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NUMERICAL STUDY ON TUNNELLING
FOR UNDERGROUND METRO RAIL SYSTEM
IN DHAKA CITY
FARIHA AZAM
MASTER OF SCIENCE IN CIVIL ENGINEERING
(GEOTECHNICAL)
Department of Civil Engineering
BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY (BUET)
May, 2014
NUMERICAL STUDY ON TUNNELLING
FOR UNDERGROUND METRO RAIL SYSTEM
IN DHAKA CITY
A Thesis Submitted by
FARIHA AZAM
In partial fulfillment of the requirement for the degree of
MASTER OF SCIENCE IN CIVIL ENGINEERING
Department of Civil Engineering
BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY (BUET)
May, 2014
DEDICATED
TO
MY PARENTS AND HUSBAND
i
The thesis titled “Numerical Study on Tunnelling for Underground Metro Rail System in Dhaka City”, submitted by Fariha Azam, Roll No. 0409042204F,
Session April 2009 has been accepted as satisfactory in partial fulfillment of the
requirement for the degree of Master of Science in Civil Engineering on 20th
May,
2014.
BOARD OF EXAMINERS
Dr. Mohammad Shariful Islam Professor Department of Civil Engineering BUET, Dhaka-1000
Chairman (Supervisor)
Dr. A.M.M. Taufiqul Anwar Professor and Head Department of Civil Engineering BUET, Dhaka-1000
Member (Ex-Officio)
Dr. K.A.M. Abdul Muqtadir Professor Department of Civil Engineering BUET, Dhaka-1000
Member
Dr. Hossain Md. Shahin Associate Professor Department of Civil Engineering Nagoya Institute of Technology GoKiso-cho, Showa-ku, Nagoya 466-8555, Japan.
Member (External)
ii
ii
DECLARATION
It is thereby declared that except for the contents where specific reference have been
made to the work of others, the study contained in this thesis are the result of
investigation carried out by the author under the supervision of Dr. Mohammad
Shariful Islam, Professor, Department of Civil Engineering, Bangladesh University of
Engineering and Technology.
No part of this thesis has been submitted to any other university or other educational
establishment for a degree, diploma or other qualification (except for publication).
-------------------------------
May 20, 2014 FARIHA AZAM
iii
ACKNOWLEDGEMENTS
At first gratefulness to Almighty Allah for His bless to give the ability for completing
this thesis work successfully.
The author is thankful and grateful to Dr. Mohammad Shariful Islam, Professor of
Civil Engineering Department, Bangladesh University of Engineering and
Technology (BUET), for his consistent and continued supervision, earnest
encouragement and guidance to take the study in to a fruitful completion.
The author is grateful to Dr. A.M.M. Taufiqul Anwar, Professor and Head of the
Department of Civil Engineering, BUET, for his support and guidance from the
Department.
Gratitude to Dr. Md. Shamsul Haque, Professor of Civil Engineering Department,
BUET, for his valuable information and suggestions that made this thesis work
resourceful. Sincere thanks to Dr. Hossain Md. Shahin, Associate Professor of Civil
Engineering Department, Nagoya Institute of Technology, Nagoya, Japan for his
hearty support by giving his valuable time.
The author is also indebted to Suravi Banik, Md. Shehab Uddin, Shamima Nasrin for
their cooperation in laboratory testing works.
Last but not the least, the author expresses her acknowledgement to her parents and
family for their continuous support and encouragement.
iv
ABSTRACT
The main objective of the research was to evaluate the prospect of tunnelling by Cut and Cover as well as New Austrian Tunnelling Method (NATM) through conventional and numerical study for underground metro rail system in Dhaka city. Mass Rapid Transit-4 (MRT-4) of Strategic Transport Plan, 2004 was selected in this study. Four locations namely Uttara, Mohakhali, Farmgate and near Dhaka University were selected along the MRT-4 route for development of sub-soil profile. Physical and strength properties of the sub-soil were determined from laboratory and field tests. In this study, two-dimensional finite element analysis using an elasto-plastic constitutive model- Subloading tij model (Nakai and Hinokio, 2004) was performed. Subloading tij model requires only a few unified material parameters and can consider influence of intermediate principal stress on the deformation and strength of soils, influence of stress path on the direction of plastic flow and influence of density and/or confining pressure. The model parameters were obtained from triaxial and consolidation test results. A conventional analysis was done for the retaining system of Cut and Cover excavation method. The constructions of tunnelling system for Cut and Cover method as well as NATM were simulated considering field scale. A comparison was made between results obtained from conventional analysis and numerical analysis for earth retaining structure of tunnel in the Cut and Cover method. In conventional analysis for the greenfield condition, earth pressures along the proposed route found to vary between 50.76 and 56.12 kN/m2 for cut and cover excavation method. For the same case, the critical bending moments varied between 76.14 and 85.16 kN-m for the sheet pile wall. From numerical analysis, earth pressures on sheet pile wall were found as 138.32 kN/m2, 165.79 kN/m2, 66.51 kN/m2 and 72.01 kN/m2, respectively for greenfield condition, loading of nearby existing structure condition, greenfield with soil-water coupling condition and both loading of nearby existing structure and soil-water conditions. The maximum lateral displacements for the respective cases were 18.8mm, 36.4mm, 220mm and 340.8mm. In NATM, it was found that the surface settlement of tunnel ranged from 52.6 to 54.1mm with an affected zone of 55 to 65m along surface road way considering different loading conditions. It was also found that surface settlement occurred at the position of existing building was larger for shallow foundation than that for the pile foundation.
It was observed that the finite element analysis with Subloading tij model (Nakai and Hinokio, 2004) can simulate the interactions of soil-structure and soil-water as per practical situation. The analysis also provides more realistic results comparing the conventional analysis which is based on many simplifications and assumptions. From analysis, it was revealed that for open spaces like Tongi to Uttara along the MRT-4, Cut and Cover is more appropriate considering its simplicity in execution. On the other hand, NATM is preferable at flyover junction points in Cantonment and structurally obstructed places (Farmgate to Sayedabad).
v
TABLE OF CONTENTS
Page No.
DECLARATION ii
ACKNOWLEDGEMENT iii
ABSTRACT iv
TABLE OF CONTENTS v
LIST OF TABLES x
LIST OF FIGURES xi
NOTATIONS xxi
CHAPTER 1 INTRODUCTION
1.1 General 1
1.2 Background 2
1.3 Objectives of the Research 5
1.4 Organization of the Thesis 6
CHAPTER 2 LITERATURE REVIEW
2.1 Introduction 7
2.2 Metro Rail Tunnelling System 7
2.3 Tunnel Construction 10
2.3.1 Cut and Cover Method 10
2.3.2 Retaining System for Cut and Cover
Method
12
2.3.2.1 Cantilever Steel Sheet Pile 13
2.3.2.2 Sheet Pile with Lateral Bracing 14
2.3.2.3 Diaphragm Walls with Lateral
Bracing
18
2.3.3 Deformation of Cantilever Walls and
Braced Cut Walls
21
vi
2.3.4 Scope of Cut and Cover Method in
Bangladesh
22
2.3.5 Tunnel Construction after Excavation 22
2.3.6 Structural Design Load of Cut and Cover
Method
24
2.3.7 New Austrian Tunnelling Method (NATM) 27
2.3.8 Broad Principles of Construction of NATM 30
2.3.9 Features of NATM Construction 31
2.3.10 Construction Procedure of NATM 31
2.3.11 Sequence of Execution of NATM 34
2.3.12 Design Criteria of NATM 38
2.3.13 Advantages and Difficulties of Using
NATM Method
38
2.3.14 Tunnel Boring Machine and Shield
Machine
39
2.3.15 Merits and Demerits of Using TBM Method 40
2.4 Past Researches on Underground Tunnelling System 40
2.5 Methods of Analyses of Tunnelling System 41
2.5.1 Conventional Methods 41
2.5.2 Apparent Pressure Envelop by Peck (1969) 42
2.5.3 Numerical Analysis 44
2.5.4 Finite Element Method (FEM) 44
2.5.5 Elasto-Plastic Model 47
2.5.6 Subloading tij 47 Model
2.6 Studies on Dhaka Sub-soil 59
CHAPTER 3 EXPERIMENTAL AND NUMERICAL TEST
PROGRAM
3.1 Introduction 60
3.2 Study Route 60
3.3 Sub-soil Investigation 62
3.3.1 Field Tests 62
vii
3.3.2 Laboratory Tests 63
3.4 Detail Layout of Tunnel Construction 65
3.5 Selection of Construction Methods 66
3.6 Analysis Scheme 67
3.7 Analysis Approach 67
3.8 Conventional Analysis for Different Retaining
Structures
68
3.8.1 Braced Cut System with Sheet Pile and
Diaphragm Wall
68
3.9 Numerical Analysis 73
3.9.1 Soil Parameters for Subloading tij 74 Model
3.9.2 Program Flowchart of Subloading tij 75 Model
3.10 Numerical Analysis for Cut and Cover Method 76
3.10.1 General Layout for Model Analysis 76
3.11 Numerical Analysis for NATM 82
3.11.1 Design Criteria of NATM 82
3.11.2 General Layout for Model Analysis 83
3.11.3 Geometry for NATM 84
CHAPTER 4 RESULTS AND DISCUSSIONS
4.1 Introduction 87
4.2 Sub-soil Profile along the Study Route 87
4.2.1 Sub-soil Profile 89 4.2.2 Soil Parameters Used for Analysis 100
4.3 Result Analysis 102
4.3.1 Conventional Analysis of Retaining System 103
4.3.1.1 Braced Cut Sheet Pile 103
4.3.1.2 Braced Cut Diaphragm 105
4.3.2 Numerical Analysis by Subloading tij 108
Model for Cut and Cover Method
4.3.2.1 Sheet Pile with Braced Cut
System: Case 1 (Greenfield
108
viii
Condition)
4.3.2.2 Sheet Pile with Braced Cut
System: Case 2 (Building with
Shallow Foundation Condition)
113
4.3.2.3 Sheet Pile with Braced Cut
System: Case 3 (Presence of Water
Table at EGL in Greenfield
Condition)
119
4.3.2.4 Sheet Pile with Braced Cut
System: Case 4 (Presence of Water
Table at EGL with Building Load
Condition)
122
4.3.2.5 Sheet Pile with Braced Cut
System: Case 5 (Greenfield
Condition: Depth of Sheet Pile and
Excavation=12m)
126
4.3.2.6 Diaphragm Wall with Braced Cut
System: Greenfield Condition
130
4.3.3 Comparison between Conventional and
Numerical Analyses for Braced Sheet Pile
of Cut and Cover Method
133
4.3.4 Numerical Analysis by Subloading tij 137
Model for NATM
4.3.4.1 Numerical Analysis for Case 1
(NATM): Greenfield Condition
137
4.3.4.2 Numerical Analysis for Case 2
(NATM): Pile Foundation
143
4.3.4.3 Numerical Analysis for Case 3
(NATM): Shallow Foundation
149
4.3.4.4 Numerical Analysis for Case 4
(NATM): Pile Foundation at Both
Sides
155
ix
CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS
5.1 Introduction 157
5.2 Summary 158
5.3 Conclusions 162
5.4 Recommendations for Future Studies 162
REFERENCES 164
APPENDIX- I Conventional Analysis for Cut and Cover Method 168
APPENDIX- II Soil Parameters Used in Analysis 189
x
LIST OF TABLES
Page No.
Table 2.1 Comparison among different retaining systems 20
Table 2.2 Comparison between tensors and scalars related to stress and
strain in the ordinary concept and the tij
56
concept
Table 3.1 List of cases of numerical analysis by FEM using Subloading
tij
67
model (Nakai and Hinokio, 2004)
Table 3.2 Material specification for analysis in NATM 84
Table 4.1 Grain size distribution of the fine sand layer and clay layer 88
Table 4.2 Index and physical properties of fine sand and clay layer 88
Table 4.3 Strength properties of clay layer 91
Table 4.4 Strength properties of fine sand layer in Dhaka soil 92
Table 4.5 Strength properties of clay layer in Dhaka soil 93
Table 4.6 Location wise soil parameters required for conventional
analysis of retaining system
100
Table 4.7 Model parameters of soil required for Subloading tij 102 model
Table 4.8 Conventional analysis of retaining system with design sections 106
Table 4.9 Conventional analysis of retaining system with design sections 107
Table 4.10 Design axial force of struts 129
xi
LIST OF FIGURES
Page No.
Figure 1.1 Changing pattern of Dhaka city development and its population 4
Figure 2.1 Proposed MRT system by Strategic Transportation Plan (STP),
2004
8
Figure 2.2 London Underground, oldest metro system in the world opened
in 1863
8
Figure 2.3 Cut and Cover construction of Paris Metro in France 11
Figure 2.4 Finished view of Cut and Cover construction method 11
Figure 2.5 Construction sequences of Cut and Cover tunnel: (a) Bottom-
Up and (b) Top-Down
12
Figure 2.6 Section interlocking steel sheet piling (Bickel et al. 1997) 13
Figure 2.7 Sheet pile with braced cut 14
Figure 2.8 Seven steps in tunnel construction by Cut and Cover method for
braced retaining system
15
Figure 2.9 General construction sequence for braced-cut (Bickel et al,
1997)
16
Figure 2.10 Internal bracing frame: (a) Plan, (b) Details (Bickel et al, 1997) 17
Figure 2.11 Sectional plan of typical slurry wall 19
Figure 2.12 Long sections of the Cut and Cover use diaphragm walls to
support the sides of the open excavation
19
Figure 2.13 General deformation modes in Cut and Cover method 21
Figure 2.14 Typical deformation modes in braced-cuts 22
Figure 2.15 Different types of tunnel sections: (a) oval tunnel, (b) double
box tunnel section, (c) single box and (d) circular tunnel
23
Figure 2.16 Tunnel construction before backfilling: (a) single box tunnel, (b)
double box tunnel before casting and (c) double box tunnel after
casting
24
xii
Figure 2.17 Cut and Cover tunnel loading diagram-bottom up construction 26
Figure 2.18 First NATM twin-tunnel bore at Frankfurt/Main in Germany,
1971
28
Figure 2.19 Typical cross section of NATM 29
Figure 2.20 Typical schematic diagram of shaft excavation for NATM 31
Figure 2.21 Step 1-Excavation of a shaft done on Piccadilly line
underground railway extension at Heathrow, UK
32
Figure 2.22 Step 2a-Shotcreting at the excavated area (primary lining) 32
Figure 2.23 Step 2b-Face recently opened sealed with shotcrete 33
Figure 2.24 Step 3-Placing of the wiremesh along the face of the tunnel 33
Figure 2.25 Step 4-Erection of the lattice girder along the face of the tunnel 33
Figure 2.26 Step 5- (a) Particular type of rock bolting and (b) Rock bolting
in progress with Rocket Boomer
34
Figure 2.27 Step 6- Shotcreting the whole arrangement (secondary lining) 34
Figure 2.28 Segmental excavation 35
Figure 2.29 Typical NATM excavation sequence in soft ground 35
Figure 2.30 Typical tunnel construction using NATM: (a) excavation with
benches, central cut and flying arch method and (b) excavation
with side wall drip method
36
Figure 2.31 Excavation sequences on a halfed cross section of NATM
(Sauer, 1990)
37
Figure 2.32 Sidewall drift method for wide excavations of NATM (Sauer,
1990)
37
Figure 2.33 (a) A tunnel boring machine that was used at Yucca Mountain,
Nevada and (b) A tunnel boring machine used to excavate the
Gotthard Base Tunnel (Switzerland), the world longest tunnel
39
Figure 2.34 Sheet pile with braced cut 42
Figure 2.35 Earth pressure diagram(Peck, 1969): (a) sandy soil, (b) soft to 43
xiii
medium clay soil when 4u
H
C
, (c) stiff clay soil when 4
u
H
C
and (d) sandy soil underlying clay soil (e) several clay layers
Figure 2.36 Shape of yield surface and normally yield surface, and definition
of
50
Figure 2.37 Definition of stress invariants (mean stress, p and deviator
stress, q ) in Cam Clay model
51
Figure 2.38 Yield surface of the Cam clay model and direction of plastic
flow on the octahedral plane
51
Figure 2.39 Yield surface of the Cam clay model and direction of plastic
flow on the octahedral plane
51
Figure 2.40 Spatially mobilized plane (SMP) in three-dimensional space 51
Figure 2.41 Three Mohr’s stress circles under three different principal
stresses
51
Figure 2.42 Definitions of stress invariant ( Nt and St ) in the tij concept 54
Figure 2.43 Definitions of strain increment invariants ( *Nd and *
Sd ) in the
tij concept
54
Figure 2.44 Initial and current yield surfaces in the p - q plane and direction
of plastic flow in an ordinary model such as Cam clay model
55
Figure 2.45 Initial and current yield surfaces in the Nt - St plane and direction
of plastic flow for the model based on the ijt concept
55
Figure 2.46 Shape of yield surface and definition of 58
Figure 3.1 Study area along MRT-4 in Dhaka city 61
Figure 3.2 Triaxial testing machine 64
Figure 3.3 Flow chart showing analysis approach for Cut and Cover 67
Figure 3.4 Flow chart of analysis approach for NATM 68
Figure 3.5 Pressure diagram for sandy soil (Peck, 1969) 69
Figure 3.6 Pressure diagram for soft to medium clay soil; when
4u
H
C
(Peck, 1969)
70
xiv
Figure 3.7 Pressure diagram for stiff clay soil; when 4u
H
C
(Peck, 1969) 70
Figure 3.8 Braced cut in layered soil. (a) Case 1: sandy soil underlying clay
soil (b) Case 2: several clay layers
71
Figure 3.9 Design of braced cut sheet pile: (a) section and plan and (b)
segregation at hinge point of strut
73
Figure 3.10 Geometry and mesh layout for cantilever sheet pile 77
Figure 3.11 Geometry for sheet pile with braced cut after bracing 78
Figure 3.12 Geometry for sheet pile with braced cut after tunnel placement 78
Figure 3.13 Geometry for sheet pile with braced cut after backfilling 78
Figure 3.14 Geometry for sheet pile with braced cut after bracing 79
Figure 3.15 Geometry for sheet pile with braced cut after tunnel placement 79
Figure 3.16 Geometry for braced sheet pile with building load after
backfilling
79
Figure 3.17 Geometry for sheet pile with braced cut considering water table
at EGL in Greenfield condition
80
Figure 3.18 Geometry for sheet pile with braced cut considering water table
with building load
80
Figure 3.19 Geometry for diaphragm wall with braced cut 81
Figure 3.20 Tunnel excavation geometry in green field or open space in
NATM
85
Figure 3.21 Tunnel excavation geometry with pile foundation in NATM 85
Figure 3.22 Tunnel excavation geometry with shallow foundation in NATM 86
Figure 3.23 Tunnel excavation geometry with pile foundation at both sides
of tunnel in NATM
86
Figure 4.1 Sub-soil profile along MRT-4 line in Dhaka city 89
Figure 4.2 Gradation curve along study route: (a) sandy soil and (b) clayey
soil
90
Figure 4.3 Unconfined compression test analysis along study route 91
xv
Figure 4.4 Direct shear test analysis along study route, (a) effective normal
stress versus peak shear stress; (b) shear displacement versus
shear stress
92
Figure 4.5 Consolidation test analysis along study route 93
Figure 4.6 Failure envelops for triaxial consolidated undrained test of
Clayey soil
94
Figure 4.7 Failure envelops for triaxial consolidated undrained test of
Sandy soil.
94
Figure 4.8 Resulted graphs from triaxial CU test for clayey soil: (a)
deviator stress versus vertical strain and (b) excess pore pressure
versus vertical strain
96
Figure 4.9 Resulted graphs from triaxial CU test for clayey soil: (a) stress
ratio versus vertical strain and (b) deviator stress versus mean
effective stress
97
Figure 4.10 Resulted graphs from triaxial CU test for sandy soil: (a) deviator
stress versus vertical strain and (b) excess pore pressure versus
vertical strain
98
Figure 4.11 Resulted graphs from triaxial CU test for sandy soil: (a) stress
ratio versus vertical strain and (b) deviator stress versus mean
effective stress
99
Figure 4.12 Resulted simulations for model parameters of sandy soil: (a)
stress-strain dilatancy relation for the mass of soil and (b)
deviatoric stress versus mean stress
101
Figure 4.13 Earth pressure diagram for braced cut sheet pile for excavation
depth of 12m (Farmgate)
103
Figure 4.14 Shear force diagram and bending moment diagram (Farmgate) 104
Figure 4.15 Diaphragm wall reinforcement details 105
Figure 4.16 Geometry for sheet pile with braced cut after bracing 108
Figure 4.17 Geometry for sheet pile with braced cut after tunnel placement 109
Figure 4.18 Geometry for sheet pile with braced cut after backfilling 109
xvi
Figure 4.19 Mesh for sheet pile with braced cut: (a) mesh used for greenfield
condition and (b) mesh showing the soil layers (the top green
part is clay and the bottom red part is sand)
110
Figure 4.20 Distribution of lateral displacement for sheet pile with braced
cut after bracing
111
Figure 4.21 Distribution of lateral displacement for sheet pile with braced
cut after tunnel placement
111
Figure 4.22 Distribution of lateral displacement for sheet pile with braced
cut after backfilling
112
Figure 4.23 Earth pressure diagram for sheet pile with braced cut
(Greenfield condition)
112
Figure 4.24 Surface settlements for sheet pile with braced cut (greenfield
condition)
113
Figure 4.25 Geometry for braced sheet pile with shallow foundation: (a)
after bracing, (b) after tunnel placement and (c) after backfilling
114
Figure 4.26 Mesh for sheet pile with braced cut with shallow foundation: (a)
mesh used for greenfield condition and (b) mesh showing the
soil layers (the top green part is clay and the bottom red part is
sand)
116
Figure 4.27 Distribution of lateral displacement for braced sheet pile after
bracing
116
Figure 4.28 Distribution of lateral displacement for braced sheet pile after
tunnel placement
117
Figure 4.29 Distribution of lateral displacement for braced sheet pile after
backfilling
117
Figure 4.30 Earth pressure diagrams of lateral displacement for braced sheet
pile with shallow foundation
118
Figure 4.31 Surface settlement for braced sheet pile with shallow foundation 118
Figure 4.32 Geometry for sheet pile with braced cut considering water table
at EGL in Greenfield condition
119
Figure 4.33 Distribution of lateral displacement for sheet pile with braced
cut considering water table at EGL in Greenfield condition
120
xvii
Figure 4.34 Earth pressure diagrams for braced sheet pile with WT at EGL 121
Figure 4.35 Surface settlements for sheet pile with braced cut considering
water table
121
Figure 4.36 Geometry for sheet pile with braced cut considering water table
with shallow foundation
122
Figure 4.37 Distribution of lateral displacement for sheet pile with braced
cut considering water table with shallow foundation
123
Figure 4.38 Earth pressure diagrams for sheet pile with braced cut
considering water table with shallow foundation
124
Figure 4.39 Surface settlements for sheet pile with braced cut considering
water table and shallow foundation
124
Figure 4.40 Comparison of shear force diagram for different cases of braced
sheet pile
125
Figure 4.41 Comparison of bending moment diagram for different cases of
braced sheet pile
126
Figure 4.42 Geometry for braced sheet pile in Greenfield condition (depth of
sheetpile and excavation =12m)
127
Figure 4.43 Distribution of lateral displacement for braced sheet pile in
Greenfield condition
127
Figure 4.44 Earth pressure diagrams for braced sheet pile in greenfield
condition
128
Figure 4.45 Shear force diagram for braced sheet pile in greenfield condition 129
Figure 4.46 Bending moment diagram for braced sheet pile in greenfield
condition
129
Figure 4.47 Geometry for braced cut diaphragm wall after bracing 130
Figure 4.48 Mesh for diaphragm wall with braced cut: (a) mesh used for
greenfield condition and (b) mesh showing the soil layers (the
top green part is clay and the bottom red part is sand)
131
Figure 4.49 Distribution of lateral displacement for braced diaphragm wall
(greenfield condition)
132
Figure 4.50 Earth pressure diagram for braced diaphragm wall (greenfield
condition)
132
xviii
Figure 4.51 Earth pressure diagram for braced cut sheet pile with depth of
sheet pile 12m: (a) conventional analysis, (b) Subloading tij
model (Nakai and Hinokio, 2004)
134
Figure 4.52 Shear force diagram for braced cut sheet pile with depth of
sheetpile 12m: (a) conventional analysis, (b) Subloading tij
model (Nakai and Hinokio, 2004)
135
Figure 4.53 Bending moment diagram for braced cut sheet pile with depth of
sheetpile 12m: (a) conventional analysis and (b) Subloading tij
model (Nakai and Hinokio, 2004)
136
Figure 4.54 Geometry in greenfield condition (NATM) 138
Figure 4.55 Mesh for greenfield condition (NATM) 138
Figure 4.56 Surface settlement for NATM in greenfield condition 139
Figure 4.57 Displacement vector diagrams for different loading steps in
greenfield condition: (a) at 500 step, (b) at 1000 step and (c) at
2000 step
140
Figure 4.58 Shear strain diagrams for different loading steps in greenfield
condition: (a) at 500 step, (b) at 1000 step and (c) at 2000 step
141
Figure 4.59 Lining stress contour diagram for NATM in greenfield condition 142
Figure 4.60 Geometry with pile load (building distance from tunnel
centre=20m)
143
Figure 4.61 Mesh with (building distance from tunnel centre=20m): (a) mesh
used with pile load and (b) mesh showing soil, pile, pile cap
144
Figure 4.62 Surface settlement with building load as pile (building distance
from tunnel centre=20m)
145
Figure 4.63 Displacement vectors at differnet loading steps with building
load as pile (building distance from tunnel centre=20m)
146
Figure 4.64 Shear strain diagrams at differnet loading steps with building
load as pile (building distance from tunnel centre=20m): (a) at
500 step, (b) 1000 step and (c) at 3000 step
147
Figure 4.65 Lining stress diagram at differnet loading steps with building
load as pile (building distance from tunnel centre=20m)
148
xix
Figure 4.66 Geometry with building load as footing (building distance from
tunnel centre=20m)
149
Figure 4.67 Mesh with (building distance from tunnel centre=20m): (a) mesh
used with footing load and (b) mesh showing soil and footing
150
Figure 4.68 Surface settlement with building load as footing (building
distance from tunnel centre=20m)
151
Figure 4.69 Displacement vector diagrams with footing load at 500 steps
(building distance from tunnel centre=20m)
151
Figure 4.70 Displacement vector diagrams with footing load at 1000 steps
(building distance from tunnel centre=20m)
152
Figure 4.71 Displacement vector diagrams with footing load at 1500 steps
(building distance from tunnel centre=20m)
152
Figure 4.72 Displacement vector diagrams with footing load at 3000 steps
(building distance from tunnel centre=20m)
152
Figure 4.73 Shear strain diagrams at differnet loading steps with building
load as fooging (building distance from tunnel centre=20m): (a)
at 500 step, (b) 1000 step and (c) at 3000 step
153
Figure 4.74 Lining stress contours at different loading with building load as
footing (building distance from tunnel centre=20m)
154
Figure 4.75 Geometry with building loads as pile at both sides of tunnel
(building distance from tunnel centre=11m for both cases)
155
Figure 4.76 Mesh with building loads as pile at both sides of tunnel
(building distance from tunnel centre=11m for both cases)
156
Figure A.1 Soil properties along the proposed soil profile of MRT-4 route 168
Figure A.2 Earth pressure diagram for braced cut sheet pile (Farmgate with
excavation depth=12m)
169
Figure A.3 Determination of SFD and BMD (Farmgate with excavation
depth=12m)
170
Figure A.4 Diaphragm wall reinforcement details (Farmgate with
excavation depth= 12m)
173
Figure A.5 Earth pressure diagram for braced cut sheet pile (Farmgate with
excavation depth=15m)
174
xx
Figure A.6 Determination of SFD and BMD (Farmgate with excavation
depth=15m)
175
Figure A.7 Diaphragm wall reinforcement details (Farmgate with
excavation depth= 15m)
178
Figure A.8 Earth pressure diagram for braced cut sheet pile (Mohakhali
with excavation depth=12m)
179
Figure A.9 Earth pressure diagram for braced cut sheet pile (Uttara with
excavation depth=12m)
180
Figure A.10 Determination of SFD and BMD (Uttara with excavation
depth=12m)
181
Figure A.11 Diaphragm wall reinforcement details (Uttara with excavation
depth=12m)
183
Figure A.12 Earth pressure diagram for braced cut sheet pile (DU campus
with excavation depth=12m)
184
Figure A.13 Determination of SFD and BMD (DU campus with excavation
depth=12m)
185
Figure A.14 Diaphragm wall reinforcement details (DU campus with
excavation depth= 12m)
188
xxi
NOTATION
a Parameter for influence of density and confining pressure
aveC Equivalent cohesion
uC Cohesion
Ne Critical void ratio,
oe Initial void ratio,
sG Specific gravity
sK Lateral earth pressure coefficient for sand
xk or yk Coefficient of permeability
N Reference void ratio on normally consolidation line (at mean principal stresses, p=98 kPa and at q= 0 kPa)
'n Coefficient of progressive failure (ranging from 0.5~1.0; average value 0.75)
uq Unconfined compression strength
1( .)
3
( )CS CS compR
Critical state stress ratio
cz Depth of tensile crack
Model parameter represents shape of yield surface Unit weight
ave Average unit weight
f Failure strain,
Unloading compresssion index or slope of unloading-reloading curve in e-log p’ curve at the loosest state
Virgin compression index or slope of virgin loading curve in e-log p’ curve at the loosest state (where e is void ratio and p’ is consolidation pressure)
Poison’s ratio Angle of internal friction
Axial strain
1
Chapter One
INTRODUCTION
1.1 General
Dhaka, the capital city of Bangladesh, is facing huge traffic congestion problem even
in this world of digitalized communication system. For the last few decades, the
population of the city has been growing at an alarming rate. The estimated rate of
population growth in 2013 is 4.2% (https:// en.wikipedia.org/wiki/Dhaka). But with
rapid urbanization and to cope up with the demands of its growing population, Dhaka
has not been developed in a planned way. Since 17th century of the Mughal period,
Dhaka has been expanding in the following pattern as shown in Figure 1.1. But the
present expanded and developed Dhaka is not sufficient enough to bear its large
population. At present, Dhaka is the world’s 9th largest metropolitan city by
population, where the total population of the City is more than 15.0 million, covering
an area of 360 square kilometers (http://en.wikipedia.org/wiki/Dhaka). Moreover, the
capital city is among the slowest in the world with commuters spending three to four
hours in jams daily. A mix of more than 200,000 motor vehicles and another half-
million cycle-rickshaws clog the roads. So, the present transportation system of the
city is now incapable to satisfy the huge demands of its population.
Generally, two options can be adopted to amplify the traffic network of an urban city,
i.e., (1) on grade or above grade: construction of road, flyover, elevated expressway,
bridge, railway etc. and (2) below grade: construction of subway tunnel, underpass,
etc. In context of a hugely crowded and infra-structured city like Dhaka, on or above
grade construction faces more obstruction than below grade construction from urban
planning point of view. So scope of research work is there to find the optimum
utilization of underground space. So, in this study emphasis has been made to utilize
the underground space by constructing a metro rail tunnel system in Dhaka city.
Construction of underground metro rail system has become very common in the
2
developed countries as well as in neighbor Asian countries. But so far very few
research works have been accomplished for underground tunnelling system in Dhaka
city. This research work is focused on underground metro railway tunnelling system
in Dhaka city with a view to minimize the traffic congestion which is the demand of
time for the city and the country as well.
1.2 Background
Since the last few years, Government of Bangladesh (GoB) has given emphasis on the
infra-structural development of the communication system and is accordingly
considering new ways of technologies in order to reduce the traffic congestion
problem of Dhaka city. Following the examples of developed countries, many
remedial approaches for different routes in Dhaka have already been implemented
like Mohakhali flyover, Moghbazar flyover, Hatirjheel project, Mirpur-Airport
flyover etc. by the Government. A policy for land transport at the national level has
been approved by the GoB in April 2004. In this regard, the GoB has approved
Strategic Transport Plan (STP) in 2004 (STP Final Report, 2004) which has been
framed by the Louis Berger Group, USA and Bangladesh Consultants Ltd (BCL),
Dhaka Transport Coordination Board (DTCB) and Ministry of Communications.
Three Mass Rapid Transit (MRT) named as MRT-4, MRT-5, MRT-6 among total six
MRT routes and three Bus Rapid transit (BRT) routes have been recommended in
STP. Recently, GoB has planned to make a feasibility study and build a metro rail on
an elevated expressway along MRT-6, financed by JICA as a part of solution
measures of traffic congestion problem.
To deal with traffic congestion and for optimum utilization of congested urban land
area, underground or subway metro rail tunnel has been treated as one of the most
effective approaches in many of the developed countries like Japan, USA, Iran,
Thailand and even in India. Metro rail system in underground can be one of the best
modes for Dhaka city. Because this system can ensure the issues described as follows:
(1) Underground or subway metro system has been practiced efficiently in most of
the overcrowded cities in the world.
3
(2) Inclusion of this new system in transportation system will be defined as a new
mode of transport pathway.
(3) This system reduces traffic overcrowding and related problems for the most
part.
(4) This system reduces the travel time.
(5) By utilizing underground space, this system can play critical role in case of
shortage of land area.
The construction of underground or subway metro system has been a great challenge
for civil engineers since mid of nineteenth century. Different excavation techniques
have been introduced in this regard. For underground tunnelling, Cut and Cover
method and New Austrian Tunnelling Method (NATM) are the two types of
excavation methods on which researches have been carried out for Dhaka city. Cut
and Cover method is a simple technology mainly suitable for shallow tunnels which
generally requires a large open space having negligible structural obstacles nearby the
alignment for its construction ease. Skilled professionals are less important in this
technique. Whereas, NATM is a “design as you go” approach where excavation work
proceeds and optimized support system is provided simultaneously based on observed
ground conditions by the machine itself.
Waheed et al. (2008) applied Cut and Cover excavation method along the existing rail
line in Dhaka city based on the conventional method and revealed that construction of
underground metro rail system is feasible in Dhaka city. Farazandeh et al. (2010) has
proposed MRT-6 route and has revealed that New Austrian Tunnelling Method is the
most effective tunnel system for the route as current urbanized Dhaka city has
congested utility services, buildings and other structures. Waheed et al. (2008) has
recommended performing the analysis of construction of underground metro tunnel
using the Finite Element Method (FEM). Farazandeh et al. (2010) has recommended
to perform a detailed study of soil characteristics along the metro route of concern.
According to the previous researches, both Cut and Cover method and NATM of
underground tunnel construction are feasible for urban Dhaka based on the existing
route conditions and structural obstacles nearby the route of interest. Generally, a
route does not enclosed by obstacles all along its way and depths of soil layers are
4
Figure 1.1 Changing pattern of Dhaka city development and its population
(http://www.geospatialworld.net/Paper/Application/ArticleView.aspx)
5
different from one point to another point of the route. However, underground metro
rail system is a subject to specific restrictions such as subsidence, crack, noise and
environment pollution during construction. So, it is require to analyze which
excavation method is effective and acceptable along the different portions of a route
in Dhaka city. Moreover, Dhaka city comprises clayey soil underlying sandy soil in
most of the part. It has become a necessity to use the numerical analysis by FEM to
explore the performance and applicability of Cut and Cover method and NATM of
excavation in the study route of Dhaka.
To analyze the deformation of ground and structure and surface settlement FEM is
required so as to obtain practical and exact results of soil-structure interactions. In this
research FEM analysis has been performed to model both the Cut and Cover and
NATM excavation methods for analyzing ground deformation and stability of earth
retention system and tunnel structures for the underground metro rail project.
1.3 Objectives of the Research
The objective of this study is to get an optimized tunnelling system as well as its earth
retention system for the construction of metro rail tunnel in Dhaka city. In view of this
aim, the following main objectives have been carried on.
a) To review the analysis by conventional method for earth retention system and
tunnel structure of the Mass Rapid Transit-4 (MRT-4) route proposed by STP
2004 in Dhaka city.
b) To perform FEM analysis to simulate tunnelling system in Dhaka city by Cut
and Cover method and New Austrian Tunnelling Method (NATM). Thus to
analyze earth retention system and tunnel structure for different loading cases
considering the typical Dhaka soil profiles existed along the proposed route.
c) To compare results obtained from FEM analyses with that obtained from
conventional analysis (Waheed et al., 2008) for different earth retention
systems and tunnel structure for the proposed metro rail tunnel.
6
1.4 Organization of the Thesis
The contents of this research study have been arranged in five chapters in the
following ways:
Chapter one has been an introductory part on the thesis topic. This chapter
summarizes the background, importance and reasons of conducting this research and
also outlines the objectives and organization of the thesis work.
Chapter Two includes reviews of different tunnelling system, advantages and
difficulties of different excavation methods of tunnel, details of Cut and Cover as well
as NATM excavation methods, previous research works of tunnel in Bangladesh,
geotechnical characterizations of Dhaka city, description of Finite Element Method
(FEM).
Chapter Three describes methodology of the research. This chapter includes study
route for tunnel, field test and laboratory tests’ procedures executed for analysis the
sub-soil profile of study area, analysis approach of Cut and Cover method as well as
NATM, conditions and assumptions considered for conventional analysis and
numerical analysis, methods and flowchart program of Subloading tij model (Nakai
and Hinokio, 2004), parametric study of model.
Chapter Four presents results and findings of the study. This chapter incorporates the
resulted values of sub-soil conditions as well as the detailed results obtained from the
Subloading tij model (Nakai and Hinokio, 2004) that have been analyzed both for Cut
and Cover excavation method and for NATM.
Findings of this study have been summarized in Chapter Five by conclusion part and
some recommendations of the study. Further research scopes have also been discussed
in this chapter.
7
Chapter Two
LITERATURE REVIEW
2.1 Introduction
There are many examples of underground tunnel system throughout the world. As of
May 2013, there are 188 metro systems in 54 countries in the world
(http://en.wikipedia.org/wiki/List_of_metro_systems). But in Bangladesh this is a new
technique and so far very little studies (Waheed et al., 2008; Farazandeh et al., 2010)
on underground tunnel system have been done. In this research, FEMtij-2D model
underground tunnel system has been simulated using numerical analysis for the
proposed route in Dhaka city. Strategic Transportation Plan (STP Final Report, 2004)
suggested three Mass Rapid Transit (MRT) routes as MRT-4, MRT-5 and MRT-6
among total six MRT routes. The layout map of proposed MRT route is shown in
Figure 2.1. For this study MRT-4 route is selected for the proposed underground
tunnel system in Dhaka city as the other routes are obstructed in too many locations.
2.2 Metro Rail Tunnelling System
A tunnel is an underground passageway dug though hill, under road or river etc. for
passage of road, train etc. It is completely enclosed except for entrance and exit
openings. In the United States, the National Fire Protection Association (NFPA)
defines tunnel as, "a underground structure with a design length greater than 23 m and
a diameter greater than 1.8 m” (http://en.wikipedia.org/wiki/Tunnel).
A metro system is defined as an urban, electric passenger transport system with high
capacity and high frequency of service, which is totally independent from other
traffic, road or pedestrians. In other words, a metro system is a rapid transit train
system. In some cases, metro systems are referred to as subways or undergrounds
(http://en.wikipedia.org/wiki/List_of_metro_systems).
8
Figure 2.1 Proposed MRT system by Strategic Transportation Plan (STP),
2004 (http://en.wikipedia.org/wiki/Dhaka_Metro)
Figure 2.2 London Underground, oldest metro system in the world opened in 1863
(http://en.wikipedia.org/wiki/List_of_metro_systems)
9
London's underground went into service in 1863 (Figure 2.2), is the oldest metro
system in the world. Initially it was steam-powered. It was then fully electrified by
1896. In the same year, first subway began operating on the European continent other
than London in Budapest, Hungary. Boston installed (1898) the first subway in the
United States; others followed in Paris (1900), Berlin (1902), New York (1904),
Madrid (1919), Tokyo (1927), and Moscow (1935). Toronto's subway, completed in
1954, was the first in Canada; Montreal's subway was completed in 1966. The Beijing
system was China's first that was opened in 1969. The Shanghai metro was opened in
1995 which is one of the world’s longest metro system having 439 km of track in
operation by 2013 (http://en.wikipedia.org/wiki/List_of_Shanghai_ Metro_stations).
By the 21st century, there were some 160 metropolitan rapid transit systems in the
world, more than half of which were traditional subway systems. In the United States,
in addition to Boston and New York, there are subways in Atlanta (1979), Baltimore
(1983), Chicago (1943), Cleveland (1955), Los Angeles (1993), Miami (1984),
Philadelphia (1908), San Francisco (1972), and Washington, D.C. (1976); many more
U.S. cities have rapid transit systems.
The Shanghai system has the longest total route 434 km and the Tokyo system carries
the most passengers annually 3.2 billion. By far the largest underground
transportation system in the United States is that of New York City. It carries 1.6
billion people and has more than 1,355 km of track on 337 km of total route; it also
has more than 6,000 cars and 468 stations i.e., more than any other system in the
world. Moscow has an elaborate subway system with tunnels 4.5m to 6.0m high
instead of the usual 3m (http://encyclopedia2.thefreedictionary.com/Underground+
railway+system).
Generally, construction of underground metro rail tunneling system includes some
focus points which are (1) Excavation methods- Cut and Cover, New Austrian
Tunnelling Method (NATM), Tunnel Boring Machine (TBM), Shield Machine (SM);
(2) Earth Retaining Structure; (3) Tunnel Structure; (4) Rail line or way; (5) Vehicle-
Metro Rail; (6) Signal system; (7) Fire fighting system; (8) Utility facilities (electrical
line, gas line, pipe line, cable line, etc.) for urban area.
10
2.3 Tunnel Construction
The method of tunnel construction depends on ground conditions, depth of
excavation, ground water conditions, the length and diameter of the tunnel drive, the
depth of the tunnel, methods of tunnel excavation, the final use and shape of the
tunnel etc. (http://encyclopedia2.thefreedictionary.com/Underground+railway+
system)
There are three basic types of tunnel construction in common uses which are as
follows (http://encyclopedia2.thefreedictionary.com/Underground+railway+system):
(1) Cut-and-cover tunnels constructed in a shallow trench and then covered over.
(2) Bored tunnels, constructed in-situ, without removing the ground above. They are
usually of circular or horseshoe cross-section.
(3) Immersed tube tunnels, sunk into a body of water and sit on, or are buried just
under, its bed.
Uses of Construction Method: Shallow tunnels are often of the cut-and-cover type (if
under water, of the immersed-tube type), while deep tunnels are excavated, often
using a tunneling shield. For intermediate levels, both methods are possible.
2.3.1 Cut and Cover Method
Cut and Cover is a simple method of construction for shallow tunnels. The general
way of Cut and Cover method is to excavate the earth up to the desired level and to
retain against lateral earth pressure during the excavation process followed by
purposed construction works. After the construction works of tunnel, backfilling is
done.
Tunnel construction is characterized as “cut-and-cover” construction when the tunnel
structure is constructed in a braced, trench-type excavation (cut) and is subsequently
backfilled (covered) (Bickel et al., 1997).
11
Figure 2.3 Cut and Cover construction of Paris Metro in France
(http://en.wikipedia.org/wiki/Tunnel)
Figure 2.4 Finished view of Cut and Cover construction method
(http://science.howstuffworks.com/engineering/civil/subway1.htm)
Two basic forms of Cut and Cover tunnelling are available (http://en.wikipedia.org
/wiki/Tunnel). The steps of them are shown in Figures 2.5 (a), (b).
(1) Bottom-up method: A trench is excavated, with ground support as necessary,
and the tunnel is constructed in it. The tunnel may be of in situ concrete, precast
12
Figure 2.5 Construction sequences of Cut and Cover tunnel: (a) Bottom-Up and
(b) Top-Down (https://www.fhwa.dot.gov/bridge/tunnel/pubs/nhi09010/05.cfm)
concrete, precast arches, or corrugated steel arches; in early days brickwork was used.
The trench is then carefully back-filled and the surface is reinstated.
(2) Top-down method: Side support walls and capping beams are constructed from
ground level by such methods as slurry walling, or contiguous bored piling.
Then a shallow excavation allows making the tunnel roof of precast beams or in
situ concrete. The surface is then reinstated except for access openings. This
allows early reinstatement of roadways, services and other surface features.
Excavation then takes place under the permanent tunnel roof, and the base slab
is constructed.
2.3.2 Retaining System for Cut and Cover Method
In Cut and Cover tunneling method, shoring walls are used to retain earth. Common
types of shoring or retaining walls that can be taken into consideration for Cut and
Cover excavation method are:
(1) Cantilever sheet pile.
(2) Sheet pile with bracings.
(3) Diaphragm wall with bracings.
(b)
(a)
13
Steel sheet piling walls are often classified as “flexible” walls. Continuous concrete
diaphragm walls are classified as “rigid” or “semi-rigid” walls depending upon actual
stiffness. In most of the cases of tunnel structure, braced cut is used to ensure the
stability of deep excavation so that it can retain the earth. Braced cut is used mainly in
build up areas.
2.3.2.1 Cantilever Steel Sheet Pile: A sheet pile wall consists of a series of sheet
piles driven side by side into the ground thus forming a continuous vertical wall for
the purpose of retaining an earth bank. Cantilever sheet pile is a type of sheet pile that
are driven to a sufficient depth in the ground to become fixed as a vertical cantilever
in resisting the lateral earth pressure. This wall has no lateral support. Earth pressures
on the active and passive side of the wall govern the design of the cantilever system.
Continuous steel sheet piles which are used in this case are made of rolled Z-shaped
or arch-shaped interlocking steel sections. Section of interlocking steel sheet piling is
shown in Figure 2.6. Z-shaped sections are used mostly in cut and cover method
because of their greater stiffness and resistance to bending.
This type of section is usually used in saturated pervious or semi-pervious soils and
also in sandy soils when ground water is not a concern. This retaining system is
economic if there are few utility crossing and other subsurface obstacles.
Figure 2.6 Section interlocking steel sheet piling (Bickel et al. 1997)
14
Construction Sequence of Sheet pile wall:
(1) Laying out a sequence of sheet pile sections, and ensuring that sheet piles will
interlock.
(2) Driving (or vibrating) the individual sheet piles to the desired depth.
(3) Driving the second sheet pile with the interlocks between the first sheet pile and
second "locked".
(4) Repeating steps 2 and 3 until the wall perimeter is completed.
(5) Using connector elements when more complex shapes are used.
Figure 2.7 Sheet pile with braced cut
2.3.2.2 Sheet Pile with Lateral Bracing: In this system, sheet pile wall consists of
lateral bracings. This type of braced shoring walls restrict the movement of the soil
behind it and active pressure which is developed. For relatively narrow excavation,
internal bracing composed of multiple tiers of horizontal support is used commonly.
The principal components of each internal bracing tier are longitudinal beams, or
“wales,” and transverse compression members, “or struts,” arranged in Figure 2.7.
During the excavation stage, the bracing tiers or wales must be positioned so that they
support the shoring wall and permit efficient construction of the permanent structure.
Vertical spacing of bracing tiers or wales is typical 3.66m to 4.88m.
15
Figure 2.8 Seven steps in tunnel construction by Cut and Cover method for braced
retaining system
The maximum depth of cut in any excavation step is usually kept to 1 m below the
centerline of the next bracing tier to be installed (dimension Z, shown in Figure 2.9).
General sequence of construction operation is shown in Figures 2.8 and 2.9.
16
Figure 2.9 General construction sequence for braced-cut (Bickel et al, 1997)
The stepwise construction sequence is pointed out below:
Step E1: Excavation to depth H1, and install tier No. 1.
Step E2: Excavation to depth H2, and install tier No. 2.
Step E3: Excavation to depth H3, and install tier No. 3.
Step E4: Excavation to depth H4 (final subgrade).
Step R1: (a) Place concrete base slab.
(b) After base slab has aged adequately, remove tier no. 3.
Step R2: (a) Complete construction of concrete box.
(b) After roof slab has aged adequately, remove tier no. 2.
Step R3: (not shown) Backfill to depth H1,2 and subsequently remove tier complete
backfill. If shoring wall is sheet piles or soldier piles or lagging steel, remove the
shoring wall. Then complete surface restoration.
17
The spacing of struts in the internal bracing framing is usually 3m to 4.57m, but larger
spacing of 7.62m (maximum) is also used to permit more clear space for construction.
But large spacing seems to be costly sometimes because of the heavier wales that are
resulted, and it is unacceptable as well because of the inward wall movement
accompanies the increased wale deflection.
Figure 2.10 Internal bracing frame: (a) Plan, (b) Details (Bickel et al, 1997)
(a)
(b)
18
Framing plans of typical and common type of internal bracing is shown in Figure
2.10. Horizontal force from the shoring or retaining wall is transferred to the wale at
each sheet pile web. The gap between wall elements and the wale is typically filled
with a structural “packing”.
The wales are supported by structural steel brackets (“lookouts”) mounted on the
sheet piles. Secondary framing may be required to brace the weak axis of struts in the
wider excavations. Settlement of the ground adjacent to the excavation is directly a
function of vertical spacing of bracing tiers or wales and shoring wall stiffness.
Increase of retaining wall stiffness will permit larger vertical spacing of bracing tiers.
These larger spacing can ensure smooth construction works.
2.3.2.3 Diaphragm Walls with Lateral Bracing: Diaphragm wall is an underground
concrete retaining wall, which may be upto 24m deep and is built in a mechanically
excavated trench that has been filled with bentonite-loaded or ordinary mud to support
it during excavation. Reinforcement is dropped into the mud and the concrete is
lowered into the bottom of the trench by tremie. This method is relatively silent and
vibration less compared with driving sheet piles.
The diaphragm wall usually refers to a continuous reinforced concrete wall placed in
a deep trench usually 0.61m to 0.91m wide. It can be constructed in soil to depths
exceeding 55m. For cut-and-cover construction, diaphragm walls deeper than about
30.5m are not common (Bickel et al, 1997).
The wall is constructed in panels. Panel length is usually in lengths of 4m to 6m. The
panel is excavated with a special clamshell type bucket. The sides of the panel
excavation are stabilized by filling the panel with a bentonite slurry and maintaining
the level of the slurry at or near the ground surface throughout the excavation. Upon
completion of the panel excavation, a preassembled steel reinforcing “cage” is
lowered into the slurry-filled panel. Concrete is then placed in the panel by tremie
techniques, displacing the slurry. It is important to notice that the joints between
panels are water tight. Figure 2.11 illustrates the joint configuration formed by this
method.
19
Figure 2.11 Sectional plan of typical slurry wall
The end pipe is a steel tube inserted at one end of the excavated panel as a stop for
tremie concrete. After the start of the tremie concrete pour, end pipe is rotated for
breaking the bond. The Figure 2.11 illustrates the sequence of operation in which
construction is done in panel after panel. In every case, end pipe is set at leading edge.
The alternate procedure is to construct “primary” panels, setting end pipes at both
ends. The “secondary” panels between primary panels are constructed thereafter.
Figure 2.12 Long sections of the Cut and Cover use diaphragm walls to support the sides of the open excavation
(http://wiki.iricen.gov.in/doku/lib/exe/fetch.php? media=823:13.pdf)
20
Table 2.1 Comparison among different retaining systems
Comparison criteria
Types of retaining system
Cantilever sheet pile Sheet pile with bracings
Diaphragm wall with bracings
Basic technology
Made of Steel Sheet with different types of section that shows comparatively flexible character against bending
Made of Steel Sheet supported by bracings (struts and wales) that is intermediately flexible.
Constructed of R.C.C. which is rigid and resistance to bending
Common use Beside water body, slope protection works, basement construction, tunnel excavation etc.
Narrow and deep excavation such as tunnel, drainage etc.
Shallow depth and wide area excavation such as basement construction for building, tunnel excavation etc.
Advantages i) Provides high resistance to driving stresses,
ii) Light weight, iii) Can be reused on
several projects, iv) Long service life
above or below water with modest protection,
v) Easy to adapt the pile length by either welding or bolting,
vi) Joints are less apt to deform during driving.
Same as cantilever sheet pile and provides improved lateral resistance.
i) Easy technology, cost effective,
ii) water retainable, iii) rigid structure so ground
movement is less compare to other flexible type earth retaining system and surface settlement adjacent to the cut is less,
iv) Vibration and noise generation is less.
Disadvantages i) Costly, ii) Requires skilled
workmanship, iii) Material is not widely
available in Bangladesh,
iv) Vibration and noise generation is high during sheet pile driving,
v) Sections can rarely be used as part of the permanent structure,
vi) Installation of sheet piles is difficult in soils with boulders or cobbles.
vii) Settlements in adjacent properties may take place due to installation vibrations
i) Moderately costly, ii) Requires skilled
workmanship, iii) Vibration and noise
generation is high during sheet pile driving,
iv) Obstruction by the bracings for constructing basement works.
i) Wall cannot be reused like sheet pile
ii) Time consuming as it requires reinforcement, shuttering, curing and dewatering throughout the construction.
Suitable sub-soil
Silty clay, Soft clay Silty Clay, Silt Sandy soil, saturated silts, loose silty or clayey sand, even in very soft to medium clays.
21
2.3.3 Deformation of Cantilever Walls and Braced Cut Walls
Sheet pile wall can be rigid and flexible depending on the stiffness of the wall and
may deform in a different way during excavation. Figure 2.13 shows the possible
range of deformations for perfectly rigid walls and flexible walls. Here, the
deformation consists of translation and rotation about the base or rotation about the
top. Moreover, wall deformation may include some bulging effects as a result of
flexure. This bulging depends upon the stiffness of the wall support system.
In case of bracing system, internally braced wall’s upper portion is restrained from
undergoing large horizontal movement especially when braces are pre-stressed and
are installed at or close to the surface. The typical deformation shapes are shown in
Figure 2.14. The degree of rotation will depend upon the toe restraint below the
bottom of the excavation.
Figure 2.13 General deformation modes in Cut and Cover method: (a) infinitely rigid
wall and (b) walls displaying flexure
(a)
(b)
22
Figure 2.14 Typical deformation modes in braced-cuts
2.3.4 Scope of Cut and Cover Method in Bangladesh
In urban Dhaka city Cut and Cover method is applicable mainly in the route where
less structural obstruction is existed comparatively. Cut and Cover method can be the
good option for underground construction works along MRT-4 route (STP Final
Report, 2004) in Dhaka as for the following reasons:
(1) Cheap technique
(2) Require simple and easy technology
(3) Require large open space with less structural obstacles nearby
(4) Require comparatively less skilled workmanship.
2.3.5 Tunnel Construction after Excavation
For a railroad or other transit system, cross section type and size depend on vertical
and horizontal clearances, number of lanes or tracks, type of ventilation system and
the method of construction. The configurations of typical cross section of tunnel for
rail transit for Cut and Cover method are shown in the Figure 2.15.
23
Figure 2.15 Different types of tunnel sections: (a) oval tunnel, (b) double box tunnel
section, (c) single box and (d) circular tunnel
According to AASHTO, 1996 (16th edition) the highway clearance for tunnel is as
follows:
Roadway width: For the passage of two-lane tunnels, the horizontal clearance or the
roadway width should not be less than 7.32m but at least 0.61m greater than approach
travelled way. The roadway width shall be increased at least 3.05m and preferably
3.66m for each additional traffic lane.
(a) (b)
(c) (d)
24
Clearance between walls: The minimum width between walls of two lane tunnels
shall be 9.15m.
Vertical clearance: The vertical clearance between walls of two-lane tunnels should
not be less than 4.3m.
Figure 2.16 Tunnel constructions before backfilling: (a) single box tunnel,
(b) double box tunnel before casting and (c) double box tunnel after casting
(http://bst1.cityu.edu.hk/e-learning/building_info_pack/BST20317/6.2-Tunnel
Construction-ppt.pdf)
2.3.6 Structural Design Load in Cut and Cover Method
The tunnel structure has to be designed to ensure structural capacity sufficient to resist
safely all loads and influences that may be expected over the life of the structure. The
principal loads to be resisted are water and earth pressures, dead load including the
Figure: Tunnel construction before backfilling.
(b) (c)
(a)
25
weight of the earth cover, surface surcharge and live load. Figure 2.17 shows typical
earth pressures on a concrete tunnel box. The loads usually considered in design code-
AASHTO, 1996 are:
1) Dead Load: The dead load to be considered for the design of Cut and Cover
methods normally consists of the weight of the basic tunnel structure, the weight
of the earth cover or backfill supported by the roof of tunnel and the weight of
the road elements.
2) Live Load: Live loads include the weight of subway vehicle load and pedestrian
load. Cut and Cover subway structures should be designed to support surface
traffic loading or other live loading. For structures having less than 2.44m of
earth cover, common practice is to design the roof of the subway structure for
the more severe of the following two conditions: (1) Actual depth of cover plus
superimposed HS 20-44 wheel load distribution is accordance with AASHTO
requirements; (2) An assumed future cover of 2.44m plus a uniform live load of
14.37 kN/m2 (Bickel et al., 1997).
3) Horizontal Earth Pressure: Horizontal earth pressure may be considered to be
lateral pressure due to both retained soil and retained water in soil when water is
present. Horizontal earth pressure may include the effect of surcharge loading
resulting from adjacent building foundation loading, surface traffic loading, or
other surface live loading.
4) Buoyancy Load: When the groundwater table lies above the bottom of the
invert or base slab of tunnel structure, an upward pressure or buoyancy force
will act on the bottom of the tunnel base slab. For a rectangular box, this upward
pressure multiplied by the width of the base slab is the buoyant force (B) per
linear ft of structure. When the reliable minimum weight of the structure plus
the fill above the structure (DL min.) exceeds by an adequate factor of safety
(FS), the structure is considered stable against uplift due to B.
26
Figure 2.17 Cut and Cover tunnel loading diagram-bottom up construction
5) Flood (FL): Where there is a potential for river floods or other flooding that
could add loads to subsurface structures, the design of the structures should
allow for this loading as required by the particular type of structure and the
conditions affecting each location.
6) Shrinkage and Thermal Forces: Between transverse joints in cut-and-cover
tunnel structures constructed of reinforced concrete, shrinkage forces and
thermal forces are accounted for by the longitudinal reinforcement in the walls,
roof and invert slab.
7) Earthquake Forces: Major codes that address the seismic design of surface
structures in the United States contain no provisions for underground structures.
The general view is that underground structures are much less affected by
seismic motion than are surface structure.
27
2.3.7 New Austrian Tunnelling Method (NATM)
New Austrian Tunnelling Method (NATM) or Sprayed Concrete Technique or
Sequential Excavation Method (SEM) is one of popular methods of tunnel excavation
and construction which use calculated and empirical real-time measurements to
provide optimized safe support to the tunnel support system or lining. It was
developed between 1957 and 1965 in Austria. Initially, NATM was developed for
rock tunnels, then the method was advanced in theory and practice and adapted for
soft ground tunnels in urban areas. The first application of NATM was in Frankfurt,
Germany in 1968. Since then NATM was used throughout the world on many projects
for transportation, water/ wastewater conveyance or other purposes.
(http://en.wikipedia.org/wiki/New_Austrian_Tunnelling_method).
NATM is mostly used in large diameter tunnels with multi stage excavation and
lining especially in shallow soft ground in urban areas. This technique ensures stable
as well as economic tunnel support systems. The principle of this technique is to
excavate as well as to provide an optimized support based on observed ground
conditions and also to monitor based on observed convergence and divergence in the
lining and mapping of prevailing rock conditions. Hence, more economical use of the
tunnel support system can be ensured.
(http://en.wikipedia.org/wiki/New_Austrian_Tunnelling_method).
The excavation is immediately protected by a layer of sprayed concrete, commonly
referred to as shotcrete or lining, after excavation. Other support measures includes
steel arches, rock bolts, lattice girders and wire mesh which are used in various
combinations to provide elasticity in initial support. Technological developments in
sprayed concrete technology have resulted in steel and polypropylene fibers being
added to the concrete mix to improve lining strength. This creates a natural load-
bearing ring, which minimizes the rock's or soil’s deformation.
(http://en.wikipedia.org/wiki/Tunnel). Any definite excavation and support techniques
cannot be specified in this method. The basic aim of NATM is for getting stable and
economic tunnel support systems.
28
Figure 2.18 First NATM twin-tunnel bore at Frankfurt/Main in Germany, 1971
Mr. Rabeciwz, the principal founder of NATM, introduced this technique in
1962.
It got worldwide recognition in 1964.
The first use of NATM in soft ground in an urban area was in Frankfurt/ Main in
Germany in 1968.
First NATM in Britain takes place at Barrow upon Soar Mine in 1987.
Definitions of NATM: According to the Rabeciwz, “a new method consisting of a
thin sprayed concrete lining, closed at the earliest possible moment by an invert to a
complete ring called an “auxiliary arch” the deformation of which is measured as a
function of time until equilibrium is obtained.”
The three key points Rabcewizc stressed were the application of thin-sprayed concrete
lining known as shotcrete, closure of the ring as soon as possible, and the systematic
deformation measurement.
In 1980, the definition of NATM was redefined by the Austrian National Committee
on Underground Construction of the International Tunneling Association as, “a
29
concept whereby the ground surrounding an underground opening becomes a load
bearing structural component through activation of a ring like body of supporting
ground”.
Leopold Muller, another advocate of NATM, proposed that it was a tunneling concept
defined by a set of principles. It was not to be viewed as method for construction, as
this actually implied a means by which to advance or drive a tunnel. Many Austrian
proponents of NATM support Muller’s approach to the method as being more of a
philosophy as opposed to a set of excavation and support techniques.
Rock bolts: A rock bolt is a long anchor bolt, for stabilizing rock excavations, which
may be used in tunnels or rock cuts. It transfers load from the unstable exterior, to the
confined (and much stronger) interior of the rock mass. Rock bolts generally consist
of plain steel rods with a mechanical or chemical anchor at one end and a face plate
and nut at the other. They are always tensioned after installation. Rock bolts are an
essential component of the New Austrian Tunneling method.
Figure 2.19 Typical cross section of NATM
(http://www.ritchiewiki.com/wiki/index.php/Talk:New_Austrian_Tunneling_
Method)
30
2.3.8 Broad Principles of Construction of NATM
The broad of principles of construction of NATM are described as follows:
(1) Mobilization of the strength of rock mass- Exploitation of the strength of native
rock mass - Relies on the inherent strength of the surrounding rock mass being
conserved as the main component of tunnel support. Primary support is directed
to enable the rock to support itself.
(2) Shotcrete protection- Loosening and excessive rock deformation must be
minimized. This is achieved by applying a thin layer of shotcrete immediately
after face advance.
(3) Measurements and monitoring- Potential deformations of the excavation must
be carefully monitored. NATM requires installation of sophisticated
measurement instrumentation. It is embedded in lining, ground, and boreholes.
In the event of observed movements, additional supports are installed only when
needed, with a resultant overall economy to the total cost of the project.
(4) Measurement flexible support by primary lining- The primary lining is thin and
reflects recent strata conditions. Active rather than passive support is used and
the tunnel is strengthened by a flexible combination of rock bolts, wire mesh
and steel ribs, not by a thicker concrete lining.
(5) Closing of the invert- Especially crucial in soft ground, the quick closing of the
invert (the bottom portion of the tunnel) which creates a load-bearing ring is
important, and has the advantage of engaging the inherent strength of the rock
mass surrounding the tunnel.
(6) Contractual arrangements- Since the NATM is based on monitoring
measurements, changes in support and construction method are possible, but
only if the contractual system enables them.
(7) Rock mass classification- Rock mass classification ranging from very hard to
very soft, determines the minimum support measures required and avoids
economic waste that comes from needlessly strong support measures. Support
system designs exist for each of the main rock classes. These serve as the
guidelines for tunnel reinforcement.
31
2.3.9 Features of NATM Construction
The construction method of NATM includes the following features:
(http://www.ritchiewiki.com/wiki/index.php/Talk:New_Austrian_Tunneling_Method)
(1) The tunnel is sequentially excavated and supported, and the excavation
sequences can be varied.
(2) The initial ground support is provided by shotcrete in combination with fiber or
welded-wire fabric reinforcement, steel arches, lattice girders, and sometimes
ground reinforcement.
(3) The permanent support is usually a cast-in-place concrete lining.
2.3.10 Construction Procedure of NATM
In this method, two main stages are considered in order to construct a tunnel. At first,
shaft is constructed and then profile is constructed as shown in Figure 2.20. Each shaft
is accompanied by proper cranes, machinery, ventilation equipments and material
elevators during construction process.
In profile construction, excavation approach by NATM is done considering different
sequential excavation steps which are designed based on the soil properties and
desired tunnel section. Sequential excavation should be designed in such a way that its
excavation does not cause any subside. Shotcrete should be applied just after the
excavation. Shotcrete is concrete (or sometimes mortar) conveyed through a hose and
pneumatically projected at high velocity onto a surface, as a construction technique.
Figure 2.20 Typical schematic diagram of shaft excavation for NATM
32
The method of tunnel construction uses the principles of the NATM, which is
effective for tunnelling in existing soil profile. In this type of construction, initial
support to the tunnel is provided by a conventional shotcrete primary lining that is
locally reinforced by a combination of mesh, lattice arch girders and rock bolts.
Stepwise procedures of tunnel construction by NATM are given in Figures 2.21 to
2.27.
Figure 2.21 Step 1-Excavation of a shaft done on Piccadilly line underground railway
extension at Heathrow, UK
(http://www.tunnels.mottmac.com/tunnellingtechniques/softgroundtunnels)
Figure 2.22 Step 2a-Shotcreting at the excavated area (primary lining)
(http://wiki.iricen.gov.in)
33
Figure 2.23 Step 2b-Face recently opened sealed with shotcrete
(http://wiki.iricen.gov.in)
Figure 2.24 (a), (b) Step 3-Placing of the wiremesh along the face of the tunnel
(http://wiki.iricen.gov.in)
Figure 2.25 (a), (b) Step 4-Erection of the lattice girder along the face of the tunnel
(http://wiki.iricen.gov.in)
(a) (b)
(a) (b)
34
Figure 2.26 Step 5- (a) Particular type of rock bolting and (b) Rock bolting in
progress with Rocket Boomer (http://wiki.iricen.gov.in)
Figure 2.27 Step 6- Shotcreting the whole arrangement (secondary lining)
(http://wiki.iricen.gov.in)
2.3.11 Sequence of Execution of NATM
Depending on the size and the geometry of the tunnel, the excavation is carried out in
six or more steps. Figure 2.28 illustrates a typical main cross-sectional geometry for a
NATM tunnel as proposed by Rabcewicz. The Roman numbers indicate the
excavation order and sequence of excavation for working in soft ground.
(a) (b)
35
Figure 2.28 Segmental excavation
(http://wiki.iricen.gov.in/doku/lib/exe/fetch.php?media=823:13.pdf)
The first step is the excavation of the top heading (I), leaving the central part to
support tunnel face. Primary lining (or shotcrete) (II) is formed and followed by
removing the top central portion (III) subsequently excavation of left and right wall
(IV) and then step V and VI so on.
Figure 2.29 Typical NATM excavation sequence in soft ground
(http://wiki.iricen.gov.in)
36
The principle of constructing large sectioned tunnel using this method is to subdivide
the tunnel section into several arched smaller sections for the sake of easier control
and safer supporting during excavation. The newly formed surfaces are often required
to temporary supported by girder sections, shotcrete nails or anchors. Several possible
alternatives can be selected to get the most of the purpose. The excavation is
performed in three stages: starting with the top crown heading followed by the bench
and then the invert as illustrated in Figure 2.29 and 2.30.
Figure 2.30 Typical tunnel construction using NATM: (a) excavation with benches, central cut and flying arch method and (b) excavation with side wall drip method
(http://google.com)
(a)
(b)
37
The excavation area may need to be reduced to several smaller headings such as side
wall drifts (Figures 2.30b, 2.31, 2.32). It may require halving the advance per round
from, for example, 1.5m to 3m. It could mean increasing the reinforcement of the
shotcrete by extra lattice girders, more wire mesh or by adding steel fibre to the mix
as well as increasing its thickness.
It may even require a decision to open up the bench and gain access to the invert in
order to close the immediate support ring of the full cross section earlier than
programmed (Sauer, 1990).
Figure 2.31 Excavation sequences on a halfed cross section of NATM (Sauer, 1990)
Figure 2.32 Sidewall drift method for wide excavations of NATM (Sauer, 1990)
38
2.3.12 Design Criteria of NATM
The design criterion of different components of NATM is described as follows:
Rock Bolts: From the studies, it is found that length of the rock bolt (LR) should be
larger or equal to one-fourth times the diameter of tunnel (D) i.e., LR D/4 and
should be in the range of 20% to 60% of the tunnel diameter i.e., LR = (20~60)% D.
Rock bolt is of steel material and with the modulus of elasticity E of 205 MPa.
Lining: Thickness of the lining in the range of 30cm to 60cm. The modulus of
elasticity, E is 50 MPa to 60 MPa.
(1) In less stable ground, immediate support should be regime of bolts, lattice
girders, mesh and shotcrete as shown in Figure 2.37. In extreme cases, the invert
must be undermined and the ring of immediate support is closed with wire mesh
and shotcrete.
(2) Moreover, ground movement should be controlled by increasing the number and
length of rock bolts as well as increasing the thickness of the shotcrete and its
reinforcement with extra lattice girders, wire mesh or steel fibres.
(3) The section of excavation should be kept as rounded and as close as possible to
a circular section. This can be done immediately by moving the feet of the side
walls closer together to at least within the diameter of the tunnel at spring line. It
is most effectively achieved by undermining the invert and closing the invert
with wire mesh and shotcrete.
2.3.13 Advantages and Difficulties of Using NATM Method
The advantages of using NATM method are described as follows:
Flexibility to adopt different excavation geometries and large cross sections
Flexibility to install additional support measures, rock bolts, dowels, steel ribs if
required
Cost effective excavation compare to Tunnel Boring Machine (TBM)
Easy to install a waterproof membrane
39
Easy to install primary support, i.e., shotcrete.
The use of NATM method has some disadvantages which are pointed as below:
High skilled construction supervisors and workers should be ensured for this
technique
Construction process cannot be halted in mid way as well as it cannot be haste.
2.3.14 Tunnel Boring Machine and Shield Machine
Mechanized excavation methods can be briefed in two groups:
(1) Full face mechanized continuous excavation method, using Tunnel Boring
Machine (TBM) for the excavation of tunnels in rock. The main problem is to
break the rock. Tunnel boring machines (TBMs) and associated back-up systems
are used to highly automate the entire tunnelling process, reducing tunnelling
costs. The size of the tunnel and the geological conditions of the rock determine
the type and the configuration of TBM that is used.
(2) Full face mechanized continuous excavation method, using mechanized shields
and with counter pressure against the face for the excavation of tunnels in soil
above and below the water table. The main problem is the stability of the tunnel
as well as the control of the groundwater.
(a) (b) Figure 2.33 (a) A tunnel boring machine that was used at Yucca Mountain, Nevada
and (b) A tunnel boring machine used to excavate the Gotthard Base Tunnel
(Switzerland), the world longest tunnel (Source: http://en.wikipedia.org/wiki/Tunnel)
40
Both the TBM (hard rock applications) and SM (Shield Machine, soft ground) fulfill
the same purposes which are as follows:
ensuring systematic and automated subsoil excavation
providing an effective protection (the shield) for the labour force at the front
stabilizing the tunnel through quickly closing of the support ring
transportation of the excavated material.
2.3.15 Merits and Demerits of Using TBM Method
TBM method has the following merits:
Higher advance rates
Continuous operations
Less rock damage
Less support requirements
Uniform muck characteristics
Greater worker safety
Potential for remote, automated Operation.
TBM method has some demerits which are as follows:
Fixed circular geometry
Limited flexibility in response to extremes of geologic conditions
Longer mobilization time
Higher capital costs.
2.4 Past Researches on Underground Tunnelling System
Very few research works have been accomplished for underground Tunnelling system
for Dhaka city in Bangladesh. Waheed et al. (2008) has applied Cut and Cover
excavation method along the existing rail line passes from Uttara junction to
Kamalapur Railway junction in Dhaka city. Based on the conventional method of
analysis Waheed et al. (2008) has revealed that construction of underground metro
rail system is feasible in Dhaka city.
41
In respect of transportation, based on a typical section with proposed length of route
and number of stations along MRT-6 route, Farazandeh et al. (2010) has revealed that
NATM is the most effective tunnel system for the route as for some findings- (1)
current urbanized Dhaka city has congested utility services and the challenges for
relocation of utility networks are less by NATM during construction, (2) Effects of
presence of buildings/structures are negligible as NATM is a deep excavation method
and (3) cost is remarkably low for construction of NATM compare to the Cut and
Cover method.
Waheed et al. (2008) has recommended to perform the analysis using Finite Element
Method (FEM) for further study. Farazandeh et al. (2010) has recommended to
perform a detailed study of soil characteristics along the metro route of concern.
2.5 Methods of Analyses of Tunnelling System
Generally, there are two approaches to analyze a system. First one is the conventional
analysis and the other one is the Numerical Analysis or analysis by Finite Element
Method (FEM). The conventional analysis involves manual calculation based on
some specific assumptions and design criteria’s which have been established from
empirical results and practical case studies. On the other side, a numerical analysis or
FEM gives an exact result based on the computer programming that has been
developed by numerical formula.
2.5.1 Conventional Methods
There are some conventional methods to analysis Cut and Cover methods for the
retaining systems- cantilever sheet pile, braced cut sheet pile and braced cut
diaphragm wall. For the analysis of braced cut retaining system (Figure 2.34), Peck
(1969) has developed design or apparent pressure envelops theory for different soil
types.
Bickle at al. (1997) has suggested some design criteria for the construction of braced
cut retaining system, some of which are mentioned as follows:
42
Figure 2.34 Sheet pile with braced cut
Struts should have a minimum vertical spacing of about 2.75m or more.
In clay soils, the depth of 1st strut below ground surface (zc) is less than the depth
of tensile crack (2Cu/γ) i.e., zc= 2Cu/γ; where Cu is cohesion and γ is unit weight of
soil.
2.5.2 Apparent Pressure Envelop by Peck (1969)
After observation of several braced cuts, Peck (1969) suggested the following use of
design pressure envelops which is also known as apparent pressure envelop for
different types of soil such as sandy soil, soft to medium clay, stiff clay and also in
layered soil or combination of sandy and clay type of soil as shown in Figure 2.35.
Limitations of Pressure Envelop by Peck (1969)
The limitation of the apparent pressure envelop as developed by Peck (1969) has the
following limitations:
(1) Earth pressure, Pa may depend on construction sequence
(2) They apply when depth of excavation, H is greater than or equal to 6m (apprx.)
(3) Ground water table is considered as below the bottom of excavation
(4) Sand is drained (i.e., uw=0)
(5) Clay is undrained (i.e., uw is not considered).
43
Figure 2.35 Earth pressure diagram (Peck, 1969): (a) sandy soil, (b) soft to
medium clay soil when 4u
H
C
, (c) stiff clay soil when 4
u
H
C
and (d) sandy
soil underlying clay soil (e) several clay layers
(a) (b)
(c)
(d) (e)
44
2.5.3 Numerical Analysis
Numerical analysis involves the study of approximation techniques for solving
mathematical problems, taking into account the extent of possible errors. Though this
analysis is an approximation, but results can be made as accurately as desired.
Numerical Analysis is widely used in geotechnical engineering for the following
reasons:
Analysis process is quick and easy to conduct the simulation.
More reliable and realistic analysis.
To understand and to determine the structural behavior practically.
To view the each structural behavioral steps of construction process, it is the
best analytical approach.
Solve for the roots of a non-linear equation.
Solve for large systems of equations.
Soil-structure interaction is accounted properly in this type of analysis.
Soil-water interaction can be simulated accurately in this analysis.
Settlement and deformation of the ground surface and structures can be
determined accurately.
2.5.4 Finite Element Method (FEM)
Finite Element Method (FEM) is one the most popular numerical procedure for its
simplicity and flexibility. This is a dominant discretization technique in structural
mechanics. The basic concept in the physical interpretation of the FEM is the
subdivision of the mathematical model into disjoint (non-overlapping) components of
simple geometry called finite elements. The response of each element is expressed in
terms of a finite number of degrees of freedom characterized as the value of an
unknown function, or functions, at a set of nodal points.
The way finite element analysis obtains the stresses, flows or other desired unknown
parameters in the finite element model are by minimizing an energy functional. An
energy functional consists of all the energies associated with the particular finite
45
element model. Based on the law of conservation of energy, the finite element energy
functional must equal zero.
The finite element method obtains the correct solution for any finite element model by
minimizing the energy functional. The minimum of the functional is found by setting
the derivative of the functional with respect to the unknown grid point potential for
zero.
Thus, the basic equation for finite element analysis is 0F
p
.
Where F is the energy functional and p is the unknown grid point potential (In
mechanics, the potential is displacement) to be calculated. This is based on the
principle fo virtual work, which states that if a particle is under equilibrium, under a
set of a system of forces, then for any displacement, the virtual work is zero. Each
finite element will have its own unique energy functional.
As an example, in stress analysis, the governing equations for a continuous rigid body
can be obtained by minimizing the total potential energy of the system. The total
potential energy can be expressed as: 12
T T TdV d bdV d qdS
where
and are the vectors of the stress and strain components at any point, respectively,
d is the vector of displacement at any point, b is the vector of body force components
per unit volume, and q is the vector of applied surface traction components at any
surface point. The volume and surface integrals are defined over the entire region of
the structure and that part of its boundary subject to load . The first term on the
right hand side of this equation represents the internal strain energy and the second
and third terms are, respectively, the potential energy contributions of the body force
loads and distributed surface loads.
In the finite element displacement method, the displacement is assumed to have
unknown values only at the nodal points, so that the variation within the element is
described in terms of the nodal values by means of interpolation functions. Thus,
within any one element, d Nu where N is the matrix of interpolation functions
termed shape functions and u is the vector of unknown nodal displacements. *u is
equivalent to p in the basic equation for finite element analysis.) The strains within
46
the element can be expressed in terms of the element nodal displacements as Bu
where B is the strain displacement matrix. Finally, the stresses may be related to the
strains by use of an elasticity matrix (e.g., Young’s modulus) as E .
The total potential energy of the discretized structure will be the sum of the energy
contributions of each individual element. Thus, ee
where e represents the
total potential energy of an individual element.
1 ( ) 02
T T T T T T T
e u B EB udV u N pdV u N qdS
Taking the derivative 1 ( ) 02
T T T Te B EB udV N udV N qdSu
one gets the
element equilibrium equation 0ku f where T Tf N udV N qdS
and
( )T Tk B EB udV
and k is known as the element stiffness matrix.
The fundamental concept is [K]{u]={F} or, {u}=[K]-1{F}
Here, K is stiffness matrix & [K] represents property; u is displacement & {u}
represents behavior and F is load & {F} represents action.
The general steps in finite element method are described as below:
(1) Discretization (or meshing): Divide structure or geometry into pieces (elements
with nodes).
(2) Assemble the elements at the nodes to form an approximate system of equations
for the whole structure (forming element matrices).
(a) Establishment of stiffness relations for each element. Material properties
and equilibrium conditions for each element are used in this establishment.
(b) Enforcement of compatibility, i.e. the elements are connected.
(c) Enforcement of equilibrium conditions for the whole structure, in the
present case for the nodal points.
(d) By means of (b) and (c) steps, the system of equations is constructed for
the whole structure. This step is called assembling.
(3) Boundary conditions are enforced.
47
(4) Solve the system of equations involving unknown quantities (displacements) at
the nodes.
(5) Calculate the desire quantities (strains and stresses) at selected elements.
2.5.5 Elasto-Plastic Model
Based on 2D FEM analyses, simulating the excavation of a tunnel, the impacts of the
employed soil models on the predicted displacements and stresses in the soil mass are
investigated in previous research works in the world. For the numerical analysis of
tunnelling using the FEM, it is generally accepted now that to model the non-linear
behavior of the soil an elasto-plastic material model should be employed. An elasto-
plastic model characterizes the stress-strain and failure behavior of soil media.
There are various kinds of elasto-plastic soil models in FEM_2D analysis. Name of
some soil models are as follows:
(1) Linear elastic constitutive relations
(2) Elasto-plastic Drucker-Prager model
(3) Elasto-plastic Mohr-Coulomb model and
(4) Elasto-plastic Cap model.
All these models have their own advantages and limitations which depend to a large
degree on the particular application. The most severe drawback associated with
refined and sophisticated models is related to the larger number of required
parameters, some of them often cannot be determined from standard tests. Therefore,
commonly, the relatively simple material models with a yield surface according to the
Drucker-Prager or to the Mohr-Coulomb criterion and an associated or a non-
associated flow rule are employed in practice.
2.5.6 Subloading tij Model
Subloading tij model (Nakai and Hinokio, 2004) is an elasto-plastic constitutive model
for two-dimensional finite element analysis used in numerical analysis. The
Subloading tij model (Nakai and Hinokio, 2004) has the following advantages over
other constitutive models:
48
(1) Subloading tij model requires only a few unified material parameters.
(2) This model can describe the characteristics of soils which are as follows:
(a) Influence of intermediate principal stress on the deformation and
strength of soil.
(b) Influence of stress path on the direction of plastic flow is considered by
splitted the plastic strain increment in to two components.
(c) Influence of density and/or confining pressure.
Nakai et al. (2011) has presented a simple and unified constitutive model for soils
considering some effects such as the influence of density, bonding, time dependent
behavior and others in one-dimensional condition which is presented here.
Constitutive models for geomaterials try to predict the deformation and failure of the
ground subjected to the forces imposed by geotechnical structures. Therefore, models
which are developed to simulate the behavior of a limited number of materials or
those tested under limited stress conditions may not be useful in practical design.
The Cam clay model (e.g., Schofield and Wroth, 1968), which was developed more
than 50 years ago, was an epoch-making constitutive model for geomaterials. This is
because the model proposed a unified framework to describe the consolidation and
shear behaviors of unstructured clays, which had been investigated separately before
that time. However, the Cam clay model cannot properly predict the soil behavior
except for remolded normally consolidated clay under the conventional axis-
symmetric triaxial compression condition. Although many constitutive models have
been proposed to overcome the limitations of the Cam clay model, most of them are
complex, and/ or the conditions to which they can be applied are still restricted. The
features of geomaterials which are not taken into consideration in the Cam clay model
are as follows:
(1) Influence of intermediate principal stress on the deformation and strength of
geomaterials
(2) Dependency of the direction of plastic flow on the stress path
(3) Positive dilatancy during strain hardening
49
(4) Stress induced anisotropy and cyclic loading
(5) Inherent anisotropy
(6) Influence of density and/ or confining pressure on the deformation and strength
(7) Beavior of structured soils such as naturally deposited clay
(8) Time-dependent behavior and rheological characteristics
(9) Temperature-dependent behavior
(10) Behavior of unsaturated soils
(11) Influence of particle crushing.
In the 1980’s, two simple constitutive models for clay and sand were developed; one
is referred to as the tij-clay model (Nakai and Matsuoka, 1986) and the other is
referred to as the tij -sand model (Nakai, 1989). In these models, “(1) the influence of
intermediated principal stress on the deformation and strength” is considered with the
adaption of the concept of modified stress tij into consideration (Nakai and Mihara,
1984) and “(2) the stress path dependency of plastic flow” is considered with the
introduction of the plastic strain increment division into two components: a plastic
stain increment which satisfies an associated flow rule in the tij space and an isotropic
plastic stain increment due to increasing mean stress. Later, these models based on the
tij concept were integrated into the unique model named Subloading tij model (Nakai
an Hinokio, 2004), in which “(3) Positive dilatancy during strain hardening” and “(6)
Influence of density and/ or confining pressure on the deformation and strength” are
taken into consideration by introducing and revising the subloading surface concept
(Hashiguchi, 1980). Furthermore, by referring to the concept of a superloading
surface as well as a subloading surface from Asaoka and collaborators (Asaoka et al,
2000a; Asaoka, 2003) and modifying it, the Subloading tij model was extended to also
describe “(7) the behavior of structured soil such as naturally deposited clay” (Nakai,
2007, Nakai et al., 2009a).
In Nakai et al. (2011), a simple and unified framework to take several of the above
mentioned features into account has been described under one-dimensional condition.
Some of the present modeling is described in a paper on applied mechanics in
Japanese as well (Nakai et al., 2009b). Three-dimensional models can easily be
developed by extending the one-dimensional models using the tij concept (Nakai and
Mihara, 1984).
50
Influence of intermediate principal stress is considered by defining yield function f
with modified stress ijt (i.e., defining the yield function with the stress invariants ( Nt
and St ) instead of ( p and q ) and considering associate flow rule in ijt -space instead
of ij -space (Nakai and Mihara (1984)). Figure 2.36 shows the yield surfaces of an
elasto-plastic model based on the ijt concept, represented on the N St t plane, in which
the direction of plastic strain increment ( )p AF
ijd is indicated by the arrow. Here, the
directions of *p
SMPd and *p
SMPd coincide with those of Nt and St , respectively.
Figure 2.36 Shape of yield surface and normally yield surface, and definition of
In the ijt concept (Nakai and Mihara, 1984), attention is focused on the so-called
spatially mobilized plane (SMP; Matsuoka and Nakai, 1974) instead of the octahedral
plane used in ordinary models, such as the Cam clay as shown in Figures 2.37 to 2.39.
The plane ABC in Figure 2.40 is the spatially mobilized plane (SMP) in the three-
dimensional stress space, where axes I, II and III imply the direction of three principal
stresses. At each of three the sides AB, AC and BC of plane ABC, the shear-normal
stress ratio is maximized between two principal stresses as shown in Figure 2.41.
51
Figure 2.37 Definition of stress invariants (mean stress, p and deviator stress, q ) in
Cam Clay model
Figure 2.38 Definitions of strain increment invariants (volumetric strain increment,
Vd and deviatorinc strain increment, dd ) in Cam Clay model
Figure 2.39 Yield surface of the Cam clay model and direction of plastic flow on the
octahedral plane
52
Figure 2.40 Spatially mobilized plane (SMP) in three-dimensional space
Figure 2.41 Three Mohr’s stress circles under three different principal stresses
From Figures 2.40 and 2.41, it can be seen that the values of the coordinate axes
intersected by the plane ABC (SMP) are proportional to the square root of the ratio
between the corresponding principal stresses, because the following equation holds:
1 sintan(45 )2 1 sinmoij moij i
moij j
( , 1,2,3; )i j i j (2.1)
Therefore, the SMP coincides with the octahedral plane only under isotropic stress
conditions and varies with possible changes of stress ratio. The direction cosines ( 1a ,
2a and 3a ) of the normal to the SMP, and the unit tensor whose principal values are
determined by these direction cosines are expressed as follows (Nakai, 1989):
53
31
2 1
Ia
I , 3
22 2
Ia
I , 3
32 3
Ia
I (2.2)
3 31 12
2 2. . ( )ij kj r kjij ik
I Ia r c I
I I
Where 11 3,ij kj r kj r kjik ikc c c I I (2.3)
Where ( 1,2,3)i i are the three principal stresses, 1I , 2I and 3I are the first, second
and third invariants of ij , and 1rI , 2rI and 3rI are the first, second and third
invariants of ijr , which is the square root of the stress tensor or ik kj ijr r . These
invariants are expressed using principal stresses and stress tensors as
1 1 2 3 iiI
22 1 2 2 3 3 1
1{( ) }2
ii ij jiI (2.4)
3 1 2 3 1 2 3ijk i j kI e
1 1 2 3r iiI r
22 1 2 2 3 3 1
1{( ) }2
r ii ij jiI r r r (2.5)
3 1 2 3 1 2 3r ijk i j kI e r r r
Where ijke is the permutation tensor. The detailed expression of ija is also described
in the paper by Nakai and Hinokio (2004). As can be seen from the above equation,
ija is a function of stress ratio and its principal axes coincide with those of ij . The
modified stress tensor ijt is then defined by the product of ika and kj as follows:
ij ik kjt a (2.6)
Its principal values are given by
1 1 1t a , 2 2 2t a , 3 3 3t a (2.7)
In conventional models, the stress invariants ( p and q ) and strain increment
invariants ( vd and dd ) are given by the normal and parallel components of the
}}
54
ordinary stress and strain increment with respect to the octahedral plane (Figures 2.37
and 2.38). On the other hand, the stress invariants ( Nt and St ) and strain increment
invariants ( *Nd , *
Sd ) in the ijt concept are defined as the normal and parallel
components of the modified stress ijt and the strain increment with respect to the SMP
(Figures 2.42 and 2.43). Hence, these invariants are given by:
Figure 2.42 Definitions of stress invariant ( Nt and St ) in the tij concept
Figure 2.43 Definitions of strain increment invariants ( *
Nd and *Sd ) in the tij
concept
55
Nt ON = 1 1 2 2 3 3 ij ijt a t a t a t a (2.8)
St NT = 2 2 2 21 1 2 2 3 31 2 3 ( )t t t t a t a t a
2( )ij ij ij ijt t t a (2.9)
*Nd ' 'O N = 1 1 2 2 3 3 ij ijd a d a d a d a (2.10)
*Sd ' 'N T = 2 2 2 2
1 1 2 2 3 31 2 3 ( )d d d d a d a d a
2( )ij ij ij ijd d d a (2.11)
A comparison between the stress and strain increment tensors and their invariants
used in the ordinary concept and the tij concept is shown in Table 2.2.
Figure 2.44 Initial and current yield surfaces in the p - q plane and direction of
plastic flow in an ordinary model such as Cam clay model
Figure 2.45 Initial and current yield surfaces in the Nt - St plane and direction of
plastic flow for the model based on the ijt concept
56
Table 2.2 Comparison between tensors and scalars related to stress and strain in the ordinary concept and the ijt concept Ordinary Concept ijt Concept
1. Tensor normal to reference plane 2. Stress tensor
ij ij
ija ijt
3. Mean stress 4. Deviatoric stress tensor 5. Deviatoric stress 6. Stress ratio tensor 7. Stress ratio
3ij ij
p
ij ij ijs p
32
ij ijq s s
ijij
s
q
p
N ij ijt t a '
ij N ijijt t t a
' 'S ij ijt t t
'ij
ij
N
tx
t
S
N
tX
t
8. Strain increment normal to reference plane
9. Deviatoric strain increment tensor 10. Strain increment parallel to reference
plane
v ij ijd d
3v ij
ij ijd
de d
2( )3
d ij ijd de de
*ij ijNd d a
' *ij N ijijd d d a
* ' 'S ij ijd d d
According to subloading surface concept, yield surface (subloading surface) has not
only to expand but also to shrink for the present stress state to lie always on the
surface, and the yield function is written as a function of the mean stress Nt and stress
ratio S
N
tX
t based on ijt by Equation (2.12).
1 1
0 0 1ln ( ) (ln ln ) 0N N e N e
N N N
t t tf X
t t t (2.12)
Here, 1Nt determines the size of the yield surface (the value of Nt at 0X ), 0Nt is
the value of Nt at reference state and 1N et is the mean stress Nt equivalent to the
present plastic volumetric strain which is related to the plastic volumetric strain p
v as
1
0 1(ln )
1N ep
vN
t
e t
(2.13)
The symbols and denote compression index and swelling index, respectively,
and 0e is the void ratio at reference state. Although 1N et coincides with 1Nt in normally
57
consolidated states, 1N et is larger than 1Nt in over consolidated states. The ratio 1
1
N e
N
t
t
corresponds to the over consolidation ratio in a broad sense. In this research, the
expression for ( )X is assumed as,
*
1( ) ( )XX
M
( : material parameter) (2.14)
The value of *M in Equation (2.15) is expressed as follows using principal stress ratio
( )SCS CS
N
tX
t and plastic strain increment ratio
*
*( )p
SMPCS CS
p
SMP
dY
d
at critical state:
1* 1( )CS CS CSM X X Y (2.15)
In elastoplastic theory, total strain consists of elastic strain and plastic strain. Here,
plastic strain increment is divided into component ( )P AF
ijd , which satisfies associate
flow rule in the space of modified stress ijt , and isotropic compression component ( )P IC
ijd as given in Equation (2.16).
( ) ( )P P AF P IC
ij ij ijd d d (2.16)
The components of strain increment are expressed as,
( )P AF
ijij
fd
t
(2.17)
( )
3ijP IC
Nijd K dt
(2.18)
Here, is the proportionality constant, ij is Kronecker’s delta and < > denotes
Macauley bracket. Dividing plastic strain increment into two components as in
Equations 2.16 to 2.18, for the same yield function, this model can take into
consideration feature (ii), i.e., the dependence of the direction of plastic flow on the
stress paths.
Referring to the subloading surface concept by Hashiguchi (1980) and revising it, i.e.,
adding the term ( )G in the denominator of the proportionality constant of
58
normal consolidated condition, influence of density is considered. Finally, and K
can be expressed in Equations (2.19 and 2.20),
1
0
1
1 ( )( )
ij N
ij N
kk N
fd dt
t
e f G
t t
(2.19)
0 1
1 1.1 ( )(1 ) N
kk
Ke G t
a
(2.20)
Figure 2.46 Shape of yield surface and definition of
The subloading concept used here is illustrated in Figure 2.46. The solid line of Figure
2.46a shows the yield surface passing though the present state of stress at P. Point A
shows the void ratio corresponding to that state of stress. Variable is the difference
between the void ratios of present state of stress (point A) and normal consolidation
condition (point B) at the same stress state. In the definition of as in Equation
(2.19), decreases with plastic deformation and eventually it becomes zero. To
59
satisfy this condition, ( )G should be a increasing function of which satisfies
(0) 0G , such as 2( ) .G a ( a : material parameter) (2.21)
From Figure 2.46, by using the ratio of 1Nt and 1N et , can be expressed as Eq. (12)
1
1( ) ln( )N e
N
t
t (2.22)
2.6 Studies on Dhaka Sub-soil
Bashar (2000) established soil profiles for Dhaka Metropolitan area where he found
that soft to very stiff cohesive layers at the top strata upto depth of 6.1m to 18.3m had
been existed. At large depths, the soil layers had been found to consist of loose to very
dense sandy soils. In some areas of the eastern region of Dhaka Metropolitan like,
Uttarkhan, Dakkhinkhan, Saterkul and Daina, cohesive layers up to depth of 30m had
been encountered.
Ameen (1985) revealed that the clay layer of Dhaka city at the top had an
approximate thickness of 9.14m, below which started a sand layer. The liquid limit of
the clay layer varied from 40% to 50%, the plastic limit varied from 19% to 25%, and
plasticity index from 19% to 29% (Eusufzai, 1967). The clay content (less than 2
micron) of Dhaka clay varied from 15% to 41%, the silt content was between 55% to
80%, and the sand content was between 3% to 11% (Ameen, 1985). The water
content of this clay varied from 18% to 36% and coefficient of consolidation was
between 0.14 to 0.34 and the soil was preloaded.
Bashar (2000) also investigated that water content, liquid limit and plasticity index
were found to decrease with the increase in soil depth. The percentage of coarser
material had been found to increase with soil depth.
60
Chapter Three
EXPERIMENTAL AND NUMERICAL
TEST PROGRAM
3.1 Introduction
In this thesis, two-dimensional finite element analyses have been carried out with
FEMtij-2D. The constitutive model used in these numerical analyses has been the
Subloading tij model (Nakai and Hinokio, 2004). These analyses simulate the
excavation sequences of Cut and Cover and NATM with earth retaining structures
considering typical soil condition of Dhaka city. Then the lateral movements of the
retaining walls as well as the surface settlements of the ground have been established.
Mass Rapid Transit 4 (MRT4) proposed in Strategic Transport Plan (STP) 2004, has
been considered as study route alignment for the study. Major portion of the route of
MRT-4 is now being used as railway of Dhaka city passing from Tongi-Uttara
junction to Kamalapur railway station via Mohakhali and Farmgate area. Four
locations (Uttara, Mohakhali, Farmgate and near Dhaka University (DU) campus
area) have been selected for geotechnical investigation and thereby to model suitable
and optimum construction techniques to be applied for underground metro rail
system.
3.2 Study Route
As mentioned in earlier chapters, among six rapid transit routes proposed by Strategic
Transport Plan (STP Final Report, 2004), MRT-4 route is selected for this study.
MRT-4 route as shown in Figure 3.1 passes from Uttara (north of Dhaka) to Khilkhet,
then Khilkhet to Mohakhali via Banani, then Mohakhali to Farmgate then ends at
Sayedabad bus terminal passing Kamalapur railway station (located at south of
Dhaka). This route covers the alignment of existing railway route mainly. The reason
of selecting MRT-4 is because this route is the most acceptable route for constructing
61
the underground metro rail tunnel as the other routes (like, MRT-5, MRT-6 as
mentions in Chapter Two) are obstructed in too many locations.
Figure 3.1 Study area along MRT-4 in Dhaka city
62
3.3 Sub-soil Investigation
To perform the numerical analysis, extensive sub-soil investigations are required to
analyze in order to get the practical and optimum results at a large extent. So,
comprehensive laboratory tests program have been carried out for the soil samples
collected along the study area. Moreover, soil reports from BRTC, BUET and
qualified companies for the selected sites have been collected to do the soil analysis.
Four locations have been selected for sub-soil analysis. The study areas located on
proposed MRT-4 line are Uttara, Mohakhali, Farmgate and near Dhaka University
(DU) campus which have been pointed out by legends in Figure 3.1. Because of
unavailability of reliable soil reports, DU which is located nearest to study route has
been selected as for sub-soil analysis. Previous soil research works have also been
used to compare the analyzed soil parameters to ensure that these parameters are
within the ranges for that typical Dhaka soil. All soil analyses are combined and
summarized to determine the required soil parameters to perform the FE analyses.
3.3.1 Field Tests
About 5 boreholes in Uttara, 3 boreholes in Mohakhali, 9 boreholes in Farmgate have
been executed. Typical boreholes of the respective area have been taken into account
to combine borelogs in order to establish the soil profile along the study (MRT-4)
route.
The soil borings of the selected locations of the studied route had been executed up to
30.5m depth. The boreholes were drilled at first. Wash boring method was followed in
drilling the boreholes after driving a 100mm diameter casing pipe. The disturbed soil
samples were extracted from each of the 1.5m depths up to the depth of the
investigation in the case of each borehole using the split spoon sampler along with the
performance of the Standard Penetration Test (SPT). The procedure of test is
described in ASTM D1586 (ASTM, 1989). This test includes dropping of a hammer
of 622N weight that falls freely over a constant height of 75cm along the drill pipe in
order to drive the sampler attached at the end of the same. The number of the blows
necessary to produce the penetration was recorded in three different stages, each at
150 mm interval. The total number of the blows required in the 2nd and 3rd 150mm of
63
the penetration of the sampler is called the SPT value and is presented by ‘N’. The
SPT values are shown in the Bore-log chart against the respective interval of the
depth. Disturbed samples were collected at an interval of 1.5m depth. The undisturbed
samples were collected in 7.62 cm diameter Shelby tubes.
3.3.2 Laboratory Tests
A detailed laboratory investigation has been carried out on soil samples collected
from the boreholes drilled at the selected sites. The laboratory testing program
consisted of carrying out moisture content, specific gravity, liquid limit, plastic limit,
particle size analysis, unconfined compression test, direct shear test, one-dimensional
consolidation test and consolidated undrained triaxial test for the collected soil
samples.
Grain Size Distribution of Sand & Clay: The grain size distribution is usually
determined by sieve analysis following the test method ASTM C 136 and ASTM D
422. From the test some of the basic soil parameters such as effective size, uniformity
coefficient and coefficient of gradation have been determined.
Specific Gravity (GS): Specific gravity signifies the weight-volume relation of soil.
The related test procedure has been followed from ASTM D 854.
Moisture Content (ws): Water or moisture content (in percentage) of soils have been
determined following the test method described in ASTM D 2216.
Liquid Limit (LL), Plastic Limit (PL) and Plasticity Index (PI): The test methods
of LL test, PL test and PI of soil have been conducted following ASTM D 4318. LL is
the moisture content (in percentage) at which the soil changes from liquid state to
plastic state whereas PL is the moisture contents (in percent) at which the soil changes
from a plastic to a semi-solid state.
Unconfined compression test: Unconfined compression test is a special case of
unconsolidated undrained triaxial test. The procedure of the test has been conducted
following ASTM D 2166.
64
Direct Shear Test: ASTM D 3080 has been followed to perform the direct shear test.
This test gives the relation between horizontal displacement and shear stress from
which angle of internal friction of sandy soil can be obtained.
Consolidation Test: The test is usually carried out on saturated specimen of clayey
soil. One-dimensional consolidation test has been carried out following the test
method as specified in ASTM D 2435.
Triaxial Test: In respect of accuracy level and reliability, tri-axial test is one of the
most important tests to get the accurate results of soil parameters to large extent which
is very necessary for model analysis. In this test a specimen is enclosed in a thin
rubber membrane and placed inside a cylindrical plastic chamber. The chamber is
filled with water and glycerine. The specimen is subjected to a confining pressure, σ3
by application of pressure to the fluid in the chamber. To cause shear failure in the
soil an axial stress Dσ is applied through a vertical loading ram. This is also referred
to as deviator stress. The axial strain is measured during the application the deviator
stress. Both cohesion and angle of internal friction values are obtained from this test.
In this research, Consolidated Undrained (CU) triaxial tests have been performed
following the specification of test procedure ASTM D 4767 in the BUET laboratory.
The tests have been executed for both clayey and sandy type of Dhaka soils. A cube
sized 30 cm 30cm 30cm clayey type undisturbed soil sample has been collected
Figure 3.2 Triaxial testing machine
65
from Gulshan site at a depth of 2.0m from existing ground level (EGL). Required
specimen (as sized 71mm 142mm) has been engraved from the cube. Triaxial CU
tests have been conducted by Geo comp machine as shown in Figure 3.2.
Drainage conditions during shearing will affect the strength parameters of soil
significantly. If the sample is drained and slow shearing takes place, pore pressures
will not develop and the test is called a “drained test.” However, if the sample is not
allowed to drain and/or shearing occurs quickly, pore pressure is developed in the
specimen and the test is called an “undrained test”. In soil mechanics, effective stress
decreases as pore pressure increases. In this consolidated undrained triaxial test,
draining has not occur during shearing, and therefore pore pressures increased and the
effective stress decreased relative to the total stress i.e., the strength parameter of the
samples decreased.
3.4 Detail Layout of Tunnel Construction
In general, Cut and Cover excavation method is suitable for an urban city having a
large open space without any nearby building or structure. Some portions of the study
area along the proposed MRT-4 route can go with the features for applying the Cut
and Cover method. This construction method has been good except for a few
locations that encountered with structural difficulties. These kinds of portions of the
MRT-4 route are obstructed in the crossing of loops at Cantonment areas and in the
crossing of flyover at Mohakhali.
NATM offers no difficulty and displacement on the nearby structures. Besides,
underground construction process can be carried out satisfactorily keeping the
existing road on its way by this method. But NATM is a costly option. So in these
cases, both Cut and Cover and NATM methods have been proposed along the
proposed route based on the ground settlement and deformation of retaining walls and
tunnel structures found from the analysis results. The layout of tunnel construction
methods along the study route has been proposed in the Chapter four.
66
3.5 Selection of Construction Methods
For Dhaka city in respect of geotechnical aspects, selection of tunnel construction
method between Cut and Cover, NATM along the proposed route can be determined
by the following characteristics:
Geological and hydrological condition
Geometry of tunnel system
Surface settlement and displacement of the earth retention system
Least disturbance of existing traffic during construction period.
Existence of Nearby Structures: The nearest structures to tunnel may consist of
buildings, roads, railroads, bridges etc. The effects and responses of these structures to
ground settlements as well as the potential damage to ground movement may vary
within extremely wide ranges. So, it is require to analysis surface settlement and
ground movement to control the effects on pre-existing buildings, utilities and
infrastructures.
Surface Settlement: Surface settlement is an important issue in terms of tunnel
stability. In Cut and Cover method, excavation depth is taken as 15m or 12m (case by
case) and in case of NATM, depth of tunnel crown is 11 m. In some portion along the
proposed tunnel route there exists building structure. So collapses or excessive
settlements during tunnel construction by both excavation methods may happen based
on the geotechnical conditions of the route. In this research, using Subloading tij
Model, surface settlement can be estimated to ensure that maximum settlement is
within the allowable limit.
Lateral Deformation: Lateral deformation of retaining structures represents the
stability of the retaining system for Cut and Cover method. It is very much important
to ensure the limitation of deformation to be within the range. In this study,
deformations of retaining system have been determined for Cut and Cover method.
67
3.6 Analysis Scheme
List of cases of consideration for analyses by Cut and Cover method along with
NATM have been presented in Table 3.1.
Table 3.1 List of cases of numerical analysis by FEM using Subloading tij model
(Nakai and Hinokio, 2004) Name of method
Condition of case Braced sheet pile Braced diaphragm wall
Before Tunnel place
After Tunnel
Before Tunnel place
Cut and Cover Method
No surface load, with WT at large depth
√ √ √
With surface load, with WT at large depth
√ √ √
With surface load, with WT at shallow depth
√ √ √
NATM No surface load, with Pile load √
3.7 Analysis Approach
Cut and Cover Method
Analysis approach for Cut and Cover Method is in the flow chart of Figure 3.3.
Figure 3.3 Flow chart showing analysis approach for Cut and Cover
Case 1: Negligible
structural load and
negligible water table
Execution of Analysis
Cut and Cover Methods
(Sheet pile with braced cut,
Diaphragm wall with braced cut)
Case 2: Presence of
structural load and
negligible water table
Case 4: Presence of
structural load and
significant water table
Stage 2: Placement of Tunnel system
Case 3: Presence of
significant water table
and negligible load
Stage 1: Excavation and provision of retaining system
Stage 3: Backfilling on completed Tunnel
68
NATM
Analysis approach for NATM is presented in the flow chart of Figure 3.4.
Figure 3.4 Flow chart of analysis approach for NATM
3.8 Conventional Analysis for Different Retaining Structures
Conventional methods have been used in this study to analysis the braced cut
retaining system of Cut and Cover methods. For the analyses of braced cut sheet pile
and braced cut diaphragm wall, the design or apparent pressure envelops theory
developed by Peck (1969) have been used for different soil profiles of Dhaka city
existed along the proposed route (MRT-4).
3.8.1 Braced Cut System with Sheet Pile and Diaphragm Wall After observation of several braced cuts, Peck (1969) suggested the following use of
design or apparent pressure envelops for different types of soil such as sandy soil, soft
to medium clay, stiff clay and also in layered soil or combination of sandy and clay
type of soil.
Case 1: Greenfield
condition
Execution of Analysis
New Austrian Tunnelling Method (NATM)
Case 2: Presence of
building load as footing
and negligible water
Case 2: Presence of
building load as pile
and negligible water
69
Bickle at al. (1997) has suggested some design criteria for the construction of braced
cut retaining system which are mentioned as follows:
Struts should have a minimum vertical spacing of about 2.75m or more.
In clay soils, the depth of 1st strut below ground surface (zc) is less than the depth
of tensile crack (2Cu/γ) i.e., zc= 2Cu/γ; where Cu is cohesion and γ is unit weight of
soil.
Braced Cuts in Sandy Soil: Earth pressure diagram for the design of braced cut
system in sandy soil by Peck (1969) has been shown in Figure 3.5. The apparent
pressure is 0.65 agHK where, is the unit weight of soil, H is the total depth of
excavation and aK is coefficient of active earth pressure.
Figure 3.5 Pressure diagram for sandy soil (Peck, 1969)
Braced Cuts in Soft to Medium Clay: In case of design of braced cut system in soft
to medium clay soil, earth pressure diagram by Peck (1969) has been shown in Figure
3.6. The apparent earth pressure is 4(1 )uC
gHgH
0.3 H where, is the unit
weight of soil, H is the total depth of excavation and uC is cohesion of soil. This
condition is valid when the condition 4u
H
C
is satisfied.
70
Figure 3.6 Pressure diagram for soft to medium clay soil; when 4u
H
C
(Peck, 1969)
Braced Cuts in Stiff Clay: Earth pressure diagram for the design of braced cut
system in stiff clay soil by Peck (1969) has been shown in Figure 3.7. The apparent
earth pressure is 0.2 0.4 gH where, is the unit weight of soil, H is the total
depth of excavationl. This condition is valid when the condition 4u
H
C
is satisfied.
Figure 3.7 Pressure diagram for stiff clay soil; when 4u
H
C
(Peck, 1969)
71
Braced Cuts in Layered Soil: For variability soil type as shown in Figure 3.8 (a) the
equivalent cohesion and average unit weight have been estimated as recommended by
Peck (1969) which is given as below:
Equivalent cohesion, 2 tan ( ) '
2s
s s s s uave
K H H H n qC
H
and average unit weight, ( )s s s ca
H H H
H
where,
HS = Height of sand layer.
H= Total height of cut.
γs= Unit weight of sand.
Ks = Lateral earth pressure coefficient for sand (≈1)
Φs= Angle of friction of sand.
qu= Unconfined compression strength of clay.
n’= Coefficient of progressive failure (ranging from 0.5~1.0; average value 0.75)
γc= Saturated unit weight of clay layer.
(a) (b)
Figure 3.8 Braced cut in layered soil. (a) Case 1: sandy soil underlying clay soil and
(b) Case 2: several clay layers
72
When several clay layers are encountered in the cut as described in Figure 3.8 (b),
the average undrained cohesion is, 1 1 2 2 ........ n nave
C H C H C HC
H
and the average unit weight, 1 1 2 2 ........ n na
H H H
H
where, C1, C2,...Cn are undrained cohesion in layers 1,2,….n. γ1, γ2,…. γn are unit
weight in layers 1,2,….n. and H1, H2,… Hn are thickness of layers 1,2,…n.
Design Approach
Based on the estimated lateral earth pressure selection of appropriate sizes of bracings
(struts and wales) and sheet pile or diaphragm wall have been constructed according
to the steps as shown in Figure 3.9. The steps are,
Lateral earth pressure varies with depth. Each strut being designed for maximum
load to which it is subjected.
Maximum moment of retaining wall can be determined and thereby design of
sheet pile in case of braced cut sheet pile and design of diaphragm wall in case of
braced cut diaphragm wall can be determined.
Wales are treated as continuous horizontal members if they are spliced properly or
conservatively treated as though they are pinned at the struts.
At level A, maximum moment,2
max( )( )
8A s
M
At level B, maximum moment, 2
1 2max
( )( )8
B B sM
At level C, maximum moment,2
1 2max
( )( )8
C C sM
At level D, maximum moment,2
max( )( )
8D s
M
Where, s = spacing of wales; A = Axial force at 1st level of strut in braced cut; B = B1
+ B2= Axial force at 2nd level of strut in braced cut; C = C1 + C2 = Axial force at 3rd
level of strut in braced cut and D = Axial force at 4th level of strut in braced cut.
73
(a) (b)
Figure 3.9 Design of braced cut sheet pile: (a) section and plan and (b) segregation at
hinge point of strut
3.9 Numerical Analysis
The numerical analysis or two-dimensional finite element analyses which is
performed in this study is the FEMtij_2D. The constitutive law which is used in this
numerical analysis is the Subloading tij model (Nakai and Hinokio, 2004). The
analyses are carried out considering plane strain drain condition. The small strain
theory is used in the numerical simulation.
74
The behaviours of different types of soil layers of Dhaka city for the selected
locations along the MRT-4 line are simulated by this model. The model analyses
simulate the excavation sequences of Cut and Cover and NATM with different earth
retaining structures considering typical soil condition of Dhaka city. Both the effects
of structural loads (with foundation types as footing, pile) and water loads are
considered in the analyses.
3.9.1 Soil Parameters for Subloading tij Model
Both elasto-plastic and elastic analysis of soil can be simulated by the Subloading tij
model (Nakai and Hinokio, 2004). The soil parameters are required to be assigned in
this model in order to define the mechanical behaviors of different soil layers. So, all
the required parameters of soil layers are determined, estimated and collected based
on laboratory test results, sub-soil analysis results for Dhaka soil. The model
parameters are:
λ = Compression index (or slope of virgin loading curve in e-log p’ curve at the
loosest state).
κ = Swelling index (or slope of unloading-reloading curve in e-log p’ curve at the
loosest state where, e is void ratio and p’ is consolidation pressure).
RCS = (1/3)cs(comp.) = Critical state stress ratio.
OCR = Overconsolidation Ratio.
N or eN = Reference void ratio on normally consolidation line at p= 98 kPa& q= 0 kPa
(or void ratio at mean principal stresses (p) 98 kPa in e-log p’ curve).
eo= Initial void ratio.
υ = Poisson’s ratio.
β = Model parameter responsible for the shape of the yield surface.
a = Model parameter responsible for the influence of density and confining pressure.
75
3.9.2 Program Flowchart of Subloading tij Model
The program of Subloading tij model is represented by a flowchart as below:
No Output Parameters Output Parameters
Input Mesh Parameter
Isoparametric element.
Infinitesimal Deformation Theory.
Solver: Skyline Method.
Integration Method: Ordinary Forward Euler Method.
Input Calculation Type
Node, Element.
Displacement Boundary.
Analysis Condition.
Material Parameter.
Input Analysis Type
Elasto-plastic Analysis of Drained Condition
Elasto-plastic Analysis of Coupling Condition
Choose Type of Elasto-plastic Model
Input Subloading tij Model Parameter
Input Soil Parameter
Execution of Analysis
Subloading tij Model
Slope of Loading Curve of e-logp’ (λ).
Slope of Unloading Curve of e-logp’ (κ).
Critical Stress Ratio (RCS).
Overconsolidation Ratio (OCR).
Void Ratio at p=98kPa (N or eo).
Initial Void Ratio (ein).
Poisson’s Ratio (υ).
Parameter for Shape of Yield Surface (β).
Model parameter (a).
Coefficient of Permeability(kx, ky).
Unit Weight of Water (γw).
Unit Weight of Soil (γs).
Input Material Parameter
Young’s Modulus of Elasticity (E).
Moment of Inertia (I).
Cross Sectional Area (A).
Poisson’s Ratio (υ).
Application of Load (if applicable)
Application of Drainage Boundary (if applicable)
Input Stress Condition
Initial Overburden Pressure.
Depth of Water Table.
Coefficient of Earth Pressure (Ko).
Get Output
If water table exists
If no water table exists
Input Smooth Boundary Condition
If No Tension Develops If Tension Develops
76
3.10 Numerical Analysis for Cut and Cover Method
In this study, numerical analysis by Subloading tij model (Nakai and Hinokio, 2004)
has been used for different retaining system by Cut and Cover methods. The analysis
has been done considering the effects of water and building load which is assumed as
existed nearby the proposed route.
3.10.1 General Layout for Model Analysis
The general layout of analysis for Cut and Cover in the Subloading tij model (Nakai
and Hinokio, 2004) is described in the following points:
(1) Model of Subsoil: The dimension of modeled subsoil must be selected depending
on the position of existing structures from the excavated area. The wideness will
be extended horizontally toward both left and right direction from the excavated
centerline so that to substantially reduce the boundary effects in the numerical
model.
(2) Mesh and Elements Used: The different types of finite element meshes under
various field cases are adopted for the analyses. The elements used here are
isoparametric 4-noded (quadrilateral type) element, 2-noded beam element, 4-
noded joint element (elasto plastic joint element by Nakai, 1985-an extension of
goodman type joint element) etc. The 4-noded quadrilateral elements have been
used to represent the soil and concrete materials. The 2-noded beam elements
have been used to simulated sheet pile, reinforcement in pile, reinforcement in
diaphragm wall. And, the joint interface between pile cap or footing and soil is
simulated using the 4-noded joint element (elasto plastic joint element by Nakai,
1985-an extension of goodman type joint element).
Different geometries with elements used for analysis in Cut and Cover methods
are describes as follows:
77
Cantilever Sheet Pile
Cantilever sheet pile in Figure 3.10 is made of steel and hence it is modeled as beam
element.
Figure 3.10 Geometry and mesh layout for cantilever sheet pile
Sheet Pile with Braced Cut System
The sheet pile is made of steel and hence it is modeled as beam element. Soil and
concrete is modeled as quadrilateral elements. The interface between soil and concrete
is simulated by joint element (elasto plastic joint element by Nakai, 1985-an extension
of goodman type joint element). The bracings or struts are modeled as elastic spring
applying axial stiffness per unit length.
The analysis is executed at all the steps at first insertion of sheet pile wall and all the
bracings (wales and struts), then placement of tunnel and backfilling. The geometry at
the three stages for greenfield condition are shown in Figure 3.11, 3.12 and 3.13. The
procedures are continued considering building load only (Figures 3.14, 3.15 and
3.16). The geometries in Figures 3.17 and 3.18 consider the effects of water in
greenfield condition and the effects of water with building load respectively.
78
Figure 3.11 Geometry for sheet pile with braced cut after bracing
Figure 3.12 Geometry for sheet pile with braced cut after tunnel placement
Figure 3.13 Geometry for sheet pile with braced cut after backfilling
79
Figure 3.14 Geometry for braced sheet pile with building load after bracing
Figure 3.15 Geometry for braced sheet pile with building load after tunnel placement
Figure 3.16 Geometry for braced sheet pile with building load after backfilling
80
Figure 3.17 Geometry for sheet pile with braced cut considering water table at EGL
in Greenfield condition
Figure 3.18 Geometry for sheet pile with braced cut considering water table with
building load
Braced Diaphragm Wall
The diaphragm wall is modeled as hybrid element (Zhang et. at., 2003) consisting
elastic solid and beam element. Diaphragm wall is a reinforced concrete (R.C.)
structure and it is made of concrete and steel bars. In FEMtij_2D, hybrid element
option has been created to represent R.C. structure and composite structure.
Moreover, in case of using beam element for modeling the diaphragm wall, the
volume of diaphragm wall is being neglected. Furthermore, in case of using elastic
element only for modeling diaphragm wall, bending effect is being neglected. So the
concept of hybrid element modeling is more realistic than either the modeling with
81
beam element or elastic solid element for diaphragm wall in finite element analyses.
The struts are modeled as elastic spring applying axial stiffness per unit length.
Figure 3.19 Geometry for diaphragm wall with braced cut
(3) Displacement Boundary: Smooth boundary conditions are used. The
displacement boundary conditions are as follows:
At bottom: Both vertical and horizontal displacements are fixed.
At left edge: The horizontal displacement is fixed but vertical movement is
allowed; i.e., vertical displacement is pinned.
At right edge: The horizontal displacement is fixed but vertical movement is
allowed; i.e., vertical displacement is pinned.
(4) Drainage Boundary: In the FEMtij_2D model performed in this study, the
drainage boundary conditions are adopted in assigning data in to analysis only
when water is present in case of modeled subsoil. According to FEMtij_2D
model, the analysis of soil and water interaction is called “soil-water coupling
analysis”. To perform soil-water coupling analysis, it is required to fix the
boundary to allow water drainage or to make the boundary impermeable in the
input data model. The analyses have been carried out based on the following
drainage boundary conditions:
82
No presence of Water: If no water table (WT) is present then no drainage
boundary condition is adopted and plane strain drained condition is applied in
analysis type.
Presence of Water: If WT is present then plane strain coupling (i.e., undrained)
condition is applied.
The ground surface is drained (or permeable condition)
The bottom or the base of the model is undrained (or impermeable
condition)
The left and right edged vertical boundaries are assumed to be undrained (or
impermeable condition).
(5) Loading: Load from nearby building structures are considered to simulate the
model. The values of load as assigned in the model analysis are 637.65 kN (or
65.00 Ton) which is similar to a five storied building load.
3.11 Numerical Analysis for NATM
Subloading tij model (Nakai and Hinokio, 2004) has been used for NATM for
different loading condition and cases in this study. The design criteria, general layout
and geometries of different cases the analysis have been summarized in the following
sections.
3.11.1 Design Criteria of NATM
The design criteria for simulation of tunnel construction by NATM have been
executed by using the following design criteria.
Tunnel
Diameter of Tunnel =9 m and the crown depth of tunnel = 11 m
Rock Bolts
Length of the rock bolt, LR D/4 where, D = Tunnel diameter
and acceptable range of rock bolt length, LR = (20 to 60)% D.
83
Rock bolt is of steel material and with the modulus of elasticity E of 205 MPa.
Lining
Thickness of the lining = (30 to 60) cm.
The modulus of elasticity, E of concrete = (50 to 60) MPa.
Ground movement has been controlled by increasing the number and length of rock
bolts as well as increasing the thickness of the shotcrete and its reinforcement with
extra lattice girders, wire mesh or steel fibres.
3.11.2 General Layout for Model Analysis
The general layout of analysis for NATM in the Subloading tij model (Nakai and
Hinokio, 2004) is described in the following points:
(1) Geometry and Sub-soil Model: The dimension of modeled subsoil for analysis
will be so way that it can substantially reduce the boundary effects in the
numerical model. Geometries of the model analyses are different based on the
loading conditions which are described in Article 3.11.3.
(2) Mesh and Elements Used: The different types of finite element meshes are
adopted for the analysis of NATM. The sub-soil is simulated by quadrilateral
elements specifying for different layers of soil. The isoparametric 4-noded
(quadrilateral) elements have been used to represent the soil and concrete
materials. The 2-noded beam elements have been used to simulate lining, rock
bolts and reinforcement in pile. The joint interface between pile cap and soil is
simulated using the 4-noded joint element (elasto plastic joint element by Nakai,
1985-an extension of goodman type joint element). The reinforced concrete pile is
made of concrete and steel bars and it is modeled as hybrid element (Zhang et. at.,
2003) consisting elastic solid and beam element.
(3) Displacement Boundary: Smooth boundary conditions are used. The
displacement boundary conditions are as follows:
At bottom: Both vertical and horizontal displacements are fixed.
84
At left edge: The horizontal displacement is fixed but vertical movement is
allowed; i.e., vertical displacement is pinned.
At right edge: The horizontal displacement is fixed but vertical movement is
allowed; i.e., vertical displacement is pinned.
(4) Drainage Boundary: No water table (WT) is present here i.e., drainage boundary
condition is neglected in the excavation of NATM.
(5) Material Specification: Concrete of pile and pile cap are simulated by
quadrilateral elements. Beam elements are used to simulate the lining, rock bolts
and pile (if present) and their specifications are presented in Table 3.3.
(6) Loading: Load from nearby building structures are considered to simulate the
model. The values of load as assigned in the model analysis are 957.85 kN (or
97.64 Ton) which is similar to a eight storied building load.
Table 3.2 Material specification for analysis in NATM
Component Element
Type
Material
Model
Type EA
(Ton-m)
EI
(Ton-
m2)
Thickness,
b (m)
Poisson
Ratio
Lining Beam Beam-
Elastic
Drained 1.54886
x 106
2.61370
x 104
0.450 0.170
Rock bolts Beam Beam-
Elastic
Drained 5.202 10.570 0.057 0.303
3.11.3 Geometry for NATM
The modeled subsoil is 33m deep and 93m ro 100m wide. In this geometry, the top
soil is clayey for 6m depth from EGL and rest 27m is sand. Excavated tunnel diameter
is 9 m and depth of crown from EGL is 11m. Some parameters such as tunnel
diameter, excavation method, excavation depth and forms of supports are constant in
this study but type of soil is changed based on location considered. According to
dimension presented in the Figures in this section the geometries of the models are
assigned in Subloading tij Model (Nakai and Hinokio, 2004).
85
Building is existed at one side of tunnel location at a distance of 20m from tunnel
centerline (Figure 3.21, 3.22). The load of building is applied as pile (Figure 3.21)
where the pile depth is 15m.and as footing load (Figure 3.22) where the footing width
is 4m. The building load is 957.85 kN (or 97.64 Ton) which is applied concentrically.
In Figure 3.23 buildings are existed at both sides at 11m distance from tunnel centre.
The loads of buildings are applied as pile load where the pile depth is 15m.
Figure 3.20 Tunnel excavation geometry in green field or open space in NATM
Figure 3.21 Tunnel excavation geometry with pile foundation in NATM
86
Figure 3.22 Tunnel excavation geometry with shallow foundation in NATM
Figure 3.23 Tunnel excavation geometry with pile foundation at both sides of tunnel
in NATM
87
Chapter Four
RESULTS AND DISCUSSIONS
4.1 Introduction
Two-dimensional finite element analyses are carried out with FEMtij-2D considering
plane strain drained condition. The small strain theory is used in the numerical
simulation. The constitutive law used in this numerical analysis is the Subloading tij
model (Nakai and Hinokio, 2004). The results of conventional and finite element
analyses for underground metro rail tunnel have been presented in this chapter. The
characteristics and behaviors of retaining systems and stability of tunnel structure for
Cut and Cover and NATM in various loading cases have been depicted. Effects of
presence of water table have also been considered to design the retaining system in
Cut and Cover method. The behaviors of retaining system are characterized by lateral
deformation, earth pressure, shear strain, volume stress, normal stresses, and
displacement vector and also by surface settlement. In case of NATM, the stability of
the method is illustrated by surface settlement, shear strain, lining pressure,
displacement vector diagram. A comparative study has also been made for lateral
deformation, earth pressure and critical design values of structural components
between the conventional analysis and numerical analysis for some retaining systems
of Cut and Cover method. Thus the appropriate excavation method throughout the
propose route of Dhaka city can be visualized.
4.2 Sub-soil Profile along the Study Route
Four locations- Uttara, Mohakhali, Farmgate and near DU campus along the proposed
MRT-4 route have been selected for sub-soil analysis. Sub-soil profile along MRT-4
considering the selected study areas is shown in Figure 4.1. From the borelogs data of
Dhaka city along the study route, it has been found that the SPT N-value varies from
1 to 8 up to depth of 10m to 12m. From 15m to 30m depth SPT N-value varies from
20 to 50. It reveals that the soil up to 10m to 12m depth is of soft consistency and
88
below 12m level soil is of very stiff to hard consistency according to Terzaghi and
Peck (1948 and 1967).
At Uttara along the proposed route, it is found that the top formation of soil is clayey
silt extends roughly to the depth of 16m. The subsequent layer of soil is sandy silt
which goes up to the depth of 25m. The soil below up to 30m depth exhibits fine
sand. At Mohakhali site it is found that the top stratification consists of clayey silt up
to the maximum depth of about 6.0m and the rest soil up to 18m depth exhibits fine
sand. At Farmgate, top 6.5m is silty clay, then the subsequent layer is silty sand up to
18.5m and it follows fine sand up to the boring depth which is 30.5m. The top of soil
formation near the DU campus displays clayey and silty clayey soil up to near 7.5m to
9.0m depth. The consecutive layer is silty sand and fine sand up to 18m depth.
Physical and Index Properties
From the soil report analysis and laboratory test, the physical and index properties of
the subsoil formation along the proposed route of Dhaka are arranged in Table 4.1 and
Table 4.2. Gradation curves along study route with sandy soil and clayey soil are
shown in Figure 4.2 (a) and (b).
Table 4.1 Grain size distribution of the fine sand layer and clay layer
Layer Sand (%) Silt (%) Clay (%) Median Grain Size, D50 (mm)
Silty clay 02~12 47~68 26~41 -
Silty fine sand 45~89 11~45 0~14 0.035~0.15
Table 4.2 Index and physical properties of fine sand and clay layer Soil Parameters DU Campus Farmgate Mohakhali Uttara
Specific Gravity, Gs 2.70~2.71 2.68 2.68~2.69 2.66~2.68
Dry Unit Weight, γd (kN/m3) 15.79~16.20 14.65~14.96 15.07~15.86 14.11
Natural Moisture Content (%) 23.0~23.2 24.5~26.7 23.8~26.0 26.0~40.0
Liquid Limit, LL (%) 49~50 52~53 48 45~56
Plastic Limit, PL (%) 18~22 24~25 21 25~28
Plasticity Index, PI (%) 29~31 28 27 20~28
89
4.2.1 Sub-soil Profile
Figure 4.1 Sub-soil profile along MRT-4 line in Dhaka city
90
0
20
40
60
80
100
0.0001 0.001 0.01 0.1 1 10 100
MohakhaliFarmgate-1Farmgate-2DU Campus-1DU Campus-2Uttara-1Uttara-2
Perc
ent F
iner
(%)
Particle Size (mm)
0
20
40
60
80
100
0.0001 0.001 0.01 0.1 1 10
MohakhaliFarmgate-1Farmgate-2DU CampusUttara-1Uttara-2
Perc
ent F
iner
(%)
Particle Size (mm)
Figure 4.2 Gradation curve along study route: (a) sandy soil and (b) clayey soil
Strength Properties
Strength properties of clay and sand layer for the selected locations along the MRT
line-4 are summarized in tabulator as well as in graphical forms which have been
presented in Table 4.3 and Figure 4.3.
To study strength properties, unconfined compressive strength tests have been carried
out on undisturbed samples. The resulted compressive stress versus axial strain curves
is presented in Figure 4.3. From the stress-strain data, compressive strength (σ) or
(a)
(b)
91
unconfined compressive strength (qu) and axial strain (Ԑ) at failure have been
determined. The average value of σ u varied in the range 62 to 139 kPa. Based on the
values the undrained shear strength, which is half of the unconfined compressive
strength was found to vary from 31 to 70 kPa, while axial strain at failure varied
between 4 to 13%.
From the Direct-shear tests in Figure 4.4 (b), it is found that the angle of friction
varies from 32o to 42o.
Table 4.3 Strength properties of clay layer
Soil Parameters DU Campus Farmgate Mohakhali Uttara
Unconfined Compressive
Strength, qu (kPa)
110~139 112~119
89~134 62
Failure Strain, εf (%) 6~8 10~12 6~10 14
Dry Unit Weight, γd (kN/m3) 15.50~15.90 14.90 15.00~15.80 14.10
Moisture Content (%) 23.0~23.8 24.5~24.8 23.7~26.0 34.5
0
40
80
120
160
200
240
0 3 6 9 12 15
Mohakhali-1Mohakhali-2Farmgate-1Farmgate-2DU-1DU-2Uttara
Com
pres
sive
Stre
ss,
(
kPa)
Axial Strain, a (%)
Figure 4.3 Unconfined compression test analysis along study route
92
Table 4.4 Strength properties of fine sand layer in Dhaka soil
Soil Parameters DU Campus Farmgate
Angle of Internal Friction, (deg.) 32~35 41~42
Cohesion, c (kPa) 0 0
Unit Weight, γ (kN/m2) 15.79~16.16 16.18~16.39
Moisture Content, w (%) 16.1~23.2 13.1~15.2
0
50
100
150
200
250
300
1 2 3 4 5 6 7 8 9
Farmgate-1(a)Farmgate-1(b)Farmgate-1(c)Farmgate-2(a)Farmgate-2(b)Farmgate-2(c)DU-1(a)DU-1(b)DU-2(a)DU-2(b)DU-2(c)Sh
ear S
tress
, kN
/m2
Shear Displacement, mm
0
50
100
150
200
250
300
350
0 50 100 150 200 250 300 350
Farmgate-1
Farmgate-2
DU-1
DU-2
Peak
She
ar S
tress
, kPa
Effective Normal Stress, kPa
Figure 4.4 Direct shear test analysis along study route, (a) effective normal stress
versus peak shear stress; (b) shear displacement versus shear stress
(a)
(b)
93
From the consolidation test of clayey soil as shown in Figure 4.5, it has been found
that the initial void ratio varies from 0.71 to 0.757 and critical void ratio ranges from
0.695 to 0.742. The virgin compression index varies from 0.115 to 0.2 whereas the
unloading compression index ranges from 0.0125 to 0.04.
From the triaxial CU test, the raw data and results have been analyzed. The effective
stress strength parameters have been determined from the test. The effective strength
grew as the initial confining pressure increased. The failure envelope was defined as
the best-fit-line tangent to all three samples (in Figure 4.6). The friction angle and the
cohesion values found from the graph is 60 and 78 kPa respectively. From Figure 4.7
the friction angle for sand is 320.
Table 4.5 Strength properties of clay layer in Dhaka soil
Soil Parameters Farmgate DU Campus
Initial Void Ratio, eo 0.710~0.757 0.735~0.749
Virgin Compression Index, Cc or λ 0.115~0.135 0.16~0.20
Unloading Compresssion Index, κ 0.0125~0.0189 0.04
Critical Void Ratio, eN 0.713~0.742 0.710~0.695
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
1 10 100 1000
Farmgate-1Farmgate-2DU Campus-1DU Campus-2
Voi
d R
atio
, e
Pressure, P (kPa or kN/m2) Figure 4.5 Consolidation test analysis along study route
94
Figure 4.6 Failure envelops for triaxial consolidated undrained test of clayey soil
126 427141 4970
100
200
300
400
500
0 100 200 300 400 500
Effe
ctiv
e She
ar st
ress
, τ (k
Pa)
Effective Normal Stress, σ (kPa)
Mohr-Circle 1 Mohr-Circle 3
Figure 4.7 Failure envelops for triaxial consolidated undrained test of sandy soil
From the triaxial CU test for clayey soil, the relation between deviator stress and
vertical strain and between excess pore pressure and vertical strain have been plotted
which are shown in Figure 4.8 (a) and (b). Also, graph of stress ratio versus vertical
95
strain and graph of deviator stress versus mean effective stress have been plotted in
Figure 4.9 (a) and (b). From the graph of stress ratio versus vertical strain of Figure
4.8, critical stress ratio is found as 3.6 which is an important parameter for model
analysis by Subloading tij model (Nakai and Hinokio, 2004).
Though in this study triaxial CU test has been conducted for sandy soil, the triaxial
consolidated drained (CD) test gives better and accurate parameters. For sandy soil
the triaxial CU test gives the relation between deviator stress and vertical strain and
between excess pore pressure and vertical strain which are plotted in Figure 4.10 (a)
and (b). Also, graph of stress ratio versus vertical strain and graph of deviator stress
versus mean effective stress have been plotted in Figure 4.11 (a) and (b). From Figure
4.11 (a), critical stress ratio is found as 1.8 for sand.
96
Figure 4.8 Resulted graphs from triaxial CU test for clayey soil: (a) deviator stress
versus vertical strain and (b) excess pore pressure versus vertical strain
(a)
(b)
97
Figure 4.9 Resulted graphs from triaxial CU test for clayey soil: (a) stress ratio versus
vertical strain and (b) deviator stress versus mean effective stress
(a)
(b)
98
0
20
40
60
80
100
120
140
160
180
200
0 5 10 15 20 25 30
Dev
iato
r stre
ss, q
(kPa
)
Vertical strain, (%)
100 kPa Effective Confining Pressure
200 kPa Effective Confining Pressure
300 kPa Effective Confining Pressure
Figure 4.10 Resulted graphs from triaxial CU test for sandy soil: (a) deviator stress
versus vertical strain and (b) excess pore pressure versus vertical strain
(a)
(b)
99
Figure 4.11 Resulted graphs from triaxial CU test for sandy soil: (a) stress ratio
versus vertical strain and (b) deviator stress versus mean effective stress
(a)
(b)
100
4.2.2 Soil Parameters Used for Analysis
Conventional Analysis: In order to conduct the conventional analysis in this study the
soil parameters obtained in this study are summarized in Table 4.5.
Table 4.6 Location wise soil parameters required for conventional analysis of retaining system
Location Type
of
soil
Depth
(m)
Cohesion,
c (kPa)
Angle
of
internal
friction,
φ
(degree)
Specific
gravity,
Gs
Dry unit
weight,
γs
(kN/m3)
Moisture
content,
w (%)
Coefficient
of
permeability
, kx=ky (m/s)
Uttara Clay 16.0 62.0 0 2.73 14.10 34.5 1.4 x 10-5
(for silty
sand)
7 x 10-7
(for clay)
Sand 14.0 0 30 2.70 16.00 14.0
Mohakhali Clay 6.0 111.5 0 2.72 15.40 24.9
Sand 12.0 0 30 2.70 15.80 16.0
Farmgate Clay 6.0 115.5 0 2.71 14.90 24.7
Sand 24.5 0 36 2.67 16.28 14.2
DU campus Clay 9.0 124.5 0 2.65 15.70 23.4
Sand 9.0 0 33.5 2.68 15.98 19.7
Numerical Analysis: All the required parameters of the subloading tij model (Nakai
and Hinokio, 2004) defining the mechanical behavior of soil layers are summarized in
Table 4.6. The related graphs of simulation of elasto-plastic model parameters are
shown in Figure 4.12a and b. Figure 4.12b shows the positive and negative dilatancy
of sandy soil. The parameters for the sandy soil have been simulated from
consolidated undrained test. However, for more accurate result consolidated drained
needs to be conducted.
101
0 5 10 15 20 251
1.2
1.4
1.6
1.8
2
Str
ess
rati
o (
1/
3)
1 (%)
Obs. Com. 100kPa 300kPa
0 50 100 150 200 250 300 3500
50
100
150
200
Dev
iato
ric
stre
ss,
q (
kP
a)
Mean stress, p (kPa)
Obs. Com. 100kPa 300kPa
Figure 4.12 Resulted simulations for model parameters of sandy soil: (a) stress-strain
dilatancy relation for the mass of soil and (b) deviatoric stress versus mean stress
(b)
(a)
102
Table 4.7 Model parameters of soil required for Subloading tij model
Type
of
soil
λ κ RCS =
(σ1/σ3)CS(comp.)
OCR N (eN at
p=98 kPa)
eo υ β aAF
Clay 0.125
~0.18
0.0157~
0.04 3.6 -
0.7025~
0.7275
0.734~
0.742 0.2 1.5 600
Sand 0.088 0.015 1.64 - 0.75 0.6 0.2 2.0 600
Note: λ = Compression index (or slope of virgin loading curve in e-log p’ curve at the
loosest state).
κ = Swelling index (or slope of unloading-reloading curve in e-log p’ curve at the
loosest state where, e is void ratio and p’ is consolidation pressure).
RCS = (1/3)cs(comp.) = Critical state stress ratio.
OCR = Overconsolidation Ratio.
N or eN = Reference void ratio on normally consolidation line at p= 98 kPa& q= 0 kPa
(or void ratio at mean principal stresses (p) 98 kPa in e-log p’ curve).
eo= Initial void ratio.
υ = Poisson’s ratio.
β = Model parameter responsible for the shape of the yield surface.
a = Model parameter responsible for the influence of density and confining pressure.
4.3 Result Analysis
The results of this study have been analyzed by performing both conventional and
finite element method. The behaviors of different types of soil layers are simulated by
the Subloading tij model (Nakai and Hinokio, 2004) under FEMtij_2D elasto-plastic
static analysis considering plane strain drained condition. Different loading conditions
have been considered for Cut and Cover as well as NATM. Effects of presence of
water table have also been considered to design the retaining system. In case of Cut
and Cover excavation method, the behaviors of retaining system are characterized by
lateral deformation, earth pressure, shear strain, volume stress, normal stresses, and
displacement vector and also by surface settlement. And, in the same case the stability
of tunnel structure have also been observed. In case of NATM, the stability of the
103
method is illustrated by surface settlement, shear strain, lining pressure, displacement
vector diagram to determine the stability of the excavation method throughout the
propose route of Dhaka city.
4.3.1 Conventional Analysis of Retaining System
Conventional analysis of sheet pile with bracings and diaphragm wall with bracings
for different location with different conditions have been summarized below. A brief
description of the analyzed results for Farmgate and Mohakhali areas with an
excavation depth of 12m has been given at first and the rest results are presented in a
tabular form in Table 4.8 and Table 4.9.
4.3.1.1 Braced Cut Sheet Pile: (Location: Farmgate and Mohakhali with depth of
excavation: 12m)
The top 6m soil layer is clay and the rest 9m is sandy soil. The depth of tensile crack
is found as 15.5m (Appendix-I). So, the 1st strut is placed at the depth of 3m from the
EGL and other struts are placed at 3m spacing c/c. The equivalent cohesion and
average unit weight and apparent pressure are calculated following resulted earth
pressure diagram as per Peck (1969). The lateral earth pressure is shown in Fig. 4.13.
The maximum apparent earth pressure is found to be 56.124 kN/m2.
Figure 4.13 Earth pressure diagram for braced cut sheet pile for excavation depth of
12m (Farmgate)
104
Figure 4.14 Shear force diagram and bending moment diagram (Farmgate)
Strut loads at level A, B and C are also determined. The detailed calculations have
been described in Appendix-I. The shear force diagram and bending moment diagram
have been shown in Figure 4.14. Maximum moment for sheet pile is found as 84.186
kN-m/m of wall. And, the sectional modulus is calculated as 509 cm3/m of wall. The
105
selected Wales are W 46074 for levels A, C and W 25067 for level B. The selected
strut is W 31032.7 for levels A, C.
4.3.1.2 Braced Cut Diaphragm Wall: (Location: Farmgate and Mohakhali with
depth of excavation: 12m)
The depth and thickness of diaphragm wall are taken as 12m and 0.5m, respectively.
Each panel width of diaphragm wall is 4m. From braced cuts of sheet pile, the
maximum moment at levels A and C is 84.186 kN-m/m of wall. For the design of
diaphragm wall, column strength interaction diagram for rectangular section (with
bars on end faces) with γ=0.75 has been used.
From the interaction diagram, minimum i.e., 1% reinforcement is required to provide
for the critical moment value. So, the vertical rod is found as 20 Nos 25mm dia. @
175 mm c/c (both phases) and the horizontal rod is found as 33 no’s 16mm Dia. @
350 mm c/c (both phases). The design details of diaphragm wall is shown in Figure
4.15.
Figure 4.15 Diaphragm wall reinforcement details
106
Table 4.8 Conventional analysis of retaining system with design sections Area Farmgate
Depth of excavation 15 m Earth pressure diagram
Maximum moment for retaining wall
-84.95 kN-m
Sectional modulus of wall 514 cm3/m of wall Section of sheet pile
Section of diaphragm wall
Moment and section of Wale
Level A 241.40 kN-m W 460 x 74; Sx= 1460 cm3
Level B 206.57 kN-m W 360 x 79; Sx= 1280 cm3
Level C 206.57 kN-m W 360 x 79; Sx= 1280 cm3
Level D 241.40 kN-m W 460 x 74; Sx= 1460 cm3
Strut Load and resultant section
Level A 643.74 kN W 310 x 38.7; Sx= 549 cm3
Level B 550.86 kN
Level C 643.74 kN W 310 x 38.7; Sx= 549 cm3
Level D 550.86 kN
107
Table 4.9 Conventional analysis of retaining system with design sections. Area Uttara DU Area
Depth of excavation
12 m 12 m
Earth pressure diagram
Maximum moment for Retaining wall
-76.14 kN-m -85.16 kN-m
Sectional modulus of wall
460 cm3/m of wall 515 cm3/m of wall.
Section of Sheet pile
Section of diaphragm wall
Wale’s moment and section
Level A
199.87 kN-m W 360 x 79; Sx= 1280 cm3
223.54 kN-m W 460 x 74; Sx= 1460 cm3
Level B
114.21 kN-m W 360x44; Sx= 693 cm3
127.73 kN-m 127.73 kN-m
Level C
199.87 kN-m W 360 x 79; Sx= 1280 cm3
223.54 kN-m W 460 x 74; Sx= 1460 cm3
Level D
--- -----
Strut Load and resultant section
Level A
532.98 kN W 310 x 32.7; Sx= 415 cm3
596.1 kN W 310 x 32.7; Sx= 415 cm3
Level B
304.56 kN 340.62 kN
Level C
532.98 kN W 310 x 32.7; Sx= 415 cm3
596.1 kN W 310 x 32.7; Sx= 415 cm3
Level D
----- ------
108
4.3.2 Numerical Analysis by Subloading tij Model for Cut and Cover Method
Using Subloading tij model (Nakai and Hinokio, 2004), Cut and Cover excavation
method with different retaining systems have been performed for different loading
cases and conditions (Case 1 to Case 4). Case 1 considers the greenfield condition
without external load and neglecting water table effects. Case 2 represents the effect
of application of building load on retaining wall and tunnel. Case 3 considers the
effect of water table without external load. Case 4 represents the effect of water table
with external load. Results obtained from the analyses are described case by cases in
this section.
4.3.2.1 Sheet Pile with Braced Cut System: Case 1 (Greenfield Condition)
Geometry
The geometry for the greenfield condition without any external load is presented in
Figures 4.16, 4.17 and 4.18. In these figures, modeled sub-soil is 30m deep from the
ground surface and 98.0m wide with 49.0 m horizontally extended toward both left
and right direction from the excavated centerline. Here, 49.0 m is about 4.9 times the
excavation width, which is sufficient to substantially reduce the boundary effects in
the numerical model. The top soil is clayey soil up to 6m depth from EGL and the
bottom part is 24m which is sand. Depth of excavation is 12m and width is 10m.
Depth of sheet pile is 18m from EGL.
Figure 4.16 Geometry for sheet pile with braced cut after bracing
109
Figure 4.17 Geometry for sheet pile with braced cut after tunnel placement
Figure 4.18 Geometry for sheet pile with braced cut after backfilling
Mesh, Types of Elements and Boundary Conditions
The mesh (Figure 4.19) is applied in 5 zones along x-direction and in 3 zones along y-
direction according to the divisions as shown in Figure 4.16 to 4.18. The position of
excavated area is located in 3rd zone along the x-direction. The isoparametric 4-noded
(quadrilateral) elements have been used to represent the soil. The 2-noded beam
elements have been used to simulate sheet pile. Smooth boundary conditions have
been applied at bottom, left and right edges of the mesh. At bottom both vertical and
horizontal displacement are fixed. At left and right edges, horizontal displacements
are fixed and vertical displacement is made free.
110
Figure 4.19 Mesh for sheet pile with braced cut: (a) mesh used for greenfield
condition and (b) mesh showing the soil layers (the top green part is clay and the
bottom red part is sand)
Lateral Displacement
The distribution of lateral displacement of sheet pile wall after the completion of
bracing systems, tunnel placement and backfilling are presented in Figure 4.20, 4.21
and 4.22, respectively. In all cases, pattern of displacement follows the typical
deformation shape of braced cut wall. Here, the braced wall’s upper portion is
restrained from undergoing large horizontal movement. From these graphs it has been
seen that, the maximum horizontal displacement occurs after completion of
excavation (100%) and the displacement is 18.8mm.
(a)
(b)
111
-0.0143
-0.0188
0.0
5.0
10.0
15.0
20.0
25.0
30.0-0.0400 -0.0300 -0.0200 -0.0100 0.0000 0.0100 0.0200 0.0300 0.0400
Dis
tanc
e fr
om e
xcav
ted
leve
l (m
)
Lateral deflection at right edge of excavation (m)
8.33% Excavation
16.67% Excavation
33.33% Excavation
58.33% Excavation
83.33% Excavation
100% Excavation
Bottom GL of excavated part
Bottom GL of Excavated Part
EGL (+-0.00)
Figure 4.20 Distribution of lateral displacement for sheet pile with braced cut after
bracing
-0.0093
-0.0188
0.0
5.0
10.0
15.0
20.0
25.0
30.0-0.0400 -0.0300 -0.0200 -0.0100 0.0000 0.0100 0.0200 0.0300 0.0400
Dis
tanc
e fr
om e
xcav
ted
leve
l (m
)
Lateral deflection at right edge of excavation (m)
8.33% Excavation
16.67% Excavation
50% Excavation
83.33% Excavation
100% Excavation
100% Excavation with Tunnel
Bottom GL of excavated part
Bottom GL of Excavated Part
EGL (+-0.00)
Figure 4.21 Distribution of lateral displacement for sheet pile with braced cut after
tunnel placement
112
-0.0093
-0.0187
0.0
5.0
10.0
15.0
20.0
25.0
30.0-0.0400 -0.0300 -0.0200 -0.0100 0.0000 0.0100 0.0200 0.0300 0.0400
Dis
tanc
e fr
om e
xcav
ted
leve
l (m
)
Lateral deflection at right edge of excavation (m)
8.33% Excavation
16.67% Excavation
50% Excavation
83.33% Excavation
100% Excavation
100% Excavation with Backfill
Bottom GL of excavated part
Bottom GL of Excavated Part
EGL (+-0.00)
Figure 4.22 Distribution of lateral displacement for braced sheet pile after backfilling
Earth Pressure Distribution
The earth pressure diagram for sheet pile with braced cut is presented in Figure 4.23.
From the graph it is seen that, the maximum earth pressure is 138.32 kN/m2.
138.321.32E+02
0
5
10
15
20
25
30
35
0 20 40 60 80 100 120 140 160
Dep
th fr
om b
otto
m o
f exc
avat
ion
(m)
Earth pressure (kN/m2)
After Bracing Fixation
After Tunnel Placement
After Backfilling
Figure 4.23 Earth pressure diagram for braced sheet pile (greenfield condition)
113
Surface Settlement
The surface settlement curve for sheet pile with braced cut in greenfield condition is
presented in Figure 4.24. From this graph it is seen that, the maximum settlement is
6.4mm which is insignificant compare to the depth of excavation which is 12m. In
this figure, it can be also seen that the value of surface settlement is abnormally high
at the interface of the retaining wall and soil. This might be due to the fact that in the
analysis no joint element at the interface has been used.
-0.0064 -0.0064
-0.0080
-0.0060
-0.0040
-0.0020
0.0000
0.0020
0.0040
0.0060
0.0080
0 10 20 30 40 50 60 70 80 90 100
Settl
emen
t (m
)
Surface distance (m)
8.33% Excavation
16.67% Excavation
33.33% Excavation
50% Excavation
66.67% Excavation
83.33% Excavation
100% Excavation
Edge Line
Figure 4.24 Surface settlements for sheet pile with braced cut (greenfield condition)
4.3.2.2 Sheet Pile with Braced Cut System: Case 2 (Building with Shallow
Foundation Condition)
Geometry
The geometry with footing as foundation of building is presented in Figure 4.25a, b
and c. In these figures, modeled sub-soil is 30m deep from the ground surface and
98.0m wide with 49.0 m horizontally extended toward both left and right direction
from the excavated centerline. Here, 49.0 m is about 4.9 times the excavation width,
which is sufficient to substantially reduce the boundary effects in numerical model.
114
Figure 4.25 Geometry for braced sheet pile with shallow foundation: (a) after
bracing, (b) after tunnel placement and (c) after backfilling
(a)
(b)
(c)
115
The top soil is clayey soil up to 6m depth from EGL and the bottom part is 24m which
is sand. Depth of excavation is 12m and width is 10m. Depth of sheet pile is 18m
from EGL. The footing is located at 16m distance from nearest excavated edge and
the footing width is 4m. The building load is 637.65 kN (or 65.00 Ton) which is
applied concentrically at centre node of footing.
Mesh, Types of Elements and Boundary Conditions
The mesh (Figure 4.26) is applied in 5 zones along x-direction and in 3 zones along y-
direction according to the divisions as shown in Figure 4.25a, b and c. The position of
excavated area is located in 3rd zone along the x-direction. The isoparametric 4-noded
(quadrilateral) elements have been used to represent the soil and concrete materials.
The 2-noded beam elements have been used to simulate sheet pile. And, the 4-noded
joint element (elasto plastic joint element by Nakai, 1985-an extension of goodman
type joint element) has been used to represent the interface of soil and footing bottom
face. The smooth boundary conditions have been applied at bottom, left and right
edges of the mesh. At bottom both vertical and horizontal displacement are fixed. At
left and right edges, horizontal displacements are fixed and vertical displacement is
made free.
Lateral Displacement
The distribution of lateral displacement of sheet pile wall considering building load
after the completion of bracing systems, tunnel placement and backfilling are
presented in Figure 4.27, 4.28 and 4.29. In all cases, pattern of displacement follows
the typical deformation shape of braced cut wall. From these graphs it is found that,
the maximum horizontal displacement occurs after backfilling which is 36.4mm.
Earth Pressure Diagram
The earth pressure diagram for sheet pile with braced cut is presented in Figure 4.30.
From the figure the value of earth pressure is found as 165.79 kN/m2.
Surface Settlement
The surface settlement curve for sheet pile with braced cut with building load as
footing is depicted in Figure 4.31. From this graph it is seen that, the maximum
settlement is 7.9mm occurs at the side of footing position.
116
Figure 4.26 Mesh for sheet pile with braced cut with shallow foundation: (a) mesh
used for greenfield condition and (b) mesh showing the soil layers (the top green part
is clay and the bottom red part is sand)
-0.0148
-0.0232
0
5
10
15
20
25
30-0.0400 -0.0300 -0.0200 -0.0100 0.0000 0.0100 0.0200 0.0300 0.0400
Dis
tanc
e fr
om e
xcav
ted
leve
l (m
)
Lateral deflection at right edge of excavation (m)
8.33% Excavation
16.67% Excavation
50% Excavation
66.67% Excavation
83.33% Excavation
100% Excavation
Bottom GL of excavated part
Bottom GL of Excavated Part
EGL (+-0.00)
Figure 4.27 Distribution of lateral displacement for braced sheet pile after bracing
(a)
(b)
117
-0.0149
-0.0236
0
5
10
15
20
25
30-0.0400 -0.0300 -0.0200 -0.0100 0.0000 0.0100 0.0200 0.0300 0.0400
Dis
tanc
e fr
om e
xcav
ted
leve
l (m
)
Lateral deflection at right edge of excavation (m)
8.33% Excavation
33.33% Excavation
50% Excavation
66.67% Excavation
100% Excavation
100% Excavation with Tunnel
Bottom GL of excavated part
Bottom GL of Excavated Part
EGL (+-0.00)
Figure 4.28 Distribution of lateral displacement for braced sheet pile after tunnel
placement
-0.0215
-0.0364
0
5
10
15
20
25
30-0.0500 -0.0400 -0.0300 -0.0200 -0.0100 0.0000 0.0100 0.0200 0.0300 0.0400
Dis
tanc
e fr
om e
xcav
ted
leve
l (m
)
Lateral deflection at right edge of excavation (m)
8.33% Excavation
33.33% Excavation
66.67% Excavation
100% Excavations
100% Excavation after Backfill
Bottom GL of excavated part
Bottom GL of Excavated Part
EGL (+-0.00)
Figure 4.29 Distribution of lateral displacement for braced sheet pile after backfilling
118
155.98165.79
0
5
10
15
20
25
30
35
0 20 40 60 80 100 120 140 160 180
Dep
th fr
om b
otto
m o
f exc
avat
ion
(m)
Earth Pressure (kN/m2)
After Bracing Fixation
After Tunnel Placement
After Backfilling
Figure 4.30 Earth pressure diagrams of lateral displacement for braced sheet pile with
shallow foundation
-0.0076 -0.0079
-0.0004
-0.0100
-0.0050
0.0000
0.0050
0 10 20 30 40 50 60 70 80 90 100
Settl
emen
t (m
)
Surface distance (m)
8.33% Excavation
33.33% Excavation
58.33% Excavation
83.33% Excavation
100% Excavation
Edge Line
Figure 4.31 Surface settlement for braced sheet pile with shallow foundation
119
4.3.2.3 Sheet Pile with Braced Cut System: Case 3 (Presence of Water Table at
EGL in Greenfield Condition)
Geometry
The geometry in greenfield condition considering the effects of water is presented in
Figure 4.32. The water table is at EGL. In this figure, modeled sub-soil is 30m deep
from the ground surface and 98.0m wide with 49.0 m horizontally extended toward
both left and right direction from the excavated centerline. Here, 49.0 m is about 4.9
times the excavation width, which is sufficient to substantially reduce the boundary
effects in numerical model. The top soil is clayey soil up to 6m depth from EGL and
the bottom part is 24m which is sand. Depth of excavation is 12m and width is 10m.
Depth of sheet pile is 18m from EGL. No external load is considered in this case.
Figure 4.32 Geometry for sheet pile with braced cut considering water table at EGL
in Greenfield condition
Elements and Boundary Conditions
The isoparametric 4-noded (quadrilateral) elements have been used to represent the
soils. The 2-noded beam elements have been used to simulate sheet pile. Smooth
boundary conditions have been applied considering both vertical and horizontal
displacement are fixed at bottom, horizontal displacements are fixed and vertical
displacement is made free at left and right edges of mesh. Due to the presence of
water, drainage boundary condition is applied. The ground surface is made drained
condition. The bottom of the base of model is set as undrained or impermeable
120
condition. Also, both left and right edged vertical boundaries are assumed as
undrained.
Lateral Displacement
The distribution of lateral displacement of sheet pile wall considering water table at
EGL in greenfield condition is presented in Figure 4.33. From the curve it is found
that the pattern of displacement follows the typical deformation shape of braced cut
wall. But due to presence of water the deformation is high. From the graph it is found
that, the maximum horizontal displacement of wall is as large as 220mm which is
because no joint elements have been simulated at interface of sheet pile wall and soil.
Earth Pressure Diagram
The earth pressure diagram for sheet pile with braced cut with effects of water is
shown in Figure 4.34. The maximum earth pressure is found to be 66.51 kN/m2.
Surface Settlement
The surface settlement curve for braced sheet pile with effects of water and building
load depicted in Figure 4.35. It is found that the maximum settlement is 172mm.
-0.1478
-0.2200
0
5
10
15
20
25
30-0.2500 -0.2000 -0.1500 -0.1000 -0.0500 0.0000 0.0500
Dis
tanc
e fr
om e
xcav
ted
leve
l (m
)
Lateral deflection at right edge of excavation (m)
8.33% Excavation
33.33% Excavation
50% Excavation
66.67% Excavation
83.33% Excavation
100% Excavation
Bottom GL of excavated part
Bottom GL of Excavated Part
EGL (+-0.00)
Figure 4.33 Distribution of lateral displacement for sheet pile with braced cut
considering water table at EGL in greenfield condition
121
66.51
56.60
0
5
10
15
20
25
30
35
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00
Dep
th fr
om b
otto
m o
f exc
avat
ion
(m)
Earth pressure (kN/m2)
Figure 4.34 Earth pressure diagrams for braced sheet pile with WT at EGL
-1.72E-01 -1.72E-01
-0.2000
-0.1800
-0.1600
-0.1400
-0.1200
-0.1000
-0.0800
-0.0600
-0.0400
-0.0200
0.0000
0.0200
0 10 20 30 40 50 60 70 80 90 100
Settl
emen
t (m
)
Surface distance (m)
8.33% Excavation
33.33% Excavation
50% Excavation
66.67% Excavation
83.33% Excavation
100% Excavation
Edge Line
Figure 4.35 Surface settlements for sheet pile with braced cut considering water table
122
4.3.2.4 Sheet Pile with Braced Cut System: Case 4 (Presence of Water Table at
EGL with Building Load Condition)
Geometry
The geometry with footing as foundation of building considering water effects is
presented in Figure 4.36. In this figure, modeled sub-soil is 30m deep from the ground
surface and 98.0m wide with 49.0 m horizontally extended toward both left and right
direction from the excavated centerline. Here, 49.0 m is about 4.9 times the
excavation width, which is sufficient to substantially reduce the boundary effects in
numerical model. The top soil is clayey soil up to 6m depth from EGL and the bottom
part is 24m which is sand. Depth of excavation is 12m and width is 10m. Depth of
sheet pile is 18m from EGL. The building foundation or footing is located at 16m
distance from nearest excavated edge and the footing width is 4m. The building load
is 637.65 kN (or 65.00 Ton) which is applied concentrically at centre node of footing.
Figure 4.36 Geometry for sheet pile with braced cut considering water table with
shallow foundation
Elements and Boundary Conditions
The 4-noded quadrilateral elements have been used to represent the soil and concrete
materials. The 2-noded beam elements have been used to simulate sheet pile. And, the
4-noded joint elements (elasto plastic joint element by Nakai, 1985-an extension of
goodman type joint element) have been used to represent the interface of soil and
footing bottom face. Smooth boundary conditions have been applied at bottom, left
and right edges of the mesh. At bottom both vertical and horizontal displacement are
123
fixed. At left and right edges, horizontal displacements are fixed and vertical
displacement is made free. Due to the presence of water, drainage boundary condition
is applied. The ground surface is made drained condition. The bottom of the base of
model is set as undrained or impermeable condition. Also, both left and right edged
vertical boundaries are assumed as undrained.
Lateral Displacement
The distribution of lateral displacement of sheet pile wall considering building load
and effects of water is presented in Figure 4.37. In this case, the pattern of
displacement follows the typical deformation shape of braced cut wall but the bulging
effect of deformation shape is highest compare to previous cases. It is found that, the
maximum horizontal displacement of wall is as large as 340.8mm. The reason is no
joint elements have been used to simulate the interface of retaining wall and soil.
Earth Pressure Diagram
The earth pressure diagram for braced sheet pile with effects of water and building
load is shown in Figure 4.38. The maximum earth pressure is found as 72.01 kN/m2.
-0.4069
-0.3408
0
5
10
15
20
25
30-0.4500 -0.4000 -0.3500 -0.3000 -0.2500 -0.2000 -0.1500 -0.1000 -0.0500 0.0000 0.0500 0.1000
Dis
tanc
e fr
om e
xcav
ted
leve
l (m
)
Lateral deflection at right edge of excavation (m)
8.33% Excavation
33.33% Excavation
50% Excavation
66.67% Excavation
83.33% Excavation
100% Excavation
Bottom GL of excavated part Bottom GL of Excavated Part
EGL (+-0.00)
Figure 4.37 Distribution of lateral displacement for sheet pile with braced cut
considering water table with shallow foundation
124
72.0161.90
10
13
16
19
22
25
28
0 10 20 30 40 50 60 70 80
Dep
th fr
om b
otto
m o
f exc
avat
ion
(m)
Earth pressure (kN/m2)
Figure 4.38 Earth pressure diagrams for sheet pile with braced cut considering water
table with building load
-0.1748
-0.3527
-3.66E-02
-0.4000
-0.3500
-0.3000
-0.2500
-0.2000
-0.1500
-0.1000
-0.0500
0.0000
0.0500
0.1000
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
Settl
emen
t (m
)
Surface distance (m)
8.33% Excavation
33.33% Excavation
50% Excavation
66.67% Excavation
83.33% Excavation
100% Excavation
Edge Line
Figure 4.39 Surface settlements for sheet pile with braced cut considering water table
and building load
125
Surface Settlement
The surface settlement curve for braced sheet pile with effects of water and building
load depicted in Figure 4.39. From this graph it is seen that, the maximum settlement
is 352.7mm. This is very high and it is for the reason that no joint elements have been
used to simulate the interface of retaining wall and soil.
Bending Moment and Shear Force Diagram Case by Case
The shear force diagram and bending moment diagram of braced sheet pile wall for
all the four Cases (described in previous articles) are combined in Figure 4.40 and
4.41, respectively.
From the comparative figures, it is found that the Case 4 representing the effects of
both water and building load governs the critical design value. The maximum shear
force is found as 390.84 kN (Figure 4.40) and the critical moment is -394.17 kN-m/m
+316.31 kN-m/m (Figure 4.41).
390.84
-153.61
0
3
6
9
12
15
18
21
-200 -100 0 100 200 300 400 500
Dep
th b
elow
EG
L (m
)
WT+LoadWT+GreenfieldBuilding LoadGreenfield
Bottom line of excavation
Shear force (kN) at right sheet wall
Figure 4.40 Comparison of shear force diagram for different cases of braced sheet
pile
126
-394.17
316.31
0
3
6
9
12
15
18
21
-500 -400 -300 -200 -100 0 100 200 300 400
Dep
th b
elow
EG
L (m
)
Bending moment (kN-m) at right sheet wall
WT+LoadWT+GreenfieldBuilding LoadGreenfield
Bottom line of excavation
Figure 4.41 Comparison of bending moment diagram for different cases of braced
sheet pile
4.3.2.5 Sheet Pile with Braced Cut System: Case 5 (Greenfield Condition: Depth
of Sheet Pile and Excavation=12m)
Geometry
The geometry of braced sheet pile for greenfield condition without the effects of
water and external load is presented in Figure 4.43. Modeled sub-soil is 30m deep
from EGL and 98.0m wide. The top soil is clayey soil up to 6m depth from EGL and
the bottom part is 24m which is sand. Depth of excavation is 12m and width is 10m.
The depth of sheet pile is assumed 12m from EGL as equal to excavation depth.
Elements and Boundary Conditions
The 4-noded quadrilateral elements and 2-noded beam elements have been used to
simulate soil and sheet pile respectively. Smooth boundary conditions have been
applied at bottom, left and right edges of the mesh. At bottom both vertical and
horizontal displacement are fixed. At left and right edges, horizontal displacements
are fixed and vertical displacement is made free.
127
Figure 4.42 Geometry for braced sheet pile in Greenfield condition (depth of
sheetpile and excavation =12m)
Lateral Displacement
The distribution of lateral displacement of sheet pile wall in Greenfield condition is
presented in Figure 4.43. In this case, pattern of displacement follows the typical
deformation shape of braced cut wall. Here, the braced wall’s upper portion is
restrained from undergoing large horizontal movement. From these graphs it is found
that, the maximum horizontal displacement of wall is 40.6mm.
-5.84E-03
-0.0115
-0.0406
0.0
5.0
10.0
15.0
20.0
25.0
30.0-0.0500 -0.0400 -0.0300 -0.0200 -0.0100 0.0000 0.0100 0.0200 0.0300 0.0400
Dis
tanc
e fr
om e
xcav
ted
leve
l (m
)
Lateral deflection at right edge of excavation (m)
8.33% Excavation
16.67% Excavation
33.33% Excavation
58.33% Excavation
83.33% Excavation
100% Excavation
Bottom GL of excavated part
Bottom GL of Excavated Part
EGL (+-0.00)
Figure 4.43 Distribution of lateral displacement for braced sheet pile in greenfield
condition
128
Earth Pressure Distribution
The earth pressure diagram for braced sheet pile of this case is presented in Figure
4.44. From these graph it is seen that, the earth pressure is 72.59 kN/m2 at final stag of
loading.
72.59
12
15
18
21
24
27
30
0 10 20 30 40 50 60 70 80
Dep
th fr
om b
otto
m o
f exc
avat
ion
(m)
Earth pressure (kN/m2)
Greenfield Condition
Figure 4.44 Earth pressure diagrams for braced sheet pile in greenfield condition
Bending Moment and Shear Force Diagram
The shear force diagram and bending moment diagram of braced sheet pile wall in
greenfield condition are shown in Figure 4.45 and 4.46, respectively. The critical
shear force and moment for sheet pile are found as 112 kN and 162 kN-m/m of wall,
respectively.
Critical Axial Force
Strut loads at level 1st, 2nd and 3rd level points are presented in Table 4.10. The critical
design axial forces at 1st, 2nd and 3rd levels are 14.91 kN, 50.23 kN and 77.79 kN
respectively.
129
Table 4.10 Design axial force of struts
Design component
Axial force at 1st level (kN)
Axial force at 2nd level (kN)
Axial force at 3rd level (kN)
Strut 14.91 50.23 77.79
1.12E+02
-9.78E+01
3.05E+01
-4.71E+01
7.85E+00
-1.03E+01
0
3
6
9
12
15
-150.00 -100.00 -50.00 0.00 50.00 100.00 150.00
Dep
th b
elow
EG
L (m
)
Greenfield
Bottom line of excavation
Shear Force (kN) at right sheet wall
Figure 4.45 Shear force diagram for braced sheet pile in greenfield condition
1.62E+02
6.38E+01
0
3
6
9
12
15
-25.00 0.00 25.00 50.00 75.00 100.00 125.00 150.00 175.00
Dep
th b
elow
EG
L (m
)
Greenfield
Bottom line of excavation
Bending moment (kN-m) at right sheet wall
Figure 4.46 Bending moment diagram for braced sheet pile in greenfield condition
130
4.3.2.6 Diaphragm Wall with Braced Cut System: Greenfield Condition
Geometry
The geometry for the greenfield condition without any external load is presented in
Figures 4.47. In the figure, modeled sub-soil is 30m deep from the ground surface and
90m wide with 45.0 m horizontally extended toward both left and right direction from
the excavated centerline. Here, 45.0 m is about 4.5 times the excavation width, which
is sufficient to substantially reduce the boundary effects in the numerical model. The
top soil is clayey soil up to 6m depth from EGL and the bottom part is 24m which is
sand. Depth of excavation is 12m and width is 10m. Depth of diaphragm wall is 12m
from EGL.
Figure 4.47 Geometry for braced cut diaphragm wall after bracing
Mesh, Types of Elements and Boundary Conditions
The mesh (Figure 4.48) is applied in 7 zones along x-direction and in 3 zones along y-
direction according to the divisions as shown in Figure 4.47. The position of
excavated area is located in 5th zone along the x-direction. The isoparametric 4-noded
(quadrilateral) elements have been used to represent the soil and the concrete of
diaphragm wall. The 2-noded beam elements have been used to simulate the
reinforcement of diaphragm wall. Smooth boundary conditions have been applied at
bottom, left and right edges of the mesh. At bottom both vertical and horizontal
displacement are fixed. At left and right edges, horizontal displacements are fixed and
vertical displacement is made free.
131
Figure 4.48 Mesh for diaphragm wall with braced cut: (a) mesh used for greenfield
condition and (b) mesh showing the soil layers (the top green part is clay and the
bottom red part is sand)
Lateral Displacement
The distribution of lateral displacement of diaphragm wall after full completion of
bracing systems is represented in Figure 4.49. Here, the pattern of displacement
follows the typical deformation shape of braced cut wall. Here, the braced wall’s
upper portion is restrained from undergoing large horizontal movement. From the
graph it has been also seen that, the maximum horizontal displacement occurs after
completion of excavation (100%) and the displacement is 12.5mm.
Earth Pressure Distribution
The earth pressure diagram for diaphragm wall with braced cut is presented in Figure
4.50. From the graph it is seen that, the maximum earth pressure is 59.15 kN/m2.
(a)
(b)
132
-0.0032
-0.0125
0
5
10
15
20
25
30-0.0150 -0.0100 -0.0050 0.0000 0.0050 0.0100 0.0150
Dis
tanc
e fr
om e
xcav
ted
leve
l (m
)
Lateral deflection at right edge of excavation (m)
14.30% Excavation
28.57% Excavation
42.86% Excavation
71.43% Excavation
100% Excavation
Bottom GL of excavated part
Bottom GL of Excavated Part
EGL (+-0.00)
Figure 4.49 Distribution of lateral displacement for braced diaphragm wall
(Greenfield condition)
59.15
23.9418
20
22
24
26
28
30
32
0 10 20 30 40 50 60 70
Dep
th fr
om b
otto
m o
f exc
avat
ion
(m)
Earth pressure (kN/m2)
Greenfield Condition
Figure 4.50 Earth pressure diagram for braced diaphragm wall (Greenfield condition)
133
4.3.3 Comparison between Conventional and Numerical Analyses for Braced
Sheet Pile of Cut and Cover Method
A comparative analysis is made in results between the conventional and numerical
analysis for greenfield condition without any effects of water table and external
structural loads. The considerations for comparison are earth pressure, shear force and
bending moment retaining wall and axial force of strut which are described as below.
Comparison in Earth Pressure Diagram
The resulted earth pressure diagrams for conventional analysis and numerical analysis
are shown in Figure 4.51a and b. From these two diagrams it is found that the earth
pressures from conventional result is 56.124 kN/m2 and from numerical result is 72.6
kN/m2. The diagram pattern resembles slightly, though the conventional analysis
shows a sharp edged trapezoidal shape and numerical analysis shows some sought of
curvilinear shape.
Comparison in Shear Force Diagram
The comparison between shear force diagram of conventional analysis and numerical
analysis reveals the similarity as per shown diagrams in Figure 4.52a and b. In
conventional shear force diagram the tendency of symmetry is evident but in case
numerical analysis there is a tendency of increasing the shear force values with depth.
Comparison in Bending Moment Diagram
If the bending moment diagrams are analyzed by conventional analysis and numerical
analysis (as shown in Figure 4.53a and b), then it can be found that there exists a
tendency of increasing the bending moment value in numerical analysis unlike the
conventional analysis. In conventional analysis the moment values keep a harmonic
nature while going to depth.
Comparison in Axial Force
From the conventional analysis (as shown in Figure 4.14) the design axial force at 1st
level, 2nd level and 3rd level of struts are 196.43 kN, 112.25 kN and 196.43 kN
respectively. In the other hand, in numerical analysis as shown in Table 4.10, the
design axial forces at 1st level, 2nd level and 3rd level of struts are 14.91 kN, 50.23 kN
134
and 77.70 kN respectively. So in conventional case the maximum force is 196.43 kN
whereas in numerical case it is 77.70 kN. It can be said that the maximum axial force
value is greater in conventional case than in the case for numerical analysis.
8.84E+01
7.26E+01
3.61E+01
18.00
20.00
22.00
24.00
26.00
28.00
30.00
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
Dep
th fr
om b
otto
m o
f exc
avat
ion
(m)
Earth Pressure (kN/m2)
At 500 steps
At 2000 steps
At 4000steps
At 6000steps
Figure 4.51 Earth pressure diagram for braced cut sheet pile with depth of sheet pile
12m: (a) conventional analysis, (b) subloading tij model (Nakai and Hinokio, 2004)
(a)
(b)
135
111.863
-97.784
30.501
-47.073
7.848
-10.292
0
3
6
9
12
15
-150.00 -100.00 -50.00 0.00 50.00 100.00 150.00
Dep
th b
elow
EG
L (m
)
Greenfield
Bottom line of excavation
Shear Force (kN) at right sheet wall
Figure 4.52 Shear force diagram for braced cut sheet pile with depth of sheetpile
12m: (a) conventional analysis, (b) Subloading tij model (Nakai and Hinokio, 2004)
(a)
(b)
136
161.605
63.821
0
3
6
9
12
15
-25.00 0.00 25.00 50.00 75.00 100.00 125.00 150.00 175.00
Dep
th b
elow
EG
L (m
)
Greenfield
Bottom line of excavation
Bending moment (kN-m) at right sheet wall
Figure 4.53 Bending moment diagram for braced cut sheet pile with depth of sheet
pile 12m: (a) conventional analysis and (b) Subloading tij model (Nakai and Hinokio,
2004)
(a)
(b)
137
4.3.4 Numerical Analysis by Subloading tij Model for NATM
Using the Subloading tij model (Nakai and Hinokio, 2004), analyses have been
executed considering greenfield condition, building loads for NATM. During the
execution of NATM, rock bolts and lining have been assigned at 25% and 40% of
stress relaxation of excavated elements, respectively. All the cases with each specific
geometry and mesh along with the results have been presented here to understand
their characteristic and behavior of performance in real case.
4.3.4.1 Numerical Analysis for Case 1(NATM): Greenfield Condition
The results obtained from different geometries have been presented and discussed
here.
Geometry
The geometry for the greenfield condition without any external load is presented in
Figure 4.54. In this figure, modeled sub-soil is 33m deep and 96m wide. Here, the
extension part at both sides from the centre of tunnel is about 4.0 times the excavation
width of tunnel, which is sufficient to substantially reduce the boundary effects in
numerical model. The top soil is clayey soil up to 6m depth from EGL and the bottom
part is 27m which is sand. Excavated tunnel diameter is 9m and depth of crown of the
tunnel from EGL is 11m.
Mesh, Types of Elements and Boundary Conditions
The mesh (Figure 4.55) is applied in 5 zones along x-direction and in 3 zones along y-
direction. The position of excavated area is located in 3rd zone along the x-direction.
The isoparametric 4-noded (quadrilateral) elements have been used to represent the
soil and concrete materials. The 2-noded beam elements have been used to simulate
lining, rock bolts. Smooth boundary conditions have been applied at bottom, left and
right edges of the mesh. At bottom both vertical and horizontal displacement are
fixed.
138
Figure 4.54 Geometry in greenfield condition (NATM)
Figure 4.55 Mesh for greenfield condition (NATM)
Surface Settlement
The graph of surface settlement is depicted in Figure 4.56 at different excavation
stages. From this graph it is seen that the maximum settlement or vertical
displacement is 54.1mm which is found at step 1000 (50% stress relaxation of
excavated elements). The width of the affected zone along surface above the tunnel
crown is around 65m.
139
-0.0262
-0.0541
-0.0600
-0.0500
-0.0400
-0.0300
-0.0200
-0.0100
0.0000
0.0100
0 10 20 30 40 50 60 70 80 90 100
Settl
emen
t (m
)Distance from left edge (m)
25% Excavation
50% Excavation
75% Excavation
100% Excavation
Figure 4.56 Surface settlement for NATM in greenfield condition
Displacement Vector
Displacement vector for both the x and y direction is presented here at different stages
of excavation (Figure 4.57a, b and c). From this vector it can be seen that at step 500
(25% stress relaxation of excavated elements) the maximum resultant displacement is
30 mm which increases up to 60 mm after 100% excavation. Here, it can also be
visualized that the intensity of vector is highest at the crown of tunnel than the invert
location of tunnel. The path of displacement vectors represents the inward stress on
lining of tunnel.
Shear Strain
The distribution of shear strain at different excavation stages are presented here in
Figure 4.58a, b and c. From these diagrams it is found that at each excavation stages
the maximum shear strain occurs at both side (in between of crown and invert) of
tunnel excavation. The maximum shear strain is found as 0.039 at final stage of total
excavation.
140
(a)
(b)
(c)
Figure 4.57 Displacement vector diagrams for different loading steps in greenfield
condition: (a) at 500 step, (b) at 1000 step and (c) at 2000 step
141
(a)
(b)
(c)
Figure 4.58 Shear strain diagrams for different loading steps in greenfield condition:
(a) at 500 step, (b) at 1000 step and (c) at 2000 step
142
Lining Pressure
The diagram of earth pressure of tunnel is presented in Figure 4.59. For initial stage
of excavation the diagram shows a general distribution of stress. Later with increase
of stress in step by step it shows more distinct characteristics of pressure distribution
especially along the rock bolt line and lining (or shotcrete).
With the excavation advances beyond 25% stress relaxation of total excavated
elements net active earth pressure around the tunnel reduces due to insertion of rock
bolts. It reduces further when shotcrete is provided against failure by pressure at 40%
stress relaxation of total excavated elements.
0.00E+00
5.00E+00
1.00E+01
1.50E+01
2.00E+01
2.50E+01
3.00E+01
3.50E+011
2 3 45
67
89
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
2829
3031
3233
343536373839404142
4344
4546
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
6566
6768
6970
71 72 73
0% Stress Relaxation of Excavated Elements 25% Stress Relaxation of Excavated Elements
50% Stress Relaxation of Excavated Elements 75% Stress Relaxation of Excavated Elements
100% Stress Relaxation of Excavated Elements
Figure 4.59 Lining stress contour diagram for NATM in greenfield condition
143
4.3.4.2 Numerical Analysis for Case-2 (NATM): Pile Foundation
The analysis results for different geometries have been presented here.
Geometry
The modeled subsoil is 33m deep and 100m wide as shown in Figure 4.60. In this
geometry, the top soil is clayey for 6m depth from EGL and rest 27m is sand.
Excavated tunnel diameter is 9 m and depth of crown from EGL is 11m. Building is
existed at one side of tunnel location at a distance of 20m from tunnel centre. The
load of building is applied as pile load where the pile depth is 15m. The building load
is 957.85 kN (or 97.64 Ton) which is applied concentrically.
Figure 4.60 Geometry with pile load (building distance from tunnel centre=20m)
Mesh, Types of Elements and Boundary Conditions
Mesh is shown in Figure 4.61. The isoparametric 4-noded (quadrilateral) elements
have been used to represent the soil and concrete materials of pile cap and pile. The 2-
noded beam elements have been used to simulate the lining, rock bolts and
reinforcement in pile. And, the joint interface between pile cap and soil is simulated
using the 4-noded joint element (elasto-plastic joint element by Nakai, 1985-an
extension of goodman type joint element). The reinforced concrete pile is made of
concrete and steel bars and it is modeled as hybrid element (Zhang et. at., 2003)
consisting elastic solid and beam element.
144
Smooth boundary conditions have been applied at bottom, left and right edges of the
mesh. At bottom both vertical and horizontal displacement are fixed. At left and right
edges, horizontal displacements are fixed and vertical displacement is made free.
Figure 4.61 Mesh with (building distance from tunnel centre=20m): (a) mesh used
with pile load and (b) mesh showing soil, pile, pile cap
Surface Settlement
The graph of surface settlement with distance from the left edge is depicted in Figure
4.62 at different excavation stages. As per graph it is found that, the maximum
settlement is 53.6mm which is found after 1500 steps (50% stress relaxation of
excavated elements). Settlement pattern shows slight unsymmetrical because of
presence of building at right side. The width of the affected zone along surface above
the tunnel crown is around 55m.
(a)
(b)
145
Displacement Vector
Displacement vector for both the x and y direction is presented here at each 500 steps
(Figure 4.63). From these vectors it can be seen that at 16.67% stress relaxation of
excavated elements, the maximum resultant displacement is 20 mm which increases
up to 60mm at 100% stress relaxation of excavated elements. Here, it can also be
visualized that the intensity of vector is highest at the crown of tunnel than the invert
location of tunnel. The path of displacement vectors represents the inward stress on
lining of tunnel. It is also seen pile which transfer the building load at deeper depth
has very negligible effect on excavation of tunnel.
-0.0149
-0.0536
-0.0600
-0.0500
-0.0400
-0.0300
-0.0200
-0.0100
0.0000
0.0100
0.00 20.00 40.00 60.00 80.00 100.00 120.00
Settl
emen
t (m
)
Distance from left edge (m)
16.67% Excavation
33.33% Excavation
50% Excavation
66.67% Excavation
100% Excavation
Figure 4.62 Surface settlement with building load as pile (building distance from
tunnel centre=20m)
Shear Strain
The resulted shear strain distribution at different excavation stages are presented here
in Figure 4.64. From these diagrams it is found that at each stages of excavation, the
maximum shear strain occurs at left side (in between of crown and invert of left side)
of tunnel excavation. The shear strain range is 0.02 at step 500 (16.67% stress
146
relaxation of excavated elements) to 0.038 at final stage (100% stress relaxation of
excavated elements) of excavation.
Figure 4.63 Displacement vectors at differnet loading steps with building load as pile
(building distance from tunnel centre=20m)
(a)
(b)
(c)
147
Figure 4.64 Shear strain diagrams at differnet loading steps with building load as pile
(building distance from tunnel centre=20m): (a) at 500 step, (b) 1000 step and (c) at
3000 step
(a)
(b)
(c)
148
Lining Pressure
The diagram of earth pressure of tunnel with building load (as pile) is presented in
Figure 4.65. It resembles the Figure 4.59 qualitatively. In this case, for initial stage of
excavation the diagram shows a general distribution of stress. Later with increase of
stress in step by step it shows more distinct characteristics of pressure distribution
especially along the rock bolt line and lining (or shotcrete).
With the excavation advances beyond 25% stress relaxation of total excavated
elements net active earth pressure around the tunnel reduces due to insertion of rock
bolts. It reduces further when shotcrete is provided against failure by pressure at 40%
stress relaxation of total excavated elements.
0.00E+00
5.00E+00
1.00E+01
1.50E+01
2.00E+01
2.50E+01
3.00E+01
3.50E+011
2 3 4 56
78
910
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
2829
3031
3233
343536373839404142
4344
4546
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
6465
6667
6869
70 71 72 73
0% Stress Relaxation of Excavated Elements 16.67% Stress Relaxation of Excavated Elements
33.33% Stress Relaxation of Excavated Elements 50% Stress Relaxation of Excavated Elements
66.67% Stress Relaxation of Excavated Elements 83.33% Stress Relaxation of Excavated Elements
100% Stress Relaxation of Excavated Elements
Figure 4.65 Lining stress diagram at differnet loading steps with building load as pile
(building distance from tunnel centre=20m)
149
4.3.4.3 Numerical Analysis for Case-3 (NATM): Shallow Foundation
The analysis results for different geometries have been presented here.
Geometry
The modeled subsoil is 33m deep and 93m wide and depicted in Figure 4.66. In this
geometry, the top soil is clayey for 6m depth from EGL and rest 27m is sand.
Excavated tunnel diameter is 9 m and depth of crown from EGL is 11m. Building is
existed at one side of tunnel location at a distance of 20m from tunnel centre line. The
load of building is applied as footing load where the footing width is 4m. The building
load 957.85 kN (or 97.64 Ton) which is applied concentrically.
Figure 4.66 Geometry with building load as footing (building distance from tunnel
centre=20m)
Elements and Boundary Conditions
The 4-noded quadrilateral elements have been used to represent the soil and concrete
material of footing (Figure 4.67). The 2-noded beam elements have been used to
simulate the lining, rock bolts. And, the 4-noded joint element (elasto-plastic joint
element by Nakai, 1985-an extension of goodman type joint element) represents the
joint interface between footing and soil. Smooth boundary conditions have been
applied at bottom, left and right edges of the mesh. At bottom both vertical and
horizontal displacement are fixed. At left and right edges, horizontal displacements
are fixed and vertical displacement is made free.
150
(a)
(b)
Figure 4.67 Mesh with (building distance from tunnel centre=20m): (a) mesh used
with footing load and (b) mesh showing soil and footing
Surface Settlement
The graph of surface settlement with distance from the left edge is depicted in Figure
4.68 at different excavation stages. From the graph it is found that, the maximum
settlement or vertical displacement is 52.6mm which is found after 1500 steps (50%
stress relaxation of total excavated elements). Settlement is not smooth at right side
because of presence of footing as foundation of building. The width of the affected
zone along surface above the tunnel crown is around 60m.
Displacement Vector
Displacement vectors for both the x and y direction are presented from Figure 4.69 to
4.72 at each excavation stages. From these vectors it can be seen that at step 500
(16.67% stress relaxation of excavated elements), the maximum resultant
151
displacement is 20mm which increases up to 60mm at step 1500 (50% stress
relaxation of excavated elements). But at final stage of excavation (100% stress
relaxation of excavated elements) the value decreases to 50mm. Here, it can also be
visualized that the intensity of vector is highest at the crown of tunnel than the invert
location of tunnel. The path of displacement vectors represents the inward stress on
lining of tunnel.
-0.0144
-0.0526
-0.0110
-0.0600
-0.0500
-0.0400
-0.0300
-0.0200
-0.0100
0.00000.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
Settl
emen
t (m
)
Distance from left edge (m)
16.67% Excavation
33.33% Excavation
50% Excavation
66.67% Excavation
83.33% Excavation
100% Excavation
Figure 4.68 Surface settlement with building load as footing (building distance from
tunnel centre=20m)
Figure 4.69 Displacement vector diagrams with footing load at 500 steps
(building distance from tunnel centre=20m)
152
Figure 4.70 Displacement vector diagrams with footing load at 1000 steps
(building distance from tunnel centre=20m)
Figure 4.71 Displacement vector diagrams with footing load at 1500 steps
(building distance from tunnel centre=20m)
Figure 4.72 Displacement vector diagrams with footing load at 3000 steps
(building distance from tunnel centre=20m)
153
Figure 4.73 Shear strain diagrams at differnet loading steps with building load as
footing (building distance from tunnel centre=20m): (a) at 500 step, (b) 1000 step
and (c) at 3000 step
(a)
(b)
(c)
154
Shear Strain
The resulted shear strain distribution at different excavation stages are presented in
Figure 4.73. From these diagrams it is found that at each stages of excavation the
maximum shear strain occurs at left side (in between of crown and invert of left side)
of tunnel. The maximum shear strain is found as 0.043 after 100% stress relaxation of
excavated elements.
Lining Stress
The diagram of earth pressure of tunnel with footing as foundation of building is
presented in Figure 4.74. It also resembles the Figure 4.59 qualitatively. For initial
stage of excavation the diagram shows a general distribution of stress. Later with
increase of stress in step by step it shows more distinct characteristics of pressure
distribution especially along the rock bolt line and lining (or shotcrete). With the
excavation advances beyond 25% stress relaxation of total excavated elements net
active earth pressure around the tunnel reduces due to insertion of rock bolts. It
reduces further when shotcrete is provided against failure by pressure at 40% stress
relaxation of total excavated elements.
0.00E+00
5.00E+00
1.00E+01
1.50E+01
2.00E+01
2.50E+01
3.00E+01
3.50E+011
2 3 45
67
89
1011
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
2829
3031
3233
343536373839404142
4344
4546
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
6465
6667
6869
7071 72 73
0% Stress Relaxation of Excavated Elements 16.67% Stress Relaxation of Excavated Element
33.33% Stress Relaxation of Excavated Element 50% Stress Relaxation of Excavated Element
66.67% Stress Relaxation of Excavated Element 83.33% Stress Relaxation of Excavated Element
100% Stress Relaxation of Excavated Element
Figure 4.74 Lining stress contours at different loading with building load as footing
(building distance from tunnel centre=20m)
155
4.3.4.4 Numerical Analysis for Case-4 (NATM): Piles Foundation at Both Sides
The analysis results for different geometries have been presented here.
Geometry
The modeled subsoil as presented in Figure 4.75 is 33m deep and 102m wide. In this
geometry, the top soil is clayey for 6m depth from EGL and rest 27m is sand.
Excavated tunnel diameter is 9 m and depth of crown from EGL is 11m. Buildings are
existed at both sides of tunnel location. In both cases, buildings are located at 11m
distance from tunnel centre. The loads of buildings are applied as pile load where the
pile depth is 15m.
Figure 4.75 Geometry with building loads as pile at both sides of tunnel
(building distance from tunnel centre=11m for both cases)
Mesh, Types of Elements and Boundary Conditions
The mesh is applied in 5 zones along x direction and in 3 zones along y direction as
shown in Figure 4.76.
The isoparametric 4-noded (quadrilateral) elements have been used to represent soils
and concrete materials of piles and pile caps. The 2-noded beam elements have been
used to simulated lining, soil rock bolts and reinforcement in pile. And, the joint
interface between pile cap and is simulated using the 4-noded joint element (elasto
plastic joint element by Nakai, 1985-an extension of goodman type joint element).
156
The reinforced concrete pile is made of concrete and steel bars and it is modeled as
hybrid element (Zhang et. at., 2003) consisting elastic solid and beam element.
(a)
(b)
Figure 4.76 Mesh with building loads as pile at both sides of tunnel (building
distance from tunnel centre=11m for both cases)
157
Chapter Five
CONCLUSIONS AND RECOMMENDATIONS
5.1 Introduction
The objectives of this study were to review the conventional analysis for earth
retention system of tunnel structure, to perform numerical analysis to simulate
tunnelling system for Cut and Cover construction along with NATM and finally to
make a comparison between results obtained from conventional analysis and
numerical analysis for earth retaining structure of tunnelling system of underground
metro rail system in Dhaka city. The findings of the study have been outlined in this
chapter. From the analysis result the stability of retaining structure and tunnel system
can be investigated for the optimized selection of construction method along the
MRT-4 route in Dhaka city.
A conventional analysis was done for the retaining system of Cut and Cover
excavation method. As a result, earth pressure diagram, bending moment diagram,
shear force diagram of retaining wall and critical axial forces at strut levels were
found.
Subloading tij model (Nakai and Hinokio, 2004) was used to simulate the construction
of tunnelling system for Cut and Cover method as well as NATM. In case of Cut and
Cover method, Subloading tij model (Nakai and Hinokio, 2004) was executed
following the sequence of general construction from the insertion of whole retaining
system to placing of tunnel structure then backfilling over completed tunnel for
greenfield condition, nearby existing building load and water load at surface. After the
execution of model for each case, the results have been analyzed based on lateral
displacement, earth pressure, bending moment, shear force and axial force of wall;
surface settlement and vector displacement at different loading stages for each cases.
In case of NATM, the models were performed considering greenfield condition and
nearby existing building loads with shallow and pile foundation. During the
158
execution, rock bolts and lining were assigned at after 25% and 40% stress relaxation
of excavated elements, respectively. In NATM the results were presented in respect of
surface settlement, distribution of shear strain, vector displacement and lining stress
(or earth pressure of tunnel).
5.2 Summary
The main findings of the study were as follows:
(1) Four locations namely Uttara, Mohakhali, Farmgate and near DU campus
along the proposed route MRT-4 were selected to determine the sub-soil
profile which represented soil type with depth. The soil parameters defining
physical and strength properties were determined from laboratory tests. Some
soil parameters along the proposed route were collected and combined. It was
found that for clay layer plastic limit varied from 18% to 28% and plasticity
index ranged from 20% to 31%. It was also observed that for red clay
unconfined compressive strength ranged from 62 kPa to 139 kPa. The
cohesion varied from 31 kPa to 70 kPa. For sand the angle of internal friction
ranged from 32o to 42o which was seen from direct shear test. From triaxial
test for clay the friction angle and the cohesion values were 60 and 78 kPa,
respectively. In case of sand the friction angle was 320. It was found that the
ranges of values for each parameter were within the typical limit as for typical
Dhaka soil.
(2) In this study an elasto-plastic constitutive model- Subloading tij model (Nakai
and Hinokio, 2004) was used for numerical analysis. The parameters of this
model were obtained from triaxial test and consolidation test. For clay the
compression index or slope of virgin loading curve in e-log p’ curve at the
loosest state (λ) (where, e is void ratio and p’ is consolidation pressure) was
found 0.125~0.18; swelling index or slope of unloading-reloading curve in e-
log p’ curve at the loosest state (κ) was 0.0157~ 0.04; critical state stress ratio
(RCS(1/3)cs(comp.)) was 3.6; the reference void ratio on normally consolidation
line at mean principal stresses, p=98 kPa and at q= 0 kPa (N) was 0.7025~
159
0.7275; poison’s ratio was 0.2; shape of yield surface was 1.5 and parameter
for influence of density and confining pressure was 600. For sand the
compression index (λ) was found 0.088; swelling index (κ) was 0.015; critical
state stress ratio (RCS(1/3)cs(comp.)) was 1.8; reference void ratio on normally
consolidation line at mean principal stresses, p=98 kPa and at q= 0 kPa (N)
was 0.75; poison’s ratio was 0.2; shape of yield surface (β) was 2.0 and
parameter for influence of density and confining pressure (a) was 600.
(3) Using the conventional method, analyses were made for the retaining system
of tunnelling for Cut and Cover excavation method considering the Dhaka
sub-soil existed along the MRT-4 route. Earth pressure diagram as proposed
by Peck (1969) of bracing system were determined for the systems of braced
cut sheet pile wall and braced cut diaphragm wall. The analyses were carried
out considering the depth of cut as 12m and 15m with three struts spaced at
3m centre to centre vertically. Wales are placed at each strut levels with 3m of
span length horizontally. The analyses were executed for greenfield condition.
For braced cut retaining wall it was found that for depth of cut 12m at
Farmgate, Mohakhali, Uttara and DU Campus, the values of apparent earth
pressure were 56.124 kN/m2, 56.124 kN/m2, 50.76 kN/m2 and 56.77 kN/m2
respectively; critical bending moments were 84.186 kN-m, 84.186 kN-m,
76.14 kN-m and 85.16 kN-m respectively. For depth of cut 15m at Farmgate,
it was also determined that the value of apparent earth pressure was 70.79
kN/m2 and critical bending moments was 84.95 kN-m.
(4) Subloading tij model (Nakai and Hinokio, 2004) analysis was conducted for
braced sheet pile system with depth of cut as 12m and depth of retaining wall
as 18m. In greenfield condition, maximum lateral displacement of sheet pile
wall was as 18.8mm were found after completion of 100% excavation. In case
of presence of building load with shallow foundation, the maximum wall
displacement of sheet pile was 36.4mm found after backfilling. But in case of
presence of water table at EGL in greenfield condition, the maximum lateral
displacement of wall was as large as 220mm. Also, in case of presence of
water table and building load with shallow foundation, the maximum wall
displacement was 340.8mm. For the last two cases, the lateral displacements
160
were abruptly high and the reason might be that no joint element (Nakai,
1985) had been simulated at the interface of sheet pile wall and soil.
The earth pressures were 138.32 kN/m2, 165.79 kN/m2, 66.51 kN/m2 and
72.01 kN/m2 in case of greenfield condition, presence of building load with
shallow foundation, greenfield with water effect and presence of water effect
and building load with shallow foundation, respectively.
The maximum surface settlements were found as 6.4mm, 7.9mm, 172mm.
352.7mm in case of greenfield condition, in presence of building, in greenfield
considering water effects and in case of considering water and loading effects,
respectively. In case of 2nd and 4th cases settlement occurs at the position of
existing building. Shahin et al. (2010) has revealed that the maximum surface
settlement due to the braced excavation does not always occur just behind the
wall, but mostly at the position of the existing structure. For the last two cases,
the surface settlements were abnormally high. It might be due to the fact that
no joint element (elasto plastic joint element by Nakai, 1985-an extension of
goodman type joint element) had been used at the interface of sheet pile wall
and soil.
From the comparison of shear force and bending moment diagrams among
four Cases, it was found that the Case considering the effects of water and
building load governs the critical design value. The maximum shear force was
390.84 kN and the critical moments were -394.17 kN-m/m +316.31 kN-m/m.
(5) A comparison was made for greenfield condition without considering any
effects of water and external structural loads (with depth of cut and retaining
wall as 12m) between the results obtained from conventional and FEM
analysis. From the analysis for braced sheet pile, it was seen that the earth
pressures from conventional result was 56.124 kN/m2 and from numerical
result was 72.6 kN/m2. In both cases, diagram patterns were resembled
slightly, though the conventional analysis showed a sharp edged trapezoidal
shape and numerical analysis showed some sort of curvilinear shape.
161
In conventional shear force diagram the tendency of symmetry was evident
but in case of numerical analysis there was a tendency of increasing the values
of shear force with depth. If the bending moment diagrams were analyzed by
conventional analysis and numerical analysis then it could be found that there
existed a tendency of increasing the bending moment value in both analyses.
In conventional analysis the moment values kept a harmonic nature while
going to depth.
(6) Subloading tij model (Nakai and Hinokio, 2004) was also used for analyses of
NATM considering greenfield condition and loading (as pile and shallow
foundation) condition of existing buildings. Shahin et al. (2010) in his research
comparing the results of different foundation types has found that for shallow
foundation the surface settlement at the position of the foundation is larger
than that for pile foundation. In this study, same depiction has been revealed.
In this study for greenfield condition, it was observed that the maximum
surface settlement was 54.1mm which was found after 1000 steps (50% stress
relaxation of excavated elements). The width affected zone along surface
above the tunnel crown was around 65m at mid zone of road way. Whereas in
presence of pile foundation of building, the critical surface settlement was
53.6mm with the affected roadway zone of 55m. Again, in presence of
shallow foundation, the maximum surface settlement was 52.6mm with the
affected roadway zone of 60m.
From the distribution of vector displacements, it was seen that at 16.57% to
25% stress relaxation of excavated elements, the maximum resultant
displacement was found as 20 mm which increased up to 50mm to 60 mm at
final step (100% stress relaxation of excavated elements) for different cases.
Here, it can also be visualized that the intensity of vector was highest at the
crown of tunnel than the invert location of tunnel. The path of displacement
vectors represented the inward stress on lining of tunnel.
From the distribution of shear strain, it was observed the maximum shear
strain occurred at both side (in between of crown and invert) of tunnel. The
162
shear strain range was 0.008 at step 500 to 0.043 at final step of 100%
excavation.
In the lining stress contour, it was found that with the excavation advances
beyond 25% stress relaxation of total excavated elements, net active earth
pressure around the tunnel reduced due to insertion of rock bolts at 25% of
excavation. It reduced further when lining (or shotcrete) was provided against
failure by pressure at 40% stress relaxation of total excavated elements.
5.3 Conclusions
From this study, it can be concluded that by performing sub-soil parameter analysis,
the numerical analysis can fairly represent the typical Dhaka soil along the MRT-4
route. It is observed that using Subloading tij model (Nakai and Hinokio, 2004)
analysis, the interactions of soil-structure and soil-water, the behavior of materials can
be simulated as per practical situation and gives more realistic results comparing the
conventional analysis which is based on many simplifications and assumptions. For
construction of underground tunnel it is revealed that NATM shows more stability in
soil retention than Cut and Cover method for congested areas in Dhaka. For open
spaces like Tongi to Uttara along the MRT-4, Cut and Cover is more appropriate
considering its simplicity in execution and NATM is preferable method at flyover
junction points in Cantonment and structurally obstructed places (Farmgate to
Sayedabad) in geotechnical consideration. Though analysis with Tunnel Boring
Machine (TBM) was beyond the scope of this study, this method may require to be
executed. Thus an optimized underground metro tunnel system can be constructed for
Dhaka city after proper prediction of ground movements and influence of tunnelling
with a sophisticated simulation tool.
5.4 Recommendations for Future Studies
In this research in case of Cut and Cover method, numerical analyses were done for
some retaining systems of tunnelling with loading from building and water. In case of
NATM the analyses were executed considering some cases of loading effects. During
the research, scopes of future studies were found.
163
(1) Though in this study triaxial consolidated undrained (CU) test has been
conducted for sandy soil, the triaxial consolidated drained (CD) test gives
better and accurate parameters. Therefore, CD test can be performed for sandy
soil for future numerical analyses.
(2) The interaction in between retaining wall and soil has not been considered in
this study for time limitations. Hence, further analysis can be executed
considering joint element (Nakai, 1985) between wall and soil.
(3) Cost analysis can be done after designing and selecting the sections of the
structural components for earth retentions systems and tunnel structure.
(4) Verification of this elasto-plastic Subloading tij model can be done by small
scale model test.
(5) The analysis by TBM method is beyond the scope of this study. So analysis by
TBM can be another option for the construction of underground metro rail
tunnel in Dhaka city.
164
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168
APPENDIX-I
A.1 CONVENTIONAL ANALYSIS FOR CUT AND COVER METHOD
Figure A.1 Soil properties along the proposed soil profile of MRT-4 route
169
A.1.1 Braced Cut Sheet Pile (Location: Farmgate and depth of excavation: 12m)
Depth of tensile crack, 2 uc
Cz
=
2
3
2 115.5 /14.9 /x kN m
kN m= 15.5m
So, the depth of 1st strut below ground surface is taken as 3m. Therefore, equivalent
cohesion,
avC = 2 tan ( ) '
2s s s s usK H H H n q
H
=3 2 216.28 / 1.0 (6 ) tan 45 (12 6) 0.75 (2 115.5 / )
2 12kN m x x m x mx x x kN m
x m
= 67.73 kN/m2
And Average unit weight,
av = ( )s s s cH H H
H
=3 316.28 / 6 (12 6) 14.9 /
12kN m x m mx kN m
m
= 15.59 kN/m3
For excavation depth of 12m, av
av
H
C
=3
2
15.59 / 1267.73 /
kN m x m
kN m=2.762 which is less 4.
So, the earth pressure diagram by Peck (1969) will be,
Figure A.2 Earth pressure diagram for braced cut sheet pile (Farmgate with
excavation depth=12m)
170
Shear Force Diagram (SFD) and Bending Moment Diagram (BMD)
Figure A.3 Determination of SFD and BMD (Farmgate with excavation depth=12m)
The apparent pressure as per Peck (1969),
(0.2 ~ 0.4)a avp H = 0.3x 15.59 kN/m3x12 m = 56.124 kN/m2
Sheet Pile Design
At any level the spacing of the struts is 3m c/c, so the total strut loads are obtained as
follows:
Strut load at level A= 196.43 kN/m x 3m = 589.29 kN
Strut load at level B= (56.124+56.124) kN/m x 3m = 336.74 kN
Strut load at level C= 196.43 kN/m x 3m = 589.29 kN
Bending moments at different points on the wall of braced cut are:
MA and MC= -84.186 kN-m/m of wall
M1= +28.05 kN-m/m of wall
171
Thus, the maximum moment is at point A and C which is -84.186 kN-m/m of wall.
So, the section modulus for this maximum bending,
max.
.x
allow
MS
= 2
84.186165,381 /
kN m
kN m
= 5.09x10-4 m3/m of wall= 509 cm3/m of wall.
[Where, .allow = 24 ksi= 2165,381 /kN m ]
Section chosen: AZ 12-700; Sx=1205 cm3/m
Wale Design
Wale’s span length, s= 3m
At level A and C, Mmax= 2196.43 3
8x =220.98 kN-m
Section modulus, 220.98165381xS = 1.34x10-3 m3 =1340 cm3
Section chosen: W 460x74; Sx= 1460 cm3
At level B, Mmax= 2(56.124 56.124) 3
8x =126.28 kN-m
Section modulus, 126.28165381xS = 7.636x10-4 m3 =764 cm3
Section chosen: W 250x67; Sx= 809 cm3
Strut Design
Strut length, l = 10 m.
At A and C, total load of strut = 589.29 kN
Steel modulus of elasticity, E= 200x106 kN/m2
Yield or ultimate strength of steel, Fy= 414x103 kN/m2
2c
y
EC
F =
6
3
2 (200 10 )414 10
x x ksi
x ksi =97.676
172
Trial 1 for strut Design
Trial section: W 360x122
The properties are: A = 15500 mm2 = 0.0155 m2; d = 363 mm; r= 153 mm
kl
r=
1.0 (10 1000)153
x x mm
mm= 65.36 which is less than
cC
2
3
1 /[1 ( ) ]2
5 3 ( / ) 1 /( )3 8 8
y
ca
c c
kl rF
CF
kl r kl r
C C
= 3 2 2
3
1 65.36(414 10 / )[1 ( ) ]2 97.676
5 3 (65.36) 1 65.36( )3 8 (97.676) 8 97.676
x kN m
= 170,903 kN/m2
Therefore, strut load, Pa= Fa x A = 170,903 kN/m2 x 0.0155 m2 = 2649 kN which is
hugely greater than design strut load.
Trial 2 for strut design
Trial section: W 310x32.7
The properties are: A = 4180 mm2 = 0.00418 m2; d = 313 mm; r= 125 mm
kl
r=
1.0 (10 1000)125
x x mm
mm= 80 which is less than cC = 97.676
2
3
1 /[1 ( ) ]2
5 3 ( / ) 1 /( )3 8 8
y
ca
c c
kl rF
CF
kl r kl r
C C
= 3 2 2
3
1 80(414 10 / )[1 ( ) ]2 97.676
5 3 (80) 1 80( )3 8 (97.676) 8 97.676
x kN m
= 144,421 kN/m2
Therefore, strut load, Pa= Fa x A = 144,421 kN/m2 x 0.00418 m2 = 603.68 kN which is
nearly greater than design strut load (589.29 kN).
Section chosen: W 310x32.7; Sx= 415 cm3
173
A.1.2 Braced Cut Diaphragm Wall (Location: Farmgate and depth of excavation:
12m)
Each panel width of diaphragm wall is 4m and the thickness of diaphragm wall is
0.5m.
From braced cuts of sheet pile, it is found that maximum moment at A and C is,
MA = MC = 84.186 kN-m/m of wall.
For the design of diaphragm wall, column strength interaction diagram for rectangular
section (with bars on end faces) with γ=0.75 has been used.
Here, 0n
gA
n
g
M
A h
= 84.186 4(4 0.5) 0.5
x
x x= 336.74 kN/m2
From the interaction diagram, only 1% reinforcement is required to provide.
Minimum reinforcement, As(min)= 0.0033xbxh= 0.0033x4mx0.5m = 6600 mm2
Required vertical reinforcement = g gAst xA = 0.01 x (4m x 0.5m) x 1000 = 20,000
mm2
So, Vertical Bar: 20-25mm @ 175mm c/c (both phases)
And, Horizontal Bar: 33-16mm @ 350mm c/c (both phases)
Figure A.4 Diaphragm wall reinforcement details (Farmgate with excavation depth
=12m)
174
A.1.3 Braced Cut Sheet Pile (Location: Farmgate and Depth of excavation: 15m)
Depth of tensile crack, 2 uc
Cz
=
2
3
2 115.5 /14.9 /x kN m
kN m= 15.5m
So, the depth of 1st strut below ground surface is taken as 3m.
Therefore, equivalent cohesion, avC = 2 tan ( ) '
2s s s s usK H H H n q
H
=3 2 216.28 / 1.0 (9 ) tan 45 (15 9) 0.75 (2 115.5 / )
2 15kN m x x m x mx x x kN m
x m
= 78.61 kN/m2
And Average unit weight,
av = ( )s s s cH H H
H
=3 316.28 / 9 (15 9) 14.9 /
15kN m x m mx kN m
m
= 15.73 kN/m3
For excavation depth of 15m,
av
av
H
C
=3
2
15.73 / 1578.61 /
kN m x m
kN m=3.00 which is less 4.
So, the earth pressure diagram by Peck (1969) will be,
Figure A.5 Earth pressure diagram for braced cut sheet pile
(Farmgate with excavation depth=15m)
175
Shear Force Diagram (SFD) and Bending Moment Diagram (BMD)
Figure A.6 Determination of SFD and BMD (Farmgate with excavation depth=15m)
The apparent pressure as per Peck (1969),
(0.2 ~ 0.4)a avp H = 0.3x 15.73 kN/m3x15 m = 70.79 kN/m2
Sheet Pile Design
Assume, at any level the spacing of the struts is 3m c/c, the total strut loads are
obtained as follows:
Strut load at level A= 214.58 kN/m x 3m = 643.74 kN
Strut load at level B & C= (77.43+106.19) kN/m x 3m = 550.86 kN
Strut load at level D= 214.58 kN/m x 3m = 643.74 kN
Bending moments at different points on the wall of braced cut are:
176
MA and MD= -84.95 kN-m/m of wall
M1= +42.2 kN-m/m of wall
Thus, the maximum moment is at point A and D which is -84.95 kN-m. So, the
section modulus for this maximum bending is,
max.
.x
allow
MS
= 2
84.95165,381 /
kN m
kN m
= 5.137x10-4 m3/m of wall= 514 cm3/m of wall.
[Where, .allow = 24 ksi= 2165,381 /kN m ]
Section chosen: AZ 12-700; Sx=1205 cm3/m.
Wale Design
Wale’s span length, s = 3m
At level A and D, Mmax= 2214.58 3
8x =241.40 kN-m
Section modulus, 241.40165381xS = 1.46x10-3 m3 =1460 cm3
Section chosen: W 460x74; Sx= 1460 cm3
At level B and C, Mmax= 2(77.43 106.19) 3
8x =206.57 kN-m
Section modulus, 206.57165381xS = 1.25x10-3 m3 =1250 cm3
Section chosen: W 360x79; Sx= 1280 cm3
Strut Design
Strut length, l = 10 m.
At A and C, Strut load = 643.74 kN
Steel modulus of elasticity, E= 200x106 kN/m2
Yield or ultimate strength of steel, Fy= 414x103 kN/m2
2c
y
EC
F =
6
3
2 (200 10 )414 10
x x ksi
x ksi =97.676
177
Trial section: W 310x38.7
The properties are: A = 4940 mm2 = 0.00494 m2; d = 310 mm; r= 131 mm
kl
r= 1.0 (10 1000)
125x x mm
mm= 80 which is less than cC = 97.676
2
3
1 /[1 ( ) ]2
5 3 ( / ) 1 /( )3 8 8
y
ca
c c
kl rF
CF
kl r kl r
C C
= 3 2 2
3
1 80(414 10 / )[1 ( ) ]2 97.676
5 3 (80) 1 80( )3 8 (97.676) 8 97.676
x kN m
= 144,421 kN/m2
Therefore, strut load, Pa= Fa x A = 144,421 kN/m2 x 0.00494 m2 = 747.65 kN which is
nearly greater than design strut load (643.74 kN).
Section chosen: W 310x38.7; Sx= 549 cm3
178
A.1.4 Braced Cut Diaphragm Wall (Location: Farmgate and Depth of excavation:
15m)
Each panel width of diaphragm wall is 4m and the thickness of diaphragm wall is
0.5m.
From braced cuts of sheet pile, it is found that maximum moment at A and D is,
MA = MC = 84.95 kN-m/m of wall
For the design of diaphragm wall, column strength interaction diagram for rectangular
section (with bars on end faces) with γ=0.75 has been used.
Here, 0n
gA
n
g
M
A h
= 84.95 4(4 0.5) 0.5
x
x x= 339.8 kN/m2
From the interaction diagram, only 1% reinforcement is required to provide.
Minimum reinforcement, As(min)= 0.0033xbxh= 0.0033x4mx0.5m = 6600 mm2
Required vertical reinforcement = g gAst xA = 0.01 x (4m x 0.5m) x 1000
= 20,000 mm2
So, Vertical Bar: 20-25mm @ 175mm c/c (both phases)
And, Horizontal Bar: 33-16mm @ 350mm c/c (both phases)
Figure A.7 Diaphragm wall reinforcement details (Farmgate with excavation depth=
15m)
179
A.1.5 Braced Cut Sheet Pile (Location: Mohakhali and depth of excavation: 12m)
Depth of tensile crack, 2 uc
Cz
=
2
3
2 111.5 /15.4 /x kN m
kN m= 14.48m
So, the depth of 1st strut below ground surface is taken as 3m.
Therefore, equivalent cohesion, avC = 2 tan ( ) '
2s s s s usK H H H n q
H
=3 2 215.8 / 1.0 (6 ) tan 45 (12 6) 0.75 (2 111.5 / )
2 12kN m x x m x mx x x kN m
x m
= 65.51 kN/m2
And Average unit weight,
av = ( )s s s cH H H
H
=3 315.8 / 6 (12 6) 15.4 /
12kN m x m mx kN m
m
= 15.6 kN/m3
For excavation depth of 12m, av
av
H
C
=3
2
15.6 / 1265.51 /
kN m x m
kN m=2.86 which is less 4.
So, the earth pressure diagram will be,
Figure A.8 Earth pressure diagram for braced cut sheet pile (Mohakhali with
excavation depth=12m)
The apparent pressure as per Peck (1969),
(0.2 ~ 0.4)a avp H = 0.3x 15.6 kN/m3x12 m = 56.16 kN/m2
The pressure value is almost similar to that of Farmgate area for excavation depth
12m. So, design values of Farmgate will be used for Mohakhali area also for both
braced cut sheet pile and braced cut diaphragm wall.
180
A.1.6 Braced Cut Sheet Pile (Location: Uttara and depth of excavation: 12m)
Depth of tensile crack, 2 uc
Cz
=
2
3
2 62 /14.1 /x kN m
kN m= 8.8m
So, the depth of 1st strut below ground surface is taken as 3m.
For excavation depth of 12m, u
H
C
=3
2
14.1 / 1262 /kN m x m
kN m=2.729 which is less 4.
So, the earth pressure diagram will be,
Figure A.9 Earth pressure diagram for braced cut sheet pile
(Uttara with excavation depth=12m)
The apparent pressure as per Peck (1969),
(0.2 ~ 0.4)a avp H = 0.3x 14.1 kN/m3x12 m = 50.76 kN/m2
Sheet Pile Design
Assume, at any level the spacing of the struts is 3m c/c, the total strut loads are
obtained as follows:
Strut load at level A= 177.66 kN/m x 3m = 532.98 kN
Strut load at level B= (50.76+50.76) kN/m x 3m = 304.56 kN
Strut load at level C= 177.66 kN/m x 3m = 532.98 kN
181
Shear Force Diagram (SFD) and Bending Moment Diagram (BMD)
Figure A.10 Determination of SFD and BMD (Uttara with excavation depth=12m)
Bending moments at different points on the wall of braced cut are:
MA and MC= -76.14 kN-m/m of wall
M1= +25.38 kN-m/m of wall
Thus, the maximum moment is at point A and C which is -76.14 kN-m. So, the
section modulus for this maximum bending,
max.
.x
allow
MS
= 2
86.05165,381 /
kN m
kN m
= 4.60x10-4 m3/m of wall= 460 cm3/m of wall.
[Where, .allow = 24 ksi= 2165,381 /kN m ]
Section chosen: AZ 12-700; Sx=1205 cm3/m.
182
Wale Design
Wale’s span, s= 3m
At level A and C, Mmax= 2177.66 3
8x =199.87 kN-m
Section modulus, 199.87165381xS = 1.21x10-3 m3 =1210 cm3
Section chosen: W 360x79; Sx= 1280 cm3
At level B, Mmax= 2(50.76 50.76) 3
8x =114.21 kN-m
Section modulus, 114.21165381xS = 6.91x10-4 m3 =691 cm3
Section chosen: W 360x44; Sx= 693 cm3
Strut Design
Strut length, l = 10 m.
At A and C, Strut load = 532.98 kN
Steel modulus of elasticity, E= 200x106 kN/m2
Yield or ultimate strength of steel, Fy= 414x103 kN/m2
2c
y
EC
F =
6
3
2 (200 10 )414 10
x x ksi
x ksi =97.676
Trial section: W 310x32.7
The properties are: A = 4180 mm2 = 0.00418 m2; d = 313 mm; r= 125 mm
kl
r= 1.0 (10 1000)
125x x mm
mm= 80 which is less than cC = 97.676
2
3
1 /[1 ( ) ]2
5 3 ( / ) 1 /( )3 8 8
y
ca
c c
kl rF
CF
kl r kl r
C C
= 3 2 2
3
1 80(414 10 / )[1 ( ) ]2 97.676
5 3 (80) 1 80( )3 8 (97.676) 8 97.676
x kN m
= 144,421 kN/m2
Therefore, strut load, Pa= Fa x A = 144,421 kN/m2 x 0.00418 m2 = 603.68 kN which is
nearly greater than design strut load (532.98 kN).
Section chosen: W 310x32.7; Sx= 415 cm3
183
A.1.7 Braced Cut Diaphragm Wall (Location: Uttara and Depth of excavation:
12m)
Each panel width of diaphragm wall is 4m and the thickness of diaphragm wall is
0.5m.
From braced cuts of sheet pile, it is found that maximum moment at A and C is,
MA = MC = 76.14 kN-m/m of wall
For the design of diaphragm wall, column strength interaction diagram for rectangular
section (with bars on end faces) with γ=0.75 has been used.
Here, 0n
gA
n
g
M
A h
= 76.14 4(4 0.5) 0.5
x
x x= 304.56 kN/m2
From the interaction diagram, only 1% reinforcement is required to provide.
Minimum reinforcement, As(min)= 0.0033xbxh= 0.0033x4mx0.5m = 6600 mm2
Required vertical reinforcement = g gAst xA = 0.01 x (4m x 0.5m) x 1000 =
20,000 mm2
So, Vertical Bar: 20-25mm @ 175mm c/c (both phases)
And, Horizontal Bar: 33-16mm @ 350mm c/c (both phases)
Figure A.11 Diaphragm wall reinforcement details (Uttara with excavation
depth=12m)
184
A.1.8 Braced Cut Sheet Pile (Location: Dhaka University Area and depth of
excavation: 12m)
Depth of tensile crack, 2 uc
Cz
=
2
3
2 124.5 /15.7 /x kN m
kN m= 15.9m
So, the depth of 1st strut below ground surface is taken as 3m.
Therefore, equivalent cohesion, avC = 2 tan ( ) '
2s s s s usK H H H n q
H
=3 2 215.98 / 1.0 (3 ) tan 45 (12 3) 0.75 (2 124.5 / )
2 12kN m x x m x mx x x kN m
x m
= 76.02 kN/m2
And Average unit weight,
av = ( )s s s cH H H
H
=3 315.98 / 3 (12 3) 15.7 /
12kN m x m mx kN m
m
= 15.77 kN/m3
For excavation depth of 12m,
av
av
H
C
=3
2
15.77 / 1276.02 /
kN m x m
kN m=2.49 which is less 4.
So, the earth pressure diagram by Peck (1969) will be,
Figure A.12 Earth pressure diagram for braced cut sheet pile
(DU campus with excavation depth=12m)
185
The apparent pressure as per Peck (1969),
(0.2 ~ 0.4)a avp H = 0.3x 15.77 kN/m3x12 m = 56.77 kN/m2
Sheet Pile Design
At any level the spacing of the struts is 3m c/c, the total strut loads are obtained as
follows from Figure A.12:
Strut load at level A= 198.7 kN/m x 3m = 596.1 kN
Strut load at level B= (56.77+56.77) kN/m x 3m = 340.62 kN
Strut load at level C= 198.7 kN/m x 3m = 596.1 kN
Bending moments at different points on the wall of braced cut are:
MA and MC= -85.16 kN-m/m of wall
M1= +28.39 kN-m/m of wall
Shear Force Diagram (SFD) and Bending Moment Diagram (BMD)
Figure A.13 Determination of SFD and BMD (DU campus with excavation
depth=12m)
186
Thus, the maximum moment is at point A and C which is -85.16 kN-m. So, the
section modulus for this maximum bending,
max.
.x
allow
MS
= 2
85.16165,381 /
kN m
kN m
= 5.15x10-4 m3/m of wall= 515 cm3/m of wall.
[Where, .allow = 24 ksi= 2165,381 /kN m ]
Section chosen: AZ 12-700; Sx=1205 cm3/m.
Wale Design
Wale’s span, s= 3m
At level A and C, Mmax= 2198.7 3
8x =223.54 kN-m
Section modulus, 223.54165381xS = 1.35x10-3 m3 =1350 cm3
Section chosen: W 460x74; Sx= 1460 cm3
At level B, Mmax= 2(56.77 56.77) 3
8x =127.73 kN-m
Section modulus, 127.73165381xS = 7.72x10-4 m3 =772 cm3
Section chosen: W 410x46.1; Sx= 774 cm3
Strut Design
Strut length, l = 10 m.
At A and C, Strut load = 596.1 kN
Steel modulus of elasticity, E= 200x106 kN/m2
Yield or ultimate strength of steel, Fy= 414x103 kN/m2
2c
y
EC
F =
6
3
2 (200 10 )414 10
x x ksi
x ksi =97.676
187
Trial section: W 310x32.7
The properties are: A = 4180 mm2 = 0.00418 m2; d = 313 mm; r= 125 mm
kl
r= 1.0 (10 1000)
125x x mm
mm= 80 which is less than cC = 97.676
2
3
1 /[1 ( ) ]2
5 3 ( / ) 1 /( )3 8 8
y
ca
c c
kl rF
CF
kl r kl r
C C
= 3 2 2
3
1 80(414 10 / )[1 ( ) ]2 97.676
5 3 (80) 1 80( )3 8 (97.676) 8 97.676
x kN m
= 144,421 kN/m2
Therefore, strut load, Pa= Fa x A = 144,421 kN/m2 x 0.00418 m2 = 603.68 kN which is
nearly greater than design strut load (596.1 kN).
Section chosen: W 310x32.7; Sx= 415 cm3
188
A.1.9 Braced Cut Diaphragm Wall (Location: Dhaka University Area and depth of
excavation: 12m
Each panel width of diaphragm wall is 4m and the thickness of diaphragm wall is
0.5m.
From braced cuts of sheet pile, it is found that maximum moment at A and C is,
MA = MC = 85.16 kN-m/m of wall
For the design of diaphragm wall, column strength interaction diagram for rectangular
section (with bars on end faces) with γ=0.75 has been used.
Here, 0n
gA
n
g
M
A h
= 85.16 4(4 0.5) 0.5
x
x x= 340.64 kN/m2
From the interaction diagram, only 1% reinforcement is required to provide.
Minimum reinforcement, As(min)= 0.0033xbxh= 0.0033x4mx0.5m = 6600 mm2
Required vertical reinforcement = g gAst xA = 0.01 x (4m x 0.5m) x 1000 =
20,000 mm2
So, Vertical Bar: 20-25mm @ 175” c/c (both phases)
And, Horizontal Bar: 33-16mm @ 350” c/c (both phases)
Figure A.14 Diaphragm wall reinforcement details (DU campus with excavation
depth= 12m)
189
APPENDIX-II
A.2 SOIL PARAMETERS USED IN ANALYSIS
A.2.1 Model Analysis Criteria for Cut and Cover (Braced Cut Sheet Pile)
Soil Model (Farmgate)
(1) Unit weight of sand:
For sand= 16.28 kN/m3 = 1.6595 Ton/m3
For clay= 14.90 kN/m3 = 1.5189 Ton/m3
For backfill= 13.73 kN/m3 = 1.40 Ton/m3
(2) Coefficient of permeability of sand, kx=ky=5.0 cm/hour = 1.3889x10-5 m/s
Coefficient of permeability of clay, kx=ky=0.05 cm/hour = 1.3889x10-7 m/s
(3) Poisson’s ratio: Sand = 0.2 and clay= 0.3
Material Property and Model
(1) Sheet Pile: Thickness, t or h = 0.1524m
Tunnel Base Slab and Top Slab: Thickness = 0.8m
Tunnel Side Wall and Middle Wall: Thickness = 0.6m
(2) Modulus of elasticity of steel, sE = 200000 MPa = 29x106 psi = 2.04x107 Ton/m2
Modulus of elasticity of concrete (with 'fc =4000 psi), Ec1= 57500 'fc (psi) =
57500√4000= 3.6x106 psi = 2.531x106 Ton/m2
(3) Moment of inertia (I):
For sheet pile = 3
12bh =
3(1 ) (0.1524)12
m x =2.95x10-4 m4
190
For tunnel base and top slab = 3
12bh =
3(1 ) (0.8)12
m x =0.4267x10-1 m4
For tunnel side and middle walls = 3
12bh =
3(1 ) (0.6)12
m x =0.018 m4
(4) Cross-sectional area:
For sheet pile= bh =1mx 0.1524m=0.1524 m2
For tunnel base and top slab = bh =1mx 0.8m=0.8 m2
For tunnel side and middle walls = bh =1mx 0.6m=0.6 m2
(5) Stiffness (EI):
For sheet pile = (2.04x107 Ton/m2) x (2.95x10-4 m4) = 6.018x103 Ton-m2
For tunnel base and top slab = (2.531x106 Ton/m2) x (0.4267x10-1 m4) =
1.079978x105 Ton-m2
For tunnel side and middle walls = (2.531x106 Ton/m2) x (0.018 m4) =
0.45558x105 Ton-m2
(6) (EA):
For sheet pile = (2.04x107 Ton/m2) x (0.1524 m2) = 3.11x106 Ton
For tunnel base and top slab = (2.531x106 Ton/m2) x (0.8 m2) = 2.0248x106 Ton
For tunnel base and top slab = (2.531x106 Ton/m2) x (0.6 m2) = 1.5186x106 Ton
A.2.2 Model Analysis Criteria for NATM
Soil Model
(1) Unit weight of sand:
For sand= 16.28 kN/m3 = 1.6595 Ton/m3
For clay= 14.90 kN/m3 = 1.5189 Ton/m3
(2) Coefficient of permeability of silty sand, kx=ky=5.0 cm/hour = 1.4x10-5 m/s
Coefficient of permeability of clay, kx=ky=0.05 cm/hour = 7x10-7 m/s
(3) Poisson’s ratio: Sand = 0.2 and clay= 0.2
191
Material Property and Model
(1) Lining: Thickness =(0.3-0.6)m=0.45m (taken); Concrete strength, 'fc =(50-60)
MPa =50 MPa (taken)=7250 psi
Rock bolt: Steel strength, yf = 205 MPa =30,000 psi = 40,000 psi (taken
considering the availability of steel standard in context of Bangladesh)
(2) Modulus of elasticity of steel, sE = 200000 MPa = 29x106 psi = 2.04x107 Ton/m2
Modulus of elasticity of concrete (with 'fc =4000 psi), Ec1= 57500 'fc (psi) =
57500√4000= 3.6x106 psi = 2.531x106 Ton/m2
Modulus of elasticity of high strength concrete (with 'fc =50 MPa or 7250 psi),
Ec2= 57500 'fc (psi)= 57500√7250= 4.895949x106 psi = 3.441913x106 Ton/m2
(3) Poisson’s ratio:
For rock bolt, pile = 0.303
For pile cap, lining=0.17
(4) Shearing modulus of steel, 2(1 )s
EG
=
7 22.04x10 Ton / m2(1 0.303)
= 1.463x04x107
Ton/m2
Shearing modulus of concrete, Gc1= 6 22.531x10 Ton / m
2(1 0.17)= 1.525 x106 Ton/m2
Shearing modulus of concrete, Gc2=6 23.441913x10 Ton / m
2(1 0.17)= 2.0734 x106 Ton/m2
(5) Moment of inertia (I):
For pile rod = 4
64D =
4(0.02)64
=7.854x10-9 m4
For lining = 3
12bh =
3(1 ) (0.45)12
m x =7.594x10-3 m4
For rock bolt = 4
64D =
4(0.057)64
=5.182x10-7 m4
192
(6) Cross-sectional area:
For pile rod= 2
4D =
2(0.02)4
=3.1416x10-4 m2
For lining= bh =1mx 0.45m=0.45 m2
For rock bolt= 2
4D =
2(0.057)4
=2.55x10-3 m2
(7) Stiffness (EI):
For lining = (3.441913x106 Ton/m2) x (7.594x10-3 m4) = 2.6137x104 Ton-m2
For rock bolt = (2.04x107 Ton/m2) x (5.182x10-7 m4) = 10.57 Ton-m2
(8) (EA):
For lining = (3.441913x106 Ton/m2) x (0.45 m2) = 1.548860x106 Ton
For rock bolt = (2.04x107 Ton/m2) x (2.55x10-3 m2) = 5.202 Ton
Pile rod and rock bolt is made of steel. Pile cap is made of concrete and Lining is
made of high strength concrete with 50MPa to 60 MPa.
Load from Building Structure
For 8 storied building, load = 250 psf x 8 = 2000 psf= 9.764 Ton/m2 = 9.764 Ton/m
(as plain strain condition) = 9.764 Ton/m x 10m [As pile cap width =10m] = 97.64
Ton
