Effect of a corner in a three dimensional excavation

EFFECT OF A CORNER IN A
THREE-DIMENSIONAL EXCAVATION



LOH CHANG KAAN
(B.ENG. (HONS.) UTM, M.ENG. (NUS))







A THESIS SUBMITTED
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
DEPARTMENT OF CIVIL ENGINEERING
NATIONAL UNIVERSITY OF SINGAPORE
2003








Dedicated to,

my mother, wife, and two children for their




……… Continual support, encouragement, and
Endless understanding



Acknowledgements
ACKNOWLEDGEMENTS

Firstly, I would like to extend my deepest gratitude to my first supervisor, Associate
Professor T. S. Tan for his concern and kindness, his continual effort on guiding,
checking and providing ideas throughout my research work. Secondly, I would like to
thank my second supervisor, Associate Professor F.H. Lee, who has provided me with
some most critical ideas and approaches on handling daunting problems that emerged
along the study. In addition, his encouragement is deeply appreciated. Both of my
supervisors’ effort on initiating this research project and shaping up the framework of
this study is acknowledged.

One of the biggest problems on pursuing three-dimensional (3D) study is the handling
of tremendous volume of data generated, compared to 2D study. It is very easy to be
drawn into a whirlpool of data, lost the direction of study, and become exhausted along
the way. It is my friend and colleague, Dr. J. Wang that helps me validate and
prioritize the data, and assists to form a clearer focus of study. His support is
invaluable for the completion of this thesis. Gratitude also extends to my senior and
friend, Dr. T.G. Ng, for his critical proofreading of the thesis, often late into the night.

I would also like to thanks all the laboratory technologists in the Geotechnical
Laboratory, especially Mr. C.Y. Wong, for their help in the experimental works.
Acknowledgement also extends to all my fellow research engineers and scholars for
sharing their experience and stimulating discussion.


i
Table of Contents
TABLE OF CONTENTS

Page


Title Page
Acknowledgements i
Table Of Contents ii
List Of Figures vi
List Of Tables xv
Summary xvi

Nomenclature xix

CHAPTER 1 INTRODUCTION
1
1.1 Three Dimensional Behaviour Of Deep Excavation 1
1.2 Current Understanding On 3D Behaviour Of Deep Excavation 2
1.3 Approach To A Better Understanding On Corner Effect In Deep
Excavation
2
1.4 Necessities Of Centrifuge Model Test 4
1.5 Objectives Of The Study 5

CHAPTER 2 LITERATURE REVIEW
8
2.1 Introduction 8
2.2 Literature Review On Centrifuge Modelling On Deep Excavation 11
2.2.1 Various Methods To Model Excavation In Centrifuge 12
2.2.1.1 Increasing-g Method 12
2.1.1.2 Excavate and Spin Method 13
2.2.1.3 Heavy Liquid Method 13
2.2.1.4 2D In-Flight Excavation Test In The Centrifuge 15
2.2.1.5 Tunnel Excavation Method 17
2.2.2 The Challenge Of 3D In-Flight Excavation Test 18
2.3 Literature Review On 3D Excavation Behaviour 19
2.3.1 General Appreciation Of 3D Excavation Behaviour 19

ii
Table of Contents
2.3.2 Quantification Of 3D Corner Effect 22
2.3.3 Influence Range Of 3D Corner Effect 25
2.3.4 Other Parameters Which Might Influence Corner Effect 29

2.4 Summary 30


CHAPTER 3 DEVELOPMENT OF 3D IN-FLIGHT EXCAVATOR AND
CENTRIFUGE MODEL TESTS
32
3.1 Design And Development Of 3D In-Flight Excavator 32
3.2 Experimental Details 35
3.2.1 The Model Retaining Wall 35
3.2.2 Soil Sample Preparation 37
3.2.3 Centrifuge Model Container Preparation 40
3.2.4 Instrumentation And Excavator Set-Up 41
3.2.5 Excavation Procedures 43
3.3 The Conditions Of In-Flight Excavation Tests 44
3.3.1 Area Modelled In The Experiments 44
3.3.2 Fixities And Water Table Boundary Conditions 45
3.4 Methodology Of Test 46
3.4.1 Parametric Study On The Effect Of Wall Stiffness 46
3.4.2 Parametric Study On The Effect Of Capping Beam 46
3.4.3 Parametric Study On Influence Of Geotechnical Effect To
3D Corner Effect
47


CHAPTER 4 EXPERIMENTAL RESULTS AND DISCUSSIONS
48
4.1 Introduction 48
4.1.1 Initial Conditions Of Tests 48
4.1.2 Soil Characterization 49
4.1.3 Prototype Modelled and Other Consideration 51

4.2 General Characteristics Of 3D Excavation Behaviour 52
4.2.1 Characteristics Of Surface Settlement And Wall Deflection 53

iii
Table of Contents
4.2.2 Characteristics Of Lateral Earth Pressure On Retaining Wall 59
4.3 2D Versus 3D Excavation Behaviour 62
4.4 Retaining Wall Thickness Effect In A Corner Excavation 67
4.5 Presence Of A Capping Beam In A 3D Excavation 70
4.6 Effect Of Soil Strength In 3D Excavation 72
4.7 Summary 74


CHAPTER 5 FUNDAMENTAL BEHAVIOUR OF CORNER EFFECT
IN EXCAVATION
76
5.1 Introduction 76
5.2 Finite Element Analysis 77
5.2.1 Parametric Studies By Varying Excavation Dimensions Of A
Corner Excavation
80
5.2.2 Parametric Studies On The Effect Of Wall Stiffness And The
Presence Of Capping Beam To 3D Corner Effect
84
5.2.3 Summary Of Findings From FEM Studies 85
5.3 Characterisation Of Corner Effects 86
5.3.1 Major Factors Affecting The Corner Effect 86
5.3.2 Characterization Of Structural Factor 88
5.3.2.1 Deformation Due To Excavation Induced Imbalance
Load

88
5.3.2.2 The Effect Of Structural Restraint At Corner 92
5.3.2.3 Corner Effect Due To Structural Restrain At Corner 94
5.3.2.4 The Corner Effect Influence Range 96
5.3.3 Characterization Of Geotechnical Factors 101
5.4 Combined Characterization Of Corner Effect 106
5.4.1 Evaluation Of Corner Effect Hypotheses 107


CHAPTER 6 CONCLUSIONS
113
6.1 Development Of 3D In-Flight Excavator 113
6.2 Summary Of Findings 114

iv
Table of Contents
6.3 Effect Of A Corner In A 3D Excavation 115
6.4 Recommendation For Future Studies 117

TABLES
FIGURES
REFERENCES
120
127
222


v
List of Figures
LIST OF FIGURES

Figure No. Description Page
Fig. 1.1 A schematic diagram showing a typical excavation
carried out in the field

127
Fig. 2.1 Observed settlements behind strutted excavation in
Chicago (after O’ Rourke et al., 1976)

128
Fig. 2.2 Observed settlements behind excavation (after Peck,
1969)

128
Fig. 2.3 Relationship between factor of safety against basal
heave and maximum lateral wall movement from case
histories (after Clough et al., 1979)

129
Fig. 2.4 Relationship between maximum ground settlements
and maximum lateral wall movement from case
histories (after Mana & Clough, 1981)

129
Fig. 2.5 Apparent pressure diagrams for computing strut loads
in braced cuts (after Terzaghi et al. 1996)

130
Fig. 2.6 Distress caused to a buried service by a shallow
trenching operation (after Needham and Howe, 1984)

131
Fig. 2.7 Schematic representation of the “Increasing-g” method
to simulate excavation

132
Fig. 2.8 Schematic representation of the “Heavy Liquid”
method to simulate excavation

132
Fig. 2.9 TIT’s in-flight excavator setup (after Kimura et al.
1994)

133
Fig. 2.10
a) Vertical cut with corner angle ∝ (after Giger
and Krizek, 1975)
b) Stability factor Ns as a function of the corner
angle ∝ (after Giger and Krizek, 1975)

134
Fig. 2.11 Stability Number versus Depth of Excavation Divided
by Radius (after Britto and Kusakabe, 1983)

135
Fig. 2.12 2D Section Used in Trench Excavation Analysis (after
De Moor, 1994)

136
Fig. 2.13 PSR Chart (After Ou et al. 1996)

137
Fig. 2.14 Typical Analysis on a 10m long x 6m deep x 1m wide
trench excavation. Ground movement along line e – e
138

vi
List of Figures
parallel to trench and located 2m below surface:
Comparison between results from three-dimensional
and plane strain analyses (after Nath, 1983)

Fig. 2.15 Variation of maximum wall displacement with the
distance from for constant sizes of complementary
wall and various sizes of primary wall, L = Length of
primary wall; B = length of complementary wall.
After Ou et al. (1996)

139
Fig. 3.1 3D in-flight excavator set-up on centrifuge

140
Fig. 3.2 Schematic diagrams of the 3D in-flight excavator

141
Fig. 3.3 Schematic representation of 3D in-flight excavator set-
up on the centrifuge during testing

142
Fig. 3.4 Indexers/drivers mounted on-board the centrifuge

143
Fig. 3.5 Internal parts of indexers/drivers strengthened by
silicone sealant. The indexers/drivers was mounted
near to the centrifuge rotating shaft to minimized
centrifugal force during spinning.

143
Fig. 3.6 Schematic drawing of a corner of an excavation
simulated

144
Fig. 3.7 2D in-flight excavation test set-up on a narrow
centrifuge container

145
Fig. 3.8 Micro-concrete wall used in the study

146
Fig. 3.9 One of the aluminum alloy wall used in the study.

146
Fig. 3.10

Plan view of the excavation set-up & LVDT set-out for
Test 3DK-2

147
Fig. 3.11

Locations of SGs and TSTs in the experiment: Test
3DK-2c

147
Fig. 3.12 Schematic representation of OCR profiles intended

148
Fig. 3.13 De-airing of pore pressure transducers by boiling

149
Fig. 3.14 Installation of pore pressure transducers into soil
sample

149
Fig. 3.15 a) Completed 3D in-flight excavation test set-up
before transporting to centrifuge room
b) 3D in-flight excavation test set-up after
150

vii
List of Figures
excavation test on centrifuge platform

Fig. 3.16 Excavation in Progress (captured by miniature camera
mounted in front of the test sample)

151
Fig. 4.1 Surface settlement versus elapsed reconsolidation time
(Test 3DK-3)

152
Fig. 4.2 Hyperbolic plot, Elapsed time/Settlement versus
Elapsed Time (Test 3DK-3)

152
Fig. 4.3 Density and undrained shear strength profiles of NC
soil used in the experiments

153
Fig. 4.4 Schematic plan view of model retaining wall edge at
container wall face

154
Fig. 4.5 Responses of LVDTs installed at difference planes
(Test 3DK-2)

155
Fig. 4.6 Flow chart showing centrifuge tests conducted

156
Fig. 4.7 Locations of LVDTs, SG and TST in the experiment:
Test 3DK-2c

157
Fig. 4.8 Test: 3DK-2c: Surface settlement at various location
behind the retaining wall

158
Fig. 4.9 Surface settlement profiles behind wall, at various
section from corner

159
Fig. 4.10 Surface settlement behind wall: Test 3DK-2c compare
2D tests and published data (after Peck 1969)
S = Surface settlement
h = Depth of excavation
D = Distance behind wall

160
Fig. 4.11 Surface settlement profiles at various distances from
corner: at 3.0m and 7.0m behind wall (Test 3DK-2c)

161
Fig. 4.12 Surface settlement contour behind retaining wall (Test
3DK-2c)

162
Fig. 4.13 Wall deflection profiles at Perspex window (Test
3DK-2c)

163
Fig. 4.14 A typical scraping of 1 layer of soil in 3D in-flight
excavation test

163
Fig. 4.15 Incremental surface settlement of a single scrapping 164

viii
List of Figures
operation. LVDTs at 7m behind wall, at various

distances from corner (x)

Fig. 4.16 Normalized incremental surface settlement at 7m
behind wall of a single scraping operation: At various
distances from corner at different excavation stages
(Test 3DK-2c)

165
Fig. 4.17 The final settlement at each stage of scrapping.
x = distance from corner

166
Fig. 4.18 Lateral earth pressures versus depth of excavation.
Total stress transducers (TSTs ) at passive and active
sides, at 8m and 15m from corner

167
Fig. 4.19 a) Coefficient of total stress lateral earth pressure
coefficient,
y
P
K
γ
=
, versus depth of excavation. P =
measured lateral earth pressure,
γ
= density of soil (16
kN/m
3

), y = depth of TST from soil level

b)
u
C
yP
2
γ
−
versus depth of excavation. P = measured
lateral earth pressure,
γ
= density of soil (16 kN/m
3
), y
= depth of TST from soil level, C
u
= undrained shear
strength at the TST level

168
Fig. 4.20 Surface settlement profiles behind wall. Test 3DK-2c
compare 2DK-1 and 2DK-3

169
Fig. 4.21 Normalized wall deflection profiles. 3D test compare
2D tests

170
Fig. 4.22 Incremental surface settlement at 7m behind wall: 2D

(Test 2DK-3) versus 3D (Tests 3DK-2 and 3DK-2c)
NF
2D
= Normalization factor for 2D test
NF
3D
= Normalization factor for 3D test

171
Fig. 4.23 Incremental wall top displacement: 2D Test (Test
2DK-3) versus 3D Test (Tests 3DK-1, 2 and 3), x =
9.1m
NF
2D
= Normalization factor for 2D test
NF
3D
= Normalization factor for 3D test

172
Fig. 4.24 PSR-sett at 7m behind wall versus distance from
corner (x) Test 3DK-2c

173
Fig. 4.25 Surface settlement at 7m behind wall versus depth of 174

ix
List of Figures
excavation: 3D tests with various wall thickness

Fig. 4.26
Lateral wall top displacement (
δ
) versus depth of
excavation: 3D tests with various wall thickness

174
Fig. 4.27 Lateral displacement at wall top at various distances
from corner: 3D tests with various thickness

175
Fig. 4.28 Surface settlement profiles at 7m behind wall at
various distances from corner: 3D tests with various
thickness

175
Fig. 4.29 Surface settlement contour behind retaining wall after
7m-excavation: 3D tests with various wall thickness

176
Fig. 4.30 Illustration of offsetting surface settlements with
settlement at the corner

177
Fig. 4.31 Sketch illustration of capping beam restrained at
corner

178
Fig. 4.32 Surface settlement: Test 3DK-2c compare Test 3DK-2

179
Fig. 4.33 Wall deflection profiles at the edge of retaining wall
(17m from corner): Test 3DK-2c compare 3DK-2

180
Fig. 4.34 Lateral displacement at wall top at various distances
from corner: 3D tests with various thickness

181
Fig. 4.35 a) Lateral wall top displacement versus distance from
corner. Soft NC compares Stiff OC soils

b) Lateral wall top displacement normalized by
dividing with displacement at x = 15.2m (furthest from
corner), at the particular stage of excavation. Soft NC
compares Stiff OC soils

182
Fig. 4.36 a) Offset-settlement versus distance from corner.
Soft NC compares Stiff OC soils
b) Offset-settlement normalized by dividing with
displacement at x = 14.5m (furthest from corner), at
the particular stage of excavation. Soft NC compares
Stiff OC soils

183

Fig. 5.1 Typical 1000 elements FEM mesh used in the study

184

Fig. 5.2 Wall deflection profiles at the edge (on Perspex
window in the experiment)

185

x
List of Figures
Fig. 5.3 Configuration of excavation case studied by Ou et al.
(1996)

186
Fig. 5.4 Schematic illustration of size of excavation studied

186
Fig. 5.5 Variation of maximum wall displacement with the
distance from for constant sizes of complementary
wall and various sizes of primary wall, L = Length of
primary wall; B = length of complementary wall.
After Ou et al. (1996)

187
Fig. 5.6 Wall top displacement at various distances from
corner, FEM analyses with primary wall length (PL) =
17, 25, 65 and 130m

188
Fig. 5.7 PSR versus distance from corner plot: FEM analyses
results. PL = 65 and 130m

189

Fig. 5.8 Variation of PSR against distance from corner, x
Wall with capping beam, with different wall stiffness

190
Fig. 5.9 Variation of PSR against distance from corner, x
Wall without capping beam, with different wall
stiffness

191
Fig. 5.10 PSR at a section of x = 30m against the depth of
excavation. For tests with and without capping beam

192
Fig. 5.11 Illustration of a simplified corner excavation

193
Fig. 5.12 Schematic representation of the boundary and loadings
conditions.

194
Fig. 5.13 Active and passive earth pressure distribution on
cantilever retaining wall

195
Fig. 5.14 Illustration of corner restrains effect

196
Fig. 5.15 Normalized wall top displacement versus x profiles:
FEM 3D excavation modelling compare beam theories

197
Fig. 5.16 Illustration and derivation of end restrain effect with a
Pin-end condition

198
Fig. 5.17 Illustration and derivation of end restrain effect with a
Pin-Moment end condition

198
Fig. 5.18 Wall top displacement versus distance from corner (x):
Test 3DK-1

199

xi
List of Figures
Fig. 5.19 Wall top displacement versus distance from corner (x):
Test 3DK-2

200
Fig. 5.20 Wall top displacement versus distance from corner (x):
Test 3DK-3

201
Fig. 5.21 Offset-surface settlement versus distance from corner
(x): Test 3DK-1

202
Fig. 5.22 Offset-surface settlement versus distance from corner
(x): Test 3DK-2

203
Fig. 5.23 Offset-surface settlement versus distance from corner
(x): Test 3DK-3

204
Fig. 5.24 Normalized wall top displacement versus x profiles:
FEM 3D excavation modelling compare beam theories

205
Fig. 5.25 a) Lateral bending moment versus distance from
corner (x): Test 3DK-2c

b) Theoretical lateral bending moment versus distance
profile

206
Fig. 5.26 a) Measured L
m
for Test 3DK-1 and hypothesis of L
m

for tests with no yielding (Tests 3DK-2 and 3DK-3)

b) Hypothesis on the relationship between L
m
and wall
area:
Normalized L
m

versus Normalized EA, where
E = Elastic modulus of wall, same for all the test (E
1
=
E
2
= E
3
)
A = Cross sectional area of the wall, which is total
depth of wall * thickness of wall. Hence:
A
3
= 3 * A
1
(A of Test 3DK-3 = 3 times of A of Test
3DK-1)
A
2
= 2 * A
1
(A of Test 3DK-2 = 2 times of A of Test
3DK-1)
L
m1
= Distance from corner when wall of Test 3DK-1
yielded = 10m

207
Fig. 5.27 Illustration showing the hypothesis of normalization of

corner effects to achieved
δ
y


208
Fig. 5.28 Total lateral earth pressure coefficient at 8m and 15m
from corner, at active and passive sides, versus depth
of excavation

209
Fig. 5.29 Schematic diagram illustrating the variation of earth
pressure effect at active side
210

xii
List of Figures

Fig. 5.30 Lateral earth pressure at the retained soil side versus
depth of excavation

211
Fig. 5.31
)2(
)3(
Da
Da
P
P
versus

u
C
h
γ
for TSTs at 8m and 15m from
corner for Test 3DK-2c

212
Fig. 5.32
)2(
)3(
Da
Da
P
P
versus
u
C
h
γ
for Test 3DK-2c (Experiment and
FEM)

213
Fig. 5.33 Relationship between R and distance from corner

213
Fig. 5.34 Wall top displacement versus distance from corner:
Test 3DK-1
a)

δ
before normalization
b)
δ
normalized with
λ
s

c)
δ
normalized with
λ
a
and
λ
s


214
Fig. 5.35 Wall top displacement versus distance from corner:
Test 3DK-2
a)
δ
before normalization
b)
δ
normalized with
λ
s

c)
δ
normalized with
λ
a
and
λ
s


215
Fig. 5.36 Wall top displacement versus distance from corner:
Test 3DK-3
a)
δ
before normalization
b)
δ
normalized with
λ
s

c)
δ
normalized with
λ
a
and
λ
s

216
Fig. 5.37 Offset-surface settlement at 7m behind wall versus x:
Test 3DK-1
a) Offset-Sett before normalization
b) Offset-Sett normalized with
λ
s

c) Offset-Sett normalized with
λ
a
and
λ
s


217
Fig. 5.38 Offset-surface settlement at 7m behind wall versus x:
Test 3DK-2
a) Offset-Sett before normalization
b) Offset-Sett normalized with
λ
s

c) Offset-Sett normalized with
λ
a
and

λ
s


218
Fig. 5.39 Offset-surface settlement at 7m behind wall versus x:
Test 3DK-3
a) Offset-Sett before normalization
219

xiii
List of Figures
b) Offset-Sett normalized with
λ
s

c) Offset-Sett normalized with
λ
a
and
λ
s


Fig. 5.40 Wall top displacement versus depth of excavation:
Tests 3DK-1, 3DK-2 and 3DK-3
a)
δ
before normalization
b)

δ
normalized with
λ
s

c)
δ
normalized with
λ
a
and
λ
s


220
Fig. 5.41 Offset-settlement versus depth of excavation: Tests
3DK-1, 3DK-2 and 3DK-3
a) Offset-Sett before normalization
b) Offset-Sett normalized with
λ
s

c) Offset-Sett normalized with
λ
a
and
λ
s

221


xiv
List of Tables

List of Tables

Table No. Description

Page No.
Table 2.1 Summary of corner effect influence range
reported/proposed

120
Table 3.1 Speed and stroke of NUS’s 3D in-flight excavator

121
Table 3.2 Properties of Malaysian Kaolin clay

122
Table 4.1 Summary of in-flight excavation tests carried out

123
Table 5.1 Summary of soil profile and soil parameters used for
FEM analyses

124
Table 5.2 Initial stress conditions of FEM analyses

125
Table 5.3 Summary of findings from centrifuge modelling and
FEM analyses

126

xv
Summary
SUMMARY

In reality, all excavations are three-dimensional (3D) in nature. In routine engineering
practices, the complicated 3D problem is often simplified and idealised into much
simpler plane strain two-dimensional (2D) problem. However, it is generally known
that such 2D analyses usually produced conservative design especially for small
basement excavation where the corner-to-corner distance is relatively short. If this
corner effect is considered in the analysis, a more accurate and economical design often
can be achieved. In the current study, the main objective was to gain a better
understanding of how a corner affects an excavation.

The current study focuses on the basic aspects of 3D corner effect, with the simplest
configuration possible. A 3D in-flight excavator for the National University of
Singapore centrifuge was developed specifically for the present study to provide
physical data for in depth mechanistic study. An un-braced excavation around a right
angle corner was modeled using a simple soil profile in the centrifuge. This model is
able to capture the salient features of 3D corner effects. From the study, it was found
that the presence of a capping beam, which usually ignored by practicing engineers in
analysis, would enhance the corner effect. The effect was more pronounced in the
early stage of excavation. Comparative study on excavation tests with stiff highly
overconsolidated and soft normally consolidated samples found that the presence of a

corner would affect the wall deflection and surface settlement more in soft soil than that
in stiff soil. However, this is in terms of absolute magnitude. In terms of relative
ratio of wall displacement or surface settlement with distance from corner as
mechanistic study is concerned, there is no apparent correlation with the soil strength. It

xvi
Summary
was also found that the behaviour of corner effect is insensitive to the depth of
excavation.

From the study, the 3D corner effect measured based on the wall displacement was
expressed as
asDD
λ
λ
δ
δ
**
23
=
.
Where
δ
3D
= Wall top displacement within the 3D corner effect influence zone

δ
2D
= Wall top displacement in 2D condition

λ
s
=

Corner effect factor due to corner structural restrain

λ
a
=

Corner effect factor due to geotechnical effect
λ
s
is derived from a beam theory. It shows to some extent how the effect of a corner is
propagated.
λ
a
is due to the variation of earth pressure along the distance from corner,
which is dependent on stability number,
u
C
h
γ
.
Where
γ
= total unit weight of the soil
h = excavation depth
C
u

= undrained shear strength of the soil

It was also found in the study that if the flexural capacity of the retaining wall is large
enough, the influence range of the corner is given by the point where the plane strain
condition starts. If not, then it is decided by the point when the flexural capacity of the
wall was exceeded. Thus L
a
=
{
}
Dm
LL
2
,.min .
Where L
m
= Length from corner when lateral flexural capacity is exceeded.
L
2D
= Length from corner when plane strain condition is achieved.
If the lateral flexural capacity is exceeded in the retaining wall, the 3D corner effect
may be expressed as
asyD
λ
λ
δ
δ
**
3
= , where

δ
y
is the wall displacement when the

xvii
Summary
wall lateral flexural capacity is exceeded. This expression was examined using
centrifuge experimental data. The results show that the equation is able to estimate the
corner effect influence to the displacement at the top of wall, as well as surface
settlement at 7m behind the wall. This shows that the
λ
s
and
λ
a
are able to explain
major aspects of 3D corner effects in the excavations.

xviii
Nomenclature
NOMENCLATURE

A cross sectional area of the retaining wall
B the width of excavation
D distance behind retaining wall
E the Young’s modulus of the wall
g gravitational force
I second moment of area

L the length of excavation

L
m
length from corner when lateral flexural capacity is exceeded
L
l
simplified corner effect influence range from corner
L
2D
length from corner when plane strain condition is first achieved
P measured lateral earth pressure

P
a
earth pressure at the active side at the toe of the wall in Equation (5.3). Also
the measured lateral earth pressure at the active side.
P
p
passive earth pressure at the passive side at the toe of the wall in Equation
(5.3). Also the measured lateral earth pressure at the passive side.
b Total depth of the wall from ground level to the toe of wall in Equation (5.3)
PL the length of primary wall in an excavation
PSR defined as the ratio of the maximum wall displacement (
δ
) of a section over
the maximum wall displacement (
δ
2D
) of the section
y depth of TST from soil level
C

u
the undrained shear strength of the soil
h excavation depth
h
w
the height of water table

xix
Nomenclature
K
o
coefficient of lateral earth pressure at rest
o
K coefficient of lateral earth pressure at rest, total stress term (include water
pressure)
a
K coefficient of lateral earth pressure at active side, total stress term
(include water pressure)
p
K coefficient of lateral earth pressure at passive side, total stress term
(include water pressure)
a
K
-active
coefficient of lateral earth pressure at active state, total stress term
(include water pressure)
q
s
the uniform surface loading on the retained soil behind the excavation
S the stability number defined as S =

u
c
h
γ

x distance from corner
δ
horizontal wall displacement
δ
3D
wall top displacement within the 3D corner effect influence zone
δ
2D
wall top displacement in 2D condition
δ
y
wall top displacement when the wall lateral flexural capacity is exceeded
λ
s
corner effect factor due to corner structural restrain
λ
a
corner effect factor due to geotechnical effect
γ

the total unit weight of soil
σ
a
the Rankine active earth pressures

σ
p
the Rankine passive earth pressures


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Chapter 1 Introduction

CHAPTER 1
INTRODUCTION


1.1 THREE DIMENSIONAL BEHAVIOUR OF DEEP EXCAVATION
Excavation of soil as part of a major infrastructure construction is a common activity in
most heavily built-up cities. Deep excavation is needed for basement, underground
road, sewerage pipe, drainage facilities and other constructions. A schematic diagram
showing a typical excavation carried out in the field is shown in Fig. 1.1. In reality,
excavations are three-dimensional (3D) in nature. At every plane with the distance
from the corner, due to the variation of geometry and influence from the corner, the
behaviour is different, and would interact with each other. This 3D behaviour is very
complicated. Hence, in most engineering practices, a much simpler plane strain two-
dimensional (2D) problem is often used to approximate the 3D problem.

The 2D assumption actually assumed that there are no interactions between adjacent
planes. This assumption is more appropriate for a long trench excavation, such as
excavation for pipe laying and drainage works. In a cofferdam excavation, such as
basement excavation where excavation size is limited, there are inevitable interactions
between adjacent planes with distance from corner. For sections near the mid-span of a
large excavation, the behaviour may be approaching that of a 2D problem. However,
the influence range and under what conditions this is valid is not well established.

In illustration shown in Fig. 1.1, it is apparent that the movement of the retaining wall
and soil at the corner would be smaller due to the 3D effect. This corner restrain would

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Chapter 1 Introduction
extend to a certain distance away from corner. Hence, if this corner effect is considered
in an analysis, a more accurate and economical design can be achieved.

1.2 CURRENT UNDERSTANDING ON 3D BEHAVIOUR OF DEEP
EXCAVATION
For an excavation supported by retaining wall, the unbalance load due to the removal of
earth would cause movement to occur. This movement is restrained by the retaining
wall and the associated bracing system. This is a classical soil-structure interaction
problem, and many 2D solutions are available. In engineering practice, it is intuitively
recognized that the presence of 3D effect, such as corner of a retaining wall, would
influence the soil-structural interaction predicted by the 2D analysis. For example, it is
generally accepted that the corner of a cofferdam is stiffer than other section far from
corner. It is also generally recognized that the movement of a small size excavation
would be smaller than that of larger excavation. In trenching works, engineers would
usually reduce the length of each panel of excavation to control ground movement.

However, to date, there is no specific reference on quantifying the corner effect, nor any
empirical method or design chart to relate the corner effect to a 2D problem. Hence, to
better make use of the 3D effect, which exists naturally in almost any excavation, to
achieve a more economical design, a better understanding on this effect is necessary.

1.3 APPROACH TO A BETTER UNDERSTANDING ON CORNER EFFECT IN
DEEP EXCAVATION
Currently, there are a number of numerical programs capable of performing 2D and 3D

excavation analyses, such as CRISP, FLAC, ABAQUS, PLAXIS and DIGDIRT.

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Chapter 1 Introduction
These programs are able to model the soil-structural interaction in a realistic sequence
of operation that follows closely the actual geometry of excavation and construction
sequences. The proper modelling of a 2D problem alone is already not easy task. The
accurate modelling of the initial stress state, boundary conditions, soil behaviour
(model), excavation sequences and the interaction between soil and wall are very
complicated. The extension of such analyses to model a true 3D problem will create
many more uncertainties. Thus, while some studies on 3D analyses of excavation were
conducted using such numerical programs, only broad trends of 3D excavation
behaviour was presented. There is little study on the fundamental aspects of 3D corner
effect in an excavation. This is due mainly to the fact that the confidence level on such
numerical analysis does not justify in-depth mechanics study. The confidence level on
such numerical analyses can definitely be improved by proper calibration of such
analyses with good physical data.

Physical data is usually obtained from instrumented field projects. From the process of
back-analysis of field data using the program and subsequent fine-tuning, the accuracy
of the numerical model can be improved. Though field data represent the most
realistic situation, it itself is complicated and is usually not ideal for calibration. The
complexities of field data arise out of a number of situations which are difficult to
avoid. Major contributing factors are complexity of soil profiles, generally unknown
initial conditions, boundary condition and not well defined excavation procedures.
Hence, field data alone is also not satisfactory for in-depth mechanics study of the
corner effect.


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