elasto-plastic three dimensional analysis of shielded tunnels, with special application on greater...

Ain Shams University Faculty of Engineering

Elasto-Plastic Three Dimensional Analysis of Shielded Tunnels, with Special Application on

Greater Cairo Metro

By Sayed Mohamed El-Sayed Mohamed Ahmed

B. Sc., Civil Engineering “Structural” - Hon. (1993) M. Sc., Civil Engineering “Structural” - (1998) Ain Shams University - Faculty of Engineering

SUBMITTED IN PARTIAL FULFILLMENT FOR THE REQUIREMENTS OF THE DEGREE OF

DOCTOR OF PHILOSOPHY

Supervisors

Prof. Dr. Mona M. Eid Professor of Geotechnical Engineering

Ain Shams University

Dr. Ali Abd El-Fathah Ali Associate Professor of Geotechnical

Engineering Ain Shams University

Dr. Hesham M. Helmy Assistant Professor of Geotechnical

Engineering Ain Shams University

Cairo - 2001

IINNFFOORRMMAATTIIOONN AABBOOUUTT TTHHEE RREESSEEAARRCCHHEERR

Name : Sayed Mohamed El-Sayed Mohamed Ahmed

Date of Birth : Jan. 20, 1970

Place of Birth : Cairo, Egypt.

Qualifications : B. Sc. Degree in Civil Engineering (Structural)

Faculty of Engineering, Ain Shams University

Hon. (1993)

M. Sc. Degree in Civil Engineering (Structural)

Faculty of Engineering, Ain Shams University (1998)

Present Job : Assistant Lecturer in Structural Engineering

Department, Faculty of Engineering, Ain Shams

University

EEXXAAMMIINNIINNGG CCOOMMMMIITTTTEEEE

Name and Affiliation Signature

1- Prof. Dr. Abd El-Rahman S. Bazaraa Professor of Structural Engineering

Faculty of Engineering – Cairo University

2- Prof. Dr. Fathalla M. El-Nahhas Professor of Geotechnical Engineering

Faculty of Engineering – Ain Shams University

3- Prof. Dr. Mona M. Eid Professor of Geotechnical Engineering


4- Dr. Ali A. A. Ahmed Associate Professor of Geotechnical Engineering


SSTTAATTEEMMEENNTT

This dissertation is submitted to Ain Shams University for the degree

of Doctor of Philosophy in Civil Engineering (Structural).

The work included in this thesis was carried out by the author in the

Department of Structural Engineering, Ain Shams University from 1998 to

2001.

No part of this thesis has been submitted for a degree or qualification

at any other university or institution.

Date : April 7, 2001

Signature : Sayed M. El-Sayed

Name : Sayed Mohamed El-Sayed Mohamed Ahmed

Ain Shams University Faculty of Engineering

Department of Structural Engineering Abstract of Ph. D. thesis submitted by:

Sayed Mohamed El-Sayed Mohamed Ahmed Title of thesis

Elasto-plastic Three Dimensional Analysis of Shielded Tunnels, with Special Application on Greater Cairo Metro

Supervisors: Prof. Mona M. Eid Dr. Ali A. Ahmed Dr. Hesham M. Helmy

ABSTRACT

The Egyptian tunneling activities have augmented in the last two decades

for several purposes such as construction of subways, sewers and road tunnels.

The preponderance of the Egyptian tunnels are constructed through soft soils

under high ground water pressures in which tunneling can trigger substantial

ground deformations. The prevailing subsurface conditions limited the

construction methods to full face tunneling machines; otherwise tunneling cannot

be proceeding. The Bentonite Slurry Shields proved to be very successful in

many mega Egyptian tunneling projects.

The objects of the present study is to introduce a sophisticated three-

dimensional numerical model of the Bentonite Slurry Tunneling Machine by

adapting the main factors affecting the pressurized Bentonite Slurry Tunneling

such as unloading forces due to excavation, ground constitutive nonlinearity,

interface condition, engineering properties of shield, rate of advance, machine

overcutting, face pressure, yielding zones, the tail grouting and the hardening

characteristics of the grout material. Soil constitutive behavior is represented

using the hyperbolic elastoplastic model to account for the effect of the stress

level, stress path and the confining pressure. Shield and tunnel lining elements

are represented by elastic elements considering the different stiffness of the liner

and the shield. The interface of the soil-shield and soil-lining is represented by a

three dimensional hyperbolic gap element and grouting element with initial

grouting stress. Special incremental technique is used to account for the variable

mesh size due to excavation and lining erection using pseudo-time technique

combined with Newton-Raphson iterative procedure. A nonlinear finite element

program was developed and used to analyze the tunneling status in three giant

projects, which are considered the foremost Bentonite Slurry tunneling projects

in Egypt. The case studies are the Greater Cairo Metro-Line 2, El-Salam Syphon

and the intersection of Al-Azhar Twin Road Tunnels and the CWO sewer.

Comparing the results of the developed numerical three-dimensional

idealization of the Bentonite Slurry Tunneling with the field measurements

compiled during the construction of the studied tunnels indicated the capability

of such sophisticated modeling to develop realistic pattern of ground subsidence

associated with tunneling. The results implied that, simulating the details of

tunneling operation through the modeling formulation is considered as the basis

for optimum idealization and is badly needed for realistic updating of the ground-

tunneling interaction. Furthermore, the three-dimensional tunneling analysis is

considered as the entirely capable arrangement to simulate very sophisticated

problems such as the intersection of multiple tunnels that cannot be preceded by

means of two-dimensional analysis or empirical approach superposition.

Consequently, the deformations and the internal forces developed in underground

pipelines and sewers due to tunneling can be estimated. The results of the

intersection of AlAzhar Road Tunnels and CWO sewer show that pre-excavation

grouting proved to be a salutary process to control the deformation and the

internal forces developed in underground structures due to tunneling. The results

of the numerical modeling of the case studies are compared with the field

measurements compiled during tunneling activities in order to assess the

proposed numerical model.

Keywords: Bentonite slurry tunneling; three-dimensional analysis; nonlinear

finite element; gap parameter; tailskin grouting; gap element; field

measurements; multiple tunnels; tunnel intersections; grouting

measures.

AACCKKNNOOWWLLEEDDGGEEMMEENNTT At the completion of this work I would like to sincerely acknowledge my

dear mentor Prof. Dr. Mona M. Eid. Her scientific and personal advice kindly

overwhelmed me all through the period of progress of this work, a fact that gave

me great momentum in completion of this thesis.

No words suffice to show how gratified am I to Dr. Ali A. Ahmed who

undertook the difficult task of genuinely advising me throughout the course of

this thesis. He kindly guided me with his distinctive advice till this work finally

came true. He spared no effort for the sake of completion and satisfaction of this

thesis. His immense support made it possible to overcome all the difficulties that

had faced me till this work was finally concluded.

I am also extremely grateful to Dr. Hesham M. Helmy for his great

support and supervision throughout this thesis. His contribution to my

personality, scientific knowledge and engineering profession is tremendously

colossal.

I would like also to extend my profound gratefulness to Prof. Dr. F. El-

Nahhas, Dr. K. Esmail and Dr. H. Abdelalla of Ain Shams University; Dr. K.

Bäppler of Herrenknecht Tunnelvortriebstechnik; and Eng. Mohamed Farghaly

for their kind help during the course of the thesis.

Finally I am greatly indebted to my family for their support and

encouragement.

Sayed M. El-Sayed

Cairo – 2001

Dedication

To my family

TTAABBLLEE OOFF CCOONNTTEENNTTSS

1. Introduction 1.1. General.............................................................................................................1

1.2. The Objects of this Research...........................................................................3

1.3. Organization of This Thesis ............................................................................4

2. Construction, Monitoring and Design of Shielded Tunnels 2.1. Introduction .....................................................................................................6

2.2. Non-pressurized Shields..................................................................................8

2.3. Pressurized Shields ........................................................................................12

2.3.1. Introduction ............................................................................................12

2.3.2. Compressed Air Shields .........................................................................16

2.3.3. Liquid Support Shields ...........................................................................19

2.3.4.Earth Support Shields ..............................................................................22

2.4. Tunnel Monitoring.........................................................................................25

2.4.1. Deformation Instrumentations................................................................30

2.4.1.1. Extensometers..................................................................................32

2.4.1.2. Inclinometers ...................................................................................32

2.4.2. Convergence Measurements...................................................................37

2.4.3. Stress Measurements ..............................................................................39

2.4.3.1. Strain Gauges...................................................................................40

2.4.3.2. Piezometers......................................................................................40

2.5.Design Aspects of Shielded Tunnels..............................................................44

2.5.1. Face Stability ..........................................................................................45

2.5.2. Ground Deformation ..............................................................................49

2.5.2.1. Ground Loss ....................................................................................49

2.5.2.2. The Deformation Field ....................................................................50

2.5.2.3. The Effect of the Ground Subsidence on Buildings........................53

2.5.3. Design of Tunnel Lining ........................................................................55

2.5.3.1. General Considerations in Lining Design .......................................55

2.5.3.2. Methods of Tunnel Lining Design ..................................................59

2.6. Tunneling Projects in Egypt ..........................................................................74

3. Tunneling Idealization 3.1. Introduction ...................................................................................................79

3.2. Finite Element Formulation...........................................................................83

3.3. The Constitutive Model.................................................................................88

3.4. Interface Formulation ....................................................................................99

3.5. Nonlinear Solution Techniques ...................................................................104

3.5.1. Incremental Techniques........................................................................104

3.5.2. Mixed Techniques ................................................................................107

3.5.3. Convergence Criteria............................................................................110

3.5.4. Calculation of Stresses from Strains ....................................................111

3.6. Excavation and Lining Installation Modeling .............................................113

3.7. Programming Aspects of the Model............................................................115

4. Greater Cairo Metro 4.1. Introduction .................................................................................................118

4.2. Line 2 - Phase 1A ........................................................................................121

4.2.1. Geological Conditions ..........................................................................121

4.2.2. TBM Selection and Operation Parameters ...........................................122

4.3. Model Verification at Lot 16.......................................................................130

4.3.1. Results of the Numerical Model...........................................................135

4.3.1.1. The Stress Level Field ...................................................................135

4.3.1.2. The Deformation field ...................................................................135

4.3.1.3. The Stress field ..............................................................................136

4.3.1.4. The Lining Deformation and Straining Actions............................146

4.4. Model Verification at Lot 12.......................................................................153

4.4.1. Numerical Simulation...........................................................................153

4.4.2. Results of the Numerical Model...........................................................155

4.5. Stabilization Measures and Deformation Field ...........................................160

4.5.1. Introduction ..........................................................................................160

4.5.2. The Face Pressure and the Face Stability.............................................160

4.5.3. Effect of the Gap Parameter on The Deformation Field ......................167

4.5.4. The Effect of Tail Grouting..................................................................168

5. Case Histories of Multiple and Twin Tunnels 5.1. Introduction .................................................................................................189

5.2. El-Salam Syphon Project.............................................................................189

5.2.1. Numerical Idealization .........................................................................192

Stratum............................................................................................................192

5.2.2. Results of the Numerical Analysis .......................................................194

5.3. Intersection of Al-Azhar Tunnels and the CWO Sewer..............................198

5.3.1. Site Geological and Geotechnical Conditions......................................199

5.3.2. Untreated Ground Analysis ..................................................................200

5.3.2.1. The model ......................................................................................200

5.3.2.2. Results of the Numerical Model....................................................203

5.3.3. Treated Ground Analysis......................................................................213

5.3.3.1. Motivation .....................................................................................213

5.3.3.2. Modeling of the grouted material ..................................................213

5.3.3.3. Results of the Numerical Model....................................................215

6. Summary, Conclusion and Recommendations for Further

Studies 6.1. Summary......................................................................................................221

6.2. Conclusion ...................................................................................................223

6.3. Recommendations for Further Studies ........................................................231

7. References and Bibliography ..........................................................232

LLIISSTT OOFF TTAABBLLEESS

Table Page

Table (2.1) Open face non-pressurized TBMs (after Monsees, 1996) …11

Table (2.2) Values of tunnel distortion (after Peck, 1969) …61

Table (4.1) TBM operational parameters (after Richards et al, 1997) …123

Table (4.2) The estimated subsurface nonlinear geotechnical

parameters

…131

Table (4.3) Lining straining actions at Lot 16 …147

Table (5.1) The estimated geotechnical nonlinear properties for El-

Salam Syphon - section “C”

…192

Table (5.2) The estimated nonlinear soil properties for the intersection

of the CWO sewer and Al-Azhar Tunnels

…200

Table (5.3) Grouting effect on the sandy soil parameters for tunneling

projects (after Tan and Clough, 1980)

…214

LLIISSTT OOFF FFIIGGUURREESS

Figure Page

Fig. (2.1) Basic feature of an open face shield (after Szechy, 1967) …10

Fig. (2.2) Segmental lining (after Ezzeldine, 1995) …14

Fig. (2.3) Tail seal systems (after Esmail, 1997) …15

Fig. (2.4) Compressed-air TBM used in Cairo Wastewater Project

(after Shalaby, 1990)

…18

Fig. (2.5) The Hydroshield (after Herrenknecht AG, Germany) …21

Fig. (2.6) The EPB TBM (after Herrenknecht AG, Germany) …24

Fig. (2.7) Schematic diagram of a pneumatic device (after Joyce,

1982)

…29

Fig. (2.8) Schematic diagram of a vibrating wire device (after Joyce,

1982)

…29

Fig. (2.9) Measuring point for monitoring surface settlement (after

EM 110-2-1908, 1995)

…31

Fig. (2.10) Single and multiple rod extensometers’ installation (after

Soil Instruments Ltd., 1999)

…33

Fig. (2.11) Installation of magnetic multiple point extensometers

(after Soil Instruments Ltd.,1999)

…34

Fig. (2.12) Installation of inclinometers (after Soil Instruments Ltd.,

1999)

…35

Fig. (2.13) Inclinometer measurement of displacement (after Soil

Instruments Ltd., 1999)

…36

Fig. (2.14) Patterns of convergence rates (after EM 1110-2901,1997) …38

Fig. (2.15) Tape extensometer installation and usage (after Soil

Instruments Ltd., 1999)

…38

Fig. (2.16) Different types of vibrating wire strain gauges (after El-

Nahhas, 1980)

…42

Fig. (2.17) Piezometer types (after Murray, 1990) …43

Fig. (2.18) Face stability coefficients for cohesionless soil (after

Atkinson and Mair, 1981)

…47

Fig. (2.19) Face stability number for cohesive soils (after Thomson,

1995)

…48

Fig. (2.20) The ground subsidence Gaussian distibution (after

Schmidt, 1967)

…52

Fig. (2.21) Shallow tunnel model (after Szechy, 1967) …64

Fig. (2.22) Check of bottom heave (after Szechy, 1967) …65

Fig. (2.23) Analysis of deep tunnels (after Szechy, 1967) …65

Fig. (2.24) Bierbäumer Theory for ground arching (after Szechy,

1967)

…66

Fig. (2.25) Bodrov-Gorelik’s Method (after Szechy, 1967) …67

Fig. (2.26) Polygonal Method (after Szechy, 1967) …67

Fig. (2.27) GRC-SRC Method (after Ahmed, 1991) …69

Fig. (2.28) Moment and thrust coefficients (after Burns et al., 1964) …72

Fig. (2.29) Egyptian tunneling projects (after El-Nahhas, 1999) …76

Fig. (2.30) Cairo Wastewater Project (after El-Nahhas, 1999) …77

Fig. (2.31) Rehabilitation of Ahmed Hamdy Tunnel (after Otsuka and

Kamel, 1994)

…78

Fig. (3.1) Modeling features of soft ground shielded tunneling …81

Fig. (3.2) Interface modeling …82

Fig. (3.3) Natural axes of hexahedral parent element …87

Fig. (3.4) Typical triaxial results …94

Fig. (3.5) Hyperbolic Stress Strain Curve (after Duncan and Chang,

1970)

…95

Fig. (3.6) Determination of Hyperbolic Model parameters (after

Duncan and Chang, 1970)

…95

Fig. (3.7) Mohr-Coulomb failure criterion …96

Fig. (3.8) Determination of the modulus number and exponent

number (after Duncan and Chang, 1970)

…96

Fig. (3.9) Determination of F and G (after Duncan et al., 1980) …97

Fig. (3.10) Determination the unloading modulus Eur (after Duncan et

al., 1984)

…97

Fig. (3.11) Effect of stress path on the soil modulii (after Duncan et

al., 1984)

…98

Fig. (3.12) Gap modeling (after Cook, 1989) …102

Fig. (3.13) Three-dimensional interface element local and global axes …103

Fig. (3.14) Stress-deformation curves for hyperbolic interface element

(after Dessouki, 1985)

…103

Fig. (3.15) Application of incremental methods in nonlinear finite

element (After Owen and Hinton, 1980)

…106

Fig. (3.16) Incremental Iterative Newton-Raphson Method (After

Owen and Hinton, 1980)

…108

Fig. (3.17) Incremental Iterative Modified Newton-Raphson Method

(After Owen and Hinton, 1980)

…109

Fig. (3.18) Stress Reversal Algorithm (after Desai and Abel, 1972) …114

Fig. (3.19) Program modules for nonlinear FE code …117

Fig. (4.1) Greater Cairo Metro Network …120

Fig. (4.2) Line 2 – Phase 1 routing (After Richards et al, 1997) …120

Fig. (4.3) Grading of the granular deposits (After Richards et al,

1997)

…124

Fig. (4.4) BSS used in the second line (after El-Nahhas, 1999) …124

Fig. (4.5) Cutting face of the BSS (After Richards et al, 1997) …125

Fig. (4.6) Bolted reinforced concrete segments (After Richards et al,

1997)

…128

Fig. (4.7) Ground water sealing measures (After Richards et al.,

1997)

…129

Fig. (4.8) Fig. (4.8) The Slurry Plant (After Richards et al, 1997) …132

Fig. (4.9) Subsurface conditions at Lot 16 (after Ardman-ACE,

1991)

…132

Fig. (4.10) Initial mesh of Lot 16 …134

Fig. (4.11) Mesh after 21 steps …134

Fig. (4.12) Maximum stress level …137

Fig. (4.13) Displacement in x direction in mm …137

Fig. (4.14) Displacement in y direction in mm …138

Fig. (4.15) Displacement in z direction in mm …138

Fig. (4.16) Surficial settlement along the tunnel axis for Lot 16 …139

Fig. (4.17) Surficial settlement perpendicular to the tunnel axis at Lot

16

…140

Fig. (4.18) Measured and estimated lateral displacement for a vertical

plane at 9.40 m from the tunnel CL

…141

Fig. (4.19) The distribution of the normal stress in x-direction (t/m2) …142

Fig. (4.20) The distribution of the normal stress in y-direction (t/m2) …142

Fig. (4.21) The distribution of the normal stress in z-direction (t/m2) …143

Fig. (4.22) The distribution of the shear stress in x-y plane (t/m2) …143

Fig. (4.23) The distribution of the shear stress in y-z plane (t/m2) …144

Fig. (4.24) The distribution of the shear stress in z-x plane (t/m2) …144

Fig. (4.25) The distribution of the major principal stress (t/m2) …145

Fig. (4.26) The distribution of the intermediate principal stress (t/m2) …145

Fig (4.27) The distribution of the minor principal stress (t/m2) …146

Fig. (4.28) Lining modes of deformation (magnification factor =

20000)

…148

Fig. (4.29) The distribution of the normal stress in x-direction (t/m2) …149

Fig. (4.30) The distribution of the normal stress in y-direction (t/m2) …149

Fig. (4.31) The distribution of the normal stress in z-direction (t/m2) …150

Fig. (4.32) The distribution of the shear stress in x-y plane (t/m2) …150

Fig. (4.33) The distribution of the shear stress in y-z plane (t/m2) …151

Fig. (4.34) The distribution of the shear stress in z-x plane (t/m2) …151

Fig. (4.35) Lining pressure in t/m2 …152

Fig. (4.36) Initial mesh for Lot 12 (after Ardman-ACE, 1991) …154

Fig. (4.37) Surficial settlement along the tunnel axis for Lot 12 …156

Fig. (4.38) Surficial settlement trough perpendicular the tunnel axis

for Lot 12

…157

Fig. (4.39) Settlement versus depth along the tunnel axis for Lot 12 …158

Fig. (4.40) Settlement versus distance at a depth of 12.50 m for Lot 12 …159

Fig. (4.41) Distribution of the face axial displacement for different

face pressure values

…162

Fig. (4.42) The effect of the face pressure on the maximum axial

displacement

…163

Fig. (4.43) The effect of the face pressure on the surface vertical

deformation

…164

Fig. (4.43) The effect of soil arching on the face limiting equilibrium …165

Fig. (4.45) The effect of the face pressure on the maximum surface vertical

deformation.

…166

Fig. (4.46) The effect of the overcutting loss on the surface vertical

deformation.

…170

Fig. (4.47) Surficial vertical deformation trough for overcutting loss =

0.0%

…171


0.05 %

…172


0.30 %

…173


0.50 %

…174


0.75 %

…175


1.00 %

…176

Fig. (4.53) The effect of the overcutting loss on the maximum surface

vertical deformation.

…177

Fig. (4.54) Surficial vertical deformation trough for (a) overcutting

loss = 0.00 % and (b) overcutting loss = 1.00 %

…178

Fig. (4.55) The distribution of vertical deformation at the tunnel CL

for overcutting loss = 0.0%

…179



…180



…181

Fig (4.58) The distribution of vertical deformation at the tunnel CL


…182



…183



…184

Fig. (4.61) The effect of the tail grouting pressure on the maximum

surface vertical deformation.

…185

Fig. (4.62) The effect of the tail grouting pressure on the vertical

deformation of the crown and the invert

…186

Fig. (4.63) The effect of the tail grouting pressure on the maximum

vertical deformation of the crown and the invert

…187

Fig. (4.64) The analogue – a man pulling bricks around a room (after

Simpson, 1993)

…188

Fig. (5.1) North Sinai Developing Project (after Mazen and Craig,

1994)

…191

Fig. (5.2) El-Salam Syphon vertical alignment (after Mazen and

Craig, 1994)

…191

Fig. (5.3) Mesh for the inclined tunnels …193

Fig. (5.4) Geotechnical subsurface conditions at the instrumented

section “C” (after Esmail, 1997)

…193

Fig. (5.5) Surficial vertical deformation after construction of tunnel

T1

…195


T2

…195


T3

…196


T4

…196

Fig. (5.9) Surficial settlement troughs due to individual tunnels …197

Fig. (5.10) General layout of Al-Azhar Road Tunnels (after Ramond

and Guillien, 1999)

…201

Fig. (5.11) Mesh for the intersection …202

Fig. (5.12) Subsurface conditions at the site of the intersection …203

Fig. (5.13) Maximum stress level after driving the north tunnel …205

Fig. (5.14) Maximum stress level after driving the south tunnel …205

Fig. (5.15) Vertical deformation in mm after driving the south tunnel …206

Fig. (5.16) Vertical deformation in mm after driving the south tunnel …206

Fig. (5.17) Surficial vertical deformation of the untreated grounds …207

Fig. (5.18) Vertical deformation of the CWO tunnel in mm (the north

tunnel heading approaches the intersection)

…208

Fig. (5.19) Axial stresses of the CWO tunnel in t/m2 (the north tunnel

heading approaches the intersection)

…208

Fig. (5.20) Vertical deformation of the CWO tunnel in mm (the north

tunnel is completed)

…209

Fig. (5.21) Axial stresses of the CWO tunnel in t/m2 (the north tunnel

is completed)

…209

Fig. (5.22) Vertical deformation of the CWO tunnel in mm (the south

tunnel heading approaches the intersection)

…210

Fig. (5.23) Axial stresses of the CWO tunnel in t/m2 (the south tunnel

heading approaches the intersection)

…210

Fig. (5.24) Vertical deformation of the CWO tunnel in mm (the south

tunnel is completed)

…211

Fig. (5.25) Axial stresses of the CWO tunnel in t/m2 (the south tunnel

is completed)

…211

Fig. (5.26) Final deformation of the CWO tunnel (deformation

magnification factor 1000)

…212

Fig. (5.27) Some projects that used grouting techniques (after Tan and

Clough, 1980) …214

Fig. (5.28) Final vertical deformation of the CWO tunnel in mm

(weak grouting)

…216

Fig. (5.29) Final axial stresses of the CWO tunnel in t/m2 (weak

grouting)

…216


(medium grouting)

…217

Fig. (5.31) Final axial stresses of the CWO tunnel in t/m2 (medium

grouting)

…217


(strong grouting)

…218

Fig. (5.33) Final axial stresses of the CWO tunnel in t/m2 (strong

grouting)

…218

Fig. (5.34) Final vertical deformation of the CWO tunnel in mm (very

strong grouting)

…219

Fig. (5.35) Final axial stresses of the CWO tunnel in t/m2 (very strong

grouting)

…219

Fig. (5.36) Effect of grouting on the maximum internal stresses in the

CWO sewer

…220

Fig. (5.37) Effect of grouting on the maximum settlement of the CWO

sewer

…220

1

Chapter One

INTRODUCTION

1.1. General

Tunnels were utilized since the dawn of history. Man made use of caverns

as shelters and dwellings in the Prehistoric Ages. The old civilizations in Egypt,

Greece, India, Iraq, and Italy used hand-tunneling techniques to dig the ground

for several purposes such as mining, water supplying, burial and war. Tunnel

construction has been accelerating significantly since the Second World War.

The use of modern metallurgy and the contemporary hard alloys enables the

tunnel boring machines (TBMs) to work in a wide spectrum of ground condition

ranging from soft soil to very competent rocks. Modern and powerful machinery

provided tools to excavate tunnels and transport the spoil away. Current

surveying and GPS systems tolerate only a few centimeters deviation of tunnel

routing during driving. The development of new pressurized techniques allows

tunnel constructing even through unfavorable conditions such as soft ground and

high water table conditions.

Public and government resistance is continually solidifying against

disruption of traffic, trade and the environment caused by open-cut tunneling in

the urban congested areas. To meet challenge of the restricted requirements of

underground works, new and sophisticated tunneling techniques are used instead

of open-cut methods. Tunneling Engineering brings under one banner a diversity

of non-disruptive procedures for the installing of the underground facilities that

enclose both empirical thumb-rules and theoretical studies. As tunneling practice

is significantly ahead of its theoretical background, empirical rules based on

observational studies are frequently exploited; however, they cannot include the

impact of the new and improved methods used in tunnel driving on the ground

2

stability and groundwater control. Since tunnel failures can be extremely

threatening to life and properties, more research is required in the field of

tunneling to transform tunneling from art to science and to provide us with a

deep insight of the behavior of tunnels. To accomplish this goal, the theoretical

studies and the tunnel monitoring programs should be integrated to assess

tunneling in diverse ground conditions using suitable installation procedures.

New studies should model the complex ground behavior as well as the new

sophisticated tunneling techniques.

Many two-dimensional researches were conducted focusing on the crucial

factors affecting the tunnel construction and the safety of the surrounding

structures models. Hamdy (1989) and Ali (1990) considered the unloading

caused by soil removal is carried out in an incremental sense. At the end of each

increment the amount of ground loss is estimated; when the ground loss reaches

a specified value, the calculation is terminated. Ahmed (1991) used the

incremental non-linear FEM combined with the Convergent-Confinement

Approach of lining analysis to update the ground-lining interaction in which

beam elements are used to model the lining while two-dimensional plane strain

elements are used to model the soil. Esmail (1997) successfully used the Gap

Parameter Technique with some modifications to allow the simulation of the

tunnel construction stages.

Although, two-dimensional models are considered superior to the

empirical rules-of-thumb through allowing some modeling to the construction

techniques, they cannot grasp all the aspect of the tunneling process. Three-

dimensional models bestow more information about the face stability, tail

grouting and displacement field around and ahead of the tunnel. Till soon, little

literature is available in which the tunnel is presented by three-dimensional

model. This type of modeling is difficult to implement because of needed

computing and numerical capabilities especially when using the advanced

nonlinear soil models and gaps or interfaces. The complications in modeling of

3

soil excavation, shield driving, overcutting and tail grouting further obstacle this

type of analysis especially for soft ground pressurized shielded tunneling.

1.2. The Objectives of the Current Research

The Egyptian tunneling activities have augmented in the last two decades

for several purposes such as construction of subways, sewers and road tunnels. It

is anticipated that tunneling activities will continue at the same rate for at least

another decade to complete the plans of infrastructure renewing (El-Nahhas,

1999). The preponderance of the Egyptian tunnels were built through soft

grounds under high ground water pressures in which the pressurized closed face

shielded tunneling is considered the due method to advance tunnels to maintain

the ground stability and safety of operators. Egyptian tunnels impose many

diverse problems during routing, design and construction. The foremost problems

are related to the damage of surrounding feeble buildings due to surface and

subsurface ground subsidence. Prediction of deformation field around tunnels is

an inevitability to anticipate the potential impairments to neighboring buildings

and utilities.

The foremost goal of this study is to develop a three-dimensional model

that can capture the different aspects of soft ground pressurized shielded

tunneling. The developed model incorporates the sophisticated ground support

measures so as to provide a realistic predication of the deformation field

associated with tunneling in the geotechnical conditions prevailing in the

Egyptian tunneling projects. The developed model is used to update the studies

related to the bentonite slurry technique, which was used in Greater Cairo Metro

Project and many other giant Egyptian projects and proved to be very successful.

To achieve the goals of the anticipated enquiries, a nonlinear finite element

program, with capabilities of three-dimensional analysis, nonlinear soil

constitutive behavior and interface modeling, was developed by the author. A

special three-dimensional hyperbolic interface prestressed element is exploited to

4

model the soil-shield-lining interface. The proposed numerical model is used to

evaluate three case studies of the giant tunneling projects constructed in Egypt

namely, Greater Cairo Metro, El-Salam Syphon and the intersection of Al-Azhar

Twin Road Tunnels and the CWO sewer pipe at Port Said Street. The later two

case histories represent multiple tunnels in which three-dimensional analysis was

seldom utilized; they are typical three-dimensional problems that cannot be

simulated precisely using two-dimensional models or empirical superposition

techniques. The precautionary pre-treatment using soil grouting to minimize the

effect of Al-Azhar tunnels on the CWO sewer is investigated. The results of the

numerical modeling of the three case studies are then compared with the field

measurements compiled during tunneling activities in order to assess the validity

of the developed numerical model.

1.3. Outline of the Thesis

The thesis consists of six chapters. In the following section, the contents

of each chapter are briefed:

Chapter (2) describes the different aspects of shielded tunneling and the

techniques used in soft ground condition. The ground water effect on

the construction techniques is illustrated. A review of tunnel

instrumentations and the geotechnical aspects of tunneling design are

elucidated. The Different methods of ground deformation estimation

and effect of these deformations on structures are reviewed. The

evaluation methods of the induced internal forces in the lining are

surveyed. Face pressure and its effect of the face stability and ground

deformation are clarified. Ground improvement techniques used to

minimize the harmful effect of tunneling and increase the tunneling

stability are discussed.

Chapter (3) describes the elements of the developed model. Finite element

idealization is formulated with emphasis on nonlinear techniques and

5

the modeling of excavation and construction. The used nonlinear

models and nonlinear numerical procedures are explained.

Hyperbolic three-dimensional interface element formulations are

described. The proposed tunnel model is illustrated emphasizing on

simulating of the different stages of tunnel construction.

Chapter (4) comprises a three-dimensional analysis of the shielded tunneling

used during the construction of Greater Cairo Metro–Line2–Phase

1A. Different ground support measures and tunneling factors

included in the analysis are evaluated parametrically. Results are

compared to the field measurement compiled during the construction

for two different Lots. The geotechnical and constructional details

affecting the resulting deformation fields are clarified to recommend

successful tunneling conditions.

Chapter (5) encloses a three-dimensional study of multiple and twin tunnels. Two

case histories are discussed; namely, El-Salam Syphon and the

intersection of Al-Azhar and the CWO sewer. Two cases represent

different cases of subsurface condition and alignments. Different

factors affecting the mutual interaction of the analyzed tunnels are

discussed. The effect of ground modification utilizing pre-grouting

measures, so as to minimize the tunneling effect in tunnel

intersections, is assessed parametrically.

Chapter (6) presents a summary of the studies that were implemented in this

thesis along with different concluding points and annotations of the

considered case histories. Finally, recommendations for further

studies are pointed out.

6

Chapter Two

CONSTRUCTION, MONITORING AND DESIGN OF

SHIELDED TUNNELS

2.1. Introduction

While in prison for debt, a French engineer, Marc Brunel, watched a

worm boring through wood, using the hard shell on its head as a shield as it

tunneled into the wood, the worm excreted a substance that formed a rigid lining

behind it. Brunel copied this idea on a large scale. He used a large iron frame to

protect the sides of a tunnel while masons are lining the inside with brick. After

he patented his idea in 1820, Brunel used it in the construction of the Thames

tunnel in Britain during the period of 1825-1843. The employed shield consisted

of twelve sections; each was three-foot wide in which workers could excavate the

face then the whole cast iron assembly was inched forward, a section of brick

lining was built behind. During the construction, the tunnel was flooded at least 5

times; the consequent toll of death, injury and disease was quite formidable.

Further significant developments in subaqueous shielded tunneling were the

application of cast iron segmental linings installed in conjunction with the shield

advance and the use of compressed air in 1873 under Hudson river to overcome

water inflow problems. The performance of shielded TBM was enormously

enhanced by introduction of the bentonite slurry and the earth pressure balance

TBMs.

Selection of appropriate shields requires consideration of ground and

water condition, tunnel size, support system and the excavation environment. The

main factor that influences the choice of tunneling technique is the ground and

water condition as it favors the choice of some methods and present major

7

limitations on some other tunneling techniques. Wittaker and Frith (1990)

divided the major categories of ground conditions in tunneling as following:

a) Soft grounds: soft grounds include clays, gravels, sands and

weathered rocks in various states of decomposition. These

materials impart no difficulties in digging out and can easily be

removed by hand-excavation. However the difficulties in tunneling

arise from their position with respect to the groundwater table that

may result in mud and other unconsolidated material inflow to the

tunnel and associated ground loss. Tunneling in soft ground

conditions generally employs shields as standard practice to

provide safe working environment for workers. Almost all the

Egyptian underground constructions are situated within water-

bearing soft ground of various soil deposits and weak rocks.

b) Rock conditions: Rock strengths cover a wide range from relatively

weak sedimentary rocks of 10-40 MPa to strong igneous rocks of

150-300 MPa. Low strength rocks may prove advantageous to

machine excavation while high rock strength may preclude

machine excavation but require minimal temporary support. Tarkoy

and Byram (1991) reported recently the use of modern tunnel

boring machines instead of the drill-and-blast techniques in many

competent rock formations in Hong Kong.

c) Mixed face conditions: Tunneling at the bedrock horizon often

results in the upper part of the tunnel face being in soil or heavily

weathered rock while the lower part of the face is in rock. This

condition presents problems with machine tunneling and in

connection with provision of effective temporary support.

The shielded machines are classified into two main types (Wittaker and

Frith, 1990; Thomson; 1995 & Sutcliffe, 1996): non-pressurized and pressurized

8

TBMs. In the first category, TBMs cannot apply counterbalancing pressure at the

face while the second type of TBMs has a bulkhead that is provided to prevent

the face from collapse by applying a counterbalancing face pressure.

2.2. Non-pressurized Shields

Non-pressurized shields do not use counterbalancing pressure at the face

that may be used to minimize the ground deformation resulting from the potential

face instability. This type of TBMs has usually open or part-open face in which

direct or limited access to the face, or to a point immediately behind the face

cutters, is available. Access to the face allows operators to identify and deal with

any natural or artificial obstructions.

Non-pressurized TBMs are used for shorter drives in stable ground

conditions. Open face shields tend to be favored where the ground is sufficiently

firm to be free standing or where no measure of face support is required. The

open non-pressurized techniques are suitable for a wide range of cohesive ground

including rock, clays and silty clays, which can be below the groundwater table.

Non-cohesive soils above the water table are also suitable, but become less

appropriate with existence of groundwater pressure in cohesionless soils.

In case of low rates of advance, drainage of the face soil takes place,

which causes the strength of cohesive soils to change from cohesive to frictional

and the stand-up time will be short. To avoid these time-dependent face stability

problems in cohesive soils, the rate of machine advance should be sufficiently

rapid to ensure that undrained conditions will prevail. As the cohesive soil

becomes less plastic and more permeable, rates of advance have to be increased

to maintain undrained conditions. Where this is not possible then some form of

pressurized support of the face is necessary to avoid instability.

9

Szechy (1967) illustrated the basic structural features of an open shield as

following:

1. Shield body. This part of the shield is essentially a steel cylindrical

shell appropriately stiffened with ribs and bracing members. The shield

body houses the equipment such as hydraulic rams and pumping

equipment for pushing the shield forward relative to the lining as

shown in Fig. (2.1). A typical length of shield body is around 2 m

although it is dependent upon the diameter of the excavation.

2. Shield tail. The tail pan of the shield structure extends behind the

shield body and serves the purpose of providing space within which

the lining segments are erected during the tunnel lining stage. The tail

width is normally about one and a half times the unit lining width.

Additionally there is the necessity for a clearance width of the order of

25 mm between the tail and lining to permit alignment corrections.

3. Cutting edge. This part of the shield forms the leading edge and

requires to be heavily reinforced with steel plating. The cutting edge is

also frequently coated with an abrasion-resistant material to assist

cutting in harder ground. A common structural feature is the provision

of a hood forming the upper half of the shield cutting edge, which

gives protection to operators particularly when adjusting and

advancing the breast boards. Not all cutting edges incorporate a hood

feature in shield tunneling projects.

Non-pressurized shields can be classified into: manual, semi-mechanical,

mechanical and blind, with a number of variations within each of these classes.

Table (2.1) describes the different types of non-pressurized TBMs.

10

Fig. (2.1) Basic feature of an open face shield (after Szechy, 1967)

Advance Cutting Edge Shield Body Tail

Hydraulic Ram

Pressure Distribution

Ring

I- Ground Excavation in preparation for shield advance

II- Shield advance by rams pushing against tunnel lining via a pressure distribution ring

III- Retraction of pushing rams and erection of next ring of segmental support.

New Ring

11

Table (2.1): Non-pressurized TBMs (after Monsees, 1996).

Type Description Notes Sketch

Hand-dug (manual)

shield

Good for short, small tunnels in hard, non-

collapsing soils. Usually equipped with

face jacks to hold breasting at the face. If soil conditions require it, this machine may have movable hood

and/or deck

A direct descendent of the Brunel shield. Now

largely replaced by more mechanized equipment. Sometimes used at the

head of large cross-section, jacked tunnels.

Semi-mechanized

Similar to the hand-dug shield, but with a back

hoe, boom cutter (roadheader) or the like

Until very recently, the most common shield. Often equipped with

“pie plate” breasting and one or more tables. Can

have trouble in soft, loose, or running

ground. Compressed air may be used for face

stability in poor ground.

Mechanized

A fully mechanized machine. Excavates

with a full-face cutter wheel and pick or disc

cutters.

Manufactured with a

wide variety of cutting tools for various soils Face openings (doors,

guillotine, and the like) can be adjusted to

control the muck taken in versus the advance of the machine May also

be used when compressed air for face stability in poor ground.

Blind shield

A blind simple shield used in very soft clays and silts. Adjusting the aperture opening and

the advance rate controls muck

discharge.

Used in harbor and river

crossings in very soft soils. Often results in a wave for mound of soil

over the machine.

12

2.3. Pressurized Shields

2.3.1. Introduction

The need for a machine capable of tunneling through non-cohesive ground

both above and below the water table, without affecting the overlying properties

gives rise to special types of TBMs known as pressurized closed face machines.

These machines incorporate a pressure chamber immediately behind the front

cutting head or disc. The chamber, filled with compressed air, water, slurry or

soil, provides a counterbalance pressure to soil and water pressures. No access to

the face is available and all operations are controlled by the machine operator,

who will be stationed at a control console in the rear of the shield. Special seals

are incorporated between the cutter head and machine body for the purpose of

sealing mud and water. Various designs of seal have been employed, with multi-

lip seals proving successful. The propelling movement of the shield requires a

longitudinally solid liner to offer the support. Special measures are required to

seal the joint between the shield tail and the installed lining segments against the

grouting pressure that is injected behind the segments. Tail grout is used to

counterbalance the ground and water radial pressure and minimize the ground

loss.

Precast concrete or cast iron segmental lining is the prevailing lining

system for soft ground TBMs. A small segment, the key, is often included in the

system; Fig.(2.2) describes this system. The segment shape is usually rectangular

or trapezoidal to allow the control of tunnel curved alignment. The assembly of

the lining system takes place inside the tail of the shield in a staggered system.

Special care must be paid to the joint insulation and compressibility. Bituminous

packing or rubber gaskets are usually used for the joint filling in the insulation

layer. Precast concrete segments are assembled either by a tongue-and-groove

interlocking system or by bolting.

13

Esmail (1997) summarized the main three types of the tail seal used for

pressurized TBMs as rubber seal, steel brush seal and Extru-concrete seal. Fig.

(2.3.a) shows a typical rubber seal. The stiffness of rubber seals is frequently

insufficient to close the gaps between inaccurately placed segments. The steel

brush seal is arranged in as many as five rows, one behind the other as shown in

Fig. (2.3.b). Grease is pumped into the chambers between the individual rows,

whereby the grease pressure in each chamber is increased towards the shield tail

so that the last chamber pressure is about 2 bars higher than the grouting pressure

in order to prevent the grout from penetrating through the brushes to the shield

interior. The Extru-concrete seal system comprises a movable steel ring used to

close the shield tail joint and supported by hydraulic jacks from the body of the

shield as shown in Fig. (2.3.c). The hydraulic jack circuit is linked to a regulated

gas reservoir, which provides the elastic spring. The steel device is sealed against

the shield tail with a rubber seal, and with spring strips against the segments.

Extru-concrete is pumped through the movable steel device into the shield tail

joint. The Extru-concrete is a normal concrete with chemical additives to

improve its hardening-rate. The gaps between inaccurately placed segments are

sealed by the concrete

Although the pressure balance machines have been designed to operate in

unstable soil conditions such as non-cohesive soils below the water table,

practically, they are used in a much wider range of soil conditions. Many

variations of pressure chamber shield have been developed some of which

incorporate crushing devices to cope with stones and boulders. Various

pressurizing techniques are employed; the oldest technique is to use the

compressed air as a counter measure against the groundwater pressure. Modern

techniques include liquid or earth supporting measures. The following section

describes the different types of the pressurized TBMs and the different aspects of

each type.

14

Fig. (2.2) Segmental lining (after Ezzeldine, 1995)

15

Fig. (2.3) Tail seal systems (after Esmail, 1997)

16

2.3.2. Compressed Air Shields

Compressed air was used as early as 1830 by a British engineer (Thomas

Cochrane) in sinking caissons. In 1873, Clinton Haskins promoted a railway

tunnel under the Hudson River in New York, which used compressed air to

support the tunnel against the pressure of water above the tunnel. Compressed air

working is used in conjunction with open face shields in subaqueous conditions

so as to hold back the soil and groundwater by applying a counterbalancing air

pressure. Fig. (2.4) shows the details of the compressed air TBM used in Cairo

Wastewater Project. The air pressure is used to prohibit groundwater intrusion

into the tunnel. The result is decreased movement of the ground into the tunnel.

Drying up of the tunnel face by the action of compressed air will encourage non-

cohesive wet soils to exhibit improved ability to stand and to be controlled by

breasting. The ground properties in the dried region must be sufficient to prevent

face instability (Ezzeldine, 1995). Sometimes, pre-grouting either from the

ground surface or from the face may be used to increase the ground strength.

Special attention needs to be paid to effectively seal the space between the

lining and the excavated tunnel sides in order to maintain steady air pressure.

Where open gravel with little interstitial material such as sand occurs, then

compressed air losses can easily arise. In this case, air losses may be limited by

the application of bentonite or a bentonite-cement mixture at the face. Escapes of

compressed air through permeable beds of overlying unconsolidated materials

can result in piping action and possibly give rise to forming a significant path for

water to flow into the tunnel. The pressurized zone extends from the tunnel face

backward up to the bulkhead at some distance behind the shield. At the shield

tail, the ground surface is under air pressure limiting the possibility of ground or

water intrusion into the working zone. Therefore, the need for the grout and the

tail seal is diminished, as they are needed to deal with ground under supportive

air pressure. A conventional grouting system may be regarded as sufficient in

many instances. In these cases, pea gravel is used as the primary grout material

17

followed by mortar sometime later. The required longitudinal reaction from the

lining system is relatively low in this type of pressurized TBMs.

A compressor air plant located above the ground surface is used for

supplying compressed air to maintain the face pressure, providing power supply

to air tools for excavation, drilling, air winching, and other purposes. A cooling

system must be incorporated into the compressor to release the generated heat

from the compressed air and to reduce its humidity by condensation. A bulkhead

is constructed to seal off the working space from outside air. The bulkhead must

include air locks to allow material and personnel passage to the face. Two

separate types of locks are necessary: locks for personnel and for materials as the

rate of air decompression of the personnel lock is regulated to be slower than that

required for the material lock for hygienic reasons. The bulkhead must be

fabricated with great care in order to insure that no voids are left for air to escape

through joints around air, slurry and power pipes passing through it. Ezzeldine

(1995) described two configurations of the compressed air bulkhead as

following:

1. The bulkhead is constructed close to the pressurized face

using a steel cylinder lock. The head part only is locked off

to avoid working in compressed air. The operator can handle

the excavating equipment in the inside pressurized zone or

in free air by observation through a glass panel or with the

aid of a TV camera. It is still possible for a man to enter the

chamber if necessary to remove any obstructions such as

boulders.

2. The bulkhead is constructed on the ground at the head of the

shaft. In this case, a T-lock may be placed at the shaft

entrance. All work in the line, the shield and the shaft

bottom is accomplished under compressed air.

18

Working in compressed air for a long time can be a serious health hazard.

So, whenever operating pressure is needed to be greater than one bar, pressurized

closed face shields offer a less hazardous alternative to compressed air working.

Fig. (2.4) Compressed-air TBM used in Cairo Wastewater Project

(after Shalaby, 1990)

Faceram

Sliding table

Backhoe 875 mm

1500 max.

4260 O/A Body 9000 STK 1375 Tail Skin Shovel Rams

19

2.3.3. Liquid Support Shields

A suspension or water is maintained at a pressure immediately behind the

cutting head in a pressure chamber to balance the excavated face. The simplest

form of the liquid support shields employs water pressure. The appropriate soil

conditions for this type of equipment are cohesive soils that may incorporate

cobbles, and sands and gravels. A cone crusher may be used to reduce all gravel

or boulder material to a defined maximum particle size before it enters the

pressure chamber to be pumped away as slurry. Frequently an auger-powered

cutter head carries the excavated spoil back into the water pressure chamber,

where it is mixed and transported to the surface by a pumped slurry system. For

this type of water-based slurry treatment and disposal are less complex and costly

than for bentonite slurries.

The pressurized Bentonite Slurry shields were introduced in the 1960s for

segmental tunneling. The basic principle of operation of this method is to inject a

pressurized slurry mixture into a chamber enclosing the working face as shown

in Fig. (2.5). The shield area in which the cutting wheel is rotating is designed as

the extraction chamber. A slurry pressure inside the chamber is set to balance the

groundwater head and the sufficient soil pressure to prevent soil instability. The

face is excavated with full-face rotating cutting faces that may be flat-faced plate,

drum or dome-shaped. The excavated material is forced into the pressurized

slurry chamber behind the head cutting head through slits or ports. Some Slurry

Shields also have a crushing capability. Stones and cobbles passing into the

pressure chamber are diverted into a crusher chamber that reduces them to an

acceptable size for pumping. Unwanted consolidation can occur through several

mechanisms including loss of groundwater into the tunnel face where face

support slurry does not precisely balance groundwater pressures. Permanent

surface settlement can be caused where face instability is allowed to develop.

20

Unless the earth pressure at the face is precisely balanced there will

always be movement at the ground surface. If the face is allowed to move

towards the shield when a tunneling shield is advancing, it will result in a zone of

surface settlement traveling in front of the shield. Conversely if the shield is

forced forward into the face so that soil moves away from the shield, it can result

in a zone of surface heave traveling in front of the shield. The required balance

between these two extremes is a shield, which advances at such a rate that the

soil neither moves towards the shield nor is thrust away. The pressure at the

shield face should ideally be maintained at the at-rest pressure to avoid horizontal

compression or expansion of the soil and prevent settlement or heave.

The difference between water-pressure and slurry-pressure machines and

when either would be appropriate to be used is not readily distinct. For some

cohesive soils it may only be necessary to use water that forms perfectly

adequate slurry for face support and spoil conveyance as it is mixed with the

natural excavated soil. In non-cohesive fine-grained soils above the water table,

the slurry will penetrate the face only a little, so no special measures are needed,

except to ensure that excess slurry pressures do not cause soil fissuring. In

coarse-grained non-cohesive soil, however, the objective is for the slurry to

create a zone of penetration and to build up a filter cake. In open-structured

ground, such as gravel or cobbles, even greater care needs to be given to the

slurry formulation and its additives to avoid loss of material and pressure. The

slurry has a bentonite base but various additives may improve its stabilizing

performance. Depending on the nature of the soil, the slurry needs to be designed

with appropriate additives, such as polymers and cellulose-based materials, if it is

to fulfill these objectives. Soils exposed at the tunnel face are penetrated by the

slurry and become sufficiently solidified to be suitable for excavation by the

cutter head of the machine. The material cut collects in the invert where agitation

causes liquefaction sufficient for pumping out of the tunnel together with soil

particles and cobbles if present. The bentonite is returned to the face after

21

separation. It should be pointed out that slurry pressure balance machines are

now often selected not only for the geotechnical advantages of pressure balance

in difficult soil conditions but also for their technical and economic efficiency

even in stable soil formations.

1. Cutting wheel 5. Compressed air lock 9. Compressed air buffer

2. Cutting wheel drive 6. Erector 10. Submerged wall

3. Extraction chamber 7. Lining segments 11. Suspension

4. Pressure wall 8. Tunneling jacks 12. Conveyor pipe

Fig. (2.5) The Hydroshield (after Herrenknecht AG, Germany)

22

2.3.4.Earth Support Shields

These shields use the excavated soil as the medium to provide the required

face pressure. Some versions operate with a disc head and ports; others with

spoke configurations in which arrangement and the opening ratio are determined

by the nature of the ground. Earth Pressure Balance Shields (EPBSs) are most

suited to soft and unstable formations including high plasticity clays, silts and

granular soils with a high percentage of fines. Machines combine a slurry

chamber with mechanical earth pressure balance, are frequently employed where

ground movement is a primary concern. These machines are less well suited to

highly permeable soils and where there are hard inclusions. As the shield

advances, the spoil is forced into the chamber behind, forming an impermeable

plastic mass, which is maintained at a predetermined balancing pressure. The

spoil is removed from this chamber by an auger conveyor. A variety of devices

control pressure and spoil discharge to the required level. The configuration of

Herrenknecht EPBS system is shown in Fig. (2.6).

Broadly speaking, slurry machines are designed primarily for sandy or

gravelly soils. As long as a bentonite cake can be formed, it is possible to

maintain face stability by applying a counter balance pressure. Slurry machines

can be used in clayey ground but the slurry treatment process may require more

time and be more costly if the clay disaggregates in the slurry mud. EPBSs are

preferred to slurry machines when the grain size of the soil decreases to silts and

clays because of its mucking system. Low permeability clayey silty layers can

safely be kept stable by applying an earth pressure. Other parameters to be

considered when selecting a tunnel machine include items such as the surface

area capacity for treatment plant with fine-grained soils, discharge regulations,

cost of additives for EPBSs, … etc.

In several cases manufacturers have combined the advantages of slurry

pressure chamber and mechanical earthpressure balance. Thomson (1995)

23

referred to these combined pressure feature machines as combined pressure

machines. Examples of the combined machines includes

• Slime Shield: The Daiho Company from Japan developed this type

of TBM for working in high groundwater pressure conditions or in

sandy soils that have no plastic flow. Slurry based on bentonite or

other chemical additives is injected into the chamber in relatively

small percentages. This is then mixed in with the natural soil to

produce the required plastic flowing material, which is also

impervious.

• Iseki Mechanical Earth Pressure Counter-Balance Shield

(MEPCBS): This type provides a degree of mechanical earth

balance by having the cutting head mounted so that it can be

independently pressed against the soil face. By using a combination

of slurry pressure and mechanical earth pressure, the shield

pressure can be maintained at a level above the active earth

pressure but below the passive earth pressure reducing the risk of

settlement and heave. It also allows a better control over the

volume of soil removed by adjusting the openings on the face disc.

MEPCBSs are particularly suited to working in water-bearing

sands, silts and clays.

• Herrenknecht Mixshield TBM: This machine involves many types

of face support measures. The counter pressure can be applied

using compressed air, slurry or the excavated ground itself. The

change from mode to another is fast and incorporated in the

machine design; thus, a wide spectrum of ground can be excavated

employing the same TBM (Herrenknecht and Maidl, 1994)

24

1. Cutting wheel 5. Compressed air lock 9. Conveyor belt

2. Cutting wheel drive 6. Erector 10. Screw Conveyor

3. Extraction chamber 7. Lining segments

4. Pressure wall 8. Tunneling jacks

Fig. (2.6) The EPB TBM (after Herrenknecht AG, Germany)

25

2.4. Tunnel Monitoring

Many construction contracts for tunnels incorporate the geotechnical

instrumentation and monitoring program as an integral part of the construction

work. Tunneling monitoring programs can be considered as a safety measure to

assure no excessive ground deformation will endanger the nearby buildings and

utilities. Another motive for conducting tunneling instrumentation program is the

subsurface conditions, which are usually too complex to ensure a reliable and

economic design of tunnels. The designer has to make some assumptions to carry

out an initial design that scopes for modification if unforeseen conditions arise on

the basis of the feedback of the monitoring observations. The instrumentation

program provides the geotechnical engineer with information for checking and

verifying his design assumptions.

An instrumentation program is a comprehensive approach that assures that

all aspects of instrumentation from planning and design through maintenance and

rehabilitation are commensurate with the overall purpose. To be fruitful, such

monitoring programs must be carried out for well-defined purposes, be well

planned, and be supported by competent staff through completion and

implementation of results from the monitoring program. The principal objectives

of a geotechnical instrumentation plan may be generally grouped into the

following four categories:

1. Analytical, assessment of the data obtained from geotechnical

instrumentation may be utilized to verify design parameters, design

assumptions and evaluate construction techniques.

2. Prediction of future performance, instrumentation data should be used in

justifiable predictions of future behavior of tunnels in similar

environments.

3. Legal evaluation, valid instrumentation data can be valuable for potential

litigation relative to construction claims.

26

4. Development and verification of future designs, analysis of the

performance of existing tunnels and instrumentation data generated during

operation, can be used to advance the state-of-the-art of design and

construction.

More than one type of the same instrument may be used to provide a

backup system even when its accuracy is significantly less than that of the

primary system. Repeatability can also give a clue to data correctness. It is often

worthwhile to take many readings over a short time span to determine whether a

lack of normal repeatability indicates suspect data. Murray (1990) discussed the

layout of the instrumentation program. He concluded that the most practical

approach is to provide detailed monitoring at a few locations where the

conditions are considered more critical and to augment this information with

settlement observations from elsewhere. The most critical areas could be those

where the structures are highest, where the soft soils are deepest, or where the

consequences of failure are most unacceptable. The wrong type of instruments

placed in inappropriate locations can provide information that may be confusing,

or divert attention away from other signs of potential distress. The factors needed

to be considered in selecting a particular design of instrument are summarized as

following:

1. The instrument must be able to be transported and installed without

damage or significant change of calibration. It must be able to

withstand the effects of construction and sustained loading.

2. The use of simple direct operating mechanisms may avoid the

problems of maintenance and reliability. Conversely, if complex

systems were to be used, possibly because of a requirement for

automation or accuracy, consideration would need to be given to how

such instruments should be maintained.

27

3. Damage by construction activity may be minimized or even prevented

by placing the monitoring system outside the area of the construction

activity.

4. A particular design of instrument may more readily lend itself to a

requirement for automatic data logging.

5. The choice of instrument on the basis of cost should include the costs

incurred in installing, reading and evaluating the data.

6. Some types of instrument employ measurement principles that have

better stability characteristics than the other ones.

7. The selection of a particular instrument to attain a desired accuracy can

have an influence on most of the other factors referred to above.

Most instrumentation measurement methods consist of three components:

a transducer, a data acquisition system, and a linkage between these two

components. A transducer is a module that translates a physical change into

analogous electrical signals whilst data acquisition systems are the portable

readout units. The different measuring techniques used in geotechnical

instrumentation are classified into one of the following categories:

(a) Pneumatic devices. Pneumatic devices are used in pneumatic piezometers,

earth pressure cells, and liquid level settlement gages. The schematic

diagram in Fig. (2.7) illustrates the structure of a pneumatic device where

the measurements are made under a condition of no gas flow. While the

increasing gas pressure applied to the inlet tube is less than the required

pressure (p), it merely builds up until the applied gas pressure just exceeds

(p). At this moment, the diaphragm deflects allowing gas to circulate

behind it into the outlet tube and flow is recognized using a gas flow

detector. The applied pressure can be read on a Bourdon tube or an

electrical pressure gage.

28

(b) Vibrating wire devices. Vibrating wire devices are used in piezometers,

earth pressure cells, and liquid level settlement gages and deformation

gages. In a vibrating wire device a length of steel wire is clamped at its

ends and tensioned so that it is free to vibrate at its natural frequency. The

frequency of the vibration of the wire varies with small relative

movements between the two end clamps of the vibrating wire device. The

wire can therefore be used as a pressure sensor as shown in Fig. (2.8). The

wire is plucked magnetically by an electrical coil attached near the wire at

its midpoint, and either this same coil or a second coil is used to measure

the period or frequency of vibration which is dependent on the bending of

the diaphragm and hence on the pressure (p). The attached wire is under

near maximum tension at zero pressure. This tension applies the greatest

demand on the clamping and annealing of wire, a condition that may

cause creeping and slippage of the wire at the clamps, which results in a

frequency reduction unrelated to strain. This is commonly known as drift

of the baseline pressure or zero drift.

(c) Electrical resistance devices. Electrical resistance devices are sued in

strain gauges, which in turn have been used in many measurement

devices. An electrical resistance strain gage is a conductor with the basic

property that resistance changes in direct proportion to change in length.

Measuring resistance a Wheatstone bridge circuit can be used to calculate

the linear deformation of the wire.

(d) Other devices that use the electric or the magnetic field changes due to

linear deformations.

Geotechnical instrumentation for tunneling projects may be classified into

two main types namely: the deformation-measuring instruments, and the stress-

measuring instruments. The deformation instruments are used to assess the

ground displacement fields and the convergence of the lining. The stress-

29

measuring instruments are used to measure the pore water pressure, the soil

pressure and stresses in lining segments. In the following, a brief description of

each type is given.

Gas Flow Detector

Inlet tube

Outlet tube

Pressure GaugeTransducer Body

Pressure (p)

Flexible diaphragmattached to

transducer bodyaround rim

Inlet valve

Gas supply

Fig. (2.7) Schematic diagram of a pneumatic device (after Joyce, 1982)

Transducer Body

Flexible diaphragm

Pressure (p) Signal cable Frequency counter

Tensioned steel vibrating wire

Electric coil Fig. (2.8) Schematic diagram of a vibrating wire device (after Joyce, 1982)

30

2.4.1. Deformation Instrumentations

The ground displacement around tunnels could be classified as ground

superficial settlement and subsurface displacements that occur in both vertical

and horizontal directions. Any instrumentation program should be designed

carefully to fulfill the requirements of those two categories of displacement.

Another type of the deformation measurements is the tunnel convergence

measurements. In this part the two categories of deformation measurements are

discussed. A main concern of tunnel construction in soft ground is the

measurements of the ground displacements caused due to tunnel excavation to

evaluate their effects on the neighboring structures. Ground deformation

measurements are used to measure the deformation of the soil or rock mass. The

measurements are taken at varying distances depending on ground conditions. If

the ground conditions change frequently, the measuring sections are arranged

more frequently. The instruments for measuring ground deformation are grouped

into the following categories:

1. Surveying Methods. Surveying methods are used to monitor the

magnitude and rate of horizontal and vertical deformations of the

surface monuments near the tunnel routing. When subsurface

deformation measuring instruments are installed, surveying methods

are also often used to relate instrument measurements to a reference

datum. Surveying methods include optical leveling, taping, traverse

lines, measuring offsets from a baseline, triangulation, electronic

distance measurement, trigonometric leveling, photogrammetric

methods, and the satellite-based global positioning system. All

surveying methods must be referenced to a stable reference datum: a

benchmark for vertical deformation measurements and a horizontal

control station for horizontal deformation measurements. Great care

must be taken to ensure stability of reference datum. Surface

measuring points (points on the surface that are used for survey

observations, and that may move) must be stable and robust points that

31

will survive throughout the project life, and must be isolated from the

influence of frost heave and seasonal moisture changes. Fig. (2.9)

shows a typical measuring point for monitoring settlement on the

surface of ground.

2. Extensometers: Extensometers are devices for monitoring the

changing distance between two or more points along a common axis.

3. Inclinometers: Inclinometers are devices for monitoring deformation

parallel and normal to the axis of a flexible pipe by means of a probe

passing along the pipe.

Fig. (2.9) Measuring point for monitoring surface settlement

(after EM 110-2-1908, 1995)

32

2.4.1.1. Extensometers

The single and multiple point rod extensometers are devices to monitor

displacements at various depths employing a rod or multi-rods, which are

anchored at one end of a borehole as shown in Fig. (2.10). Relative movements

between the end anchors and the reference tube of the borehole are measured

with either a dial depth gauge or a vibrating wire transducer. The multi-point

magnetic extensometer contains ring magnets sliding on a central access tube.

The magnets are fixed in the ground at locations where movement is to be

monitored as shown in Fig. (2.11). A probe within the access tube and senses the

positions of magnets outside the tube. The rod probes incorporate two switches at

a fixed gauge length separation, permitting precise measurements between pairs

of adjacent magnet targets. Switches close on entering a magnetic field activating

a buzzer or indicator light in the reading instrument or cable drum. The magnetic

multi-point extensometers can monitor any number of points at little extra cost

and with no increase of borehole diameter. Displacements can be measured in

two or three dimensions by combining this instrument with an inclinometer or

settlement gauge.

2.4.1.2. Inclinometers

An inclinometer is a device for measuring the inclination from the vertical

of a structure or casing to which the inclinometer is attached. The inclinometer

system involves a torpedo probe, fitted with guide wheels. The probe contains a

tilt sensor, connected by a graduated cable to a digital readout unit. Fig. (2.12)

shows the component and the installation of the inclinometer. The inclinometer

probe is inserted into the grooves of specially installed access tubing. The tilt

sensor enables the horizontal deviation between the probe axis and the vertical

plane to be recorded. Measurement of tilt and probe depth are used to compute

the horizontal deviation of installed access tubing from true vertical. The

installation borehole is drilled to a depth beyond the zone of anticipated

movement to ensure that a satisfactory fixed datum is provided. The borehole is

33

either grouted before or after access tubing installation or can be backfilled with

sand or pea-gravel after access tubing installation. Access tubes are joined using

couplings and filled with water to overcome buoyancy and ingress of grout

during installation. Readings are taken at regular depth intervals of 0.5 m or l.0 m

within the access tubing, measured by graduation markers on the cable. Figs.

(2.13) shows the measuring technique of the inclinometer system. The lateral

displacement of the access tubing is obtained by integration of the observed

horizontal deviation from the initial base readings. Measurement of vertical

deviation caused by settlement or heave can be obtained by fitting the

inclinometer access tubing with magnetic targets that is retained by leaf springs

in boreholes, or attached to plates embedded in soil or fill.

Fig. (2.10) Rod extensometer installation

(after Soil Instruments Ltd., 1999)

34

Fig. (2.11) Installation of magnetic multiple point extensometers


35

Fig. (2.12) Installation of inclinometers


36

Fig. (2.13) Inclinometer measurement of displacement


θ

x sin θ

37

2.4.2. Convergence Measurements

The behavior of a tunnel is generally exhibited in the convergence of the

tunnel lining and the enfolding ground. Convergence of the tunnel lining is an

important indicator of tunnel stability, which is relatively easier to measure than

loads, strains, and stresses. The rate of convergence is the most important

parameter to be observed. Fig. (2.14) shows conceptually several time plots of

rate of convergence; curves (a) and (b) show decreasing convergence, indicating

eventual stability of the structure while curves (c), (d) and (e) indicate instability

problem of the tunnel.

The common convergence measurement is one taken across the horizontal

diameter. Vertical measurements are not usually taken due to interference with

equipment and traffic. There are two techniques for convergence measurements;

namely:

1. Surveying: Using of precision tapes and precision leveling techniques

to measure absolute displacement of fixed points or relative

displacements between measuring points. This method of measurement

has high degree of accuracy that ranges between 0.01 and 0.1 mm for

relative displacement and 2 mm for absolute displacement. Obtaining

access clear sight to the reference points, locating instrument stations

out of the way of construction and providing stable reference datum

are the major problems in using these techniques.

2. Tape extensometers: The tape extensometer is portable tape used to

measure displacement between pairs of permanently fixed reference

studs or eyebolts grouted into shallow drill holes in the lining as shown

in Fig. (2.15). The tape unit comprises a stainless steel measuring tape

with equally spaced precision punched holes. The resolution of the dial

gauge is usually 0.05mm.

38

Con

verg

ence

Rat

e

Time

b

c

de

a

Fig. (2.14) Patterns of convergence rates

(after EM 1110-2-2901, 1997)

Fig. (2.15) Tape extensometer installation and usage


39

2.4.3. Stress Measurements

Pressures exist in a soil mass due to the weight of overburden, water, and

external loads. Tunneling changes the state of stresses in the soil mass in the

neighborhood of the tunnel. It may be important to quantify the effect of tunnel

on the state of stress in soil to estimate the contact stress between the soil mass

and the tunnel lining. However, these types of measurements are usually not

successful, because the presence of the soil stress instruments affects the

measured stresses and the installation will also obscure the work of the TBM

(O’Rouke, 1979). A better alternative is to equip the lining with sets of strain

gages for determining strains and loads in the lining and hence revealing the

acting soil pressure on the lining using back analysis. Tunnels and tunnel

construction techniques may affect the water pressure inside the soil. In this case

the groundwater requires monitoring for the following reasons:

1. Groundwater resources must be protected for environmental and

economical reasons.

2. The tunnel could act as a groundwater drain and causes problems of

ground stability.

3. Groundwater lowering could result in unacceptable formation

compaction or consolidation, resulting in ground surface settlements.

4. Hydraulic tunnels’ leakage could propagate through the soil and cause

seepage that may lead to ground stability problems.

Piezometers are used to measure groundwater pressure. They are installed

in boreholes from the ground surface and from the tunnel lining. In the following

sections, the different types of strain gauges and piezometers are described.

40

2.4.3.1. Strain Gauges

Strain gauges are used for measuring the strains in concrete or steel lining.

The stresses within these sections are calculated from the strains by using

theories of elasticity that relate the strain state to the stress state. Bending

moments and thrust forces in the lining are then calculated from the stresses.

Two types of gages are generally used for measuring strains: surface gages and

embedded gages. Strain gages can be further divided into short and long-term

depending on the duration of measurements.

Usually short-term strains are best measured by electrical type gages,

while some long-term strains (e.g., creep and shrinkage) can be conveniently

measured using detachable mechanical gages. El-Nahhas (1980) describes three

types of vibrating wire strain gauges to be used in tunnel monitoring programs,

namely: weldable gauges used for steel lining, surface gauges and embedded

gauges used for inside and outside walls of concrete lining. Fig. (2.16) shows

some details of the three types of strain gauges.

2.4.3.2. Piezometers

The basic principle of all piezometers is that the porewater pressure in the

soil is transmitted through a porous element to a measuring mechanism. Most

piezometers require some movement of pore water to activate the measuring unit.

The time required for water to flow to or from the piezometer to create

equalization with the porewater pressure is called the time lag. Time lag is not

significant when piezometers are installed in highly pervious soils such as coarse

sands.

Standpipes or Casagrande piezometers are the simplest and the cheapest

piezometers. They consist of simple tubes with a porous tip connected to its

lower end. Groundwater level corresponds to the height of the water surface in

the standpipe above the piezometer tip, which is measured with a dipmeter or

41

using Bourdon gauge for artesian water. Bentonite and grout are used to seal the

borehole above the tip. The vibrating-wire or pressure transducer piezometer has

a tip comprises a porous element integral with a diaphragm type vibrating wire

pressure transducer, installed in boreholes. The pore pressure is transmitted

through the porous element causing a deflection in a diaphragm. The deflection is

measured using the vibrating-wire transducer. An airline is required to maintain

atmospheric pressure on the non-water side of the diaphragm. The volume of

flow required for pressure equalization at a diaphragm piezometer is very small,

and the time lag is very short.

The pneumatic piezometer has a tip comprises a porous element integral

with a proven diaphragm transducer, installed either in a borehole or by pushing

into shallow depths in soft soil. Twin tubes connect the transducer to the portable

readout unit. Air or nitrogen is forced down one line and when its pressure equals

the pore water pressure it forces open the membrane valve and flows up the

return line to a flow indicator. The balance pressure can then be read off a

Bourdon gauge.

The hydraulic piezometer has a porous piezometer tip installed and sealed

above the measuring level. The tip is connected to the readout location by twin

tubes. De-aired water is circulated through the tubes until the tubes and the tip

fire completely filled; they remain filled throughout the working life of the

installation and can at any time be re-flushed to remove air or gases that may

have accumulated. The pore water pressure at the piezometer tip can then be

measured at the remote end of either water tube, making a correction for the head

difference between the tip and the measuring gauge. The instrument measures

pore pressures by measuring the head of water using mercury manometers. Fig.

(2.17) shows the features of the different piezometer types.

42

Fig. (2.16) Different types of vibrating wire

strain gauges (after El-Nahhas, 1980)

43

Fig. (2.17) Piezometer Types (after Murray, 1990)

44

2.5.Design Aspects of Shielded Tunnels

Performance deficiencies and failures in tunneling not only endanger the

tunnel itself but also may imperil nearby buildings and utilities resulting in life

and property losses. The tunnel designer has every obligation to elude any

conceivable harmful tunneling effects and to guarantee a competent and

economical method of tunneling. There are several basic considerations in the

design of soft ground shielded tunnels; Monsees (1996) concluded the following

design aspects of soft ground tunnels:

1. Face stability: Face stability prognosis along the full tunnel routing is

required to assess the prospects of the collapse of the excavated face to

into the tunnel and to choose the amended equipment and methods of

tunnel construction. The stability of the tunnel face is contingent upon the

type of the ground being excavated, the ground inherent stress and

groundwater condition, the rate of advancement, the face size and face

supporting technique.

2. Ground deformation: Excavation of tunnels causes dilatation of

enfolding ground into the excavation. The magnitude of those movements

is a function of soil type, the presence of water, rates of tunnel advance,

the tunnel size and the tunnel support. Ground disturbance at the tunnel

triggers off a chain of movements up to ground surface leading to

formation of subsidence troughs that may cause damage to nearby

structures at the ground surface.

3. Lining stability: Tunnel lining is the structural system that maintains

the shape and the stability of the excavated tunnel by means of supporting

the surrounding ground after shield advancement. The induced lining

stresses and deformations arising from interaction with the surrounding

convergent ground must be estimated to ensure satisfactory performance

of the constructed tunnel. Lining waterproofing, invulnerability to the

hydrostatic ground pressures and appropriate countermeasures to water

45

ingress or egress are vital to guarantee safe construction and operation of

the tunnel.

4. Ground improvement: In designing a tunneling project, it may be

feasible to use prior treatment (e.g., dewatering, grouting, freezing, etc.) of

the ground in order to provide stable working conditions (Korbin and

Brekke, 1978; & Jones and Brown, 1978). Pre-treatment of the ground is a

usual measure in open-cut and shaft sinking (Flint, 1994) but much less

common in tunneling due to its high costs.

In this section, the different considerations and precautionary measures

related to face stability, ground deformation and lining analysis are enlightened.

2.5.1. Face Stability

There are two approaches to assure the face stability namely: the empirical

approach and the rational approach. The empirical approach is based on the

observations of face stability during past mining and tunneling activities. This

approach was put forward in a system of ground classifications (Terzaghi, 1950).

Conversely, the quantitative approach is based on soil mechanics and employing

the limit equilibrium methods in which the ratio of restoring force to failure-

driving force is calculated as a factor of safety. A factor of safety of magnitude

less than unity indicates instability and collapse, whereas a factor of one or more

indicates stability against inward movement. The higher the factor of safety, the

smaller the likely magnitude of inward movement and the greater the possibility

of outward movement. Thomson (1995) described the factor of safety as a “factor

of safety against inward movement” with a recommended value not less than 1.5

and not greater than 2.

Atkinson and Mair (1981) described a method of analysis for calculating

the required face support pressure (pF) to maintain stability in drained

cohesionless soil using the following equation:

46

γ′+= TpqTp cosF + the porewater pressure … (2.1)

where q is ground surface surcharge, p'co is soil effective overburden pressure at

the crown level, Tγ is tunnel face stability coefficient for soil weight and Ts is the

tunnel face stability coefficient for surface surcharge. The face stability

coefficient can be determined from Fig. (2.18). The stability of cohesive soils is

determined using undrained shear strength analysis. Peck (1969) employed the

overload factor or the stability number (Ns) that was proposed by Broms and

Bennermark (1967). The stability factor is given by:

u

Fsos C

ppN −= … (2.2)

where pso is soil total overburden pressure at the springline level and Cu is

undrained shear strength of soil. Peck established that the unit value of the

stability number or less would ensure face stability. Thomson (1995) indicated

that the safe stability number depends on the ratio of springline depth and the

tunnel diameter as shown in Fig. (2.19). The designer has to assess the undrained

shear strength based on the nature of the cohesive soil as undrained analysis

refers to the immediate condition only. If a cohesive soil has a high permeability

due to its structure then the undrained strength will eventually reduce with time

after excavation and the stability number calculated will rise.

Eisenstein and Ezzeldine (1994) conducted a total stress three-dimensional

and axisymmetric finite element analysis to study the face stability; they

concluded that the required face pressure could be given by:

( ) ( )acsoaF Kc2IpKIp −= φ …(2.3)

where Iφ is the influence factor of frictional resistance, Ic is the influence factor of

cohesive resistance and Ka is the coefficient of active earth pressure. They

compared the results of their analytic model to 23 case histories, in which good

agreements were exhibited between the model results and the observed face

stability.

47

0

1

2

0 10 20 30 40

φ' (o)

T

0

0.5

1

0 10 20 30 40

φ' (o)

Ts

Fig. (2.18) Face stability coefficients for cohesionless soil

(after Atkinson and Mair, 1981)

Crown depth/tunnel diameter

0.5

1.0

2.0 3.0

48

0

1

2

3

4

5

0 1 2 3 4 5

Ns

Fig. (2.19) Face stability number for cohesive soils

(after Thomson, 1995)

Unstable

Stable

Depth of springline/tunnel diameter

49

2.5.2. Ground Deformation

2.5.2.1. Ground Loss

Three capital roots of ground subsidence accompanying tunneling

activities are the axial ground losses in front of the tunnel, the radial ground

losses at the peripherals of the tunnel, consolidation and local instability.

Settlements occurring as a result of ground loss are controlled by the affinity of

the soil to dilate or densify when sheared. Dilation results in a small influenced

zone localized in the area above the tunnel, whereas densification is usually

coupled with movements expanding towards the surface of the soil. In undrained

cohesive soils, constant volume shearing is anticipated.

The ground losses (Vt) of tunnels in clays depend theoretically on the

stability number (Ns). Employing the cylindrical cavity contraction theory (Peck,

1969), the following equations are depicting the relation between the stability

number and the ground loss as following:

For (Ns ≥ 1)

)1Nexp(EC3

)1Nexp(C3E)1Nexp(C3V s

u

u

suu

sut −≅

−+−

=

and for (Ns ≤ 1)

u

ust E

CN3V =

…(2.4)

…(2.5)

where (Eu) is the undrained modulus of elasticity for the clay. Attewell et al.

(1986) estimated the total ground loss due to tunneling (Vt) as following:

434214434421shield behind the

gu

shield over the

ypbft VVVVVVV +++++= + time dependent consolidation …(2.6)

where (Vf) is the face loss, (Vb) is the radial loss over the shield, (Vp) is the

losses due to the upward pitch of the shield to account for the heavy nose of the

shield, (Vy) is the losses due to the curve maneuvering of the shield, (Vu) is the

radial loss over the erected lining and before grouting and (Vg) is the radial loss

over the erected lining after grouting. Consolidation in cohesive soil arises due to

50

the stress field changes during tunneling, which is generally characterized by

increasing the tangential stress and reduction of radial stresses. Long-term

seepage (if the tunnel works as an underground drain) can also cause increased

effective stresses and hence consolidation. The dissipation of pore water

pressures generated during excavation and construction can also result in

consolidation of the surrounding soil (Ghaboussi and Gioda, 1977; & Palmer and

Belshaw, 1978).

The value of ground losses is typically calculated as a percentage of the

volume of excavated material. An appropriate percentage can be estimated for

the ground, excavation and support conditions based on the literature on

tunneling. Glossop 1977) expressed empirically volume loss for stability number

ranging from (1.5-4) from his observations as:

Vt (%) = 1.33 Ns − 1.4 …(2.7)

In non-cohesive soils, contraction on disturbance could cause the surface loss to

be significantly greater than that at the TBM, while dilatation reduce the effect of

ground loss. Attewell et al. (1986) suggest a range of 3% to 10%, with a typical

value of 5% based on previous monitored projects.

2.5.2.2. The Deformation Field

There are three fundamental methods for predicting the deformation field;

namely: the empirical method that is based on normal probability curve fitting to

surface subsidence; the theoretical methods that are based on analogy between

tunneling and submerged sinks and continuum mechanics describing a new

cylindrical cavity in a prestressed medium; and the numerical methods that

employ the finite element method or the boundary element method. Schmidt

(1969) and Peck (1969) used the normal probability distribution curve for

predicting surface settlement as shown in Fig. (2.20) in which the maximum

surface settlement (Smax) occurs above the tunnel centerline. The volume of the

settlement trough (Vs) is given:

51

iS5.2iS2V maxmaxs ≅π= …(2.8)

where i is the distance between the peak and the point of inflexion of the curve.

From normal probability theory, the settlement at any point on the curve (S) at a

distance (x) from the centerline can be found using

−= 2

2

max i2xexpSS …(2.9)

For undrained deformation, the volume of settlement trough (Vs) will equal to the

ground loss volume (Vt). In non-cohesive soils, the choice of volume loss is

much more uncertain. The dilation or contraction of the soil will result in very

different volume losses at the surface. The estimation of the location of point of

inflection (i) depends upon both the depth of tunnel cover and shield diameter

(D) and the shear strength of the soil near to the surface. O'Reilly et al. (1982)

recommend the following expression

i = K z …(2.10)

where K is a constant and z is depth to tunnel center. They recommended values

of K of approximately 0.5 for cohesive soils, with typical values of

approximately 0.4 for stiff clays ranging to 0.7 for very soft clays, and 0.25 for

cohesionless soils. Schmidt (1969) proposed the following equation to estimate

(i) for clays:

i/D = 0.5 (z/D)0.8 …(2.11)

Attewell et al. (1986) conferred equations for the complete strain and

deformation fields around tunnels based on the Gauss Distribution assumption.

Atkinson et al. (1975); Butler and Hampton (1975); Cording and Hansmire

(1975); El-Nahhas (1980), (1986), (1991) and (1994); O’Reilly et al. (1982);

Clough et al. (1983); Hansmire and Cording (1985) Maidl and Hou (1990); and

Clough and Leca (1993) presented the measured deformation fields for some

tunneling projects.

52

Fig.

(2.2

0) T

he g

roun

d su

bsid

ence

Gau

ssia

n di

stib

utio

n (a

fter S

chm

idt,

1969

)

53

The theoretical methods for predicting the deformation field of tunnels

employed either the approach of submerged sinks in fluid mechanics or the

principles of continuum mechanics. The fluid flow techniques for estimation of

ground movements during tunneling use the analogy of submerged sink in an

ideal incompressible fluid. Sagaseta (1987) used this technique model

displacement field in incompressible (undrained) soil. This method has produced

good correlation with field data. The surface profile is similar to that produced by

the normal probability method but thought to better estimate the subsurface

movements, particularly those occurring close to the shield. The continuum

mechanics approach uses either the method of unloaded cylindrical cavity in an

elastic medium (Chew, 1994), or more complicated method of contracting

cylindrical cavity in an elastic-perfect plastic medium (Mair and Taylor, 1993).

The finite element provides a powerful tool to simulate the tunneling

construction. With the quick improvement in computer efficiency and

availability of very powerful codes, the finite element analysis is becoming a

versatile tool in tunneling analysis and estimation of ground subsidence (Gunn,

1993; & Loganathan and Poulos, 1998). The non-linearity of the ground and

lining can be introduced into the finite element analysis giving a good estimate of

the stress and deformation fields around tunnels (Orr et al., 1978; & Mair and

Taylor, 1993).

2.5.2.3. The Effect of the Ground Subsidence on Buildings

As the tunneling is advancing, a trough of settlement develops. Any structure

within the predominance of the developed settlement trough will be affected, and

on the other hand the presence of the structure modifies the trough. Tunneling

induced damage to buildings can be estimated roughly using the free field

displacement combined with a damage criterion. Skempton and MacDonald

(1956) presented the observational criterion of angular distortion. According to

their work, an angular distortion less than 1/300 is recommended for load bearing

54

walls and masonry-infilled panels in traditional frame building. Bjerrum (1963)

presented a relation between angular distortion and different building

performance. Grant et al. (1975) questioned Skempton-MacDonald Criterion to

assess potential damage to buildings by comparing the measured angular

distortion in about 200 case histories. Burland and Wroth (1975) presented an

analytical study in which they modeled any building as deep, elastic, simply

supported beam. They use the tensile strain as a measure of damage. Boscardin

and Cording (1989) and Broone (1997) modified the criterion of Burland and

Wroth to include the ground horizontal strain in calculation of the tensile strain.

Attewell et al. (1986) and Yoshida and Kusabuka (1994) used a method of

two-stage procedures to investigate the effect of the building existence on the

induced settlement trough. Firstly, the free surface settlement due to tunneling is

calculated using one of the analytical methods; then the final settlement can be

calculated using the following relation:

[ ] [ ]( ){ } [ ]{ }wKdKK gdsgds =+ …(2.12)

in which [Ks] presents the stiffness matrix of the structure, [Kgd] presents the

stiffness matrix of the ground interface with the building, {w} is the free field

displacement vector of the ground interface and {ds} is structure response. They

presented the ground as a Winkler medium and a half space using the finite

element method. Chen et al. (1999) employed a similar two-stage procedure to

assess the effect of tunneling on a previously installed pile. The free field

deformation was calculated using an analytical method and then applied on a pile

modeled using a combination of beam and boundary elements.

55

2.5.3. Design of Tunnel Lining

2.5.3.1. General Considerations in Lining Design

A lining is required to support the ring axial load, the circumferential

bending (and possible longitudinal bending when passing through different

strata), local buckling, shield jacking loads, asymmetrical loading at junctions

and enlargements, construction handling and erection loading, and is required to

resist corrosion. The practical and empirical rules of tunnel lining construction to

possess sufficient stability have preceded any supporting theory for many years.

The need for a scientific insight of the interaction between the tunnel lining and

the surrounding ground has arisen due to catastrophic nature of tunnel failures

and the unfamiliar nature of tunneling environment. The development of tunnel

lining design methods has lead to diminution of tunnel failures and optimization

of lining on both geotechnical and economical bases (O'Rouke, 1984).

Wittaker and Frith (1990) grouped tunnel linings into three main forms

some or all of which may be used in the construction of a tunnel: temporary

ground support, primary lining and secondary lining. In rock and stiff soil tunnels

where the ground has little stand-up time to allow the construction of the primary

lining some distance behind the face, then some form of temporary ground

support applied at the tunnel face is required e.g. rock bolts, shotcrete and steel

sets. Such support is not required in soft ground in conjunction with a shield

driven tunnel as the body of the shield provides temporary ground support itself.

A primary lining is the main structural component of the tunnel support system,

which is required to sustain the loads and deformations that the ground may

induce during the tunnel’s intended working life. Additional loads may be

imposed onto the lining during handling and erection as well as those induced as

a result of the shoving forward of the shielded tunneling machine by jacking

against the last support ring. Such loads may well exceed those imparted as a

result of ground loading in certain situations. A further function performed by the

primary lining is the control of water egress and ingress. A secondary lining

56

performs certain duties to supplement those of the primary lining, which do not

involve ground loading. Various tunnels require smooth bore profiles for their

intended use, e.g. sewer and water tunnels or aesthetic finishes for public usage,

e.g. highway and pedestrian tunnels. Erosion and corrosion protection for the

primary lining and further waterproofing may also be required, all of which are

provided by secondary linings.

The main consideration in the design of a tunnel lining is constructability

or its inter-relationship with the tunneling method to be employed to drive the

tunnel. In soft ground conditions where a shield driven tunnel is required, some

form of segmental lining will be required, either bolted or unbolted. Conversely,

if the tunnel has an appreciable stand-up time allowing dispensing of the

tunneling shield, then the use of a temporary support such as shotcrete followed

by either a poured or precast concrete primary lining may be appropriate. In

ground with good stand-up times, ribs and lagging or rock-bolting can be used as

the temporary support followed by a cast insitu primary concrete lining. Thus the

choice of lining type may well be made prior to any considerations concerning

the likely ground conditions. Finally the designer should be aware of the tunnel

usage, for example, a water transport tunnel requires a lining with good hydraulic

efficiency characteristics, thus leading to choice of a smooth bore lining.

Similarly, pedestrian and highway tunnels require aesthetic and durable finishes.

Segmental linings are usually associated with soft ground tunnels. They

are erected within the protection of a cylindrical tail shield. In these conditions

they can provide a one-pass system, furnishing both stabilization of the tunnel

opening during construction and a permanent service lining, or two-pass systems,

with the segments providing only construction stabilization, and a second-pass

poured concrete lining added for permanent service. Both types are structural

mechanisms that derive their stability wholly from the support provided by the

surrounding ground.

57

One of the very important considerations in designing a tunnel lining is if

the lining has to resist hydrostatic pressures either externally or internally then

this will in general govern the lining design and control the success of the

tunneling operation. There are various methods available to facilitate the

waterproofing of a tunnel varying from simple sealing of the longitudinal and

radial joints of the lining to the installation of a full waterproof membrane

between either the temporary and primary or primary and secondary linings. Any

water trapped behind the lining as a result of such measures is then channeled

away. The most common method is that of joint sealing which will inevitably not

achieve a completely dry tunnel but may reduce the water inflows to acceptable

levels. Bolted cast iron linings give better waterproofing than bolted concrete

linings in similar conditions. This is a result of cast iron linings lending

themselves to sealing and not suffering further cracking during handling and

construction.

The design of tunnels subjected to internal water pressures is a different

concept altogether as in many instances no leakage can be tolerated due to the

very high pressures in the tunnel and the disastrous effects that leakage may

cause to the surrounding environment. In such cases the tunnel can be made

completely impervious by the use of a steel lining backfilled with concrete. In

less severe cases where the internal pressure is reduced, measures include

increasing the rating of the rock mass by rock reinforcement thus enhancing its

resistance to internal pressure, or pressure grouting behind the concrete lining to

increase the external pressure opposing the internal pressure. Both techniques

effectively reduce the likelihood of the lining cracking and causing water loss.

Kuesel (1996) discussed the concepts that must be accounted for in

designing tunnel lining. He introduced some common characteristics that pervade

all lining systems:

58

1. The process of ground pretreatment, excavation, and ground

stabilization alter the primitive state of stress in the ground,

before the lining comes into contact with the ground.

2. The design of a tunnel lining cannot be considered as a

structure being subjected to well-defined values of loading, as

there is no absolute certainty of the actual ground behavior

following excavation. Thus, the problem should be considered

as one related to ground and structural behavior rather than

simply one governed entirely by structural features.

3. A lining cannot be loaded by ground deformations that occur

prior to its “activation”.

4. Tunnel lining behavior is a four dimensional problem.

During construction ground conditions at the tunnel heading

involve both transverse arching and longitudinal arching from

the unexcavated face. All ground properties are time

dependent particularly in the short term, which leads to the

commonly observed stand-up time phenomenon, which is

very beneficial in practical tunnel construction methods. The

timing of installation is very important variable in estimating

the loading carried by the lining.

5. In most cases (especially when considering the segmented

lining), the bending stiffness of structural linings is small

compared with its axial stiffness. Bending stiffness is

generally undesirable as it induces bending stresses in the

lining. Axial stiffness is of primary importance, as it

facilitates the redistribution of unequally distributed active

pressures and mobilizes passive pressures. The proper

criterion for judging lining behavior is therefore not adequate

59

strength to resist bending stresses, but adequate ductility to

conform to imposed deformations. However, it is essential to

perform effective contact grouting around the tunnel

periphery in order to benefit fully from the above mechanism.

This only applies to closed supports with circular and

elliptical profiles rather than to open supports such as arch

profiles without inverts or rock reinforcement techniques.

6. The most serious structural problems encountered with actual

lining behavior are related to absence of support - inadvertent

void left behind the lining- rather than to intensity and

distribution of loads.

7. Constructability considerations are likely to govern the

dimensions of the lining. The length and width of precast

concrete or metal segments are governed by shipping,

erection limitations, joint configuration, shield jacking loads

and handling stresses.

8. Grouting pressure is maximum at grouting ports and it is

reduced by friction at locations remote from the ports. Lining

design procedures usually neglect this action

2.5.3.2. Methods of Tunnel Lining Design

Methods of tunnel lining design emphasize the stage of the ground liner

interaction. Once the lining system is assembled to cover the tunnel

circumference, the lining is in position to start interacting with the surrounding

ground (the lining activation point). Stresses inside the lining and in the

surrounding ground undergo readjustments to reach the state of equilibrium. The

process of ground-liner interaction is affected by the lining and the surrounding

ground relative rigidity and stress changes during the construction stage. The

60

methods of tunnel lining design are divided into three distinct approaches,

namely: observational methods, analytical methods and numerical methods. In

the following sections, the three approaches are discussed.

2.5.3.2.1. OBSERVATIONAL LINING DESIGN

Peck (1969) and Peck et al. (1972) formulated recommendations based on

some observations of tunnel lining behavior in a variety of soil conditions. These

recommendations have become widely accepted as design criteria of flexible

circular tunnel linings. Peck concluded from his observations that flexible lining

should be designed for a uniform ring compression corresponding to the

overburden pressure at springline plus an arbitrary imposed distortion measured

as a percentage change in tunnel radius. The ring distortion can be controlled, if

necessary, by temporary internal tie rods or struts, until grouting is completed

and the ground is stabilized. He suggested considering the lining as fully flexible

ring if the following condition is satisfied

ELIL/Rm3 < 5 qu …(2.13)

where EL is the effective modulus of elasticity of the lining (reduced to half its

value in segmental lining), IL is the effective moment of inertia of lining per unit

length of the tunnel (reduced to 60-80% of the gross inertia in segmented lining)

and Rm is the mean radius of the lining. Tunnels constructed in sand, which

generally possess a higher stiffness than clays, can be considered as flexible rings

(Kuesel, 1996). The compressive stresses resulting from the assumed thrust is

given by

tRp mso=σ …(2.14)

where t is thickness of the tunnel lining. The bending stresses resulting from the

lining distortion is given by:

m

m

mL R

RR

tE5.1 ∆±=σ …(2.15)

where ∆Rm/Rm is a assumed according to the type of soil as given in Table (2.2).

61

Table (2.2) Values of tunnel distortion (after Peck, 1969)* Soil Type ∆Rm/Rm

Stiff to hard clays, stability number <2.5-3 Soft clays or silt, stability number >2.5-3 Dense or non-cohesive sand and most residual soils Loose sand

0.15-0.40 % 0.25-0.75 % 0.05-0.25 % 0.10-0.35 %

* Add 0.10-0.30 % for tunnels in compressed air. Add appropriate distortion of external effect

as passing neighbor tunnel. Values assume reasonable care in construction, excavation and

lining method.

2.5.3.2.2. Analytical Methods

In these methods, the analysis consists of representing the problem by

tractable equations based on well-established theories and empirical rules and

then solving them. No analytical solution could be found that fully satisfies all

requisites of the geometry, rock/soil behavioral laws and boundary conditions of

the problem. The use and development of analytical solutions, however, has

played an important role in the development of tunnel lining design (Iftimie,

1994). It is important to bear in mind, that analytical solutions are based on sets

of assumptions concerning all aspects of the problem, especially the ground

behavior laws, so it may be difficult to extrapolate the results directly to field

conditions. Considerable judgment may be required for meaningful application

of the results. Nevertheless, the solutions can be useful in giving additional

support to the results of more sophisticated design methods and as a means of

evaluating the sensitivity of the problem to changes in various parameters

affecting the design. This will assist in indicating the parameters that are of

primary and secondary importance.

62

2.5.3.2.3.Methods Based on Assumed Ground Pressures

These methods assume hypothetical or empirical ground pressure

distribution used to determine the internal forces and deformations of the lining.

The most important potential loads acting on tunnels are earth pressures and

water pressure. Loads due to vehicle traffic on the surface can be safely neglected

unless the tunnel is of the cut and cover type or the depth of overburden is very

small. Szechy (1967) divided the earth pressure into roof pressure, lateral

pressure and bottom pressure. Roof pressure results from the overburden soil

above the tunnel. Bottom pressure results from the bottom reaction and the heave

of the tunnel bottom due to the stress relief. Lateral pressure results from the

lining supporting action to the ground. He has pointed out that more exact

determination of lateral earthpressure must consider the passive resistance

mobilized by deformation and lateral outward displacement of the lining. This

has been accomplished in the other methods that consider the ground as either

Winkler springs or as a continuum.

The methods based on assumed ground pressures do not consider the

stress changes due to method of tunnel installation. This may explain their poor

correlation with field measurements. Water pressure can be estimated based on

the static distribution of the water pressures inside the soil mass unless the

seepage forces arise from the tunnel existence.

Terzaghi (1936) studied the soil arching using a moving trapdoor at the

bottom of a container full of compacted sands. Terzaghi noticed that the arching

is taking effect 2.5B above the trapdoor, where B is the trapdoor width). He

assumed a vertical failure surfaces and concluded that the pressure acting on the

trap-door is given by:

φ−⋅+

φ−−

φ−γ

=σ tanB

zk2expqtanB

zk2exp1tank2

)B/c2(B rr

rv

…(2.16)

63

where q is the surcharge acting on the top of the soil surface and kr is the

earthpressure coefficient, which he assumed to be unity. The vertical pressure on

the yielding door at very large depth is given by

γ=σ B87.0v …(2.17)

Terzaghi (1946) used the trapdoor results to calculate the load acting on

tunnels. He considered a rectangular tunnel as shown in Fig. (2.21). The roof

pressure is given by:

φ−⋅+

φ−−

φ−γ

=σ tanB

Hk2expqtanB

Hk2exp1tank2

)B/c2(B rr

rv

…(2.18)

The sides are treated as retaining walls where active earthpressure is assumed.

The bottom must be checked for heaving as shown in Fig. (2.22). Terzaghi also

studied the arching of deep tunnels (H>5B). He assumed that arching occurs in

5B above the tunnel and rest of the overburden can be considered as a surcharge

load acting over the failure zone as shown in Fig. (2.23).

Bierbäumer (Szechy, 1967) also introduced a similar theory wehere the

roof pressure σv is given by:

σ α γv H= …(2.19)

αφ φ

φ= −

⋅ −+ ⋅ −

1 45 22 45 2

2tan tan ( / )tan( / )

o

o

Hb m

…(2.20)

where H, B and m are shown in Fig. (2.24); α varies from 1.0 for shallow tunnels

to tan4 (45o-φ/2) for deep tunnels (H>5B). The sides are treated as retaining walls

where the total horizontal force (P) is given by active earth pressure as in

Terzaghi’s Method.

64

Peck (1969) reported that, according to records of measurements in a

number of tunnels, the magnitude of lining pressure after stress relief at the

construction stage could be as low as 20% of the overburden pressure. He

suggested it would be a safe assumption to let the magnitude of the lining load

equal to the full overburden pressure because the amount of stress relief is

unquantifiable. He stated that the lining stress tends to approach the original

overburden pressure in the long term due to soil creep. This assumption is

justified in shallow tunnels where the arching has little effect on the lining

pressure.

Fig. (2.21) Shallow tunnel model (after Szechy, 1967)

65

Fig. (2.22) Check of bottom heave (after Szechy, 1967)

Fig. (2.23) Analysis of deep tunnels (after Szechy, 1967)

66

Fig. (2.24) Bierbäumer Theory for ground arching

(after Szechy, 1967)

2.5.3.2.4. Methods Based on Subgrade Reaction Theory

Unlike the previous analysis, the methods based on subgrade reaction

theory consider the dependency of the soil pressure on lining deformation. Soil

behavior is described by Winkler's subgrade reaction coefficient. Bodrov and

Gorelik (Szechy, 1967) applied the principle of least potential energy to solution

of elastically embedded ring in Winkler medium. Whenever the section deforms

outward, elastic reactions are mobilized as shown in Fig. (2.25). The solution

procedure uses Fourier series to present the load and the reaction resulting in

very intricate mathematical formulae. An alternative procedure to Bodrov-

Gorelik method is to reduce the tedious mathematics required for solution of the

elastically restrained ring by replacing it by a polygon. Radial rods that can resist

the outward displacements but cannot resist the inward displacements provide the

ground reactions as shown in Fig. (2.26). Bougayeva and Davidov (Szechy,

1967) simplified the analysis by assuming the ground reaction. Ebaid (1978)

used Bougayeva’s Method in determining the moment in segmental lining by

considering the lining is a series of circular hinged-end frame elements. Ebaid

67

and Hammad (1978) and Hammad (1978) gave a solution for maximum moment

using this method. Hammad (1977) used a method based on subgrade reaction to

assess the stresses in U-shaped tunnels. The foremost shortcoming of the

methods based on the subgrade reaction is that they do not consider the effect of

tunnel construction procedures.

Fig. (2.25) Bodrov-Gorelik’s Method (after Szechy, 1967)

Fig. (2.26) Polygonal Method (after Szechy, 1967)

68

2.5.3.2.5. Methods Based on Convergence-Confinement Approach (CC)

The convergence-confinement approach is a procedure in which the soil-

lining interaction is analyzed by considering the behavior of each of the soil and

the liner independently using the ground reaction curve (GRC) and the support

reaction curve (SRC) to determine the equilibrium condition of the soil-lining

interaction (Ahmed, 1991).

This method enables calculation of the pressure applied to the support by

the intersection of the two characteristic curves of the lining (SRC) and the

enfolding ground (GRC) relating the radial stresses as a function of radial strain,

as shown in Fig. (2.27). The reaction curves offer a more realistic representation

of the interaction sequence of the lining with the surrounding soil. They are of

great value when used as a tool for qualitative discussions on some of the

parameters involved in the design of linings for tunnels in soil.

El-Nahhas (1980) and Ahmed (1991) gave a brief history of development

of the Convergence-Confinement Approach. It was introduced for rock tunnels

by Pacher (1964). Rabcewicz (1964, 1965) uses this approach as a design tool

for the NATM. Deere et al. (1969) discussed the use of the reaction curves for

soft ground tunnels. Lombardi (1970, 1973) examined analytically the factors

affecting the ground and support reaction curves. Kaiser (1981), Brown et al.

(1981) and Hoek (1968) presented closed form solutions for the GRC. Eisenstein

and Negro (1985) examined the nonlinear constitutive soil relations on the

ground characteristic curve and the combination of this method with finite

element analysis.

69

F

S

C

σrf

σrc

σrs

σrf

σrc

σrs σ

rs

GRCSRCRigid SRC

δrRadial Displacement

σ rR

adia

l Str

ess

Fig. (2.27) Convergence-Confinement Approach

(after Ahmed, 1991)

C

S

F

70

2.5.3.2.6. Methods Based on Continuum Mechanics

Closed-form solutions for the interaction of an elastic medium with a

buried cylinder were derived by Burns and Richard (1964) and Hoek (1986)

using extensional shell theory for the shell and Michell's formulation of Airy's

stress function for the soil medium. Although the analysis was originally

developed to study the behavior of culverts, Peck et al. (1972) and Einstein and

Schwarz (1979) used it to calculate the internal forces and deformation of a

tunnel lining of intermediate flexibility. They assumed that the case of full

slippage between the lining and the soil would approximate more nearly the

behavior of soft ground tunnel lining.

The lining stiffness is divided into two separate and distinct types. The

first is an extensional stiffness, represented by the Compressibility Ratio "C",

which is a measure of the equal all-around uniform pressure necessary to cause a

unit diametrical strain of the lining with no change in shape. The second is a

flexural stiffness, represented by the Flexibility Ratio "F", which is a measure of

the magnitude of the non-uniform pressure necessary to cause a unit diametrical

strain which results in a change in shape of the lining. The derived formulas for

these coefficients are given in the following:

m2L

L

ss

s

R)1(tE

)21)(1(E

C

ν−

ν−ν+=

…(2.21)

and

3m

2L

LL

s

s

R)1(IE6

)1(E

F

ν−

ν+=

…(2.22)

71

where Es is the modulus of deformation of the ground, υs is the Poisson’s ratio of

the ground, IL is the second moment of inertia of the liner plate and υL is the

Poisson’s ratio of the liner plate.

The variation of bending moment with the flexibility ratio, and the

variation of thrust with the compressibility ratio are given in dimensionless form

in Fig. (2.28). Generally, the plots indicate that the lining behaves as a flexible

lining if the Flexibility Ratio is greater than 10.

A similar attempt to analyze the behavior of a tunnel lining, using the Airy

stress function, is given by Morgan (1961). His analysis was based on the

assumption that the lining deforms in an elliptical mode. This analysis was

corrected and extended to more realistic conditions by Muir Wood (1975). Curtis

et al. (1976); & Curtis and Rock (1977) studied the effect of shear stresses on the

radial deformation of the soil. They gave formulae for the thrust and bending

moments in the lining for cases of no shear interaction and full shear interaction

between the lining and the surrounding soil as it was described before.

The methods based on continuum mechanics have introduced a few

factors, which were overlooked by some of the preceding methods. The

assumptions of continuum mechanics analyses however, limit their use to deep

tunnels in a homogeneous, isotropic, elastic ground. The derivation of similar

formulas for different boundary conditions, different construction techniques and

considering nonlinear constitutive soil behavior would be tedious and

formidable.

72

Fig.

(2.2

8) M

omen

t and

thru

st c

oeff

icie

nts (

afte

r Bur

ns e

t al.,

196

4)

73

2.5.3.2.7. Numerical Methods

The assumptions made in formulating analytical solutions are generally

too simple to allow it to retain a degree of relationship to the problem in

question. Moreover, the inclusion of the method of construction of the tunnel and

soil nonlinearity in the analytical solution is practically unfeasible. The

development of faster, cheaper computers and improved knowledge concerning

the behavior of soils and modeling construction stages, have soared the design

techniques that are based on numerical simulation. Several numerical models

employing two-dimensional plane strain or axisymmetric models have been

reported (Ranken and Ghaboussi, 1975; Ghaboussi and Gioda, 1977; Orr et al.,

1978; Ghaboussi et al, 1983; Rowe et al, 1983; Hamdy, 1989; Ahmed, 1991,

Adashi et al., 1991; Gunn, 1993; Mair and Taylor, 1993; Ahmed, 1994; Yoshida

and Kusabuka, 1994; Esmail, 1997; Abdrabbo et al., 1998 and Chen et al., 1999)

Little literature is available in which tunneling is presented using three-

dimensional numerical models. Complications in presenting soil excavation,

shield driving, overcutting and tailskin grouting obstacles this type of analysis in

addition to its high computational cost especially when employing the nonlinear

soil models (Smith and Griffiths, 1998). Nomoto et al. (1999) considered the

centrifugal testing as a three-dimensional model that is superior to numerical

ones. Recently, some research work was directed towards to three-dimensional

numerical analysis (Ezzeldine, 1995; Mansour, 1996; Augrade, 1997, Abu-

Krisha, 1998 and Shou, 2000). Newly developed models based on probabilistic

models and soft computing have been recently utilized (Touran et al., 1997 and

Shi et al., 1998).

74

2.6. Tunneling Projects in Egypt

During the last two decades, several tunneling projects have been

executed in Egypt including sewage tunnels, syphons, subways and road tunnels.

Fig. (2.29) shows the location of some of the Egyptian tunneling projects. El-

Nahhas (1999) and The International Tunneling Authority (ITA) web site1

surveyed many of these projects. The following tunneling projects have been

reported:

• Cairo Wastewater Project: The project comprises the construction

a spinal deep collecting tunnel from Maadi in the South to Ameria

in the North as shown in Fig. (2.30). The construction of the main

part of the spine tunnel was accomplished using five-meter

compressed air TBM. Work on the main tunnels of Cairo

wastewater project (Contract 15) has been completed in 1997. The

Maadi rock tunnel commenced using a 5.35 m Herrenknecht TBM

with hard rock cutter head in which approximately 100 m had been

driven by the end of march 2000. Design work for the connecting

tunnels required to discharge sewage flows to the Maadi Rock

tunnel section of the main spine sewer is under preparation.

• Greater Cairo Metro: The first line of the Greater Cairo Metro or

the regional line was completed in 1989 and was the first subway

metro line in Africa and the Middle East. The second line was

completed recently using bentonite slurry technology. The second

line extends from Shubra El-Kheima to Giza Suburban areas.

Details of the second line project are elucidated in Chapter (4). The

third line is planned to extend about 7 km from Embaba to El

Darasah.

1 www.ita-aites.org

75

• Al-Azhar Road Tunnels: Work on the first of Al-Azhar Twin Road

tunnels below the old Islamic heart of Cairo has been completed.

The second tunnel is anticipated to be completed by year 2001.

Each tunnel will be about 2.6 km long in which 1.8 km are bored

using bentonite slurry TBM and the remaining being the cut-and-

cover entrances and exits. The subsurface works of the two

ventilation shafts and the installation of the electromechanical plant

have been completed. Chapter (5) provides an analysis for the

intersection of Al-Azhar tunnels with the Cairo Wastewater spinal

tunnel.

• Suez Canal Road Tunnels: The only road tunnel connecting Sinai

with the east coast of the Suez Canal, Ahmed Hamdy Tunnel, was

finished in 1983 using open-face tunneling. The deteriorating lining

of this tunnel was covered during rehabilitation with a new cast-in-

place reinforced concrete lining, 450 mm thick (Otsuka and Kamel,

1994 & Ahmed, 2000) as shown in Fig. (2.31). The Authority for

Tunnels has received proposals for the construction of a road

tunnel, on a BOT basis, below the Suez Canal, 20 km south of Port

Said from 2 consortia, one Egyptian and one French. The tunnel

will carry traffic to the proposed harbor and industrial development

planned on the east side of the Canal as well as forming part of the

international coastal highway.

• El-Salam Syphon: This project was intended to transport the Nile

water below Suez Canal to Sinai for land reclamation using four

parallel tunnels. Each tunnel is about 750 m long. Chapter (5)

includes a description of this project.

• Alexandria Wastewater Project: The central main collector of the

proposed network was constructed under central Alexandria,

76

starting from the Mediterranean coast and advancing southwards

using EPB TBMs of about 2.25 m diameter.

Fig. (2.29) Egyptian tunneling projects (after El-Nahhas, 1999)

77

Fig. (2.30) Cairo tunneling projects (after El-Nahhas, 1999)

78

Fig. (2.31) Rehabilitation of Ahmed Hamdy Tunnel

(after Otsuka and Kamel, 1994)

79

Chapter Three

TUNNELING IDEALIZATION

3.1. Introduction Tunneling is an intricate nonlinear time-dependent three-dimensional

process. The comprehensive features in tunneling simulation that should be

included in the requisite modeling are illustrated in Fig. (3.1) and summarized as

following:

• The nonlinear soil constitutive behavior, which depends mainly on the

stress path, confining pressure and rate of loading;

• The unloading forces developed during ground excavation and the

potential seepage towards or away from the tunnel;

• The radial and axial ground loss and the overcutting gap;

• The pressurized excavation boundaries and ground support measures;

• The effect of the potential marginal yield zones around the tunnel;

• The tailskin grouting and the hardening of grouting material with time;

• TBM advancement and lining installation;

• The mutual interaction between the excavated tunnel and the surrounding

underground pre-erected pipelines and tunnels.

In view of the preceding modeling features, we cannot regard the

observational rules, which are commonly used to describe the tunneling

deformation fields and lining stresses, as reliable bases for tunneling analysis

even under the same ground conditions (which is very unlikely as well), as the

different installation procedures and various modeling features are not

deliberated in these rules. Tunneling researches frequently employed two-

dimensional models to simulate tunneling installations and different phases of

80

ground-lining interaction. The displacement field is approximated in plain strain

models by neglecting the non-radial deformations while the stress and

displacement field is approximated into symmetric fields in axisymmetric

models. Although two-dimensional numerical models are superior to the rules-

of-thumb, the oversimplifications in the analysis in two-dimensional models

materialize a justifiable source of uncertainty in employing the obtained results in

design and analysis. Little literature is available in which soft ground tunneling is

idealized using three-dimensional models due to the required high computational

cost especially when employing the nonlinear soil models.

In the present research, a nonlinear three-dimensional model is developed

to present a genuine simulation of the induced displacement fields. The soil,

shield and liner are modeled using eight-node hexahedral isoparametric finite

elements. Soils constitutive behavior is presented by employing hyperbolic

nonlinear model having a variable modulii according to confining pressure and

stress path.

The shield-soil interface is modeled using a hyperbolic gap element. The

liner-grout-soil interface is modeled by introducing grout elements with

incremental strength parameters; time hardening characteristics; and initial

hydrostatic pressure equal to the grouting pressure. Fig. (3.2) illustrates the

proposed arrangement of the interface modeling. The tunnel heading and face

pressure is introduced to examine the face stability and effect of the face losses

on the deformation field.

The excavation of ground, the liner activation and the liner-ground

interaction are considered in a special incremental pseudo-time iterative

technique. In this chapter, the numerical aspects of proposed tunneling

simulation are established. The techniques to simulate the complex nonlinear

shield–lining–soil interaction and the construction technique of the pressurized

shielded tunneling are demonstrated.

81

Fig.

(3.1

) Mod

elin

g fe

atur

es o

f sof

t gro

und

shie

lded

tunn

elin

g

Ove

rcut

Segm

enta

l lin

ing

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Pressurized face

Inst

alla

tion

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t

Prob

able

def

orm

atio

n fie

ld

Soft

pres

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ed

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t H

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t

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vatio

n

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kin

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ting

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g in

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82

Fig. (3.2) Interface modeling

Overcut

Hexahedra shield elements

Gap elements

Hexahedra soil elements

(a) Shield-soil interface modeling

Hexahedral liner elements

Hexahedral soil elements

Hexahedral grouting elements (initially

under hydrostatic grouting pressure)

(b) Liner-grouting-soil interface modeling

Tail gap

Shield/Liner

Enfolding ground

83

3.2. Finite Element Formulation Finite element (FE) procedures are employed because of their great

capability to deal with the nonlinear geotechnical problems (ETL 1110-2-544,

1995). The FE uses interpolation basis functions or shape functions [Ne], which

are spatial polynomials relating the generic displacement vector {ue} at any point

in a sub-domain or element to the nodal displacement vector {Ue} of the element

(Zienkiewics, 1977) as following:

{ue} = [Ne] {Ue} …(3.1)

The same shape functions are used to relate the coordinates of any point inside

the element {xe} to the coordinate of the nodal points {Xe}, i.e.

{xe} = [Ne] {Xe} …(3.2)

The eight-node hexahedral tri-linear element is used to model soil, lining

and grouting. Axelsson and Baker (1984) pointed out that the usage of linear

elements is advantageous in dense meshes (h-refined meshes) other than higher

order elements in coarse meshes (p-refined meshes) because of their small

spectral number. The shape functions of used element are formulated in the

natural system of coordinates {ξ} as shown in Fig. (3.3) by the following indicial

expression (Pullan, 1998):

Ni = (1+ξi ξ)(1+ηi η)(1+ζi ζ)/8 …(3.3)

The relations between the generic displacement vector {ue} and the strain

vector {εe} is defined using a an operator [Ae] as

{εe} = [Ae] {ue} …(3.4)

in which [Ae] is given by:

84

[ ]

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

=

x0

z

yz0

0xy

z00

0y

0

00x

Ae

…(3.5)

The relation between the nodal displacement and the strain can be written as:

{εe} = [Be] {Ue} …(3.6)

where

[Be] = [Ae] [Ne] …(3.7)

The constitutive matrix [De] describes the relation between the stress and

the strain as following:

{σe} = [De] {εe} …(3.8)

so

{σe} = [Be][De]{Ue} …(3.9)

Applying the principle of virtual work

{ } { } { } { } { } { } { } { }eT

eS

eT

eV

eT

eV

eT

e PUdStudVudVeee

+δ+γδ=σδε ∫∫∫ …(3.10)

85

where { } { } { }eee Uandu, δδδε are a compatible set of virtual strains, displacements

and nodal displacements; {γe} is the body force vector (usually the gravitational

forces) applied to volume of element Ve ; {te} is the surface traction vector along

the boundary of the element Se and {Pe} is the nodal force vector

Replacing { }eδε by [Be]{δUe} and {δue} by [Ne]{δUe} we get another

version of the virtual work equation with no required virtual displacement field:

[ ] { } [ ] { } [ ] { } { }eS

eT

eV

eT

eV

eT

e PdStNdVNdVBeee

++γ=σ ∫∫∫ …(3.11)

Substitute for {σe} by [Be] {Ue} we get

[ ] [ ][ ] { } [ ] { } [ ] { } { }eS

eT

eV

eT

eeV

eeT

e PdStNdVNUdVBDBeee

++γ= ∫∫∫ …(3.12)

or

[Ke] {Ue} = {Fe} …(3.13)

where

[Ke] The element stiffness matrix = [ ] [ ] [ ]∫eV

eeT

e dVBDB …(3.14)

and

{Fe} The element load vector = { } [ ] { } [ ] { }∫∫ +γ+ee S

eT

eV

eT

ee dStNdVNP …(3.15)

In order to form the [Be] matrix, the derivatives of the shape functions are

required with respect to the global spatial coordinates. For any shape function Nk,

the derivative with respect to {x} can be calculated using the chain rule as

following:

{ } [ ] { }ξ∂∂

=∂∂ − k1k NJ

xN …(3.16)

86

where

[J] is the Jacobian matrix = }{}x{

ξ∂∂ = [ ] { }( )ee XN

}{ξ∂∂ …(3.17)

The stiffness matrix is written as:

[ ] [ ] [ ] [ ]∫=mapV

mapeeT

ee dV)Jdet(BDB]K[ …(3.18)

Where Vmap is the volume of the parent (mapped) element in the natural

coordinates’ space {ξ}. A similar expression can be used to evaluate the body

forces, i.e.

[ ] { } [ ] { }∫∫ γ=γmape V

mapeT

eV

eT

e dV])Jdet([NdVN …(3.19)

Numerical integration technique is used to evaluate the element matrices.

The element matrices are then assembled to form the system matrix. The nodal

forces resulting from inter-element tractions are canceling each other. Surface

tractions contribute to the load vector in case of external boundaries only. When

summed, element nodal point loads are grouped into external nodal forces.

87

Fig. (3.3) Natural axes of hexahedral parent element

1 2

3 4

5 6

7 8

ξ

η

ζ

88

3.3. The Constitutive Model The nonlinear finite element Method is characterized by the dependence

of the stiffness coefficients on the state of stress and the stress path. The foremost

source of nonlinearity is the material constitutive relations because they are

highly dependent on the state of stress. There are many models to account for the

material nonlinearity. The stress-strain relationship of soil should be expressed in

incremental form to account for the path-dependency. Using the incremental

form of the constitutive matrix [Det], the element stiffness matrix [Ket] can be

rewritten as:

[ ] [ ] [ ][ ]∫=eV

eett

eet dVBDBK …(3.20)

Duncan and Chang (1970) proposed the hyperbolic model and used it in

analyzing embankment deformation. The parameters of the model can be

determined from conventional triaxial test results. Because of its simplicity, this

model has been used in many other geotechnical applications (Chan, 1989;

Ahmed, 1991; Abdel-Rahman, 1993; Esmail, 1997; and Duncan, 1996). A

typical triaxial compression test yields the results shown in Fig. (3.4). The

deviator stress and axial strain relationship can be approximated by a hyperbola

passing through the origin and has an asymptotic value of (σ1 - σ3)ult and initial

tangent (E0) as shown in Fig. (3.5).The equation of the hyperbola is:

( )

( )ult310

31

E1

σ−σε

+

ε=σ−σ

…(3.21)

To determine the values of E0 and (σ1 - σ3)ult from the conventional

triaxial test results, the previous equation can be rewritten a linear form:

89

( ) ( )ult31031 E1

σ−σε

+=σ−σ

ε …(3.22)

Taking ε as the abscissa and ( )31 σ−σε as the ordinate, the parameters used to

describe the hyperbola can be determined as shown in Fig. (3.6). The value of

(σ1-σ3)ult , which is reached only at strain equal to infinity, is always greater than

the actual deviator stress at failure (σ1 - σ3)f , so a ratio called the Failure Ratio

(Rf) is introduced to related the ultimate and actual failure stresses, Rf is defined

as:

( )( )ult31

f31fR

σ−σσ−σ

= …(3.23)

Hence, the stress-strain relation is given by:

( )

( )f31

f

0

31 RE1

σ−σε⋅

+

ε=σ−σ

…(3.24)

The value of (σ1 - σ3)f can be determined from the Mohr-Coulomb failure

criterion as shown in Fig. (3.7) and as given by the following equation:

( )φ−

φσ+φ=σ−σ

sin1sin2cosC2 3

f31 …(3.25)

Substituting in the hyperbola equation

( ) ( )φσ+φ

φ−⋅ε⋅+

ε=σ−σ

sin2cosC2sin1R

E1

3

f

0

31

…(3.26)

The above equation can be rewritten as:

90

( )( ) ( )

φσ+φ

φ−⋅σ−σ⋅−

σ−σ=ε

sin2cosC2sin1R1E

3

31f0

31

…(3.27)

Nonlinear analysis should be performed in increments, so it is necessary to

determine the incremental stiffness of the material. In the hyperbolic model, the

tangent modulus can be determined by differentiating the stress strain curve of

the material at constant confining stress σ3 as:

( )( ) 2

3

31f0

31

31t sin2cosC2

sin1R1E

)(dd1

d)(dE

φσ+φφ−σ−σ

−=

σ−σε

=ε

σ−σ=

…(3.28)

Janbu (1963) suggested that the initial tangent modulus is dependent of

the confining pressure (σ3). He proposed the following relation:

n

a

3a0 p

KpE

σ=

…(3.29)

where pa is the atmospheric pressure = 1 bar = 10.3 t/m2, K is the modulus

number (dimensionless) and n is the exponent number (dimensionless). Janbu’s

equation suggests that the initial modulus increases with the confining pressure

(σ3) according to a power law relationship. The confining pressure (σ3) increases

with soil depth. Stiffness of most soils cannot increase indefinitely with increase

in depth. A value of n less than one implies that the effect of σ3 on the rate of

increase of the initial modulus is diminishing with increasing depth. Value of n

greater than one has been reported in soft soils, however this can result in

unrealistically high modulus at great depth. The modulus number and the

exponent number can be determined from triaxial test results by taking the

logarithm of both sides of previous equation resulting as following:

91

( )

σ+=

a

3

a

0

plognKlog

pElog

…(3.30)

Value of (log (K)) can be determined from the intercept of the straight line at σ3

= Pa and n can be determined from the slope as shown in Fig. (3.8). Substituting

for E0 in Et

( )( ) n

a

3

2

3

31fat psin2cosC2

sin1R1KpE

σ

φσ+φφ−σ−σ

−= …(3.31)

It should be noted that, if tension exists in the soil, the minor principal stress (σ3)

will become negative and the tangent modulus can not be evaluated if (σ3) is less

than zero, so a very small value of E is assumed in tension zones.

A constant Poisson’s ratio may be assumed in the hyperbolic model.

Duncan et al. (1980) presented a hyperbolic relationship for the axial strain in

relation to the radial strain under triaxial test condition. They proposed the

following formula for Poisson’s ratio

2a

3

rt )A1(

plogFG

dd

−

σ⋅−

=εε

−=ν

…(3.32)

under the constraint

5.00 t <ν≤ …(3.33)

where

92

( )( ) n

a

3

3

31fa

31

psin2cosC2sin1R1Kp

d)(A

σ

φσ+φφ−σ−σ

−

σ−σ=

…(3.34)

and εr is the radial strain; G, F and d are material parameters than be determined

from Fig. (3.9)

Unloading is modeled by specifying a different modulus, which results in

non-zero strains when returning to the initial state of stress of the material, as

shown in Fig. (3.10). The modulus Eur is used during the unloading-reloading

cycle. Eur is given by:

n

a

3aurur p

pKE

σ=

…(3.35)

where Kur is the number of unloading modulus and may be assumed from twice

to three times the loading modulus number (K). During the finite element

analysis, it is not possible to determine the region, which is subjected to loading

or unloading in advance in order to decide whether the loading modulus or

unloading modulus should be used during the first iteration. Since the loading

modulus is normally lower than the unloading modulus, the use of the loading

modulus can lead to numerical divergence when unloading occurs. Using the

unloading-reloading modulus during the first iteration of every loading step will

underestimate the displacement in the first iteration if loading occurs. The correct

loading or unloading modulus will be used in subsequent iterations according to

a parameter defined by Duncan et al. (1984). This parameter is called the loading

level (LL) and defined as:

4

a

3

3

31

psincosC)(LL

σ⋅

φσ+φσ−σ

= …(3.36)

LL is calculated for each Gauss point and compared to the maximum value

93

reached during the loading history at the same Gauss point (LLmax). Three

different cases may arise, namely:

1. If ( maxLLLL ≥ ) then loading is taking place and the used modulus E’=Et

2. If ( maxLL75.0LL ≤ ) then unloading is taking place and used modulus E’=Eur

3. If ( maxmax LL75.0LLLL >> ) then neutral loading is taking place and the used

modulus E is given by interpolation as shown in Fig. (3.11)

After determining the appropriate value of (E´) and (υt) the constitutive

matrix [Det] can be formed as:

[ ]

ν−

ν−

ν−ν−νν

νν−νννν−

ν−ν+′

=

2)21(00000

02

)21(0000

002

)21(000

000)1(000)1(000)1(

)21)(1(ED

t

t

t

ttt

ttt

ttt

ttet

…(3.37)

The resulting constitutive matrix [De] is symmetric; therefore, the element

elastoplastic stiffness matrix is symmetric too. The previous property is a major

advantage of this model especially in three-dimensional analysis as the resulting

system stiffness matrix may be placed in a symmetric half-banded storage.

94

Fig. (3.4) Typical triaxial results

Intermediate σ3

High σ3

Low σ3

ε

σ1 − σ3

Low σ3

Intermediate σ3

High σ3

ε

εv = ε + 2εr

95

Fig. (3.5) Hyperbolic Stress Strain Curve (after Duncan and Chang, 1970)

Fig. (3.6) Determination of Hyperbolic Model

parameters (after Duncan and Chang, 1970)

σ1−σ3

(σ1−σ3)ult

ε 1

Ε0

31 σ−σε

ε

ult31 )(1σ−σ

1

1/Eo

96

Fig. (3.7) Mohr-Coulomb yield criterion

Fig. (3.8) Determination of the modulus number and

exponent number (after Duncan and Chang, 1970)

σ

τ

φ

σ3 σ1

C

σ

a

3

plog

a

i

pElog

Log (pa)

Log(K) 1

n

97

Fig. (3.9) Determination of F and G (after Duncan et al., 1980)

Fig. (3.10) Determination of the unloading modulus Eur

(after Duncan et al., 1984)

ε

σ1−σ3

1

n

a

3aurur p

pKE

σ=

G

σ

a

3

plog

Log (pa)

vt (1-A2)

1

F

98

Fig. (3.11) Effect of stress path on the soil modulii (after Duncan et al., 1984)

LLmax 0.75 LLmax

Et

Eur

LL

E

99

3.4. Interface Formulation In order to obtain a good estimate of the deformability of different

continua at their interfaces, interface finite elements are inserted between the

nodes of the different material boundaries to account for the potential relative

movements between their boundaries. Cook et al. (1989) illustrates the concept

of gap element using the one-dimensional module shown in Fig. (3.12). The gap

element has a stiffness discontinuity between the tension fictitious stiffness (s)

and the compression substantial stiffness (s+S). Cook pointed out that the force

increment must be small enough to grasp the point of gap closure.

The spring type hyperbolic interface element used by Dessouki (1985),

gave a consistent representation of the state of normal and shearing stresses

between the soil media and the structural elements. It has only two nodes as

shown in Fig. (3.13), which are initially separated by a gap when no stresses exist

between the two materials. The element local stiffness matrix [k’e] is based on

two uncoupled stiffness coefficients (kn) for formal force and (kt) for shear force.

[ ]

−−

−−

−−

=′

tt

tt

nn

tt

tt

nn

e

k00k000k00k000k00kk00k000k00k000k00k

k

…(3.38)

The shear stiffness (kt) increases with an increase in the normal stress and

decreases with increasing the shear stress (Duncan et al., 1998). Its variation is

nonlinear as shown in Fig. (3.14). This nonlinear shear stress-shear displacement

relationship can be given in a hyperbolic form as:

ultti

ixy vk1

vA

τ′

+

′=τ

…(3.39)

100

where v' is the displacement along local y’ axis, Kti is the initial shear stiffness,

τult is asymptotic value of shear stress and Ai is the area between adjacent

interfaces. Similarly

ultti

ixz wk1

wA

τ′

+

′=τ

…(3.40)

Where w' is the displacement along local z’ axis. The initial shear stiffness (ksi)

is related to the normal stress at the interface by Janbu power relation:

p

a

niwiti p

Akk

σγ=

…(3.41)

where ki is a dimensionless stiffness number, γw is the unit weight of water, σn is

the normal stress at the interface and p is the shear stiffness exponent. The

ultimate shear stress (τult) is related the failure shear stress (τf) by the relation:

ultfsf R τ=τ …(3.42)

The relation relates the failure shear stress to the normal stress at the interface is:

δσ=τ tannf …(3.43)

The tangential shear stiffness (kt) is obtained by differentiating τ w.r.t. v’, hence:

p

a

n

2

n

sfiwit ptan

R1Akk

σ

δσ

τ−γ=

…(3.44)

The relation between global stiffness matrix [Ke] and local stiffness matrix [K’e]

101

is given by:

[ ] [ ] [ ][ ]TKTK et

e ′= …(3.45)

The transformation matrix [T] is given by:

[ ]

=

333

222

111

333

222

111

nml000nml000nml000000nml000nml000nml

T …(3.46)

where (l1, m1, n1), (l2, m2, n2) and (l3, m3, n3) are the direction cosines for the

local axes x’, y’ and z’ respectively (Weaver and Johnston, 1984).

The grouting is introduced behind the TBM by applying a hydrostatic

pressure equal to the grouting pressure. The force vector {Fgrouting} due to

applying this initial grouting pressure is estimated by the following equations.

{ } [ ] { }∑ ∫ σ−=elementsgrouting V

eT

egrouting

e

dVBF …(3.47)

The stiffness of the grouting element undergoes time hardening. Adopting a

hyperbolic relation, the uniaxial strength (f) of the grouting is given by:

c50

ftt

tf ′+

= …(3.48)

where (fc’) is the cylinder strength after 28 days, (t) is the time and (t50) is the

time at which the cylinder strength is half the value of (fc’). Assuming the rate

and the advance distance of the TBM is (R) and (D) respectively, then the

previous equation may be rewritten in the following form:

c50

fR/Dt

R/Df ′+

= …(3.49)

102

Fig. (3.12) Gap modeling (after Cook et al., 1989)

g

s

S

δ

f

f

δ s 1

S + s

1

g

103

Fig. (3.13) Three-dimensional interface element local and global axes

Fig. (3.14) Stress-deformation curves for hyperbolic interface element

(after Dessouki, 1985)

x

y

z

x' y'

z' g

w

v

u

w'

u'

v'

τ A

i

v' or w'

τult Ai

1

kti

kt 1

104

3.5. Nonlinear Solution Techniques Chan (1996) discussed the formulation and solution techniques for nonlinear

finite elements. They classified the used techniques into three categories; namely:

the iterative methods; the incremental or step-wise methods; and the mixed or

step-iterative methods. Iterative methods are not usually used in solution of

elastoplastic systems for the following reasons:

1. The material constitutive relations are usually described incrementally,

which imposes the use of incremental and mixed methods

2. The nonlinear systems are path-dependent and iterations alone may be

misleading in determining the loading and the unloading localities in the

system.

3. The loading is usually given in an incremental form.

In the following sections, the nonlinear formulation techniques of the finite

element are reviewed with emphasis on the methods implemented in the model.

3.5.1. Incremental Techniques

After we assemble the element matrices into system matrices we can get

the following equation:

[ ]{ } { }FUK t&& = …(3.50)

where:

[Kt] is the system tangential matrix = [ ]∑=

elementsof.No

1eetK …(3.51)

and

{ }F& is the increment load vector = { }∑=

elementsof.No

1eeF& …(3.52)

Equation (3.50) may be rewritten in the following form

{ }{ } [ ]tKUF

=∂∂ …(3.53)

105

To solve the previous differential equation, we can use the following techniques:

1. Euler Integration Scheme: In this method, the relation between the load

increment }F{& and the displacement increment }U{ & is approximated by:

[ ] { } { }FUK ttEuler

ttt

t && ∆+∆+= …(3.54)

Where left superscript denotes a pseudo time used to describe the load and

displacement increments. The time (t) indicates the beginning of the step

and time (t+∆t) indicates the end of the increment. The displacement

increments are obtained using the previous equation and the total

displacement is given by:

{ } { } { }Eulerttttt UUU &∆+∆+ +≅ …(3.55)

The stiffness matrix is evaluated at the end of the previous step, which

may lead to a gross error as shown in Fig. (3.15).

2.Modified Euler Integration Scheme: To increase the accuracy, the

Modified-Euler scheme may be used. In this method, the solution is

carried out for the half increment of load so we can get

[ ] { } { }F5.0UK tt2/ttt && ∆+∆+⋅= …(3.56)

Using the above equation, we can get { }U2/tt &∆+ and hence we can calculate

[ ]K2/tt ∆+ . The displacement increment { }Utt &∆+ is obtained using:

[ ] { } { }FUK tttt2/tt && ∆+∆+∆+ = …(3.57)

106

A comparison between the integration schemas is shown in Fig. (3.15),

which reveals increasing of accuracy by using Modified Euler integration

scheme.

Fig. (3.15) Application of incremental methods in nonlinear finite element

(after Owen and Hinton, 1980)

Euler.Mtt U&∆+

Eulertt U&∆+

F

U

t+∆tF

tF Ftt &∆+

tU tUEuler tUM.Euler

1 tKt

1 t+∆t/2Kt

1

t+∆t/2Kt

107

3.5.2. Mixed Techniques

These techniques employ the initial stress method that was described by

Zienkiewics (1977). The equilibrium equations are casted in residual forms using

either tangent stiffness or constant stiffness matrices during each increment. Two

main types have been used by most of the finite element codes namely:

1.The Incremental Iterative Newton-Raphson Method (NR): In this

method, the load vector is the residual vector resulting from the difference

between the applied force and the resisting straining forces. The stiffness

matrix and the residual vector are calculated at the beginning of each

iteration. The i+1 iteration is described by the following equation:

[ ] { } { }RUK tt1i

tt1i

itt ∆++

∆+

+∆+ =& …(3.58)

where

{ } { } [ ] { }∑ ∫=

∆+∆+∆++ σ−==

elements of No.

1e Ve

tti

Te

tttt1i

e

dVBFVector ResidualR …(3.59)

and

{ } { } { }UUU tt1i

tti

tt1i

&∆+

+∆+∆+

+ += …(3.60)

The left subscript denotes the iteration process. If the iteration superscript

is zero that means the matrix or vector is calculated at the end of the

previous time step. Fig. (3.16) shows the application of this method on a

single degree of freedom.

2.The Incremental Iterative Modified Newton-Raphson Method (MNR):

The residual vector is updated at the beginning of each iteration. A

constant stiffness matrix (usually elastic) is used. The i+1 iteration is

described by the following equation:

108

[ ] { } { }RUK tt1i

tt1i

0 ∆++

∆+

+ =& …(3.61)

The MNR method is shown diagrammatically for a single degree of

freedom in Fig. (3.17).

Due to inclusion of special interface element that has a high sensitivity to

displacement state along the interfaces, the NR was preferred to be used in the

code. Open gap elements were excluded from contribution to the residual vector.

The tensile stiffness was not set to trivial values to allow monotonic gradual

closure of the gap other than an unstable convergence that may result in

undesired changes in the stress path (Duncan et al., 1998)

Fig. (3.16) Incremental Iterative Newton-Raphson Method


Rtt2

∆+ Ftt ∆+

Ft

RF tt1

tt ∆+∆+ =&

[ ] { }∑ ∫=

∆+ σelements of No.

1e Ve

tti

Te

e

dVB

UU tt0

t ∆+= Utt1

∆+ Utt2

∆+ U

F

Utt1&∆+

1

KK tt0

t ∆+=

1

Ktt1

∆+

Utt2&∆+

109

Fig. (3.17) Incremental Iterative Modified Newton-Raphson Method


Rtt3

∆+

[ ] { }∑ ∫=

∆+ σelements of No.

1e Ve

tti

Te

e

dVB

K0

Rtt2

∆+

Ftt ∆+

Ft

RF tt1

tt ∆+∆+ =&

UU tt0

t ∆+= Utt1

∆+ Utt2

∆+ U

F

Utt1&∆+

1

Utt2&∆+

K0 1

110

3.5.3. Convergence Criteria

NR and MNR methods seek an approximate solution to the problem,

therefore there is always some error associated with the solution. It is important

that this error is not too large to ensure that the solution obtained represents a

realistic solution to the problem. On the other hand, increased accuracy of the

solution requires more computer time and increases the time and cost of the

analysis. Consequently a measure of convergence is required to optimize the use

of computer resource and to terminate the calculation at the appropriate time.

Such measure will also give the convergence characteristics of the problem if the

solution becomes unstable and diverge. There are two basic methods to measure

the convergence characteristic for the displacement finite element method;

namely:

1. Displacement Criterion: The displacement criterion uses nodal

displacements as the basic measure of the convergence characteristic.

Since there are many nodal points in a finite element mesh, the

displacement norm is used instead of the displacement at a particular

node. The Euclidean norm of a vector {U} is defined as:

{ }U Uii

n

==∑ 2

1

…(3.62)

Therefore convergence is defined as:

{ }{ } utt

i

tti

U

Uε≤

∆+

∆+ &

…(3.63)

Where ε u is the displacement tolerance.

2. Force Criterion: The force criterion uses the residual vector norm as

the basic measure of the convergence characteristic. The force

convergence is defined as:

111

{ }{ } Ftt

0

tt1i

R

Rε≤

∆+

∆++

…(3.64)

Where Fε is the force tolerance.

The choice of the convergence criteria and tolerance is largely dependent

on the problem being analyzed. The displacement criterion is adopted in this

thesis because of the existence of interface elements in the analysis. Interfaces

with significant compression stiffness coefficients extremely magnify the

residuals. The displacement criterion may be considered as more “stable”

criterion in this case as it exhibits a unified trend of convergence.

3.5.4. Calculation of Stresses from Strains

The calculation of stresses is not only required as an output quantity but

also affects the solution in the next iterations and increments as the constitutive

relations is a function of the calculated stress. Therefore the stresses must be

calculated as accurate as possible. The incremental strain vector at each Gauss

point can be calculated from:

{ } [ ] { }ett1iee

tt1i UB &&

∆+

+∆++ =ε …(3.65)

The tangential constitutive matrix is given by:

{ }{ } [ ]et

e

e D=ε∂σ∂ …(3.66)

hence, the stress increment can be calculated from the following integration

(Chan, 1989):

112

{ } { } { } { } [ ] { }{ }

{ }

∫ε

ε

∆+∆++

∆+∆++

∆++

∆+

ε+σ=σ+σ=σtt1i

tti

dDettti

tt1i

tti

tt1i &

…(3.67)

Numerical integration may be used to evaluate the integral in the stress

calculations. There are many schemes to evaluate the integral, one of the simplest

method is to use Euler Integration Scheme by approximate the integral as

following:

{ } { } [ ] { }ε+σ≅σ ∆++

∆+∆+∆++ &tt

1iettti

tti

tt1i D …(3.68)

A more elaborate method is to use Modified Euler Integration Scheme as

following:

{ } { } [ ] { }ε+σ≅σ ∆++

∆+∆+∆++ &tt

1iettti

tti

tt2/1i D …(3.69)

Then we calculate [ ]ettt2/1i D∆+

+ using the predicated stress { }σ∆++

tt2/1i . The stress can be

calculated using

{ } { } [ ] { }ε+σ≅σ ∆++

∆++

∆+∆++ &tt

1iettt2/1i

tti

tt1i D …(3.70)

Other methods include the Runge-Kutta methods of various orders. To

minimize errors induced with this integration the strain increment may be divided

into small sub-increment and one of the integration methods is used. Smith and

Griffiths (1998) and Chen and Mizuno (1990) described another algorithm to

retrieve the stress increment from the strain increment in an elastoplastic model.

This algorithm assures that the state of stress will not violate the yield surface,

however it is very convoluted and limited to constant elastic modulii.

113

3.6. Excavation and Lining Installation Modeling The tunnel excavation is a continuous and not a discrete process; yet, the

excavation is modeled by removing a cluster of ground elements from the finite

element meshing. The accuracy of the process increases as the number and size

of excavated (removed) elements per every excavation step are kept as small as

possible. The Stress Reversal Algorithm (SRA) can model excavation by

considering the traction pressures t{Τ} between the excavated and the

unexcavated elements. This traction is in equilibrium with stress t{σ}, the applied

gravity body load t{γ} and any external nodal load (Desai and Abel, 1972). The

excavation is formed by relaxing t{Τ} along the boundary surface between the

excavated and the unexcavated grounds (Sexc), that may be implemented by

applying a pressure − t{Τ} along the excavated boundary as shown in Fig. (3.18),

resulting in a new residual load vector given by:

{ } [ ] { }FdS}T{NR tt

.elements unexc. S

tTe

tt1

exc

&∆+∆+ +−= ∑ ∫ …(3.71)

Ghabossi et al. (1983) presented the Multiple Forming Residual Algorithm

(MFRA), which is an equivalent scheme to calculate the effect of the relaxed

traction vector that is better than the SRA from the computational point of view.

By studying the equilibrium unexcavated ground equilibrium at pseudo time (t),

we will get the following:

{ } [ ] [ ]∑ ∫∑ ∫==

σ=+elements unexc.

1e Ve

tTe

elements unexc.

1e S

tTe

t

unexexc

dV}{BdS}T{NF …(3.72)

where Vunex is volume of the unexcavated ground. Rearranging the last equation

114

[ ] { } [ ]∑ ∫∑ ∫==

σ−=−elements unexc.

1e Ve

tTe

telements unexc.

1e S

tTe

unexexc

dV}{BFdS}T{N …(3.73)

consequently, the residual form at time (t+∆t) is given by

{ } { } [ ] { } [ ]∑ ∫∑ ∫=

∆+∆+

=

∆+∆+ σ−=σ−=elements unexc.

1e Ve

tt0

Te

ttelements unexc.

1e Ve

tTe

tttt

unexunex

dV}{BFdV}{BFR …(3.74)

Hence the excavation is simply introduced into analysis by reforming the residual

vector for the unexcavated ground using the stresses calculated from previous

stage (Bentler, 1998). Another aspect of changing the solution domain is that we

have to renumber the steering vector used in stiffness assembly and recalculate

the size of the system matrices. The lining elements are new elements that must

be added to the mesh by activating these elements. The required changes are to

reconstruct the residual vector, the steering vector and recalculate the size of the

global matrices.

Fig. (3.18) Stress Reversal Algorithm (after Desai and Abel, 1972)

σv

σh

τ

σ

Before Excavation

τ

σ

Excavation

Increment

τvh

Sexc

115

3.7. Programming Aspects of the Model Using the previous modeling concepts, a computer program was prepared

employing a skyline solver in order to minimize the storage size of the assembled

stiffness matrix (Zienkiewics, 1977). The program is divided into twelve key

modules in which each module is subdivided into one or more subroutines. The

processing and data flow through the modules are shown schematically in Fig.

(3.19). The modules and their functions are described in following section:

1- Master module: This module controls the flow of data and calculation

steps.

2- Initialization or zeroing module: This module functions to initialize to

zero various vectors and matrices at the beginning of the solution

process.

3- Data input and checking module: This module handles input data

defining the initial geometry, boundary conditions, material properties

and initial stress field. The data are checked using diagnostic routines.

If errors occur, they will be flagged and the program is terminated.

Once used, this module is not invoked again.

4- Staging module: This module reads changes in the loading and

application of excavation, lining installation, face pressure and tailskin

grouting.

5- Loading module: This module organizes the calculations of nodal

forces due to various forms of loading (gravitational, traction, etc.) for

each stage.

6- Residual force module: The function of this module is to calculate the

residual or ‘out of balance’ nodal forces at the active stage.

7- Residual increment module: This module precedes an incremental

scheme of the applied residual vector evaluated by the residual force

module.

8- Stiffness module: this module organizes the evaluations of the stiffness

matrix for each element according to its type. The stiffness matrices are

assembled in a system stiffness matrix.

116

9- Solution module: The purpose of this module is to reduce and solve the

governing set of simultaneous equations to give the nodal displacement

and force reactions at the restrained nodal points.

10- The stress and strain calculation module: This module is used to

calculate the stress and strain.

11- Convergence module: In this module, the convergence of the nonlinear

solution is checked against a given criterion.

12- The output module: This module is used to print out output of the

computer analysis.

117

Fig. (3.19) Program modules for nonlinear FE code

Initialization or zeroing module

Input data and checking module

Staging module

Residual incrementing module

Stiffness module

Solution module

Stress and strain cal. module

Convergence module

Output module

Main or master module

NR

Loading module

Residual force module

Increment loop

Iteration loop

Staging loop

118

Chapter Four

GREATER CAIRO METRO

4.1. Introduction Cairo population has soared in the recent decades from 3.5 millions in

1960 to more than 20 millions today; it is considered now as one of the most

congested cities in the world. As Cairo began its rapid population explosion in

the 1960's and 1970's, the need for a new mass transportation system was

inevitable. Studies carried out between 1970 and 1974 suggested to construct the

Greater Cairo Metro to be the major mass transportation system.

The Greater Cairo Metro comprises a regional line and two urban lines.

The first line of the Greater Cairo Metro or the regional line was completed in

1989 and was the first subway metro line in Africa and the Middle East. It is 42.5

km long from El-Marg at the North of Cairo to Helwan at the South with about

4.5 km underground part through downtown area. The underground part of the

first line was constructed employing the Cut-and-Cover (C&C) techniques. The

second line extends from Shubra El-Kheima to Giza suburban areas. The third

line is planned to extend about 7 km from Embaba to El Darasah. Fig. (4.1)

shows the arrangement of this network.

The second line is a double deck circular bored tunnel having an

excavated diameter of 9.4m and extending about 18.5km. The line serves 18

Stations including 12 underground. The route of the 2nd Line generally follows

existing streets in order to minimize the tunneling effect on the adjacent

structures as it passes through the most heavily populated and congested areas in

Cairo. Starting as a surface line in Shubra El-Kheima north of Cairo, the line

119

heads south on a viaduct then down into the tunnel part. The tunnel crosses

Ismailia Canal to Cairo Governorate then pursues southward to central Cairo

where it turns west to cross the two Nile branches to Giza Governorate then

changes to on-grade line at Boulak El-Dakrour and continues southward parallel

to the Upper Egypt Railways up to its terminal Station at the Giza suburban

areas.

The 2nd line was constructed and put into operation in two phases. Phase

1A, from Shubra El-Kheima to its intersection with Line 1 at Mubarak Station.

Phase 1B starts from Mubarak Station and terminates at Sadat Station which

forms another interchange with the older first line. Phase 2 extends across to the

west bank of the Nile and terminates at Giza Suburban Station south of Cairo.

The vertical alignment of Phase 1 is shown in Fig. (4.2).

Phase 1 includes a 2.4 km long surficial section and an 8.5 km

underground section in which only 1.4 km was constructed using the C&C

method employing diaphragm walls and sheet piling. Grouted plugs at the toe

level of the diaphragm wall were used to cut off seepage in a manner similar to

the construction of Stations. Slurry cut-off walls divide the tunnel length into

sections and allow excavation to begin in one section while the grouting work

and diaphragm walling continues farther along. The crossing of the Ismailia

Canal was constructed within overlapping sheet piled cofferdams. On completion

of the sheet piling, the cofferdam was backfilled to allow ground treatment to be

carried outs again forming a plug at the base of the excavation.

The following sections describe the construction and instrumentation

details of the bored tunnel of Line 2 – Phase 1A as reported by Richards et al

(1997); Esmail(1997); El-Nahhas (1999); and Ezzeldine (1999).

120

Line 1

Line 2-Phase 1 Line 2-Phase 2

Line 3 Fig. (4.1) Greater Cairo Metro Network

Fig. (4.2) Line 2 – Phase 1 routing (after Richards et al, 1997)

Phase 2

121

4.2. Line 2 – Phase 1A

4.2.1. Geological Conditions The geology of Cairo has been outlined by Shata (1988); he concluded

that Cairo is underlain by tertiary sedimentary rocks and quaternary soils, both

underlain by older basement rocks. The project area lies totally within the

geomorphic unit known as the young alluvial plain that represents the majority of

the lowland portion of the Nile Valley in the Cairo area. The Nile River deposits

governed the subsurface and groundwater conditions. The Pleistocene age

sediments in the alluvial plain are generally fairly consistent with depth, but vary

somewhat laterally as a result of the long history of river meanders, and alternate

cycles of sedimentation and erosion before the construction of Aswan High Dam

in Upper Egypt in the 1960's. These sediments are approximately 60-90 meters

thick in the Cairo area.

According to the Ardman-ACE (1991) and Hamza Associates (1993), the

geotechnical features of the project comprise a surficial man-made fill layer,

which varies in thickness from place to place according to human activities,

underlain by a natural deposit of medium to stiff, relatively massive cohesive

clay-silt layer, which also varies in thickness. This cohesive layer is underlain by

a silty sand transition zone followed by an extensive deposit of coarse sand,

which extends downward beneath the limits for Metro construction. The sandy

deposits are usually poorly graded containing lenses of silts and clays or gravels,

and infrequently contains layers of cobbles and sometimes boulders at depths up

to about 30m.

The ground water level varies seasonally with the level of the Nile River,

with the water level low in the winter when releases from Aswan High Dam are

at a minimum. In addition, it varies annually with the river level as some years

have a higher flow rate than others depending upon precipitation and run off rates

122

in Central Africa in the watershed of the upper Nile. Broadly speaking, the

groundwater regime in Cairo region consists of two distinct categories:

1. The groundwater above the clay layer and within the fill layer, which is

generally a perched water table and often recharged by leaky utilities.

2. The groundwater below the clay layer, which is not usually influenced by

surficial sources as it lies within the confined aquifer formed by the deep

granular deposits.

4.2.2. TBM Selection and Operation Parameters The prevailing subsurface conditions of the bored tunnel are generally

water bearing granular soils consisting of a deep coarse sand deposit overlain

with a finer stained transition layer. Such geological formations limit the tunnel

construction methods to pressurized full face tunneling machines. The fines

content (size less than 0.075 mm) would vary from approximately 7 or 8 percent

in the deep sand stratum to about 60 percent or more in the overlying finer

grained deposits. The gradation of the coarse sand and the overlying transition

zone are shown in Fig. (4.3). Compressed air tunneling with such a large face

area was not feasible due to the difference in water pressure from the crown to

invert of the tunnel and because of the expected high air losses in the permeable

ground. Two identical Herrenknecht BSS TBMs of 9.4m diameter, were selected

to drive the tunnels. The details of the employed TBM are shown in Fig. (4.4).

The TBM is composed of three basic components: the cutterhead, the main shield

body and the tailskin with a total weight of about 600 tons. To satisfy the

required schedule, one of the TBMs was installed at Khalafawi and drove

through the completed box at St. Theresa then removed at Rod El-Farag. The

second TBM was installed at Rod el-Farag, drove through the completed box at

Masarra and removed at Mubarak. Both TBMs then were transported to Attaba,

where one of them drove back towards Mubarak and the other drove through the

completed box at Awkaf to Sadat.

123

The cutterhead of the TBM is capable of operation in either direction of

rotation, with cutter teeth arranged accordingly. The cutterhead was initially

equipped with 280 cutter teeth and 21 dual 38 cm diameter roller disc cutters as

show in Fig. (4.5). However, after the initial tunnel drive in Lot 12, nine of the

central roller disc pairs were removed to provide more open area in the

cutterhead face to allow better material flows into the cutting chamber. The

openings in the cutterhead face allowed passage of material up to 200 mm in

size. The machine was not equipped with a crusher to break this material size

into smaller pieces in order to minimize potential blockages of the mucking

system. Inside the cutting chamber, two counter-rotating agitator wheels were

installed to keep the excavated solids in suspension until removal by the slurry

suction pumps. Face pressure of the bentonite slurry was provided and controlled

by an air chamber built into the body of the shield. The shield was equipped with

a two-chamber air lock to allow up to four workmen to enter the cutting chamber

to repair or replace machine components as required. Table (4.1) summarized the

various TBM operating parameters.

Table (4.1) TBM operational parameters (after Richards et al, 1997)

Operational parameter Unit Installed capacity Normal range of operation

Total installed power kW (HP) 2450 (3264) --- Rotary drive power kW (HP) 1000 (1360) ---

Rotary power/face area kW/m2 14.3 --- Torque m.t. 770 440

Rotation speed rpm 0-2.25 1-1.5 Advance rate mm/min 50 25-45

Agitator speed rpm 0-50 50 No. of jacks pairs 15 All Total thrust Tons 6000 2000-2500

Slurry pump power kW (HP) 2190 (2978) --- Slurry pump feed m3/hr 1400 1100-1300

Bentonite face pressure bars 3 1.5-2.5 Grout injection capacity m3/hr 40 15-20 Grout injection pressure bars >40 3.0-3.5

124

Fig. (4.3) Grading of the granular deposits

(after Richards et al, 1997)

Fig. (4.4) BSS used in the second line

(after El-Nahhas, 1999)

125

Fig. (4.5) Cutting face of the BSS


The TBMs were designed to include automatic tail void grouting as the

machine advanced. Injection pressure was controlled by upper and lower limit

sensors, with the limits adjustable. The injection pipes were embedded in the tail-

skin of the machine at four sets of dual (normal and spare) injection pipes

embedded in the perimeter of the tailskin of the shield. The normal injection

points were located at the 2, 4, 8, and 10 o'clock positions. Backup or spare

injection ports were located at approximately the 3, 6, 9 and 12 o'clock positions.

The tail void grout used was a lime and silica fume based mortar. This mortar

provided strengths of about 1.0-1.2 MPa (10-12 kg/cm2) in 28 days, and had

setting times of about 12-16 hours. This long setting time prevented set up of the

grout in the grout mixing tank, pump, and injection piping system during short

126

repair stoppage period. The tailskin was equipped with a fat plate seal at the rear,

backed up by two wire brush seals as illustrated in Chapter (2) and shown in Fig.

(4.4). A paper pulp based mastic material was continuously injected between the

tail seals to provide a supplemental seal against ground water and tail void grout

ingress around the perimeter of the erected lining. The pressure was always in

excess of the hydrostatic water pressure in order to allow a certain amount of the

mixture water to bleed into the surrounding ground, leaving a more dense (and

higher strength) mortar material than in the laboratory specimens. The injection

system allows for immediate adjustment of injection parameters such as volumes

and pressures.

The measured surface settlements associated with tunneling were less than

14mm on average basis, and alignment deviations averaging less than 25mm.

Production rates up to 580m/month were achieved, with average production of

4.8m/shift, 13.4m/day and 78m/week. The completed tunnels in the second line

are lined with seven bolted precast reinforced concrete segments of 1.5 m length

and a key as shown in Fig. (4.6). The lining has 8.35 m inside diameter and 40

cm thickness producing an external diameter of 9.15 m. The segments were

assembled within the machine shield tail. The lining should be completely

watertight under a head of approximately 2 bar of water pressure employing

elastomeric gaskets and a hydrophilic seal installed behind the elastomeric

gaskets. The tunnel lining joints between individual segments were required by

specification to be caulked in a groove cast into the four sides of each segment at

the inside surface as shown in Fig. (4.7). The specified water tightness of the

tunnel should be achieved without this caulking. The shield used an

electromechanical erector for segment installation, having 6 degrees of freedom

and a lifting capacity of eight tons. The erector used a vacuum pick up system,

with the vacuum seals arranged to provide seals for both the larger regular

segments and the smaller key segment. Installation procedures required

127

retightening the bolts after starting the shove for the next ring in order to

compensate for bolt loosening resulting from gasket compression.

A treatment plant was designed for slurry processing at a rate of 1500

m3/hr at a density between 1.0 and 1.2 gm/cm3. It was designed to handle a

maximum of 15 percent of the solids > 7.5mm in size, 99 percent between

7.5mm and 80 microns, and 15 percent smaller than 80 microns. The treatment

process included several steps of solids removal, starting with passage of the

slurry over a vibrator screen to remove particles > 7.5mm. The next step passed

the slurry through six cyclone desanding units removing particles down to 150

microns. Finally, the slurry passed through two units of eight cyclones each for

silt removal down to 80 microns in size. The layout of the treatment plant is

shown in Fig. (4.8).

The technical specification and contract documents of the second line

included a special section on insitu geotechnical monitoring implemented by the

contractors during construction of the tunnel. The monitoring program was

partitioned into the following four phases (El-Nahhas, 1999):

1. Dilapidation survey of existing buildings and other structures located in

the vicinity of the tunnel route.

2. An extensively instrumented test section located at the early stage of

advance of each TBM.

3. Measurement of settlement troughs at control sections at intervals of

about 20 m along the tunnel route.

4. Detailed monitoring of special structures situated along the route.

Two test sections, south of El-Khalafawy Station (Lot 12) and south of

Rod El-Farag Station (Lot 16), were heavily instrumented during the construction

128

Line 2 - Phase 1A. Hamza Associates (1995) presented a detailed report to

evaluate the tunnel monitoring for Lots 12 and 16 in addition to some

instrumentations at Lot 14. The instrumentation observations were used to

evaluate the tunneling techniques and the ground response during the stages of

the advance of the TBMs.

Fig. (4.6) Bolted reinforced concrete segments


129

Fig. (4.7) Lining groundwater sealing measures

(after Richards et al., 1997)

1. Screen: size > 7.5 mm. 2. Cyclone: 7.5mm ≤ size ≥ 150 microns. 3. Cyclone: 150 microns ≤ size ≥ 80 microns. 4. Intermediate holding tank. 5. Muck discharge conveyor 6. Bentonite supply

Fig. (4.8) The slurry treatment plant


130

4.3. Model Verification at Lot 16 This section authenticates the proposed numerical model at Lot 16

(between Rod El Farag Station. and Masarra Station). The analysis of

displacements and stresses around the tunnel is carried out using the proposed

model as described in Chapter (3). The results are compared with the field

measurements compiled during the construction of the tunnel to verify the model

assumption and study the prevailing parameters affecting tunneling. The

subsurface conditions were investigated using deep borings. According to

Ardman-ACE (1991) and Hamza Associates (1993), the soil log in Lot 16 is

shown in Fig. (4.9). The following distinctive layers are identified:

1. FILL: Appears at the ground surface and extends to a depth of about 3.0

m. The fill contains asphalt, sand, clay and limestone pieces.

2. CLAY-SILT: A medium to stiff silty clay or clayey silt layer exists below

the fill and extends to a depth of about 4.50 m below ground surface.

3. SAND: A medium dense to very dense fine to medium sand layer

underlies the previous clay and extends to the end of the borings. This

sand contains a substantial percentage of silt, which becomes lesser with

depth. The top 5 meters have substantial silt content and may be classified

as silty sand. Some clay pockets, gravel and cobbles exist at different

depths.

4. GROUNDWATER: Groundwater appears at about 1.9 m

Soil elements are represented using the hyperbolic elastoplastic model to

account for the effect of the stress level, stress path and confining pressure on the

stress-strain relationship. Nonlinear soil parameters used in the FE discretization

are estimated according to the geotechnical properties of the acknowledged

layers and are summarized in Table (4.2).

131

Table (4.2) The estimated subsurface nonlinear geotechnical parameters Stratum FILL CLAY – SILT Silty SAND Dense SAND

φ 15 0 30 37

C (kg/cm2) 0 0.8 0 0

γ (t/m3) 1.7 1.8 1.9 2.0

ko 1.0 0.74 0.50 0.40

K 150 225 350 600

N 0.6 0.55 0.5 0.5

Rf 0.70 0.75 0.8 0.8

υ 0.4 0.4 0.35 0.3

Shield and tunnel lining elements are represented by elastic elements with

different elastic properties to account for the different stiffness of the lining and

the shield. The shields modulus of elasticity is assumed to be 2000 t/cm2 with a

Poison’s ratio of 0.3. The lining is assumed to have a 140 t/cm2 modulus with a

Poison’s ratio of 0.15. The assumed lining modulus contains a judicial reduction

of about 30% to account for its segmental nature. The interface of the soil-shield

and soil-lining is represented by a three dimensional hyperbolic gap element and

grouting element with initial grouting pressure at the Gauss points. The grouting

elements have a variable stiffness in accordance with the advance rate of the

TBM as described in Chapter (3) assuming that the rate of advance of the

machine is 13 m/day and the half-strength time is 3days.

Special incremental technique is used to account for the variable mesh

size due to excavation and lining installation using the incremental pseudo time

technique combined with Newton-Raphson Iterative Technique. The technical

data of the employed TBM recommended the total ground loss as 0.5%. The

measured insitu ground surface settlements were used to compute the volume of

ground surface settlement trough, which is converted to a volume of ground loss

around the TBM. Hamza Associates (1995) reported the total volume of about

132

0.23%ground loss. The face loss was estimated to be about 0.09%, i.e. the loss

along perimeter of the TBM (which is mainly due to the overcutting) is about

0.14%. These data were introduced into the model. The grouting pressure is

assumed to be 3.25 bar. The face pressure is assigned to 2.0 bars.

Fig. (4.9) Subsurface conditions at Lot 16

(after Ardman-ACE, 1991)

Excavated diameter 9.40 m

133

The finite elements mesh used in the analysis is shown in Fig. (4.10) with

total of 3276 nodes, 2592 solid hexahedral elements and 207 joint elements to

represent the interface between the soil and lining. The analysis required about 6

hours using an INTEL PENTIUM II 300 computer with 64 MB RAM. The

tunneling activity was idealized in 21 incremental steps. The mesh at the end of

the 21st steps is shown in Fig. (4.11).

The idealization incorporates different constructional aspects of the TBM,

i.e. the face pressure, the overcutting, the tail gap, the tailskin grouting and lining

installation, as well as the nonlinear constitutive soil relations and the time-

hardening behavior of the grouting material as illustrated in Chapter (3). The

analysis is based on the effective stresses. Seepage towards or away from the

tunnel is neglected. This assumption is justified by the field measurements of the

excess water pressures, which are generally insignificant due to the effect of the

developed mud cake at the tunnel face. The GID pre/post processor1 was used to

visualize the developed analysis.

The GID environment accepts only nodal quantities; as the maximum

stress level and the stresses are computed at the Gauss points of the elements

during the solution stage for best possible accuracy, a special program that

applies an interpolation scheme was employed to obtain the stress level and the

stresses at the nodes. The visualization capabilities of the GID support element

layering that can be used to plot sub-regions of the mesh. Using the layering

feature, three rows of elements were removed from the plotting to minimize the

boundary condition effect on the results. The soil elements and the lining

elements are presented individually because of their different modeling.

1 Shareware from International Center For Numerical Methods In Engineering (CIMNE)-Spain, URL

http://gid.cimne.upc.es

134

Fig. (4.10) Initial mesh of Lot 16

Fig. (4.11) Mesh after 21 steps

56 m

76 m

18 m

27 m

Tunnel advance direction 45 m

135

4.3.1. Results of the Numerical Model

4.3.1.1. The Stress Level Field

The stress level is defined as the ratio between the actual deviator stress

and the maximum deviator stress that can be sustained by the soil as defined by

Mohr-Coulomb criterion. The maximum stress level distribution in soil elements

is depicted in Fig. (4.12).

The results show a pronounced increase in the maximum stress level

around the tunnel environs, i.e. this zone is fully or partially yielded due to the

tunneling activities. The yielded zone is substantially revealed at the crown and

at the springline. At the invert the stress level is near its pre-tunneling value.

Another yielded zone is shown at the face due to the partial stress release at the

tunnel heading. The face yielded zone is nearly a semi-sphere while the

peripheral yielded zone has an eccentric cylindrical shape. The presence of the

yield zone affects the deformation field profoundly due to the stiffness

degradation around the tunnel.

4.3.1.2. The Deformation field

Figs. (4.13 to 4.15) demonstrate the deformation field around the tunnel.

The horizontal displacement in x direction shows a movement towards the tunnel

at the ground surface and in the inverse direction below, this may be attributed to

high grouting pressure compared to the much lower horizontal soil pressure. The

vertical deformation comprises settlement above the crown and heave beneath

the invert due to radial stress relief at the tunnel and the face.

The settlement above the crown increases with depth up to the plastic zone

where it shows a decreasing rate due to influence of the grouting pressure. The

axial deformation of the lining shows a surface deformation towards the shield

and a face deformation towards the tunnel. Figs. (4.16 to 4.18) show a good

136

agreement between the results of the numerical model and the observed surface

settlement as well as lateral displacement. The maximum surface settlement is

about 18 mm. The settlement at the face is 7 mm (i.e. 40% of the maximum

settlement). The settlement trough extends to a distance of 25 m ahead of the

tunnel, which is about 2.6 times the excavated diameter of the tunnel. The

settlement increases after the passing of the TBM to a distance of 45 m, which is

about 4.8 times the excavated diameter. The actual settlement trough is wider

than the predicated one. The settlement trough extends to a distance of 20 meters

(i.e. about 2 times the excavated diameter).

4.3.1.3. The Stress field

Figs. (4.19 to 4.27) show the soil stress field. The compressive stresses are

positive and the values are in t/m2. The vertical stress (σy) shows a relaxation

trend towards the tunnel’s crown and the invert. The stress above the crown has a

conspicuous uniform trend resulting from the arching effect that mitigates the

overburden soil. The reduction in vertical stress however is more significant

below the invert, however a minor heave is connoted due to the elastic nature of

the tunnel peripheral underneath the invert.

The distribution of horizontal stress in x-direction (σx) shows a perceptible

increase at the springline with inconsequential changes elsewhere. The horizontal

stress in z-direction (σz) shows a noticeable decrease around the tunnel and at the

face. The major and the minor principal stresses show a significant decrease

around the tunnel while the intermediate stress is almost unaltered due to the

adjacent tunneling process. The shear stress distribution shows that the

components in the y-z and x-z planes are more substantial than the shear stresses

in the x-y plane. The plain strain analysis is less adequate in view of these

distributions.

137

Fig. (4.12) Maximum stress level

Fig. (4.13) Displacement in x direction (mm)

138

Fig. (4.14) Displacement in y direction (mm)

Fig. (4.15) Displacement in z direction (mm)

139

Fig.

(4.1

6) S

urfic

ial s

ettle

men

t alo

ng th

e tu

nnel

axi

s for

Lot

16

140

Fig.

(4.1

7) S

urfic

ial s

ettle

men

t per

pend

icul

ar to

the

tunn

el a

xis a

t Lot

16

141

Fig. (4.18) Measured and estimated lateral displacement for

a vertical plane at 9.40 m from the tunnel CL

FE Measured (after Hamza Associates, 1995)

Lateral displacement (mm) D

epth

(m)

142

Fig. (4.19) The distribution of the normal stress in x-direction (t/m2)

Fig. (4.20) The distribution of the normal stress in y-direction (t/m2)

143

Fig. (4.21) The distribution of the normal stress in z-direction (t/m2)

Fig. (4.22) The distribution of the shear stress in x-y plane (t/m2)

144

Fig. (4.23) The distribution of the shear stress in y-z plane (t/m2)

Fig. (4.24) The distribution of the shear stress in z-x plane (t/m2)

145

Fig. (4.25) The distribution of the major principal stress (t/m2)

Fig. (4.26) The distribution of the intermediate principal stress (t/m2)

146

Fig (4.27) The distribution of the minor principal stress (t/m2)

4.3.1.4. The Lining Deformation and Straining Actions

Fig. (4.28) shows the deformation modes of the lining. An oval shape is

commonly perceived. The invert heave and the crown settlement are generally

greater than the springline outward deformation. The crown settlement increases

with the distance from the tail. Final deformation mode, Fig. (4.28.f), is

characterized with less invert heave compared to the crown settlement. The

springline deformation decreases vaguely to smaller values with the increase of

the time of installation. Figs. (4.29) to (4.34) show the stresses in the lining due

to the effective earth stresses; the negative normal stresses indicate a tension zone

and the positive values indicate compressive stresses. The water pressure causes

an additional radial compressive stress of about 18kg/cm2. The face support

counter reaction causes an additional axial compressive stress of 26 kg/cm2. The

147

results of the FE plus the additional stresses for a section 48m behind the tail, are

shown in Table (4.3). The thrust and the bending moments are also calculated by

the integration of the stresses and shown in the following Table.

Table (4.3) Lining straining actions at Lot 16

External surface Internal surface

Location

Radial

normal

stress

(kg/cm2)

Axial

normal

stress

(kg/cm2)

Radial

normal

stress

(kg/cm2)

Axial

normal

stress

(kg/cm2)

Radial

thrust

(t/m)

Radial

moment

(m.t/m)

Crown 28.8 42.5 22.6 39.4 103 0.1

Springline 31.3 29.3 42.5 30.3 148 -0.18

Invert 28.4 21.5 21.7 20.7 100 0.11

The concluded results show that the thrusting force is the major straining

action in the lining. The moment is very small and may be justifiably neglected.

Consequently, no special modeling is needed to account for the segmental nature

of the lining. The maximum thrust occurs at the springline with a value of 148

t/m, which is very close to the assumption of no arching. Fig. (4.35) compares

the results of the insitu radial stresses and the estimated lining pressure. The

figure shows a minor reduction of the stress at the invert and a trivial increase at

the springline and at the crown. The tunnel is classified as a shallow tunnel in

which the arching effect is small. The axial force at the crown is unexpectedly

larger than the force at the invert. Embedded strain gauges indicate a tensile

strain at the invert, which is not accountable based on the fact that the face

support gives a higher reaction at the lining invert. This may be attributed to the

friction between the lower part of the lining and surrounding unyielded soil. A

much less friction is anticipated at the upper half due to the relatively low

overburden and the higher tendency to yield.

148

Original shape

Deformed shape

Fig. (4.28) Lining modes of deformation

(magnification factor = 20000)

149

Fig. (4.29) The distribution of the normal stress in x-direction (t/m2)

Fig. (4.30) The distribution of the normal stress in y-direction (t/m2)

150

Fig. (4.31) The distribution of the normal stress in z-direction (t/m2)

Fig. (4.32) The distribution of the shear stress in x-y plane (t/m2)

151

Fig. (4.33) The distribution of the shear stress in y-z plane (t/m2)

Fig. (4.34) The distribution of the shear stress in z-x plane (t/m2)

152

Fig. (4.35) tunnel lining pressure in t/m2:

(a),(b),(c) distribution of estimated lining pressure

(d),(e),(f) distribution of the initial insitu radial stresses

153

4.4. Model Verification at Lot 12

4.4.1. Numerical Simulation This section verifies the proposed numerical model at Lot 12 (between El-

Khalafawi and St. Theresa). The analysis results are evaluated using the field

measurements compiled during the construction of the tunnel. According to

Hamza Associates (1993) and Ezzeldine (1999), the prevailing soil profile at Lot

12 is shown in Fig. (4.36). The soil is presumptuously composed of the following

distinctive layers:

1. FILL: Appears at the ground surface and extends to a depth of

about 1.5 m below ground surface.

2. CLAY-SILT: A medium stiff silty clay layer exists below the fill

and extends to a depth of about 6.5m below ground surface.

3. SAND: A medium dense to very dense fine to medium sand layer

underlies the previous clay and extends to the end of the borings.

This sand contains a substantial percentage of silt becomes lesser

with depth. The top 3 meters is classified as silty sand.

4. GROUNDWATER: Groundwater appears at about 3.0 m

The nonlinear ground parameters are assigned as updated at Lot 16.

Hyperbolic elastoplastic soil elements are used. Shield and tunnel lining elements

are represented by elastic materials with different elastic characteristics to

comprise the different stiffness of the lining and the shield. The interface of the

soil-shield and soil-lining is represented by a three dimensional hyperbolic gap

element and grouting element with initial grouting stress. The finite elements

mesh used in the analysis comprises 2968 nodes, 2322 solid hexahedral elements

and 198 joint elements to represent the interface between the soil and lining.

154

Fig. (4.36) Subsurface conditions at Lot 12

(after Ardman-ACE, 1991)

Excavated diameter 9.40 m

155

4.4.2. Results of the Numerical Model The different geotechnical and constructional details of the tunneling

status at Lot 12 were incorporated in the proposed geotechnical model. Face

pressure and grouting characteristics of Lot 16 were adopted herein.

The analysis results are compared with the field measurements. Figs. (4.37

and 4.38) show a good agreement between the surface settlement troughs

resulting from the model compared to the measured values. The maximum

settlement in this case is about 11 mm. The maximum settlement is less than Lot

16 due to the different soil profile and depth of the tunnel center. The settlement

trough extends 25 m ahead of the TBM face and 45 m behind the TBM face,

which are the same limits for Lot 16. The settlement trough width is about 18 m.

The model predicates some heave beyond settlement trough with a maximum

value of 1.5 mm.

Fig. (4.39) shows the variation of the vertical deformation with depth. The

final settlement (48 m behind the face) is almost constant with depth up to about

10 m then it increases slightly in a distance of 2.5 m to reach a value of 12.5 mm

and then decreases to the tunnel crown. The tunnel invert experiences a heave of

6.5 mm, which slightly decreases to the end of the mesh. According to Hamza

Associates instrumentation report (1995), the constant settlement variation in

tunneling was observed frequently during the monitoring phase.

A deep settlement point at depth of 12.5 m was indicated in Fig. (4.39)

along with a surface settlement point; the two points show a good conformity

with the analysis results. The observations of the deep settlement points versus

the TBM passage distance are shown in Fig. (4.40) with the FE results. Fair

agreement is observed between the predicated profile and measured values.

156

Fig.

(4.3

7) S

urfic

ial s

ettle

men

t alo

ng th

e tu

nnel

axi

s for

Lot

12

157

Fig.

(4.3

8) S

urfic

ial s

ettle

men

t tro

ugh

perp

endi

cula

r the

tunn

el a

xis f

or L

ot 1

2

158

Fig. (4.39) Settlement versus depth along the tunnel axis for Lot 12

159

Fig.

(4.4

0) S

ettle

men

t ver

sus t

he fa

ce d

ista

nce

at d

epth

of 1

2.5

m fo

r Lot

12

160

4.5. Stabilization Measures and Deformation Field

4.5.1. Introduction The model incorporates the different measures used to stabilize the

excavation; namely: The face pressure, tail grouting and the lining installation.

The face pressure is applied as a traction pressure on the face elements while the

grouting pressure is applied through using of special pre-stressed grouting

elements that have a hardening behavior with time.

Excavation and lining installation cause an incessantly altering to the

mesh and thus necessitating special numerical procedures in the program. The

overcutting loss is modeled using a peripheral gap element that allows the ground

convergence around the TBM. In this section, different ground stabilization

means related to construction of Greater Cairo Metro–Line 2 (Lot 12) are

studied quantitatively in conjunction with the effect of overcutting losses (the

Gap Parameter) on the ground deformation field.

4.5.2. The Face Pressure and the Face Stability The face stability is a major concern in the design of soft grounds tunnels.

Face failures may lead to catastrophes and life losses inside the tunnel and

enormous ground deformation endangering the surrounding buildings and buried

utilities above or in vicinity of the tunnel. The BSS supplies the required face

stabilization through a slurry pressure that exceeds the water pressure by a

fraction of the effective overburden pressure as it was described in Chapter (3).

The effective slurry pressure (face pressure that is in excess of the

hydrostatic pore water pressure) is studied parametrically assuming values of 0.0,

2.0, 4.5, 9.0 and 18.0 t/m2. The resulting face axial deformation is shown in Fig.

(4.41). This figure shows large axial deformation towards the tunnel for the face

161

pressure values of (pf’ = 0) and (pf’ = 2 t/m2) and much less for the case of (pf’ =

4.5 t/m2). The axial deformation tends to reverse direction for ((pf’ = 9 t/m2) and

(pf’ = 18 t/m2). The maximum axial deformation versus the face pressure is

shown in Fig. (4.42). The limiting pressure appears at 2 t/m2, i.e. 40% of the

effective active pressure (about 5 t/m2) of the far field. The difference between

the estimated limiting face pressure and active earth pressure of the overburden

pressure results from the arching effect which occurs due to stiffness degradation

in the yielded zone near the face resulting in a reduction in the face pressure as

shown in Fig. (4.43).

The surface settlement for different values of the face pressure is shown in

Fig. (4.44). Increasing the face pressure causes little heave in front of the tunnel

face and reduces the maximum settlement slightly. Fig. (4.45) depicts the

surficial settlement and heave versus the face pressure. The figure shows that the

maximum heave in front of the face is increased in the same rate as the maximum

settlement is reduced behind the TBM.

Adapting a safety factor of 2, the analysis shows that 80% of active

earthpressure can be a good estimate of the safe face pressure in shallow tunnels

in which the face losses are substantially reduced. Increasing the face pressure

furthermore will cause some heave in front of the TBM that can slightly reduce

the maximum settlement by the same amount. It should be noted that the slurry

pressure is higher than the hydrostatic water pressure by the effective face

support value. This excess causes outward flow pattern from the slurry chamber

to the ground in the vicinity of the face. This flow tendency helps to form the

bentonite cake at the excavated face and reduces the effect of any seepage

towards the face. The slurry cake also reduces the effect of the inverse flow from

the slurry chamber to grounds enfolding the tunnel and this explains the minimal

increase in the water pressure due to the tunnel construction.

162

Fig. (4.41) Distribution of the face axial displacement for

different face pressure values

Axial displacement of the face (mm)

Dis

tanc

e fr

om th

e in

vert/

tunn

el d

iam

eter

163

Fig. (4.42) The effect of the face pressure on the

maximum axial displacement

Effective face pressure (t/m2)

Axi

al d

ispl

acem

ent o

f the

face

cen

ter

(mm

)

164

Fig. (4.43) The effect of soil arching on the face limiting equilibrium

σv

ko σv

σv’

ka σv’

Yielded zone having

degraded stiffness

TBM

Limiting effective face pressure

σv ko σv ka σv

State of stress in the

far field

σ

τ

Shear envelope

σv’ ka σv

’

Limiting circle without the effect of arching

Limiting circle with the effect of arching

165

Fig.

(4.4

4) T

he e

ffec

t of t

he fa

ce p

ress

ure

on th

e su

rfac

e ve

rtica

l def

orm

atio

n

166

Fig.

(4.4

5) T

he e

ffec

t of t

he fa

ce p

ress

ure

on th

e m

axim

um su

rfac

e ve

rtica

l def

orm

atio

n

167

4.5.3. Effect of the Gap Parameter on The Deformation Field The overcutting loss is one of the most pronounced sources of the ground

deformation in tunnels. The overcutting is modeled as a peripheral ground loss

around the TBM. A special nonlinear interface element is employed to fulfill the

compatibility between the tunnel and the enfolding ground taking void between

them into considerations.

The effect of the overcutting on the surficial ground deformation is shown

in Figs. (4.46) to (4.53) for different overcutting losses (0.00, 0.05, 0.3, 0.5, 0.75

and 1.00%) as well as the verification case (overcutting loss = 0.15%). For no

radial loss around the TBM (overcutting loss = 0.00), the ground settlement

above the tunnel CL is accompanied with a heave of the same magnitude away

from the CL. The heave is reduced and settlement increases considerably when

increasing the overcutting loss by a slight percentile (0.05%). Increasing the

overcutting loss furthermore reduces the heave to almost nil while the settlement

increases substantially as shown in Fig. (4.53).

The width of the settlement trough increases with the increase of the radial

loss from about 8 m at no overcutting to 27 m at 1% overcutting loss in contrast

to the common rules of thumb that relate the width of the settlement trough to the

geometrical configuration only as stated in Chapter (2). Fig. (4.54) shows an

isometric view of the surficial deformation field for the extreme case (overcutting

loss = 0.00 and 1.00%). The figure shows how the deformation field

characteristics are considerably dependent of the overcutting. Although

overcutting can significantly increase the settlement associated with tunneling, it

is inevitable because it helps driving the TBM specially at curved routing.

The vertical distributions of the vertical deformation at the tunnel CL are

shown in Figs. (4.55) to (4.60) for the different overcutting losses. The

168

distribution of the vertical deformation is generally settlement above the crown

and heave below the invert. The settlement distribution for low overcutting losses

(less than 0.5%) is more or less constant to a depth of 8 m. The settlement rate

from the previous depth increases up to a depth of 10 m and then decreases to the

tunnel crown due to the effect of the tail grouting.

The ratio between the surface settlement and crown settlement for

overcutting losses less than 0.5% is generally less than unity due to the tail

grouting. The ratio increases above unity for cases above 0.5% (about 1.35% at

1.00% overcutting loss). The heave below the invert decreases from 10 mm at no

overcutting to 5 mm at 1% overcutting loss. The difference is localized in the top

2 m below the invert where sudden increase is conspicuous in low overcutting

losses.

4.5.4. The Effect of Tail Grouting The function of the tail grouting is to fill the annular void between the

erected lining rings and the excavated ground. The grouting pressure should be

always greater than the hydrostatic water pressure in order to allow the mixture

water to bleed into nearby ground and was commonly selected equal to the soil

total stress at the springline.

The effect of the tail grouting on the surficial deformation field was

studied parametrically assuming the effective tail grouting pressure equal to 0,

17.5 and 40 t/m2. Fig. (4.61) shows the effect of the grouting pressure of the

surface settlement, which appears to be trivial. Figs. (4.62) and (4.63)

demonstrate the effect of the grouting pressure on vertical deformation of the

crown and the invert. The crown experiences settlement at low grouting pressure

(0 and 17.5 t/m2); however, the deformation turns to heave at higher grouting

pressures (40 t/m2). The invert undergoes heave that is almost insensitive to the

169

grouting pressure. This result may be attributed to the existence of yielded zone

around the tunnel especially in the crown zone causing the soil to compress

locally without affecting the ground surface. In the invert zone, the ground

behaves elastically so that the effect of the grouting pressure is minimal.

A conceptional model to present the effect of tail grouting on the surface

settlement trough was offered by Simpson (1993). Observing the results of

laboratory tests of reversal stress paths, he concluded that soils generally offer

less resistance to continuation of straining in the direction they were previously

following than they do to the reverse direction, which means that on reversal of

the stress path, the strains tend to continue in their previous direction before

swinging round to follow the new path. He mimicked that behavior by a man

pulling strings attached to bricks during his turning back as shown in Fig. (4.64).

Similar conclusion was offered by El-Nahhas (1999) in comparing

between the performance of the tail grouting of Cairo Wastewater Project (3-6%

ground loss) and tailskin grouting of Greater Cairo Metro project (generally less

than 1%) in which the grouting pressure values were not foremost factor other

than the location in which the tail grouting started to be functional as tail

grouting in Cairo Wastewater project started after installation of a few rings to

prevent potential damages to tail seal.

During the construction of greater Cairo Metro, the tail annular void’s

volume was 7.24 m3/m. The grouting volume usually exceeded by 9% in average

to allow grouting bleeding and in some extreme cases by 160% in which the

grouting material flowed past the TBM to the face producing no heave to the

surface ground.

170

Fig.

(4.4

6) T

he e

ffec

t of t

he o

verc

uttin

g lo

ss o

n th

e su

rfac

e ve

rtica

l def

orm

atio

n

171

Fig.

(4.4

7) S

urfic

ial v

ertic

al d

efor

mat

ion

troug

h fo

r ove

rcut

ting

loss

= 0

.0%

172

Fig.

(4.4

8) S

urfic

ial v

ertic

al d

efor

mat

ion

troug

h fo

r ove

rcut

ting

loss

= 0

.05

%

173

Figu

re (4

.49)

Sur

ficia

l ver

tical

def

orm

atio

n tro

ugh

for o

verc

uttin

g lo

ss =

0.3

0 %

174

Fig.

(4.5

0) S

urfic

ial v

ertic

al d

efor

mat

ion

troug

h fo

r ove

rcut

ting

loss

= 0

.50

%

175

Fig.

(4.5

1) S

urfic

ial v

ertic

al d

efor

mat

ion

troug

h fo

r ove

rcut

ting

loss

= 0

.75

%

176

Fig.

(4.5

2) S

urfic

ial v

ertic

al d

efor

mat

ion

troug

h fo

r ove

rcut

ting

loss

= 1

.00

%

177

Fig.

(4.5

3) T

he e

ffec

t of t

he o

verc

uttin

g lo

ss o

n th

e m

axim

um su

rfac

e ve

rtica

l def

orm

atio

n

178

Fig. (4.54) Surficial vertical deformation trough for

(a) overcutting loss = 0.00 % and (b) overcutting loss = 1.00 %

(a)

(b)

179



180



181



182



183



184



185

Fig.

(4.6

1) T

he e

ffec

t of t

he ta

il gr

outin

g pr

essu

re o

n th

e m

axim

um su

rfac

e ve

rtica

l def

orm

atio

n

186

Fig.

(4.6

2) T

he e

ffec

t of t

he ta

il gr

outin

g pr

essu

re o

n th

e ve

rtica

l def

orm

atio

n of

the

crow

n an

d th

e in

vert

187

Fig.

(4.6

3) T

he e

ffec

t of t

he ta

il gr

outin

g pr

essu

re o

n th

e m

axim

um v

ertic

al d

efor

mat

ion

of th

e cr

own

and

the

inve

rt

188

Fig. (4.64) The analogue – a man pulling bricks around a room

(after Simpson, 1993)

189

Chapter Five

CASE HISTORIES OF MULTIPLE AND TWIN TUNNELS

5.1. Introduction Tunneling deformation fields are significantly modified due to mutual

interaction of adjacent or intersecting tunnels. Multiple tunnels comprise

distinguishable convoluted three-dimensional problems that cannot be analyzed

precisely utilizing simplified two-dimensional analysis or empirical superposition

techniques. The nonlinear three-dimensional simulation presented for the Greater

Cairo Metro analysis can be viewed in broader perspective as it is extended in

this chapter, bidding an appropriate framework to analyze multiple tunnels

constructed using the same technique. Two cases of multiple tunnels are

analyzed; namely: El-Salam Syphon; and Al-Azhar Twin Road tunnels at the

location of their intersection with the CWO sewer. The modifications to ground

deformation fields are investigated. The pre-grouting measure used to minimize

the effect of tunneling on the CWO sewer is evaluated parametrically.

5.2. El-Salam Syphon Project The population explosion devotes Egypt no alternative but to accelerate

land reclamation projects such as North Sinai Development Project. This project

was first conceived in the late 1970s in order to develop a total area of 400,000

feddans in Northern Sinai as shown in Fig. (5.1). The project comprises three

main elements, namely: E1-Salam Canal, west of the Suez Canal; the syphon

under the Suez Canal; and El-Sheikh Gaber Canal, in Northern Sinai. The

irrigation for this development requires up to 160 m3/sec of water to be

transferred from the existing El-Salam Canal on the west bank to El-Sheikh

190

Gaber Canal on the east bank. The transferred irrigation water is provided from

the Damietta branch of the River Nile, El-Sirw drain and Bahr Hadous drain. The

water is transported from the east to the west of the Suez Canal under the Suez

Canal through El-Salam Syphon, which comprises four bored tunnels. Fig. (5.2)

shows the vertical alignment of the four tunnels.

The geological nature of the subsurface is predominately gray silty clays

and yellowish gray sand. The surficial soft clays layer thickness ranges between

4 and 50 m of high to very high plasticity covered by "Sabkha", which is very

salty dark gray silty clay with very low consistencies. The sensitivity of these

clays is medium and ranges around 2 and the consistency varies from very soft to

stiff. The tunnel alignment enters into the sand layer that is under artesian water

pressure. The coefficient of permeability of this sand layer is high at about 10-4

m/sec. The maximum water pressure is estimated to be 4.5 bars. The tunnel

boring machine (6.54 m outer diameter) chosen by the contractor to excavate and

construct the primary segmental linings of the tunnels is a Herrenknecht

mixshield. The machine has been specially designed to work at 4.5 bar operating

pressure, on inclinations of up to 20%, and is capable of negotiating curves of

500 m radius. The overcutting void was estimated to be 1.00% of the excavated

ground volume that might be increased to 1.85% in some abnormal difficult

conditions. The annular gap between the cut annulus and the external surface of

the primary lining is filled with a grout injected through special pipes integrated

in the TBM tailskin. The tailskin is fitted with three rows of wire brush seal

enclosing two grease filled voids that are continually pumped full of grease at

pressure during the operation of the TBM to ensure an effective seal against

ingress of ground water.

A circular waterproofed bolted reinforced concrete segmental lining was

chosen as the primary lining. The external diameter of the primary lining is

6.34m with 30 cm thickness, consisting of 7 segments in addition to a key

191

segment forming each ring. The primary lining has been designed to withstand

75% of overburden and 100% hydrostatic pressure at the maximum depth to axis

of approximately 45 meters. A secondary insitu unreinforced concrete lining with

an internal diameter of 5.100 m was poured to enhance the hydraulic

performance, increase durability and reduce maintenance costs. The secondary

lining has been designed to withstand the full overburden and hydrostatic

pressures. Different aspects of the project are described by Mazen and Craig

(1994); & Esmail (1997).

Fig. (5.1) North Sinai Developing Project (after Mazen and Craig, 1994)

Fig. (5.2) El-Salam Syphon vertical alignment (after Mazen and Craig, 1994)

C

192

5.2.1. Numerical Idealization A numerical analysis was performed to simulate the tunneling conditions

and to estimate the tunneling-induced ground deformation field. The analyzed

section corresponding to instrumented section "C", which is located at the east

shoulder near Ismailia - Port said highway. The monitoring system at this section

consisted of ground surface settlement points distributed along a line

perpendicular to the tunnels centerline (Esmail, 1997).

The analysis commenced with simulation of the construction of the first

tunnel T1 (the tunnel to the north) and ending with excavation of last tunnel T4

(the tunnel to the south). The section lies at a sloping route (1V : 5H). The finite

element model is shown in Fig. (5.3). The mesh incorporates 3094 nodes, 2640

hexahedral elements and 416 interface elements. The analysis stages were carried

out through 480 increments. The nonlinear analysis was performed in a similarly

to Greater Cairo Metro. The geotechnical nonlinear properties of the subsurface

strata are summarized in Fig. (5.4) and Table (5.1).

Table (5.1) The estimated nonlinear properties for El-Salam Syphon at

section “C”

Stratum Very soft to soft CLAY Medium dense to dense SAND

φ 0 33

C (kg/cm2) 2 0

γ (t/m3) 1.7 1.8

ko 1.00 0.46

K 150 350

N 0.55 0.5

Rf 0.75 0.8

υ 0.49 0.3

193

Fig. (5.3) Initial mesh for the inclined El-Salam tunnels

Fig. (5.4) Geotechnical subsurface conditions at the instrumented section “C”

(after Esmail, 1997)

40 m

105 m 48.6 m

T4 T3

T2 T1

Excavated diameter

6.54 m

194

5.2.2. Results of the Numerical Analysis During the analysis, the tunnels were excavated in a sequential order

beginning with T1, then T2, T3 and finally T4. Due to the reported difficulty in

driving the first tunnel, the overcut was estimated to be 1.85% (Esmail, 1997).

Surficial settlement troughs were concluded from the analysis results. The

settlement trough after construction of the first tunnel (T1) is outlined in Fig.

(5.5). The trough is slightly unsymmetrical, due to the variation in the mesh

density, showing a fairly broader values that the reported settlement with a close

agreement above the tunnel. The maximum surficial settlement is about 15mm

above the T1. A wider settlement trough is anticipated after the construction of

all tunnels as shown in Figs. (5.6) to (5.8). The maximum settlement changes to

29 mm after construction of T2, 40 mm after construction of T3 and 48 mm after

construction of T4. Due to the constraint of the available monitoring data, only

the trough of the first tunnel was compared to the analysis results.

The incremental settlement troughs after construction of each tunnel are

shown in Fig. (5.9). The settlement trough of each tunnel is estimated by

subtraction of consecutive troughs resulting from the construction of two

sequential tunnels. The troughs are fairly symmetric yet showing some tendency

to increase towards the newer tunnels. The settlements due to the new tunnels are

always greater than those resulting from older ones.

Considering the individual troughs in Fig. (5.9), we can deduce that the

minimum peak is shown at the trough of T1 with a value of about 15 mm while

the maximum peak of the settlement trough resulting from the construction of T4

is about 21 mm. This difference may be attributed to the overlapping of the

yielding zones of the old and the new tunnels. The maximum total settlement is

located above T3.

195

Fig. (5.5) Surficial vertical deformation after construction of tunnel T1


Distance (m)

Surf

icia

l ver

tical

dis

plac

emen

t (m

m)

Distance (m)

Surf

icia

l ver

tical

dis

plac

emen

t (m

m)

Predicated Measured (after Esmail, 1997)

196



Distance (m)

Surf

icia

l ver

tical

dis

plac

emen

t (m

m)

Distance (m)

Surf

icia

l ver

tical

dis

plac

emen

t (m

m)

197

Fig.

(5.9

) Sur

ficia

l set

tlem

ent t

roug

hs d

ue to

indi

vidu

al tu

nnel

s

198

5.3. Intersection of Al-Azhar Tunnels and the CWO Sewer

Assessment of tunneling effects on the buried utilities is an intricate three-

dimensional problem. Previous studies tried to predict the induced internal

stresses in pipeline due to their intersection with tunnel routing using a simplified

Winkler model (Attewell et al, 1986) or simplified plane strain finite element

model (Ghaboussi et al. 1983).

Attewell et al (1986) elucidated the different measures to be taken to

reduce the effect of tunneling on existing pipelines. Controlling the ground loss

induced by tunneling proves to be the most beneficial measure to reduce the

effect of tunneling to adjacent utilities. Supplementary measures incorporate

increasing the tunnel depth and using ground modification procedures to enhance

the strength parameters and deformation parameters of the soil.

A three-dimensional model is used to analyze the tunneling conditions at

the intersection of Al-Azhar Road Tunnels (excavated diameter 9.40 m and

spaced 18.7 m apart) and the CWO sewer (5 m external diameter) at Port Said

Street. The specific crossing is especially important because tunneling is

designed to pass underneath the CWO sewer with a minimum distance of 4 m.

Precautionary measures to minimize the tunneling effect on the existing CWO

pipe included the reinforcing of the ground underneath the sewer with grout

injection in form of two walls and carrying out intense instrumentation plan

during the TBM passage.

The instrumentation scheme applied at the CWO crossing includes

Settlement Points at shallow depths and Extensometers to provide information

about settlement at different depths. Elevation Reference Points were constructed

on buildings to provide information about building movements. Inclinometers

points were constructed deep in ground to provide information about horizontal

199

movement at selected depths. Fig. (5.10) shows the layout of Al-Azhar Twin

Road Tunnels and site of the intersection near Port Said Street.

5.3.1. Site Geological and Geotechnical Conditions According to the AMBRIC (1983) and Hamza Associates (1998), the

major soil units for zone of the intersection of Al-Azhar and CWO tunnels are as

following:

1. MAN-MADE FILL: The depth of this layer was found to be erratic

in level and ranged between 0.3 and 12.6 m below ground surface

with an average value of 6.66 m. A broad spectrum of grading was

encountered in layer varying from silty clay to gravelly cobbles.

The average texture is clayey, sandy, gravelly silt of intermediate

plasticity (MI).

2. SILTY CLAY AND CLAYEY SILT: This layer follows the man-made

fill with thickness varying between 0 to 17 m. According to the site

investigation reports, this layer extends from depth 6.66 m to depth

11.66 m at the intersection. The layer is logged as gray or brown

and varies in consistency from very soft to very stiff and often

highly fissured. The fissures sometimes contain an infill or dusting

of silt or fine sand. Occasionally slickensiding is reported. The

predominating minerals are intermediate to high plasticity clays (CI

to CH).

3. VERY SILTY SAND: This layer has a fine material (finer than sieve

# 200) that varies between 15% and 35% with a median value of

24%. The layer extends from depth 11.66 m to depth 15 m.

4. SAND: This layer was encountered in the majority of the boreholes.

Clay lenses are found in some boreholes within this layer. In

borehole (210) the layer extends from depth 15 m to depth 20 m

200

(end of borehole). The grading tests showed mostly clean medium

sand (fine materials are less than 5%) with fairly uniform texture.

The mean value of the effective diameter is 0.17 mm.

5. SAND - GRAVEL: This unit may be located as a band or lenses

within the previous layer. The layer lower bound is not defined.

The mean grading of this unit is gravelly, medium to coarse sand.

The average effective diameter is 0.27 mm.

6. The groundwater: The groundwater depth varies from about 3 m to

5 m from the ground surface. At the intersection location, the

ground water depth was reported at 3.40 m

5.3.2. Untreated Ground Analysis

5.3.2.1. The model

The finite elements mesh used in the analysis is shown in Fig. (5.11) with

total of 3421 nodes, 2816 soil elements, 512 lining and grouting elements and

272 joint elements to represent the interface between the soil and lining. The

values of the soil parameters are given in Table (5.2) and Fig (5.12).

Table (5.2) The estimated nonlinear soil properties for the intersection of the

CWO sewer and Al-Azhar Tunnels.

Stratum FILL CLAY –

SILT Silty SAND

Dense

SAND

Gravelly

SAND

φ 23 0 30 35 41

C (kg/cm2) 0.2 1.0 0 0 0

γ (t/m3) 1.65 1.8 1.90 1.95 2.0

ko 1.00 0.74 0.50 0.43 0.35

K 150 200 350 600 750

N 0.6 0.55 0.5 0.5 0.5

Rf 0.73 0.75 0.8 0.8 0.8

υ 0.4 0.4 0.35 0.3 0.3

201

Fig.

(5.1

0) G

ener

al la

yout

of A

l-Azh

ar R

oad

Tunn

els (

afte

r Ram

ond

and

Gui

llien

199

9)

The

inte

rsec

tion

with

the

CW

O

Sew

er

202

Fig. (5.11) Mesh for the intersection

29.1 m

29.8 m

18.7 m

40.0 m

40.0 m 38.0 m

38.0 m

CWO

203

Fig. (5.12) Subsurface conditions at the site of the intersection

(after Hamza Associates, 1998)

5.3.2.2. Results of the Numerical Model

5.3.2.2.1. The maximum stress level field The results of the maximum stress level field are shown in Figs. (5.13)

and (5.14). These figures show a zone of yielded soil in the vicinity of the

tunnels. The significance of this zone was illustrated in the results of the analysis

of the Greater Cairo Metro and El-Salam Syphon. The pre-existence of the north-

tunnel yielding zone before construction of the south tunnel, leads to some bias

in the settlement trough towards the south tunnel in a similar way to El-Salam

Syphon Case

First tunnel Second tunnel

204

5.3.2.2.2. The deformation field The vertical deformation field is shown in Figs. (5.15) and (5.16). The

settlement of the zone far from the CWO crossing (average values from the mesh

edges) shows a fair agreement with the measured trough during driving of the

north tunnel as shown in Fig. (5.17). The settlement trough above the CWO has

less maximum values due to the restraining action of the CWO sewer. The

maximum value of the settlement during driving of the north tunnel is about 4.2

mm but increases to about 9 mm after the south tunnel is completed. The

monitoring data compiled during the construction of the south tunnel was

unavailable during the time of the thesis.

5.3.2.2.3. Effect of the Deformation Field on the CWO Tunnel Construction of Al-Azhar twin tunnels is coupled with surface and

subsurface ground movements as illustrated in the previous section. The resulting

deformation causes potential impairments to the neighboring CWO tunnel

especially as the elevation difference between the CWO invert and the crown of

Al-Azhar Tunnels is only 4m.

The effect of the construction of Al-Azhar Road Tunnels on the

deformation and the internal stresses of the CWO sewer is shown in Figs. (5.18)

to (5.25). The vertical settlement increases from 2.36 mm (as the north tunnel

heading approaches the CWO tunnel) to a final value of 13.7 mm. The axial

compression stress changes from 4 kg/cm2 to 15.6 kg/cm2 and the axial tension

stress changes from 1.84 kg/cm2 to 11.6 kg/cm2. The deformed shape of the

CWO after completion of the south tunnel is shown in Fig. (5.26). It must be

noted that the analysis detects two zones affected by the tensile stresses; namely,

the invert at the intersection zone and the crown beyond the intersection zone,

which corresponds to two conditions of hanging and sagging moments.

205

Fig. (5.13) Maximum stress level after driving the north tunnel

Fig. (5.14) Maximum stress level after driving the south tunnel

206

Fig. (5.15) Vertical deformation in mm after driving the north tunnel

Fig. (5.16) Vertical deformation in mm after driving the south tunnel

207

Fig.

(5.1

7) S

urfic

ial v

ertic

al d

efor

mat

ion

of th

e un

treat

ed g

roun

ds

(Firs

t) (S

econ

d)

208

Fig. (5.18) Vertical deformation of the CWO tunnel in mm

(the north tunnel heading approaches the intersection)

Fig. (5.19) Axial stresses of the CWO tunnel in t/m2

(the north tunnel heading approaches the intersection)

209


(the north tunnel is completed)


(the north tunnel is completed)

210


(the south tunnel heading approaches the intersection)


(the south tunnel heading approaches the intersection)

211


(the south tunnel is completed)


(the south tunnel is completed)

212

Fig. (5.26) Final deformation of the CWO tunnel

(deformation magnification factor 1000)

213

5.3.3. Treated Ground Analysis

5.3.3.1. Motivation

The construction of Al-Azhar Road Tunnels without protective measures

would cause substantial stresses in the CWO sewer located above the twin

tunnel. The selected ground stabilization scheme was to form two grouted walls

on the sides of the sewer tunnel. Grouting proved to be a very salutary process to

minimize the deformation field resulting from tunneling. Tan and Clough (1980)

studied the grouting utilization in tunnels. They enumerated some projects where

injection proved to be a very beneficial practice during construction of tunnels.

Some of these projects are shown in Fig. (5.27).

The effect of grouting can be recognized as increasing the soil stiffness

and shear parameters. During their study, Tan and Clough (1980) provide a scale

of the effect of grouting on sandy soil properties. The scale is shown in Table

(5.3). In this section, the using of grouting as a protective measure to minimize

the effect of the construction of Al-Azhar Tunnels on the CWO sewer is studied

parametrically using the scale proposed by Tan and Clough.

5.3.3.2. Modeling of the grouted material

Bell (1993) showed that the change in the angle of friction (φ) of sandy

soil caused by grouting is generally insignificant. Using Table (5.3), the cohesion

parameter of the grouted soil can be estimated (assuming no change in the

frictional angle of the stabilized soil) using the following equation:

φ

+=

245tan2

qco

ungrouted

…(5.1)

where qun is the unconfined compressive strength of grouted soil. The effect of

grouting on the soil stiffness is implemented sing the ratio SR, defined in Table

(5.3), as following

214

KSRKgrouted ⋅= …(5.2)

where Kgrouted is Duncan and Chang strength parameter for grouted soil and K is

the strength parameter of the ungrouted soil. Grouting may change the state of

stresses inside the soil mass but no quantifiable measurements of this effect was

reported in the literature. The present study ignores such effect and concentrates

on the effect of grouting in increasing strength and stiffness of the grouted soil.

Table (5.3) Grouting effect on the sandy soil parameters for tunneling projects (after Tan and Clough, 1980)

Unconfined compressive strength for

different relative density (t/m2) Grouting

designation Loose Medium Dense

Ratio of stiffness of

grouted to ungrouted

soil (SR)

Weak

Medium

Strong

Very Strong

0.87

2.18

4.35

6.96

1.81

4.57

9.14

14.6

3.84

9.57

19.1

30.6

1.50

2.25

3.50

5.00

Fig. (5.27) The use of grouting in different tunneling projects

(after Tan and Clough, 1980)

215

5.3.3.3. Results of the Numerical Model

Employing the previous formulation of the effect of grouting on sandy soil

strength and stiffness, the deformation and the internal stresses of the CWO

sewer are concluded for different grouting categories. Figs (5.28) and (5.29)

show the final vertical deformation and axial stress of the CWO tunnel for a

stabilized soil employing weak grouting. The maximum deformation reduced

from 13.7 mm to 11.2 mm while the maximum compression reduced from 15.6

to 13.2 kg/cm2 and the maximum tensile stress reduced from 11.6 kg/cm2 to 8.3

kg/cm2.

Increasing the grouting effect reduces the internal stresses and the

deformation furthermore as shown in Figs. (5.30) to (5.35). The maximum

settlement of the CWO is reduced to 8.54 mm using very strong grouting. The

compression stress can be reduced to 12.8 kg/cm2 and tensile stress to 6.2 kg/cm2

using the same grouting category. It should be noted that, at high grouting

categories, the maximum tensile stress is found to occur at the crown;

conversely, at low grouting categories it occurs at the invert.

Figs. (5.36) and (5.37) summarized the effect of grouting on the internal

stresses and the settlement of the CWO sewer. The compression stresses

apparently approaches a limit that cannot be affected by higher stabilization

category other than strong grouting; however, the tensile stress and the settlement

reduced monotonically with increasing the grouting category but with a declining

rate.

The grouting measure proved to be successful by reducing the settlement

by 38% and tensile stress by 47%. Compression stress can only be reduced by

22% yet the most detrimental effect may result from the tensile stresses and the

deformation due to jointed nature of the sewer lining.

216


(weak grouting)

Fig. (5.29) Final axial stresses of the CWO tunnel in t/m2

(weak grouting)

217


(medium grouting)


(medium grouting)

218


(strong grouting)


(strong grouting)

219


(very strong grouting)


(very strong grouting)

220

Ungrou

tedWea

k

Medium

Strong

V. stro

ng

Grouting Category

0

2

4

6

8

10

12

14

16

Stre

ss (k

g/sq

. cm

)

Compression stress Tensile stress

Fig. (5.36) Effect of grouting on the maximum

internal stresses in the CWO sewer

Ungrou

tedWea

k

Medium

Strong

V. stro

ng

Grouting Category

0

2

4

6

8

10

12

14

16

Settl

emen

t (m

m)

Fig. (5.37) Effect of grouting on the maximum

settlement of the CWO sewer

221

Chapter Six

SUMMARY, CONCLUSION AND RECOMMENDATIONS FOR

FURTHER STUDIES

6.1. Summary

Recently, many Egyptian tunnels have been constructed for several

purposes such as subways, sewers and road tunnels. Egyptian tunneling activities

are anticipated to carry on for at least a decade to achieve the proposed plans of

infrastructure refurbishment. The geotechnical conditions encountered during the

construction of these mega projects were typically soft soils or weak rocks under

high groundwater pressures in which tunneling must be conducted using

pressurized shielded tunneling. Soft ground tunneling imposes many engineering

challenges related to stability of the constructed tunnels and the hazard effect of

the resulting deformation field on the buried utilities and the structures in the

proximity of the tunnels. The ground deformations depend on the tunnel

installation procedure, the ground support measures, the soil stiffness in the

tunnel vicinity and ground restraints formed by underground structures.

An indispensable prerequisite to successful tunneling projects is to predict

the deformation in order to avert any potential damage of buildings or buried

utilities. Numerical simulation of tunneling processes is considered the most

appropriate tool for analysis of tunnels as the observational rules-of-thumb

cannot be considered reliable bases of analysis and design even for the same

ground condition as they cannot introduce the installation procedure into account.

Numerous researches employed either plane strain or axisymmetric models in

which the displacement field is approximated by neglecting the non-radial

222

deformations in the plane strain models and the stress and displacement field is

approximated by symmetric fields in axisymmetric models. Two-dimensional

models are superior to the observational rules; yet, the approximations in the

analysis form justifiable basis of unreliability in employing the obtained results

in design and analysis.

Three-dimensional models are intricate to implement because of needed

high capacity computing resources, which are not available beyond certain

academic institutions in the developing countries; besides the complications in

modeling of soil excavation, shield driving, overcutting and tailskin grouting. In

the present research, a nonlinear three-dimensional finite element model is

developed. Different sources of nonlinearly are deliberated; namely, the

nonlinear soil constitutive relationship, which is affected by the stress-path and

confining pressure; pressurized excavation boundaries and ground support

measures; ground loss and the overcutting gap; grouting pressure and hardening

of grouting material with time; and the changes in boundary conditions and size

of the mesh during the analysis, i.e. ground excavation, TBM advancement and

lining installation.

The soil, shield and liner are modeled using hexahedral solid elements

with hyperbolic non-linear behavior according to confining pressure and the

stress path. The shield-soil interface is simulated using a special hyperbolic gap

element with non-trivial tensile stiffness to model appropriately the convergent

behavior of the gap. The liner-grout-soil interface is introduced using grout

elements with incremental time-hardening parameters and initial hydrostatic

pressure equal to the grouting pressure. The tunnel construction process is

modeled by removing the excavated elements from the finite element meshing

and adding the lining elements to the mesh. The residual force vector for the

223

modified mesh is formed using the stresses calculated from previous staged

iteration. The changes are introduced as an incremental-iterative process.

A special nonlinear three-dimensional finite element program was

prepared using the proposed formulation of tunneling construction processes.

The model was applied in analysis of the single shallow bored tunnel of Greater

Cairo Metro - Line 2- Phase 1A at Lot 12 and Lot 16. The results of the

numerical model are compared with the measurements compiled during the

construction of the tunnel. A parametric study was conducted to divulge the

effects of the different tunneling conditions and the ground support measures on

the deformation field and lining stresses. The model was also extended to study

the deformation fields of the multiple deep tunnels of El-Salam Syphon and the

intersection of Al-Azhar Road Tunnels and the CWO sewer at Port Said Street.

The proposed numerical simulation was used to parametrically evaluate the pre-

grouting measure that was undertaken to minimize the effect of tunneling on the

CWO.

6.2. Conclusion

The case histories considered in this thesis, represent diverse tunneling

conditions. The single shallow tunnel of the Greater Cairo Metro was constructed

in the sand deposits while the deep Al-Azhar Twin Road Tunnels are constructed

in gravelly sand. El-Salam Syphon comprises four deep tunnels of smaller

diameter that were constructed in cohesive soft silty clay. The results of the

introduced three-dimensional model, which includes the different features of

bentonite slurry tunneling, soil nonlinearity and the interface conditions were

verified by comparing with field measurements compiled during implementation

of the monitoring program. Fair agreements between the predicated and the

224

measurement were concluded. From the results of the analysis and the parametric

study performed for each case history, the following points are concluded:

Greater Cairo Metro – Line 2 Phase 1A

1. A pronounced upsurge in the maximum stress level (which is

defined as the ratio between the actual deviator stress and the

maximum deviator stress) around the tunnel environs was

perceived. The tunnel vicinity is partially yielded due to the

tunneling activities in which the yielded zone is substantially

revealed at the crown and at the springline. At the invert the stress

level is estimated to be near its pre-tunneling value. Another

yielded zone is shown at the face due to the partial stress release at

the tunnel heading. The face yielded zone is nearly a semi-sphere

while the peripheral yielded zone has an eccentric cylindrical

shape. The presence of the yield zone affects the deformation field

profoundly due to the stiffness degradation around the tunnel. The

effect of the marginal yield zone is frequently considered in the

stability analysis yet its effect is underestimated in the deformation

analysis in the tunneling literature.

2. Due to its three-dimensional temperament, the model provides the

deformation field ahead, at, and after the passage of TBM. The

surficial settlement above the TBM face is estimated to be about

40% of the maximum settlement. The longitudinal settlement

trough extends to a distance of about 2.5 times the excavated

diameter of the tunnel before the TBM heading and about 5 times

the excavated diameter behind the TBM face.

225

3. The vertical stress shows a relaxation trend towards the tunnel’s

crown and the invert. The stress above the crown has a uniform

trend resulting from the arching effect that mitigates the overburden

soil. The reduction in vertical stress however is more significant

below the invert, however a minor heave is indicated due to the

elastic nature of the tunnel peripheral underneath the invert. The

major and the minor principal stresses show some decrease around

the tunnel while the intermediate stress is almost unaltered due to

the adjacent tunneling process.

4. The lining assumes an oval shape during the stage of its interaction

with the enfolding ground. The invert heave and the crown

settlement are generally greater than the springline outward

deformation. The crown settlement increases with the distance from

the tail. Deformation mode far from the TBM tail is characterized

with less invert heave compared to the crown settlement. The

springline deformation decreases vaguely to smaller values with the

increase of the time of installation.

5. The thrusting force is the major straining action in the lining. The

moment is very small and may be justifiably neglected.

Consequently, no special modeling is needed to account for the

segmental nature of the lining. The maximum thrust occurs at the

springline following the assumption of inconsequential arching. A

minor reduction of the stress occurs at the invert and a trivial

increase at the springline and at the crown. The tunnel is classified

as a shallow tunnel in which the arching effect is small. The axial

force at the crown is unexpectedly larger than the force at the invert

due to the friction between the lower part of the lining and

surrounding elastic soil. A much less friction is anticipated at the

226

upper half of the lining as a result of the relatively low overburden

and the higher tendency to yield.

6. The effective limiting face pressure is about 40% of the effective

active pressure, which is known to be the minimum principal stress

for the far field. The difference between the estimated limiting face

pressure and active earth pressure of the insitu stresses results from

the arching effect which occurs due to stiffness degradation in the

yielded zone near the face. Adapting a safety factor of 2, the

analysis shows that 80% of active earthpressure can be a good

estimate of the safe face pressure in case of shallow tunnels.

7. Increasing the face pressure furthermore will cause some heave in

front of the TBM that can slightly reduce the maximum settlement

by the same amount. On the other hand, the effective slurry

pressure causes outward flow pattern from the slurry chamber to

the ground in the vicinity of the face. This flow tendency helps to

form the bentonite cake at the excavated face and reduces the effect

of any seepage towards or away from the face. This explains the

minimal increase in the water pressure observed during the tunnel

construction.

8. The width of the settlement trough at Lot 12 increases by about 3.5

times with the increase of the radial loss from nil to 1%

respectively. This result contradicts the common rules-of-thumb

that relate the width of the settlement trough to the geometrical

configuration only.

9. The settlement distribution above the crown is more or less

constant to about 80% of the soil cover above the tunnel for low

overcutting losses (less than 0.5%) then a sudden increase occurs

227

due to the development of weak plastic zone above the crown. A

decrease in the settlement is estimated near the tunnel crown due to

the effect of the tail grouting. The ratio between the surface

settlement and crown settlement for overcutting losses smaller than

0.5% is generally less than unity due to the tail grouting. The ratio

increases above unity for cases above 0.5% (about 1.35 at 1.00%

overcutting loss).

10. The heave below the invert decreases by 50% when increasing the

overcutting losses from nil to 1%. The difference is localized in the

top 2 m below the invert where sudden increase is observed in low

overcutting losses.

11. The effect of tailskin grouting pressure was studied parametrically.

The crown experiences settlement at grouting pressure up to the

overburden pressure; however, the deformation turns to heave at

higher grouting pressures. The invert undergoes heave that is

almost insensitive to the grouting pressure. This development may

be attributed to the existence of plastic zone around the tunnel

especially at the crown neighborhood causing the soil to compress

locally without affecting the ground surface. At the invert, the

ground behaves elastically so that the effect of the grouting

pressure is minimal due to the relatively high confining pressure

and consequently high unloading-reloading modulus.

12. The grouting pressure can be interpreted as a mean to consolidate

the grout especially in the high permeability medium around the

tunnel provided by the sandy deposits; thus increasing the stiffness

of the annular tail void and decrease the possible ground loss at the

tail. However, tail grouting is not adequate measure against losses

that have already taken place before its application, as the surface

228

settlement trough is affected subtlety due to the presence of the

plastic zone around the tunnel.

13. The control of the surface and subsurface ground deformations in

Greater Cairo Metro is attributed to low peripheral overcutting

(about 0.15%) and swift application of the tail grouting at the tail of

the TBM.

Multiple Tunnels

El-Salam Syphon and Al-Azhar Twin Road Tunnels

1. The troughs of the four tunnels of El-Salam Syphon are fairly

symmetric yet showing some tendency to increase towards the

newer tunnel due to the interference of the developed plastic zones.

The minimum peak is shown at the trough of the first tunnel while

the maximum peak of the settlement trough resulting from the

construction of the fourth tunnel is about 40% greater than the first

peak. The maximum total settlement is located above the third

tunnel. Similarly, the existence of the Al-Azhar North tunnel

yielding zone before construction of the South tunnel, leads to

greater settlement above the newer tunnel.

2. The crossing of Al-Azhar Twin Road Tunnels and the CWO sewer

was assessed as the construction of Al-Azhar tunnels may cause

impairments to the neighboring CWO tunnel especially as the

elevation difference between the CWO invert and the crown of Al-

Azhar Tunnels is only 4m. The model provided the evolution of the

229

deformations and the internal stresses in the CWO during Al-Azhar

tunnels construction for untreated and pretreated grounds. The

vertical settlement increases by about 6 times as the north tunnel

heading approaches the CWO tunnel to its final value considering

the untreated ground condition; the axial compression stress

changes also by 4 times and the axial tension stress changes by 6

times of the values estimated as the north tunnel approaches the

crossing. The analysis detects two zones affected by the tensile

stresses; namely, the invert at the intersection zone and the crown

beyond the intersection zone, which corresponds to two conditions

of hanging and sagging moments.

3. Increasing the grouting effect reduces the internal stresses and the

deformation. At high grouting categories, the maximum tensile

stress is found to occur at the crown; conversely, at low grouting

categories it occurs at the invert. The compression stresses

apparently approach a limit that cannot be affected by higher

stabilization category other than strong grouting; however, the

tensile stress and the settlement reduced monotonically with

increasing the grouting category but with a declining rate.

4. The results of the intersection of Al-Azhar Road Tunnels and CWO

show that grouting proved to be a salutary process to control the

deformation and the internal forces (especially tensile stresses)

developed in underground structures due to tunneling. Grouting

reduces the settlement by 38% and tensile stress by 47%.

Compression stress can only be reduced by 22%.

General Conclusion

230

1. Comparing the results of the proposed numerical three-

dimensional idealization of the Bentonite Slurry Tunneling

with the field measurements compiled during the

construction of three major tunnel projects constructed in

Cairo indicated the capability of such sophisticated

modeling to develop realistic pattern of ground subsidence

associated with tunneling. Practicing the proposed numerical

model to the Greater Cairo Metro, El-Salam Syphon and Al-

Azhar tunnels confirmed precise results of the proposed

numerical model. The results implied that, simulating the

details of tunneling operation through the modeling

formulation is considered as the basis for an optimum

tunneling idealization. Adapting the main factors affecting

the pressurized bentonite slurry tunneling such as; unloading

forces due to excavation, ground nonlinearity, interface

condition, engineering properties of shield, rate of advance,

machine overcutting, face pressure, yielding zones and the

tail grouting, are needed for realistic updating of the ground-

tunneling interaction.

2. The three-dimensional tunneling analysis is considered as

the entirely capable arrangement to simulate very

sophisticated problems such as twin and multiple tunnels

and the intersection of different tunnels that cannot be

preceded by means of two-dimensional analysis or empirical

approach superposition. Consequently, the deformations and

the internal forces developed in underground pipelines and

sewers due to tunneling can be estimated.

231

3. The principle of tunneling analysis considering the Gap

Parameter Approach is very dependent on the amount of the

machine overcutting; hence, the application of the machine

overcutting in such models must be treated very carefully to

sustain a realistic ground subsidence.

4. The overcutting losses influence, to a great extent, the

pattern of ground deformation associated with tunneling.

The ground loss measures are less efficient in reducing the

amount of surficial deformation if considerable overcutting

losses are incorporated due to the constitutive nature of soils

to resist reversed stress-path than to continue straining in the

same path.

5. Updating the tailskin grout hardening strength characteristics

around the tunnel lining is considered a main item in a good

tunneling idealization of the ground-lining-gap interaction to

obtain realistic results.

6. The state-of-art bentonite slurry tunneling technology that

was employed in Greater Cairo Metro and Al-Azhar Road

Tunnels, is considered as a very powerful technique to

provide the required stability measures for large diameter

tunnels driven in the Cairo geotechnical conditions, which

are generally described as pervious or semi-previous soft

soils under high groundwater pressure. The elements of

tunnel construction such as machine overcutting, face

pressure, lining erection and tailskin grouting provided

stable tunneling conditions characterized with high rate of

advance and minimum ground subsidence.

232

6.3. Recommendations for Further Studies The following aspects are recommended for research as an augmentation to

the present work:

1. Determination of the mechanical properties of tailskin grouting by

testing it under conditions that are similar to those prevailing in the

proximity of tunnels and not by using laboratory-prepared

specimens.

2. The flow of the water to or from the tunnel and its potential effects

on the ground stability and tunneling functionality.

3. The effect of injection on the state of stress of the ground to

provide basis for simulation of the pre-grouting processes to control

the deformation fields in neighborhood of newly constructed

tunnels.

4. Time dependent effects (creep and consolidation) of the cohesive

soil for multiple and twin tunnels.

5. The use of neurofuzzy and soft computing models as an alternative

to currently employed deterministic simulations.

6. The dynamic nature of the traffic loads inside urban subway and

road tunnels and their effects on surrounding structures.

233

REFERENCES AND BIBLIOGRAPHY

1.Abdel-Rahman, A. H., 1993, “Numerical Modelling of Concrete Diaphragm

Walls", M. Sc. Thesis, Ain Shams University, Cairo, Egypt.

2.Abdrabbo, E. M., Abd El-Lateef, H. A., and El-Nahhas, F. M., 1998,

"Effect of Tunneling on Adjacent Structures", Proc. of the 8th International

Congress, International Association for Engineering, Geology and

Environment, Vancouver, Canada.

3.Abu-Krisha, A. A., 1998, "Numerical Modeling of TBM Tunnelling in

Consolidated Clay", Ph. D. Thesis, Thesis, University of Innsbruck,

Austria.

4.Adashi, T., Yashima, A. and Kojima, K., 1991, "Behaviour and Simulation

of Sandy Ground Tunnels", Developments in Geotechnical Aspects of

Embankments, Excavation and Buried Structures, Edited By

Balasubramaniam A. S. et al., Balkema, Rotterdam, Netherlands, pp.291-

329.

5.Ahmed, A. A., 1991, "Interaction of Tunnel Lining and Ground", Ph. D.

Thesis, Ain Shams University, Cairo, Egypt.

6.Ahmed, A. A., 1994, "Analysis of Deck Road Tunnels", Proc. of

International Congress on Tunneling and Ground Conditions, ITA., Cairo,

Published by Balkema, Netherlands, pp. 469-476.

7.Ahmed, A. A., 2000, "Study on the Stability of Submerged Tunnels",

Scientific Bulletin, Vol. 35, No. 1, Ain Shams University, Faculty of

Engineering, pp. 27-41.

8.Ali, M. A. I., 1990, "Analysis of Shallow Soft Ground Tunnels", M. Sc.

Thesis, Ain Shams University, Cairo, Egypt.

234

9.AMBRIC, 1983, "Contract No. 4, Tunnels- Souk El Samak to Abdeen:

Geotechnical Information", Vol. 3, Ministry of Reconstruction and State for

Housing and Land Reclamation, Organization for the Execution of the

Greater Cairo Wastewater Project.

10.Ardaman-ACE, 1991, "Updating of Studies, Contract 21/M, Design Stage,

Phase 1, Geotechnical Report", Greater Cairo Metro, NAT, DS-01-L-T2.

11.Atkinson, J. H., Brown, E. T. and Potts, D. M., 1975, "Subsidence above

Shallow Tunnels in Soft Grounds", J. of Soil Mech. And Found. Div.,

ASCE, Vol. 103, GT9, pp. 307-325.

12.Atkinson, J. H. and Mair, R. J., 1981, "Soil Mechanics Aspect of Soft

Ground Tunnelling", Ground Engineering, Vol. 14, No. 5, pp. 20-28,

quoted from Thomson (1995).

13.Attewell, P., Yeates, J. and Selby, A., 1986, "Soil Movements Induced by

Tunnelling and Their Effects on Pipielines and Structures", Blackie & Sons

Ltd., Glasgow.

14.Augarde, C. E., 1997, "Numerical Modelling of Tunneling Processes for

Assessment of Damage to Structures", Ph. D. Thesis, University of Oxford.

15. Axelsson, O. and Baker, V., 1984," Finite Element Solution of Boundary

Value Problem: Theory and Computation", Academic Press Inc., Orlando.

16.Bejerrum, L., 1963, "Discussion on 'Proceeding of the European

Conference on Soil Mechanics and Foundation Engineering", Vol. III,

Publication No. 98, NGI, Oslo, Norway, quoted from Boone (1997).

17.Bell, F. G., 1993, "Engineering Treatment of Soils", E & FN SPON,

London, UK.

18.Bentler, D. J., 1998, "Finite Element Analysis of Deep Excavation", Ph. D.

Thesis, Virginia Polytechnic Institute and State University,Dept. of Civil

Engineering, USA.

19.Boscardin, M. D. and Cording, E. J., 1989, "Building Response to

235

Excavation-Induced Settlement", J. of Geotech. Eng., ASCE, Vol. 115, No.

1, pp. 1-21.

20.Broms, B. B. and Bennermark, H., 1967, "Stability of Clay at Vertical

Openings", J. of Soil Mechanics and Foundation Div., ASCE, Vol. 93,

SM1, pp. 71-94.

21.Broone, J. S., 1997, "Ground-Movement-Related Building Damage", J. of

Geotech. Eng., ASCE, Vol. 122, No. 11, pp. 886-896.

22.Brown, E. T., Bray, J. W., Ladanyi, B. and Hoek, E., 1981, "Ground

Response Curves for Rock Tunnels", J. of Geotechnical Engineering Div.,

ASCE, Vol. 109, No. 1, pp. 15-55.

23.Bulson, P. S., 1985, "Buried Structures: Static and Dynamic Strength",

Chapman and Hall, London.

24.Burland, J. B. and Wroth, C. P., 1975, "Settlment of Buildings and

Associated Damage", Build. Res. Establishment Current Paper, 33(75),

Building Research Establishment, Watford, England, quoted from Broone

(1997).

25.Burns, J. Q. and Richard, R. M., 1964, "Attenuation of Stresses for Buried

Cylinders", Proc. on Symposium on Soil-Structure Interaction, Tucson, pp.

378-392, quoted from O'Rouke (1984).

26.Butler, R. A. and Hampton, D., 1975, "Subsidence Over Soft Ground

Tunnel", J. of Geotech. Eng., ASCE, Vol. 105, No. 4, pp. 499-518.

27.Campenon Bernard-SGE, 1999, "Tunneling at the CWO Crossing, Results

of Montoring", El Azhar Road Tunnels Project, Detailed Design, NAT.

28.Chan, D., 1989, "SAGE: A Computer Program for Stress Analysis in

Geotechnical Engineering", Dept. of Civil Engineering, University of

Alberta, Edmonton, Alberta, T6G 2G7.

29.Chan, D., 1996, "Numerical Analysis of Soil Deformation in Geotechnical

Engineering", 7th ICSGE, Ain Shams University, Cairo, pp.147-186.

236

30.Chen, L. T., Poulos, H. G. and Loganathan, N., 1999, "Pile Responses

Caused by Tunneling", J. of Geotech. and Geoenvir. Eng., ASCE, Vol. 125,

No. 3, pp. 207-215.

31.Chen, W. F. and Mizuno, E., 1990, "Nonlinear Analysis in Soil Mechanics;

Theory and Implementation", Developments in Geotech. Eng., Elsevier,

Amsterdam, Netherlands.

32.Chew, L., 1994, "The Prediction of Surface Settlements due to Tunneling

in Soft Ground", M. Sc. Thesis, University of Oxford, quoted from

Augrade(1997).

33.Clough, J. W. and Leca, E., 1993, "EPB Shield Tunneling in Mixed Face

Conditions", J. of Geotech., ASCE, Vol. 119, No. 10, pp. 1640-1656.

34.Clough, J. W., Sweeney, B. P. and Finno, R. J., 1983, "Measured Soil

Response to EPB Shield Tunneling", J. of Geotech. Eng., ASCE, Vol. 109,

No. 2, pp. 131-149.

35.Cook, R. D., Malkus, D. S. and Plesha, M. E., 1989, "Concepts and

Applications of Finite Element Analysis", 3rd Ed., John Wiley and Sons.

36.Cording, E. J. and Hansmire, W. H., 1975, "Displacement Around Soft

Ground Tunnels", General Report, Proc. of the 5th Pan-American Conf. on

SMFE, Buenos Aires, Argentina, Vol. 4, pp. 571-633, quoted from El-

Nahhas (1980).

37.Curtis, D. J., Mott, Hay & Croydon, A., 1976, Correspondence on Wood

M., "The Circular Tunnels in Elastic Ground", Geotechnique, March,

quoted from Ebaid and Hammad (1978).

38.Curtis, D. J. and Rock, T. A., 1977, "Tunnel Lining – Design?", Computer

Methods in Tunnel Design, The Institution of Civil Engineers, London, pp.

175-182.

39.Deere, D. U., Peck, R. B., Monsees, J. E. and Schmidt, B., 1969, "Design

of Tunnel Liners and Support Systems", Report prepared for US

Department of Transportation, NTIS NO. PB 183 799, quoted from El-

237

Nahhas (1980).

40.Desai, C. S. and Abel, J. F., 1972, "Introduction to The Finite Element

Method", Van Nostrand Reinhold Co., NY, USA.

41.Dessouki, A. K., 1985, "Stability of Soil-Steel Structures", Ph. D. Thesis,

Dept. of Civil Engineering, University of Windsor, Ontario, Canada.

42.Duncan, J. M., 1996, "State-of-the-art: Limit Equilibrium and Finite

Element Analysis of Slopes", J. of Geotech. And Geoenvir. Eng., ASCE,

Vol. 122, No. 7, pp. 577-596.

43.Duncan, J. M., Bentler, D. J., Morrison, C. S. and Esterhuizen, J. J. B.,

1998, "SAGE User's Guide: A Finite Element Program for Static Analysis

of Geotechnical Engineering Problems", Virginia Polytechnic Institute and

State University,Dept. of Civil Engineering, USA.

44.Duncan, J. M., Byrne, P., Wong, K. S., Mabry, P., 1980, “Strength, Stress-

Strain and Bulk Modulus Parameters for Finite Element Analysis of

Stresses and Movements in Soil Masses”, Report No. UBC/GT/80-01,

University of California, quoted from Chan (1989).

45.Duncan, J. M. and Chang, C. Y., 1970, "Nonlinear Analysis of Stresses and

Strains in Soils", Journal of Soil Mech. And Found. Div., ASCE, Vol. 96,

No. SM5, pp. 1629-1653.

46.Duncan, J. M., Seed, R. B. Wong, K. S. and Ozawa, Y., 1984,

"FEADAM84, A Computer Program for Finite Element Analysis of Dams",

Virginia Polytechnic Inst. and State University, Dept. of Civil Engineering,

USA.

47.Ebaid, G. S., 1978, "Effect of Joints on Circular Tunnel Design", The

Bulletin of the Faculty of Engineering - Ain Shams University, No. 9, pp.

C11/1-C11/21.

48.Ebaid, G. S. and Hammad, M. E., 1978, "Some Aspects of the Design of

Circular Tunnels", Bulletin of the Faculty of Engineering, Ain Shams

University, No. 8, C83-C104.

238

49.Einstein, H. H. and Schwarz, C. W., 1979, "Simplified Analysis for Tunnel

Supports", J. of Geotech. Eng., ASCE, Vol. 105, No. 4, pp. 499-518.

50.Eisenstein, Z. and Ezzeldine, O., 1994, "The Role of Face Pressure for

Shields with Positive Ground Control", Proc. of the Int. Congress on

Tunnelling and Ground Conditions, Cairo, pp. 557-571.

51.Eisenstein, Z. and Negro, A., 1985, "Comprehensive Design Method for

Shallow Tunnels", Proc. Underground Structures in Urban Areas, ITA,

Praug, Vol. 1, pp.375-391.

52.El-Nahhas, F., 1980, "The Behaviour of Tunnels in Stiff Soils", Ph. D.

Thesis, Alberta University, Edmonton, Canada.

53.El-Nahhas, F. M., 1986, "Spatial Mode of Ground Subsidence above

Advancing Shielded Tunnels", Proc. of Int. Congress on Large

Underground Openings, Firenze, Italy, pp. 720-725.

54.El-Nahhas, F. M., 1991, "Ground Settlement Above Urban Tunnels

Constructed using Bentonite Slurry Machines", Proc. of the Int. Symposium

on Tunneling in Congested Cities, Cairo, pp. 61-74.

55.El-Nahhas, F. M., 1994, "Some Geotechnical Aspects of Shield Tunneling

in Cairo Area", Proc. of International Congress on Tunneling and Ground

Conditions, ITA., Cairo, Published by Balkema, Netherlands.

56.El-Nahhas, F. M., 1999, "Soft Ground Tunnelling In Egypt: Geotechnical

Challenges and Expectations", Tunnelling and Underground Space

Technology, Vol. 14, No. 3, pp. 245-256.

57.EM 1110-2-1908, 1995, "Instrumentation of Embankment Dams and

Levees", Washington D.C., Corps of Engineers, USA.

58.EM 1110-2-2901, 1997, "Tunnels and Shafts in Rock", Washington D.C.,

Corps of Engineers, USA.

59.Esmail, K. A., 1997, "Numerical Modeling of Deformation around Closed

Face Tunneling", Ph. D. Thesis, Ain Shams University, Cairo, Egypt.

239

60.ETL 1110-2-544, 1995, "Geotechnical Analysis by the Finite Element

Method", Washington D.C., Corps of Engineers, USA.

61.Ezzeldine, O. Y., 1995, "Design of Tunnels Constructed using Pressurized

Shield Methods", Ph. D. Thesis, University of Alberta, Canada.

62.Ezzeldine, O. Y., 1999, "Estimation of the Surface Displacement Field due

to Construction of Cairo Metro Line, El Khalafawy - St. Therese",

Tunnelling and Underground Space Technology, Vol. 14, No. 3, pp. 267-

279.

63.Finno, R. J. and Clough, G. W., 1985, "Evaluation of Soil Response to EPB

Shield Tunneling", J. of Geotech. Eng., ASCE, Vol. 111, No. 2, pp. 155-

173.

64.Flint, G. R., 1994, "Ameria Tunnel Junction using Freezing Technique",

Proc. of International Congress on Tunneling and Ground Conditions, ITA.,

Cairo, Published by Balkema, Netherlands, pp. 117-126.

65.Ghaboussi, J. and Gioda G., 1977, "On the Time-dependent Effect in

Advancing Tunnels", Int. J. for Numerical and Analytical Methods in

Geomechanics, Vol. 1, pp. 249-269.

66.Ghaboussi, J., Hansmire, W. H. and Harvey, P. W., 1983, "Finite Element

Simulation of Tunneling over Subways", J. of Geotechnical Engineering,

ASCE, Vol. 109, No. 3, pp. 318-334.

67.Gloosop, N. H., 1977, "Soil Deformations Caused by Soft Ground

Tuneelling", Ph. D. Thesis, University of Durham, UK, quoted from

Thomson (1995).

68.Grant, R., Christian, J. and Vanmarcke, E., 1975, "Differential Settlement

of Buildings", J. of Geotech. Eng., ASCE, Vol. 100, No. GT9, pp. 973-991.

69.Gunn, M. J., 1993 "The Prediction of Surface Settlement Profiles due to

Tunneling", Predictive Soil Mechanics, Proc. of the Wroth Memorial

Symposium, St. Catherine College, Oxford, UK.

240

70.Hamdy, U., 1989, "Deformation Analysis of Tunnels in Stiff Cohesive

Soils", M. Sc. Thesis, Ain Shams University, Cairo, Egypt.

71.Hammad, M. E., 1977, "Subgrade Reaction in U-Shaped Tunnels", J. of the

Egyptian Society of Engineers, Vol. XYI, No. 4, pp. 64-72.

72.Hammad, M. E., 1978, "Design of Circular Syphons Bored in Elastic

Ground", Bulletin of the Faculty of Engineering, Ain Shams University,

No. 9, C3/1-C3/12.

73.Hamza Associates, 1993, "Greater Cairo Metro Line 2, Shobra El Kheima

to Giza, Phase 1, Recommended Geotechnical Properties", Geotechnical

Report, NAT.

74.Hamza Associate, 1995, "Greater Cairo Metro: Phase (2) Tunnel

Monitoring", Comprehensive Report.

75.Hamza Associates, 1998, "Al Azhar Road Tunnel; Port Said, Al Azhar &

El Mosky Street", Geotechnical Report, NAT.

76.Hansmire, W. H. and Cording, E. J., 1985, "Soil Test Section: Case History

Summary", J. of Geotech. Eng., ASCE, Vol. 111, No. GT11, pp. 1301-

1320.

77.Herrenknecht, M. and Maidl, B., 1994, "Transferring the European

Experience Using Mix-shields for the Employment in Cairo", Proc.of the

Int. Congress on Tunneling and Ground Conditions, Cairo, pp. 333-337.

78.Hoek, K., 1968, "Stresses Against Underground Structural Cylinders", J. of

Soil Mech. and Found. Div., ASCE, Vol. 94, No. SM4, pp. 833-858.

79.Hosny, A. and El-Nahhas F., 1994, "Role of Geotechnical Monitoring in

Quality Management of Tunnelling Projects", Proc. of International

Congress on Tunneling and Ground Conditions, ITA., Cairo, Published by

Balkema, Netherlands, pp. 587-591.

80.Iftimie, T., 1994, "Prefabricated Lining, Conceptional Analysis and

Comparative Studies for Optimal Solution", Proc. of International Congress

241

on Tunneling and Ground Conditions, ITA., Cairo, Published by Balkema,

Netherlands, pp. 339-346.

81.Janbu, N., 1963, “Soil Compressibility as Determined by the Oedometer

and the Triaxial Tests”, Proc. European Conf. on SMFE, Wiesbaden, Vol.

1, pp. 19-25, quoted from Ahmed (1991).

82.Jenny, R. J., 1983, "Compressed Air Use in Soft Ground Tunneling", ", J.

of Const. Eng. and Man., ASCE, Vol. 109, No. 2, pp. 206-213.

83.Jones, S. J. and Brown, R. E., 1978, "Temporary Tunnel Support by

Artificial Ground Freezing", J. of Geotech. Eng., ASCE, Vol. 104, GT10,

pp. 1257-1276.

84.Joyce, M. C., 1982, "Site Investigation Practice", J. W. Arrowsmith Ltd,

Bristol, UK.

85.Kaiser, P. K., 1981, "Effect of Stress History on the Deformation

Behaviour of Underground Openings", 13th Canadian Rock Mechanics

Symposium, pp. 133-140, quoted from Ahmed (1991).

86.Korbin, G. and Brekke, L., 1978, "Field Study of Tunnel

Prereinforcement", J. of Geotechnical Engineering Div., ASCE, Vol. 104,

No. GT8, pp. 1091-1108.

87.Kuesel, T. R., 1996, "Tunnel Stabilization and Lining", In "Tunnel

Engineering Handbook", Chapman & Hall Publishing Co., NY,US, pp. 80-

96.

88.Loganathan, N. and Poulos, H. G., 1998, "Analytical Prediction for

Tunneling-Induced Ground Movements in Clays", J. of Geotech. and

Geoenvir. Eng., ASCE, Vol. 124, No. 9, pp. 846-856.

89.Lombardi, G., 1970, "The Influence of Rock Characteristics on the

Stability of Rock Cavities", Tunnels and Tunneling, Vol. 2, pp. 104-109,

quoted from El-Nahhas (1980).

90.Lombardi, G., 1973, "Dimensioning of Tunnel Linings with Regards to

242

Constructional Procedure", Tunnels and Tunneling, Vol. 5, pp. 340-351 ,

quoted from El-Nahhas (1980).

91.Maidl, B. and Hou, X., 1990, "Field Measurement of Ground Movements

and Variations of Pore Water Pressure Caused by EBP Shield

Construction", Tunnel and Underground Works Today and Future, Proc. of

the Int. Congress, ITA Annual Meeting, pp.335-347.

92.Mair, R. and Taylor R. , 1993, "Prediction of Clay Behaviour around

Tunnels using Plasticity Solutions", Predictive Soil Mechanics (Proc.,

Worth mem Symp.), Thomas Telfor, pp. 449-463.

93.Mansour, M., 1996, "Three-Dimensional Numerical Modelling of

Hydroshield Tunneling", Ph. D. Thesis, University of Innsbruck, Austria.

94.Matsumoto Y. and Nishioka, T., 1991, Theoretical Tunnel Mechanics",

Tokyo University, University of Tokyo Press.

95.Mazen, A. and Craig, R., 1994, "El-Salam Syphon under Suez Canal",

Proc. of the Int. Congress on Tunnelling and Ground Conditions, Cairo, pp.

181-186.

96.Monsees, J. M., 1996, "Soft Ground Tunneling", in "Tunnel Engineering

Handbook", Chapman & Hall Publishing Co., NY, USA, pp. 97-121.

97.Morgan, H. D., 1961," A Contribution to the Analysis of Stress in a

Circular Tunnel", Geotechnique, Vol. 11, pp. 37-46.

98.Muir Wood, A. M., 1975, "The Circular Tunnel in Elastic Ground",

Geotechnique, Vol. 25, pp. 115-127.

99.Murray, R. T., 1990, "Rapporteur's paper", Geotechnical Instrumentation in

Practice, Proceedings of the conference of geotechnical instrumentation in

civil engineering projects, Thomas Telford, London, England, pp 75-85.

100.Nomoto, T., Imamura, S., Hagiwara, T., Kusakabe, O and Fujii, N, 1999,

"Shield Tunnel Construction in Centrifuge", J. of Geotech. and Geoenv.

Eng., ASCE, Vol. 125, No. 4, pp. 289-300.

243

101.O'Rouke, J. E., 1979, "Soil Stress Measurement Experiences", J. of

Geotech. Eng., ASCE, Vol. 104, No. GT12, pp. 1501-1514.

102.O'Rouke, T. D., 1984, "Guidelines for Tunnel Lining Design", the

Technical Committee on Tunnel Lining Design of the Underground

Technology Research, ASCE.

103.O'Reilly, M., Mykes, P and New, B. M., 1982, "Settlements Above

Tunnels in the United Kingdom - Their Magnitude and Prediction", Proc. of

Tunneling' 82 Symposium, IMM, London, 1982, quoted from Atewell et al.

(1986).

104.Orr, T. L., Atkinson, C. P., Wroth, C. P., 1978, "Finite Element

Calculation for the Deformation Around Model Tunnels", Computer

Methods in Tunnel Design, The Institution of Civil Engineers, London, pp.

121-144.

105.Otsuka, T. and Kamel, I. A., 1994,"Rehabilitation of Ahmed Hamdy

Tunnel under Suez Canal – Part 1, Study and Design",Proc. of International



106.Owen, D. R. and Hinton, E. H., 1980, "Finite Element in Plasticity:

Theory and Application", Pineridge Press Ltd., Swansea, UK.

107.Pacher, F., 1964, "Measurements of Deformation in a Test Gallery as a

Means of Investigating the Behaviour of the Rock Mass and of Specifying

Lining Requirements", Rock Mechanics and Engineering Geology,

Supplement I, pp. 146-161, quoted from El-Nahhas (1980).

108.Palmer, J. H. L. and Belshaw, D. J., 1978, "Deformations and Pore

Pressures in the Vicinity of a Precast, Segmented, Concrete-Lined Tunnel

in Clay", 31st Canadian Geotechnical Conference, Winnipeg, Alta., pp.174-

184.

109.Peck, R. B., 1969, "Deep Excavation and Tunneling in Soft Ground",

State-of-the-Art, Proceeding of the 7th International Conference on Soil

244

Mechanics and Foundation Engineering, Mexico City, Mexico, pp. 225-

290.

110.Peck, R. B., Hendron, Jr., A. J. & Mohraz, B., 1972, "State-of-the-Art of

Soft Ground Tunnelling" Proceedings of the 1st North American Rapid

Excavation and Tunneling Conference, Vol. 1, pp. 259-286.

111.Pullan, A., 1998, "FEM/BEM Notes", Dept. of Engineering Science, The

University of Auckland, New Zealand.

112.Rabcewicz, L. V., 1964, "The New Austrian Tunneling Method", Water

Power, Vol. 16, pp. 453-457, quoted from El-Nahhas (1980).

113.Rabcewicz, L. V., 1965, "The New Austrian Tunneling Method", Water

Power, Vol. 17, pp. 511-515, quoted from El-Nahhas (1980).

114.Ramond, P. and Guillien, S., 1999, "El Azhar Road Tunnels", Tunneling

and Underground Space Technology, Elsevier Science Ltd., Vol. 14, No. 3,

pp. 291-317.

115.Ranken, R. E. and Ghaboussi, J., 1975, "Tunnel Design Considerations:

Analysis of Stresses and Deformations Around Advancing Tunnels",

Report prepared for US Deportment of Transportation, UILU-ENG75-2016.

116.Richards, D. P., Ramond, P. and Herrenkenecht, M., 1997, "Slurry Shield

Tunnels on the Cairo Metro", General Report, RETC, Las Vegas, USA.

117.Rowe, R. K., Lo, K. Y. and Kack, G. J., 1983, "A Method of Estimating

Surface Settlement above Tunnels Constructed in Soft Grounds", Can.

Geotech. J., Vol. 20, pp. 11-22.

118.Sagaseta, C., 1987, "Analysis of Undrained Soil Deformation due to

Ground Loss", Geotechnique, Vol. 36, No. 3.

119.Saitoh, A., Gomi, K. and Shiraishi, T., 1994, "Influence Forecast and

Field Measurement of a Tunnel Excavation Crossing Right Above Existing

Tunnels", Proc. of International Congress on Tunneling and Ground

Conditions, ITA., Cairo, Published by Balkema, Netherlands, pp. 83-90.

245

120.Schmidt, B., 1969, "Settlement and Ground Movement Associated with

Tunneling in Soil", Ph. D. Thesis, University of Illinois, Urbana, Illinois,

USA.

121.Shalaby, A. G., 1990, "Behavior of tunnels in some Egyptian Soils", Ph.

D. Thesis, Ain Shames University, Cairo, Egypt.

122.Shata, A. A., 1988, “Geology of Cairo, Egypt”, Bulletin of the

Association of Engineering Geologists, Vol. XXV, No. 2, pp. 149-183.,

quoted from Richards (1997).

123.Shi, J., Ortigao, J. A. R. and Bai, J., 1998, "Modular Neural Networks for

Predicting Settlements During Tunneling", J. of Geotech. and Geoenvir.

Eng., ASCE, Vol. 124, No. 5, pp. 389-395.

124.Shou, K. J., 2000, "A Three-Dimensional Hybrid Boundary Element

Method for Non-linear Analysis of a Weak Plane Near an Underground

Excavation", Tunneling and Underground Space Technology, Elsevier

Science Ltd., Vol. 15, No. 2, pp. 215-226

125.Simpson, B., 1993, "Development and Application of a New Soil Model

for Predication of Ground Movements", Predictive Soil Mechanics, Proc. of

the Wroth Memorial Symposium, St. Catherine College, Oxford, UK.

126.Skempton, A. W. and MacDonald, D. H., 1956, "The Allowable

Settlements of Buildings", Proc., Inst. of Civil Engrs., Part III, The

Institution of Civil Engrs., London, pp. 727-768, quoted from Broone

(1997).

127.Smith, I. M. and Griffiths, D. V., 1998, "Programming the Finite Element

Method", 3rd Ed., John Wiley and Sons, NY, USA.

128.Soil Instruments Ltd., 1999, "Technical Data File", requested from

www.soil.co.uk.

129.Sutcliffe, H., 1996, "Tunnel Boring Machines"; in "Tunnel Engineering

Handbook", edited by Brickel, J. O., Kuesel, T. R. and King, E. H.,

Chapman & Hall, NY, USA.

246

130.Szechy, K, 1967, "The Art of Tunnelling", Akademia Kiado, Budapest,

Hungary,

131.Tan, D. Y. and Clough G. W., 1980, "Ground Control for Shallow

Tunnels by Soil Grouting", J. of Geotech. Eng., ASCE, Vol. 106, No. GT9,

pp. 1037-1057.

132.Tarkoy, P. J. and Byram, J. E., 1991, "The Advangaes of Tunnel Boring:

A Qualitative/Quantitive Comparison of D&B and TBM Excavation",

Hong Kong Engineer, Hong Kong.

133.Terzaghi, K., 1936, "Stress Distribution in Dry and in Saturated Sand

above a Yielding Trapdoor", Proc. 1st Intl. Congress on Soil Mech.,

Cambridge, MA, Vol. 1, quoted from Bulson (1985).

134.Terzaghi, K., 1946, "Rock Defects and Loads on Tunnel Support", in

"Rock Tunneling with Steel Supports", Edited by R. V. Proctor, T. White,

Commerial Shearing Co., Youngstown, Ohio, pp. 15-99, quoted from

O'Rouke (1984).

135.Terzaghi, K., 1950, "Geological Aspects pf Soft Ground Tunnelling",

Chapter 11 in "Applied Sedimentation, Edited by P. Transk, John Wiley &

Sons, NY, 1950, quoted from Thomson (1995).

136.Thomson, J., 1995, "Pipe Jacking and Microtunneling", 2nd edition,

Blackie Academic and Professional, Glasgow, UK.

137.Touran, A, 1997, "A Probabilistic Model for a Tunneling Project using a

Markov Chain", J. of Const. Eng. and Man., ASCE, Vol. 123, No. 4, pp.

444-449.

138.Touran, A. and Asai, T., 1987, "Simulation of Tunneling Operations", J.

of Const. Eng. and Man., ASCE, Vol. 113, No. 4, pp. 554-568

139.Weaver, W., Johnston, P., 1984, “Finite Elements for Structural

Analysis”, Prentice-Hall, NJ,USA.

140.Wittaker, B. N. and Frith, R. C., 1990, "Tunnelling: Design, Stability and

247

Construction", published by The Institution of Mining and Metallurgy,

London, U.K.

141.Yoshida, T. and Kusabuka, M., 1994, "Behaviour of Ground and Adjacent

Underground Piping During Shield Tunneling", Proc. of International



142.Zienkiewics, O. C., 1977, "The Finite Element Method", 3rd ed.,

McGraw-Hill Book Company, London.

elasto-plastic three dimensional analysis of shielded tunnels, with special application on greater...

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