a
factor safety is near 1.4 against undrained failure:
18

(2.6)
Where:
Sp = The end-of-primary settlement resulting from compression of the
voids.
Equation 2.6 indicates that for a properly engineered embankment, i.e., with a
factor of safety against undrained bearing capacity failure greater than 1.4, the settlement
resulting from lateral deformation is expected to be small as compared to the total
settlement. Terzaghi et al. (1996) stated that the settlement caused by flow of soil from
under the structure is then likely to be less than 10% of the end-primary-settlement
resulting from compression of the voids.
It is clear that there is a need for a simple empirical procedure for predicting the
undrained shear settlement when the factor of safety is different from 1.4. For factor of
safety less than 1.4 the embankment foundation may experience large undrained plastic
flow resulting in large undrained settlement or failure.
Bjerrum (1972), in describing Ska Edeby test embankment VI, mentioned that
"The factor of safety of the embankment is low, probably of the order of 1.2 when the
rate effect on undrained shear strength is taken into account. The component of the
settlements resulting from the lateral yield is unusually large, as it amounts to more than a
quarter of the total settlements". Ska Edeby VI is considered to be an important example
of large shear deformation (Kallstenius and Bergau 1961, Osterman and Lindskog 1963,
Burland 1971, Holtz and Lindskog 1972, Marche and Chapuis 1974, Holm and Hotz
1977, Hansbo et al. 1981, Larsson 1986).
Larsson (1986) calculated undrained settlement due lateral deformation for Ska
Edeby Test Embankment VI directly after full load application in amount of 5 cm based
19

on empirical relations between undrained shear strength, plasticity index and calculated
factor of safety.
Foott et a1. (1987) estimated the undrained settlement for the Chek Lap Kok main
test embankment by examining the measured settlement and lateral deformation profiles.
It was concluded that the total undrained settlement resulting from undrained lateral
deformation was about 13 to 22 cm. However, it is not clear how they came up with
these numbers. Foot et a1. (1987) stated "Undrained settlement was estimated by an
examination of the load/settlement plots and by consideration of the lateral mud
deformations recorded by inclinometers on the periphery of the main test area. Total
undrained settlements of 0.08-0.13 m were estimated for the first 250 contract days, with
an additional 0.050-0.09 m occurring between approximately CD 400 and 4350." (CD =
Contract day).
2.4.2 Lateral Deformation during Construction
Lateral deformation of the ground reSUlting from embankment loading has been
the subject of numerous studies for years. There has been an interest in predicting lateral
deformation because of the observed detrimental effect of lateral deformation on adjacent
structure~ (O~terman 1952, Heyman 1965, Stermac et a1. 1968, Leussink and Wenz 1969,
Broms 1972. Stewart et a1. 1994, and Goh et a1. 1997) and also because plastic flow that
produces Literal deformation may lead to ground failure. However, even in the absence
of a ground failure and adjacent structures, lateral deformation is important because it
contribute" to differential settlement of the embankments, storage facilities, and
structures on soft ground. In some situations part of lateral deformation results from
multidimensional consolidation.
Ta'enas et a1. (1979) stated that lack of success in predicting the lateral
deformation in clay foundation under embankments is not only due to the reasons
20

presented by Poulos (1972b), but also due to the basic assumption of a truly undrained
response of the clay foundation during embankment construction. Tavenas et al. (1979)
indicated that when the preconsolidation pressure is only slightly in excess of the
effective overburden pressure, the foundation clay becomes normally consolidated at an
early stage of construction and the development of lateral deformations is governed by
undrained shear distortion of the clay. In this case, the maximum lateral deformation at
the toe, Dm , is equal to the construction settlement at the center. The Lanester test
embankment (Pilot et al. 1973) exhibited this behavior under the O.4-m-high initial
working platform where the final effective vertical stress exceeded the preconsolidation
pressure, as shown in Fig. 2.19.
To understand the influence of preconsolidation pressure, cr'p on clay behavior,
Tavenas et al. (1979) studied the variation of the maximum lateral displacement, Dm,
with the height of fill. The results are shown in Fig. 2.20(a). They noticed that for all
cases Dm remains small initially, increasing at a rate of about 1 cm per meter of fill.
However, at a later stage of construction the displacement increments are very large,
typically reaching 8 cm per meter of fill. They observed that the change in the rate of
increase of Dm was relatively abrupt and occurred at a height of fill that was 25-75% of
the height at failure.
Tavenas et al. (1979) stated that when the clay foundation is in an
overconsolidated condition, the stiffness and the coefficient of consolidation are
relatively high. Excess pore water pressures induced by an embankment load can
dissipate partially or fully, allowing the clay to consolidate. During consolidation of the
clay shear stresses induced by the embankment load are not large enough in comparison
to the strength of soil to cause significant lateral movement. Hence, the lateral
deformation increments are small in comparison to the vertical settlement increments
which are shown in Fig. 2.20(b). Tavenas et al. (1979) found from observations on 21
embankments that Dm/St vary between 0.06 and 0.36 with mean value of 0.18, during the
partially drained loading in the recompression range. In summary, Tavenas et al. (1979)
21

obtained from their empirical study the following:
For overconsolidated states at the beginning of banking:
Dm = (0.18 ± 0.09) St (2.7)
For normally consolidated states during embankment construction:
(2.8)
Suzuki (1988) observed settlement and lateral deformation of 11 embankments.
He found that the relationship between the lateral deformation and embankment settle-
ment for partially drained loading of the preconsolidated clay in recompression could be
expressed as;
Dm = (0.208 ±0.052)St (2.9)
Leroueil et al. (1990) reviewed these empirical rules for prediction of lateral
deformation and concluded that there is insufficient data to establish a relationship for
variable depths of soft clay.
2.4.3 Long Term Lateral Deformation
Tavenas et al. (1979) collected data on lateral deformation with time during
consolidation for 14 embankments. As shown in Fig. 2.21 they found that during primary
consolidation the increment of maximum vertical settlement and increment of maximum
lateral deformation are related linearly with an average ratio according to:
(2. 10)
For Ska Edeby VI embankment settlement and lateral deformation measurements
have been carried out for 17 years. Using these measurements Tavenas et al. (1979)
computed Wm / D"St up to 17 years according to Eq. 2.11.
22

(2. 11)
They explained the drop m LlDmlLlSt in terms of increased significance of
"secondary deformations at this site", (apparently implying secondary compression
contributes to settlement but not to lateral deformation).
Suzuki (1988) found that the relationship between the increment of the maximum lateral
deformation and the increment of the maximum vertical settlement during each stage of
the stage-construction of 8 embankments to be:
Wm = (O.24±O.03)LlSr (2. 12)
Equation 2.12 was obtained from observations for consolidation periods
immediately after construction. Therefore, it is not possible to consider Eq. 2.12 for long
term lateral deformation after the completion of construction.
2.4.4 Lateral Deformation during Stage-construction
Construction in stages has been used to assure stability of embankments during
construction. Biemond (1936) took advantage of the increase in shear strength during
consolidation by construction of an embankment in stages which otherwise would have
failed. In addition, Middlebrooks (1936) described a case where the increase in the
undrained shear strength that took place during construction stabilized the embankment.
Development of maximum lateral deformation Dm with the settlements St,
observed under the Palavas test fill (Bourges et al. 1973) is shown in Figure 2.22, during
two stages of construction and consolidation. The 25.7 m thick foundation deposit
consists of an upper normally consolidated plastic clay layer, 14 m thick, overlying
slightly overconsolidated clay. During the first loading, the upper clay layer immediately
became normally consolidated, but the lower layer remained over-consolidated. As a
result, the deformations were essentially governed by the behavior of the upper layer.
23

During the first consolidation period, lasting for 9 months, Dm was observed to increase
with St at a rate corresponding to mm = 0.15 ~St. During this period, the thickness of
the zone in a normally consolidated state apparently increased somewhat (Fig. 2.23) due
to the increase in cr'v. As shown in Fig. 2.22, the application of the second loading stage
produced increment of Dm almost equal to the increment of settlement. The increased
embankment load at the end of this second loading was sufficient to bring the foundation
to a normally consolidated state, and the distribution of lateral deformations with depth
was modified accordingly (Fig. 2.23). In the final 11 month period of consolidation,
lateral deformations increased at a rate mm = 0.34 ~St (Fig. 2.22), probably because of
the reduced factor of safety (FS) of the embankment (at the end of the second loading, FS
=1.25, as compared to FS =1.6 at the end of the first loading).
Teparaksa (1992) presented the lateral deformation with time for the stage
construction in Bang Na-Bang Pakong highway. Figure 2.24 shows that the rate of
lateral deformation mm/~t, was 0.029 cm/day during the first stage, decreased after
halting the construction in the first stage, and then it increased to 0.061 cm/day during the
second stage of loading. The relationship between maximum lateral deformation and
maximum vertical settlement at the first stage and second stage of construction is shown
in Fig. 2.25. It can be seen that the ratio of maximum lateral deformation to the
maximum vertical settlement (mm/~St) increased from 0.33 during the first stage to 0.46
during the second stage. The increase in the rate of lateral deformation and the increase
in the ratio (mml~St) in Figs. 2.24 & 2.25 are consistent with the increase in rate of
loading.
2.4.5 Effect of Vertical Drains on Lateral Deformation
When a soft clay layer is very thick or the permeability is low, the preloading
technique is likely to be inefficient when used alone because an inordinately long period
of time will be needed to bring about significant compression. In these circumstances,
24

radical improvements in the preloading time can be affected by the installation of vertical
drains to shorten the drainage path during consolidation of the clay. The advantage of
vertical drains is assessed in terms of the acceleration achieved in primary consolidation
over the consolidation rate that would have occurred without the drains.
Using vertical drains allows rapid increases in the undrained modulus and the
undrained shear strength, and thus less settlement resulting from undrained deformation
should develop with time. Ladd (1991) studied the effect of vertical drains on Dm versus
St using the measurements of Palavas test fill. Case A in Fig. 2.26 represents
construction without drains and it showed the essential features described by Tavenas et
al. (1979); i.e., partially drained and then undrained behavior during filling, followed by
consolidation having mm/LlSt = 0.15. Case B has an identical loading history, but the
vertical drains now cause significant drainage throughout filling; much larger EOC St and
slightly smaller EOC Dm. Rapid consolidation also reduces mm/LlSt after construction
from 0.15 to 0.10 due to smaller effects of undrained creep. Case C places more fill in
less time, resulting in a much larger mm/LlSt = 0.4 during filling, which also produces
larger mm/LlSt during consolidation due to higher rates of creep.
2.4.6 Field Deformation Analysis (FDA)
Loganathan et al. (1993) presented a methodology called Field Deformation
analysis (FDA) to separate and quantify settlement components for both loading and post
loading stages of embankments. FDA is a formulation based on volume of deformation
concept and developing linear relationships between measured quantities and settlement
components.
2.4.6.1 Loading Stage
The basic components of settlement observed beneath embankments were
classified as undrained settlement, consolidation settlement, and secondary compression.
In the case of stage constructed embankments on soft soils the settlements and lateral
25

deformations observed by field instrumentation are considered separately for loading and
post loading stages. Figure 2.27 shows the subsoil deformation pattern, which is likely to
occur during a loading stage. Undrained settlement volume, which is designated as AOC
in the figure, should be equal to the lateral deformation volume APM if undrained
conditions prevail during loading stage. However, some dissipation of excess pore water
pressures during loading stage may simultaneously cause consolidation. The resulting
volume changes due to consolidation during loading stage are designated as ABC
vertically and APMQA laterally in Fig. 2.27. It should be noted that the volumes referred
to here are for the unit length of the embankment. The volume changes at any time
interval are obtained by integrating field measurements as given in Eqs. 2.13 & 2.14
BI2
VVL = JSx' dx
o
Where:
(2. 13)
VVL = the observed settlement volume in the field from settlement gauge
readings, for half the embankments.
Sx =settlement at a distance x from the centerline of the embankment.
B = the width of the embankment.
(2. 14)
Where:
VDL = the observed lateral displacement volume in the field from
26

inclinometer measurements.
Dz = the lateral displacement measured at the depth z.
Lo =the thickness of the soil stratum.
Loganathan et al. (1993) defined the volume changes at any time interval during
construction as in Eqs. 2.15 & 2.16.
(2. 15)
(2. 16)
Lateral consolidation volume
ex =--------------
Consolidation settlement volume (VdL)
(2. 17)
Where: The subscript L stands for loading and,
VVL = observed vertical settlement volume in the field, from
settlement gauge readings, for half the embankments.
VDL = observed lateral deformation volume in the field, from
inclinometer measurements near the toe.
"dL =volume of consolidation settlement.
VuL =volume of undrained settlement.
aVdL =lateral volume reduction during consolidation.
a = ratio of lateral consolidation volume to consolidation
27

settlement volume (Vd).
From Eqs. 2.15 & 2.16, the lateral deformation volume components of an
embankment foundation (undrained and drained) during construction stage can be
separated as given in Eqs. 2.18 & 2.19.
v - VVL - V DL
dL - l+a (2. 18)
(2. 19)
Loganathan et al. (1993) found a value by assuming that for plane strain
conditions the undrained settlement is linearly related to embankment height (i.e., VuL =
A . h, where A is a constant). They based this assumption on the expression for elastic
immediate settlement expressed by Eq. 2.20, assuming B(1-v2
)I/E to be a constant.
However, assuming B(1-v2
)I/E as a constant for different loading stages including the
modulus of elasticity, underestimates the values of E for the consecutive loading stages,
especially if there is a consolidation period between them.
(2.20)
Where:
q =Net foundation pressure.
28

B = Width of the loaded area.
v =Poisson's ratio. (v = 0.5 for saturated clays).
I =Influence value, depending on the shape of the loaded area and the
depth of the elastic layer.
E =Young's modulus.
Because B(1-v2
)I/E is assumed to be constant, the load applied on embankment
foundation is proportional to the height of the embankment. Loganathan et al. (1993)
evaluated the constant A at the end of each loading stage using Eqs. 2.21 & 2.22.
Stage j
(2.21)
Stage j+1
(VVL )j+! (VDL )j+!
()
a. +
A = V uL j+! = h j +! hj+l
hj +! 1+a
(2.22)
Because A is assumed to be a constant by (Eqs. 2.21 & 2.22) the value a can be
obtained as follows:
29

(2.23)
2.4.6.2 Post-Loading Stage
It is considered that the total settlement observed in the field during the post
loading stage is the resultant of consolidation settlement Sd and undrained settlement SUo
The lateral consolidation volume ratio a and the lateral shear deformations volume ratio
~ compared to their respective settlement volumes are assumed as:
Lateral consolidation volume
ex =---------------
Consolidation settlement volume (VdC)
(2. 24)
f3 = Lateral deformation volume
Undrained settlement volume (Vue)
(2.25)
f3 = 1, if its assumed that only undrained shear deformation takes place in the field,
and drained shear deformation is ignored
The volume change pattern during post loading stage of an embankment is shown
in Fig. 2.28. As derived for the loading stage, the volumes Vvc and VDC can be written
as Eqs. 2.26 & 2.27.
30

(2.26)
(2.27)
Where C stands for post-construction
From Eqs. 2.26 & 2.27, the volumetric deformation of the embankment
foundation due to consolidation and undrained shear deformation can be written as in
Eqs. 2.28 & 2.29.
v - f3 Vvc - VDC
dC - ex + f3 (2.28)
(2.29)
In both normally consolidated and overconsolidated clays, time dependent
deformation due to shear deformations can be quite large (Christian and Watt 1972).
Because shear deformation is a time-dependent parameter, Loganathan et al. (1993)
assumed that:
31

(2.30)
where Band 'Yare constants. For different post loading stages the constant B can be
obtained as for loading stage.
Stage j, t =tj
B= at;r)jH(V;;)j]
a+f3
(2. 31)
Stage j+1
a .[(VV~)j+!1 + [(VD~ )j+!]
t j+! t j+!
B =-=-----=--=-----=
a+f3
(2.32)
By equating Eqs. 2.31 & 2.32 the ratio ex can be evaluated as shown in Eq. 2.33.
(2. 33)
32

Loganathan et al. (1993) stated that coupling of drained shear deformations in the
analysis with the undrained shear deformations is more oppressive. Consideration of
drained shear deformations increases the number of unknowns and, thus, results in
indeterminacy in the formulation of FDA. Therefore, it was assumed that only undrained
shear deformations takes place in the field (i.e., ~ =1).
The field deformation analysis (FDA) methodology was implemented on the
Malaysian Trial Embankments (scheme 3/2) and (scheme 6/6). Both embankments were
constructed as control embankment without any foundation ground improvement, 3m and
6m high respectively. The lateral deformation volume characteristics during loading
were established by computing ex, values using Eq. 2.23. Figure 2.29 shows that values of
ex, obtained for both embankments at different stages of loading, are in the range of 0.10-
0.32. These suggest an average ex, value of 0.24. The approximate deformation volume
characteristics of the control embankments during loading stage due to undrained
deformation and consolidation were evaluated by substituting the average ex, value in Eqs.
2.18 & 2.19 as follows:
v - VVL - VDL
dL - 1.24
aVVL - V DL
V =--'-=-_":::='"
uL 1.24
(2.34)
(2.35)
The values of VVL and VDL were calculated from the field settlement gauge and
inclinometer measurements using Eqs. 2.13 & 2.14. It was observed from the surface
settlement profile, during different stages of loading, that the surface settlements (St)
33

were uniformly related with the settlement volumes (Vv). These relationships for both 3
m and 6 m control embankments are given as:
V
3 m control embankment - St = _V_
12.5
(2.36)
V
6 m control embankment - St = _V_
23.0
(2.37)
Where:
St =the settlement at the centerline of the embankment.
Vv =the settlement volume.
Using these linear relationships, for the loading stage, the undrained and the
consolidation settlement components were obtained. The relationship between undrained
settlement and consolidation settlement during construction are shown in Fig. 2.30. To
obtain consolidation and undrained settlement components, a similar analysis was
performed for the post-construction stage. The relationship of these two settlement
component;, with time is shown in Fig. 2.31. As can be seen in Figs. 2.30 & 2.31, the
field deformation analysis (FDA) was successful in correlating the settlement
component". However, the total settlement obtained by adding the settlement
component... from FDA, does not represent the total settlement observed in the field for
long dur..Ilion of construction period.
Clnlcloglu and Togrol (1995) described the FDA with its formulation based on
volumetric deformation concept as an important contribution to the present design
practice. However, they stated that there is still a requirement for a method which is
based on fundamental soil behavior and which can be used in conjunction with stress path
behavior, so that links can be established from field measurements to the design
34

considerations. Therefore, they proposed a methodology using the Cam clay model of
the critical state theory.
35

Table 2.1 Elastic settlement of a layer of infinite thickness subjected to uniform strip
load.
Reference, assumption
Steinbrenner (1934)
Eu constant with depth, v =0.5
Janbu, Bjerrum and Kjaemsli (1956)
Eu constant with depth, v = 0.5
Davis and Poulos (1968)
Eu not constant with depth, v =0.5
Equation for maximum settlement
Su = (qB)0.75F1
Eu
B =width of foundation.
Fl =Steinbrenner factor.
(2.9)
qB
Su =E 110111 (2.6)
u
!J,o and !J,1 from Fig. 2.2; modified by Christian
and Carrier (1978), Fig. 2.3
Ll<ix, Ll<iy and Ll<iz are computed at mid depth of
Llz from elastic distribution.
D'Appolonia et al. (1970), (1971) S = _1 qB I
v = 0.5, take into account local U SR Eu
(2.2)
yielding.
Elastic settlement under an
embankment Giroud (1973)
v =0.5, elastic layer, finite thickness.
SR = Se/Su where Se is settlement without taking
into account local yielding, Figs. 2.4 and 2.5.
(2.3)
q ='Y HE where 'Y =unit weight of embankment
and HE height of embankment.
b1, b2, rl and r2 are defined on Fig. 2.6.
36

Table 2.2 Results of parametric studies of seven factors on surface settlement for
elastic layer constructed on elastic foundation (after Poulos 1972).
SUMMARY OF EFFECT OF VARIOUS FACTORS
Factor
Effect on settlemetn, Effect on lateral
Remarks
(1)
Su deformation, D
(4)(2) (3)
Poisson's ratio v Su increases as D Increases as v Effect on D much
of Soil v decreases decreases greater than on Su
Anisotropy of soil. Su increases as EhlEv D Increases as Effects most
(cross anisotropy) decreases
EhlEv decreases
pronounced for D
EhlEv when EhlEv < 1
VVH
Very significant
Effect on D greater
Very significant than on Su
increase in Su as VVH
increase in D as VVH
decreases,
decreases
(forEhlEv = 2)
Little effect for D increases as VH
Effect on D greater
VH
decreases
than on Su
E~v=2
Nonlinear stress Local yield Local yielding Effect on D greater
strain soil behavior increases, Su increases D and than on Su
changes distribution
of D versus depth
Embankment Very little effect Little effect Effect on D greater
stiffness than on Su, but is
probably negligible
Roughness at base Small reduction in Very significant Effect on D greater
of elastic layer Su for full adhesion, reduction in D for
than on Su, not
as compared to no full adhesion as
adhesion compared to no relevant to case
adhesion studies
Eh, Ev = Young's modulus in horizontal and vertical directions, respectively.
VVH = Poisson's ratio for effect of horizontal strain on vertical strain.
VH =Poisson's ratio for effect of horizontal strain on complementary horizontal strain.
37

R
111111~q
'777f?? j"»'
L =00 i
1 i
I
(a)
q
I
I
Lo =5 Rj
I
I
I
/
~I~
r/.l
II
......"""
4-<
0
IZl
Q)
::l
-cd
>
~I~
r/.l
II
......"""
4-<
0
IZl
Q)
::l
C;;
>
(b)
0
1
2
0
1
2
R
Radial distance
R
1
~~I
1
1
---'--1--
1
1
I
I I
-------~--------~--
R
I
I
~=5 I
R I
--------1--
~=O.3 I
v=O.2 I
v=O.O 1
I I
-------~--------~--
O~--------~~~~~~~---
//1/////////////////////'
(c)
~I~
r/.l
II
......"""
4-<
o
IZl
Q)
::l
~ 1
R
v=O.5
b------
1
I
1
R 3
1
1
I
I--1---------1--
1 1
Figure 2.1 Settlement of flexible load on circular area on surface of elastic layer for three
different depth ratios (After Terzaghi 1943).
38

3-0
L
LIB
/
100/
L =length
~
/
50
n q / oIIII!!II"""
2-5
'f'JII'//-1t--Y /,)...'- I///-",</A
D l - a:. ........ " ~
U'- t---, 20
T
,
H If"" ~ I-"""'""
/ ../
) =0-5 /"'
10
2-0
////////////////// V
----I""""
~ ~
5/ ~
fJ-, 1-5
POo
s = q Bi (-LO(-Ll-
E
-
1-0
~
./
/~
0-5 ~ ~
~
~
ioo"""
0-0
........
0-' 0-2 0-5
1·0
O-g
0·8
0·7
0·6
0·5
0,' 0·2 0·5
1// ~
~~.JIIII'
h
D'
, ~
L/"
----
2
2
---
5 10 20
H/B
5 10 20
D/B
2
~ Square I
"H Circle I
50 100 1000
50 100 1000
Figure 2_2 Coefficients for vertical displacement (After Janbu, Bjerrum, and
Kjaemsli 1956)_
39

1.5~--------~--------~~~----~---5----~
I-ll 1.0 t-------+-----:l~__+-----;_----___1
Square
Circle
0.5~--------~~~--~--------~--------~
O~~~~~~~~~~~--~~~~--~~~~
0.1 1 10
HIB
100 1000
1.O.-----.------~~----._----_,
I-lo 0.9 t--~~__t__-__+_-__+_-_____I~-------r---~~--~
0.8 ______...1..-_______--'-_ _ _ _-.1._ _ _ _-----1
o -"
15
Figure 2.3 Values of I-lo and I-ll for elastic settlement calculation
(After Christian and Carrier 1978)
40
20

1.0 r---r----r---.,-----,--~-___r-~-_r__r_,___,
0.6~~~~------~------------_+------~----~--_4
CLAY
0.4
.:......___-BOSTON BLUE CLAY
I0.2 r-t-----~~s.s;:::::==::::, CLAY
'. -0.2 t--t----------___r-----
(i] UNDISTURBED OSLO CLAY
-0." o UNDISTURBED KAWASAKI CLAY
X REMOLDED VICKSBURG BUCKSHOT
-0.6L-~______~____~______~____~__~__~--~~~~
4 6 e 10
Overconsolidation Ratio
Figure 2.4 Relationship between initial shear stress ratio and
overconsolidation ratio (After D'Appolonia et al. 1971)
41

::l
IZl
-<I.)
IZl
II
e>::
IZl
0.8 ~---+-~..:--~-----J:Ioo...,...---.:::!I.....t--o .........--1
0.6~---~---~~~--~---
0.4 ~---~---~-----+---"'-,,~-+---...--;
0L---~---L--~----~--~--~__-4__~____~__~
o 0.2 0.4 0.6 0.8 1.0
Applied Stress Ratio, q / qu
1.0 r----,.........,.'T'""--,-'"'I::""-r-....~.....,-~r__-T"""-"T'""-...,
0.6~---+---~~---4-~~-~~-~-~
0.4~----4----~~~---~~----+-~.-~
0.2 LIB =1.0
o
0.2 0.4 0.6 o.e 1.0
1.0
0.8
0.6
0.4
0.2 t----L IB =1.5 --+-----+-----+--"'"'.......:----1
o
°0
Figure 2.5
O~ 0.6 0.8 1.0
Relationship between settlement ratio and applied stress ratio
for strip foundation on homogeneous isotropic elastic layer
(After D'Appolonia et al. 1971).
42

.j:>..
VJ ~
f)
,......
I-t
x / bl or x / b2
-o·~to:;bj>~i g Iii ~o
La
15 1 1('1• i I )
v=O.5
2.0~IL----+----4----~----+---~---
Incompressible layer
Immediate settlement at point M:
2 [ ( )2]S - rh bl r; _ b2 r:
/I - E b -b I b 2
/I I 2 I
2.5' t. •
Figure 2.6 Graph for calculating immediate settlement under embankment load(after Giroud 1973).

S<.)
";>
-+::>. (/)
-+::>.
x,m
0
/
5
- --
10
15
20
25
30
35
- - LolB= 10
- - - LolB = 0.5
40
Figure 2.7 Undrained settlement trough across the embankment width using Giroud's method
(1973) for thick and thin deposit at embankment height of 11m.

xlb
_0.2 0 1 2
- 0.'
>
0....,
0.1
0.2
0.3
0.4
(a)
qb
Sll =-·lv
Etl
00 01 Q2 0.3 0.40.5
0.2
>-4
0
0.4
N O.6
0.8
1.0 '---~""'--"---'---.J
(b)
S = qLo. 1It E v
It
Uniformly
loaded
strip X
0
0.0
..c:....,
-0.1
0
0
0.2
004
t::3
NO.6
0.8
1.0
Ca;e
v = 0.49 Lo = 1.7b
xlb
1 2
(c)
qb
Ds =-'[h
Etl
Ih
- 0.1 - 0.2 - 0.3
D = qLo. 1
E h
u
2
E o5
2,
(d)
0 ~
3
,.
GZ
Figure 2.8 Influence of soil inhomgeneity on displacements (After Poulos 1972).
45

a =Radius
r =Radial distance
q =Applied pressure
Eit G
Case Vh Vvh Vhv -
Ev Ev
e 2.0 0.2 0.2 0.4 1.0
f 1.0 0.2 0.2 0.2 0.83
g 0.5 0.2 0.2 0.1 0.5
ria ria
0 1 2 0 1 2
0 0
0.5 0.5
1.0
1.0
;>
......,
1.5 ..c;
......,
1.5
2.0
2.5 2.0
qa qa
(a) Su =-·Iv (b) Ds =-·IIt
Ev Ev
Displacement on surface
Ds = horizontal displacement at the edge of
the loaded area, at the ground surface
Figure 2.9 Effect of modular ratio EhlEv on settlement and surface lateral displacement
by a circular loading of semi-infinite cross anisotropic soil (After Poulos 1972).
46

oj::>. S
--.l ..d.....
0..
Q)
Q
Lateral Deformation, cm
012345678012345678910 0 1 2345678910 012345678
Ol'TTT"nTrTTT1TrTTT1TT1TTTTT"lTTTTTTTT"1rTTTT1
5
10
15
20
25
30
35
40
45
50
55
60
65
/
SI-l SI-3
(49 m L of c.L.) (16 m R of C.L.)
/
}
/
/
SI-4
(33 m R of c.L.)
- - Measured values for embnakment elevation 12.5 m at Nov. - Dec. 1968
- - Predicted values (initial movement only)
/
/
/SI-5
I
J
j
(56 m R of c.L.)
Figure 2.10 Comparison between measured and predicted lateral deformation at various locations of 1-95 sec. 246 embankment
(After Poulos 1972).

10
lc
.2
:;,. ·20
.!/
UJ
.]0
...0
620 (EOC) 2lXX>
•~!!-- --~~~~-'~--+---~
F
o 4 • 12 16 0 4 •
Laleral Deneclion (em)
../....
t
'r'".j.....
.j.....
i
Figure 2.11 Comparison of MIT-E3 predictions and measured horizontal displacements
(After Ladd et al. 1994).
·10
!
g
.~
•• ·20
~
.]0
"'0
B
..;-........
u C..:0
·;·0·····
.g........
8 E~
F
o 4 • 12 0 4 • 12 16 0 4 •
Lateral Defleclion (em)
o 4 •
Figure 2.12 Comparison of MCC predictions and measured horizontal displacements
(After Ladd et al. 1994).
48

8
8
t::
0
.-......
ro
8;...
t.8<l)
Q
c;j
;...
<l)
......
ro
.....4
(a) (b)
Lateral Deformation
h = 1.3 m
0
8 4
..c....
h = 1.3 m 0..
<l)
Q
-20 -10 8
100
11
II
0
8
..d' 4
......
0..
<l)
0
Q
D 8
-+
h=2.0m
-aJ -10 0 10 11
D
-+
h = 2.8 m -10 o
-20
10
8
13 4r--+~~--~--~-H~~~~+-~
fr
Q
Distance (m) from Embankment Toe Distance (m) from Embankment Toe
Run F = FEECON Undrained
Run U = CRISP Undrained
Run C = CRISP Coupled Consolidation
Figure 2.13 Finite element analyses with measurements of Rio De Janeiro trial
embankment at three stages of construction, (a) lateral deformation
at embankment base, (b) lateral deformation at inclinometers
(After Almeida and Ramalho-Ortigao 1982).
49

E
E
600
500
d' 400
o
.-.......
c<:S
E
~ 300
0)
"d
100
Range of finite element results
"'"
Observed
O~~----L-------~'-------L------~------~------~----~
o 20 40
Nov.
1992
60 80
Time, weeks
Nov.
1993
100
Nov.
1994
120
Figure 2.14 Observed and predicted lateral deformation at Whitewall Creek
embankment (After Russell 1996).
50
140

a()
a()
~
50
/
/
•
/
•
••
5 10 15 20 25 30
Computed maximum Lateral Deformation, Dm(calc)' em
.1
, /.
./
/
•
35
o~~~LL~-L~~-L~~-L~~~~~LL~~LL~-L~
o 10 20 30 40 50 60 70 80
Computed Settlement at center, S calc' em
Fig 2.15 Comparison of predictions using finite element technique and
observations of construction settlements St and lateral deformation D
(After Tavenas et al. 1979).
51

1.0
- BIH=2
0.8
• - •. BIH =3
_.- BIH=4
- .- BIH=6
0.6CI:l
>
-0
>
0.4
0.2
o
20 40 60 80 100
Degree of Consolidation, (Uv)ec (%)
Figure 2.16 The ratio of lateral displacement volumes to settlement volume plotted
against the degree of consolidation (After Sekiguchi et al. (1988).
B/2 B12
VrJ2
Soft Clay Soft Clay
Firm Stratum
(a) (b)
Figure 2.17 Cross-section of an embankment foundation system together with
principal symbols indicated.
52

,-....
~
'-'
~ §o .....
.- ........ (.)
.a 2.........
- C/l
o ~
C/l 0
~ (.)
o,-+-<
U 0
'-+-<-0
o ~
I!) I!)
I!) I!)
I-<..c
~ ....
O~
time Factor
0.001 0.01 0.1 1 10
0
10
20
30
40
50
60
70
80
90
100
Figure 2.18 Calculated relationship between the degree of consolidation and
construction time factor (After Sekiguchi et al. 1988).
53

28
E 24u
ci
0
'.g
E 20i-<
t8OJ
Q
'Cd
16i-<
~
...J
E:::I
E 12
'R
ro
~
"E
8Q
4
o~~~~~~-L~-L~~~~~~~~-L~-L~-L~~~~
o 4 8 12 16 20 24 28 32
St' Total Construction Settlement at center, cm
Figure 2.19 Variation of the maximum lateral deformation at the toe with the construction
settlement for Lanester embankment (After Tavenas et al. 1979).
54

8(J
=.S::01-'
ro
8;...
<2ClJ
Q
c;a;...
ClJ01-'
ro
.....:l
8
::l
8
><ro
~
Q-
........
u
-..,
....
-;...
-,.;:;
u
""'
..
u
-
.-...
.,...
£
-
""
20
Development of a normally
Hconsolidated state as indicated
by pore-pressure observations
15
10
5
(a)
o~~art~~~~~~~~~~~~~~
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
H, Height of fill, m
--.- Cubzac les Ponts - A
- Kalix
15
-0- King's Lynn
-0- Tickton
10
(b)
o~~~~~wu~~~~~~~~~~~~~~~
o 5 10 15 20 25 30 35 40 45 50
St' Settlement dring consturction, cm
Figure 2.20 Variations of the maximum lateral deformation with (a) the height of fill and
(b) the construction settlement in slightly overconsolidated clay foundations
(After Tavenas et al. 1979).
55

25
:=
Cubzac B0 7
.-~
20 0 ProvinsS.....
0 Palavas, with drains.8Q)
• Palavas, without drain0
~ 15 !:::,. St. Alban B..... 0Q)
Drammen II~
...
.....:l
• SkaEdeby VI
S;:j 10
S.><
ro
;;S
5~E
0<]
o ~~~~~~~~~~~~~~~~~~~~~~~~~~
o 10 20 30 40 50 60 70 80 90 100
~St' Maximum Verical Settlement, cm
Figure 2.21 Relationship between the maximum lateral deformation and the total settlement after
the end of construction under seven embankments (After Tavenas et al. 1979).
56

8
a
-r.;::
6
4-<
0
4......
...c:
b.O.,...,
C)
2::r:
...c:
0
0 100 200 300 400
Time, day
1st loading Consolidation 2nd loading
stage during 268 days stage
500 600
Consolidation
during 335 days
700
100 ~~~--------~~----~~------------------~
80
40 B=60m
IE ~I
20 /3:1 ~
tLO= 26 m
0
0 20 40 60 80 100 120 140 160 180
St' Total Settlement at the center during consturction , em
800
200
Figure 2.22 Development of maximum lateral deformation with the settlement
during stage constructin - Palavas test fill (After Tavenas et al. 1979).
57

~-
N
II
N
Z
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.0 rrlrTI-,--r.."..,--r-,....,,....,-T'"'T",,.,rTI-r-T.,--r-........-r-r,....,-T'"'T",..........,,.....,.....,o:::r-r-r-l<,,...,....,.....,.....,....,....,....,
0.1 ----- 1st Loading stage
- - 2nd
Loading stage
0.2
0.3
0.4
0.5 /
0.6
0.7
0.8
0.9
1.0
Figure 2.23 Lateral deformation profiles at variours stages of construction
under the Palavas test fill (After Tavenas et al. 1979).
58

22 Feb 02Jun 10 Sep 19 Dec
1991 1991 1991 1991
10
S 9u
d
.s 8.....~
S 7I-<
<211)
6Q
'"@
5I-<
11)
Cil
.....:l
S
4
S 3
·R
~
2 2nd loading stage
:;s Fill height = 2.02 m
~E
1 Rate of lateral
Q deformation = 0.061 em/day
0
0 50 100 150 200 250 300 350 400
Time (days since 22 Feb'91)
Figure 2.24 Variations of the maximum lateral deformation with the time during stage
constructin - Bang Na-Bang Pakong (After Teparaksa 1992).
59

12
S(.)
ci 100
.-~
SI-<
8t80)
0
C;
6I-<
0)
......
~
.-:l
E
4
E.;<
~
~ 2
~E
0
0
0 2 4 6 8 10 12
St' Total Settlement, em
2nd loading stage
Fill height = 2.02 ill
.:iDm/.:iS, =0.46
14 16 18 20
Figure 2.25 Variations of the maximum lateral deformation with total settlement
during stage eonstruetin - Bang Na-Bang Pakong (After Teparaksa 1992).
60

~
o
..g 50
8I-<
<2Q.) 40
q
~
I-<
~ 30
8
S 20.~
C'Q
~
"6 10
q
Note: (0.15) = Value of I:!.Dm/I:!.St
____--Case A & B
Time
[F;~~.31-- ~)~ C: Vertical Drain
EOC
[FS =1.3]
,/'" -..- A: No Drains
~--,..
,/'" J -
(O.~ ~ EOC
,/'" - - - [FS > 1.3]
___ --:;.- B: Vertical Drain
(0.10)
o ~~~~~~~~~~~~~~~~~~~~~~~~WL~
o 10 20 30 40 50 60 70 80 90 100
St' Consturetion Settlement, ern
Figure 2.26 Variations of the maximum lateral deformation with the settlement
for first stage eonstruetin - Palavas test fill (After Ladd 1991).
61

r___B/2
x
. _~(U~D~)_~-t---
C....
B~---
UD - u
d n
b
I H1V' ----._co - consolidation
deformation
boundary
/ / I
M
Flfure 2.27 Deformation pattern of embankment foundation at end of loading stage
(After Loganathan et al. 1993).
62

tI
Embankment
LoodinQ
End of Loading
(EL)
BL-----
EL......-~
I
F----
H
I
I
/
/
/
• •
(CO)
cr - creep
deformation
boundary
M
Figure 2.28 Defonnation pattern of embankment foundation at end of consolidation
(After Loganathan et al. 1993).
63

1.00.-------------------------1
Define Stage 1 Stage 2 Stage 3
0.80
Scheme 312 0.27 0.33 0.14
Scheme 6/6 0.27 0.10 0.33
0.60
()-O-{) Scheme 3/2
<1) ....... Scheme 6/6
;:l
c;3
>
c::5
0.40
,.
....
0.20
....
""- , /
..
".... ..... /....
"
,
'fl
0.00
0 100 200 300
Time, days
Figure 2.29 a-values for different stages of construction (After Loganathan et al. 1993).
64

§ 100
iQ)
a~
:::::Q)
C/)
c
o0.g
:-9
'0rJl
§ 200
u
50
Undrained Settlement, mm
100 150 200 250
Loading Stage
htL-
Time, days
•
300------------------------------------------------~
Figure 2.30 Relationship between undrained settlement and consolidation settlement
during construction (After Loganathan et al. 1993).
65

Undrained Settlement, mm
o 100 150 200
• Consolidation Stage
100
8
8
h
t/-- •
......s
Time, daysc(!)
8
~............(!)
CI)
c
.S......
ro
~
-0
rn
C
0
U
200
•
300
Su =0.0012 Sd·2
Sd =in mm
•
400+-------------------------------------------------1
Figure 2.31 Relationship between undrained settlement and consolidation settlement
during post-construction (After Loganathan et al. 1993).
66

CHAPTER 3
BEHAVIOR OF CLAY FOUNDATIONS SUBJECTED
TO EMBANKMENT LOADING
3.1 Yielding of Clay Foundations Subjected to Embankment Loading
3.1.1 Yielding of Clay Structure
The concept of yielding is very important for understanding the behavior of clay
foundation beneath embankments. After yielding, the deformation of soil includes plastic
flow causing irrecoverable deformation. Also the soil compressibility and associated
pore water pressure increase. Yield stress separates 'elastic' and 'plastic' deformation
states of the soil, however, for any mode of loading, it depends on the rate of loading.
Evidence that natural clays possess a yield locus comes from the work of Mitchell (1970)
and others (Loudon 1967, Crooks and Graham 1976, Tavenas and Leroueil 1979,
Baracos et al. 1980).
The most common observation of yielding for clays is the preconsolidation
pressure measured in one-dimensional consolidation tests (Casagrande, 1936). Terzaghi
et al. (1996) stated that the one dimensional consolidation in odometer test represents one
of an infinite number of stress paths that could be generated to cause yielding under a
drained condition. The effective stress path and the corresponding compression curve for
an oedometer test are shown in Fig. 3.1. Yield envelope can be defined by obtaining
sufficient number of yield points. The preconsolidation pressure (Jp' corresponds to the
effective major principal stress at yield for the oedometer mode of loading. At effective
vertical stresses less than the yield stress compression of the specimen is small and
mostly recoverable. At stresses exceeding the yield stress. The compression is relatively
large and mostly irrecoverable. In drained tests the specimens suffer large volume
67

compression and associated distortion as the stress path crosses the yield envelope. In the
undrained condition yield occurs when the structure of the soil breaks down and
relatively high pore water pressures develop.
The most complete experimental work has been carried out on highly sensitive or
structured natural clays (Mitchell 1970, Pender et al. 1975, Wood 1980, Tavenas and
Leroueil 1977 & 1979, Leroueil et aI. 1979 and Tavenas et aI., 1979). For these
materials, yielding is very pronounced and causes a drastic change in observed behavior
which is assumed to be caused by destructuring of the material (Leroueil et al. 1979)
beyond the yield condition (Mitchell 1970, Tavenas et aI. 1979). From a modeling
perspective, these clays do not exhibit normalized behavior.
Secondary compression leads to an increase in the yield loci for clays (Bjerrum
1967, 1972, Mesri and Choi 1979, 1984, Mesri 1993).
3.1.2 Yielding of Clay Foundation under Embankments
Most natural soft clay deposits, as they occur in situ, have developed some degree
of preconsolidation in a sense that they display a preconsolidation pressure greater than
the present effective overburden pressure. This overconsolidation can be a result of
secondary compression, thixotropic hardening, chemical changes, or geologic process,
such as erosion, water table fluctuations, and temporary snow loads, or any combination
of these processes (Mesri 1993). A recompression range and preconsolidation pressure,
as exhibited on a plot of end of primary void ratio-logarithm of effective stress (EOP e-
log cr'v), result from the preconsolidation. A typical EOP e-log cr'v for structured soft clay
with a preconsolidation pressure, cr'p, is presented in Fig. 3.2. This overconsolidation
results in large coefficients of consolidation, Cy , typically of the order of 5 to 50 m2/year
in the recompression range(Mesri and Rokhsar 1974, Tavenas et aI. 1979, Terzaghi et al.
1996).
68

When an embankment is constructed on a clay foundation that exhibits a
preconsolidation pressure, significant pore water pressure dissipation can occur during
the initial stages of construction (Mesri and Rokhsar 1974). Leroueil et al. (1978)
observed this behavior under 29 embankments on slightly preconsolidated clay
foundations. During recompression consolidation, drainage occurs, and lateral
deformation is expected to be small.
If the final effective vertical stress, cr'vf, due to the embankment load is less than
cr'p, lateral deformations may be negligible. However, if cr'vf due to the embankment load
exceeds cr'p, the preconsolidation pressure is surpassed during embankment construction.
In this case, the soil yields while total stress is still increasing. When the effective stress
reaches the preconsolidation pressure, the soil yields, and additional increases in total
stress occur under a practically undrained condition. An undrained condition is expected
because of the increase in compressibility associated with the yielding of soil. In an
undrained state. increments of lateral deformation near the toe should be approximately
equal to Increments of vertical deformation at the center. This condition will apply until
the end of construction. At the end of construction, total stress increase is complete, and
drainage occurs. This drainage allows consolidation, and further lateral deformation
(creep) 1sexpected to develop at a decreasing rate.
3.1.3 Foundation Behavior Described Using Effective Stress Path
Til ena" et al. (1979) qualitatively described the above behavior and the
de'elopment of lateral deformation in terms of effective stress path based on data
collected b:- Leroueil et al. (1978b), as shown in Fig. 3.3. Figure 3.3 presents a typical
effectie stress path for a preconsolidated clay foundation subjected to an embankment
load. Points 0 and 0' represent the total and effective stress states of the foundation
before embankment loading, respectively. Segments OPFR represent the total stress path
of the clay throughout loading.
69

Upon initial loading, the effective stress path follows O/p/. This path corresponds
to the behavior of a preconsolidated soil, and represents a soil in the recompression range
on the field BOP e-Iog d y curve. In terms of elastic analysis, this path corresponds to a
drained loading, and a Poisson's ratio less than 0.5. (A Poisson's ratio of 0.5 represents
undrained elastic behavior, and is typically employed in elastic analyses throughout the
construction period.) From point 0 1
to pi on the effective stress path, lateral deformations
are expected to be small.
The effective stress path reaches the yield envelope (or limit surface) at an
effective vertical stress approximately equal to the preconsolidation pressure. At this
point, the soil yields and becomes normally consolidated. From point pi, continued
increase in total stress, i.e. continued embankment construction would cause the stress
path to follow the yield envelope from P' to F'. Along this path, loading causes an
undrained plastic flow of the clay, and lateral strain increments should be equal to
vertical strain increments. At point FI, progressive failure begins, and continued
embankment loading will cause strain softening until the soil reaches the critical state at
point R/.
Folkes and Crooks (1985) also analyzed the effective stress paths measured under
several embankments. They concluded that soft clay behavior under embankment loading
cannot be characterized by a single effective stress path. In a discussion of the work
conducted by Folkes and Crooks (1985), Leroueil and Tavenas (1986) concede that more
than one effective stress path is needed to properly describe soft clay foundation
behavior. However, Leroueil and Tavenas (1986) point out that a majority of the 45
embankments analyzed at that time had behaved according to the model described in Fig.
3.3. They described three effective stress paths and pore pressure generation to
characterize the behavior of soft clay under embankment loading. Pore pressure
generation is described by the pore pressure coefficient BI = flu/flcry • During undrained
loading, BI assumes a value of 1.0, and under drained conditions, i.e., during
consolidation, BI assumes a value less than unity dependent upon the value of Cy , length
of the drainage path, and rate of construction. Leroueil and Tavenas (1986) anticipated
70

that at least one additional effective stress path and pore pressure generation is necessary
to describe possible foundation behavior under embankment loading. Figure 3.4
illustrates the five cases of effective stress path and pore pressure generation.
Effective stress path (A) is observed in a foundation soil when yielding and
failure are reached at the same time (point Y in Fig. 3.4a). This behavior has been
observed in clay foundations where the value of cr'p - cr'yO was small and apparently either
very rapid construction or rather low Cy and thick layer. In other words, this represents a
soil with a small preconsolidation pressure and corresponding low undrained shear
strength. In this case, the excess porewater pressure increase, Llu, is slightly less than the
increase in total vertical stress, Llcry , i.e., B' is slightly less than one corresponding to a
normally consolidated condition. Upon reaching point Y, strain softening occurs and the
value of B' becomes larger than one.
Effective stress path (B1) (see Fig. 3.4b) is observed in a foundation soil that exhibits a
significant preconsolidation pressure. At the beginning of construction, drainage and
consolidation occur, resulting in a value of B' less than one. Upon reaching the
preconsolidation pressure, continued loading until the end of construction occurs under
an undrained condition. While undrained, B' is equal to unity.
Effective stress path (B2) (see Fig. 3.4c) is a special case of effective stress path (Bl)
where the end of construction occurs after local failure of the soil. This is the case
described by Tavenas et al. (1979). The B' coefficient initially behaves in the same
manner as in case (B 1), however, after failure of the foundation clay, large shear-induced
excess pore water pressures resulting from local failure cause B' to assume a value larger
than one until the end of construction.
Effective stress path (C) (see Fig. 3.4d) corresponds to a clay foundation with a
preconsolidation pressure, and a value of (cr'yf that is greater than cr'p). In this case, the
end of construction occurs before sufficient consolidation has taken place to reach the
yielding of the clay (apparently fast loading or thick layer with low cy ). During
71

Dr. Malek Smadi, Ph.D. thesis lateral deformation and associated settlement resulting from embankment loading of soft clay and silt deposits