Predicting the movements

PREDICTING THE GROUND MOVEMENTS ABOVE TWIN TUNNELS CONSTRUCTED IN LONDON CLAY

By

DEXTER HUNT (MEng)

A thesis submitted to the University of Birmingham for the degree of DOCTOR OF PHILOSOPHY

Department of Civil Engineering School of Engineering The University of Birmingham September 2004

i

Abstract

ABSTRACT This thesis provides an improved understanding of surface and sub-surface movements above twin and triple tunnel constructions in London Clay and puts in place a framework for improving the current semi-empirical predictive methods (i.e. a Gaussian curves) for estimating ground movements. The thesis reports the results of 2D plain strain undrained tunnel analyses using the ABAQUS finite element modelling package in conjunction with a small strain stiffness soil model (Jardine et al 1986) and a modified gap parameter. The actual and relative changes in displacement are reported for single tunnels with varying diameter, depth and volume loss. These are also reported for twin tunnels (in a side-by-side, piggyback and offset alignment) and triple tunnels (in a side-by-side alignment) using different construction sequences. The multiple tunnels are constructed with a time delay which includes stiffness changes with no consolidation. The results of a 1/50 small-scale model of twin unlined side-by-side tunnels, constructed using two types of tunnelling procedure (i.e. augering and coring), conducted at 1g in a heavily overconsolidated sample of Kaolin clay are also reported. Based on the finite element results a Modification Factor is presented which is applied to existing semi-empirical methods in order to improve significantly the prediction of displacements above side-by-side twin and triple tunnel constructions for several published case histories.

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Acknowledgements

ACKNOWLEDGEMENTS Firstly I must thank my supervisor Prof. Chris Rogers for his endless encouragement during my undergraduate studies and for providing me with the opportunity to undertake postgraduate studies at the University of Birmingham. I would also like to thank him for the continued support which he has given me during the programme. It has been a privilege to study underneath him and I would like to thank him for his maintained confidence in my ability to conduct research. I would like to thank Dr David Chapman, my co-supervisor, for sharing his knowledge, for providing exceptional guidance and for his continued encouragement throughout the duration of the project. I am grateful to the Engineering and Physical Sciences Research Council (EPSRC) who have given their financial support for the duration of the project, without which this research would not have been possible. Many thanks are given to Tom Sanford who, whilst on sabbatical from the United States of America, gave helpful advice during the early stages of the project for modelling ground movements using the ABAQUS finite element package. Particular gratitude must be paid to Fred Wan, for his wisdom and encouragement offered during the small-scale laboratory testing. Fred sadly died in 2003 and will be greatly missed. Particular gratitude must also be given to the following people: Vincent Thereau (MSc Student) who helped with the preparation of samples for the small scale model tests. The long days spent mixing indoors during the summer months would not have been possible without him. Mike Vanderstam (Technician) for his help with the construction of and subsequent maintenance to the consolidation tank. Thanks must also be given to David Cope, John Edgerton and Bruce Read for their valuable contributions towards many aspects of the project. Ken Goodey (Librarian) from the Institute of Civil Engineers Library who spent many hours photocopying hundreds of papers for me. Dr Mike Cooper, for his time, interest, enthusiasm and friendship during the course of this study. My Mother must be commended for her hours of patience, understanding, enthusiasm and financial commitment towards me. Without her the completion of this project would never have been possible. D.Hunt - 2004

iii

Acknowledgements

I certify that, except where specific reference has been made in the text to the work of others, the contents of this thesis are original and have not been submitted to any other university. This thesis is the result of my own work. September 2004

D.V.L. Hunt

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Contents

TABLE OF CONTENTS

Page No:

ABSTRACT………………………………………………………………………….

i

ACKNOWLEDGEMENTS……………………………………………………….…

iii

LIST OF CONTENTS..……………………………………………….………….….

v

LIST OF TABLES……………………………………………………………………

xi

LIST OF FIGURES…………………………………………………………………..

xii

NOTATION……….………………………………………………………………….

xxvi

Chapter One INTRODUCTION 1.1 GENERAL…………………………………………………………………….

1

1.2 SCOPE…………………………………………………………………………

3

1.3 LAYOUT………………………………………………………………………

4

Chapter Two CURRENT ENGINEERING PRACTICE FOR PREDICTING GROUND MOVEMENTS ABOVE SINGLE AND TWIN TUNNELS

2.1 INTRODUCTION………………………………………………………………....

7

2.2 VOLUME LOSS…………………………………………………………………..

7

2.2.1 Definitions and Sources of Volume loss…………………………………..

7

2.2.2 Typical Volume Losses for Clays…………………………………………

9

2.2.3 Relationship between Stability and Volume Loss………………………...

10

2.3 SURFACE DISPLACEMENTS………………………………………………......

12

2.3.1 Modelling the Settlement Profile Transverse to a Single Tunnel………….

12

2.3.2 Relationship between Wmax and Volume Loss. …………………………...

13

2.3.3 Transverse Ground Slope, Curvatures and Strains………………………...

13

2.3.4 Developing a Longitudinal Settlement Profile ……………………………

14

2.4 TROUGH WIDTH PARAMETER……………………………………………….

15

2.4.1 Description and Prediction. ……………………………………………....

15

2.4.2 Clays. …………………………………………………………………….

17

2.4.3 Granular Materials. ………………………………………………………..

18

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2.4.4 Mixed Bedding………………………………………………………........

18

2.5 SUB-SURFACE DISPLACEMENTS. ………………………………………….

19

2.5.1 Variation of ix with Zo. …………………………………………………..

20

2.5.2 Variation of Wmax with Zo. ………………………………………………..

22

2.5.3 Variation of iy and W with Zo………………………………………........

22

2.5.4 Wmax in relation to Wcrown…………………………………………………

23

2.6 HORIZONTAL DISPLACEMENTS…………………………………………….

24

2.6.1 Surface (Transverse to Tunnel)…………………………………………..

24

2.6.2 Sub-Surface (Transverse to Tunnel).….…………………………………...

25

2.6.3 Sub-surface Strains (Transverse to Tunnel)...……………………………..

26

2.6.4 Vector focus. ……………………………………………………………..

26

2.6.5 Surface (Longitudinal to Tunnel)………………………………………...

27

2.6.6 Sub-Surface (Longitudinal to Tunnel).…………………………………….

27

2.6.7 Idealised Three-Dimensional Behaviour…..………………………………

28

2.6 DISPLACEMENTS ABOVE TWIN AND TRIPLE TUNNELS………………..

28

2.6.1 Parallel (Side-by-Side) Tunnels……………………………………………

28

2.6.2 Predicting Movements for Parallel (Side-by-Side) Tunnels……………….

31

2.7.3 Piggyback (Stacked) Tunnels ...…………………………………………...

32

2.7.4 Offset Tunnels. ………………………………………………………........

32

2.7.5 Transverse (Cross-Cutting) and skew tunnels. .…………………………..

33

2.8 TIME RELATED (LONG TERM) MOVEMENTS………………………………

34

2.9 DAMAGE TO BUILDINGS AND OVERLYING STRUCTURES……………...

36

2.10 CONCLUSIONS…………………………………………………………………..

38

Chapter Three THE FINITE ELEMENT METHOD AND TUNNEL CONSTRUCTION

3.1 INTRODUCTION………………………………………………………………...

55

3.2 THE FINITE ELEMENT METHOD……………………………………………..

55

3.2.1 Element Discretisation…………………………………………………….

55

3.2.2 Displacement Approximation……………………………………………...

56

3.2.3 Element Equations………………………………………………………...

57

3.2.4 Global Equations…………………………………………………………..

58

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3.2.5 Boundary Conditions………………………………………………….......

58

3.2.6 Equation Solutions………………………………………………………...

58

3.3 SPECIFIC DETAILS THE FINITE ELEMENT MODEL …………...…………

59

3.3.1 Software and Hardware details…………………………………………...

59

3.3.2 Constitutive Models for London Clay…………………………….............

59

3.3.2.1 Pre-yield model………………………………………………….

59

3.3.2.2 Yield model……………………………………………………...

62

3.3.3 Contact Elements ……………………………………………….................

63

3.3.4 Material Properties for the Soil..………………………………………….

64

3.3.5 Material Properties for Tunnel Liners and Anchorage System.……..……

64

3.3.6 Boundary Conditions……………………………………………………...

65

3.4 MODELLING A SINGLE TUNNEL ANALYSIS………………………………

66

3.4.1 Stress Reduction ……………………………………………………..........

66

3.4.2 Stiffness Reduction………………………………………………………...

67

3.4.3 Volume Loss Method.……………………………………………………

67

3.4.4 The “Gap” Parameter……………………………………………………...

67

3.4.5 Using a Modified Gap Parameter to Model Volume Loss (This research)..

69

3.5 DISCUSSION……………………………………………………………………….

71

Chapter Four MOVEMENTS ABOVE A SINGLE TUNNEL 4.1 INTRODUCTION………………………………………………………………...

78

4.2 SINGLE TUNNEL DETAILS……………………………………………………

80

4.3 RESULTS OF SINGLE TUNNEL ANALYSES………………………………...

81

4.3.1 Displacements…………………………………………………………….

81

4.3.2 Liner Behaviour…………………………………………………...............

83

4.4 EMPIRICAL PREDICTIONS COMPARED TO FINITE ELEMENT PREDICTIONS …………………………………………………………………………. 4.4.1 Surface Displacements……………………………………………………...

84 84

4.4.1.1

Volume loss………………………………………………………

85

4.4.1.2

Effect of depth……………………………………………………

86

4.4.1.3

Settlement profile shape……………………………………........

86

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4.4.2 Sub-Surface Displacements………………………………………………...

86

4.4.3 ‘Relative Changes’ in Surface Displacement………………………………

87

4.5 CONCLUSIONS……………………………………………………………………

88

Chapter Five MOVEMENTS ABOVE TWIN TUNNELS 5.1

INTRODUCTION…………………………………………………………………

107

5.2

TWIN TUNNEL MODEL DETAILS………………………………………...…...

110

5.2.1

Tunnel Geometry….………………………………………………………

110

5.2.2

Material Properties………………………………………………………..

111

5.2.3

Boundary Conditions……………………………………………………...

111

5.2.4

Modelling Twin Tunnels and Controlling Volume Losses……………......

112

RESULTS OF SIDE BY SIDE TUNNELS..……………………………………...

115

5.3.1

Surface and Sub-Surface Displacements…………….………………….....

115

5.3.1.1 9.0m diameter tunnels……………………………………………

115

5.3.1.2 4.0m diameter tunnels……………………………………………

118

5.3.1.3 The effect of volume loss………………………………………...

118

5.3.2

Liner Deformation …..………………………………………………….....

119

5.3.3

General Behaviour of Twin Tunnels………………………………………

120

5.3.3.1 Contours of W/Wmax……………………………………………

120

5.3.3.2 Relative changes in displacement (W1 / W2) ……………………

120

5.3.3.3 Eccentricity of W max and relative changes in W ………………...

122

5.3.3.4 Eccentricity of Umax (near) and Umax (remote) and U=0…………

123

5.3.3.5 Mohr Coulomb model……………………………………………

124

RESULTS OF PIGGY BACK TUNNELS ……………………………………….

124

5.4.1

Lower Tunnel Driven First ……………………………………….……….

125

5.4.2

Upper Tunnel Driven First……………………………….………………...

126

5.4.3

Deformation of Tunnel Liners……………………………………………..

127

RESULTS OF OFFSET TUNNELS..……………………………………………..

128

5.5.1

Lower Tunnel Driven First ……………………………………….…….....

128

5.5.2

Upper Tunnel Driven First……………………………….………………...

130

5.3

5.4

5.5

5.6 DISCUSSION………………………………………………………………...........

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5.6.1

Side-by-Side Tunnels………………………………………………………

132

5.6.2

Piggyback Tunnels…………………………………………………………

133

5.6.3

Offset Tunnels……………………………………………………………..

135

Chapter Six MOVEMENTS ABOVE TRIPLE TUNNELS 6.1 INTRODUCTION………………………………………………………………...

189

6.2 FINITE ELEMENT MODEL...…………………………………………………..

189

6.3 FINITE ELEMENT RESULTS...………………………………………………...

191

6.3.1 Construction Sequence 1.………………………………………………......

191

6.3.2 Construction Sequence 2.………………………………………………......

192

6.3.3 Relative changes in displacement …………………………………….........

193

6.3.4 Construction Sequence 3 (Heathrow Express)……………….

194

6.4 HEATHROW EXPRESS CASE HISTORY...………………………………….....

195

6.5 CONCLUSIONS.....…………………………………………………………….....

196

Chapter Seven SMALL SCALE LABORATORY MODELLING OF TWIN TUNNELS 7.1 INTRODUCTION………………………………………………………………...

210

7.2 APPARATUS DESIGN…………………………………………………………..

211

7.2.1 Consolidation tank………………………………………………………...

212

7.2.2 Drainage…………………………………………………………………...

214

7.2.3 Reaction frame…………………………………………………………….

214

7.2.4 Pressure system……………………………………………………………

215

7.2.4.1

Pneumatic……………………………………………………….

215

7.2.4.2

Power booster…………………………………………………..

215

7.2.4.3

Hydraulic system……………………………………………….

216

7.2.5 Speswhite………………………………………………………………….

217

7.2.6 Consolidation theory and soil strength calculation………………………..

218

7.2.6.1

Deriving water content from the undrained shear strength……..

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7.2.6.2

Height of sample and quantities of material required…………..

220

7.2.6.3

Time for consolidation………………………………………….

221

7.2.7 Tunnelling machine……………………………………………………….

222

7.2.8 Monitoring equipment ……………………………………………………

224

7.2.8.1

Vibrating wire Pore Pressure Tranducers (PPT)..………………

224

7.2.8.2

Vibrating wire Total Pressure Transducers (TPT)……………..

225

7.2.8.3

LVDT transducers………………………………………………

225

7.2.8.4

Dial gauges……………………………………………………..

226

7.2.8.5

Load cell ……………………………………………………….

226

7.2.8.6

Data loggers ……………………………………………………

226

7.2.8.7

Marker beads and Digital photography ………………………..

227

7.3 EXPERIMENTAL PROCEDURE………………………………………………..

228

7.4 RESULTS…………………………………………………………………………

231

7.4.1 Consolidation, shear strength and water content results…………………..

231

7.4.2 Displacements (surface and sub-surface)...………………………………..

231

7.5 RECOMMENDATIONS………………………………………………………….

232

Chapter Eight IMPROVING CURRENT PREDICTIVE TECHNIQUES BY USE OF A MODIFICATION FACTOR

8.1 INTRODUCTION…………………………………………………………….......

248

8.2 USING FINITE ELEMENT ANALYSES AND CASE HISTORY DATA TO ESTABLISH A VIABLE IMPROVED METHOD ………………………………

250

8.3 PARAMETER SELECTION……………………………………………………..

252

8.3.1 Trough width parameter…………………………………………………...

252

8.3.2 Volume loss……………………………………………………………….

253

8.3.3 Vector focus……………………………………………………………….

253

8.4 MODIFICATION METHOD……………………………………………………..

254

8.4.1 Defining the method………………………………………………………

254

8.4.2 Surface settlement…………………………………………………………

256

8.4.3 Sub-surface settlements…………………………………………………...

257

8.4.4 Changes to trough width parameter, K…………………………………….

258

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8.4.5 Changes in U………………………………………………………………

258

8.5 APPLICATION OF THE METHOD TO TYPICAL EXAMPLES………………

259

8.5.1 Surface settlements………………………………………………………..

259

8.5.2 Horizontal movements…………………………………………………….

261

8.5.3 Volume loss……………………………………………………………….

262

8.5.4 Sub-surface movements…………………………………………………...

262

8.6 COMPARISON TO CASE HISTORIES…………………………………………

263

8.6.1 Case history A - Heathrow Express………………………………………..

264

8.6.2 Case history B - Lafayette Park……………………………………............

265

8.6.3 Case history C - St James Park…………………………………………….

265

8.7 PIGGY BACK TUNNELS………………………………………………………..

265

8.8 DISCUSSION……………………………………………………………………...

266

Chapter 9 CONCLUSIONS AND RECOMMENDATIONS 9.1 INTRODUCTION…………………………………………………………………..

286

9.2 FINITE ELEMENT MODELLING………………………………………………...

288

9.2.1

Single Tunnels……………………………………………………………

288

9.2.2

Side-by-Side Tunnels…………………………………………………….

291

9.2.3

Piggyback Tunnels……………………………………………………….

293

9.2.4 Offset Tunnels……………………………………………………………………

295

9.2.5 Triple Side-by-Side Tunnels……………………………………………………..

296

9.3 PHYSICAL MODELLING………………………………………………………….

297

9.4 IMPROVING CURRENTLY AVAILABLE PREDICTIVE TECHNIQUES FOR MULTIPLE TUNNEL CONSTRUCTIONS………………………………………..

299

9.5 FUTURE RESEARCH……………………………………………………………...

300

REFERENCES BIBLIOGRAPHY

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List of tables

LIST OF TABLES Table 2.1

Page No:

Damage categories due to ground strains (after Boscardin and Cording, 1989)…………………….……………………………………………………

36

Table 3.1

Small strain parameters from Addenbrooke (1996)...………………………… 61

Table 3.2

Mohr-Coulomb yield surface and plastic potential parameters and unit weight …………………………………………..…………………………….

63

Table 4.1

Analyses performed…………………………………………………………...

80

Table 4.2

Comparison between the results of the finite element predictions and empirical predictions………………………………………………………..… 88

Table 5.1

Parameters used in twin tunnel analyses performed…………………..………

110

Table 7.1

Properties of Speswhite Kaolin clay obtained from various references ...……

217

Table 7.2

Properties of Speswhite Kaolin (Imerys inerals Co, 2003)…………………...

217

Table 8.1

Case history parameter details………………………………………………...

263

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List of figures

LIST OF FIGURES

Page No:

Figure 2.1

Sources of volume loss for a shield driven tunnel (after Cording 1975)……..

39

Figure 2.2

Volume loss assumptions for an undrained clay …………………………......

39

Figure 2.3

Volume loss versus load factor (after Macklin, 2000)………………………..

40

Figure 2.4

Stochastic modelling of the settlement process (after Schmidt, 1969)………..

40

Figure 2.5

Transverse settlement profile above a single tunnel…………………………..

41

Figure 2.6

Longitudinal settlement profile above a single tunnel………………………... 41

Figure 2.7

Relationship between  and half trough width T (after Cording and Hansmire, 1975)………………………………………..…

42

Figure 2.8

Relationship between  and full trough width 2T (after Attewell, 1978)…….

42

Figure 2.9

Longitudinal angle of draw above a single tunnel (after Attewell, 1978)…….

43

Figure 2.10

Variation of trough width parameter, i, with tunnel depth for tunnels in London Clay (after Mair et al, 1997)………………………………………….

43

Figure 2.11

Full trough width for multilayered soil (after Selby, 1988)………………….

45

Figure 2.12

Angle of draw in multilayered soil (after Ata, 1996)…………………………

45

Figure 2.13

Variation of i with depth a single tunnel ……………………………………..

46

Figure 2.14 Figure 2.15

Variation of K with depth for a single tunnel (after Mair et al, 1993)………... 46 Sub-surface ground movements above a single tunnel……………………….. 47

Figure 2.16

Suggested distribution of i with depth including vector focus………………..

Figure 2.17 Figure 2.18

Suggested distribution of i with depth (after Grant and Taylor, 2000)……….. 48 3D profile of settlement above a single tunnel (after Yeates, 1985)………… 48

Figure 2.19

Settlement over tunnels in dense sand above groundwater level (Peck, 1969).

Figure 2.20

Settlement above twin tunnels – Market Street (Moretto, 1969)……………... 49

Figure 2.21

Settlement above twin tunnels showing asymmetry (Bartlett and Bubbers, 1970)………………………………………………………………..…………

Figure 2.22

49

50

Volume loss due to interference during driving of a second tunnel (after Cording and Hansmire, 1975)…………………………………………..

Figure 2.23

47

50

Effect of pillar width on Increased volume loss for second tunnel driven (after Cording and Hansmire, 1975)………………………………………….

51

Figure 2.24

Effect of pillar width on eccentricity of Smax (Addenbrooke, 1996)………….

51

Figure 2.25

Effect of pillar width on tunnel deformation (Addenbrooke, 1996) …………

52

Figure 2.26

Influence of pillar width on liner distortion (after Kim, 1996)……………….. 52

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List of figures

Figure 2.27

Empirical predictive method for twin tunnels ………………………………..

53

Figure 2.28

Settlement above twin perpendicular tunnels (Keusel, 1972)………………...

53

Figure 2.29

Effect of pillar width on trough width for piggy back tunnels (Addenbrooke,

54

1996)………………………………………………………………………….. Figure 2.30

Surface and sub-surface movements for offset tunnels (Shirlaw et al, 1988)...

54

Figure 3.1

8-noded CPE8R element……………………………………………………… 72

Figure 3.2

Small strain stiffness model (after Jardine, 1986)…………………………….

Figure 3.3

Mohr Coulomb failure criterion (tension positive)…………………………… 73

Figure 3.4

Tunnel geometry and material properties……………………………………..

74

Figure 3.5

Stiffness reduction (Panet and Guenot, 1982) …………………………..........

75

Figure 3.6

Stiffness reduction (Swodoba, 1979)…………………………………………. 75

Figure 3.7

Volume loss method (Addenbrooke, 1996)…………………………………...

Figure 3.8

(a) Gap parameter (Rowe et al, 1983) and (b) Modified gap parameter……… 76

Figure 3.9

Modelling a single tunnel using a gap parameter in the finite element

72

76

method………………………………………………………………………..

77

Figure 4.1

Typical finite element mesh for single 9.0m and 4.0m diameter tunnels……..

91

Figure 4.2

Sub-surface and surface settlements above a single 9.0m tunnel at 26.0m depth using Soil 1 with a 1.3% volume loss…………………………………..

Figure 4.3


Figure 4.4

97

Sub-surface and surface settlements above a single 4.0m tunnel at 33.4m depth using Soil 1 with a 1.3% volume loss. …………………………………

Figure 4.9

96

Sub-surface and surface settlements above a single 9.0m tunnel at 16.4m depth in Soil 1 with a 1.3% volume loss…………………………………..

Figure 4.8

95


Figure 4.7

94


Figure 4.6

93


Figure 4.5

92

Sub-surface and surface settlements above a single 9.0m tunnel at 33.4m

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List of figures

depth using Soil 1 with a 1.3% volume loss. …………………………

99

Figure 4.10

Movement and deformation of a single tunnel liner…………………………

100

Figure 4.11

Comparison between W and U for empirical and finite element predictions based on Mair et al (1993) for a 9.0m tunnel at 26.0m depth using Soil 1 and a 1.3% volume loss. ………………………………………………………….

Figure 4.12

101

Comparison of sub-surface displacement contours from a finite element analysis and empirical predictions based on Mair et al (1993) (9.0m diameter, 1.3% volume loss, 26.0m depth and Soil 1) ……………………….

Figure 4.13

101

Comparison of results from a finite element analysis with predictions made by an existing empirical technique for a single 4.0m diameter tunnel at a depth of 26.0m with a volume loss of 1.3% and 2.0%.……………………….

Figure 4.14

102

Comparison of results from a finite element analysis with predictions made by existing empirical techniques for a single 4.0m diameter tunnel at a depth of 16.4m and 33.4m and with a volume loss of 1.3%.……………………….

Figure 4.15

Normalised plots of surface displacements obtained from empirical and fine element results (diameter, volume loss and depth shown) …………………..

Figure 4.16

106

Relationship between maximum horizontal and vertical displacements obtained from empirical and finite element results for sub-surface levels……

Figure 5.1

105

Relative changes in relative distance to Umax (i) sub-surface compared to the distance to Umax (i0) at the surface...........................................................

Figure 4.20

105

Relative changes in maximum sub-surface (Wmax ss) and surface settlement (Wmax 0) with tunnel depth…………………………………………………….

Figure 4.19

104

Relationship between horizontal (U) and vertical (W) displacements along the settlement trough profile for the empirical and finite element results……

Figure 4.18

104

Normalised plots of surface displacements obtained from empirical and finite element results (diameter, volume loss and depth shown)……………………

Figure 4.17

103

106

Geometry of cases modelled in twin tunnels analyses (a) Twin side by side tunnel geometry………………………………………..

137

(b) Twin piggy back tunnel geometry………………………………………… 137 (c) Twin offset tunnel geometry…………………………………………........ Figure 5.2

137

(a) Finite element mesh for a side-by-side 9.0m and 4m diameter twin tunnel analysis (Z = 26.0m, 20.0m spacing)…………………………………………. 138 (b) Finite element mesh for piggyback 9.0m and 4.0m diameter twin tunnel

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List of figures

analyses (Z = 16.4m and 33.4m)……………………………………………… 139 (c) Finite element mesh for a offset 9.0m diameter twin tunnel analysis Z = 17.4m and 30.9.0m, 20.0m spacing. …………………………………….. Figure 5.3

140

Settlement above tunnel one with varying tunnel to boundary distance (distance to right-hand-side boundary shown) ………………………….……. 141

Figure 5.4

Settlement above tunnel one with varying tunnel to boundary distance (distance to right-hand-side boundary shown) ………………………….……. 141

Figure 5.5

Surface and sub-surface vertical displacements above Tunnel 2 when considering twin tunnels 9.0m diameter tunnels at 26.0m depth with a 20.0m centre-to-centre spacing (V1 and V2 = 1.3%)…………………………………

Figure 5.6

142

Surface and sub-surface horizontal displacements above Tunnel 2 when considering twin 9.0m diameter tunnels at 26.0m depth with a 20.0m centre-to-centre spacing (V1 and V2 = 1.3%)…………………………………

Figure 5.7

143

Surface and sub-surface vertical displacements above Tunnel 2 when considering twin 9.0m diameter tunnels at 26.0m depth with a 30.0m centreto-centre spacing (V1 and V2 = 1.3%)………………………………………... 144

Figure 5.8

Surface and sub-surface horizontal displacements above Tunnel 2 when considering twin 9.0m diameter tunnels at 26.0m depth with a 30.0m centreto-centre spacing (V1 and V2 = 1.3%)………………………………………… 145

Figure 5.9

Surface and sub-surface vertical displacements above Tunnel 2 when considering twin 9.0m diameter tunnels at 26.0m depth with a 50.0m centre-to-centre spacing (V1 and V2 = 1.3%)…………………………………

Figure 5.10

146

Surface and sub-surface horizontal displacements above Tunnel 2 when considering twin 9.0m diameter tunnels at 26.0m depth with a 50.0m centreto-centre spacing (V1 and V2 = 1.3%)………………………………………… 147

Figure 5.11

Surface and sub-surface vertical displacements above Tunnel 2 when considering twin 9.0m diameter tunnels at 26.0m depth with a 20.0m centreto-centre spacing (V1 and V2 = 1.3%) - Soil type 2…………………………..

Figure 5.12

148

Surface and sub-surface horizontal displacements above Tunnel 2 when considering twin 9.0m diameter tunnels at 26.0m depth with a 20.0m centreto-centre spacing (V1 and V2 = 1.3%) - Soil type 2…………………………...

Figure 5.13

Surface and sub-surface vertical displacements above Tunnel 2 when considering twin 4.0m tunnels at 26.0m depth with a 20.0m centre-to-centre

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spacing (V1 = V2 = 1.3%)…………………………..…………………………. 150 Figure 5.14

Surface and sub-surface horizontal displacements above Tunnel 2 when considering twin 4.0m diameter tunnels at 26.0m depth with a 30.0m centreto-centre spacing (V1 = 1.3%, V2 = 1.3%)…………………………..………... 151

Figure 5.15

Surface and sub-surface vertical displacements above Tunnel 2 when considering twin 4.0m diameter tunnels at 26.0m depth with a 30.0m centreto-centre spacing (V1 = 1.3%, V2 = 1.3%)……………………………………. 152

Figure 5.16

Surface and sub-surface horizontal displacements above Tunnel 2 when considering twin 4.0m diameter tunnels at 26.0m depth with 30.0m centreto-centre spacing (V1 = 1.3%, V2 = 1.3%)……………………………………. 153

Figure 5.17


Figure 5.18

Surface and sub-surface horizontal displacements above Tunnel 2 when considering twin 4.0m diameter tunnels at 26.0m depth with a 50.0m centreto-centre spacing (V1 = 1.3%, V2 = 1.3%)……………………………………. 155

Figure 5.19


Figure 5.20

Surface and sub-surface horizontal displacements above Tunnel 2 when considering twin 4.0m diameter tunnels at 26.0m depth with 20.0m centreto-centre spacing (V1 = 2.0%, V2 = 2.0%)……………………………………. 157

Figure 5.21


Figure 5.22

Surface and sub-surface horizontal displacements above Tunnel 2 when considering twin 4.0m diameter tunnels at 26.0m depth with a 20.0m centreto-centre spacing (V1 = 1.3%, V2 = 2.0%)……………………………………. 159

Figure 5.23

(a) Liner behaviour of Tunnel 1 (26.0m depth, 9.0m diameter tunnel) at 20.0, 30.0, 50.0 and 80.0m centre-to-centre spacing. ……………………..

160

(b) Liner behaviour for Tunnel 1 (26.0m depth, 9.0m diameter tunnel) due to the construction of Tunnel 2 at a centre-to-centre spacing of 20.0, 30.0, 50.0 and 80.0m. . ……………………... ……………………... ………………….

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Figure 5.24

Contours of W/Wmax for all sub-surface depths at 30.0m spacing (Vl=1.3%, V2=1.3%). . ……………………... ……………………... ………………….

Figure 5.25

161

Relative changes in surface and sub-surface ground settlements above Tunnel 2 (W2/W1) for twin 9.0m diameter tunnels with a 20.0m centre-tocentre spacing (Vl=1.3%, V2=1.3%) .……………………...………....………. 162

Figure 5.26

Relative changes in surface settlement above Tunnel 2 (W2/W1) for twin 9.0m diameter tunnels at various centre-to-centre spacings using a volume loss of 1.3% and Soil 1…………...……………………...…………..………..

Figure 5.27

162

Relative changes in surface settlement above Tunnel 2 (W2/W1) for twin 9.0m diameter tunnels at various centre-to-centre spacings using a volume loss of 1.3% and Soil 2 …………...……………………...………….………..

Figure 5.28

163

Relative changes in surface settlement above Tunnel 2 (W2/W1) for twin 4.0m diameter tunnels at various centre-to-centre spacings using a volume loss of 1.3% and Soil 1.…………...……………………...………….………..

Figure 5.29

163

Relative changes in surface settlement above Tunnel 2 (W2/W1) for twin 4.0m diameter tunnels at various centre-to-centre spacings with a volume loss of 2% and Soil 1.…………...……………………...………….………….

164

Figure 5.30

Effect of volume loss and tunnel diameter on relative changes (W2/W1)…….

164

Figure 5.31

Relative changes in surface settlement above Tunnel 2 (W2/W1) for a 4.0m diameter tunnels at various centre-to-centre spacings with a volume loss of 1.3% for Tunnel 1 and 2.0% for Tunnel 2 .…………...……………………...

Figure 5.32

Range of values of M with varying centre-to-centre tunnel spacing for 4.0m and 9.0m diameter tunnels ……………….…………...……………………...

Figure 5.33

165 165

Eccentricity of Wmax normalised by centre-to-centre spacing (e/d') for surface (0Z) and sub-surface (0.21, 0.26, 0.44, 0.55 and 0.60Z) depths (tunnel diameter shown in brackets) .…….…………...……………………...

166

Figure 5.34

Deviation of position of U=0 and Umax, i.e. i (near) and i (remote)…………..

166

Figure 5.35

Surface and sub-surface vertical displacements above Tunnel 2 when considering piggyback 9.0m diameter tunnels at depths of 16.4m and 33.4m (V1 & V2 = 1.3%); lower tunnel constructed first..…………...………………

Figure 5.36

167

Surface and sub-surface horizontal displacements above Tunnel 2 when considering piggyback 9.0m diameter tunnels at depths of 16.4m and 33.4m (V1 & V2 = 1.3%); lower tunnel constructed first …………...……………….. 168

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List of figures

Figure 5.37

Surface and sub-surface vertical displacements above Tunnel 2 when considering piggyback 4.0m diameter tunnels at depths of 16.4m and 33.4mV1 & V2 = 1.3%); lower tunnel constructed first …...…………………. 169

Figure 5.38

Surface and sub-surface horizontal displacements above Tunnel 2 when considering piggyback 4.0m diameter tunnels at depths of 16.4m and 33.4m (V1 & V2 = 1.3%); lower tunnel constructed first …...……………………….

Figure 5.39

170

Surface and sub-surface vertical displacements above Tunnel 2 when considering piggyback 9.0m diameter tunnels at depths of 16.4m and 33.4m (V1 & V2 = 1.3%); upper tunnel constructed first …...………………………. 171

Figure 5.40

Surface and sub-surface horizontal displacements above Tunnel 2 when considering piggyback 9.0m diameter tunnels at depths of 16.4m and 33.4m (V1 & V2 = 1.3%); upper tunnel constructed first .…...………………………. 172

Figure 5.41

Surface and sub-surface vertical displacements above Tunnel 2 when considering piggyback 4.0m diameter tunnels at depths of 16.4m and 33.4m (V1 & V2 = 1.3%); upper tunnel constructed first …...……………………….

Figure 5.42

173

Surface and sub-surface horizontal displacements above Tunnel 2 when considering piggyback 4.0m diameter tunnels at depths of 16.4m and 33.4m (V1 & V2 = 1.3%); upper tunnel constructed first …...……………………….

Figure 5.43

174

Deviation in position of Umax due to the construction of piggyback tunnels at depths of 33.4m depth and 16.4m with a volume loss of 1.3%. For 4.0m and 9.0m diameter tunnels and changing construction sequence ..……………….

Figure 5.44

175

Displacement of upper tunnel lining (Tunnel 2) when considering the construction of 9.0m diameter piggyback tunnels at depths of 16.4m and 33.4 m (lower tunnel driven first) …...………………………………………..

175

Surface and sub-surface vertical displacements above Tunnel 2 when Figure 5.45

considering offset 9.0m diameter tunnels at depths of 17.4m and 30.9m with a centre-to-centre spacing of 20.0m (V1 & V2 = 1.3%), lower tunnel constructed first …...……………………….…...…………………………….. 176 Surface and sub-surface horizontal displacements above Tunnel 2 when

Figure 5.46

considering offset 9.0m diameter tunnels at depths of 17.4m and 30.9m with a centre-to-centre spacing of 20.0m (V1 & V2 = 1.3%), lower tunnel constructed first…...……………………….…...……………………………... 177 Surface and sub-surface vertical displacements above Tunnel 2 when

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List of figures

Figure 5.47

considering offset 9.0m diameter tunnels at depths of 17.4m and 30.9m and a centre-to-centre spacing of 30.0m (V1 & V2 = 1.3%), lower tunnel constructed first…...……………………….…...……………………………... 178 Surface and sub-surface horizontal displacements above Tunnel 2 when

Figure 5.48

considering offset 9.0m diameter tunnels at depths of 17.4m and 30.9m and a centre-to-centre spacing of 30.0m (V1 & V2 = 1.3%), lower tunnel constructed first…...……………………….…...……………………………... 179 Surface and sub-surface vertical displacements above Tunnel 2 when

Figure 5.49

considering offset 9.0m diameter tunnels at depths of 17.4m and 30.9m and a centre-to-centre spacing of 50.0m (V1 & V2 = 1.3%), lower tunnel constructed first…...……………………….…...……………………………... 180

Figure 5.50

Surface and sub-surface horizontal displacements above Tunnel 2 when considering offset 9.0m diameter tunnels at depths of 17.4m and 30.9m and a centre-to-centre spacing of 50.0m (V1 & V2 = 1.3%), lower tunnel constructed first…...……………………….…...……………………………... 181

Figure 5.51

Eccentricity of Wmax when constructing offset 9.0m diameter tunnels with various centre-to-centre spacings at depths of 17.4m and 30.9m (V1 & V2 = 1.3%), lower tunnel constructed first……….…...……………………………. 182

Figure 5.52

Deviation of Umax and U=0 when constructing offset 9.0m diameter tunnels at depths of 17.4m and 30.9m with various centre-to-centre spacings (V1 & V2 = 1.3%), lower tunnel constructed first...…...…………………………….

Figure 5.53

182

Surface and sub-surface vertical displacements above Tunnel 2 when considering offset 9.0m diameter tunnels at depths of 17.4m and 30.9m and a centre-to-centre spacing of 20.0m (V1 & V2 = 1.3%), upper tunnel constructed first...…...………………………………………………………… 183

Figure 5.54

Surface and sub-surface horizontal displacements above Tunnel 2 when considering offset 9.0m diameter tunnels at depths of 17.4m and 30.9m and a centre-to-centre spacing of 20.0m (V1 & V2 = 1.3%), upper tunnel constructed first...…...………………………………………………………… 184

Figure 5.55


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List of figures

Figure 5.56

Surface and sub-surface horizontal displacements above Tunnel 2 when considering offset 9.0m diameter tunnels at depths of 17.4m and 30.9m and a centre-to-centre spacing of 30.0m (V1 & V2 = 1.3%), upper tunnel constructed first ...…...………………………………………………………

Figure 5.57

186


Figure 5.58

Surface and sub-surface horizontal displacements above Tunnel 2 when considering offset 9.0m diameter tunnels at depths of 17.4m and 30.9m and a centre-to-centre spacing of 50.0m (V1 & V2 = 1.3%), upper tunnel constructed first...…...………………………………………………………… 188

Figure 6.1

Geometry of triple tunnel analyses showing the construction sequence (Construction Sequence1). …………………………………………………… 197

Figure 6.2

Geometry of triple tunnel analyses showing an alternative construction sequence. (Construction Sequence 2). ………………………………………..

Figure 6.3

Geometry of triple tunnel analyses showing the construction sequence employed for the Heathrow Express Tunnels (Construction Sequence 3)……

Figure 6.4

197 197

Finite element Mesh for side by side 9m and 4m diameter triple tunnels analysis (Z = 26.0m shown). …………………………………………………. 198

Figure 6.5

Surface and sub-surface vertical displacements due to the construction of Tunnel 2, using Construction Sequence 1 with a 9.0m diameter tunnel at 26.0m depth (V1 = V2 = 1.3%).……………………………………………….. 199

Figure 6.6

Surface and sub-surface horizontal displacements due to the construction of Tunnel 2, using Construction Sequence 1 with a 9.0m diameter tunnel at 26.0m depth (V1 = V2 = 1.3%).……………………………………………….. 200

Figure 6.7

Surface and sub-surface vertical displacements due to the construction of Tunnel 3, using Construction Sequence 1 with a 9.0m diameter tunnel at 26.0m depth (V1, V2 and V3 = 1.3%).…………………………………………

Figure 6.8

201

Surface and sub-surface vertical displacements due to the construction of Tunnel 3, using Construction Sequence 1 with a 9.0m diameter tunnel at 26.0m depth (V1, V2 and V3 = 1.3%).…………………………………………

Figure 6.9

Surface and sub-surface vertical displacements due to the construction of

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List of figures

Tunnel 2, using Construction Sequence 2 with a 9.0m diameter tunnel at 26.0m depth (V1 = V2 = 1.3%).………………………………………………. Figure 6.10

203

Surface and sub-surface horizontal displacements due to the construction of Tunnel 2, using Construction Sequence 2 with a 9.0m diameter tunnel at 26.0m depth (V1 = V2 = 1.3%).……………………………………………….

Figure 6.11

204

Surface and sub-surface vertical displacements due to the construction of Tunnel 3, using construction sequence 2 with a 9.0m diameter tunnel at 26.0m depth. (V1, V2 and V2 = 1.3%).………………………………………

Figure 6.12

205

Surface and sub-surface horizontal displacements due to the construction of Tunnel 3, using construction sequence 2 with a 9.0m diameter tunnel at 26.0m depth. (V1, V2 and V2 = 1.3%).………………………………………

Figure 6.13

206

Relative changes in surface settlement above Tunnel 2 and Tunnel 3 when constructing 9.0m diameter triple tunnels at 26.0m below ground level using Construction Sequence 1. (V1, V2, V3 = 1.3%)……………………………….. 207

Figure 6.14

Relative changes in surface settlement above Tunnel 2 and Tunnel 3 when constructing 9.0m diameter triple tunnels at 26.0m below ground level using Construction Sequence 2. (V1, V2, V3 = 1.3%)……………………………….. 207

Figure 6.15

Sub-surface displacements above Tunnel 2 (Upline) at 13.0m below ground surface (Construction Sequence 3) …………………………………………...

Figure 6.16

Sub-surface displacements above Tunnel 3 (Downline) at 13.0m below ground surface (Construction Sequence 3) …………………………………...

Figure 6.17

208 208

Sub-surface vertical displacements caused by the construction of triple 9.0m diameter tunnels as part of the Heathrow Express project recorded at 13.0m below ground level (Inside the Inner Piccadilly Line tunnel). (Modified after Cooper and Chapman,1998) (a) Total settlement profile after each stage of construction………………….. 209 (b) Contribution of Upline, (Concourse displacements superimposed)………. 209 (c) Contribution of Dowline (Concourse displacements superimposed)……... 209

Figure 7.1

Consolidation tank details………………………………...…………………... 234

Figure 7.2

Sections of tank showing taps and instrumentation…………………………... 235

Figure 7.3

Hydraulic and pneumatic system for consolidation…………………………... 236

Figure 7.4

Air pressure control unit…………………………............................................

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List of figures

Figure 7.5

Spencer Franklin booster…………………………...........................................

237

Figure 7.6

Heypac power booster…………………………...............................................

237

Figure 7.7

Jacking system…………………………...........................................................

237

Figure 7.8

Trial of tunneling machine in test tank…………………………......................

237

Figure 7.9

Trial of concrete corer (machine Type 1) ………………………….................

237

Figure 7.10

Resulting heave from Type 1 tunneling machine…………………………......

238

Figure 7.11

Dispersion of lubrication on Type 2 tunneling machine……………………… 238

Figure 7.12

Unsupported tunnel after using Type 2 tunneling machine…………………...

Figure 7.13

Type 3 tunneling machine………………………….......................................... 238

Figure 7.14

Front cutting blade (Type 4) …………………….............................................

Figure 7.15

Water jet system (Type 4) ……………………................................................. 238

Figure 7.16

Drilling system and procedure………………...................................................

Figure 7.17

Monitoring Equipment………………............................................................... 240

Figure 7.18

Position of camera equipment, LVDTs and dial gauges.................................... 240

Figure 7.19

Bottom tank section (no side walls or top extension section) ........................... 241

Figure 7.20

Instrumentation and Vyon covered drainage holes............................................ 241

Figure 7.21

Layer of Leighton Buzzard sand........................................................................ 241

Figure 7.22

Layer of Vyon sheet over sand layer.................................................................

241

Figure 7.23

Lifting mixed clay into place.............................................................................

241

Figure 7.24

Tank filled with clay showing top layer of Vyon and sand…………………...

241

Figure 7.25

Day 1 - loading plate and load cell in place (prior to consolidation)…………. 242

Figure 7.26

Side restraints for Tank...................................................................................... 242

Figure 7.27

Day 23 - After consolidation (water removed from top plate)………………..

242

Figure 7.28

Extension section being removed......................................................................

242

Figure 7.29

Loading plate removed exposing sand layer...................................................... 242

Figure 7.30

Sand removed exposing Vyon sheet..................................................................

242

Figure 7.31

Top of clay sample being trimmed....................................................................

243

Figure 7.32

Cover plate in place...........................................................................................

243

Figure 7.33

Tank lifted out of reaction frame (prior to turning) ..........................................

243

Figure 7.34

Tank turned on side. Side restraints and perspex face removed........................

243

Figure 7.35

Marker beads being positioned in clay surface.................................................. 243

Figure 7.36

Front face: Tank back in reaction frame. LVDTs and camera track in place… 243

Figure 7.37

Rear face: dial gauges in place........................................................................... 244

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List of figures

Figure 7.38

Tunneling machine in position..........................................................................

244

Figure 7.39

Prior to drilling first 100mm (Tunnel 2 shown) ...............................................

244

Figure 7.40

Tunneling 450mm through clay (spoil removal shown) ................................... 244

Figure 7.41

Tunnel after jacking complete(Tunnel 2 shown) ..............................................

244

Figure 7.42

Shear vane testing of clay..................................................................................

245

Figure 7.43

Consolidation results (Test 2) ...........................................................................

245

Figure 7.44

Undrained shear strength and corresponding moisture content......................... 245

Figure 7.45

Target selection method for monitoring displacements..................................... 246

Figure 7.46

Displacement above Tunnel 1 and Tunnel 2...................................................... 247

Figure 8.1

Possible changes to trough width for a second tunnel.......................................

Figure 8.2

Subsequent settlement profile above a second tunnel (Vl constant)…………. 268

Figure 8.3

Subsequent settlement profile above a second tunnel (Wmax constant)……….

Figure 8.4

Changes to the settlement profile caused by changes in volume loss above a second tunnel...................................................... ..............................................

268 269 269

Figure 8.5

Role of vertical placement of Vector focus above a second tunnel………...… 270

Figure 8.6

Subsequent settlement profile above a second tunnel for different vector focus .................................................................................................................. 270

Figure 8.7

Modification factors for settlement above a second tunnel...............................

271

Figure 8.8

Modification factors for the settlement above a second tunnel.........................

272

Figure 8.9

Horizontal displacement profile caused by changing Xf (Zf constant)………..

272

Figure 8.10

Settlement predictions at 10m centre-to-centre spacing ...................................

273

Figure 8.11

Settlement predictions at 20m centre-to-centre spacing....................................

273

Figure 8.12

Settlement predictions at 30m centre-to-centre spacing...................................

274

Figure 8.13

Settlement predictions at 40m centre-to-centre spacing...................................

274

Figure 8.14

Eccentricity of W max with tunnel separation................................................... 275

Figure 8.15

Modified horizontal surface displacements for a 4.0m diameter tunnel at 20m spacing...............................................................................................................

275

Figure 8.16

Volume losses into second tunnel using modification factors………………... 276

Figure 8.17

Comparing the use of different modification factors to field data and FE data. 276

Figure 8.18

Modified sub-surface settlements from 5m to 20m below ground level for twin 4m tunnels at 20m centre spacing.............................................................. 277

Figure 8.19

Eccentricity of Wmax with depth for Tunnel 2 (20m spacing)………………...

Figure 8.20

Sub-surface settlement predictions for Tunnel 1 and Tunnel 2 of the

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List of figures

Heathrow Express tunnels U.K. (Case history A)……………………………. Figure 8.21

278

Overlapping bounds to movement and modification factor for Tunnel 1 and Tunnel 2 of the Heathrow Express tunnels U.K. (Case history A)…………… 279

Figure 8.22

Sub-surface settlement predictions for Tunnel 3 of the Heathrow Express tunnels U.K. (Case history A)………………………………………..

Figure 8.23

279

Overlapping bounds to movement and modification factor for Tunnel 1 and Tunnel 3 of the Heathrow Express tunnels U.K. (Case history A)…………… 280

Figure 8.24

Total sub-surface settlement predictions for tunnels on the Heathrow Express tunnels, U.K. (Case history A) .......................................................................... 280

Figure 8.25

Surface vertical and horizontal ground displacement predictions for Lafayette Park, U.S.A (Case history B) ......................................................

Figure 8.26

281

Surface vertical and horizontal ground displacement predictions for St James Park, U.K. (Case history C) ..............................................................................

281

Figure 8.27

Piggy back trough deviation .............................................................................

282

Figure 8.28

Displacements above Tunnel 1 (Greenfield) compared to those above Tunnel 2 (Predicted) ...................................................................................................... 282

Figure 8.29

Predicting displacements above Tunnel 1…………………………………….

283

Figure 8.30

Predicting displacements above Tunnel 2 (side-by-side alignment)………….

284

Figure 8.31

Predicting displacements above Tunnel 2 (offset alignment)………………… 285

Figure 9.1

Three dimensional mesh constructed within ABAQUS………………………

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Notation

NOTATION A B C D Cu Eu G H K K1 K2 Kn L1 L2 LF N Ncr T U Wmax V V1 V2 Vb Vf Vg VL Vn Vp Vr VS Vt Vy W W1 W2 Wc Wmax X Xf Y Z Zn Zo Zt Zf

Scaling parameter used in Jardine soil model Scaling parameter used in Jardine soil model Scaling parameter used in Jardine soil model Tunnel diameter (m) Undrained shear strength (kPa) Undrained elastic modulus (kPa) Cumulative distribution function Distance between vector focus and plane of interest (m) Constant relating i to Z (Trough width parameter) Trough width parameter for Tunnel 1 Trough width parameter for Tunnel 2 (separate values for near and remote limb) Trough width parameter for layer n Height of layer 1 (m) Height of layer 2 (m) Load Factor Stability ratios Critical stability ratio at collapse Half trough with (m) Horizontal displacement in x direction (mm) Maximum horizontal displacement (mm) Horizontal displacement in y direction (mm) Volume loss for Tunnel 1 Volume loss for Tunnel 2 Shield loss (m3/m) Face loss (m3/m) Losses after grouting (m3/m) Volume loss as a percentage of tunnel face volume per metre length (m3/m) Volume of near limb (m3/m) Loss attributable to mechanics of shield driving (m3/m) Volume of remote limb (m3/m) Volume of surface settlement trough per m length (m3/m) Volume loss at tunnel (m3/m) Loss attributable to mechanics of shield driving (m3/m) Vertical displacement (mm) Vertical displacement for Tunnel 1(mm) Vertical displacement for Tunnel 2 (mm) Vertical displacement at tunnel crown (mm) Maximum vertical displacement (mm) Transverse plane X coordinate of vector focus (m) Longitudinal plane Vertical plane Height of layer n (m) Depth to tunnel axis (m) Height above tunnel (m) Z Coordinate of vector focus(m)

c'

Cohesion

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Notation

c d' i io in ir ix iy n x xf y

Empirical constant used in Jardine soil model Pillar width – distance between centrelines of two tunnels (m) Trough width parameter (m) Trough width parameter at surface (m) Distance to the point of Umax on near limb (m) Distance to the point of Umax on remote limb (m) Distance to point of inflection in X plane (m) Distance to point of inflection in Y plane (m) Constant dependent on soil type Transverse distance in X plane (m) Transverse distance from point of vector focus in X plane (m) Longitudinal distance in Y plane (m)

dW dx d 2W dx 2

Ground slope transverse to tunnel

α β γ εa ε σs σT ω Ø χ ∆/l

Empirical constant used in Jardine soil model Angle of draw Empirical constant used in Jardine soil model Strains within elastic range bound by maximum and minimum values Ground strain Surface surcharge pressure (kPa) Tunnel support pressure (kPa) Angle between axis level and line defining full trough width Angle of internal shearing resistance (90- ω) Deflection ratio

Ground curvature transverse to tunnel

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Chapter 1- Introduction

- 1Chapter One INTRODUCTION

1.1 GENERAL

In the Oxford English Dictionary the word ‘tunnel’ is described as an ‘underground passage’. Whilst this definition in its briefest sense is true, it very much underplays the various roles which tunnels have in our modern society. These tunnels can be used as corridors for road and rail networks, utilities and pedestrian movement. There are currently many styles of tunnel design in existence (e.g. oval, circular or square) which have been constructed over many years using various tunnelling techniques. Historically the earliest tunnels were designed to convey clean and dirty water to and from the major cities. In Egypt, Greece and Rome some of these tunnels are still used for the same purpose today. Many of these early ancient examples, based on the design of the arch, were constructed in hard rock by hand mining methods using temporary timber supports. This method of support provided little safety to the workers inside the tunnels and was the cause of catastrophic collapses where many lives were lost. Needless to say the method of tunnel construction remained in place for many centuries until Brunel, one of the pioneering engineers of the 19th Century, invented the tunnelling shield in 1819. The shield was originally conceived in order to prevent the ingress of material into the tunnel face whilst constructing a tunnel under the River Thames, where soil conditions were poor. The shield was supposed to reduce ground movements and provide greater safety for the workers within, although collapses still occurred (due to the amount overlying silt and water) during the tunnel’s construction between 1825 and 1843. The rail line housed in this tunnel currently forms part of the massive London Underground network and is still in daily use. This method of tunnel construction was modified slightly during its use in the 20th century and has proved to be so successful that it is still in use today. The method is currently referred to as an ‘open-faced’ method, due to the fact that the face is exposed during construction. The advancement in tunnel design during the 20th Century led to the replacement of arched roof

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tunnels with perfectly circular tunnel linings. These liners proved to be a very efficient way for carrying soil loading. Over the last thirty years greater volumes of people, caused by an expanding global economy, are travelling in congested city centres. This demand for space has necessitated the movement of the transport infrastructure below ground and has seen the birth and subsequent growth of many modern underground Metro systems. At the dawn of this new millennium the increasing competition for space below ground in modern urbanised cities is almost as large as that above. With many new tunnel and sewer networks being introduced many are being constructed within the vicinity of existing structures and services. With such a boom of tunnelling projects the modern day engineer has a much-improved knowledge and understanding of the possible ground movements that can occur above single tunnels. The art of tunnelling has undergone many innovative changes from the early tunnelling days of Brunel. Unlike Brunel, the modern engineer can refer to years of tunnelling experience and a large dossier of tunnelling examples when designing new tunnels with various sizes, depths, construction methods and soil type. This improved knowledge has enabled the engineer to assess all possible risks and minimise them in order to avoid damage to existing overlying buried structures. The main risk to these structures comes in the form of ground movements (vertical and horizontal displacements) which must be accurately predicted in order that they and/or their effects may be minimised. There are two ways to reduce these ground movements and hence reduce the risk to buildings. The first is minimisation at the face and the second is compensation in the ground as the settlements occur. Reduction of movements at the face can be achieved through improvement in tunnelling method (i.e tunnelling machine or the use of reinforcement methods for the soil at the face) and tunnel liner design. An example of a modern innovation in the tunnelling method has been the Earth Pressure Balance Machine (EPBM), which balances the forces at the tunnel face between the soil and the machine and hence reduces ground movements. Over the last thirty years the use of spayed concrete, immediately after excavation in overconsolidated clay, known as the New Austrian Tunnelling Method (NATM), has also helped in reducing ground movements. The second approach to reducing ground movements as they occur is by compensation grouting (Harris et al, 2000). It is common for important overlying buildings (e.g. Big Ben in the U.K.) to be monitored for movements as tunnel construction occurs below. When movement becomes apparent (above a specified tolerance) concrete is pumped into the soil above the tunnel and below the building

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in order to compensate for these movements. For many projects undertaken today some or all of the minimisation methods referred to above are now adopted. These advances in tunnelling method have undoubtedly helped to minimise the ground movements occurring due to soft ground tunnelling operations. However, when considering a new tunnel construction the assessment of risk to existing overlying structures or sub-surface structures is only as accurate as the prediction of ground movements that are made. The shortterm behaviour of the soil above single tunnels in greenfield conditions is currently well understood. Semi-empirical methods exist for the prediction of surface and sub-surface ground movements that occur above these single tunnels, which have been used, with good accuracy, over many years. These methods have also been extended to describe the short-term behaviour of twin tunnels when they are driven simultaneously. The total ground movements in this case can easily be predicted by superimposing the results for each individual tunnel. However, when a time delay is expected between the construction of closely spaced twintunnels the settlement profile above the second tunnel has been found to change. For this reason the prime aim of the thesis is to: ‘improve the understanding of surface and sub-surface movements above twin tunnel constructions and put in place a framework for improving the current semi-empirical predictive methods for estimating ground movements’. 1.2 SCOPE In order to achieve this aim, the scope of the project has, by necessity, been relatively broad. Due to the time constraints of the project it has been restricted to the behaviour of twin tunnels in soft ground. For this project the soft ground is assumed to be London Clay, a stiff clay common to many tunnels constructed on the London Underground network in the U.K. The improvements to empirical predictions are based upon the results of finite element analyses undertaken at the University of Birmingham. The analyses were conducted using the ABAQUS finite element package and considering a non-linear small strain stiffness pre yield soil model first proposed by Jardine et al (1986). The ground movements were created within the package using a ‘modified gap parameter’, which gave the user full control over the volume loss, a factor that becomes a variable in most other analyses. Through numerical analyses the thesis investigates the changes in settlement profile above a second tunnel when considering three different types of alignment:

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Chapter 1- Introduction 

Side-by-side



Piggyback



Offset

- 4-

The thesis also considers the changing effect on the settlement profile above a second and third tunnel when constructing triple tunnels in a side-by-side alignment. The effect of changing tunnel spacing, construction sequence and tunnel diameter are also considered. The thesis concludes by showing how the improved prediction of ground movements above twin/triple tunnels can be made through the use of parameter selection and a modification factor. Guidance is given on the use of a modification factor which was derived during this research work from the finite element analyses. This thesis also reports on the application of a 1/50 scale laboratory test (conducted under gravity) for modelling the ground movements above twin tunnels in Speswhite Clay. As far as the author is aware this is the first time the construction and subsequent monitoring of twin tunnels has been performed at this scale and without using a centrifuge. Measurable results have been achieved during early trial tests which are encouraging. The resulting displacements do not currently form any part of the improvement to the existing predictive methods. 1.3 LAYOUT The thesis is presented according to the following chapter headings, the content of which is also briefly described below: Chapter 2 describes the current engineering practice for predicting movements above single and twin tunnels in soft ground. A substantial review of the currently available semi-empirical predictive methods for ground movements above single and twin-tunnels is presented. Case history data for both single tunnels and twin tunnels cases are reported and recommendations made. Chapter 3 introduces the concept of the finite element method in relation to modelling tunnel behaviour. The chapter details the theory behind the finite element analysis technique and describes the equilibrium equations which must be solved. The possible methods for modelling tunnelling behaviour using finite elements are compared to the modelling method D.Hunt - 2004


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employed in ABAQUS. The soil constitutive models, soil properties, element selection for liners and soil, and the process of excavation and tunnel construction procedure are all considered. Chapter 4 applies the finite element method discussed in Chapter 4 to the problem of modelling single tunnels in greenfield conditions. This chapter details the ground displacements resulting from a single tunnel construction considering a range of diameters, depths, volume loss and soil conditions. The resulting displacements are compared to he values obtained from empirical predictive methods throughout and recommendations are made accordingly. Chapter 5 details the results from the finite element analyses modelling twin tunnel constructions. The ground displacement above twin side-by-side tunnels, piggyback tunnels and offset tunnels in a homogeneous undrained soil with no overlying structures are presented. The effect of centre-to-centre spacing is considered for the side-by-side and offset tunnels. The effects of changing the volume loss and tunnel diameter are also considered for the side-by-side tunnels. The effect of the tunnel construction sequences are considered for piggyback and offset tunnels, with the effect of tunnel diameter also being considered for the former. Chapter 6 details the results from the finite element analyses modelling triple tunnel constructions. The ground displacements above tunnels in a side-by-side alignment are presented. Previously published field data for the Heathrow Express tunnels and their effects on the Piccadilly Line tunnels at the Central Terminal Area (U.K.) are compared to the results from the finite element analysis. The effect of changing the construction sequence is also examined and results are compared to those obtained for the twin-tunnels. Chapter 7 reports the use of a consolidation tank, constructed during the project for replicating the behaviour above twin 4.0 m diameter tunnels using a 1/50 scale model in the laboratory. The chapter considers the use of an ‘augering’ type tunnelling machine for boring 83mm diameter tunnels in Speswhite clay. The chapter details the consolidation process for preparing the sample, the testing stage, all the monitoring equipment involved, difficulties faced and finally the results obtained. Due to the time constraints it was only possible to conduct two tests in a heavily overconsolidated sample, which resulted in surface and subD.Hunt - 2004


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surface displacements being produced in the clay. Many important lessons have been learnt from this work, which have been discussed in this thesis and which have been used to facilitate continued research work in this area which is currently underway at the University of Birmingham,. Chapter 8 draws on the results of Chapters 4, 5 and 6. Methods of modifying greenfield settlement profiles above a second tunnel by the use of parameter selection and a modification factor are introduced. The application of the method is considered in relation to available case history data from the Heathrow Express construction (U.K.), the Jubilee Line Extension construction at St James’ Park (U.K.) and the Washington Metro construction at Lafayette Park (U.S.A.). Chapter 9 draws together all the conclusions presented in the various chapters in the thesis. Recommendations are made for design practice based on the findings of this research and the possible scope for future investigations.

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Chapter 2- Current practice for predicting movements above single and twin tunnels

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Chapter Two CURRENT PRACTICE FOR PREDICTING GROUND MOVEMENTS ABOVE SINGLE AND TWIN TUNNELS

2.1 INTRODUCTION The construction of bored tunnels in soft ground causes ground movements. These movements, both horizontal and vertical, have been reported by many authors for different tunnelling situations. The most widely cited papers have been produced by Peck (1969), Cording and Hansmire (1975), Clough and Schmidt (1981), Ward and Pender (1981), O'Reilly and New (1982), Attewell et al (1986), Rankin (1988), Uriel and Sagaseta (1989), Cording (1991), New and O'Reilly (1991), Fujita (1987, 1994), Mair (1996) and Mair and Taylor (1997). These authors have shown that the ground movements above tunnels are influenced by many factors including: tunnel diameter, tunnel depth, type of construction method and soil type. This chapter details some of these factors as they affect ground movements due to tunnelling in soft soils. 2.2 VOLUME LOSS 2.2.1 Definition and Sources of Volume Loss The magnitude of the ground displacements which occur above a tunnel of any diameter can be related to a parameter called the ‘volume loss’. The volume loss, Vt, (sometimes referred to as ground loss) is the amount of ground lost in the region close to the tunnel due to the construction process. Cording and Hansmire (1975) considered these losses to be divided into four stages: (A) face loss, (B) shield loss, (C) losses due to erection of the shield and (D) time dependent losses. Methods of calculating each component of the ground loss caused by A-D have been reported by Attewell and Boden (1971) Attewell and Farmer (1974a, b, 1975) and Attewell et al (1978), with further research being reported by Cording et al (1978). Attewell et al (1986) reported the findings of this earlier work, quoting formulae for each D.Hunt - 2004


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stage of lost ground. Equation 2.1 shows how the total ground loss can be calculated from its constitutive parts. Exact methods of calculating each component given below as reported by various authors, are shown in Attewell et al (1986). Vt = Vf + Vb + Vp + Vy + Vu + Vg where

Vf

=

face loss

Vb

=

shield loss (radial)

Vy ,Vp =

Eqn 2.1

losses attributable to mechanics of shield driving

Vu

=

losses after lining erection

Vg

=

losses after grouting

This method is not precise because that the components are not quantitative, being based upon workmanship and tunnelling method. The value of volume loss is usually predicted by engineering judgement and by comparison with previous field data. Figure 2.1 shows the five main components of ground movement associated with shield tunnelling as reported by Cording (1991). The various components are described below after Mair and Taylor (1997): 1.

Deformation of the ground towards the face.

2.

Passage of the shield.

3.

Tail void.

4.

Deflection of the lining.

5.

Consolidation.

Ward (1969) and Mair and Taylor (1996) have highlighted the importance of Component 1 for open-faced tunnelling in clays. This component results from stress relief and can be negligible if the face pressure is carefully controlled when using closed-face methods. Component 2, can cause appreciable losses due to the presence of an over-cutting bead, and if steering problems with the shield (i.e. ploughing, pitching and yawing) occur (Peck 1969). Component 3 is caused by the existence of a gap between the tail skin of the shield and the lining which can cause further radial ground movements to occur into this gap. Minimisation of this component is achieved by expanding the segmental lining as quickly as possible or filling with grout (referred to as tail void grouting). Component 4 is the smallest component of volume loss in both segmental and Sprayed Concrete Liners (SCL) which occurs as ground D.Hunt - 2004


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loading develops. Component 5 is important in soft clays where additional ground movements occur as pore water pressures in the ground change to their long-term equilibrium values. In cases where there is no tunnelling shield for example when SCL’s are used, components 1, 4 and 5 are still applicable (Mair and Taylor, 1997). Whatever the soil type, it is convenient to express the volume loss of the surface settlement trough (VS) as a percentage fraction of the excavated area of the tunnel (Vl). Equation 2.2 shows the volume loss for a circular tunnel.  D 2 Vs  Vl   4 

   

Eqn 2.2

where D is the tunnel diameter. The value of VS is dependent on the soil conditions and the type of tunnelling machine used. Equation 2.2 was first reported by the British Research Establishment (BRE) and the Transport and Road Research Laboratory (TRRL) and provides a basis on which to relate ground movements in both clays and sands. When tunnelling in clays, ground movements usually occur under undrained (constant volume) conditions and therefore it is assumed that VS = Vt. For simplicity Vt, (defined in Equation 2.1), is assumed to be the difference between the volume per metre length of the tunnel and the volume per metre length of the liner, i.e. the area of the gap shown in Figure 2.2. 2.2.2 Typical Volume Losses for Clays O’Reilly and New (1982) reported volume losses of 1.0-1.4% for open-faced shield driven tunnels in London clay.

New and Bowers (1994) reported values of 1.0-1.3% for the

Heathrow Express trial tunnels in London clay. Barakat (1996) reported volume losses in the range of 0.7-1.6% for a tunnel driven using the open-faced method in London clay. Mair (1996) reported on several case histories and concluded that losses associated with open face methods in London Clay were in the range of 1.0-2.0% compared to 0.5-1.5% when using sprayed concrete, also known as the New Austrian Tunnelling Method (NATM). Broms and Shirlaw (1989) have reported volume losses of < 1.0% for closed-face tunnelling through soft clay using an Earth Pressure Balance Machine (EPBM). The reduction in volume loss is due D.Hunt - 2004


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to the increased stability obtained from the use of an EPBM since the EPBM equalises the pressure at the cutting face to the earth pressure. Mair and Taylor (1996) reviewed several papers and reported typical losses for an EPBM or slurry shield in soft clay in the range 1.0-2.0%. The magnitude of the volume loss is dependent on the type of tunnelling machine and the quality of workmanship. 2.2.3 Relationship between Stability and Volume loss Broms and Bennermark (1967), drawing on earlier work of Bjerrum and Eide (1956) postulated the idea of a stability ratio (N). The stability ratio compares the overburden stress to the undrained shear strength in the form of a ratio as shown in Equation 2.3.

N

where

 s  Z   T Cu

s

=

surface surcharge



=

unit weight of soil

Z

=

depth to tunnel axis (C + D/2, D = diameter, C = cover)

T

=

tunnel support pressure

su

=

undrained shear strength at depth Z

Eqn 2.3

Broms and Bennermark performed extrusion tests on a clay face supported by a vertical retaining wall with a hole. Clay extrusion occurred at a stability ratio of around 6-8 while similar stability ratios were reported for several tunnelling projects at the time (Peck 1969, Moretto 1969 and Kuesel 1972). Attewell and Boden (1971) extended this concept to include intrusions into a tunnel face. These authors reported no measurable intrusions for stability ratios less than 4.5, for typical cover depth to tunnel diameter (C/D) ratios (e.g. 1-6). Ward and Pender (1981) considered the soil to be elastic at stability ratio of 1.0, whereas Lake et al (1992) considered N=2.0 to be elastic and the face stable. Lake et al (1993) reported local plastic yielding for ratios of between 2.0–4.0 and general plastic yielding for ratios between 4.0-6.0. Kimura and Mair (1981) (based on earlier work by Mair, 1979) found that the critical stability number, Ncr (i.e. the value of stability ratio at collapse) was dependent on the tunnel geometry, presented in terms of the C/D ratio and P/D ratio (where P is the distance from face D.Hunt - 2004

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of tunnel heading to structural lining) when using 2D and 3D centrifuge models. Glossop (1977) first proposed a simple relationship between stability (N) and volume loss (VL): VL = 1.33 N – 1.4

Eqn 2.4

Mitchell (1983) provided an alternative method of relating the two parameters as:

C VL   u  Eu

  Exp 0.5 N   

Eqn 2.5

where su/Eu is the ratio of undrained shear strength to undrained stiffness. Kimura and Mair (1981) developed the concept of a Load Factor (LF), essentially a reciprocal of the factor of safety to relate the stability of similar shallow tunnels under different working conditions, as shown in Equation 2.6.

 N LF    N cr

   

Eqn 2.6

where N is the stability ratio under working conditions and Ncr is the stability factor at failure. Both Equations 2.4 and 2.5 use N, which gives no consideration to the tunnel diameter, whereas Mair et al (1981) found that VL was better related to LF, which is influenced by the tunnel diameter (Ncr, is dependent on C/D). Macklin (1999) proposed an alternative relationship: VL  0.23 exp 4.4(LF)

Eqn 2.7 Equation 2.7 was based on a large amount of case history data which have been plotted in Figure 2.3. The data appear to lie within a distinct range enclosed by the upper and lower bound lines. The method was used by Bloodworth and Macklin (2000), who obtained good correspondence between actual and predicted volume losses for reported case history data above a 2.44m diameter tunnel constructed entirely in London Clay under Longford Street (London, U.K.). D.Hunt - 2004


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2.3 SURFACE DISPLACEMENTS 2.3.1 Modelling the Settlement Profile Transverse to a Single Tunnel Several authors have tried to model accurately the shape of the surface settlement trough above a single tunnel. One of the first authors was Litwiniszyn (1956) who proposed a model for the application of stochastic processes to the mechanics of loose bodies. In the model the ground was represented by an assemblage of stacked discs as shown in Figure 2.4. Ground movement was caused by removal of a disc, which caused an inward movement towards the opening analogous to the tunnel volume loss. Martos (1958), based on field observations of settlements above mine openings, Sweat and Bognadof (1965), Schmidt (1969), Peck (1969) and subsequently many other authors, have shown that the transverse settlement trough, immediately following tunnel construction, can be well-described by a Gaussian distribution curve as:  - x2 W  Wmax exp   2i 2 

where

   

W

=

Settlement

W max

=

maximum settlement on the tunnel centreline

x

=

horizontal distance from the tunnel centreline

i

=

trough width parameter (see Section 2.4).

Eqn 2.8

Equation 2.8 was derived by Attewell and Woodman (1982) assuming a point source of loss at the tunnel axis (x = 0, y = 0). The transverse settlement trough is shown in Figure 2.5. The general shape of the curve is independent of tunnel diameter and depth. Celestino et al (2000) reported an alternative method of predicting the settlement profile above a single tunnel in stiff clay that was capable of accounting for tunnel diameter and tunnel depth (Equation 2.9).

W  Wmax

1  X   1  a   

b

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Eqn 2.9


-13-

where, ‘ a ’ was described by a / D = 0.39 (Z/D) + 0.31, ‘b’ ranged from 2.0-2.8 for stiff clays and the other symbols have their usual meaning. The parameter ‘ a ’ controls the trough width and parameter ‘b’ controls the settlement shape. New and Bowers (1994) reported an alternative method of predicting the shape of the transverse settlement profile. The method was based on the exp function and the erf (x) function reported by New and O’Reilly (1991). Here it was assumed that the ground loss occurred at a linear translating point at the invert of the excavation at a constant rate and at constant volume. New and Bowers extended this concept to include a ribbon-shaped zone of ground loss. The method was shown to improve the prediction of sub-surface ground movements near to the tunnel (i.e. within one diameter). 2.3.2 Relationship between Wmax and Volume Loss The volume loss is the cause of surface settlements and as such relationships exist which relate the two parameters.

Attewell and Farmer (1974a) used a Gaussian profile for

transverse settlements and longitudinal settlement profiles.

By performing a double

integration they found the relationship shown in Equation 2.10.

Vs  i Wmax 2

Eqn 2.10

Combining Equations 2.2, 2.8, 2.14 and 2.24 (assuming K = 0.5 for clays) gives:

Wmax  0.313Vl

D2 i

Eqn 2.11

where D is the tunnel diameter. 2.3.3 Transverse Ground Slope Curvatures and Strains Attewell et al (1982) reported formulae for the slope and curvature of the ground surface derived from Equation 2.8, as shown in Equations 2.12 and 2.13 respectively. W max has been substituted using a rearranged form of Equation 2.10.

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  x2  dW -Vx  3 s exp 2  dx i 2  2i  V

-14-

Eqn 2.12

   x2 Vs  x 2 d 2W   exp  2   1 2 dx 2 i 3 2  i   2i

  

Eqn 2.13

(N.B. The value of i depends on the value of K and Z selected, see Section 2.4.2.) O’Reilly et al (1982) reported the generalised vertical ground strains due to bending shown in Equation 2.14. The positions of maximum strain and curvature have been highlighted in Figure 2.5.

   x2 Vs x  x 2 dW   1 exp  2 w   dx kZ 2 2  i 2   2i

  

Eqn 2.14

2.3.4 Developing a Longitudinal Settlement Profile Attewell and Woodman (1982) and O’Reilly and New (1982) derived equations to describe the movements in a plane parallel to a tunnel, assuming a linear source of loss. These authors recognised that the settlement trough increased in magnitude as the tunnel progressed and proposed that the profile be represented by a cumulative frequency function:

Wx

  x-x   x-x f  Wmax G  s -G       i y   i y

   

Eqn 2.15

where G represents the cumulative distribution function of a standardised normal variable and xi and xf are the initial and final locations of the tunnel face. Figure 2.6 shows the development of the surface settlement trough above and ahead of an advancing heading, in stiff clays (for the case of a single tunnel in 'greenfield’ conditions.) Attewell and Woodman (1982) showed that for tunnels in stiff clay, 30 - 50% of the total settlement occurred behind the tunnel face (i.e. W / Wmax above the tunnel face in the longitudinal direction ranged from 0.3-0.5). These authors reported good agreement between the cumulative profile and case history data (Attewell and Farmer, 1974a & 1974b) when considering longitudinal settlements. Attewell and Hurrell (1985) reported that the best fit between case history data in London clays and the cumulative curve could be found when using a W / Wmax value of 0.5 D.Hunt - 2004


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above the tunnel face. These authors found that for tunnels in sand (Glossop and Farmer 1977 and Glossop 1980), a W / Wmax value of 0.25-0.30 gave the best fit. New and O’Reilly (1991) reported similar values for sands and clays. Corresponding ground strains can be found from Equation 2.15, which are shown in Figure 2.6. 2.4 TROUGH WIDTH PARAMETER 2.4.1 Description and Prediction The trough width parameter (i) is the distance from the tunnel centreline to the point of inflexion of the settlement trough. Peck (1969) suggested that a relationship existed between the tunnel depth, the tunnel diameter and the trough width (i). This relationship was found to be dependent on the ground conditions. The trough width (ix) can be represented by an empirical equation derived by Schmidt (1969) and shown in Equation 2.16.

2i x Z  K o  D D where

n

ix

=

distance from tunnel centreline to point of inflexion

D

=

diameter of excavation

Zo

=

depth from surface to tunnel axis

n

=

constant dependent on soil type

K

=

constant dependent on soil type

Eqn 2.16

Peck (1969) indicated that the value of n should be taken as 0.8 and that K would vary from 1.0, for stiff clays to 1.0-2.0 for sands below the water table. Clough and Schmidt (1981) assumed K=1 and n=0.8 (based on case history results for tunnels in soft ground) and proposed the relationship for i as shown in Equation 2.17:

 D Z  i   o   2  D 

0.8

Eqn 2.17

Cording and Hansmire (1975) reported an alternative method of relating the trough width to depth. The method is an extension of that used previously in mining. The settlement D.Hunt - 2004


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trough is of triangular form shown in Figure 2.7, in which the half trough width (W) is related to the angle of draw (). The relationship is shown as:

W - r  Tan     Z 

Eqn 2.18

The fully developed half trough width is equal to 2.5i, as compared to 3.0i for the half trough width usually associated with the Gaussian curve. This method was found to give good agreement when used by Szechy (1970), for his work on the Budapest Metro. Attewell and Farmer (1974a) assumed the fully developed trough width to be 3i and redefined the method of relating the trough width to the angle () between axis level and a line that rises from the circumference of the tunnel to the fully developed trough width. The full trough width (2T) in this case is given by Equation 2.19. 2T = 2(r cosec  + (C + r)) cot 

Eqn 2.19

where C is the depth to the tunnel axis. Attewell (1978) quoted a similar method for transverse predictions although the half–width of the settlement trough is now related to a new angle Ψ, (i.e. 900 - ) as shown in Figure 2.8. The full trough width (2T) is now given by Equation 2.20: 2T = 2 (r sec Ψ + (C + r)) tan Ψ

Eqn 2.20

where Ψ = 45 - ’/2 (’ represents the angle of friction) and. The full longitudinal profile shown in Figure 2.9 is found from T1 + T2 where: T1 = C tan Ψ

(distance behind the face)

Eqn 2.21

and T2 = (C + D) tan Ψ

(distance in front of face)

Eqn 2.22

where D is the diameter of the tunnel and r is the tunnel radius. The method is only accurate for predicting surface troughs and has not been extended to predict sub-surface trough widths,

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although an extension of the method to incorporate sub-surface movements would be possible. 2.4.2 Clays Various methods exist for predicting the trough width above tunnels in clay. O’Reilly and New (1982) proposed a relationship based on variable regression analyses of case data, revealing the relationship: i = 0.43 Zo + 1.1

Eqn 2.23

The regression lines passed close to the origin and for most practical purposes can be simplified to the form. i

= K Zo

Eqn 2.24

where K is the trough width parameter and Zo has been previously defined (Equation 2.16). For practical purposes the value of K can be taken as 0.5 for tunnels in clays (Figure 2.10). Values can range from 0.4 for stiff clays to 0.7 for soft clays. The value of 0.5 is consistent with findings by Fujita (1981), who reported several case histories in Japan, for different construction methods. O’Reilly and New (1982) found that the trough width parameter was independent of the construction method and had no significant correlation with the tunnel diameter. This has been shown to be the case where the tunnel cover exceeds about one diameter (New and O’Reilly, 1991). Alternative formulations of Equation 2.23 have been offered by Leach (1985) but they tend to be site specific. Equation 2.16 can be used to predict the trough width in clays, for which field data by Schmidt (1981) and research by Fujita (1981) suggest that the value of n applicable to clays is 1.0. Using n=1.0 changes Equation 2.16 to the more familiar linear form used in general practice (i.e. Equation 2.24). The validity of Equation 2.24 was confirmed by Rankin (1988) for a wide range of tunnels and for most clays encountered worldwide. Lake et al (1992) and more recently, Mair and Taylor (1997) have confirmed this for an increased data set. The data for clays presented by Mair and Taylor (1997) is shown in Figure 2.10. The referencing system is the same as that given by Mair and Taylor (1997). Only data for materials that are predominantly clays have been plotted on the figure. D.Hunt - 2004

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2.4.3 Granular Materials Peck (1969), Rankin (1988), Lake et al (1992) and Mair and Taylor (1997) have reported values of i (in metres) for granular material. Values of i were found to lie in the range 0.25 Z - 0.45 Z with an average of 0.35 Z for granular soils. O’Reilly and New (1982) proposed an alternative for predicting the trough width parameter above tunnels in sands based on U.K. case history data: i = 0.28 Z –0.1

Eqn 2.26

The case history data reported for granular soils tend to show more scatter than the data for clays presumably die to the variability in soils considered. O’Reilly and New (1982) suggested a range for K from 0.2-0.3 (for granular materials above the water table). The authors reported the value of K below the watertable to be similar to those in clays, which confirmed the findings of Peck (1969). However, Mair and Taylor (1997) suggest that there appears to be no variations in i for tunnels above and below ground water level, thus contradicting Peck (1969). Cording (1991) noted the width of the surface settlement trough, and hence i, to be related to the magnitude of the settlement. 2.4.4 Mixed Bedding Stratified (layered) soils are not uncommon when tunnelling in the U.K. Notably stiff clays overlain by sand and/or gravel and vice versa. Selby (1988) modified Equations 2.23 and 2.26 to model layered strata. Equation 2.27 is for tunnels in clay overlain by sand and Equation 2.28 is for tunnels in sand overlain by clay. i = 0.43 Z2 + 1.1 + 0.28 Z1

Eqn 2.27

i = 0.28 Z2 – 0.1 + 0.43 Z1

Eqn 2.28

where Z1 refers to the depth of the top layer and Z2 is the depth of the bottom layer. Figure 2.11 shows the proposed behaviour in layered soils. The method was used by Selby (1988) to predict settlements at Heathrow and it gave good agreement with those measured. O’Reilly and New (1991) suggested that the trough width could be predicted from Equation 2.29: D.Hunt - 2004

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i = K1 Z1 + K2 Z2 + …… Kn Zn

Eqn 2.29

although this was not confirmed with case history data. Mair (1993) presented data suggesting that the value of K for clays is not constant for sub-surface regions and hence the current author feels this derivation may be less reliable if used to predict movements in regions close to the tunnel. Ata (1996) modified Equation 2.18, originally proposed by Cording and Hansmire (1975), to predict the trough width for stratified soils on the Cairo Metro. The soil layers comprised fill, clay and silty sand overlying sand. Good agreement was found between predicted and measured trough widths. Figure 2.12 shows how the angle of draw can be used for two layers. The corresponding modified form being given by:

i

r  L1 tan  1  L2 Tan β1 2.5

Eqn 2.30

Grant and Taylor (1996) modelled stratified soils in a centrifuge using reconstituted Kaolinite overlain by sand. The results suggested that a K value of 0.3 for the sand layer was reasonable, but the value of 0.5 used for the clay layer underestimated the trough width. Superposition of movements between the layers is a complicated process, each layer being influenced by the adjacent layer. The research reported by Grant and Taylor (1996) highlighted the relationship between soil stiffness and the length of the trough width, an important consideration for twin tunnel constructions. Further details of these centrifuge tests are reported by Grant (1998). 2.5 SUB-SURFACE DISPLACEMENTS Over the last twenty-five years urban areas have seen constraints placed on available space, hence it has become necessary to construct tunnels under existing foundations, pipelines and tunnels. In this context the sub-surface movements have become as important as the surface movements mentioned in previous sections. Potts (1976) reported on early case histories of sub-surface movements as reported by Cording and Hansmire (1975).

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2.5.1 Variation of ix with Zo O’Reilly and New (1981) having adopted the idea of radial flow, assumed that the width of the zone of deformed ground varied linearly with depth. Mair et al (1993) analysed subsurface data from various tunnel projects in stiff and soft clays, together with centrifuge model test data in soft clays. They showed that sub-surface settlement profiles could be reasonably approximated in the form of a Gaussian distribution and used the linear regression technique on case history data in order to improve the prediction of i at depth. The relationship between surface settlement trough width and depth for tunnels in clay is shown in Equation 2.31.

 i Z  0.175  0.325 1 Zo  Zo

  

Eqn 2.31

Equation 2.31 assumes a vector point of focus at 0.175/0.325 Zo below the tunnel axis. The equation has been shown to compare well with field data (Mair et al, 1993). Grant and Taylor (2000) report that i is over-predicted close to the surface and under-predicted when within 0.5D of the tunnel, when using Equation 2.31. The trough width is dependent on the vector focus point as reported by Grant and Taylor (2000). These authors implied that three points of focus may be more appropriate in estimating the trough width as described in Section 2.6.2. From analogy with Equation 2.24 the trough width parameter (i) can be expressed as: i = K(Zo - Z)

Eqn 2.32

Combining Equations 2.31 and 2.32 gives:

 Z 0.175  0.325 1  Zo K Z 1 Zo

  

Eqn 2.33

Equation 2.33 results in a non-linear variation in K with depth. Dyer et al (1996) used a modified derivation of Equation 2.33 for granular materials. These authors found that this modified equation (not shown here) provided better prediction in regions close to the pipe D.Hunt - 2004

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jacked tunnels, however, they also emphasised that the equation had no dependency on tunnel diameter. Moh and Hwang (1996) proposed an alternative method of calculating sub-surface movements as shown in Equation 2.34. The method originally derived by Moh and Hwang (1993) was used accurately to predict movements on the Taipei Rapid Transit system. The authors compared the results with those obtained by using Equation 2.33. The equation derived by Mair et al (1993) was found to underestimate the trough width at depth. Based on these findings the authors recommended the use of Equation 2.34 in preference to Equation 2.33. Primarily because i was thought to be dependent on D close to the tunnel and this dependency was not included in Equation 2.33.

0.8

 D   Z   Z  Z  i     o   o  2   D   Z o 

m

Eqn 2.34

where m is a constant relating to soil type (m= 0.4 for clays and m = 0.8 for silty clays). Heath and West (1996) proposed a different relationship between sub-surface trough width i at height Zt above the tunnel axis and the trough width i0 at ground surface level (Equation 2.35).

 i   Zt        io   Z o 

0.5

Eqn 2.35

Equation 2.35 assumes a vector focus at the tunnel axis level and was compared to methods by Attewell (1978, Equation 2.20) and Mair et al (1993, Equation 2.33) and also field data from Regents Park, Green Park, Gresham Club and the Wine Vaults in London (U.K.). The method seemed to fit the field data better than the one proposed by Mair et al, although both methods should be confirmed with further field data. Interestingly, the variation in i with depth given by Equation 2.35 would be the same as that given by Equation 2.34 if the value of the constant (m) in the former were taken as 0.5. Figures 2.13 shows the ratio of surface (is) to sub-surface (iss) values of i obtained from Equations 2.32, 2.33, 2.34 and 2.35 with the corresponding values of K being shown in Figure 2.14. Observations have shown that the sub-surface settlement profile changes with depth, in most cases the trough width decreasing. However, monitoring of sub-surface movements close to the tunnel is difficult and depends on the type of tunnel construction D.Hunt - 2004


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procedure being used. Nyren (1998) measured sub-surface movements of a 4.75m diameter tunnel driven 31m below the surface in London Clay. Nyren reported a general decrease in trough width with depth, but an increase was recorded at a distance 2m vertically above the tunnel lining. Alternative predictions of sub-surface displacements based on closed-form solutions can be found in Lognathon and Poulos (1998). 2.5.2 Variation of Wmax with Zo Mair et al (1993) combined Equations 2.15 and 2.31 to obtain a method of finding the variation of W max with depth for London clays (Equation 2.36):

Wmax a  a Zo

1.25Vl  Z 0.175  0.325 1  Zo

  

Eqn 2.36

where a = tunnel radius. The underlying assumption for finding sub-surface settlements is based on the assumption that the volume per unit length of the settlement trough remains unchanged for sub-surface regions. Figure 2.15 shows that the ratio of surface to sub-surface values of i with depth is inversely proportional to the ratio of sub-surface (Wss) to surface (Ws) values of W (i.e. is/iss = Wss/Ws). Alternative derivations of Wmax for sub-surface levels can then be found by combining Equation 2.8 with any of the Equations 2.32, 2.34 or 2.35. 2.5.3 Variation of iy and W with Zo Attewell and Hurrel (1985) showed that iy was bigger than ix for several case histories, but indicated that the trough width parameter in the transverse direction (ix) can be assumed equal to that in the longitudinal direction (iy) for practical estimation purpose. Attewell and Hurrel verified the application of this assumption by comparing field data recorded by Glossop (1977) with theoretical curves, calculated assuming ix = iy. Nyren (1998) recorded longitudinal sub-surface settlements for a 4.75m diameter tunnel driven 31 m below surface level. The trough seems to remain as a cumulative function with depth such that the trough width decreases with depth and W in the y direction (Wy) increases. The current author believes that there are, at present, no techniques available for finding how iy changes with depth presumably, due to the fact that longitudinal movements are only in the short term and D.Hunt - 2004

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are assumed less important. The movements are, however, important when considering the effects of tunnelling under existing structures. The assumption that ix = iy for sub-surface movements would seem appropriate but no papers relating to this type of assumption have been found. 2.5.4 Wmax in relation to Wcrown Clough and Schmidt (1981) proposed the following empirical equation for relating the settlement at the surface to the settlement at the crown (Equation 2.37).

Wmax  2r     Wc  Zo 

0.8

Eqn 2.37

This relationship has been compared with field data with good accuracy by Ward and Pender (1981). Craig (1975) reported on crown settlements compared to surface settlements for shield driven tunnels concluding that the settlement at the crown was greater than the maximum surface settlement. A typical cast iron lining in London Clay with a C/D ratio of 7 (Z0 / r =14) showed the settlement at the crown to be 2.5 times that at the ground surface. Alternative empirically based methods of finding Wmax /Wc have been proposed by Lo et al (1984) using the ‘gap’ parameter (see Section 3.5.4.). Lo et al (1984) and Ng (1984) reviewed several case histories and suggested that Wmax /Wc = 0.33 was an appropriate relationship in most cases. Methods of relating Wc to the stability number (N) were also reported. Lee (1996) provides a recent case history where the method has been used and found to be successful. The settlement at the crown can also be related to the volume loss via a relationship proposed by Cording et al (1976) and given in Equation 2.38. The method was based upon case history data reported for tunnels constructed on the Washington Metro (U.S.A.). V = 2 W c (r + (C –z))

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Eqn 2.38


2.6

-24-

HORIZONTAL DISPLACEMENTS

2.6.1 Surface (Transverse to Tunnel) It is often necessary to predict horizontal strains induced in a building and therefore the horizontal component of movement, U, due to tunnelling is required (Taylor, 1995a). Traditionally, horizontal displacements are related to vertical displacements by assuming a point of vector focus. Mair (1979) suggested that the vectors of ground movement were directed towards the tunnel axis, and this was later confirmed by O’Reilly and New (1981) (Figure 2.16). On the basis of this assumption a simple relationship between vertical ground movements (W) and horizontal ground movements (U) was derived by O’Reilly and New (1981) as shown in Equation 2.39 and in Figure 2.5:

UW

x Zo

Eqn 2.39

where the parameters have been previously defined. Attewell and Woodman (1982) plotted theoretical horizontal surface displacements for a transverse section of ground above an ongoing tunnel construction and found good agreement between Equation 2.39 and the reported data. They found that the horizontal movements increased as the tunnel face advances and that the maximum settlement, Umax, is reached when the tunnel face has advanced sufficiently in front of the plane of interest (e.g. 3i to 4i in front of the tunnel face). Equation 2.39 is sometimes reported erroneously with W substituted by Wmax exp(-x2/2i2). For a settlement trough following the shape of a normal probability curve both the assumptions lead to Equation 2.40:   x2 U x  1.65 exp 2 U max i  2i

  

Eqn 2.40

x

Equation 2.40 has been shown to be consistent with field observations made by Attewell (1978) for tunnels driven in clay. Hong and Bae (1995) used Equation 2.40 for comparison with field data for sands on the Pusan Subway in Korea. There was good agreement between Equation 2.40 and field data for displacements close to the tunnel, although at the edges of the settlement trough the displacements were underestimated. An alternative distribution D.Hunt - 2004


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based on the work of Mair et al (1993) is: U Wx

x  0.175  1  Z o  0.325 

Eqn 2.41

Mair and Taylor (1993) reported vertical and horizontal movements for five case studies in London Clay and reported no horizontal movement at the tunnel axis at distances in excess of 1.5D. The methods of tunnelling were by hand mining methods; four used shields and one did not. Mair and Taylor (1993) have derived methods of estimating horizontal movements using closed-form solutions, with more recent solutions being formulated by Lognathon and Poulos (1998). The solutions were found to give better predictions of displacements in close proximity to a tunnel. These methods are not examined further because they are beyond the scope of this thesis. Strains induced by horizontal movement derived by O’Reilly and New (1982) are shown in Equation 2.42:

x 

 x2  Vs d 2v  2  1  exp 2 3 dx i 2 i 

By comparison with Equation 2.11 it can be shown that  x = 

Eqn 2.42

z.

The effects of horizontal

strain are particularly important when considering damage to buildings or tunnels above a new tunnel. 2.6.2 Sub-Surface (Transverse to Tunnel) Extrapolating Equation 2.35 to include the sub-surface region yields Equation 2.43 (see Figure 2.16):

U W x

x Zo  Z

Eqn 2.43

Following the work of Mair and Taylor (1993), an alternative distribution has been reported by Grant and Taylor (2000) as shown in Equation 2.44 and Figure 2.17:

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U Wx

x H

-26-

Eqn 2.44

where H represents the distance between the plane of interest and the vector focus for ground movements. Deane and Basset (1995) reported displacements around the trial tunnels for the Heathrow Express tunnels. Sub-surface horizontal movements were found to increase with depth, especially in regions close to the tunnel, when using open-faced tunnelling methods in stiff London Clay. For tunnels driven using an EPBM in soft clay, sub-surface movements have been reported to be either inward or outward (depending on the pressure used at the face). Clough et al (1983) reported outward movements for a 3.7m tunnel driven in San Francisco Bay mud.

De Moor and Taylor (1991) also reported outward horizontal

movements due to pipe jacking techniques for a 2.1m diameter tunnel in very soft alluvium, the largest movements were reported at the tunnel axis. Fujita (1994) noticed inward and outward movements during the construction of a tunnel using a slurry shield. The movements were found to be highly dependent on the face pressure. 2.6.3 Sub-Surface Strains (Transverse to Tunnel) Sub-surface strains close to the tunnel have been recorded in the centrifuge (Atkinson et al, 1977) and in the field by various other authors, for example Rowe et al (1983) and Cording and Hansmire (1975). Eisenstein et al (1981) performed back analysis of field data to find strains around a 2.56m diameter tunnel at 24m depth in till. Contours of volumetric strain showed a decrease in volume above and below the tunnel, with large increases in volume close to the tunnel. Empirical methods for predicting sub-surface horizontal strains are based upon predictions for the horizontal movements. 2.6.4 Vector Focus Equation 2.36 assumes a vector focus at the tunnel axis and Equation 2.38 assumes a point of vector focus at a distance of (0.175/0.325) Zo below the tunnel axis, as reported by Taylor (1995b) and shown in Figure 2.16. The methods of finding horizontal movements shown above relate to two specific points of focus. Grant and Taylor (2000) have extrapolated this method of finding horizontal movements for any point of focus. Figure 2.17 shows the how D.Hunt - 2004


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the point of vector focus could be assumed to change with depth. Nyren (1998) suggested two points of focus, but Grant and Taylor (2000) reported that three points of focus were more appropriate in describing transverse movements. The current author was unable to find research relating to changes in the position of the vector focus when considering sub-surface horizontal movements in the transverse direction for sands and in the longitudinal direction (i.e. parallel to the tunnel) for sands and clays. Deane and Basset (1995) reported sub-surface movements for the Heathrow Express trial tunnels driven in London clay. The point of vector focus for each tunnel was between the tunnel axis and invert for the one tunnel and below the invert for the other. 2.6.5 Surface (Longitudinal to Tunnel) According to the literature, only limited attention seems to have been given to longitudinal horizontal movements. Attewell and Woodman (1982) derived Equation 2.42 for horizontal movements parallel to the tunnel as shown in Equation 2.45 V  Wy

y Zo

Eqn 2.45

This assumes a vector displacement towards the centre of the tunnel face. The corresponding ground strains derived from Equation 2.45 can be found in Attewell and Woodman (1982). Alternative derivations could be found by choosing a different value for distance to vector focus (i.e. by replacing the Z0 term shown in Equation 3.27). 2.6.6 Sub-Surface (Longitudinal to Tunnel) There are currently no methods for predicting sub-surface horizontal movements in the plane parallel with the tunnel direction. The extension of the assumption that the surface and subsurface profiles are represented by a cumulative curve would seem appropriate. Taking this assumption and the assumption, made for surface settlements that ix = iy could provide an initial estimate. Alternatively the longitudinal draw angles described in Equation 2.21 and 2.22 could also be used.

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2.6.7 Idealised Three-Dimensional Behaviour Attewell et al (1986) use Equation 2.8 (for the transverse settlement trough), in conjunction with Equation 2.13 (for the longitudinal settlement trough), to produce an idealised 3D settlement profile:

W x ,y 

  x2  Wmax exp  2  2i

   x-x s  G      i y

  x-x f -G    i   y

   

Eqn 2.46

Equation 2.46 can be used to find vertical displacements above a single tunnel. The total profile can be seen in Figure 2.18. Similar three-dimensional behaviour has been reported by Yamada (1986) for tunnels in cohesive soils in Japan. Sandy soils show a different profile that is not modelled by Equation 2.46 due to a region of loosening occurring directly above the tunnel. 2.7 DISPLACEMENTS ABOVE TWIN AND TRIPLE TUNNELS Tunnels are commonly constructed in pairs or even in sets of three. Accurate predictive methods for finding displacements above multiple constructions are not well documented. Hence this section details the current knowledge relating to multiple constructions. 2.7.1 Parallel Tunnels Terzaghi (1942) published the first paper presenting field data of settlements above twin tunnels (double tubes). Terzaghi found that the settlements recorded above the second tunnel were larger than those recorded above the first.

Peck (1969) reported the results of

monitoring data for vertical displacements above twin tunnels driven in dense sand. Peck assumed that the ordinates of the two tunnels could be added together for a first approximation of the total settlement profile, although he reported that in most circumstances the volume loss associated with the second tunnel was greater than that for the first. The settlement profiles were also non-symmetric with the increased magnitudes of vertical displacement occurring over the second tunnel as shown in Figure 2.19. Greater settlement above the second tunnel driven has also been reported by Moretto (1969) for twin tunnels D.Hunt - 2004


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constructed as part of the San Francisco subway (Figure 2.20). The tunnels were constructed in dense silty sand, overlying firm clay. The tendency for the settlement of the second tunnel to have a maximum value set closer to the first tunnel driven has also been reported by Bartlett and Bubbers (1970).

These authors reported the movement above twin 3.81m

diameter tunnels driven in clay at a depth of 22m with a centre-to-centre spacing of 25m (Figure 2.21). The eccentric position of Wmax and related asymmetry has been found in many case histories such as those reported by Perez Saiz et al (1981) and Cooper and Chapman (1998). Cording and Hansmire (1975) also reported an increased volume loss for the second tunnel when constructing twin tunnels in medium dense silty sand and gravel on the Washington Metro (Figure 2.22). These authors introduced the concept of an additional interference volume loss (Vint) due to the second tunnel which occurred in addition to the total greenfield settlement above the tunnels given by Vs1 + Vs2. Cording and Hansmire (1975) also proposed a relationship between Vint normalised by V2 (the greenfield volume loss due to the construction of Tunnel 2) and the horizontal distance between the outer perimeters of each tunnel (sometimes referred to as the Pillar width). Perez Saiz et al (1981) provided additional data to this original plot as shown in Figure 2.23. The sub-surface data reported by Cooper and Chapman (1998), has not been added as Vint/Vs2 may not be constant for sub-surface regions. Hanya (1977) reported 39 cases of ground movements for 21 shield driven twin running tunnels in Japan having various depths, diameters, pillar widths and soil types. For most cases increased losses were found above a second tunnel driven in relatively close proximity. Lo et al (1987) reported the movements of twin 5.95m diameter tunnels driven 15m below ground level at 15.5m centres in estuarine clay on the MRT in Singapore. Lo et al (1987) reported a significant bias in the position of the maximum settlement towards the first tunnel driven, although only four data points were available. During recent years, the extension of the Jubilee line in London (U.K.) has produced very good quality data for twin tunnels in London Clay. This is due to the fact that many of the tunnels were constructed below important buildings in London, which were extensively monitored for movements. In Old Jamaica Road, Southwark Park and Niagara Court greenfield movements above twin tunnel constructions were reported (Withers, 2002). The respective tunnel depths were 19.5m, 21.0m and 17.0m below ground level with centre-tocentre spacings of 26.0m, 28.0m and 20.0m respectively. The EPBM tunnelling method was used with varying face pressures for all the tunnels. Southwark Park was the most extensively monitored section with 32 data points. However, due to the fact that the twin tunnels were D.Hunt - 2004


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driven almost simultaneously the effects caused by a delay between drives described previously were not evident. For most cases, therefore, predictions based on Equation 2.46 (reported in Section 2.7.2) would have been accurate. Cording and Hansmire (1975) reported sub-surface displacements and strains above twin 6.0m diameter tunnels at 9.0m centres constructed 15.0m below ground level in silty sand and clay. Additional soil displacements were highlighted as occurring over the centreline of the first tunnel driven while the effects of the first tunnel on the displacement profile above the second tunnel were shown to decrease with depth. Hanya (1977) reported on sub-surface movements for several case histories in Japan. The shape of the total settlement trough (due to both tunnels) was found to change for sub-surface levels when considering tunnels with a centre-to-centre spacing of more than 1D (diameter) apart. This phenomenon can be observed when using empirical predictive equations and by assuming unchanged bounds to movement for each tunnel (shown later in Figure 2.27). Akins and Abramson (1983) recorded subsurface movements above 6.1m diameter twin tunnels constructed for the Metropolitan Atlanta Rapid Transit Authority (MARTA) in residual soils. The tunnels were driven 15.0m below Broad Street at a centre-to-centre spacing of about 6.0m using a pilot and enlargement method. The first tunnel was fully completed before the second tunnel was driven. The subsurface settlements were reported for each stage of construction and showed larger displacements and volume losses for the second tunnel driven. Numerical modelling has also been shown to highlight the asymmetry in settlements and a larger volume loss for the second tunnel driven. Ottaviano and Pelli (1983) highlighted this behaviour when conducting non-linear finite element analysis of twin 6m diameter tunnels at various depths and spacing in stiff clay in Rome. Addenbrooke (1996) also reported similar findings when modelling 4.8m diameter twin tunnels at a depth of 34.0m with varying centreto-centre spacing using various constitutive models with finite elements. Figure 2.24 shows the decrease in eccentricity of Wmax with increasing tunnel spacing reported by Addenbrooke (1996). Figure 2.25 shows the corresponding deformation of the Tunnel Lining 1 due to the construction of Tunnel Lining 2. The liner diameter was seen to shorten in the vertical plane and increase in the horizontal plane, the liner being drawn towards the second tunnel driven in all cases. Kim et al (1996) reported very similar findings when conducting finite element analyses using OXFEM (a geotechnical package developed at Oxford University) to model small-scale parallel tunnels. They reported the radial deformation of an existing tunnel liner due to the construction of a second parallel tunnel at a centre-to-centre spacing of 0.4D and 1.0D (Figure 2.26). As expected, the largest deformation was caused by the construction of a D.Hunt - 2004


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nearer tunnel at a centre-to-centre spacing of 0.4D. The results showed good agreement with liner deformations found in the laboratory when conducting tests under gravity in Kaolin clay. 2.7.2

Predicting Movements for Parallel (Side-by-Side) Tunnels

New and O’Reilly (1991) provide a method of calculating surface settlement for twin tunnels. The same method has been reported by GCG (1992). The method simply sums together the settlement trough above each tunnel as shown in Equation 2.47.   x2   x  d 2    W x ,z  W max  exp exp 2i 2   2i 2 

   

Eqn 2.47

where d, represents the distance between tunnel centres (Figure 2.27). The other symbols have been defined for Equation 2.8. The subsequent longitudinal displacements, horizontal displacements, ground slopes, curvatures and ground strains can also be found by summation and have been reported by New and O’Reilly (1991). The method has been found to give realistic predictions when twin tunnels are driven simultaneously. The method was derived for predicting surface displacements, although it can easily be extended to sub-surface regions by assuming unchanged bounds to movement. However, twin tunnels are not always driven simultaneously and a time delay may occur between drives. This delay can lead to asymmetry, eccentricity of Wmax and an increase in volume loss, and none of these can be taken into account in the equation. Soliman et al (1993), based on earlier work of Duddeck and Erdman (1982), have reported alternative methods for assessing deformations of tunnel liners due to the construction of adjacent parallel tunnels. The tunnel spacings considered in these analyses were taken as 0.5r and r, where r was the radius. Kimmance et al (1996) extrapolated the design lines proposed by the previous authors to include deformations for wider spacings. The method involves estimating the increase in deformation of an existing tunnel due to the influence of a new parallel tunnel. The ratio of Wexisting/Wnew for the invert and axis level can be found for various tunnel separations. The results of liner deformation reported by Addenbrooke (1996) and shown in Figure 2.25 could also be used to predict tunnel deformation.

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2.7.3 Piggyback (Stacked) Tunnels Kuesel (1972) reported the surface settlements above four tunnels (i.e. two pairs of side-byside tunnels, one above the other) driven under Market Street for the BART system in San Francisco. The surface settlements above the lower side-by-side tunnels, which were constructed first, were reported by Moretto (1969) and have been discussed in Section 2.7.1. Figure 2.28 shows the surface settlements after the construction of the upper side-by-side tunnels. The largest movements occurred for the upper tunnels, with larger displacements being evident above the fourth tunnel driven, which was directly above the second tunnel to be driven, than the third. Wang and Chang (1992) performed a linear elastic analysis of twin 6.0m diameter tunnels in a piggy back (stacked) alignment with a centre-to-centre spacing of 8.0m. The authors reported that it is common practice to drive the lower tunnel first. The second (upper) tunnel would then be driven through a zone highly disturbed from the previous construction of the first (lower) tunnel. Therefore the ground subsidence may be much more than twice the amount from a single tunnel. Addenbrooke et al (1997) modelled 4.1m diameter piggyback tunnels using finite elements. The lower tunnel was constructed at 34.0m below ground level with an upper tunnel at 16.0m, 20.0m or 24.0m below ground level. Two construction sequences were employed i.e. either the lower tunnel or upper tunnel was constructed first. The effect of tunnel spacing on the settlement profile when constructing the lower tunnel first can be seen in Figure 2.29. Increases in trough width and volume loss were reported for all tunnel spacing and construction sequences employed, with the largest increases evident for the closely spaced tunnels. Cooper et al (2000) reported the movement of existing twin running 4.88m diameter tunnels near Old Street station, due to the enlargement (from 3.20m diameter to 3.56m) of an 80.0m length of the existing Northern Line twin tunnels situated 10.0m below. The existing tunnels were situated 16.0m below ground level beneath the City Road at a centre-to-centre spacing of 10.0m. Displacement was measured in the longitudinal direction along the centreline of the existing tunnels. Larger displacements were found above the second enlargement. 2.7.4 Offset tunnels Shirlaw et al (1988) reported the movements for offset running tunnels constructed by the NATM in stiff boulder clay on the Singapore Mass Rapid Transit. The 6.0m diameter D.Hunt - 2004


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tunnels had a separation of only 1.7m between the outer linings. Figure 2.30 shows the surface settlement profiles after each construction (i.e. northbound and southbound). The settlement trough was wider and deeper over the shallower northbound tunnel, which was the second tunnel driven as expected. (It is interesting to note that the position of the maximum vertical displacement changes inexplicably from being biased towards the first tunnel, at one measuring station, to being biased towards the second tunnel, at another measuring station). Standing et al (1996) reported movements at St James’s Park for twin 4.75m diameter tunnels, offset vertically by 14.3m (1.2D) and horizontally by 21.5m (3.5D). Bigger volume losses were reported for the second shallower tunnel driven. Nyren (1998) reported a full set of surface and sub-surface movements for the Eastbound and Southbound tunnels at St James’s Park and reported an increase in volume loss with depth. Addenbrooke (1996) conducted a numerical simulation of the offset tunnels at St James Park and found the offset tunnels showed influences of both side-by-side and piggyback tunnels. A larger volume loss was found for the second tunnel driven together with a bigger trough width on the near limb and a maximum settlement offset towards the first excavation. It is interesting to note that Nyren (1998) found no offset in the position of the maximum settlement above the second tunnel driven. 2.7.5 Transverse (Cross-Cutting) and Skew Tunnels Kimmance et al (1996) reported that the movement of existing overlying tunnels (situated at 90o to a new tunnel construction below) could be assumed to deform to a shape which was identical to a greenfield sub-surface settlement profile, providing that the tunnel was sufficiently flexible. These findings have been confirmed by Standing and Selman (2002) who reported on the displacement profile within three existing tunnels, referred to as the Northern Line, Bakerloo line and Waterloo line. The tunnels overlay the new tunnel construction at different locations along its length and were monitored for movements during the construction of the Jubilee Line Extension (JLE). The tunnels had different diameters and were situated at various centre-to-centre distances from the underlying JLE. From back analysis using actual data, predictions based on Equations 2.47 and 2.32 and the assumption made by Kimmance et al (1996) were found to compare favourably. The similarity is due to the fact that the tunnels were driven almost simultaneously. Kim et al (1996) modelled transverse tunnels at small scale in the laboratory. These authors found that deformation was induced on an existing tunnel by driving tunnels D.Hunt - 2004


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transversely 0.4D above, in one case, and 1.0D below in another. Greater deformation was recorded on the existing tunnel due to the tunnel driven below. Cooper and Chapman (1998) reported on the movement of the Piccadilly Line tunnels due to the driving of three new tunnels 13.0m below the tunnel axis at a skew of 70 degrees. The original tunnels had a diameter of 3.81m with the tunnel axis at 13.0m below ground. The three new tunnels, the Concourse (constructed using NATM), Upline and Downline (both constructed with bolted ring segments) tunnels were 9.0m in diameter with a tunnel axis 26.0m below ground level. In skew tunnels additional movements are apparent, namely the effects of rotation and distortion, which can potentially cause damage to underground structures due to shearing. Both asymmetry and eccentricity of the maximum settlements were observed and these were thought to be due to a time delay between drives and the role of previously strained soil (Mair and Taylor, 1997). Attewell et al (1986) reported methods for finding the movement of pipes due to tunnels driven underneath at a skew and this method could presumably be applied, with caution, to tunnels. The influence of constructing tunnels transverse to and above existing tunnels was found to cause the lower tunnel to heave (Saitoh et al, 1994). 2.8 TIME RELATED (LONG-TERM) MOVEMENTS This thesis is primarily concerned with multiple tunnel constructions with a time delay between each construction. While in this thesis they are assumed to be short-term delays it is possible that some significant degree of consolidation/pore water pressure changes could occur between constructions and hence these movements are included in this section for completeness. ‘Time related’ refers to the fact that these ground movements occur post construction and in some cases occur years after the initial construction has been completed. In most cases it can be shown that these time dependent movements above a single tunnel will cause a deepening and often a widening of the settlement trough (see factor 1-4). The small increases in horizontal strains for long-term movements are important with respect to the response of buildings to ground movements. The total ground movements can be found by summing short-term and long-term movements. Typical examples of consolidation settlements have been reported by Hanya (1977), Glossop and O’Reilly (1982), Shirlaw et al (1988), O’Reilly et al (1991) and Bowers et al (1996). The long-term movements can be related to the following four main factors: D.Hunt - 2004


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1. Pre-construction pore water pressures and post-construction excess pore water pressures. The change in pore water pressures is either due to the unloading or loading (i.e. stressing) of the soil near to the tunnel. In open-face tunnelling through clays the ground is considered to be unloaded and in closed-face tunnelling it is considered to be loaded. In open-face shield tunnelling the unloading causes excess pore water pressures. which are usually negative near the tunnel (due to dilation) and positive further away (due to shearing) (Schmidt 1989). In closed-face, such as a EPB or Slurry shield tunnelling, the ground will receive additional loading. If the pressure at the tunnel face exceeds the insitu stresses or if excessive pressures are used for grouting, this results in an increase in pore water pressures. It is not conclusive as to whether the trough width increases, although increased settlements do occur. In clays the excess pore water pressure caused by tunnelling can occur up to a distance of one diameter away from the tunnel wall and can take several months to dissipate in clays (Schmidt 1989). 2. Permeability of the soil and liner, and specifically their relative values. The permeability of the liner with respect to the tunnel determines its ability to act as a drain (i.e. Terzaghi 1942, Eden and Bozozuk 1969 and De lorry et al 1979). If the tunnel lining has a permeability equal to or greater than the surrounding ground (k ~ 10-10 ms-1 for London clay) it will act as a permanent drain (Schmidt 1989). The result is a steady seepage towards the tunnel and a widespread reduction in pore water pressures surrounding the tunnel. Ward and Pender (1981), through field measurements of Palmer and Belshaw (1980), confirm that most tunnels in clay soils act as drains in the long term. O’Reilly et al (1991) showed that no reduction in pore water pressures were recorded close to the tunnel in Grimsby, which led to the conclusion that the liner was of low permeability and that the tunnel did not act as a drain. Vaughan (1989) reported that the rate of consolidation above shallow tunnels should greater than that above deep tunnels. This is thought to be due to the shorter drainage path and greater permeability of soil associated with the shallower tunnel. 3. Compressibility of the soil and flexibility of the liner. The liner will deform due to the earth pressure loading and cause ground movements. This deformation will be dependent on the compressibility of the soil and the flexibility of the liner, as well as the items shown in 4. 4. Depth and diameter of the tunnel. (Factors 1-3 are also related to these) Various predictive methods exist in the literature including methods proposed by Howland D.Hunt - 2004


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(1980), Hurrel (1985), Selby and Attewell (1988) and Bowers et al (1996). Further details of the parameters involved are beyond the scope of this research. The consolidation settlements occurring above twin tunnels has also reported by many authors including Hanya (1977), Moretto (1969), Chapman and Cooper (1999) and Standing and Selman (2002). In general the settlement profile shows a large increase in depth with time and little increase in width. For most cases there appears to be only a small increase in horizontal movement and hence only a small increase in horizontal strain. 2.9 DAMAGE TO BUILDINGS AND OVERLYING STRUCTURES Underground tunnel construction has the potential to disturb or damage any structure that lies above, or in close proximity to, the operation. The damaging effect of tunnel-induced movements can be apparent on many surface and sub-surface structures. For example overlying buildings (e.g. Attewell 1978, Geddes 1977, National Coal Board 1975, Burland et al 1973, 1977) or piled foundations (e.g. Mitchell and Treharne 1976, Morton and King 1979, Vermeer and Bonnier 1991, Mair 1993, Lee et al 1994, Bezuijen and van der schrier 1994, Hergarden et al 1996, Forth and Thorley 1996, Mair and Taylor 1997, Chen et al 1999, Lognathon and Poulos 1998, Potts et al 1999, Higgins et al 2000). Mair and Taylor (1997) suggest that buildings on continuous foundations such as rafts are likely to experience negligible horizontal strain from bored tunnel construction with no resulting damage. Damage has also been reported on gas and water mains due to the ground movements above single tunnels (e.g. Needham and Howe 1979, New et al 1980, Owen 1987, Attewell et al 1986 and Bracegirdle et al 1996). Accurate assessments of the potential damage to buildings are of particular importance so that a scheme can be designed to minimise the risk. The classification and assessment procedure allows particularly sensitive buildings to be highlighted and appropriate action considered. A three-stage approach is commonly used: Stage 1: Structures at risk are highlighted by greenfield predictions of ground-slope and settlement; subsequently limiting criteria can be set. Stage 2: Structures identified in Stage 1 can be assessed using critical strain (tensile), relative rotation and modes of deformation, with classifications being set. Stage 3: Assessment of 3D effects, structure stiffness and the effect on piles involving FE analysis or analysis by an expert. This is not a compulsory stage for all projects.

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Boscardin and Cording (1989) showed that the damage categories put forward by Burland et al (1977) could be related to the size of estimated limiting tensile strain in the building, as shown in Table 2.1. Table 2.1: Damage categories due to ground strains (after Boscardin and Cording, 1989) CATEGORY OF DAMAGE

CLASSIFICATION OF DAMAGE

LIMITING TENSILE STRAIN (LIM) (%)

0

Negligible

0 - 0.05

1

Very slight

0.05 - 0.075

2

Slight

0.075 - 0.15

3

Moderate*

0.15 - 0.3

4&5

Severe to very severe

>0.3

Several other damage categories have been reported which take into account the deflection ratio /l (e.g. Burland 1995), where  is the displacement relative to the line connecting two reference points at a distance L apart. It is common practice when assessing the potential damage to buildings to find the average horizontal ground strain and combine it with either the bending strain or the diagonal strain for use in Table 2.1. The average ground strain for a building is the average of the ground strain values at either end of the building. The bending strain and diagonal strain can be found from methods proposed by Burland et al (1977). When assessing building movements it is possible to assume the building deforms according to the greenfield settlement trough. However, this assumption does not take into account the actual stiffness of the building, leading to an overestimation of the strains. Accounting for the stiffness of the building reduces the deflection ratio and horizontal strains (e.g. Breth and Chambosse 1974, Frischmann et al 1994). Geddes (1990) discussed earlier papers presented by Burland et al (1977) and Geddes (1977, 1980 and 1985). The author considers the relationship between ground movements, ground strains, structural movements and structural strain and reports that tensile structural strains can still be exhibited when the ground is in compression. Numerical studies by Potts and Addenbrooke (1996 and 1997) show that the building stiffness would greatly influence the settlement profile above tunnels. Predictive methods based on building stiffness were reported, and have been seen to compare well with measured building behaviour by Bloodworth and Macklin (2000). Simpson and Grosse (1996) advise that the changes of stiffness that occur due to cracking should be considered when analysing results found from these predictive methods.

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2.10 CONCLUSIONS This chapter has highlighted the behaviour of soft soils (clays and sands) due to the construction of a single tunnel and reviewed the currently existing methods for prediction of ground displacements. The methods have been shown to provide an accurate method for estimating both horizontal and vertical displacements above a single tunnel. Drawing from this earlier work it is a logical first step to assume that the prediction of movements above multiple tunnels can be achieved by summing the greenfield displacements for each tunnel, based on any of the empirical equations shown in Chapter 2. For the case of side-by-side twin tunnels the use of Equation 2.47 has been shown to be a reasonably accurate method of predicting vertical displacements when the tunnels are constructed consecutively. However, this chapter has highlighted some of the changes to the settlement profile that can occur when these tunnels are not constructed consecutively. The vertical displacement profile above the second tunnel is no longer Gaussian in shape and hence the use of Equation 2.47 is no longer valid. By conducting the literature review a research need for improving the prediction of displacements above twin tunnels in London Clay (when construction is not simultaneous) has highlighted. As far as the author is aware there are at present no accurate methods for predicting surface and sub-surface movements when a delay in construction occurs between the first and second tunnel. Finite element methods have been used on many occasions to bridge this gap in knowledge. However, the method is expensive in terms of resources and still has a long way to go in predicting accurately the actual magnitudes of displacement that occur above a single tunnel in the field. The numerical analysis of twin tunnels conducted by Addenbrooke (1996) has provided an improved understanding of the behaviour of vertical ground surface displacements above twin tunnels. Unfortunately, the sub-surface vertical displacements were never reported and the horizontal displacements were only reported for a in the vertical plane. Reporting of displacements in the horizontal plane has been undertaken by previous authors (Attewell and Woodman (1982) when considering case history data and the method allows easier direct comparison with the vertical displacements when performing back analyses. There are many tools available for improving existing empirical methods of prediction for displacements above twin tunnels (i.e. numerical studies, case history data and physical modelling). Due to the holistic nature of this project all of these methods are being considered.

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Chapter 2- Engineering practice for predicting movements above single and twin tunnel

1 Face loss 2 Passage of the shield 3 Closure of the tail void 4 Lining deflection 5 Consolidation 2 5

1

4

Figure 2.1

2

3

3

5

4 Short term

Long term

Sources of volume loss for a shield driven tunnel (after Cording 1991)

Free surface

Vs Vt

Z0

V s = Vt

Figure 2.2 Volume loss assumptions for an undrained clay

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10

O'Reilly et al (1988) Mackilin and Field (1998) Bloodworth and Macklin (2000) Macklin (in house) Standing et al (1996) Umney and heath (1996) Bowers et al (1996) Harris et al (1994) Eden and Bozozuk (1969) Saur and Lama (1973) Bourke (1957) Shirlaw (1988) Attewell andFarmer (1974) Temporal and Lawrence (1985) Simic and Craig (1997) Equation 2.7

1 (%)

Volume loss (%)

Upper bound

Lower bound

0.1 0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

LF

Figure 2.3

Volume loss versus load factor (after Macklin, 1999)

x=0

x Error function curve

Probability of disc or sphere moving down 1 16

1 4 1 8

3 8 3 8

1 4

1 4 3 8

1 2 1 2

1 16 1 8

1 4 1 2

1

Remove a single disc or sphere at y0, Z0

Figure 2.4

Z

Stochastic modelling of the settlement process (after Schmidt, 1969)

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Half trough width

0.0 0.607 Wmax

0.2

Wmax

0.4

 x2   Wx   Wmax exp    2 i2   

0.6 0.8

3i

3i

i

1.0

x Z

Transverse distance from centreline 4

3

2

1

Vertical displacement, W Horizontal displacement, U Horizontal strain, 

1

Point of W max, Point of maximum curvature (sagging)

d 2w dx 2

W  0.446 max i2

Point of maximum horizontal strain (compressive) umax = 2

W dw  0.607 max dy i

maximum horizontal displacement U max  0.607

i Wmax Z0

Point of maximum horizontal strain (tensile) umax = Point of maximum curvature (hogging)

4

dx

W  0.446 max Z0

Point of inflexion, Point of maximum slope

3

dv

2

d y dx 2

dv dx

W  0.446 max i2

Point of W = 0 and position of half trough width

Figure 2.5 Transverse settlement profile above a single tunnel D.Hunt - 2004

W  0.446 max Z0

Settlement, W, as a proportion of Wmax

U max

umax

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Full trough width

Full width Fulltrough trough width 0.0

 vmax

0.5Wmax

0.841Wmax

 vmax

0.0

0.159Wmax

0.2 0.4

Wmax

0.6

-i -i

3

x=0

i

0.8

y =Face 0 i position Face position

3

2

2

Distance behind face

1.0

y Z

1

1

Settlement, W, as a proportion of W max

Wmax

Settlement, W, as a proportion of Wmax

0.2 Vmax

0.4 0.6 0.8

Distance ahead of face

Vertical displacement, W Horizontal displacement, V Horizontal strain, v Vertical displacement, W Horizontal displacement, V Horizontal strain, v

1

Point of maximum curvature (hogging)

d 2w dy

2

W  0.242 max i2

Point of maximum horizontal strain (tensile) v max = 2

dy

W  0.242 max Z0

Point of inflexion, Point of maximum slope

W du  0.399 max dy i

maximum horizontal displacement Vmax  0.399

3

dv

i Wmax Z0

Point of maximum horizontal strain (compresive) Point of maximum curvature (sagging) v max =

dv dy

d 2w dy

2

W  0.242 max i2

W  0.242 max Z0

Figure 2.6 Longitudinal settlement profile above a single tunnel D.Hunt - 2004

1.0

y Z


2.5i Free surface

W Wmax

Z0 



2r

Figure 2.7

Relationship between  and half trough width T (after Cording and Hansmire, 1975)

3i 2T = 2 (r sec  + (C + r) tan )

Free surface

Wmax r cos 

C Z0 



[C + r (1 + sin )] tan   = 45 -  /2

D r

Figure 2.8 Relationship between  and full trough width 2T (after Attewell, 1978) D.Hunt - 2004

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T1

T2 r

C tan 

Free surface

(C + r) tan 

Wmax

C 

Direction of drive

D

Z0



Tunnel  = 45 -  /2

Figure 2.9 Longitudinal angle of draw above a single tunnel (after Attewell, 1978)

Offset to point of inflection (m) 0

5

10

15

20

0

Hanya (1977) Attewell and Farmer (1974) Attewell (1978)

5

Glossop et al (1979) Toombs (1980) West et al (1981)

Depth to tunnel axis, Z 0 (m)

10

Attewell et al (1978) Muir Wood and Gibb (1971) Glossop and O'Reilly (1982) Eden and Bozozuk (1968)

15

Henry (1974) Morreto (1969) Lake et al (1992)

20

Hanya (1977) Peck (1969) Peck (1969)

25

O'Reilly and New (1982)

i = 0.6Z0

O'Reilly and New (1982) O'Reilly and New (1982)

30

Attewell (1978)

i = 0.5Z0

Barrat and Tyler (1976) Mcaul (1978) New and Bowers (1994)

35

Kuwamura (1997)

i = 0.4Z0

Shirlaw et al (1988)

40

Figure 2.10

Variation of trough width parameter, i, with tunnel depth for tunnels in London Clay (after Mair and Taylor, 1997)

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Free surface

Clay (E2)

Z1

Z0

Sand (E1)

Z2

2r

Free surface

Sand (E1)

Z1

Z0

Clay (E2)

Z2

2r

Figure 2.11 Full trough width for multilayered soil (after Selby, 1988)

2T = 2r + L1 tan 1 + L2 tan  2

Free surface

Wmax L2

Clay (E2)

2 Z0 1

Sand (E1)

L1 2r

Figure 2.12 Angle of draw in multilayered soil (after Ata, 1996)

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iss/is 0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

Z0

Z/Zo

0.6

0.8

Tunnel axis level

1

1.2

0.175/0.325Z0

using I = K(Zo-Z) where K = 0.5 Mair et al (1993) Heath and West (1996) Moh et al (1996)

1.4

1.6

Figure 2.13

Variation of i with depth a single tunnel

K = i/(Z0-Z) 0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 Equations: 0.1

using I = K(Zo-Z) where K = 0.5 Mair et al (1993) Heath and West (1996) Moh et al (1996)

0.2

Field data:

0.3

Mair (1979) - Centrifuge Mair (1979) - Centrifuge Attewell and farmer (1978) Barrat and Tyler (1976) Barrat and Tyler (1976) Glossop (1978)

0.4 Z/Z0

0.5 0.6 0.7 0.8

Range of values for various ranges of values for D and Z

0.9 1

Figure 2.14

Variation of K with depth for a single tunnel (after Mair at al, 1993)

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1.6


Full surface trough width of 6i is

Free surface Wmax s

Vs

Z

i ss Wmax ss

Z0

( Z0-Z)

Vss

 is  i  ss

Figure 2.15

  Wss   W   s

  Ks   K   ss

 Z 0   Z  Z  0

  when Vs = Vss  

Sub-surface ground movements above a single tunnel At surface i = 0.5Z

Free surface

Z0 Mair et al (1993) O’Reilly and New (1982)

Vector focus 0.175/0.325 Z0

Figure 2.16 Suggested distribution of i with depth including vector focus

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-48-


Free surface Zone 1 Distribution of i Zone 2

Zone 3

Points of Vector focus

Z0

1

2

Tangent to distribution of i

3

Figure 2.17 Suggested distribution of i with depth (after Grant and Taylor, 2000)

Extent of surface settlement trough

V U W X

Z0 Wmax Y

Crown Shoulder Axis level Knee Tunnel key:

Invert

Figure 2.18 3D profile of settlement above a single tunnel (after Yeates, 1985)

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Street surface (feet) -20

-15

-10

-5

0

5

10

15

20

First tunnel

Second tunnel

2 4

34-44 feet

Settlement (in)

0

Total

6 26 feet 17.5 feet

1foot = 0.305m

Figure 2.19 Settlement over tunnels in dense sand above groundwater level (Peck, 1969)

22’

22’

76’

0.2’ max settlement

(a) (b) (c) (d) (e)

1st tunnel excavated 1st tunnel grouted 2nd tunnel excavated 2nd tunnel grouted Two Months after

Tunnel 1 Tunnel 2

45.5’ 1 foot = 1’ = 0.305m

Figure 2.20 Settlement above twin tunnels – Market Street (Moretto, 1969)

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65’

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Depth (m) Surface settlements (mm)

0

5

10

15 20

25

30 35

40

45 50

55

60

65 0

-5 -10

-5

-15

Made ground Stiff sandy clay Coarse sandy gravel Stiff brown clay

-10

Measured data showing range from different locations

-15

-20

Tunnel depth = 22m Tunnel diameter = 4.1m

-25

Tunnel

Figure 2.21

Stiff blue clay

Tunnel 2 (Driven after 2 weeks)

Settlement above twin tunnels showing asymmetry. (Bartlett and Bubbers, 1970)

Vs1 + Vs2 V

Equation 2.47

int



Tunnel 1

Actual behaviour

Tunnel 2

Figure 2.22 Volume loss due to interference during driving of a second tunnel (after Cording and Hansmire, 1975)

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1.5 ?

Vint/Vs2

Perez Saiz et al (1981) Cording and Hansmire (1975) ? Estimated

?

Increment of volume

1.0

0.5

?

0

0.5

1.0

1.5

d’/2R

Figure 2.23 Effect of pillar width on increased volume loss for second tunnel driven (after Cording and Hansmire, 1975, with additional data added)

Figure 2.24 Effect of pillar width on eccentricity of Smax (Addenbrooke, 1996)

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Figure 2.25 Effect of pillar width on tunnel deformation (Addenbrooke, 1996)

Scale model FE analysis

Tunnel 1

Tunnel 1

1.0D 2

0.4D 1

3

Figure 2.26 Influence of pillar width on liner distortion (after Kim, 1996)

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x

2.5 i

Free surface Wmax Z

Wmax

Zo

D 0.175 Zo 0.325

Tunnel 1

Tunnel 2

d'

W (Single tunnel) W (Total)

Figure 2.27 Empirical predictive method for twin tunnels

SETTLEMENT (FEET)

0.0 -0.1 -0.2 -0.3 -0.4

After 1 and 2

After 3 and 4

-0.5 -0.6

-60

–50

–40

–30

–20

–10

0

10

20

FEET

22’

30

40

50

60

22’

76’

24’

3

Tunnels driven in order primarily in dense sand

18’

1

4

65’

2 45.5’

1 foot = 1’= 0.305m

Figure 2.28 Settlement above twin perpendicular tunnels (Kuesel, 1972)

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Figure 2.29 Effect of pillar width on trough width for piggy back tunnels (Addenbrooke, 1996)

Figure 2.30 Surface and sub-surface movements for offset tunnels (Shirlaw et al., 1988) D.Hunt - 2004

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Chapter 3 – The Finite Element method and Tunnel construction

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Chapter Three THE FINITE ELEMENT METHOD AND TUNNEL CONSTRUCTION

3.1 INTRODUCTION This chapter describes the finite element method, the equations to be solved and the solution method used, when modelling the construction of a single tunnel in London Clay. The computer package used to conduct the analyses during this research (i.e. those reported in Chapters 4, 5 and 6) is ABAQUS, a commercial finite element computational package. Details of the constitutive models and materials properties for the soils and liners used within the analyses are described in this chapter together with the relevant procedure for modelling volume loss. This chapter reports the use of a modified gap parameter, a new method for modelling volume loss, and a new method for liner restraint, both are compared and contrasted to currently available procedures. 3.2 THE FINITE ELEMENT METHOD The finite element method involves a number of stages, as outlined by Potts and Zdravkovic (1999): 

Element discretisation;



Displacement approximation;



Element equations;



Global equations;



Boundary conditions; and



Equation solution;

3.2.1 Element Discretisation Discretisation is a process in which the geometry of the problem, in this case a tunnel at depth, is assembled from smaller finite elements connected together at node points. In the D.Hunt - 2004


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analyses described in this thesis the soil and tunnel linings were modelled using 8-noded ‘isoparametric’ elements (see 3.2.2) referred to as CPE8R elements to be consistent with the ABAQUS user manual (see Hibbet et al, 1997) as shown in Figure 3.1. The geometry of the problem under consideration necessitated the use of curved boundaries and curved material interfaces in regions close to, and including, the tunnel lining. The use of these higher order elements with mid-sided nodes are recommended for this situation. 3.2.2 Displacement Approximation In finite element analyses the displacement field is the unknown quantity which must be assumed over the area in question. The stresses and strains are secondary quantities which can be found from the assumed displacement field. In 2D analyses this displacement field is assumed to have polynomial form whose order depends on the number of nodes in the element. The displacements u and v in the x and y directions are expressed at each node, with linear variation occurring across the element (or linear variation over each quadrant in an 8 noded element). The assumed field is given by Equation 3.1.

d   N d n

Eqn 3.1

where N  is the matrix of shape functions and where d n contains the list of nodal displacements (u and v) for a single element. For accuracy to increase with the use of smaller elements the displacement field must satisfy compatibility conditions, i.e. be continuous (no gaps), able to show translation and rotation (rigid body movements) and represent constant strain rates (Potts and Zdravkovic, 1999). Each node has two unknown degrees of freedom in displacement (u and v) corresponding to the global axis, which must be determined. The ‘isoparametric’ elements mentioned in Section 3.2.1 are widely used in geotechnical problems. The name comes from the fact that the equations, describing the unknown displacements, are the same as those used to map the geometry from the global axis to the natural axis (Naylor and Pande, 1981). The advantage of using isoparametric formulation is that the element equations need only be evaluated in the parent element coordinate system (Potts and Zdravkovic, 1999). In order to avoid non-unique global-to-parent mapping of these elements all corner angles lie between 45 and 135. In order that the uniqueness of this mapping is unaffected, the radius of curvature is longer than the length of the longest side. D.Hunt - 2004


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While to avoid ill conditioning the ratio of the longest to shortest sides should be less than 5:1. 3.2.3 Element Equations Element equations combine the compatibility, equilibrium and constitutive conditions. They essentially govern the deformation of each element. The constitutive model usually takes the form of a stress-strain relationship as that shown in Equation 3.2, and therefore provides a link between equilibrium and compatability (Potts and Zdravkovic, 1999). This relationship is usually written as

  D

Eqn 3.2

where D  is the constitutive matrix and  and  are the total stress and strain vectors respectively. For linear soil materials this matrix remains constant, whereas when assuming non-linear behaviour the matrix changes with stress and/or strain. The strain-displacement relationship is given by

  Bd n

Eqn 3.3

where B  contains only derivatives of the shape function and d n contains the list of nodal displacements for a single tunnel. The element equations are derived by applying the principal of minimum potential energy where: ‘Total Potential Energy (E) = Strain Energy (W) – Work Done by the Applied Load’ The problem is reduced to summing the equilibrium equation shown in Equation 3.4 for all the elements.

K E d n  RE 

Eqn 3.4

where K E is the elemental stiffness matrix given by Equation 3.5 and RE  is the vector of incremental nodal forces. 1

1

K E     tBT DB J dSdT 1 1

D.Hunt - 2004

Eqn 3.5

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where J is the jacobian determinant derived from the jacobian matrix. In order to evaluate this equation, matrix integration is required. The most common method for 8-noded elements is Gaussian integration which uses Gauss points. For the analyses conducted here reduced integration is used. This refers to the fact that four integration points are required within the solid element compared to nine in a full integration scheme. Reduced integration was employed as it gives better results and is less expensive in terms of resources when using second order elements (Potts and Zdravkovic, 1999). 3.2.4 Global Equations The global equation is formed from the assemblage of the separate element stiffness matrices into a global matrix using the direct stiffness method. The global matrix is shown in Equation 3.6.

kG d nG  RG 

Eqn 3.6

where k G  is the global stiffness matrix, d nG is the vector of nodal displacements in the entire mesh and RG  is the nodal force vector. For non-linear soils the global equation becomes

kG i d i nG  RG i

Eqn 3.7

where each term previously described becomes incremental and i is the increment number. 3.2.5 Boundary Conditions When considering boundary conditions in Equation 3.7, the loadings will affect RG  while i

displacements will affect d  nG . i

3.2.6 Equation Solutions For a complete theoretical solution the following four conditions should be satisfied: D.Hunt - 2004




Equilibrium



Compatability



Material constitutive behaviour



Boundary conditions.

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The solution to Equation 3.6 can be found through mathematical techniques such as Gauss elimination. However, due to the non-linear constitutive behaviour used for analyses performed in this research (see Section 3.3.2.1), the value of the incremental stiffness matrix

k G i is dependent on the current stress and strain levels and is not constant. The solution to Equation 3.7 can subsequently be achieved through the Tangent Stiffness Method, Visco Plastic Method or the Modified Newton Raphson Method (Potts and Zdravkovic, 1999). 3.3 SPECIFIC DETAILS OF THE FINITE ELEMENT MODEL 3.3.1 Software and Hardware Details All analyses were undertaken using ABAQUS version 5.8-19. The analyses were performed on a desktop computer with a 466MHz Pentium II processor and 512Mb of RAM running a Windows NT4 operating system. 3.3.2 Constitutive Models for London Clay 3.3.2.1 Pre-yield model In recent years an accurate assessment of the behaviour of soils at small strains has been possible, particularly the large and rapid change in stiffness of the soil when subjected to relatively small changes in strain. Mair (1993) showed typical strain ranges for tunnels to be in the region in which the greatest variation in stiffness occurred (0.03-1.00%). The nonlinear variation in stiffness with strain was considered to be the influencing factor in tunnelling problems. Inclusion of a non-linear yield model for representing ground behaviour when considering tunnelling problems in undrained conditions has been found to improve results. Gunn (1993), Addenbrooke (1996) and Shin (2001) have all reported deeper and D.Hunt - 2004

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wider trough predictions compared to linear predictions. The non-linear small strain stiffness soil model was incorporated into ABAQUS as a subroutine. The model was based upon that reported by Jardine et al (1986), which in turn was based on earlier work of Jardine et al (1984). The later model offered a better fit to the reported data than that provided by the earlier work, although this was at the expense of a more complicated formulation. The soil model exhibits non-linear stress-strain behaviour at small strains modelling the behaviour found from field and laboratory data as shown in Figure 3.2. Equation 3.8 is a logarithmic trigonometric function and fits laboratory data reasonably well.

  Eu  A  B cos  log su  

   1 0   

a      C   



Eqn 3.8

where Eu is the secant modulus su is the undrained shear strength A, B, C,  and  are constants which can be quickly determined from test data as described in by Jardine et al (1986). The Secant modulus (Eu) is normalised by the undrained shear strength (su) and corresponds to an axial strain (a) observed in triaxial tests. The equation only holds for a specified range of strain values (where a min and a max define limits to the equation). For strains outside this range a fixed tangent stiffness is assumed. To use the ‘Jardine’ model in a finite element analysis, the secant expression given by Equation 3.8 is differentiated to give the Tangent modulus (Eut) shown in Equation 3.9: Eut BI  1  A  B cos I   sin I  su 2.303









Eqn 3.9

where I = Log10 (a/C) and the other symbols have been defined previously. By substituting a with the deviatoric strain invariant, d, Equation 3.9 can be incorporated into non-linear finite element computer programs such as ABAQUS. Values for the equation applicable to London Clay are shown in Table 3.1.

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Table 3.1 Small strain parameters from Addenbrooke (1996) A

B

1120 1016

C (%)





d min (%)

d max (%)

1.0 x 10-4

1.335

0.617

8.66025 x 10-4

0.692820

Alternative formulations for Equation 3.8 based on this substitution have been proposed by Addenbrooke (1996) as shown in Equations 3.10 and 3.11.

    3G     C  C cos  log 1 0    1 2 '  p      

 K    C  C cos  log 4 5 p'   

 d       3C3    

    1 0   

  v       C6    



Eqn 3.10



Eqn 3.11

where G is the secant shear modulus, K is the secant bulk modulus and p´ is the mean effective stress defined as: p' 

1   2   3 3

Eqn 3.12

C1, C2, C3, C4, C5, C6, , ,  and  are all constants, v is the volumetric strain and d is the deviatoric strain invariant which is related to a (the axial strain observed in the undrained triaxial test) defined respectively as: v = 1 + 2 + 3 d 

Eqn 3.13 Eqn 3.14

3 a

where d  2



1 1   2 2  1   3 2   2   3 2 6



Eqn 3.15

and 1, 2 and 3 are principal strains. The constants for stiff clays (i.e. London Clay) have been reported by Addenbrooke (1996) and are obtained by fitting a curve to laboratory data from stress path tests. By inspection of Equation 3.10 it can be seen that the secant modulus, G, is used instead of the undrained modulus, Eu, the deviatoric strain invariant, d, is used instead of the axial strain, a, and the D.Hunt - 2004


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mean effective stress, p´ is used instead of su. The relationship of shear modulus to Youngs modulus is G = E/2 (1 + ). For undrained shear,  = 0.5, thus G = E/3. Addenbrooke used Eu/P´ as this was found to be less sensitive to OCR and generally more acceptable than Eu/ su. However, p´ is found from an expression for pore pressures developed during undrained shear, which have not been considered in the current research. Hence, Equation 3.8 has been implemented into ABAQUS. The stiffness is continually changing throughout an analysis and depends on the current strain and undrained shear strength (or current mean effective stress) depending on whether Equation 3.8 or 3.10 is used. The groundwater was not considered separately but included in the total weight of the soil. The Poissons’ ratio should ideally be taken as 0.5 for undrained saturated conditions. However, this results in severe numerical problems, as all terms of the [D] matrix becoming infinite. Potts and Zdravkovic (1999), based on earlier work of Poulos (1967), reported that once the value exceeds 0.499, the value has little effect on the prediction, hence  was taken as 0.499. (A value of 0.49999 was found to cause errors in the solution.) 3.3.2.2 Yield model The three-dimensional Mohr-Coulomb failure criterion has been employed for the yielding of stiff clay in all of the analyses presented in this thesis. The Mohr-Coulomb yield criterion is a straight line in the meridonal plane and irregular hexagonal cone in principal stress space showing six-fold symmetry in the deviatoric plane (Figure 3.3). The irregularity is due to the fact that 2 is not taken into account. The yield surface F  shown in Figure 3.3 is defined in Equation 3.16:

F   

J 1  0  p  a g  

Eqn 3.16

where a is the adhesion (a = c/g()), g() is the function describing the yield surface in the deviatoric plane, c is the cohesion intercept,  is Lodes angle and J is the deviatoric stress defined as:

J 

2 2 2 1                        1  1  2 2  3  3         6  

D.Hunt - 2004

Eqn 3.17

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g  

sin  1 cos   sin  sin  3

Eqn 3.18

  2   3    2b  1  where    tan 1   , and where b            3   1 3  

and  is the angle of internal shearing resistance, with a tension positive sign convention. The model uses a flow potential that has a hyperbolic shape in the meridional stress plane and has no corners in the deviatoric stress space. The flow potential used in ABAQUS is completely smooth based upon the deviatoric elliptic function used by Menetrey and Williams (1995). The Mohr-Coulomb yield surface parameters, plastic potential parameters and unit weight for London clay are shown in Table 4.2. Table 3.2 Typical Mohr-Coulomb yield surface and plastic potential parameters and unit weight (Addenbrooke, 1996). Yield surface - strength parameters

Plastic potential - dilation angle

Bulk unit weight



c (kPa)

ψ'

kN/m3

25.0O

5.0

12.5O

20

3.3.3 Contact Elements The interaction between the liner and the soil has been modelled using contact elements. Contact elements provide a more accurate way of modelling the soil structure interaction that occurs between the liner and the soil (Potts and Zdravkovic, 1999). The finite sliding rigid contact is implemented by means of a family of contact elements, employing Mohr-Coulomb friction, automatically generated by the ABAQUS program, based on the data associated with the contact pair (Hibbet et al, 1997). For a single tunnel interaction the ABAQUS program generated 96 contact elements between the soil and the liner elements. The soil was defined as the ‘slave’ surface and the liner was defined as the ‘master’ surface. This slave surface was not allowed to penetrate the master surface. The maximum elastic slippage was set at 0.5% of the average length of the contact elements (a default value in ABAQUS). D.Hunt - 2004

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3.3.4 Material Properties for the Soil All the analyses were carried out using case history data for a typically elastic stiff London clay as shown in Figure 3.4. The undrained modulus varied linearly with depth according case history data reported by Burland and Kalra (1986) as shown in Equation 3.19. Eu (Pa) =1000000*(10+5.20Z)

Soil 1

Eqn 3.19

Eu (Pa) =1000000*(65+19.5Z)

Soil 2

Eqn 3.20

where Z is the depth in (m), Equation 3.19 leads to an undrained modulus of Eu=145.2MPa at a tunnel axis depth of 26.0m Equation 3.20 provides an upper bound to the data presented by Burland and Kalra (1986). The undrained strength was assumed to vary linearly with depth according to the case history data reported by reported by Mott-MacDonald (1991) as shown in Equation 3.21. Equation 3.22 is an upper bound value to the data. su (Pa) = 1000*(50+8Z)

Soil 1

Eqn 3.21

su (Pa) = 1000*(110+17.5Z)

Soil 2

Eqn 3.22

For the analyses conducted in Chapters 4 and 5 two types of soil are considered referred to as Soil 1 which utilises Equations 3.19 and 3.21 and, Soil 2, which utilises Equation 3.20 and 3.22. For the finite element mesh (Figure 4.1 in Chapter 4) the material properties mentioned above were specified at the midpoint of the vertical elevation of each of the 28 layers of elements over the depth. For the irregular shaped elements that surround the tunnels properties were still assigned at the midpoint node of their vertical elevation. This was subsequently found to improve the horizontal ground movement predictions within this region. 3.3.5 Material Properties for Tunnel Liners and Anchorage System The concrete liners were modelled using continuum elements (i.e. the same 8-noded elements used to model the soil). Many researchers have reported the use of beam elements to model the liner (e.g. Addenbrooke, 1996). However, in this research beam elements were not used D.Hunt - 2004


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due to the modelling method proposed. In addition ABAQUS does not allow beam elements to be removed or added to the mesh during calculation. The modelling process proposed here requires the removal and addition of liner elements for the analysis of a single tunnel. Tang et al (2000) and Guedos de Melo and Pereira (2000) reported that removal of the liner elements can only be achieved in ABAQUS when using continuum elements to model the liner. These elements have been shown to give realistic liner behaviour when compared to beam elements (Augarde and Burd, 2001). The 200mm thick concrete liners were assumed to be elastic and isotropic. The values of unit weight (24kN/m3), Young’s Modulus (28 x 109 Pa) and Poissons’ ratio (0.15) were consistent with those adopted by Addenbrooke (1996). Due to the presence of a physical gap between the liner and the soil, the liner must be restrained (anchored) to a fixed location during the analysis to avoid rigid body movements. The anchorage could have been achieved by using springs. However, the method chosen for these analyses was to incorporate an anchorage ring of elements on the inside of the liner (referred to as anchor elements). The inner edge of these anchor elements were initially assigned as a fixed boundary. The anchor elements were also assigned material properties that would allow realistic liner deformation to occur as the soil made contact with the liner. The liner could be held rigid with a stiff material or allowed to drop toward the tunnel invert with a softer material. 3.3.6 Boundary Conditions Oteo and Sagaseta (1982) suggested that the distance to the boundary should be taken as >10 diameters from the tunnel centreline to the outer vertical boundary in order to avoid boundary effects when employing a linear elastic analysis. Various authors have used non-linear small strain soil models with similar sized boundaries. Addenbrooke (1996) employed a boundary distance of 70m for a 4.16m tunnel at 20m depth in London clay and Shin (2001) employed a 102m boundary distance for an 8.2m by 5.0m NATM tunnel at 20m depth in decomposed granite. For the analyses reported in this research the distance from the tunnel centreline to the boundary was taken as 105m which equates to >10 diameters for the larger 9.0m tunnels and >26 diameters for the 4.0m tunnels. The effect of boundary distance on settlement profiles is discussed further in Chapter 6. Different boundary conditions, such as applied loadings and fixed displacement conditions, were applied during the tunnel construction phase; these are described in detail in Section 3.5.5. D.Hunt - 2004

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3.4 MODELLING A SINGLE TUNNEL ANALYSIS Three types of model exist for analysing tunnels in two dimensions: these are, longitudinal, axi-symmetric and transverse. The longitudinal model considers a plane along the tunnel axis and the axi-symmetric model incorporates some 3-D conditions in axi-symmetric space (without a ground surface). The most common technique is the transverse technique, which considers a plane strain analysis of a cut section perpendicular to the tunnel. This type of twodimensional modelling does not consider the out of plane movements that occur in front of the tunnel, especially for open faced tunnelling, although the idealization becomes closer to reality when considering closed faced tunnelling (Mair and Taylor, 1997). The various methods available for simulating a tunnel construction using the transverse technique are considered below. 3.4.1 Stress reduction The stress reduction method is also referred to as convergence/confinement method (Panet and Guenot, 1982). The method considered 2D finite element analysis based on the ground reaction curve concept reported by Peck (1969). The 3D effects are assumed as equivalent to those obtained by applying an internal radial pressure to the boundary that will ultimately be the tunnel periphery. The method simply reduces a portion of the stresses imposed on the tunnel boundary, before installing the tunnel lining. This can be simplified by considering the radial stresses, r, for plane strain conditions as shown in Equation 3.23 and Figure 3.5: r

= (1 - ) o

Eqn 3.23

where o is the initial ground stress prior to tunnelling and  is the stress release factor (which varies between 0 and 1). As the stress is removed from the tunnel boundary, radial displacements occur which are equivalent to the volume loss. Leca and Clough (1992) suggested a design value for  of 0.5 when predicting movements in plastic clay above the Washington Metro. Bernat et al (1999) reported the convergence/confinement method used to analyse the behaviour of twin tunnels on the Lyons Vaise metro. The method assumed no support in the tunnel and difficulties arose in finding a value for  applicable to the project. Bernat (1995) used  = 0.35 in order to obtain settlements between 20-30mm, when using D.Hunt - 2004


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back analyses of field data in various clays. This value was subsequently used by Guedes de Melo and Pereira (2000) for 2D and 3D simulations of shallow tunnel construction. Kim et al (1996) reported a method of tunnel construction for modelling small-scale tunnels in 2D that involved the removal of soil elements and then the application of an internal suction called ‘hoop shrinkage’. The method has also been associated with 3D analyses (e.g. Akagi and Komiya, 1996 and Augarde et al, 1999). 3.4.2 Stiffness Reduction Swoboda (1979) reported a method of analysis called the “Progressive Softening Approach”. The method was initially devised for simulating a benched excavation when considering the construction of NATM tunnels. The method reduces the stiffness of the soil within the tunnel area prior to excavation and placement of the tunnel lining. This softening can be achieved by multiplying the initial Young’s modulus prior to excavation, E0, by a stiffness reduction factor, , in order to achieve a softer E prior to the lining installation as shown in Figure 3.6. The factor  can be seen to be analogous to  described in Section 3.5.1. The amount by which the stiffness is reduced requires considerable experience and judgement. Atzl and Mayr (1994) recommended a value of 0.2 when analysing both the side-drift and enlargement of the Heathrow Expressway tunnel in London Clay. 3.4.3 Volume Loss Method The volume loss method is a relatively recent development proposed by Addenbrooke et al (1997) and is similar to the convergence/confinement method. The procedure is applicable to cohesive soils where the volume lost into the tunnel is the same as the volume of the surface settlement trough. With the convergence/confinement method the outward forces are gradually reduced until at a certain value the liner is installed. With the volume loss method the first step is to find the outward forces that act on the tunnel boundary. Secondly, these forces are applied inwards and are gradually increased in increments until an appropriate value of volume loss has been achieved. At this stage the lining is installed (Figure 3.7).

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3.4.4 The ‘Gap’ Parameter Rowe et al (1983) introduced the ‘gap’ parameter as a two-dimensional tool for representing the full three-dimensional losses occurring above a single tunnel construction. Rowe and Lee (1992b) proposed that the surface settlement was largely related to the volume of lost ground at the tunnel and could be represented by a gap parameter as shown in Figure 3.8. Rowe et al (1992a) used an elasto-plastic 3D finite element analysis to develop a means of quantifying the gap parameter for use in a 2D analysis. The ‘gap’ parameter represents the geometric clearance between the outer skin of the shield and the lining. Both the tunnel and the lining are assumed circular, although the lining is positioned at the base of the tunnel resulting in a non-uniform gap (Gap) as shown in Figure 3.8 (b). The appropriate parameters relevant to the gap parameter are shown in Equation 3.23. Gap = U* 3d + ω + ( 2 + ) Where

Eqn 3.23

U* 3d

=

over excavation due to 3D movements ahead of the tunnel face (m)

ω

=

factor depending on workmanship (m)



=

thickness of the tail piece (m)



=

clearance required for the erection of the lining (m).

The ‘gap’ parameter requires experience to use it properly and the value used depends on the tunnelling machine technique, soil type, liner characteristics and the skill of the operator. Some factors such as ω are hard to evaluate. Rowe and Lee (1992a) used the gap parameter in 2D FE analyses for four tunnelling case histories and reported good agreement with field observations. The method works well when closed-face techniques, such as EPBM or slurry shields, are used to provide full support to the face. However, where stress relief occurs at the face, as in open-faced tunnelling, 2D idealisations are inevitably more approximate. The gap parameter is usually used in conjunction with some type of contact surface. When displacement of the node indicates that the void has been closed and the soil is in contact with the pre-defined liner position, soil/lining interaction is activated at the node. The gap parameter can be used empirically as reported by Lo et al (1984) and Lee (1996).

D.Hunt - 2004

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3.4.5 Using a Modified ‘Gap Parameter’ to Model Volume Loss (This Research) A modified ‘Gap parameter’ method similar to that reported in Section 3.4.4 Rowe et al (1983) was used to obtain a volume loss for all the analyses reported in this thesis. The volume loss was created in the model by incorporating a physical gap between the liner and the tunnel. The method provided a simple way of controlling the amount of volume loss required by changing the size of the gap. The method proposed here is different to that suggested by Rowe et al (1983), in which effects of workmanship and 3D effects were included when determining the size of the gap. However, due to the parametric nature of the current study their inclusion into this study was not considered relevant. In preference, the gap was specified as a percentage volume of the tunnel volume per metre length of excavation. The volume per unit length of the gap exactly matches that of the surface settlement trough due to the undrained behaviour assumed in the analysis. The amount of soil to be removed varied according to the diameter of the tunnel to be excavated and the required volume loss. The nodes around the tunnel boundary were situated so as to include a prescribed gap between the liner and the tunnel. In each case this gap was the volume loss for the analysis. The size of the gap (Gapm) was specified by Equation 3.24 and is shown in Figure 3.8 (b).

  Dt  Gap m   2    where

   1  1 V    1  l   100   

Dt

=

Diameter of tunnel (m)

Vl

=

Volume loss (%)

Eqn 3.24

Applying Equation 3.24 to a 4.5m radius tunnel with a 1.3% volume loss this leads to a gap of 29.5mm The non uniform ‘gap’ parameter (Gap) proposed by Rowe et al (1983) is assumed non-uniform in shape with the maximum dimension between the tunnel crown and the tail void with zero thickness between the tail void and the tunnel invert. The ‘Gap m’ parameter described in Equation 3.24 is slightly different, as the liner was initially located in the centre of the tunnel leading to a uniform void around the periphery. This method was chosen in D.Hunt - 2004


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preference to the Rowe et al (1983) method due to the difficulties involved in producing full closure of the void when using contact elements with that original method. The final position of the liner is not affected significantly by this new approach. As the soil is gradually released onto the liner, due to the restraining system adopted, it is pushed towards the invert of the tunnel. ABAQUS required all the elements to be present at the start of the analysis; consequently this meant the liner elements, anchorage elements and contact elements were deactivated at the start of the analysis and reactivated at the appropriate stage in the analysis. The soil inside the tunnel was active at the start of the analysis and deactivated before the tunnel was constructed. Figure 3.9 a-d shows an enlarged section of the soil surrounding a single tunnel at various stages of the modelling process. To model a single tunnel two analyses must be performed. The first analysis produces the required information for the final analysis, as described below. Analysis 1.

Initially all the liners, anchors and soil are present in the model. The first step

requires deactivation of the liners and the anchors. The second step applies gravity to all the soil in the model. In the third step a fixed boundary is introduced to the node set making up the tunnel boundary within which the soil is subsequently removed. The reaction forces required to hold the soil up inside tunnel (i.e. hold the nodes in equilibrium) are then found (Figure 3.9a). Analysis 2.

Analysis 1 is rerun with additional stages. After the soil is removed in the

tunnel the reaction forces found in Analysis 1 are used to hold the soil up (i.e. hold the nodes in equilibrium) (Figure 3.9b). The liners and the anchorage system are reactivated inside the open tunnel and gravity is then applied (Figure 3.9c). The reaction forces holding the soil in equilibrium are gradually released in a stepped manner until the soil is fully in contact with the liner surface (Figure 3.9d). The soil is released in 9 steps from 100% to 0% (i.e. 100, 95, 85, 75, 60, 45, 30, 20, 10 and then 0%) The magnitude of reduction is imposed over the whole tunnel perimeter for each step respectively. The anchorage system is removed when the soil and liner are fully contacted. [N.B. The gradual releasing of forces in a stepped manner was found to reduce numerical errors, such as zero pivot and negative Eigenvalues. The stepped reduction in reaction forces also causes gradual increases in vertical displacement, which are analogous to an advancing tunnel face in three dimensions.]

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3.5 DISCUSSION Ultimately, the results of the finite element analyses conducted during this research will be used in Chapter 8 to improve the existing predictive methods for movements above twin tunnels reported in Chapter 2. This chapter has shown that there are an abundance of simple methods for implementing volume loss into 2D models for single tunnels, some of which have been applied to twin tunnels (e.g. the ‘volume loss’ method by Addenbrooke, 1996). This chapter has also shown how a modified 2D gap parameter can be used to model volume loss for a tunnel. The method was subsequently found to be a robust method for modelling volume loss when used for the analyses conducted during this research. There may be scope for further investigation into this modelling method when considering the way in which the forces (described in Section 3.4.5), used to hold the soil up, are reduced. For the analyses conducted during this research, the forces were reduced equally around the periphery of the tunnel in specified increments. The author is aware, however, that the effect of reducing these forces at different rates for the invert and crown may result in a different ground settlement profile. However, this was beyond the time-frame of this project and could be considered as part of future research. Based on the work of Mair (1993) and Addenbrooke (1996), a nonlinear soil model was chosen in order to replicate the variation in stiffness with strain level, which is a key aspect in influencing ground response due to tunnelling. The parametric nature of the study warranted the use of 2D modelling (in preference to 3D) in order to make a first stage improvement to this predictive method. The use of full 3D analyses would have required the development of a robust method for modelling volume loss within ABAQUS. In conjunction with this the implementation of a non-linear soil model formulated for the purpose of 3D modelling would also have been required. Both of these would have required a lot of time to implement. The lack of computer power at the time would also have resulted in long run times for analyses. However, with recent advances in computing power the use of this type of modelling may now be possible and the application of 3D modelling could be carried forward in any future research undertaken.

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1

8

4

Eight noded solid element

5

2

7

6

3

Figure 3.1 8-noded CPE8R element

Trigonometric function

2500

Eu Cu

2000

1500

Linear region stiffness Eu varies with Cu

1000 Linear region stiffness Eu varies with Cu

Linear region stiffness Eu varies with strain level and Cu

500

0

amax

amin Axial Strain (%)

Figure 3.2 Small strain stiffness model (after Jardine, 1986) D.Hunt - 2004

-500

'1  = 30 Chapter 3 – The Finite Element method and Tunnel construction

 = 0

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 = -30

 J

g()

F(') g()

'2

'3

P'

a

a) Failure criterion

'1

Space diagonal 1 = 2 = 3 '2

b) View in principal stress space '3

'1  = 30

 = 0  = -30



Space diagonal

g()

'2

'3

c) View in deviatoric plane

Figure 3.3 Mohr Coulomb failure criterion (tension positive) '1

D.Hunt - 2004

6

Soil 2 Eu =10 (65 + 19.5Z)

Soil 1 Eu = 106 (10 + 5.2Z) Burland and Kalra (1986)

Zo

Zo

D.Hunt - 2004

Depth (m)

-70

-60

-50

-40

-30

-20

Figure 3.4 Tunnel geometry and material properties

London Clay parameters

= 16.4, 26, 30.9 & 33.4m Diameter 4m and 9m

0

0.5

1

su x 106 (kPa)

Depth (m)

-70

-60

-50

-40

-30

-20

-10

15

-10

1 0

0.5

0

0

Eu x 109 (kPa) 1.5

Soil 2 s u = 103 (100 + 15.5Z)

Soil 1 su = 103 (50 + 8Z) Mott-MacDonald, (1991)


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Initial

Excavation/ unloading

 o 

 d 

 i    o 

Lining installation/ unloading

   *  d 

 d    d  o 

 d *  1  d  o 

Figure 3.5 Stress reduction (Panet and Guenot, 1982)

Initial

Stiffness reduction and unloading

o 

Eo

Eo Ee

Eo=Ee

E e'

E e' =  E o

Figure 3.6 Stiffness reduction (Swodoba, 1979) D.Hunt - 2004

excavation, lining installation and unloading

  *

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Free surface Vs

Z0

Vs = V e - V t Vs = volume of settlement trough Ve = excavated tunnel volume Vt = final tunnel volume

F

- F

Forces imposed on tunnel boundary due to excavation

Forces imposed by soil to be excavated

Figure 3.7 Volume loss method (Addenbrooke, 1996)

Initial position of tunnel Final position of tunnel

Gap

Gap m

Initial position of liner Dl

Dt Dl

Final position of tunnel and liner

Dt = Diameter tunnel Dl = Diameter liner

(a)

(b)

Figure 3.8 (a) Gap parameter (Rowe et al, 1983) and (b) Modified gap parameter D.Hunt - 2004

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SOL1

Symbols used:

Reaction forces applied at each of the tunnel nodes in the X and Y directions (RF-X and RF-Y respectively)

Fixed boundary (for finding RF-Y and RF-X) Reaction forces used to prop open tunnel Tunnel liner and anchor elements

RF-Y

RF-X

N.B. Tunnel liner not to scale

a) Tunnel boundary fixed to find reaction forces.

c) Tunnel liner and anchor elements reactivated, fixed boundary within anchor imposed. Soil gradually released.

b)

Soil ins ide fixed boundary (SOL1) removed and reaction forces applied to nodes.

d) Soil fully released and in contact with liner. Inner fixed boundary and anchor elements removed.

.

Figure 3.9. Modelling a single tunnel using a gap parameter in the finite element method.

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Chapter 4 - Movements above a single tunnel

Chapter Four MOVEMENTS ABOVE A SINGLE TUNNEL

4.1 INTRODUCTION This chapter considers the analysis of single tunnel constructions in London Clay. Greenfield conditions are assumed for all the analyses undertaken. The analyses were performed using ABAQUS in combination with a non-linear pre yield model (Chapter 3). One of the aims of the analyses is to ascertain the effect of changes to tunnel depth, diameter, volume loss and soil stiffness on the settlement profile. The various values chosen for each of these variables were: 

tunnel depth (16.4, 26.0, 30.9 and 33.4m);



tunnel diameter (4.0 and 9.0m);



volume loss (1.3 and 2.0%);



soil stiffness (Soil 1 and Soil 2, stiff to very stiff - see Chapter 3).

. The reasons for choosing these parameter ranges is detailed in Section 4.2. The chapter reports the resulting horizontal and vertical displacements for surface and sub-surface regions obtained from these analyses. The accuracy of the displacement profile predicted using the finite element method is assessed by comparison with predictions made using currently available empirical predictive methods (e.g. O’Reilly and New 1982, Mair et al 1993, Heath and West 1996 and Grant and Taylor 2000). The comparisons between the profiles are made by looking at the position and magnitude of certain key features: 

Wmax



Umax



Umax / Wmax



i (i.e. position of Umax)

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

Length of full trough width taken as a multiple of i (usually 6i for empirical predictions)

where the symbols have been previously defined in Chapter 2. Consideration of the shape of the displacement profile is undertaken by comparing the distributions along the settlement profile of: 

U/ Umax



W/ Wmax



U/W

The ‘relative’ changes of the settlement profile for sub-surface regions are considered by comparing the values of different sub-surface regions: 

Wmax ss (sub-surface) / Wmax (surface)



Umax / Wmax



i (sub-surface) / i0 (surface)

These ‘relative’ changes can then be directly compared to empirical methods in a manner which avoids comparing magnitudes of displacement. This chapter highlights the ability of the finite element modelling method to react to specific parameter changes (e.g. volume loss, depth and tunnel diameter) and to compare the behaviour to empirical predictions. Challenges for the finite element model, based on the ‘relative’ changes in behaviour caused by changes to parameter selection for the empirical model, are shown below: 1. Does doubling the tunnel depth halve the maximum settlement (Wmax) and double the distance to the position of Umax? 2. Does increasing the volume loss from 1.3% to 2.0% increase the maximum settlement by the same amount? 3. Does increasing the tunnel diameter from 4.0m to 9.0m increase the maximum settlement by the same ratio for both models?

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This chapter considers the capabilities of the current finite element modelling method when predicting these ‘relative’ changes in displacement compared to those found from empirical predictive methods. The most important of these ‘relative’ changes is the response of the finite element model to changes in soil stiffness, which occur when constructing tunnels at different depths (i.e. the soil stiffness increases with depth). 4.2 SINGLE TUNNEL DETAILS The tunnel geometry, soil properties, liner details and construction method and boundary conditions have all been fully described in Chapter 3. The details of all the analyses undertaken in this chapter are shown in Table 4.1. Table 4.1 Analyses performed Tunnel Depth (m) 16.4 16.4 26.0 26.0 26.0 26.0 33.4 33.4

Tunnel diameter (m) 4.0 9.0 9.0 9.0 4.0 4.0 4.0 9.0

Volume loss (%) 1.3 1.3 1.3 1.3 1.3 2.0 1.3 1.3

Soil Type 1 1 1 2 1 1 1 1

The geometries of the tunnels are representative of tunnels found in London (U.K.). The 9.0m-diameter tunnels constructed at a depth of 26.0m represented the same dimensions as the Heathrow Express tunnels in London, which were constructed between 1994 and 1997 (referred to as the Concourse, Upline and Downline tunnels by Cooper and Chapman 1998). The 4.0m diameter tunnels represent the smaller diameter tunnels often used, such as those found on the Piccadilly Lines or under St James’ Park (Addenbrooke, 1996). For simplicity the 9.0m and 4.0m diameter tunnel liners were modelled as continuous concrete rings. The liner thickness was taken as 200mm thick, which is comparable to the liners used (further details can be found in Chapter 3). The soil material was assumed to be stiff London Clay, to allow comparison with previous work for tunnels found in London (U.K.) Addenbrooke (1996) performed several numerical analyses, using the soil model proposed by Jardine et al (1986), to investigate the ground movements resulting from the consruction of 4.0m diameter tunnels at St James Park in London at depths of 20.0m and 34.0m. The study performed by Addenbrooke (1996) can be used for comparison with this study. The D.Hunt - 2004

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current research considers a more robust method for modelling volume loss using a modified ‘gap parameter’ compared to the ‘volume loss’ method used by Addenbrooke (1996) and reported in Chapter 3. This study also considers horizontal movements for surface and subsurface regions, which were not considered in the study by Addenbrooke (1996). The volume losses, taken as 1.3% and 2.0% in the analyses, represents the range of values reported for the 9.0m diameter tunnels by Cooper and Chapman (1998). The values are typical of the volume losses experienced when constructing tunnels using an open-faced excavation with a shield (Chapter 2). These tunnel geometries (e.g. liner details, volume losses and depths) were subsequently used in the side-by-side, piggy back, offset and triple tunnel analyses reported in Chapters 5 and 6, respectively. The general mesh used for a single tunnel at a depth of 26m is shown in Figure 4.1. The mesh consists of 28 rows of ‘isoparametric’ elements, refined in regions where detailed displacement information is required (i.e. near the surface and in a region directly above each tunnel) and less refined where less detailed information is required (i.e. near the base boundary and near to the vertical boundaries of the model). The mesh was modified to account for deeper and shallower tunnels by adding or removing rows of elements respectively. Due to the parametric nature of the project the results of the finite element analyses in this chapter are compared to greenfield predictions using empirical methods and not to case history data. This allows for simpler analysis of the data meaning that similarities and discrepancies between the two methods can be highlighted. 4.3 RESULTS OF SINGLE TUNNEL ANALYSES 4.3.1 Displacements Figure 4.2 shows the horizontal and vertical displacements above a 9.0m diameter tunnel constructed at 26m below ground level (bgl) with a volume loss of 1.3%. Soil 1was used in the analysis (see Section 3.3.3). The maximum vertical surface displacement, Wmax, was found to be 11.9mm and was situated above the centreline of the tunnel. The maximum horizontal displacement, Umax, was found to be 6.8mm and was situated at 20.0m from, and on both sides of, the tunnel centreline. For sub-surface regions the value of Wmax increases with depth, with values of 16mm, 19mm and 22mm were recorded at depths of 6.9m, 11.4m and 15.9m below ground level respectively. The magnitudes of Umax recorded with depth D.Hunt - 2004

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were 6.8mm, 5.7mm, 5.8mm and 6.8mm for depths of 0.0m, 6.9m, 11.4m and 15.9m bgl respectively. The position of Umax from the tunnel centreline can be seen to decrease with depth from 20.0m at the ground surface level to 18.0m, 15.0m, and 11.0m at depths of 6.9m, 11.4m and 15.4m bgl respectively. Figure 4.3 shows the effect of using a stiffer soil (i.e. Soil 2), while keeping the depth (26m), tunnel diameter (9.0m) and volume loss (1.3%) constant. When comparing the finite element predictions of Soil 2 with Soil 1 it can be seen that the magnitudes of the vertical displacement increased for all surface and sub-surface regions. An increase from 11.9mm to 14.5mm was found for the ground surface level and an increase from 22.0mm to 26.6mm for the sub-surface level of 15.4m bgl. The magnitudes of the horizontal displacements remained relatively unchanged for all sub-surface regions, although a slight increase from 6.8 to 7.0mm was found for the ground surface level. The position of Umax reduced by 17% for the surface level (i.e. from 20.0m to 16.6m) and by 7% for the sub-surface level of 15.4m bgl (i.e. from 11.0m to 10.2m). The settlement profiles resulting from the use of a smaller 4.0m diameter tunnel, whilst keeping the depth (26m) and volume loss (1.3%) constant and using Soil 1 are shown in Figure 4.4. The values of Wmax increase with depth from a value of 2.5mm at the ground surface to 4.9mm at 15.4m bgl. The value of Umax at the surface is 1.3mm around 50% of the value of Wmax which is 2.5mm. At a depth of 15.4m bgl the value of Umax has increased to 1.45mm and is now only 30% of the value of Wmax which is 4.9mm. This shows that there is a non-linear relationship between U and W for sub-surface regions, which is in agreement with the work reported by Grant and Taylor (2000). When comparing the ground surface displacements for the 4.0m tunnel with those found for the 9.0m tunnel (Figure 4.2) the value of Wmax is reduced from 11.9mm to 2.5mm and the value of Umax is reduced from 6.8mm to 1.3mm. It is apparent that by reducing the tunnel from a 9.0m tunnel diameter to a 4.0m diameter that the magnitudes of displacement (horizontal and vertical) are reduced by around 80%. The position of Umax (i) is situated at 20.0m from the centreline of the tunnel for both the 9.0m and 4.0m diameter tunnels. The sub-surface values of (i) are slightly smaller for the 4.0m diameter tunnel than the 9.0m diameter tunnel. This shows that there is some dependency of i on the tunnel diameter in regions close to the tunnel, which is in agreement with the findings of Moh and Hwang (1993). This analysis of the 4.0m tunnel was re-run using a larger volume loss of 2.0%. The increase in volume loss was achieved by increasing the gap surrounding the tunnel liner. The effect of increasing the volume loss on the displacement profiles predicted from the finite D.Hunt - 2004

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element method can be seen in Figure 4.5. The vertical surface ground displacements are increased from 2.5mm to 4.1mm when compared to Figure 4.4 (i.e. an increase of 63%) with the horizontal displacements increasing from 1.3mm to 2.0mm (i.e. an increase of 54%). The sub-surface displacements at 15.9m bgl showed the same increases in magnitude from 4.9mm to 8.0mm (i.e. an increase of 63%) for the vertical displacements and from 1.5mm to 2.2mm (i.e. an increase of 52%) for the horizontal displacements. The effect of tunnel depth on the predictions is highlighted by analysing both the 4.0m and 9.0m diameter tunnels at depths of 16.4m and 33.4m, using a 1.3% volume loss and Soil 1 for all four analyses. The displacements above the 4.0m and 9.0m tunnels at a depth of 16.4m are shown in Figure 4.6 and Figure 4.7 respectively. The value of Wmax at the surface for the 9.0m diameter tunnels is 15.0mm and for the 4.0m diameter tunnel is 3.8mm. The value of Umax for the 9.0m diameter tunnel is 8.5mm and is situated at a distance of 12.0m from the centreline of the tunnel, whereas Umax for the 4.0m diameter tunnels is 2.0mm and this is situated at 14.0m from the tunnel centreline. The reduction in diameter from 9.0m to 4.0m reduces the maximum vertical displacements by around 80% and the horizontal displacements by around 77%. Both of these values are close to the values found when reducing the tunnel diameter from 9.0m to 4.0m at a depth of 26.0m (reported earlier in this section). The displacements above the 4.0m and 9.0m tunnel at a depth of 33.4m are shown in Figure 4.8 and Figure 4.9 respectively. The value of Wmax at the surface is 1.9mm for the 4.0m diameter tunnel and 9.7mm value for the 9.0m tunnel. The values of Umax are 1.0mm and 5.1mm respectively for the 4.0m and 9.0m tunnels, both being situated at 23.0m from the tunnel centreline. Once again it can be seen that the reduction in tunnel diameter from 9.0m to 4.0m reduces the displacements (vertical and horizontal) by around 80%. Comparing the displacements for a tunnel at a depth of 16.4m with those above a tunnel at 26.0m and 33.4m depth (assuming a constant volume loss and tunnel diameter) it becomes apparent that the deeper the tunnel the smaller the displacements (surface and sub-surface) become. This is in broad agreement with case history data reported by Mair and Taylor (1997). 4.3.2 Liner Behaviour Figure 4.10 (a) shows the behaviour of a 9.0m tunnel constructed at a depth of 26.0m bgl. The movement of the liner was found by recording the movement at four points on the tunnel D.Hunt - 2004

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liner. The points were situated at the tunnel crown, the axis level (both sides) and the invert. The difference between the crown and invert was measured before and after the analysis in order to assess the vertical deformation of the tunnel liner (sometimes termed ‘squat’). The tunnel initially drops by around 4.8mm and is vertically extended by 0.7mm. The tunnel deformation is relatively small when compared to the vertical displacement. It must be noted that the tunnel did not move the full distance to the base of the invert for the 9.0m diameter tunnels. A 4.0m diameter tunnel constructed at a depth of 26.0m bgl displaced downwards by 1.8mm and experienced 0.1mm of squat (Figure 4.10 (b)). 4.4

EMPIRICAL

PREDICTIONS

COMPARED

TO

FINITE

ELEMENT

PREDICTIONS 4.4.1 Surface Displacements Figure 4.11 shows the surface settlement profile for the finite element analysis of a 9.0m diameter tunnel at a depth of 26.0m bgl using a volume loss of 1.3% in Soil 1 and compares it with an empirical prediction based on Equations 2.8, 2.10, 2.31 and 2.39 proposed by Mair et al (1993). The trough width parameter (K) is assumed to be 0.5 and the vector focus for movements is assumed to be at the tunnel axis for the empirical model. The finite element analysis predicts a Wmax of 11.9mm, which is only 47% of the 25.4mm predicted by the empirical method. The magnitude of Umax is found to be 6.8mm from finite element analyses, an over-prediction of 36% compared to the 5.0mm displacement predicted by the empirical method. When assuming a vector focus at the tunnel axis the empirical model predicts a value of Umax / Wmax of 0.202, whereas the finite element model predicts a value of 0.570. The position of Umax from the centreline of the tunnel, referred to as (ife) for the finite element analysis and (ie) for the empirical method, are 20.0m and 13.0m respectively (i.e an overprediction of 53%). The full trough width for the empirical predictions is shown to occur at 3ie or 39m. However, for the finite element model it is impossible to gauge where the full trough width occurs because the displacements at >5ife or 105m are still large (i.e. approximately 2mm). Figure 4.12 shows a sub-surface contour plot of W/Wmax for the tunnel analysis shown in Figure 4.11 for the finite element analysis and empirical prediction (again determined from empirical equations proposed by Mair et al, 1993). The contour plots form the sub-surface vertical displacement contours in the z plane, comparable to the vertical surface displacement D.Hunt - 2004

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contour plot in the (x,y) plane reported by Attewell et al (1986). Wmax is taken as the value specific to the sub-surface depth (i.e. its value increases with depth). The contours of W/Wmax = 1 and 0, and the position of Umax are highlighted for both sets of predictions. At the ground surface the position of Umax for the empirical prediction is 13.0m compared to 20.0m for the finite element prediction, i.e. the finite element model over predicts the position of Umax by 54%. This is also evident for sub-surface movements. The position of Umax lies on the contour of W/Wmax = 0.606 for all the empirical predictions, whereas it lies on the contour of W/W max = 0.500 for the finite element predictions. The contour of Wmax = 0 reduces with depth from 39.0m at ground surface level (assuming a full trough width of 3i e) to 25.0m at 15.4m bgl for the empirical prediction. The finite element analysis does not give a clear indication of where the full trough actually finishes for either the surface or sub-surface regions. 4.4.1.1 Volume loss Figure 4.13 contrasts the changes in displacement profiles caused by increasing the volume loss for the finite element predictions with those from empirical predictions. The tunnel is 4.0m in diameter and is assumed to be at a depth of 26.0m bgl. The assumptions for empirical predictions are the same as those described in Section 4.4.1. For a volume loss of 1.3% the finite element prediction for Wmax is 2.5mm compared to 5.0mm for the empirical prediction, i.e. an under-prediction of 50%. For a volume loss of 2.0% the values are 4.1mm and 7.7mm i.e. an under-prediction of 55%. The magnitude of Umax is over-predicted by 30% and 33% respectively for the finite element predictions compared to the empirical predictions for volume losses of 1.3% and 2.0%. The position of Umax is over-predicted by 54% for the finite element predictions compared to the empirical predictions for both volume losses. The magnitudes of displacement for both of the finite element analyses are quite different when compared to the empirical predictions. However, it is reassuring that both the finite element method and empirical predictions show an increase in the magnitudes of W max and Umax by a factor of 2.0/1.3 when the volume loss is increased from 1.3 to 2.0%. Both analyses also predict no change in the position of Umax with this increased volume loss, i.e. within the confinements of the finite element model the relative changes in displacement due to variations in volume loss appear to be identical for both predictive methods. 4.4.1.2 Effect of Depth

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It is again interesting to note the very good comparison in behaviour between the finite element predictions and empirical predictions when analysing ‘relative’ changes in displacement with increased tunnel depth. Figure 4.14 shows the effect of doubling the tunnel depth from 16.4m to 33.4m. The value of Wmax is halved for both finite element and empirical predictions. The magnitude of Umax is also halved and its relative position doubled for both predictive methods. 4.4.1.3 Settlement profile shape Figures 4.15 and 4.16 show the general shape of the settlement profile for all of the finite element analyses and empirical predictions. The shape of the finite element trough is in good agreement with the shape of the empirical curve up to the point of inflection (i.e. within one trough width parameter of the maximum settlement). However, after this point the finite element analyses over-predict the vertical and horizontal displacements compared to empirical predictions. This may be because the soil within one trough width parameter of the maximum has been vertically extended and horizontally compressed, whereas the soil outside has been horizontally extended and vertically compressed. The normalised shape of the trough for the empirical predictions is assumed to always be the same regardless of the tunnel diameter, depth or volume loss as its shape is being based on an exponential function. The finite element predictions show small changes in shape with depth and tunnel diameter and this is in agreement with the findings of Celestino et al (2000), who reported the shape of the settlement profile to be dependent on both tunnel depth and diameter (Section 2.3.1). The relationship between U and W with transverse distance is shown in Figure 4.17. There is similarity in the behaviour of the empirical and finite element predictions up to the point where y/i = 1.5, where-after the value of U decreases rapidly in comparison to the value of W for the finite element model. [N.B. In the region y/i > 1.5 the actual values of U and W for the empirical model are very small and are therefore ignored.] 4.4.2 Sub-Surface Displacements A complete normalised set of results for maximum surface vertical displacement and trough width (for surface and sub-surface regions) are shown in Figures 4.18 – 4.20. Here the general behaviour of different sizes of tunnel at different depths has been normalised with depth. Figure 4.18 shows the increase in maximum sub-surface settlement (Wmax ss) in terms D.Hunt - 2004

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of the maximum surface settlement (Wmax 0). The data are shown for all the analyses conducted on single tunnels in this study. The relative increase in settlement for sub-surface regions based on four empirical methods for predicting the changes in trough width parameter, i, for sub-surface regions are also highlighted. Three methods include a non-linear variation in K with depth (i.e. Mair et al 1993, Moh et al 1996 and Heath and West 1996) and the fourth method assumes a linear variation with K = 0.5 for the surface and all sub-surface regions (i.e. O’Reilly and New 1982). The finite element results show a relative increase in settlement with depth, while the results lie within the bounds set by the linear and non-linear predictive methods. Figure 4.19 shows the variation in the trough width parameter, i, with depth. The values are normalised with respect to the surface value i0 (i.e. at the surface i0/i = 1). The parameter is inversely proportional to the maximum settlement when assuming no volume change (i.e. the volume per metre length of each settlement curve is assumed constant). The finite element results again lie within the bounds set by empirical predictive methods, although the trough width parameter is over-predicted between ground surface level and depths of Z/Z0 = 0.3. The linear sub-surface variation in Umax/Wmax is shown for current empirical methods in Figure 4.20 where the value of U is always a fixed amount of W (i.e 0.202 or 0.101). The finite element results show a non-linear relationship between these two parameters for subsurface regions, which is in agreement with the findings of Grant and Taylor (2000). 4.4.3 ‘Relative Changes’ in Surface Displacement Although the finite element predictions are of the wrong magnitude, the method does appear to have the ability to identify realistic relative changes in behaviour when considering changes in tunnel diameter, volume loss and depth. Table 4.2 shows the relative changes in the settlement profile for the finite element predictions when these changes are made. The relative changes are compared to those found using Equations 2.8, 2.10, 2.31 and 2.39. The ability of the method to react to the challenges posed on page 79 and highlighted as (1-3) are also shown.

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Table 4.2: Comparison between the results of the finite element predictions and empirical predictions Case 1 2 3 4 5

Zo (m) 26.0 26.0 26.0 33.4 16.4

D (m) 9.0 4.0 4.0 4.0 4.0

Vl (%) 1.3 1.3 2.0 1.3 1.3

2/1 3/2 5/4

1.0 1.0 2.0

0.4 1.0 1.0

1.0 1.5 1.0

Finite element Wmax Umax i (mm) (mm) (m) 11.9 6.8 20.0 2.5 1.3 20.0 4.1 2.0 20.0 1.9 1.0 23.0 3.8 2.0 12.0 0.2 1.6 2.0

0.2 1.5 2.0

1.0 1.0 0.52

Empirical Wmax Umax (mm) (mm) 25.4 5.0 5.0 1.0 7.7 1.5 3.9 0.8 7.9 1.6 0.2 1.5 2.0

0.2 1.5 2.0

i (m) 13.0 13.0 13.0 17.0 8.0 1.0 1.0 0.48

N.B. Doubling the depth of a 9.0m diameter tunnel from 16.4m to 33.4m does not double the trough width or halve the magnitudes of the displacements.

1.

Doubling the tunnel depth from 16.4m to 33.4m (Cases 4 and 5 in Table 4.2) is found to cause the magnitudes of the displacements (both vertical and horizontal) to halve, and the trough width to double, for both methods.

2.

The effect of increasing the volume loss from 1.3% to 2.0% (Cases 2 and 3 in Table 4.2) for a 4.0m diameter tunnel at a depth of 26.0m increases the displacements by 64% with no increase in trough width. Again this was very similar to the increase reported from empirical predictions.

3.

By decreasing the tunnel diameter from 9.0m to 4.0m (Cases 1 and 2 in Table 4.2), the finite element method predicts no change in trough width and an 80% decrease in the values of the vertical and horizontal displacements. Interestingly the reduction was the same as that found when using the empirical predictive methods.

4.5 CONCLUSIONS The following conclusions can be made for the results of the finite element analyses single tunnels using the ‘gap parameter’ method for volume loss in combination with the soil model proposed by ‘Jardine et al’ (1984): 

The effect of increasing the depth, while keeping the tunnel diameter and volume loss constant, is to decrease the magnitude of surface and sub-surface displacements. The

D.Hunt - 2004

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increases in displacement are accompanied by a reduction in the distance to the point of Umax. Due to the assumption of undrained conditions the two are inversely proportional. 

Reducing the tunnel diameter from 9.0m to 4.0m while keeping the volume loss and tunnel diameter constant has little effect on the position of Umax (i.e. the trough width parameter is unaffected). In regions close to the tunnel (1.5i).

These results highlight the inability of the current finite element analyses to predict accurately movements above a single tunnel in stiff London clay under greenfield conditions. The results confirm the findings of other authors when comparing magnitudes of displacements predicted by finite elements methods to those from empirical methods (e.g. Lee and Rowe 1990, Gunn 1993, and Addenbrooke 1996). At first glance the results of the finite element analyses, and hence the model proposed by Jardine et al (1984), could be dismissed as inaccurate and therefore be judged as an unreliable D.Hunt - 2004

- 90 -


predictive method for finding displacements above a single tunnel. However, this research has shown it is dependent on how Finite Element results are used in general. If the method is used to show ‘relative’ changes in displacement due to changes in depth, volume loss and tunnel diameter the method reacts reasonably well. These realistic ‘relative’ changes are shown below: 

Increasing the volume loss by a percentage, whilst keeping the depth (Zo) and tunnel diameter (D) constant, results in the same relative increase in the value of the maximum displacements (Wmax and Umax) for both the empirical model and the finite element model;



The values of the maximum sub-surface displacement (Wmax and Umax) increase with depth below ground surface, this relative increase is very similar irrespective of the volume loss or tunnel diameter. The same relative changes in the magnitudes of the maximum displacements are seen for both the empirical model and the finite element model;



Increasing the tunnel diameter by a percentage, whilst keeping the volume loss and depth constant results in the same relative increase in the value of the maximum displacements (Wmax and Umax) for both the empirical model and the finite element model. The results of the finite element analyses conducted in this study and those for more

complicated tunnelling situations such as those considered in Chapter 5 and 6 (i.e. twin and triple tunnel problems) will be considered in terms of the ‘relative changes’ in displacement in order to allow for easier translation into an empirical model in Chapter 8.

D.Hunt - 2004

- 91-

Figure 4.1 Typical finite element mesh for single 9.0m and 4.0m diameter tunnels

105.0m


Symbols used: Fixed boundary Reaction forces used to prop open tunnel Tunnel liner and anchor

40m

3

Z

Zo m

105.0m


D.Hunt - 2004

- 92-


Distance from tunnel centreline (m) 5

45

-5

55

105

-55

-105

10

-20m

Umax = 6.8mm at 20.0m

5

Depth (m)

0

0.0

5 Wmax = 11.9mm

10

5.7mm at 18m

10

1.00E02

5

5.00E03

Chainage0(m)

0.00E+0 0

16mm at 0m

45 5.76mm at 15m

Displacement (mm)

isplacement above

10 15

Wmax = 16.0mm

-1.50E02 -2.00E02

10

-5

1.00E-2.50E02 02 -105

-55

5

5.00E03

0

0.00E+0 0

5

-5.00E03

10

-1.00E02

15

5

11.4 Se ttl e m en t (m m)

-2.00E02

6.7mm at 11.3m 45


-1.50E02

Wmax = 19.0mm

20

19mm at 0

6.9

Se -5.00E- ttl e 03 m en -1.00E- t 02 (m m)

5

placement above


-5

-2.50E02 -105

-55

Umax = 6.8mm at 11.0m 15.4

0 5 10 15 22mm at 0m

20

Wmax = 22.0mm

Tunnel axis 45

-5

-55

26.0 105

Figure 4.2 Sub-surface and surface settlements above a single 9.0m tunnel at 26.0m depth using Soil 1 with a 1.3% volume loss.

D.Hunt - 2004

- 93-



55

105

10

1 .0 0 E -0 2

5

5 .0 0 E -0 3

0

0 .0 0 E + 0 0

5

-5 .0 0 E -0 3


Depth (m)

Wmax = 14.5mm

10

0.0

-1 .0 0 E -0 2

-1 .5 0 E -0 2

10

1 .0 0 E -0 2 -2 .0 0 E -0 2


5

4 5

-5

Displacement (mm)

5 10

-1 .0 0 E -0 2

15

-1 .5 0 E -0 2

Wmax = 18.7mm

s e ttle m e n ts a b o v e 2 5 m d e e p tw in 9 m d ia m e te r tu n n e ls a t 3 0 m M e a s u r e d a t 1 1 .4 m b e lo w g r o u n d le v e l. T 1

10

6.9

-2 .0 0 E -0 2

s p a c in g

-2 .5 0 E -0 2 1 .0 0 E -0 2

T 2

5

45

0 .0 0 E + 0 0 -3 .0 0 E -0 2 -1 0 5 -5 .0 0 E -0 3

-5 5

S e ttle m e nt (m m )

T 2

0

-5

-5 5

U

-3 .0 0 E -0 2 max - 1 0 55 . 0 0 E - 0 3

C h a in a g e (m )

11.4

0

0 .0 0 E + 0 0

5

-5 .0 0 E -0 3

10

-1 .0 0 E -0 2

15

= 5.9mm at 13.4m

-1 .5 0 E -0 2

S e ttle m e n t (m m )

T 1

5 .0 0 E -0 3 -2 .5 0 E -0 2

Wmax = 22.5mm

20

-2 .0 0 E -0 2 1 .0 0 E -0 2


-2 .5 0 E -0 2

T 2

5 45

5 .0 0 E -0 3

-3 .0 0 E -0 2 -5

0

-5 5

C h a in a g e (m )

-1 0 5

0 .0 0 E + 0 0

5

-5 .0 0 E -0 3

10

-1 .0 0 E -0 2

15

-1 .5 0 E -0 2

20

-2 .0 0 E -0 2

Wmax = 26.6mm

25

-2 .5 0 E -0 2

T 2

T 1 45

-5 C h a in a g e (m )

15.4

S e t t le m e n t ( m m )

T 1

Tunnel axis

-5 5

-3 .0 0 E -0 2 -1 0 5

26.0

Figure 4.3 Sub-surface and surface settlements above a single 9.0m tunnel at 26.0m depth using Soil 2 with a 1.3% volume loss. D.Hunt - 2004

- 94-


Distance from tunnel centreline (m)

Settlement above 25 m deep twin 9m diameter tunnels at 20m spacing Measured at 0.0 m below ground level.

45

95 Umax = 1.3mm at 20.0m

1

Depth (m)

0

0.0

1 Wmax =at2.5mm Settlement above 25 m deep twin 50m spacing 2 9m diameter tunnels Measured at 6.9 m below ground level.

Settlement above tunnel 1 (1.3% loss)

0 -55

6.9

-5

45

95

Displacement (mm)

Chainage (m) Settlement above 25 m deep twin diameter tunnels at 50m spacing 1 9m Measured at 11.4 m below ground level.

2 3

Wmax = 3.3mm

Settlement above tunnel 1 (1.3% loss) Horizontal displacement above Tunnel 1

1

Umax = 1.2mm at 13.2m 11.4

0

-55


Horizontal displacement above Tunnel 1

1

-5

45

95

Chainage (m)

1

ettlement above 25 m deep twin 9m diameter tunnels at 50m spacing Measured at 15.42m below ground level.

3 Wmax = 4.0mm

4

Umax = 1.5mm at 10.0m 1 0

15.4

1


2 3 -55

4-5 5

-65

-45

-25

-5

454.9mm Wmax =

95

Chainage (m)

15 Chainage (m)

35

55

75 Tunnel axis 95

115

26.0


- 95-



95


Umax =2.0mm at 17.6m

2

Depth (m)

0

0.0

2 Wmax = 4.1mm

4


Settlement above 25 m deep twin 9m diameter tunnels at 50m spacing Measured at 6.9 m below ground level. -55

-5

45


95

Chainage (m)

2 0

6.9

Displacement (mm)

2

-55

4 6

Wmax = 5.5mm Settlement above tunnel 1 (1.3% loss) Horizontal displacement above Tunnel 1

-5

45

95

Chainage (m)



2

11.4

0 2 4 6

Wmax = 6.6mm

-55 -5 45 Settlement above 25 m deep twin 9m diameter Chainage (m) unnels at Measured 50m spacing at 15.4 m below ground level.

95


2 0

15.4

2 4 6 8

Wmax = 8.0mm

10 65

45

25

Figure 4.5

-5

1 5 Chainage (m)

3 5

5 5

7 5

9 5

Tunnel axis

11 5

26.0

Sub-surface and surface settlements above a single 4.0m tunnel at 26.0m depth using Soil 1 with a 2.0% volume loss. D.Hunt - 2004

- 96-



95 12.0m Umax 2mm atat12m max = 2.0mm

2

Depth (m)

0

0.0

2 W max = 3.8mm

4

s o n

o f tw in

o ffs e t 4 m M e a s u r e d

d ia m e te r tu n n e ls d r iv e n 3 0 .4 m a n d 1 6 .4 m T 2 a t 1 7 m C -C s p a c in g a t 2 .9 m b e lo w g r o u n d le v e l (S o il 1 ).

b e lo w

g r o u n d

T 1

Umax = 1.7mm at max = U at 12.0m 12m

2

-5 .5 0 E + 0 1

-5 .0 0 E + 0 0 C h a in a g e

4 .5 0 E + 0 1

9 .5 0 E + 0 1

(m )

0

2.9

-5 .5 0 E + 0 1

Displacement (mm)

2 4 6

T 2

W max = 4.7mm

T 1

-5 .0 0 E + 0 0 C h a in a g e

4 .5 0 E + 0 1

9 .5 0 E + 0 1

(m )

Umax = 1.6mm at 11.0m U max = 1.6mm at 11m

2

4.9

0 2 4 6

W max = 5.2mm

T 2

T 1

-5 .5 0 E + 0 1

-5 .0 0 E + 0 0 C h a in a g e

4 .5 0 E + 0 1

9 .5 0 E + 0 1

(m )

U max = 1.7mm at 8.6m 2 0

6.9

2 4 6 T 1

8 -5 .5 0 E + 0 1

W max = 5.9mm

-5 .0 0 E + 0 0 C h a in a g e

10

4 .5 0 E + 0 1

9 .5 0 E + 0 1

(m )

Tunnel axis

26.0 16.4


- 97-


Distance from tunnel centreline (m) on of twin piggyback 9m diameter tunnels driven 33.4m and 16.4m below ground at 17m C-C spacing Measured at 0.0 m below ground level (Soil 1). 45

95 Umax = 8.5mm at 14.0m

10 5

Depth (m)

0

0.0

5 Wmax = 15.0mm

10

f twin piggy back 9m diameter tunnels driven 33.4m and 16.4m below ground 15 at 17m C-C spacing Measured at 2.9 m below T2 ground level (Soil 1).

10 5-5

-55


T1

45

95

Chainage (m)

2.9

0 Displacement (mm)

5 10

Wmax = 18.0mm 15 of twin offset 9m diameter tunnels driven 33.4m and 16.4m below

ground

at 17m C-C spacing Measured at 4.9 m below ground level (Soil 1).

-55

10

T2

5

T1


-5

45

0

95

Chainage (m)

4.9

5 10 15

Wmax = 21.0mm on of twin 9m diameter tunnels driven 33.4m and 16.4m below ground at 17m C-C spacing 20 Measured at 6.9 m below ground level (Soil 1). T2

-55


T1

5 -5

45

95

0

Chainage (m)

6.9

5 10 15 20

Wmax = 23.0mm

25 -55

T1

-5 Chainage (m)

Figure 4.7

45

Tunnel axis

95

16.4

Sub-surface and surface settlements above a single 9.0m tunnel at 16.4m depth in Soil 1 with a 1.3% volume loss D.Hunt - 2004

- 98-



ison of twin piggyback 9m diameter tunnels driven 33.4m and 16.4m below ground at 17m C-C spacing Measured at 0.0 m below ground level (Soil 1).

45

95 Umax = 1.0mm at 23.0m

1

Depth (m)

0

0.0

1 2

Wmax = 1.9mm

n of twin 9m diameter tunnels driven 33.4m and 16.4m below ground at 17m C-C spacing Measured at 6.9 m below ground level (Soil 1).

Umax = 0.9mm at 23.0m 1 0 -5

-55


45

6.9

95

Chainage (m)

Displacement (mm)

1 2 3

Wmax = 2.4mm

Settlement above tunnel 1 (1.3% loss) n of twin 9m diameter tunnels driven 33.4m and 16.4m below ground Horizontal displacement above Tunnel 1 at 17m C-C spacing Measured at 6.9 m below ground level (Soil 1).

-55

-5

45

95

Chainage (m)

1

Umax = 1.5mm at 10.0m 16.4

0 1

twin offset 9m diameter tunnels driven 30.926m and 17.41m below ground at 20m C-C 2spacing Measured at 24.9 m below ground level (Soil 1).

3

Wmax = 3.4 mm Settlement above tunnel 1 (1.3% loss) Horizontal displacement above Tunnel 1

-55

-5

2

45


95

Chainage (m)

0

24.9

1 2 3 4

Wmax = 5.3mm

5 33.4

Tunnel axis -5.50E+01

-5.00E+00

4.50E+01

9.50E+01

Chainage (m)


- 99-



on of twin offset 9m diameter tunnels driven 30.926m and 17.41m below ground at 20m C-C spacing 95 Measured at 0.0 m below ground level (Soil 45 1).

Umax = 5.1mm at 23.0m 5

Depth (m)

0

0.0

5

n of twin offset 9m diameter 10 tunnels driven 30.926m 17.41m below ground Wmax =and 9.7mm at 20m C-C spacing Measured at 6.9 m below ground level (Soil 1).


T2

5

Settlement above tunnel 1 (1.3% loss) T1


0 -5.50E+01

6.9

-5.00E+00

4.50E+01

9.50E+01

Chainage (m)

Displacement (mm)

5

10 15

Wmax = 13.0mm

on of twin offset 9m diameter tunnels driven 30.926m and 17.41m below ground at 20m C-C spacing Measured at 6.9 m below ground level (Soil 1).

-55


-5

5

45

95


Chainage (m)

16.4

0 5 10 15

W

= 16.0mm

of twin offset 9m diameter tunnels driven 33.4m andmax 16.4m below ground at 17m C-C spacing Measured at 24.9 m below ground level (Soil 1). Settlement above tunnel 1 (1.3% loss) Horizontal displacement above Tunnel 1


5 -55

-5

0

45

95

Chainage (m)

24.9

5 10 15 20 25 -5.50E+01

Wmax = 24.0mm T2

-5.00E+00 Chainage (m)

4.50E+01

Tunnel axis

9.50E+01

33.4

Figure 4.9 Sub-surface and surface settlements above a single 9.0m tunnel with at 33.4m depth using Soil 1 with a 1.3% volume loss. D.Hunt - 2004

- 100-


Tunnel 1 Liner deformation

A 4.1mm

Tunnel 1 -17

2.1mm -18

Origional liner D 4.8mm

Depth

-19 B 4.8mm

20mm settlement

Deformed after tunnel 2

20 se

1.8mm

-20

-21

-22

C

4.8mm

2.0mm -23 -3.00E+00

-2.00E+00

-1.00E+00

0.00E+00 Chainage

(a) 9.0m diameter tunnel Tunnel 1 Liner deformation

4.1mm A

Tunnel 1 Liner deformation -17

2.1mm -18

Origional liner

20mm settlement

Depth

-19 B 4.8mm

Deformed after tunnel 2 20mm settlement

Origional liner

1.8mm

1.8mm

-20

-21

-22

C

4.8mm

2.0mm -23 -3.00E+00

-2.00E+00

-1.00E+00

0.00E+00

1.00E+00

2.00E+00

Chainage

(b) 4.0m diameter tunnel Figure 4.10 Movement and deformation of a single tunnel liner D.Hunt - 2004

3.00E+00


- 101-


Chainage (m) -45

0

55

105

5.0mm at 13.0m 1.00E-02 0.01

6.8mm at 20.0m

10

Displacement (mm)

5.00E-03 0.005 0.00E+00 0

-5.00E-03 0.005

-1.00E-02 -0.01

-1.50E-02 0.015

5 0 5 10 15

-2.00E-02 -0.02

20

-2.50E-02 0.025

25

39.0m

Wmax = 25.4mm

-3.00E-02 -0.03 95

95

105.0m

Wmax = 11.9mm

Empirical

4545

-5 -5

Finite elements-55-55

-105-105

Finite element vertical displacement (26.0m) Finite element horizontal displacement (26.0m) Empirical vertical displacement (26.0m) Empirical horizontal displacement (26.0m)

Figure 4.11 Comparison between W and U for empirical and finite element predictions based on Mair et al (1993) for a 9.0m tunnel at 26.0m depth using Soil 1 and a 1.3% volume loss. Chainage (m) -40

-20

0

20

40

60

80

100

5%

-15.4

Empirical

Finite elements

W/Wmax contours at 5% intervals Line of W/Wmax = 1 (F.E. and Empirical) Contour of Umax (F.E. at 0.5Wmax, Empirical at 0.606Wmax) Line of W/Wmax = 0 (Empirical)

-26.0

Figure 4.12

Finite element boundary

Depth (m)

0.0

Comparison of sub-surface displacement contours from a finite element analysis and empirical predictions based on Mair et al (1993) (9.0m diameter, 1.3% volume loss, 26.0m depth and Soil 1) D.Hunt - 2004

- 102-


ement above 25 m deep twin 9m diameter tunnels at 20m spacing Measured at 0.0 m below ground level. Chainage (m) 0

45

95

2.0mm at 20.0m 2

1.3mm at 20.0m

Displacement (mm)

1

Finite element Prediction

c

0 1

105m

2

Wmax = 2.5mm

3

Wmax = 4.1mm

4

T1

-55

Greenfield vertical displacements (1.3%) Greenfield horizontal displacements (1.3%) Greenfield vertical displacements (2.0%) Greenfield horizontal displacements (2.0%)

T2

-5

45

95

Chainage (m)

Chainage (m) 0 -5

0

5

10

5

10

15 15

20

25

30

20

25

30

35 35

40 40

Displacement (mm)

2

1.5mm at 13.0m 45 0.002 1.0mm at 13.0m

1

0.001

0

0

1

-0.001

2

-0.002

39.0m

3 4 5

-0.003

-0.004

Wmax = 5.0mm

-0.005

6

-0.006

7

-0.007

8

Wmax = 7.7mm

9

Figure 4.13

Empirical prediction

-0.008

-0.009

Comparison of results from a finite element analysis with predictions made by an existing empirical technique for a single 4.0m diameter tunnel at a depth of 26.0m with a volume loss of 1.3% and 2.0%. D.Hunt - 2004

Chainage (m) 0

45

95

2.0mm at 12.0m

2

1.0mm at 23.0m Displacement (mm)

1

Finite element Prediction

0 1

105.0 m

Wmax = 1.9mm

2 3

Wmax = 3.8mm 4

-5.00E+00

4.50E+01

Greenfield9.50E+01 vertical displacements (16.4m) Greenfield horizontal displacements (16.4m) Greenfield vertical displacements (33.4m) Greenfield horizontal displacements (33.4m)

Chainage (m)

Chainage (m) 0 0

1010

2020

30 30

40 40

50

50

60 0.003

1.6mm at 8.0m 0.8mm at 17.0m

2

0.002

1

0.001

Empirical prediction

0

0

-0.001

1

Displacement (mm)

E+01

- 103-


-0.002

2

24.6m

3 4

50.1m

-0.003 -0.004

Wmax = 3.9mm

-0.005

5

-0.006

6

-0.007

7 8

-0.008

Wmax = 7.9mm

-0.009

9

Figure 4.14

Comparison of results from a finite element analysis with predictions made by existing empirical techniques for a single 4.0m diameter tunnel at a depth of 16.4m and 33.4m and with a volume loss of 1.3%. D.Hunt - 2004

- 104-


y/i 0.0

1.0

0.00E+00 0.00E+00

1.00E+00

0.0

2.0 2.00E+00

3.0 3.00E+00

4.0 4.00E+00

5.0

6.0

5.00E+00

6.00E+00

7.0 7.00E+00

8.0 8.00E+00

9.0 9.00E+00

-2.00E-01 0.2

W/Wmax -4.00E-01 0.4

-6.00E-01 0.6

4m - 1.3% - 26 4m - 2.0% - 26 4m - 1.3% - 16.4 9m - 1.3% - 33.4 4m - 1.3% - 33.4 9m - 1.3% - 16.4 Empirical prediction (3i)

-8.00E-01 0.8

-1.00E+00

1.0

Figure 4.15

Normalised plots of surface displacements obtained from empirical and finite element results (diameter, volume loss and depth shown)

1 Empirical prediction (3i) 9m-1.3%-26

0.8

4m-1.3%-26 4m-1.3%-33.4 4m-1.3%-30.4 4m-1.3%-16.4

0.6

U/Umax 0.4

0.2

0

0

1

2

3

4

5

6

7

8

y/i

Figure 4.16

Normalised plots of surface displacements obtained from empirical and finite element results (diameter, volume loss and depth shown) D.Hunt - 2004

- 105-


y/i 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0

0.2

End of Empirically predicted trough width assumed as 3i (i=0.5Z0)

0.4

0.6

U/W 0.8

1

1.2

u/w = y/z (empirical) u/w = 0.65 y/z (empirical) D=9m, (Z-Z0)=26m, V 1.3% D=4m, (Z-Z0)=26m, V 1.3% D=4m, (Z-Z0)=33.4m, V 1.3%

1.4

1.6

Figure 4.17

Relationship between horizontal (U) and vertical (W) displacements along the settlement trough profile for the empirical and finite element results. Wmax 0 /Wmax ss

1

1.5

2

2.5

3

3.5

4

0 D=9m, Z=26m, V=1.3% D=4m, Z=26m, V=1.3% D=4m, Z=26m, V=2.0% D=4m, Z=16.4m, V=1.3% D=9m, Z=16.4m, V=1.3% D=4m, Z=33.4m, V=1.3% D=9m, Z=33.4m, V=1.3% using i = K(Zo-Z) where K = 0.5 Mair et al (1993) Heath and West (1996) Moh et al (1996)

0.1 0.2 0.3

Z/Zo

0.4 0.5 0.6 0.7 0.8 0.9 1

Figure 4.18

Relative changes in maximum sub-surface (Wmax ss) and surface settlement (Wmax 0) with tunnel depth. D.Hunt - 2004

4.5

- 106-


i/i0 0

0.2

0.4

0.6

0.8

1

0 D=9m, Z=26m, V=1.3% D=4m, Z=26m, V=1.3% D=4m, Z=26m, V=2.0% D=4m, Z=16.4m, V=1.3% D=9m, Z=16.4m, V=1.3% D=4m, Z=33.4m, V=1.3% D=9m, Z=33.4m, V=1.3% using i = K(Zo-Z) where K = 0.5 Mair et al (1993) Heath and West (1996) Moh et al (1996)

0.1 0.2 0.3

Z/Zo

0.4 0.5 0.6 0.7 0.8 0.9 1

Figure 4.19

Relative changes in relative distance to Umax (i) sub-surface compared to the distance to Umax (i0) at the surface. Umax /W max

0

0.1

0.2

0.3

0.4

0.5

0.6

0

0.1

0.2

0.3

Z/Z0Z/Z

0.4 D=9.0m, Vl=1.3%, Z=26.0m, Soil 1 D=9.0m, Vl=1.3%, Z=26.0m, Soil 2 0.5

D=4.0m, Vl=1.3%, Z=26.0m, Soil 1 D=4.0m, Vl=2.0%, Z=26.0m, Soil 1 D=4.0m, Vl=1.3%, Z=16.6m, Soil 1 D=9.0m, Vl=1.3%, Z=16.6m, Soil 1 D=4.0m, Vl=1.3%, Z=33.4m, Soil 1

0.6

D=4.0m, Vl=1.3%, Z=33.4m, Soil 1 O'Reilly and New (1982)

0.7

Mair et al (1993)

0.8

Figure 4.20

Relationship between maximum horizontal and vertical displacements obtained from empirical and finite element results for sub-surface levels. D.Hunt - 2004

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Chapter 5 - Movements above twin tunnels

Chapter Five

MOVEMENTS ABOVE TWIN TUNNELS

5.1 INTRODUCTION The requirement for improved transportation links in modern urbanised areas has resulted in an increasing amount of tunnelling operations being undertaken. These tunnelling operations involve the construction of tunnels on their own (i.e. single tunnels) or in pairs (i.e. twin tunnels). The various alignments for twin tunnels can be categorised as: 

Side-by-side tunnels (same horizontal tunnel axis),



Piggyback tunnels (same vertical axis),



Offset tunnels (different horizontal and vertical axes).

With increasing competition for underground space, particularly in urban settings, such as the U.K.’s capital, London, it is becoming increasingly likely that twin tunnel constructions will be in close proximity to each other. For some of these close proximity twin tunnels a time delay may also occur between the construction of the first tunnel (Tunnel 1) and the second tunnel (Tunnel 2). When considering this type of construction scenario it is inherent that Tunnel 2 will cause ground movements in the soil above, some of which will have been previously disturbed by Tunnel 1 (i.e. this soil will already have undergone changes in stiffness). Initial estimates of the horizontal and vertical displacements above the twin tunnel constructions are currently based upon empirical predictive methods (i.e. Gaussian type curves) and tunnelling experience. The initial estimate is made by assuming a greenfield displacement profile for both Tunnel 1 and Tunnel 2. These profiles are assumed to be of the same magnitude (i.e. same volume loss and Gaussian shape). The total settlement profile is found by simple addition of the two profiles (e.g. O’Reilly and New, 1991). The use of empirical predictive methods has been shown by many authors to be relatively accurate when considering single tunnels (Chapter 2). The extension of the method to predicting movements

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above twin tunnels has also been shown to be valid when the construction of Tunnel 1 and 2 are simultaneous. However, extension of the method to twin tunnels with a time delay between the constructions of each remains at best uncertain, and indeed Chapter 2 has shown via the work of many authors, that the displacement profile above Tunnel 2 can be markedly different to the profile above Tunnel 1 when this time delay occurs. The following changes to the settlement profile were noted: 

distribution of W



position of Wmax



magnitude of Wmax



distribution of U



position of Umax (used to indicate changes to the trough width)



magnitude of Umax



position of U = O

The underlying aim of this chapter is to identify and categorise these changes through numerical analyses in order that an improvement can be made to the current empirical predictive method. The analyses used the same Jardine et al. (1986) small strain stiffness model described in Chapter 3 and implemented in Chapter 4 for single tunnel analyses. The primary aim of these analyses is to describe fully the behaviour of side-by-side tunnels and hence more of the chapter is set aside for this type of geometry, although much consideration is also given to piggyback and offset tunnels. Consideration to the following parameter changes is given in the analyses: 

centre-to-centre spacing (20, 30, 50, 80 and 120m) for both side-by-side and offset tunnels;



stiffer soil (Soil 2) for side-by-side tunnels only;



tunnel diameter (4.0 m and 9.0 m) for side-by-side and piggyback tunnels;



volume loss (1.3% or 2.0%).

For each analysis undertaken the horizontal (U) and vertical (W) displacement profiles above Tunnel 2 are compared to the greenfield displacements (i.e. the displacements that occurred above Tunnel 1 are superimposed over Tunnel 2) for surface and sub-surface levels. The

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displacements above Tunnel 1 have been discussed in Chapter 4. Different construction sequences are considered for both the offset and piggyback tunnels: 

shallower (upper) tunnel first



deeper (lower) tunnel first

For many projects involving twin tunnels, more detailed predictions of ground movements are based upon the actual results of finite element modelling. However, the results of single tunnel analyses conducted during this current research (reported in Chapter 4) and the results of previous researchers (e.g. Lo et al 1984, Gunn 1993 and Addenbrooke 1996) have shown the finite element method to over-predict the width of the displacement trough and underestimate the magnitudes of horizontal and vertical displacements. Based on these conclusions it would seem unreasonable to expect the predictions above twin tunnels to be any more accurate. However, based on the conclusions drawn from Chapter 4, less attention is paid to the magnitudes of displacement; instead particular attention is given to the ‘relative changes’ in displacement for each analysis. In analysing the results for the side-by-side tunnels the changing shape of the displacement profiles are analysed by considering changes to: 

V2r/V2n (used to show asymmetry of curves)



W2/W1 (used to find ‘relative changes’ in vertical displacement)



i/ig (for near and remote limbs)

where V2r is the volume of the remote limb of the settlement trough and V2n is the volume of the near limb (Cooper and Chapman, 2002), W1 is the greenfield vertical displacement above Tunnel 2 (i.e. the same as Tunnel 1) and W2 is the predicted vertical displacement above Tunnel 2, i is the predicted distance to the point of maximum horizontal movement and ig is the greenfield value. The chapter draws conclusions for the ‘relative changes’ in behaviour of side-by-side tunnels, piggyback tunnels and offset tunnels. These conclusions are subsequently used in Chapter 8 to improve the currently available empirical predictive methods for twin tunnels.

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5.2 TWIN TUNNEL MODEL DETAILS 5.2.1 Tunnel Geometry The details of all the analyses undertaken in this chapter including alignment, depth, diameter, volume loss and soil type are shown in Table 5.1. Table 5.1 Parameters used in twin tunnel analyses performed Alignment Side-by-side

Piggyback

Offset

Tunnel Depth Centre-to(m) centre spacing (m) 1 2 20,30,50,80,120 26.0 26.0 20,30,50,80,120 26.0 26.0 20,30,50,80,120 26.0 26.0 20,30,50,80,120 26.0 26.0 20,30,50,80,120 26.0 26.0 Constant 16.4 33.4 Constant 16.4 33.4 Constant 33.4 16.4 Constant 33.4 16.4 20,30,50,80,120 17.4 30.9 20,30,50,80,120 30.9 17.4

Diameter (m) 1 2 9.0 9.0 9.0 9.0 4.0 4.0 4.0 4.0 4.0 4.0 9.0 9.0 4.0 4.0 9.0 9.0 4.0 4.0 9.0 9.0 9.0 9.0

Volume loss (%) 1 2 1.3 1.3 1.3 1.3 1.3 1.3 2.0 2.0 1.3 2.0 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3

Soil type 1 2 1 1 1 1 1 1 1 1 1

Figure 5.1a shows the geometry of the side-by-side tunnels. The tunnels are positioned at a depth of 26.0 m below ground level with a varying centre-to-centre spacing of 20.0, 30.0, 50.0, 80.0 and 120.0m. Centre-to-centre spacings of 15.9m and 36.8m are considered for 9.0m tunnels as part of the triple tunnel analyses reported in Chapter 6. The side-by-side tunnel analyses were conducted with 4.0m and 9.0m diameter tunnels with various volume loss combinations highlighted in Table 5.1. For all analyses the left-hand tunnel (Tunnel 1) was fully constructed before the right-hand tunnel (Tunnel 2). The geometry of the twin tunnels is similar to those analysed by Addenbrooke (1996) in order that comparisons could be made between the two studies. Figure 5.1b shows the geometry of the piggyback tunnels. The upper tunnel was positioned at 16.4 m below ground level with the lower tunnel at 33.4 m below ground level. A volume loss of 1.3% was assumed in the construction of the 9.0m diameter tunnels and the 4.0m tunnels, while consideration was also given to the role of the construction sequence for both sizes of tunnel.

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Figure 5.1c shows the geometry of the offset tunnels. The upper tunnel and lower tunnel were constructed at 17.4m and 30.9m below ground surface respectively. The centre-tocentre spacing was considered at 20.0, 30.0, 50.0, 80.0 and 120.0m. The meshes for side-by-side, piggyback and offset tunnels are shown in Figures 5.2a, 5.2b and 5.2c respectively. The increased tunnel spacing for the offset and side-by-side tunnels was achieved by adding extra columns of elements into the mesh between the centrelines of each tunnel (e.g. for each 10m increase in spacing three extra columns of evenly sized elements were added). 5.2.2 Material Properties All of the analyses were conducted with the same material properties for London clay (referred to as Soil 1 in Section 3.3.3) as those used in the single tunnel analyses. For the side-by-side tunnels the effect of using Soil 2 was also considered. For all analyses the Poissons’ ratio (ν) was assumed to be 0.499. Two types of pre-yield soil model were employed in the analyses: the Mohr-Coulomb Model (MC) and the Non-Linear Small Strain Stiffness model reported by Jardine et al (1986). Both models are discussed in more detail in Section 3.3. For all analyses the liners were assumed to be 200mm thick with a unit weight of 24kN/m3 and Young’s Modulus of 28 x 109 Pa and were modelled using the Mohr-Coulomb model. 5.2.3 Boundary Conditions The boundary conditions were the same as those prescribed in Section 3.3.5 for a single tunnel. Both vertical boundaries were restrained in the horizontal direction and unrestrained in the vertical direction. The horizontal boundary at the base was restrained in both directions. The distance from the vertical boundary to the centreline of the nearest tunnel was taken as 105.0m (i.e. the same as that for a single tunnel). The increased spacing of the tunnels for the side-by-side and offset tunnel analyses consequently increased the tunnel to boundary distance on the right-hand side of Tunnel 1 and on the left-hand side of Tunnel 2. This resulted in a bigger boundary-to-tunnel distance on one side of a tunnel compared to the other. Due to the parametric nature of the study it was important that the effect of increasing the boundary distance should not influence the

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settlement profiles for each tunnel (i.e. they should be identical). Hence a study of boundary effects was undertaken. A first set of analyses was conducted considering a minimum boundary distance from the tunnel centreline to the left boundary of 65.0m, while a range of distances was considered from the tunnel centreline to the right boundary (i.e. 85.0, 95.0, 115.0 and 145.0m). These single tunnel analyses considered the same procedure for tunnel construction as reported in Chapter 4. The resulting vertical and horizontal surface displacements for the various boundary distances are shown in Figure 5.3. The figure clearly shows smaller horizontal displacments on left side of the tunnel (constant 65.0m boundary) compared to the right side of the tunnel (gradually extended boundary), while the effect of increasing the boundary distance on right side causes an increase in the horizontal and vertical displacements on the same side, each settlement profile having different values for Wmax and Umax.. Effectively this meant that a boundary distance of 65.0m for a 9.0m diameter tunnel was too short. A second set of analyses was conducted with a minimum boundary distance of 105.0m from the tunnel centreline to the left boundary. A range of distances from the tunnel centreline to the right boundary were considered (125.0, 135.0, 155.0, 185.0, and 225.0m). Figure 5.4 shows the position and magnitude of Umax on both the left and right side of the tunnel to be almost identical for each increase in boundary distance. The vertical displacements (W) and the value of Wmax were unaffected by increasing the boundary distance on the right side. It was therefore concluded that the effect of increasing the boundary distance on the right side of the tunnel on the settlement profiles was acceptably small. One important point to note is that due to the boundary conditions chosen, the horizontal movements at the boundary edge are always zero, i.e. if the boundary edge was moved from 125.0m to 225.0m the position of U=0 changes accordingly. However, by moving this boundary the horizontal movements at 125.0m are no longer zero. Due to the fact that the profile is mostly unaffected by an increase in boundary distance when a minimum tunnel-to-boundary of 105.0m is used, this was adopted for all analyses involving both single and double tunnels. 5.2.4 Modelling Twin Tunnels and Controlling Volume Losses The twin tunnel analyses were conducted using the same ‘gap parameter’ used for the single tunnel analyses (Section 5.3.2). For this reason direct comparisons can be made between the

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results reported in this chapter (twin tunnels) and those reported in Chapter 4 for single tunnels. When considering the modelling of twin tunnel constructions using the finite element method many methods of simulating a volume loss can be applied (Section 3.4). Addenbrooke (1996) reported the method of ‘stress relaxation’ for twin tunnels and found that ‘By controlling the percentage unloading of the second tunnel the volume loss became a variable’. Due to the parametric nature of this study it was necessary to be able to control fully the volume loss for the construction of a second tunnel. This was possible through the use of the ‘gap parameter’ where the volume loss could be exactly quantified in order to keep the value constant for both tunnels or alternatively incorporate a small increase in value for Tunnel 2 alone. The different values of volume loss prescribed for each of the tunnels were: 

1.3% volume loss for both Tunnel 1 and 2;



1.3% loss for Tunnel 1 and a 2.0% loss for Tunnel 2;



2.0% losses for both Tunnel 1 and Tunnel 2.

The procedure for constructing Tunnel 1 was the same as that for a single tunnel analysis reported in Chapter 4 (i.e. two analyses were required for the construction of Tunnel 1). Due to the use of large displacement theory as a solution method, once this tunnel was constructed the nodes in the mesh had moved (unlike small displacement theory where the nodes are fixed), i.e. when the first tunnel is constructed the soil nodes move towards the liner until full closure of the gap between the liner and the soil has been achieved. When considering a single tunnel analysis the inward movement of these nodes only needed to be monitored for displacements. However, when analysing twin tunnels the movement of these nodes becomes very important and required careful consideration prior to the construction of Tunnel 2. During the analyses two element sets would be removed from the model in order to create the tunnel opening within which the liner would be placed. These were referred to as SOL1 for Tunnel 1 and SOL2 for Tunnel 2. During the construction of Tunnel 1 the nodes around the periphery of element set SOL2 moved, which meant that the nodes outlining the gap between the liner and the soil for Tunnel 2 were out of alignment (i.e. the prescribed gap was distorted). Hence, in order to ensure that the same gap was prescribed for Tunnel 2 as for Tunnel 1 these nodes needed to be reset to their original position (i.e. the position prior to the construction of Tunnel 1).

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This was achieved by the straight forward process of re-meshing, which only involved resetting one ring of 48 nodes around the periphery of SOL2. This was done by first computing the data for vertical and horizontal movements of this periphery node set after the construction of Tunnel 1. The original mesh was then reconstructed with this node set reset in a direction opposite to the movements that occurred after the construction of Tunnel 1 and prior to the construction of Tunnel 2. In order to perform a twin tunnel analysis, four separate analyses were required. The information gained from Analyses 1 was used for Analysis 2, and so on for all four analyses. Analysis 1 was the same as that conducted for a single tunnel: Analysis 2 was the same as that conducted for a single tunnel except that the movement of the periphery nodes around Tunnel 2 were output as a last step. Analysis 4 was performed including the information gathered in all of the previous three analyses. The steps involved in each of the four analyses were: Analysis 1. (Refer to Chapter 4 as this remains unchanged) Analysis 2. (Refer to Chapter 4 as this remains unchanged) In addition, the last step of the analysis outputs the horizontal and vertical displacements of the nodes around the periphery of SOL2 for Tunnel 2. Analysis 3. Analysis 2 is rerun with a new mesh. (The new mesh was created by resetting the nodes around the periphery of SOL2 in a direction opposite to those found at the end of Analysis 2.) Once this was done the boundary for Tunnel 2 was fixed and the soil inside removed. The reaction forces required to hold up the soil inside Tunnel 2 were then found (the process being essentially the same as Analysis 1, only this time applied to Tunnel 2). Analysis 4.

Based on the information found in the previous three analyses, a full analysis

for the construction of Tunnel 1 followed by Tunnel 2 was performed. The construction procedure for Tunnel 2 was the same as Tunnel 1, outlined in Analysis 2, with reaction forces being applied to inner edge of SOL2 (N.B. The reaction forces for Tunnel 1 and Tunnel 2 are different.) The steps involved removing SOL2, applying reaction forces, reactivating the liner, contact and anchor elements, applying gravity, reducing the reaction forces in a stepped manner, and, upon final closure of the gap subsequent removing of anchor elements.

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With twin tunnel constructions there are likely to be stress path reversals on the commencement of excavation for the second tunnel (Addenbrooke, 1996). There are models which automatically take into account this stress path reversal and reinvoke high stiffness expected at small strains (e.g. the small strain model proposed by Puzrin and Burland, 1995). Addenbrooke (1996) reported that is possible to reinvoke this stiffness in the model first proposed by Jardine et al (1986) by zeroing strains part way through the analysis (i.e. after the construction of Tunnel 1). Addenbrooke (1996) conducted a thorough investigation of this method and reported a lower volume loss for the second tunnel construction compared to the first. This result contradicts case history data which would suggest a higher volume loss for the second tunnel, which is the assumption taken for this research. The method of reinvoking high stiffness through zeroing strains has not been considered in this current research. 5.3 RESULTS FOR THE SIDE-BY-SIDETUNNELS 5.3.1 Surface and Sub-Surface Displacements All of the side-by-side analyses were conducted with tunnels at a fixed depth of 26.0m, as shown in Table 5.1. The resulting settlement profiles (horizontal and vertical) above the second tunnel are shown herein. Two displacement profiles are shown for each analysis conducted, the greenfield profile (equivalent to that above Tunnel 1) and the predicted profile for the second tunnel driven. The greenfield profiles are the same as those reported in Chapter 4 for single tunnels. The displacement profiles are given for surface levels and sub-surface depths of 6.9m, 11.4m and 15.4m below ground level. The 15.4m depth equates to approximately 0.7D above the tunnel lining when considering 9.0m tunnels. 5.3.1.1 9.0m diameter tunnels The first analysis considered twin 9.0m diameter tunnels with a centre-to-centre spacing of 20.0m. The analysis was performed using a 1.3% volume loss for both Tunnel 1 and Tunnel 2 using Soil 1. The resulting vertical displacement profiles are shown in Figure 5.5, in which it can be seen that the shape of the settlement profile is very different to the greenfield profile. The magnitude of Wmax at the surface has increased by 20% compared to the greenfield profile (11.9mm to 14.2mm) and similar increases, although not as large, were seen for

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depths of 6.9m and 11.4m below the surface. However, at a depth of 15.4m, Wmax was found to reduce in magnitude by 4% compared to the greenfield profile (22.0mm to 21.5mm). The position of Wmax at the surface was eccentrically placed 8.5m towards Tunnel 1 (i.e. away from the centreline of Tunnel 2), this position was seen to decrease with depth to a value of 2.3m at 15.4m below the surface. The effects of the construction of Tunnel 1 on the horizontal displacements above Tunnel 2 are very evident (Figure 5.6). At the surface the magnitude of the horizontal displacements has increased for the near limb (6.8mm to 6.9mm) and reduced for the remote limb (6.8mm to 4.9mm). The value on the remote limb is therefore 70% of the value on the near limb. The position of Umax is eccentrically displaced 5.0m towards Tunnel 1 on the near limb and 6.4m towards Tunnel 1 on the remote limb. The position of U = 0 has been eccentrically placed 6.8m towards Tunnel 1 from its greenfield position (i.e. the centreline of Tunnel 2). At the sub-surface of 15.4m, the magnitude of Umax has increased on the near limb (6.7mm to 8.7mm) and is eccentrically displaced 2.7m away from Tunnel 1. The magnitude of Umax has decreased on the remote limb (6.7mm to 3.4mm) and is eccentrically displaced 2.3m away from Tunnel 1 on the remote side. The maximum horizontal displacement is therefore 40% of the value on the near limb. The position of U = 0 has been eccentrically displaced 3.6m away from Tunnel 1 on the remote limb. In contrast to the greenfield predictions, the position of U=0 and W=Wmax are no longer coincident. Figure 5.7 shows the vertical displacements above Tunnel 2 when the centre-to-centre spacing is increased to 30.0m. At the surface Wmax shows an increase in magnitude of 13% (11.9 to 13.5mm) compared to the greenfield profile and its position is eccentrically displaced 10.2m towards Tunnel 1. The increase in Wmax is thus less than that found for the 20.0m spacing, although interestingly the eccentricity is larger. At the sub-surface of 15.4m the magnitude of Wmax shows a 14% decrease in its magnitude (22.0 to 19.0mm) compared to the greenfield profile, which is larger than the decrease found for the 20.0m centre-to-centre spacing. The position of Wmax is eccentrically displaced 1.1m towards Tunnel 1 which is less than that found for the 20.0m spacing. The corresponding horizontal movements are shown in Figure 5.8. The maximum horizontal movement on the remote limb (4.2mm) is 67% of that on the near limb (6.3mm). The displacements on both limbs are smaller than those for greenfield conditions. The position of Umax is eccentrically displaced 6.4m towards Tunnel 1 on the near limb and is not eccentrically displaced on the remote limb. The position of U = 0 has been eccentrically displaced 2.0m towards Tunnel 1 from its greenfield position (i.e. the centreline of Tunnel 2), D.Hunt - 2004

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showing a reduction compared to the 6.8 m found for a centre-to-centre spacing of 20.0m. At a depth of 15.4m below ground surface the position of U=0 is eccentrically displaced 3.6m away from Tunnel 1 on the remote limb, this value being the same as that found for a tunnel at 20.0m centre-to-centre spacing. The maximum horizontal movement on the remote limb (3.8mm) is 50% of that on the near limb (7.6mm). The distance from the point where U=0 to the point where U=Umax appears to have increased for both surface and sub-surface regions on both limbs. Figures 5.9 and 5.10 show the vertical and horizontal displacements respectively for tunnels at 50.0m spacing. The position of Wmax is now coincident with the vertical axis that runs through the centreline of Tunnel 2 (i.e. no eccentricity). The surface magnitude of Wmax (11.0mm) has reduced compared to the greenfield value (11.9mm). The increases in settlement are still evident above the centreline of Tunnel 1 and can be seen to reduce for sub-surface depths. The position of U=0 is now only very slightly displaced away from the centreline of Tunnel 2, although, the magnitudes of horizontal displacements are greater on the near limb compared to those on the remote limb. The distance between U=0 and Umax has increased for all sub-surface levels, with the biggest increase occurring on the near limb at surface. The resulting displacements (horizontal and vertical) for twin tunnels at centre-to-centre spacings of 80.0m and 120.0m are not shown in this thesis. They were found to show similar characteristics to those of the 50.0m spaced tunnels, although the profile was seen to approach that of a greenfield settlement profile as the spacing increased. For all the profiles large increases in settlement were seen over the centreline of Tunnel 1. The effect of using Soil 2 on the displacements can be seen in Figures 5.11 and 5.12. In Section 4 the use of stiffer clay had resulted in higher magnitudes of displacement (vertical and horizontal) above a single tunnel accompanied by a smaller trough width. The magnitude of Wmax for the twin tunnel problems and the eccentricity of Wmax was not as large as that found when using Soil 1. At the surface the offset was only 6.8m for Soil 2 soil, compared to the 8.5m found using Soil 1 (see Figure 5.5). At a level of 15.4m below ground level the eccentricity was approximately the same as that for Soil 1 (Figure 5.5).. At a sub-surface depth of 15.4m the value of Wmax was larger than the greenfield value, whereas the use of Soil 1 showed a decrease in value compared to the greenfield value.

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5.3.1.2 4.0m diameter tunnels The vertical and horizontal displacements for the twin 4.0m diameter tunnels at 20.0m centreto-centre spacing, both with 1.3% volume loss, are shown in Figures 5.13 and Figure 5.14. The magnitude of Wmax increased by 28% at the surface compared to the greenfield profile (2.5mm to 3.2mm), which was larger than that found for the 9.0m diameter tunnels. The position of Wmax is eccentrically displaced 5.1m from the centreline of Tunnel 2 towards Tunnel 1, which was less than the 6.8m found for the 9.0m tunnel. At 15.4m below ground level, Wmax increased by 4% compared to the greenfield profile (4.9mm to 5.1mm) and its position is displaced 2.5m towards Tunnel 1, values similar to those for the 9.0m tunnels. Once again both the relative increase in magnitude of Wmax and the eccentricity decrease with depth. The surface value of Umax is unchanged from the greenfield value on both limbs of the profile. However, the positions of these have both been eccentrically displaced 6.5m towards Tunnel 1. For sub-surface regions the magnitude of Umax gradually increases until it exceeds the greenfield value on the near limb at 15.4m below the surface and reduces below the greenfield value on the remote limb. The position of U=0 is eccentrically displaced 3.0m towards Tunnel 1 at the surface and this eccentricity decreases to 1.0m at a depth of 15.4m below ground level. The resulting displacement profiles of the 4.0m tunnels at a centre-to-centre spacing of 30m and 50m are shown in Figures 5.15-5.18. Individual comment is not made on these because the behaviour closely matches that of the 9.0m tunnels. The results of the 80.0m spacing and 120.0m spacing are not shown for the same reason. Further discussion on the relative changes in displacement above the 4.0m tunnels at these spacings can be found in Section 5.3.3. 5.3.1.3 The effect of volume loss The effect of increasing the centre-to-centre spacing, while using a volume loss of 2.0% for both of the 4.0m diameter tunnels and maintaining a depth of 26.0m is considered here. The vertical and horizontal displacements for the twin 4.0m diameter tunnels at 20.0m centre-tocentre spacing are shown in Figures 5.19 and 5.20. The eccentricity of Wmax was found to be the same as that for the twin 4.0m diameter tunnels with volume losses of 1.3%. The effect of increasing the centre-to-centre spacing and using a volume loss of 1.3% for the first tunnel and 2.0% for the second tunnel and maintaining the depth (26.0m) and diameter (4.0m) was also considered based on the findings of Cooper and Chapman (1998). D.Hunt - 2004

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Figures 5.21 and Figure 5.22 show the vertical and horizontal displacements respectively above Tunnel 2. The general behaviour is very similar to that observed when assuming a 1.3% loss for Tunnels 1 and 2. The maximum eccentricity of Wmax is 5.0m at the surface as when using a volume loss of 1.3% (Figure 5.13) or 2.0% (Figure 5.19) for both tunnels, and the eccentricity decreases for sub-surface levels, though to a lower value at 15.4m (1.1m). The horizontal displacements can also be seen to be higher on the near limb compared to the remote limb. 5.3.2 Liner Deformation Although the project was not directly concerned with stresses induced in tunnel linings, it was important that the mode and magnitude of liner deformation was realistic and comparable to that found by other researchers (e.g. Kim 1996 and Addenbrooke 1996). For this reason only the tunnel deformations are reported here. The deformation of the first tunnel (due to the driving of a second tunnel) was found by subtracting the greenfield displacements from the predicted displacements for Tunnel 2. The greenfield deformation was the same as that which occurred for Tunnel 1 (Refer to Figure 4.10) and was constant for all tunnel spacings. The deformations of the first (9.0m) tunnel liner due to the driving of a second tunnel at various centre-to-centre spacings are shown in Figure 5.23 (a). The vector displacements are shown for 48 nodal points around the tunnel periphery. Displacements in the X and Y directions are also presented for the crown (A), tunnel axis right (B), invert (C) and tunnel axis left (D). The construction of Tunnel 2 causes the liner for Tunnel 1 to shorten in the vertical plane and extend in the horizontal plane towards Tunnel 1, these effects decreasing with an increased centre-to-centre spacing. The maximum vertical squat and horizontal extension reported at a spacing of 20m was 8.1mm (i.e. 10.5 - 2.4mm) and 8.7mm (i.e. 12.2 – 3.5) respectively. This general behaviour is similar to that reported by Addenbrooke (1996) and Kim et al (1996). Figure 5.23 (b) shows the non-linear relationship between horizontal and vertical displacements at points A to D for different values of spacing to diameter (d'/D).

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5.3.3 General Behaviour of Twin Tunnels 5.3.3.1 Contours of W/Wmax Figure 5.24 shows contours of W/Wmax above a second 9.0m diameter tunnel constructed at a centre-to-centre spacing of 30.0m from the first tunnel. Contours are shown from ground surface to 15.4 m below ground level, considering only the contribution of Tunnel 2. The value of Wmax used to derive the contours for each respective sub-surface was taken as the greenfield value for Tunnel 2 (i.e. assuming Tunnel 1 was not present). The contours on the remote limb of Tunnel 2 appear to be relatively unchanged compared to those found above a single tunnel in greenfield conditions (Figure 4.12). However, the contours on the near limb are significantly changed and appear to be angled towards Tunnel 1, indicating an increase in trough width. The figure relates directly to Figure 5.7 from where it is possible to see the corresponding predicted values of eccentricity and Wmax. 5.3.3.2 Relative changes in displacement (W1 / W2) Figure 5.25 shows the greenfield settlements for Tunnel 2 assuming Tunnel 1 not present (W1) divided by the predicted settlements for Tunnel 2 (W2) (i.e. the relative changes to the settlement profile) for the 9.0m diameter tunnels. The curve shows how the vertical displacements have been redistributed due to the short-term effects of soil stiffness changes caused by Tunnel 1. The horizontal line at W1/W2 =1 refers to specific points where the predicted ‘second tunnel driven’ settlement profile is the same as the greenfield profile (i.e. it is unchanged). The relative changes in settlement for the surface (Z=0.0m) and two subsurface levels (Z=6.9 and 15.4m) are remarkably similar, with the largest relative increase in settlement occurring over the centreline of Tunnel 1 and having a value of 1.6 (i.e. 60% increase). This increase in settlement occurs over a distinct region either side of Tunnel 1. Relative decreases in settlement occur towards the edges of the settlement trough, although these correspond to cases in which displacements are initially small. Figure 5.26 shows the relative changes in settlement (W2/W1) for the 9.0m diameter, at 26.0m deep tunnels at centre-to-centre spacings of 20.0m, 30.0m, 50.0m, 80.0m and 120.0m. The maximum increase in settlement appears to be close to the centreline of Tunnel 1, although some eccentricity beyond Tunnel 1 is present. For a spacing of 20.0m the increase in settlement over Tunnel 1 is approximately 60%, whereas at 120.0m spacing the increase is D.Hunt - 2004

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150%. While the value of W2/W1 over the centreline of Tunnel 1 increases with increased spacing, the values of vertical displacement above Tunnel 1 are decreasing. The relative changes in W2/W1 for Soil 2 can be seen in Figure 5.27 demonstrating that the relative redistribution is the same as that for Soil 1. There is a 60% increase in settlement above the centreline of Tunnel 1 for a centre-to-centre spacing of 20.0m which ranges up to 150% for a spacing of 120.0m. The results of W2/W1 for the 26m deep, 4.0m diameter tunnels with a volume loss of 1.3% are shown in Figure 5.28. The soil above the 4.0m diameter tunnels behaves in a similar manner to that above the 9.0m diameter tunnels. The maximum relative increase in settlement is found to occur close to the centreline of Tunnel 1 with an increase in settlement of 60% for a tunnel spacing of 20.0m. and 70% for a spacing of 120.0m, although the eccentricity of the maxima increases marginally at the larger (50.0 to 120.0) spacings. The effect of increasing the volume loss from 1.3% to 2.0% for both tunnels can be seen in Figure 5.29. The ratio of W2/W1 is very similar when using a volume loss of 1.3% or 2.0% with a varying centre-to-centre spacing. The maximum relative increase in settlement is approximately 60% for the closest spacing (20.0m) and is very close to the centreline of Tunnel 1. The effect of using a 1.3% volume loss for the first tunnel and a 2.0% volume loss for the second tunnel was also considered. These analyses were performed for two reasons: 

Firstly to show if the maximum relative increase in settlement would still occur above Tunnel 1 when a bigger volume loss was assumed for Tunnel 2.



Secondly to find if there was a limit to the amount of extra relative settlement that would occur above Tunnel 1 and determine how the settlement profile would be redistributed.

Figure 5.30 shows the relative changes in displacement above the 4.0m tunnels at a spacing of 20.0m with various volume losses for Tunnel 1 (V1) and Tunnel 2 (V2). The effect of increasing the volume loss from 1.3% to 2.0% for both tunnels is found to have little effect on the shape of the profile. When using a higher volume loss for Tunnel 2 (2.0%) than Tunnel 1 (1.3%) it can be seen that the relative changes in displacement are again of the same shape as the others, but of larger magnitude.

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The effect of increasing the spacing when using a 2% volume loss for Tunnel 2 and a 1.3% volume loss for Tunnel 1 can be seen in Figure 5.31. It appears that as the spacing increases (50.0, 80.0 and 120.0m) the maximum relative increase in displacement still occurs approximately over Tunnel 1 with values ranging from of 150-170%. However, there is evidence that large relative increases in displacement now occur also over the centreline of Tunnel 2. In other words the effect of the previously strained soil above Tunnel 1 is less dominant than the strains now being induced in the soil above Tunnel 2. Intuitively it would be possible to find the volume loss at a particular spacing that would cause an increase in settlement over Tunnel 1, but not over Tunnel 2. The range of values of the maximum relative increase in settlement above Tunnel 1 (M) for the various volume losses tunnel diameters and centre-to-centre spacing can be seen in Figure 5.32. The range varies from 0.5 to 1.6 when considering the various values of volume loss used. When considering a d’/Z value of 2 or less and a constant volume loss for Tunnel 1 and Tunnel 2, the values of M are within the range of 0.5 to 0.8. 5.3.3.3 Eccentricity of W max and relative changes in W Figure 5.33 shows the eccentricity of Wmax for all surface and sub-surface regions. For a d'/Zo spacing of less than 2 the position of Wmax is always placed eccentricity towards Tunnel 1. The behaviour of Wmax appears to follow a clear pattern of behaviour: 

the eccentricity is largest when the tunnel spacing is smallest;



the magnitude of eccentricity decreases non-linearly with increased tunnel spacing;



the magnitude of eccentricity decreases non-linearly for sub-surface regions.

The first two findings confirm those reported by Addenbrooke (1996), the last finding (not reported by Addenbrooke, 1996) provides a valuable new insight into the behaviour of the settlement trough for sub-surface regions. The eccentricity of Wmax at a depth of 0.6Z is the same for both 4.0m and 9.0m diameter tunnels for all d'/Z spacings. However, the eccentricity of Wmax at the ground surface due to the 4.0m diameter tunnels was less than that for the 9.0m diameter tunnels. This indicates that tunnel diameter or the d' spacing is more influential on the eccentricity at surface levels compared to the sub-surface regions. The effect of changing the volume loss had little effect on the amount of eccentricity. The zone of

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previously strained soil between the two tunnels will reduce with depth and may be the cause of the decrease in eccentricity (see Chapter 8). The decrease in eccentricity with depth is backed up by case history data reported by Cording and Hansmire (1975) which has been plotted with the finite element data on Figure 5.33. The data are for displacements above a second 6.4m diameter tunnel driven 14.6m below ground level in stiff clay at a centre-to-centre spacing of 10.8m. The data shows a similar decrease in eccentricity to the finite element results for a 4.0m diameter tunnel and an encouragingly close correlation in values. 5.3.3.4 Eccentricity of Umax (near) and Umax (remote) and U=0. In empirical predictions the position of W = 0 indicates the position of the full extent of the trough width. Due to the problems highlighted for predicting movements above single tunnels using the finite element method (Chapter 4) this position did not occur for the analyses conducted as part of this research project. In greenfield empirical predictions the position of Umax is coincident with the point of inflexion or trough width parameter (ig). By using a multiplier (usually 2.5 or 3.0) the full trough width can be found. Hence, in back analysis the changing position of Umax (i) can be used to indicate changes to the full trough width. Figure 5.34 shows the changing position of Umax (i) relative to the greenfield value (ig) for surface and sub-surface regions. Values are given for 9.0m and 4.0m diameter tunnels at varying centre-to-centre spacing on the near and remote limb. At ground surface the value of i (remote) decreases compared to the greenfield value (i.e deviates towards Tunnel 1), whereas at a depth of 0.6Z the trough width increases compared to the greenfield value (i.e deviates away from Tunnel 1). The biggest deviation of i on the remote limb is found for the tunnels at a spacing of 50.0m. At the surface the value of i(near) increases (i.e deviates towards Tunnel 1), whereas at depth of 0.6Z the trough width reduces (i.e deviates away from Tunnel 1). The deviations in behaviour for the 4.0m tunnels were in the same direction as those for the 9.0m tunnels although the relative changes were far less. The general behaviour of i (near and remote) mirror the relative changes in the position of U=0. For greenfield predictions above a tunnel the position of Wmax coincides with the position of U=0. Intuitively one would expect the same behaviour for movements above a second tunnel driven. However, after back analysis of the finite element analyses it becomes apparent that they are not coincident. In all the analyses reported here the position of Wmax was only ever pulled towards Tunnel 1 for surface and sub-surface levels (Figure 5.34) D.Hunt - 2004

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whereas the position of U=0 was pulled towards Tunnel 1 at the surface (Figure 5.35) and away from Tunnel 1 at depths below Z/Zo=0.4. 5.3.3.5 Mohr Coulomb model In order to verify that the effects reported in Sections 5.3 were directly due to the inclusion of the non-linear soil model various twin tunnel analyses were re-run using the Mohr-Coulomb yield model alone. In conclusion the effects (i.e. relative increases in displacement and eccentricities) seen in these analyses are as a direct consequence of the non linear soil model. 5.4 RESULTS OF PIGGYBACK TUNNELS The tunnel geometry was described in Section 5.2.1. The lower tunnel being situated at 33.4m below ground level i.e. twice the depth (16.4m) of the upper tunnel. This geometry was chosen because the greenfield displacements, predicted by both empirical and finite element analyses showed easily quantifiable behaviour (Chapter 4), i.e. the settlement above the lower tunnel should be half as great as the upper tunnel and the trough width of the lower tunnel should be twice as large as the upper tunnel. Both 4.0m and 9.0m diameter tunnels were used in the modelling with a volume loss of 1.3% for each. The spacing was kept constant in all analyses, leading to a d' value of 3D for the 4.0m tunnels. The analyses considered two construction sequences for each tunnel diameter: the lower tunnel followed by the upper tunnel and the upper tunnel followed by the lower tunnel. (Instinctively for new tunnels in practice the latter construction sequence would be avoided as the construction of the lower tunnel affects a newly constructed tunnel) Prior to the analyses it was expected that the behaviour of the second tunnel would be very different under each of these construction sequences. By driving the lower tunnel first, the second upper tunnel would be constructed completely within the bounds to movement of the lower tunnel and within soil which had been previously strained. However, when constructing the upper tunnel first, the bounds to movement for the second lower tunnel would envelope the bounds to movement for the upper tunnel. The second tunnel would be drawing from previously strained soil disturbed by the upper tunnel and the surrounding undisturbed soil. In addition to this the presence of an existing tunnel, within the bounds to movement for the second tunnel and in a position where maximum displacement would be expected, would have considerable effect on the settlement profile. The displacements for

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each of the analyses are reported for the surface levels and sub-surface depths of 2.9, 5.9 and 7.9m below ground level. 5.4.1 Lower Tunnel Driven First The first piggyback analysis was undertaken with 9.0m diameter tunnels and the lower tunnel constructed first. Figure 5.35 shows the predicted vertical displacement due to the construction of the upper tunnel only, and compares it to the greenfield displacement (i.e. the displacement which would have occurred if Tunnel 1 had not been present). The greenfield profile shows a maximum vertical displacement of 15.0mm at the surface, whereas the predicted displacements show 3.3mm of heave above the tunnel centreline the tendency to heave reducing for sub-surface levels. The outer edges of the trough show increases in vertical displacement compared to the greenfield profile at all levels. At a depth of 7.9m the settlement above the tunnel centreline is 0.9mm compared to 24.0mm for the greenfield prediction. The heave above the centreline is due to the deformation/movement of the second (upper) liner (See Section 5.4.3). The corresponding horizontal displacements are shown in Figure 5.36. At the surface the horizontal movements have decreased from 8.5mm (greenfield) to 7.1mm (predicted) while the position of Umax has increased from 14.0mm to 29.0mm. If the position of Umax is considered to be a direct indication of trough width, it indicates that the trough width has doubled (i.e. it has deviated to the bounds to movement for the lower tunnel). This deviation in position of Umax decreased for sub-surface levels. The second analysis was conducted using 4.0m diameter tunnels with the same construction sequence. Figure 5.37 shows the vertical displacements above Tunnel 2. The maximum vertical displacement occurs above the centreline of Tunnel 2 and was found to be 2.0mm (interestingly this was the same as the greenfield value for the 33.4m tunnel, see later for possible explanation). This displacement is only 52% of the 3.8mm found for the greenfield conditions, i.e. it has halved. For all sub-surface regions the actual vertical displacements were lower than the greenfield displacements, although the percentage reduction decreased with depth. At a depth of 7.9m, Wmax was found to be 63% of the greenfield value. Figure 5.38 shows the corresponding horizontal movements above Tunnel 2. The value of Umax for the ground surface is 1.5mm, only 80% of the 1.9mm found for greenfield conditions while the position of Umax is increased by 44% from 12.5m to 18.0m. At a depth of 7.9m the value

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and position of the greenfield predictions and predictions are similar. In summary, a larger deviation in trough width occurs at the surface than in regions closer the tunnel axis. When constructing a second tunnel directly above a first tunnel within a short time frame (i.e. no consolidation is allowed) and assuming the same volume loss for each tunnel, both of these analyses indicate that angle of draw, or trough width, will increase. For the 9.0m diameter tunnels the trough width (position of Umax) doubles and for the 4.0m diameter tunnels the trough width increases by 44% and the maximum vertical displacement halves. If it is assumed that the trough width at the ground surface for the Tunnel 2 had extended to the edge of the bounds to movement for Tunnel 1 (while using a constant volume loss) the empirical predictive model indicates two distinct changes to the profile: 

The vertical displacement profile above Tunnel 2 would have a maximum that is half of the greenfield prediction and consequently the profile above Tunnel 1 and Tunnel 2 would be almost identical.



The magnitude of Umax for the second tunnel would decrease compared to the greenfield prediction due to the fact that W has decreased. Unlike the vertical displacements the horizontal displacements would be expected to be higher for Tunnel 2 than Tunnel 1 due to the different depths of the vector focus assumed for each tunnel.



The distance from U=O to U=Umax would also double compared to the greenfield prediction. These changes were all noted in the analyses reported above. Only the increase in trough

width for the ground surface displacements was suggested by Addenbrooke (1996). 5.4.2 Upper Tunnel Driven First The first of these analyses considers constructing a 9.0m tunnel at 16.4m below ground level followed by the construction of an identical second tunnel a depth of 33.4m (i.e. 17.0m below Tunnel 1). The displacements which occur above (Upper) Tunnel 1 are not shown in the figures, although they are the same as the greenfield displacements shown in Figures 5.35 and 5.36. Figure 5.39 shows the greenfield displacements (i.e. the profile which would have occurred if Tunnel 1 had not been present) against the predicted displacements due to the construction of Tunnel 2. The settlement profile is approximately the same size and shape as the greenfield prediction. However, the presence of the 9.0m tunnel within the zone of

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previously disturbed soil results in a reduction in settlement above the centreline of Tunnel 2. i.e. there is a ‘humped’ zone due to the presence of the tunnel which acts to stiffen the ground in this zone. The horizontal displacements show a very small increase in magnitude compared to the greenfield values (Figure 5.40). Once again a 44% increase in the position of Umax is evident at the ground surface with only a 13% increase evident at 7.9m below ground level. The behaviour of the ground associated with the construction of 4.0m diameter tunnels (Figure 5.41) is very similar to the 9.0m diameter tunnels. For the 4.0m diameter piggyback tunnels W is very similar away from the centreline, although once again a hump was noted above the centreline of Tunnel 2. This ‘humped’ shape has previously been reported by Attewell et al (1986) when considering the longitudinal surface settlement profile above a tunnel driven below and perpendicular to an existing pipeline. Figure 5.42 shows the corresponding horizontal displacements above Tunnel 2. Once again a small increase in the magnitude of Umax is noted (approximately 25%) with identical increases in the position of Umax on both limbs. The relative increases in the position of Umax or i/ig (where i is the predicted value and ig is the greenfield value) are shown in Figure 5.43 for all the piggyback analyses. It can be seen that an increase in trough width is evident in both types of tunnel construction sequence, although, larger increases are shown when constructing the lower tunnel first. 5.4.3 Deformation of Tunnel Liner Figure 5.44 shows the deformation of Tunnel 2, the upper 9.0m diameter tunnel liner driven as a second tunnel in a piggyback arrangement. The position of the liner has moved upwards from its original position. Considering the displacement of the liner at the crown, invert and axis level it is apparent that the tunnel shape has changed, being extended in the vertical plane and reduced in the horizontal plane. This lifting of the liner is consistent with the heave seen in Figure 5.35. It may be possible to explain why the tunnel deforms like this by considering what has happened to the surrounding soil. The shape of the tunnel must be a direct result of the zone of previously strained soil in which it was constructed (i.e. a soil which underwent vertical extension and horizontal compression). The heaving must be due to the large amount of soil which has been removed causing a relief in the overburden stress. The deformation of the 4.0m diameter tunnel (not shown) was similar to that of 9.0m diameter tunnel, although of smaller magnitude. However, no upward movement of the liner was evident with the 4.0m diameter tunnels. D.Hunt - 2004

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5.5 RESULTS OF OFFSET TUNNELS The offset tunnels were assumed to be situated at 17.4m and 30.9m below ground level (referred to as the lower and upper tunnel respectively). The 9.0m tunnel diameters were constructed with using volume loss 1.3% of for all of the analyses. Two construction sequences were considered: the lower tunnel followed by the upper and the upper tunnel followed by the lower. The effect of an increased centre-to-centre spacing was also considered for both construction sequences. The resulting displacements are reported for the surface and sub-surface levels (i.e. 2.9m, 5.9m and 8.9m below ground level). The offset tunnel analyses provide a geometry which shares the characteristics of side-byside tunnels and piggyback tunnels. One would intuitively expect that the behaviour of this type of alignment would include a mixture of effects found from both side-by-side and piggyback tunnel analyses (e.g. Addenbrooke, 1996). 5.5.1 Lower Tunnel Driven First The vertical displacements above Tunnel 2 caused by driving the lower tunnel first are shown in Figure 5.45, in which it is apparent that there has been a considerable amount of displacement redistribution. the maximum vertical displacement at the surface is 12.0mm, only 80% of the 14.5mm which would have occurred under greenfield conditions. The position of this maximum displacement was eccentrically displaced 20.0m towards Tunnel 1. There is also evidence of considerable increases in settlement over the centreline of the first tunnel driven, which is accompanied by larger decreases in settlement over the remote limb than the near limb for Tunnel 2. At a depth of 8.9m below ground level there are still large increases in settlement occurring over the centreline of Tunnel 1, although not as large as those noted at the surface. The maximum settlement was 14.2mm at this depth, which was only 60% of the 24.3mm found for greenfield conditions. At this depth the maximum displacement is eccentrically displaced by only 3.7m towards Tunnel 1, considerably less than at the surface. The reduction in the value of Wmax compared to the greenfield profile is similar to the behaviour of the piggyback tunnels. whereas the eccentricity of Wmax is similar to the behaviour of side-by-side tunnels. The corresponding horizontal displacements are D.Hunt - 2004

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shown in Figure 5.46. At the surface there is a 33% increases in Umax (i.e. 8.2 to 11.0mm) on the near limb and a 70% decrease on the remote limb (i.e. 8.2 to 2.6mm). The horizontal movements at the surface are 4.2 times larger on the near limb (11.0mm) than those on the remote limb (2.6mm). At 8.9m below ground the movements are 4.7 times larger on the near limb (14.6mm) compared to the remote limb (3.1mm). The distance between U=0 and Umax can be seen to increase on the remote and near limbs at both the surface and sub-surface levels, indicating a widening in the trough width. The position of U=0 has also displaced from the centreline of Tunnel 2 onto the remote limb by 5.0m at the surface and by 6.8m for sub-surface levels. This is similar to the behaviour of piggyback tunnels, whereas the increase in value of Umax on the near limb and the reduction in the value of Umax on the remote limb are characteristics of side-by-side tunnels. Similar observations were found at a spacing of 30.0m, as shown in Figures 5.47 and 5.48. The eccentricity of Wmax is less than for the 20.0m spacing at all levels (i.e. 15.0m at the ground surface and only 1.3m at 8.9m below ground level). Again large increases in settlement were found over the centreline of Tunnel 1, with decreases in settlement over Tunnel 2, compared to the greenfield condition. The distance of Umax from U=0 is increased on both limbs of the settlement trough, with larger displacements occurring on the near than the remote limb. The eccentricity of U=0 exactly matches the values for the 20.0m spacing. For a centre-to-centre spacing of 50.0m large settlements can be seen over the centreline of Tunnel 1 with reductions in settlement over Tunnel 2 (Figure 5.49). The settlement recorded above Tunnel 1 decreases from 4.9mm at the ground surface to 3.6mm a depth of 8.9m. The changes in vertical and horizontal displacements (Figure 5.50) show similarities with those found above side-by-side tunnels at a spacing of 50.0m (Figures 5.9 and 5.10). Figure 5.51 shows the eccentricity of Wmax for surface and sub-surface levels and varying spacing of the tunnels. The eccentricity (e/d') decreases with increased spacing, and also for sub-surface levels in the same manner as the side-by-side tunnels. The value of eccentricity is considerably larger for the offset tunnels than for the side-by-side tunnels (Figure 5.33). Figure 5.52 shows changes to the position of Umax and the position of U=0 for ground surface and sub-surface levels. The behaviour on the near limb is similar to that of the sideby-side tunnels (Figure 5.34) with a 60% increase in the value of i/ig at the surface level. However, the behaviour on the remote limb is differs, with increases in the value of i/ig occurring for both surface and sub-surface levels. The position of U=0 is offset on the remote limb for surface and sub-surface levels.

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5.5.2

Upper Tunnel Driven First

The second set of analyses considers construction of the upper tunnel first followed by the lower tunnel. Figure 5.53 shows the vertical displacements above the second (lower) tunnel driven at a spacing of 20.0m from the first tunnel. The settlements above the second tunnel are larger than the greenfield settlements, a pattern different to that found when constructing the lower tunnel first. At the surface the settlement increases by 24% from 11.0mm to 13.6mm. The maximum is not eccentrically displaced towards Tunnel 1 and lies directly above the centreline of Tunnel 2. Reductions in settlement occur above Tunnel 1 compared to the greenfield case, which is opposite to the behaviour when the lower tunnel is constructed first (Figure 5.45). This behaviour is due to the presence of Tunnel 1 within the bounds to movement for Tunnel 2, i.e. Tunnel 1 shields Tunnel 2 from the previously strained soil above Tunnel 1. This is clearly seen through the horizontal displacements shown in Figure 5.54. At the surface the position of Umax is approximately the same as for the greenfield value, while at a depth of 8.9m the position of Umax has more than doubled (21.0m compared to 45.6m). The movements on the near limb are higher than those on the remote limb, at all levels, the predicted values being consistently larger on the near limb and smaller on the remote limb than those for the greenfield case. There is a large eccentric displacement in the position of U=0 on the remote limb which increases with depth from 10.0m at the ground surface to 15.0m at 8.9m below ground level. Similar observations are found for tunnels at a centre-to-centre spacing of 30.0m. The presence of Tunnel 1 within the bounds to movement for Tunnel 2 is reflected in both the vertical and horizontal displacements (Figure 5.55 and Figure 5.56). The eccentric placement of U=0 is also evident with values of 8.5m at the surface and 10.0m at 8.9m below ground level. At a centre-to-centre spacing of 50.0m (Figure 5.57) the vertical displacements are similar to those found above side-by-side tunnels with the same spacing (Figure 5.9). A small relative increase in settlement is seen above the centreline of Tunnel 1. The horizontal displacements (Figure 5.58), show that the magnitudes and position of the horizontal displacements are almost identical to the greenfield displacements. On the remote limb, however, the decrease in the value of U and the increase in the position of Umax suggest that the trough width has increased. D.Hunt - 2004

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5.6 DISCUSSION It is clear from the analyses undertaken as part of this research project that the changes in the displacement profile which occur above a second tunnel, in close proximity to the first tunnel, are influenced by a variety of factors. The main factors are: 1

Changes in volume loss

2

Changes in trough width

3

The effect of pre-failure soil stiffness

4

Presence/behaviour of a tunnel within bounds to movement

Increases in volume loss are considered in Chapter 4 for the analysis of single tunnels using the finite element method. The effects of an increased volume loss for a single tunnel are increases in W, Wmax, U and Umax, while the position of Wmax and Umax remain almost unchanged. Deviations in the trough width are measured by changes in the position of Umax. For single tunnels these deviations are found to be highly dependent on tunnel depth and are almost independent of the volume loss assumed. Consequently for most of the twin tunnel analyses reported in this chapter the volume loss is kept constant, as such for twin tunnels it can be concluded that the changes in position and magnitude of W, Wmax, U and Umax are attributed directly to the pre-failure soil stiffness. This is in contrast to work of previous authors where increases in volume loss were also incorporated (e.g. Addenbrooke, 1996). The effect of pre-failure soil stiffness can only be highlighted through the use of finite element analyses. This chapter has shown how important it is to relate greenfield displacement profiles to predicted profiles for both surface and sub-surface levels. This is equally important for the horizontal displacement profiles, which are all too often ignored by authors. This information is vital in order to understand fully the changes which occur to the displacement profiles above twin tunnels. While simple comparisons of greenfield profiles to predicted profiles is easy to accomplish, they remain absent from many publications considering numerical analyses of multiple tunnels.

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5.6.1 Side-by-Side Tunnels The main conclusions related to the vertical displacements obtained from the side-by-side tunnel analyses are listed below: 

Side-by-side tunnels have been shown to be susceptible to a relative increase in settlement that always occurs above, or very close to, the centreline of Tunnel 1.



The relative increases were shown to range from 60%, for tunnels with a 20.0m centre-tocentre spacing, up to 150% for a spacing of 120.0m. The relative decreases in settlement that occurred at the edges of the trough were less significant due to the fact that the displacements were already relatively small.



The relative increases in vertical displacement were found to be virtually independent of the volume loss assumed and tunnel diameter used.



The changes in the settlement profile are caused by the redistribution of soil displacements that are primarily related to the changes in soil stiffness. The increased volume loss only exaggerates the effects.



The near limb of the settlement profile (i.e. the side nearest Tunnel 1) has been found to be susceptible to increases in vertical and horizontal displacements.



The remote limb of the settlement profile (i.e. the side furthest from Tunnel 1) has been found to be susceptible to decreases in vertical and horizontal displacements.



The eccentricity of Wmax has been found to be largest when the tunnel spacing is closest, which is in agreement with the work of Addenbrooke (1996).



The eccentricity decreases with increased tunnel spacing and depth (i.e. for sub-surface levels), and is almost independent of the volume loss assumed for both tunnels.



The inclusion of a larger volume loss for the second tunnel causes increases in the magnitude of the displacements obtained when the volume losses were the same.

While these conclusions have been drawn for clays in undrained conditions, reported case history data has shown similar behaviour for side-by-side tunnels in both sands and residual soils (e.g. Brahma and Ku, 1982 and Hanya, 1977). The results show that the changes to the

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horizontal displacements are more complex than the vertical displacements and hence less easy to draw conclusions for. The conclusions for the horizontal displacements above sideby-side tunnels are: 

For side-by-side tunnels, the position of U=0 and Wmax no longer coincide (i.e. unlike the greenfield settlement profiles).



For surface settlements the position of U=0 is pulled towards Tunnel 1 in a manner similar to that for Wmax. However, for sub-surface regions the position of U=0 moves away from Tunnel 1.



The horizontal displacements are larger on the near limb than the remote limb.



The position of Umax (near and remote limbs) is drawn towards Tunnel 1 at the surface and away from Tunnel 1 at depth.



For a close tunnel spacing (20.0m) the distance from U=0 to Umax on both the near and remote limbs is reduced compared to the greenfield profile at the surface only. For subsurface levels and for spacings above 20.0m the distance from U=0 to Umax increases on both the near limb and the remote limb.

The changes to the horizontal movements caused by the previous construction of a tunnel in close proximity are more complicated to understand than the vertical movements and require case history or experimental data to clarify. 5.6.2 Piggyback Tunnels The individual values of greenfield displacement above each of the piggyback tunnels is reported in Chapter 4. It can be concluded that the behaviour of piggyback tunnels i.e. when constructing a second tunnel constructed directly above or below a previously completed tunnel, is very different to that of side-by-side tunnels. The following conclusions were drawn from the results reported in this chapter when constructing the lower tunnel first: 

The displacement profiles above Tunnel 2 are perfectly symmetric for all analyses.



When keeping the volume loss constant for each tunnel it has been found that no relative increase in settlement occurs over the centreline of the previously constructed Tunnel 1. This is opposite to the behaviour seen for side-by-side tunnels.

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

When constructing small tunnels (4.0m diameter) the value of Wmax above the centreline of Tunnel 2 is found to be reduced compared to the greenfield value. For the larger (9.0m diameter) tunnels there is also evidence of heave.



The value of W at the outer extents of each limb for Tunnel 2 increases compared to the greenfield values.



The magnitudes of the horizontal displacements were lower than the greenfield predictions. The distance from U=0 to Umax was also found to increase. Both of these observations are indicative of increases in trough width. This behaviour was evident for both the 9.0m and 4.0m diameter tunnels.

The general behaviour reported above is very similar to that reported by Addenbrooke (2001). The changes to the settlement profile reported here are caused through pre-failure soil stiffness alone and do not consider any increase in volume loss for Tunnel 2. However the author is aware that Tunnel 2 (upper) will be driven through a zone of highly disturbed soil from the previous construction which may result in subsidence of more than twice the amount from a single tunnel (Wang and Chang, 1992). In practice it would be very uncommon to construct an upper tunnel first. However, for the purpose of this research it is interesting to find out exactly what would happen if this scenario ever occurred. The conclusions are: 

The displacement profiles above Tunnel 2 are perfectly symmetric for all analyses.



When keeping the volume loss constant for each tunnel it has been found that no relative increase in settlement occurs over the centreline of the previously constructed Tunnel 1. This is opposite to the behaviour seen for side-by-side tunnels.



The value of W at the outer extents of each limb for Tunnel 2 increases compared to the greenfield values.



The magnitudes of the horizontal displacements were lower than the greenfield predictions. The distance from U=0 to Umax was also found to increase. Both of these observations are indicative of increases in trough width. This behaviour was evident for both the 9.0m and 4.0m diameter tunnels.



There is evidence of large reductions in settlement above Tunnel 2 for both the 4.0m diameter tunnels and the 9.0m diameter tunnels. This is quite plausible as the stiffness of

D.Hunt - 2004

- 135 -


the lining for Tunnel 1 (in the longitudinal plane) will reinforce the soil and so reduce ground displacements. 

The distortion of the 9m liner was very influential on the settlement profile. This would indicate some dependency on the d' spacing between the liners rather than the centre-tocentre spacing.

The difference in behaviour of the side-by-side tunnels compared to the piggyback tunnels may be due to the fact that there are differences in the strains induced in the soil. Both the tunnels in the side-by-side analyses would induce similar magnitudes of strains into the soil because they are at the same depth. However, for the piggyback tunnels the range of strains induced into the soil by the upper and lower tunnels are different. i.e. the upper tunnel induces much larger strains in the soil than the lower tunnel. 5.6.3 Offset tunnels The results of the offset tunnel analyses have shown that the settlement profile is directly influenced by the construction sequence. The profile has characteristics similar to both sideby-side tunnels and piggyback tunnels. When the volume loss is kept constant and the lower tunnel is driven first, it was concluded that: 

The value of Wmax decreases for ground surface and sub-surface levels for all centreto-centre spacings.



The position of Wmax is eccentrically displaced towards Tunnel 2 (upper) and this eccentricity is much larger than the values found for side-by-side tunnels. The eccentricity decreases with increased centre-to-centre spacing.



The increase in W over the centreline of Tunnel 1 (lower) is much greater than that found for the side-by-side tunnels.



Large increases in the value of Umax are apparent on the near limb and large decreases in the value of Umax are apparent on the remote limb. These changes are much larger than those found above the side-by-side tunnels.



Increases in the offset position of Umax (i) occur on both the near and remote limbs, which are larger than those for the side-by-side case, and decrease with depth. This increased value of i is in agreement with the case history data reported by Shirlaw et

D.Hunt - 2004

- 136 -


al. (1988), who reported an unusually wide value of i for the shallower tunnel that was generally closer to the value measured for the lower tunnel. 

The position of U = 0 is only offset on the remote limb away from Tunnel 1 (lower).

These large changes in the position of Umax and the decrease in magnitude of Wmax are similar to the behaviour of the piggyback tunnels. However, the large increases in settlement over Tunnel 1, the eccentric displacement of Wmax and the much larger horizontal displacements on the near limb compared to the remote are all characteristics of the side-by-side tunnels. When the volume loss is kept constant and the upper tunnel is driven first, it was concluded that: 

At close centre-to-centre spacings (20.0m) of the tunnels there are reductions in displacement over Tunnel 1. This is opposite to the behaviour found when constructing the lower tunnel first and that of the side-by-side case.



At close spacings of the tunnels (20.0m) there is an increase in maximum settlement which occurs very close to the centreline of Tunnel 2 (i.e. very little eccentricity is present). At a spacing of 30.0m the eccentricity becomes more pronounced and the value of Wmax reduces.



The magnitude of Umax is larger on the remote limb than the near limb for all ground surface and sub-surface levels, and for all spacings. For spacings of 20.0m and 30.0m the value on the near limb is higher than the greenfield value and the value on the remote limb is lower than the greenfield value. This behaviour is completely opposite to that shown when driving the lower tunnel first.



The position of Umax reduced on the remote limb compared to the greenfield value and increased on the near limb. The largest increase in the position of Umax occurs at a close centre-to-centre spacing (20.0m) for Tunnel 1 and Tunnel 2.

The differences in behaviour for this case are due to the presence of a tunnel within the bounds to movement for the second tunnel. The behaviour is similar to that of the piggyback tunnel case when constructing the upper tunnel first. The tunnel provides stiffness within the soil, and shields the previously strained soil above Tunnel 1. It can be concluded that the effect of this previously strained soil on the profile above Tunnel 2 is less apparent when driving the lower tunnel second. While this is a reasonable conclusion to make based on the

D.Hunt - 2004

- 137 -


results found there is currently a lack of case history data for tunnels constructed using this sequence. As this information becomes available the claims can be endorsed or refuted.

D.Hunt - 2004

’ = 25 0

D =4.0m and 9.0m

- 137 -


centre-to-centre spacing (d')

centre-to-centre spacing (d') 26m 17.4m

30.9m

Upper

London Clay C’ = 5kPa ’ = 25 0

Lower

d' = 20.0, 30.0, 50.0, 80.0 & 120.0m 4.0m30.0, and 9.0m d'D==20.0, 50.0, 80.0 & 120.0m


D = 9.0m

(a) Twin side by side tunnel geometry

16.4m

Upper 33.4m

Lower


D =4.0m and 9.0m

(b) Twin piggy back tunnel geometry centre-to-centre spacing (d') centre-to-centre spacing (d')

26m

17.4m

30.9m

Upper

London Clay C’ = 5kPa ’ = 25 0 d' = 20.0, 30.0, 50.0, 80.0 & 120.0m D = 4.0m and 9.0m d' = 20.0, 30.0, 50.0, 80.0 & 120.0m D = 9.0m

Lower London Clay C’ = 5kPa ’ = 25 0

(c) Twin offset tunnel geometry Figure 5.1 Geometry of cases modelled in twin tunnels analyses Upper

D.Hunt - 2004 33.4m

16.4m

- 138 -

Figure 5.2a Finite element mesh for a side-by-side 9.0m and 4m diameter twin tunnel analysis (Z = 26.0m, 20.0m spacing)

d' (various spacing)

105.0m


Symbols used: Fixed boundary Reaction forces used to prop open tunnel Tunnel liner and anchor N.B. Tunnel liner not to scale


40.0m

26.0m

105.0m


D.Hunt - 2004

- 139 -

Symbols used:

Figure 5.2b Finite element mesh for piggyback 9.0m and 4.0m diameter twin tunnel analyses (Z = 16.4m and 33.4m.)

105.0m


Symbols used:

Fixed boundary

Fixed boundary

Reaction forces used to prop open tunnel

Reaction forces used to prop open tunnel

Tunnel liner and anchor

Tunnel liner and anchor


40.0m

17.0m

16.4m

105.0m


D.Hunt - 2004

3

- 140 -

d' (Various spacing )

105.0m

Figure 5.2c Finite element mesh for a offset 9.0m diameter twin tunnel analysis Z = 17.4m and 30.9.0m, 20.0m spacing.




40.0m

13.5m

17.4m

105.0m


D.Hunt - 2004

4

- 141 -


Fixed distance – 65m

145m

115m

95m

85m

Varying distance to boundary

Displacement (mm)

5 0 5 10 15

Tunnel

-65

-15

35

85

135

Chainage (m)

Figure 5.3 Settlement above tunnel one with varying tunnel to boundary distance (distance to right-hand-side boundary shown) Fixed distance – 105m

Displacement (mm)

225m

185m

155m

5

135m

125m

Varying distance to boundary

0

-5 Vertical (125m) Horizontal (125m) Vertical (135m) Horizontal (135m) Vertical (155m) Horizontal (155m) Vertical (185m) Horizontal (185m) Vertical (225m) Horizontal (225m)

-10 Tunnel

-15 -105

-55

-5

45

95

145

Chainage (m)

Figure 5.4

Settlement above tunnel one with varying tunnel to boundary distance (distance to right-hand-side boundary shown)

D.Hunt - 2004

195

- 142 -


Distance from centreline of Tunnel 2 (m) -105 0

-55

-5

5

55

Depth (m)

105

0.0

0

5

Settlement (m)

-0.005

10 -0.01 15

Wmax = 11.9mm at 0.0m

-0.015

Wmax = 14.2mm at -8.5m -0.02 95

45

-5

-55

-105

Chainage (m)

0

0.00E+00

5

-5.00E-03

10

-1.00E-02

-1.50E-02

15

Wmax = 16.0mm at 0.0m -2.00E-02

Wmax = 17.4mm at -6.8m 95

45

-5

-2.50E-02 0.00E+00 -105

-55

-5.00E-03

5 10

-1.00E-02

15

-1.50E-02

20 0.01

Wmax = 19.0mm at 0.0m Wmax = 19.2mm at -5m

0.005 95

45

-5

-55

-2.00E-02

-2.50E-02 -105

Chainage (m)

Settlement (m)

-11.4

Settlement (mm)

Displacement (mm)

0

0

Settlement (mm)

-6.9

-15.4

0

-0.005 5

10-0.01 -0.015 15

20-0.02 Wmax =22.0mm at 0.0m -0.025

Wmax =21.5mm at -2.3m

-0.03 95

45

-5

-55

Chainage (m)

-105

Tunnel axis

-26.0

Tunnel 1 Tunnel 2

Symbols:

Figure 5.5

Greenfield displacement

Predicted displacement

Surface and sub-surface vertical displacements above Tunnel 2 when considering twin tunnels 9.0m diameter tunnels at 26.0m depth with a 20.0m centre-to-centre spacing (V1 and V2 = 1.3%)

D.Hunt - 2004

- 143 -


10 1.00E-02

6.8mm at –20.0m 6.82mm at -20m 6.9mm at -25.0m

6.8mmat at 6.82mm 20m20.0m 4.9mm at 13.6m 4.88mm at 13.6m

6.94mm at -25m

5 5.00E-03 Depth (m)

U = 0 at -6.8m

0 0.00E+00

0.0

6.8m 10

-5.00E-03

1.00E-02

5.7mm at –18.0m 5.7mm at -18.8m 5.6mm at 5.6mm -22.0mat -22m

5.75.7mm at 18.8mat 18.0m 3.6mm 5.00E-03 11.9mm3.6mm at 0mat 18m at 18.0m

5

-1.00E-02

14.2mm at 6.8m U = 0 at -0.0m

0

-5.00E-03

6.35mm at -

5.9mm at13m -15.0m

5.8mm at 15.0m 5.8mm at 15m

5.8mm at -15m

5

-2.50E-02 0

5.00E-03

3.3mm at 18.0m 3.3mm at 18m

95

45

-5

U = 0 at +2.5m

-55

-1.00E-02

-105

2.5m

0.00E+00

8.7mm8.7mm at –8.6m at 8.6m

19mm at 0m 17.4mm6.7mm at6.7mm 8.5mat at11.3m 11.3m

at 11.3m 6.7mm6.7mm at –11.3m

3.4mm at at13.6m 3.4mm 13.6m

5.00E-035

-5.00E-03

-2.00E-02 -1.00E-02

U = 0 at +3.6m

0

0.00E+00 -105 95

-55 45

-3.00E-02

55-55

-15.4

Tunnel axis-2.00E-02

-26.0

Tunnel 1 Tunnel 2

95

-2.50E-02

-55

18.8mm at 0m 19.2mm at 5m

-1.00E-02

-2.00E-02

3.6m-5

-2.50E-02 105-105-1.50E-02

Distance from centreline of Tunnel 2 (m)

-5.00E-03

Figure 5.6

-11.4

-1.50E-02

1.00E-02 10

-1.50E-02

Settlement (mm)

-2.00E-02

1.00E-02 6.4mm at –13.0m

Settlement (mm)

Displacement (mm)

10

-6.9

0.00E+00

-1.50E-02

Symbols:

45


Chainage (m)

-5

-55


21.5mm at 2.3m 22mm at 0m

-2.50E-02 -105

Surface and sub-surface horizontal displacements above Tunnel 2 when considering twin 9.0m diameter tunnels at 26.0m depth with a 20.0m centre-to-centre spacing (V1 and V2 = 1.3%) D.Hunt - 2004

- 144 -


Distance from centreline of Tunnel 2 (m) -95

-45

5

55

Depth (m)

105

0

0.0

0.00E+00

5 10


15


-1.00E-02

-1.50E-02

Settlement (mm)

-5.00E-03

-2.00E-02

0

95

45

-5

-6.9

0.00E+00 -2.50E-02 -105

-55

5

-5.00E-03

10

-1.00E-02

15


-1.50E-02

Settlement (mm)

Chainage (m)

Wmax = 16.0mm at 0.0m -2.00E-02 Settlement above tunnel 1 (1.3% loss)

0

95

Settlements above tunnel 1

T2

45

-5

-11.4

-2.50E-02 0.00E+00 -105

-55

Chainage (m)

5

-5.00E-03

10

-1.00E-02

15

-1.50E-02

20


Settlement (mm)

Displacement (mm)

T1

-2.00E-02


Comparison of twin 9m diameter tunnels at 30m C-C spacing measured at 15.4m below ground level (Soil 1) 45

-5

-55

Chainage (m)

0

-2.50E-02 -105 0.00E+00

5

-5.00E-03

10

-1.00E-02

15

-1.50E-02

20

-15.4

Settlement (mm)

95

-2.00E-02

Wmax = 19.0mm at1.1m 95

45

-5

Wmax = 22.0mm at 0.0m -55

-2.50E-02 -105

Chainage (m)

Tunnel axis Tunnel 1 Tunnel 2

Symbols:

Figure 5.7



Surface and sub-surface vertical displacements above Tunnel 2 when considering twin 9.0m diameter tunnels at 26.0m depth with a 30.0m centre-to-centre spacing (V1 and V2 = 1.3%) D.Hunt - 2004

-26.0

- 145 -


10

1.00E-02

6.8mm at –20.0m 6.8mm at 20.0m

6.3mm at –26.4m

5

5.00E-03

4.2mm at 20.0m

Depth (m)

U = 0 at -2.0m

0

10

1.00E-02 -5.00E-03

5.7mm at –18m 5.0mm at –21.5m

5.7mm at 18.0m

5

U = 0 at +2.0m

0

1.00E-02 -5.00E-03 -2.00E-02

5.7mm at –13.4m 5.8mm at -15.0m

5.8mm at 15.0m

5

5.00E-03 -1.00E-02 -2.50E-02 -105

3.3mm at 20.0m

95 0

10

45

-5

-55

Comparison Uof =twin diameter tunnels at 30m C-C spacing 0 at9m +3.6m Chainage (m)ground level (Soil 1) measured at 15.4m below

-1.50E-02 0.00E+00 -11.4

1.00E-02

7.6mm at –10.0m 6.7mm at –11.3m

T1

Horizontal displacement above Tunnel 1 -2.00E-02 -5.00E-03 Horizontal displacements 6.7mm at 11.3m

T2

3.8mm at 15.5m

5

95

45

-5

-55

5

55

5.00E-03

-2.50E-02 -1.00E-02 -105

U = 0 at +3.6m

Chainage (m)

0 -95

-45

-1.50E-02

Distance from centreline of Tunnel 2 (m) -5.00E-03

-2.00E-02 -26.0

Tunnel axis Tunnel 1

Symbols:

-15.4

0.00E+00

105

-1.00E-02

Tunnel 2

95 45 -5 Greenfield displacement Chainage (m)

-55 Predicted displacement

Settlement (mm)

10

Settlement (mm)

0.00E+00 -6.9 -1.50E-02

Settle me nt (mm)

Displacement (mm)

5.00E-03 -1.00E-02

3.4mm at 22.6m

Settlement (mm)

0.00E+00 0.0

-2.50E-02 -105 -1.50E-02

-2.00E-02

Figure 5.8

Surface and sub-surface horizontal displacements above Tunnel 2 when considering twin 9.0m diameter tunnels at 26.0m depth with a 30.0m -2.50E-02 centre-to-centre spacing (V1 and V2 = 1.3%) 95

45

-5

Chainage (m)

D.Hunt - 2004

-55

-105

- 146 -



-95 -45 5 at 50m C-C spacing 55 Comparison of twin 9m diameter tunnels

Depth (m)

105

measured at 0.0m below ground level (soil 1)

0

0.0

0.00E+00

5 10


15


Settlement (mm)

-5.00E-03

-1.00E-02

-1.50E-02

-2.00E-02

Comparison of twin 9m diameter tunnels at 50m C-C spacing measured at 6.9m below ground level (soil 1) T1

0

T2

-6.9

0.00E+00

145

95

45

-5

-2.50E-02 -105

-55

5

-5.00E-03

10

-1.00E-02

15

Wmax = 14.0mm at 0.0m Wmax = 16.0mm at 0.0m

20

-2.00E-02

5.00E-03


145

95


T2

45

-5

-2.50E-02 -105

-55

0.00E+00

Chainage (m)

0

-5.00E-03

5 10

-1.00E-02

15

-11.4 Settlement (mm)

T1

-1.50E-02

20

Wmax = 16.0mm at 0.0m T1

T2

-2.00E-02


Comparison of twin 9m diameter tunnels at 50m C-C spacing measured at 15.4m below ground level (soil 1)

0

-2.50E-02

-15.4

0.00E+00

Chainage (m)

5

-5.00E-03

10

-1.00E-02

15

-1.50E-02

20


Settlement (mm)

Displacement (mm)

-1.50E-02 1.00E-02

Settlement (mm)

Chainage (m)

-2.00E-02

Wmax = 22.0mm at 0.0m 145

95

45

-5

-55

-2.50E-02 -105

Chainage (m)


Symbols:

Figure 5.9


Tunnel 2


Surface and sub-surface vertical displacements above Tunnel 2 when considering twin 9.0m diameter tunnels at 26.0m depth with a 50.0m centre-to-centre spacing (V1 and V2 = 1.3%)

D.Hunt - 2004

-26.0

- 147 -


1.00E-02 10

6.8mm at –20.0m 6.8mm at 20.0m

6.7mm at -25.0m

4.9mm at 22.0m

5 5.00E-03

0 0.00E+00

0.0

10

-5.00E-03

1.00E-02

5.7mm at –18.0m 5.6mm at -22.0m

5.7mm at 18.0m

Greenfield vertical 4.3mm at 22.0m 5.00E-03 displacement

5

-1.00E-02 U = 0 at 1.0m

0

Centre line of tunnel 1

Displacement (mm)

-1.50E-02 10

-2.00E-02

5.8mm at -15.0m 6.5mm at –18.0m

T1

-2.50E-02 145

95

45

U = 0 at +1.0m

0.00E+00

Actual vertical displacement

1.00E-02 -5.00E-03

at 15.0m Actual5.8mm horizontal 3.3mm at 18.0m displacements

T2

5

0

Greenfield horizontal displacement

-5

-55

5.00E-03 -1.00E-02

-105

-6.9

Settlement (mm)

Settlement (m)

Depth (m)

U = 0 at 0.5m

0.00E+00 -1.50E-02

-11.4

10

1.00E-02 -5.00E-03 -2.00E-02

7.8mm at –13.6m 6.7mm at –11.3m

6.7mm at 11.3m

-55

5.00E-03 -1.00E-02 -2.50E-02 -105

55

0.00E+00 -1.50E-02 105

5.1mm at 13.6m

5 145

95

45

-5

Settlement (mm)

Chainage (m)

Chainage (m)

0 -135

-95

-45

5


Settlement (mm)

U = 0 at +0.5m

-15.4

-5.00E-03 -2.00E-02 T1

T2

Tunnel 1

Symbols:

Tunnel axis

-1.00E-02 -2.50E-02

Tunnel 2 Chainage (m)


-26.0


-1.50E-02

-2.00E-02 2 when Surface and sub-surface horizontal displacements above Tunnel considering twin 9.0m diameter tunnels at 26.0m depth with a 50.0m centre-to-centre spacing (V1 and V2 = 1.3%)

Figure 5.10

145

95

45

-5 Chainage (m)

D.Hunt - 2004

-55

-2.50E-02 -105

- 148 -


Distance from centreline of Tunnel 2 (m) -95 5 26m below ground at55 Comparison of twin -45 9m diameter tunnels driven 20m C-C spacing

Depth (m)

105

Measured at 0.0 m below ground level (Soil 2).

0

0.0

0.00E+00

5

-5.00E-03

10


15

Wmax = 18.0mm at -6.8m

-1.00E-02

-1.50E-02

Comparison of twin 9m diameter tunnels driven 26m below ground at 20m C-C spacing Measured at 6.9 m below ground level (Soil 2).

0

T1

95

45

-2.00E-02

-6.9

0.00E+00

T2

-5

-2.50E-02 -105

-55

5

-5.00E-03

10

-1.00E-02

15


20


-1.50E-02

-2.00E-02

Displacement (mm)

Comparison of twin 9m diameter tunnels driven 26m below ground at 20m C-C spacing Measured at 11.4 m below ground level (Soil 2). 95

0

45

-5

-2.50E-02 -105

-55

-11.4

0.00E+00

5

-5.00E-03

10

-1.00E-02

Comparison of twin 9m diameter tunnels driven 26m below ground at 20m C-C spacing Measured at 15.4 m below ground level (Soil 2).

15 20

T1

0

95

45

-1.50E-02

-2.00E-02


1.00E-02

Wmax = 24.5mm at –3.6m

5.00E-03

-2.50E-02

T2

-5

-3.00E-02 0.00E+00 -105

-55

-15.4

-5.00E-03

5

-1.00E-02

10 -1.50E-02

15 -2.00E-02

20

-2.50E-02


-3.00E-02

Wmax = 28.0mm at –2.2m 95

45

-5

-55

-3.50E-02 -105

Tunnel axis

Tunnel 1 Tunnel 2 Symbols:

Figure 5.11



Surface and sub-surface vertical displacements above Tunnel 2 when considering twin 9.0m diameter tunnels at 26.0m depth with a 20.0m centre-to-centre spacing (V1 and V2 = 1.3%) - Soil type 2

D.Hunt - 2004

-26.0

- 149 -


Comparison of twin 9m diameter tunnels driven 26m below ground at 20m C-C spacing Measured at 0.0 m below ground level (Soil 2). 10

1.00E-02

7.5mm at –17.6m 7.5mm at 17.6m

7.8mm at –22.2m

6.5mm at 12.0m

5

0

5.00E-03

10

0.00E+00

5.8mm at 15.6m

5

4.0.mm at 13.6m

Comparison of twin 9mU =diameter tunnels driven 26m below ground at 20m C-C spacing 0 at +0.0m Measured at 11.4 m below ground level (Soil 2).

0

T1

5.9mm at –13.4m

T2

5.9mm at 13.4m

5 45

-5

-2.50E-02 -1.00E-02 5.00E-03 -105

3.5mm at 12.0m

-55

Comparison of twin 9m diameter tunnels driven 26m below ground at 20m C-C spacing U = 0 at at 15.4 +2.2m Measured m below ground level (Soil 2).

10

-1.50E-02

0.00E+00

-5.00E-03

7.0mm at –9.6m

7.0mm at 9.6m 3.7mm at 10.6m

5 45

-95

-45

5.00E-03 -2.50E-02

-5

-55

-1.00E-02 -105

5

55

0.00E+00 105

U = 0 at +3.6m

0

-5.00E-03 Tunnel axis-2.00E-02

Tunnel 1 Tunnel 2 Greenfield displacement

T1

T2

-15.4

-1.50E-02

Centreline Distance of tunnel 1 from centreline of Tunnel Centreline 2 (m)of tunnel 2

Symbols:

-11.4

1.00E-02 -2.00E-02

9.7mm at –6.8m

95

-6.9

-5.00E-03 -2.00E-02 1.00E-02

7.3mm at –11.5m

0

5.00E-03 -1.00E-02

0.00E+00 -1.50E-02

10

95

0.0

1.00E-02 -5.00E-03

5.8mm at –15.6m 6.0mm at –17.8m

Displacement (mm)

Depth (m)

Comparison of twin 9mU diameter tunnels driven 26m below ground at 20m C-C spacing = 0 at -5.0m Measured at 6.9 m below ground level (Soil 2).

Horizontal displacement above Tunnel 1 Horizontal displacements Predicted displacement

-26.0

-1.00E-02

-2.50E-02 -1.50E-02

-3.00E-02

Figure 5.12

Centrelinsub-surface e of tunnel 1 45 Centreline of tunnel 95 and -5 displacements -55 2 above Tunnel -105 Surface horizontal 2 when -2.00E-02

considering twin 9.0m diameter tunnels at 26.0m depth with a 20.0m centre-to-centre spacing (V1 and V2 = 1.3%) - Soil type 2 -2.50E-02

D.Hunt - 2004

T1

T2

Horizontal displacement above Tunnel 1 Horizontal displacement

-3.00E-02

-3.50E-02

- 150 -

Chapter 5 - Movements above twin tunnels 2.00E-03 1.3mm at 0.0m 1.3mm at 2.2m

1.00E-03 -125


-75

-25

1.3mm at 33.5m 1.3mm at 40m

25

75

0.0

0.00E+00 0

Settlement (mm)

Depth (m)

1 -1.00E-03 2 -2.00E-03

Settlement above 25 m deep twin 9m diameter tunnels atW20m=spacing 2.5mm at max Measured at 6.9 m below ground level (EXTENDED).

3

-3.00E-03

0.0m


2.00E-03

-4.00E-03 T1

1.00E-03

Settlement (mm)

-5.00E-03 0.00E+00 -1.05E+02 0

-5.50E+01

T2

-5.00E+00

4.50E+01

9.50E+01

-6.9

Chainage (m)

1

-1.00E-03

2

Settlement above 25 m deep twin 9m diameter tunnels at 20m spacing Measured at 11.4 m below ground level (EXTENDED).

-2.00E-03

3

2.00E-03

-3.00E-03


1.00E-03


-4.00E-03

-11.4

0

Displacement (mm) Settlement(mm)

0.00E+00

-5.00E-03 -1.05E+02

1

-1.00E-03

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

Chainage (m)

2

-2.00E-03

3

-3.00E-03

Settlement above 25 m deep twin 9m diameter tunnels at 20m spacing Measured at 15.4 m below ground level (EXTENDED). W = 4.0mm at 0.0m max

4

-4.00E-03 2.00E-03


-5.00E-03 1.00E-03 -1.05E+02

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

Chainage (m)

-15.4

0.00E+00

Settlement (mm)

0

-1.00E-03

1 2

-2.00E-03

3

-3.00E-03


4

-4.00E-03


5

-5.00E-03

-6.00E-03 -1.05E+02

-5.50E+01

-5.00E+00

4.50E+01

Chainage (m)

Tunnel 1

Symbols:

Figure 5.13


9.50E+01

Tunnel axis

-26.0

Tunnel 2


Surface and sub-surface vertical displacements above Tunnel 2 when considering twin 4.0m tunnels at 26.0m depth with a 20.0m centre-to-centre spacing (V1 = V2 = 1.3%)

D.Hunt - 2004

- 151 -


2 2.00E-03

1.3mm at –20.0m

1.3mm at 13.5m

1.3mm at –26.4m

1.3mm at 20.0m

1 1.00E-03

0 0.00E+00 Settlement (mm)

Depth (m)

Settlement above 25 m deep twin 9m diameter tunnels at 20m spacing U = 0 at -3.0m Measured at 6.9 m below ground level (EXTENDED).

0.0

2.00E-03

2 -1.00E-03

1.1mm at –18.0m 1.1mm at 18.0m 1.0mm at –20.0m

1.00E-03 1

2.5mm at 20m

-2.00E-03

3.2mm at 14.9m

0 0.00E+00 -3.00E-03

0.99mm at 13.5m

U = 0 at -2.0m

Settlement (mm)

Greenfield horizontal displacement

Displacement (mm)

-4.00E-03 2 -1.00E-03 2.00E-03

Actual horizontal displacements

T2

1.2mm at 13.0m 8.2mm at 12.0m

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

U = 0 at +0.0m

Chainage (m)

0 0.00E+00 -3.00E-03 Settlement (mm)

T1

1.2mm at -13.0m 1.1mm at -8.6m

-5.00E-03 1 1.00E-03 -2.00E-03 -1.05E+02

Settlement (mm)

-6.9


-11.4



2 2.00E-03 -1.00E-03 -4.00E-03

3.93mm 1.5mm at 10.0m


1.6mm at -8.5m

Settlements1.5mm above tunnel 1 at 10.0m Horizontal displacements

0.9mm at 10.0m

1 1.00E-03 -2.00E-03

-5.00E-03 -1.05E+02 0 0.00E+00 -3.00E-03 -105

-5.50E+01 -75

U =-5.00E+00 0 at 1.0m

4.50E+01

9.50E+01 -15.4

Chainage (m) 25

25

75

Distance from centreline of Tunnel 2 (m) Horizontal displacement above Tunnel 1 4.5mm Horizontal displacements Tunnel axis

-1.00E-03 -4.00E-03

-2.00E-03 -5.00E-03 -1.05E+02

-5.50E+01

-3.00E-03 Symbols:

Tunnel 1 -5.00E+00

Tunnel 2

4.50E+01

-26.0

9.50E+01

Chainage (m)



-4.00E-03

Figure 5.14 -5.00E-03

-6.00E-03 -1.05E+02

Horizontal displacement above Tunnel 1 Surface and sub-surface horizontal displacements above Tunnel 2 when Horizontal displacement considering twin 4.0m diameter tunnels at 26.0m depth with a 30.0m 5mm centre-to-centre spacing (V1 = 1.3%, V2 = 1.3%)

-5.50E+01

-5.00E+00

4.50E+01

D.Hunt Chainage (m) - 2004

9.50E+01

- 152 -

Chapter 5 - Movements Comparison above twin tunnels above 4m twin tunnels at 30m CC spacing. of settlements 2.00E-03

Distance from centreline of Tunnel 2 (m) 1.00E-03

-135

-85

-35

15

65

0.0

0.00E+00

0

Settlement (mm)

Depth (m)

1

-1.00E-03

2

-2.00E-03

W

= 2.5mm at 0.0m

maxspacing Settlement above 26 m deep twin 4m diameter tunnels at 30m Measured at 6.9 m below ground level.

3 -3.00E-03


2.86mm

2.00E-03


-4.00E-03

Settlement above tunnel 2

1.00E-03

-5.00E-03 -105 0.00E+00

-55

Settlement (mm)

0

-5

45

95

Chainage (m)

-6.9

1

-1.00E-03

2


-2.00E-03

3

-3.00E-03 2.00E-03


Displacement (mm) Settlement (mm)

-4.00E-03 1.00E-03


-11.4

0

-5.00E-03 0.00E+00 -105

-55

-5

45

95

Chainage (m)

1

-1.00E-03

2

-2.00E-03

3

-3.00E-03

Settlement above 26m deep twin 4m diameter tunnels at 30m spacing Measured at 15.4 m below ground level.


2.00E-03 -4.00E-03

4


1.00E-03 -5.00E-03 -105

-55

-5

45

95

Chainage (m)

-15.4

0

Settlement (mm)

0.00E+00

1

-1.00E-03

2

-2.00E-03

3

-3.00E-03

4


5


-4.00E-03

-5.00E-03 -105

-55

-5

45

95

Chainage (m)


Symbols:

Figure 5.15


-26.0

Tunnel 2


Surface and sub-surface vertical displacements above Tunnel 2 when considering twin 4.0m diameter tunnels at 26.0m depth with a 30.0m centre-to-centre spacing (V1 = 1.3%, V2 = 1.3%)

D.Hunt - 2004

- 153 -

Chapter 5 - Movements above twin tunnels Comparison of settlements above 4m twin tunnels at 30m CC spacing.

2 2.00E-03

1.3mm at –20.0m 1.3mm at 20.0m 1.2mm at –23.0m

1.1mm at 18.0m

1 1.00E-03

Settlement (mm)

0.00E+00 0

Depth (m)

Settlement above 26 Um =deep 0 at twin -2.0m4m diameter tunnels at 30m spacing Measured at 6.9 m below ground level.

0.0

2 2.00E-03 -1.00E-03 1.1mm at –18.0m

1 -2.00E-03 1.00E-03

Settlement (mm) (mm) Displacement

-3.00E-03 0 0.00E+00

1.1mm at 18.0m

1.0mm at –18.5m

0.8mm at 17.5m

U = 0 at -0.0m


-6.9

-4.00E-03

-1.00E-03 2 2.00E-03

-5.00E-03

-2.00E-03 1 -105 1.00E-03

1.2mm at 13.0m

-55

-5

45

0.8mm 95 at 13.0m

Chainage (m)

-3.00E-03 0 0.00E+00

Settlement (mm)

1.2mm at -13.0m 1.1mm at -13.0m

U = 0 at +0.0m

3.47mm

2.00E-03 2


1.5mm at 10.0m

-4.00E-03 -1.00E-03

Horizontal displacements

1.6mm at 10.0m

1.00E-03 1 -5.00E-03 -2.00E-03 -105

Settlement (mm)

1.5mm at 10.0m 0.9mm at 10.0m

-55

-5

45

95

U = 0 at Chainage 0.0m (m)

0.00E+00 0

-3.00E-03 -105

-11.4

Settlement above 26m deep twin 4m diameter tunnels at 30m spacing Measured at 15.4 m below ground level.

-95

-45

-15.4 5

55


-1.00E-03


-4.00E-03

Horizontal displacementsTunnel axis

3.95mm

-26.0

-2.00E-03

-5.00E-03 -105

Tunnel 1 -55

-5

-3.00E-03

Symbols: -4.00E-03

Figure 5.16 -5.00E-03 -105

Tunnel 2


45 Chainage (m)

95


Horizontal displacement above Tunnel 1 Surface and sub-surface horizontal displacements above Tunnel 2 when Horizontal displacement considering twin 4.0m diameter tunnels at 26.0m depth with 30.0m centre-to-centre spacing (V1 = 1.3%, V2 = 1.3%) -55

-5

45 Chainage (m)

D.Hunt - 2004

95

- 154 -

Chapter 5 - Movements above twin tunnels Settlement above 26 m deep twin 4m diameter tunnels at 50m spacing Measured at 0.0 m below ground level (Fixed). 2.00E-03


-155

-105

-55

-5

45

95

0.0

0.00E+00

Settlement (mm)

0 1

-1.00E-03

2

-2.00E-03

Settlement above 26 m deep twin 4m diameter tunnels at 50m spacing Wmax = 2.5mm at 0.0m Measured at 6.9 m below ground level.

3


-3.00E-03 2.00E-03


-4.00E-03 1.00E-03


-5.00E-03 0.00E+00 -105

0

Settlement (mm)

Depth (m)

-55

-5

45

95

145

-6.9

Chainage (m)

1

-1.00E-03

2


-2.00E-03

2.00E-03

3

-3.00E-03


1.00E-03


-4.00E-03

-11.4

Settlement (mm)

Displacement (mm)

0.00E+00

0

-5.00E-03 -105 -1.00E-03

-55

1

-5

45

95

145

Chainage (m)

2

-2.00E-03


3

-3.00E-03 2.00E-03


4

-4.00E-03


1.00E-03

-5.00E-03 -105 0.00E+00

-55

Settlement (mm)

0

-5

45

95

145

Chainage (m)

-15.4

1

-1.00E-03

2

-2.00E-03

3 -3.00E-03

4 Wmax = 4.6mm at 0.0m

-4.00E-03

5


-5.00E-03 -105

-55

-5

45

95

Chainage (m)

Tunnel 1

Symbols:

Figure 5.17


145

Tunnel axis

-26.0

Tunnel 2



D.Hunt - 2004

- 155 -

Chapter 5 - Movements above twin tunnels Settlement above 26 m deep twin 4m diameter tunnels at 50m spacing Measured at 0.0 m below ground level (Fixed). 2

1.3mm at –20.0m

2.00E-03

1.3mm at 20.0m 1.2mm at –23.0m

1.2mm at 18.0m

1.00E-031

Depth (m) U = 0 at 0.0m


Settlement (mm)

0.00E+000

2 -1.00E-03 2.00E-03

-2.00E-031

1.00E-03

1.1mm at –18.0m

1.1mm at 18.0m

1.1mm at –18.5m

1.0mm at 18.0m

U = 0 at -0.0m

-3.00E-03


0.00E+000


-1.00E-03

2.00E-03 2

-5.00E-03 -2.00E-03-105

-55

1 1.00E-03

1.2mm at -13.0m 1.2mm at -13.5m

-5

45

1.2mm at 13.0m

95

U = 0 at +0.0m

0 0.00E+00

-11.4



-4.00E-03 2 2.00E-03


1.5mm at 10.0m

-1.00E-03

1.5mm at 10.0m

1.6mm at 10.0m

1.3mm at 10.0m

-5.00E-03 1 1.00E-03 -2.00E-03-105

-55

-5

45

95

145

Chainage (m) U = 0 at 0.0m

0.00E+00 0

-3.00E-03 Settlement (mm)

145

1.0mm at 13.0m

Chainage (m)

-3.00E-03

Settlement (mm)

-6.9


-4.00E-03

Displacement (mm)

Settlement (mm)

0.0

-105

-15.4

-55

-5

55

105


-1.00E-03

-4.00E-03

Horizontal displacement Tunnel above Tunnelaxis 1 Horizontal displacements

-2.00E-03

Tunnel 1

-5.00E-03 -105 -3.00E-03

-55

Symbols:

-4.00E-03

Figure 5.18 -5.00E-03 -105

Tunnel 2

-5


-26.0

45 Chainage (m)

95

145


Horizontal displacement above Tunnel 1 Surface and sub-surface horizontal displacements above Tunnel 2 when Horizontal displacement considering twin 4.0m diameter tunnels at 26.0m depth with a 50.0m centre-to-centre spacing (V1 = 1.3%, V2 = 1.3%) -55

-5

45 Chainage (m)

D.Hunt - 2004

95

145

- 156 -



2.00E-03

2.2mm at 38m 2.2mm at -2m

-125

-75

-25

2.2mm at 32m 2.2mm at 38m

25

75

0.0

0.00E+00

Settlement (mm)

Depth (m)

0

-2.00E-03 2

4 -4.00E-03 Wmax = 4.1mm at Settlement above 25 m deep twin 4m diameter tunnels at 20m spacing (Vl1 = 2%, Vl2 = 2%) Measured at 6.9 m below ground level (EXTENDED).

6

-6.00E-03

0.0m

Wmax =Greenfield 5.7mm atvertical -5.1mdisplacement

4.00E-03

T1

-8.00E-03 2.00E-03 -1.05E+02

-5.50E+01

T2

Actual vertical displacement

-5.00E+00

4.50E+01

9.50E+01

Chainage (m) Settlement (mm)

0.00E+00

-6.9

0 2

-2.00E-03

4

-4.00E-03

Settlement above 25 m deep twin 4m diameter tunnels at 20m spacing (Vl1 = 2%, Vl2 = 2%) Measured at 11.4 m below ground level (EXTENDED).

6

-6.00E-03


2.00E-03

8

-8.00E-03 -1.05E+02

-5.50E+01

W

4.50E+01 max

-5.00E+00

= 6.5mm at 9.50E+01 -5.0m

Chainage (m)

-11.4

0

Settlement (mm)

Displacement (mm)

0.00E+00

-2.00E-03

2 4

-4.00E-03

6

-6.00E-03

Wmaxspacing = 6.6mm Settlement above 25 m deep twin 4m diameter tunnels at 20m (Vl1 = 2%, Vl2 = 2%) Measured at 15.4 m below ground level (EXTENDED).

8


-8.00E-03 T1

2.00E-03

-1.00E-02 -1.05E+02 0.00E+00

-5.50E+01

Settlement (mm)

4.50E+01

9.50E+01

Chainage (m)

-15.4

-2.00E-03

4

-4.00E-03

6

-6.00E-03

8

-8.00E-03

10

T1

-5.00E+00

0 2

at 0.0m

Wmax = 8.0mm at 0.0m Wmax = 8.3mm at -2.3m

-1.00E-02 -1.05E+02

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

Chainage (m)


Symbols:

Figure 5.19


-26.0

Tunnel 2



D.Hunt - 2004

- 157 -


4 4.00E-03

2.2mm at –22.0m

2.2mm at 12.0m

2.2mm at –20.0m

2.2mm at 17.6m

2 2.00E-03

Settlement (mm)

Depth (m) 0 0.00E+00

0.0

Settlement above 25 m deep twin 4m diameter tunnels at 20m spacing (Vl1 = 2%, Vl2 = 2%) Measured at 6.9 m below ground level (EXTENDED).

4

4.00E-03 -2.00E-03

2

2.00E-03 -4.00E-03

0 0.00E+00

Settlement (mm)

-6.00E-03

Displacement (mm)

U = 0 at -5.1m

1.8mm at –16.4m

1.3mm at 13.0m

1.6mm at –18.0m

1.8mm at 16.4m

U = 0 at -1.0m

Settlement above 25 m deep twin 4m diameter tunnels at 20mGreenfield spacing horizontal displacement T2 ground level (EXTENDED). (Vl1 = 2%, Vl2 = 2%) Measured atT111.4 m below Actual horizontal displacements

-2.00E-03

4 -8.00E-03 4.00E-03 -1.05E+02

1.8mm at -13.2m -5.00E+00 -5.50E+01

-6.00E-03

Settlement (mm)

-8.00E-03 44.00E-03 -2.00E-03 -1.05E+02

1.3mm at 12.0m

U = 0 at +1.0m

2.5mm at -8.5m -5.00E+00 -5.50E+01

4.50E+01

1.3mm at 10.0m

U = 0 at +1.0m

-75

-15.4

-25

25

75

Distance from centreline of Tunnel 2 displacement (m) Horizontal above Tunnel 1

-2.00E-03 -8.00E-03

Horizontal displacements T1

-4.00E-03 -1.00E-02 -1.05E+02

9.50E+01 2.2mm at 9.6m

2.2mm at -9.6m

00.00E+00 -6.00E-03 --105

-11.4

Settlement above 25 m deep twin 4m diameter tunnels at 20m spacing T1 T2 (Vl1 = 2%, Vl2 = 2%) Measured at 15.4 m below ground level (EXTENDED).

Chainage (m)

22.00E-03 -4.00E-03

9.50E+01 1.8mm at 13.2m

Chainage (m)

22.00E-03

0 0.00E+00

4.50E+01

1.8mm at -13.2m

-4.00E-03

Settlement (mm)

-6.9

-5.50E+01

Tunnel -5.00E+00 1

Tunnel axis

T1

Tunnel 4.50E+01 2

-26.0

9.50E+01

Chainage (m) -6.00E-03

Symbols:



-8.00E-03

Figure 5.20 Surface and sub-surface horizontal displacements above Tunnel 2 when considering twin 4.0m diameter tunnels at 26.0m depth with 20.0m centre-to-centre -1.00E-02 spacing (V = 2.0%, V = 2.0%) 1 2 -1.05E+02

-5.50E+01

-5.00E+00

4.50E+01

Chainage (m)

D.Hunt - 2004

9.50E+01

- 158 -


Distance from centreline of Tunnel 2 (m) 2.3mm at 2.2m 2.00E-03

-125

-75

1.3mm at 0.0m

1.9mm at 33.5m

-25

25

75

1.3mm at 40m

0.0

0

0.00E+00

Settlement (mm)

Depth (m)

2

-2.00E-03

4

-4.00E-03


6

Settlement above 25 m deep twin 4m diameter tunnels at 20m spacing W (EXTENDED). = 4.9mm at -5.0m (Vl1 = 1.3%, Vl2 = 2%) Measured at 6.9 m below ground levelmax

-6.00E-03

T1 -8.00E-03 2.00E-03 -1.05E+02

-5.50E+01

T2

-5.00E+00

4.50E+01

9.50E+01

Chainage (m)

-6.9

0

Settlement (mm)

0.00E+00

2

-2.00E-03

4

-4.00E-03

Wmax =spacing 3.3mm at 0.0m Settlement above 25 m deep twin 4m diameter tunnels at 20m (Vl1 = 1.3%, Vl2 = 2%) Measured at 11.4 m below ground level (EXTENDED).

6


-6.00E-03 T1

T2

2.00E-03 -8.00E-03 -1.05E+02

-5.50E+01

-5.00E+00

Settlement (mm)

Displacement (mm)

4.50E+01

9.50E+01

Chainage (m)

0

0.00E+00

-11.4

-2.00E-03

2

-4.00E-03

4


-6.00E-03

6

W

= 6.9mm at –3.6m

Settlement above 25 m deep twin 4m diameter tunnels at max 20m spacing (Vl1 = 1.3%, Vl2 = 2%) Measured at 15.4 m below ground level (EXTENDED).

-8.00E-03

8

T1

-1.00E-02 2.00E-03 -1.05E+02

-5.50E+01

T1

-5.00E+00

4.50E+01

9.50E+01

Chainage (m)

-15.4

0.00E+00

Settlement (mm)

0 2

-2.00E-03

4

-4.00E-03


6

-6.00E-03


8

-8.00E-03

10 -1.00E-02 -1.05E+02

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

Chainage (m)


Symbols:

Figure 5.21


-26.0

Tunnel 2



D.Hunt - 2004

- 159 -


3.00E-03 2

2.3mm at –22.0m

2.00E-03

1.9mm at 13.5m

Settlement above 25 m deep twin 4m diameter tunnels at 20m spacing 1.3mm at 20.0m (Vl1 = 1.3%, Vl2 = 2%) Measured at 6.9 m below ground level (EXTENDED).

1.3mm at –20.0m

1

1.00E-03

Depth (m) U = 0 at -5.0m

Settlement (mm)

Displacement (mm)

Settlement (mm)

0 0.00E+00 3.00E-03

0.0

Settlement above 25 m deep twin 4m diameter tunnels at 20m spacing (Vl1 = 1.32.5mm %, Vl2at=20m2%) Measured at 11.4 m below ground level (EXTENDED).

2 -1.00E-03 2.00E-03 1 -2.00E-03 1.00E-03

1.4mm at 16.0m

1.1mm at –18.0m

1.1mm at 18.0m

U = 0 at -1.0m

-3.00E-03 0.00E+00 3.000E-03

-6.9

-4.00E-03 -1.00E-03 2.020E-03

4.9mm at 14.9m

1.9mm at -11.4m 1.2mm at -13.0m

-5.00E-03 -2.00E-03 1

1.3mm at 12.0m

1.00E-03

1.2mm at 13.0m

-6.00E-03 -3.00E-03

= 0 at +1.0m Settlement above 25 mUdeep twin 4m diameter tunnels at 20m spacing (Vl1 = 1.3%, Vl2 = 2%) Measured atT115.4 m below T2 ground level (EXTENDED).

0.000E+00

-7.00E-03 -4.00E-03 2 3.00E-03

-1.00E-03 -2.1.00E-03 00E-03

1.5mm at 10.0m 1.5mm at -10.0m

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

1.5mm at 10.0m

Chainage (m)

-6.00E-03


U = 0 at 0.0m

0 0.00E+00

-3.00E-03 --105

-75

-7.00E-03 -1.00E-03

-25

T1 centreline T2 of Tunnel 2 (m) Distance from

-4.00E-03

-8.00E-03 -1.05E+02 -3.00E-03

-5.00E-03

Tunnel axis

-5.50E+01

Tunnel -5.00E+001

Symbols:

-6.00E-03

-7.00E-03

-7.00E-03

-8.00E-03

-8.00E-03 -9.00E-03

-9.00E-03

-1.00E-02

Tunnel 2 4.50E+01

-26.0

9.50E+01

Chainage (m)

-4.00E-03

Figure 5.22

-15.4

Horizontal displacements75

25

-2.00E-03

-6.00E-03 -5.00E-03

-11.4

2.5mm at 14.0m

-8.00E-03 2.00E-03 -5.00E-03 1 -1.05E+02 (mm) Settlement (mm) Settlement

1.7mm at –18.0m



Surface and sub-surface horizontal displacements above Tunnel 2 when considering twin 4.0m diameter tunnels at 26.0m depth with a 20.0m centre-to-centre spacing (V1 = 1.3%, V2 = 2.0%)

Horizontal displacement above Tunnel 1 D.Hunt - 2004

T1

T1

T2

T1


HoriHorizontal zontal didisplacement splacements

- 160 -


Tunnel 1 Liner deformation (caused by tunnel 2)

A

B

D

D

Original liner Deformed after tunnel 2

Origional line Deformed aft

B

20mm 20mm displacement


displacement

displacement

C

C

x

(a) d' = 20m

(b) d' = 30m A

y

A

D

B

Origional liner

D

B



20m 20mm m displacement

displacement

displacement

C

C

(c) d' = 50m

d' (m) 20 30 50 80

Tunnel 1 Liner defo after tunnel 2

A

A (x) 6.7 2.7 2.9 1.9

(d) d' = 80m

A (y) A 10.5 2.9 2.5 1.3

B (x) 12.2 4.6 3.4 2.1

Displacement (mm) B (y) C (x) C (y) 7.4 6.6 2.4 2.4 2.7 1.8 1.9 2.3 1.0 0.8 1.4 0.4

d'

1

D

D (x) 3.5 1.5 1.9 1.2

D (y) 5.3 3.2 1.5 0.8

Original liner

2

B

Deformed after Tunnel 2

20mm settlement

Figure 5.23(a) Liner behaviour of Tunnel 1 (26.0m depth, 9.0m diameter tunnel) at 20.0, 30.0, 50.0 and 80.0m centre-to-centre spacing. C

D.Hunt - 2004

Origional liner Deformed after tunnel 2

- 161 -


14 A (x) A (y) B (x) B (y) C (x) C (y) D (x) D (y)

12

Displacement (mm)

10

8

6

4

2

0 0

1

2

3

4

5

6

7

8

9

10

d'/D

Figure 5.23(b) Liner behaviour for Tunnel 1 (26.0m depth, 9.0m diameter tunnel) due to the construction of Tunnel 2 at a centre-to-centre spacing of 20.0, 30.0, 50.0 and 80.0m.

Centreline Of Tunnel 2

Centreline Of Tunnel 1 New Line of W max

0.0

Depth (m)

10%

-5.0 10 % 5% 5%

-10.0.

-15.0

-100

-80

-60

-40

-20

0

20

40

60

80

100

Chainage (m)

Figure 5.24

Contours of W/Wmax for all sub-surface depths at 30.0m spacing (Vl=1.3%, V2=1.3%)

D.Hunt - 2004

120

3.0


- 162 -

MAXIMUM INCREASE ALWAYS NEAR CENTRELINE OF FIRST TUNNEL

2.5

Tunnel depth (Z0)

2.0

0.0m 6.9m 15.4m

W2/W1

1.5 INCREASE

1.0

0.5

DECREASE

1 0.0 -105

-55

2

-5

45

95

145

Distance from Tunnel 1 (m)

Figure 5.25

Relative changes in surface and sub-surface ground settlements above Tunnel 2 (W2/W1) for twin 9.0m diameter tunnels with a 20.0m centre-to-centre spacing (Vl=1.3%, V2=1.3%)

3

2.5 (20.0m) (30m) (50m) (80m) (120.0m)

W2/W1

2

1.5

INCREASE

1

0.5 DECREASE

0 -105

Figure 5.26

-55

1

-5

Varying centre-to-centre spacing for Tunnel 2

45 95 Distance from Tunnel 1 (m)

2 145

195

Relative changes in surface settlement above Tunnel 2 (W2/W1) for twin 9.0m diameter tunnels at various centre-to-centre spacings using a volume loss of 1.3% and Soil 1

D.Hunt - 2004

- 163 -

Chapter 5 - Movements above twin tunnels Factors of settlement above 25 m deep twin 9m diameter tunnels at 80m spacing Measured at 0.0 m below ground level (Soil type 2). 3

2.5

(20m) (30m) (50m) (80m)

2 W2 /W1

(120m)

1.5

INCREASE

1

0.5 DECREASE


1

2

0 -65

-15

35

85

-135

-185


Figure 5.27


2 (20.0m) (30m) (50m) (80m) (120.0m)

W2/W1

1.5

INCREASE 1 DECREASE

0.5

1 0 -105

-55

-5


45

95

2 145

195


Figure 5.28


D.Hunt - 2004

- 164 -


Factors of settlement above 25 m deep twin 4m diameter tunnels at 30m spacing (Vl1=2.0%, Vl2=2.0%) Measured at 0.0 m below ground level (Type 1 soil).

2.5 (20m) (30m) (50m) (80m)

W2/W1

2

1.5

INCREASE

1

DECREASE

0.5

1 0 -105

-55


-5

2

45

95

145

195


Figure 5.29 Relative changes in surface settlement above Tunnel 2 (W2/W1) for twin 4.0m diameter tunnels at various centre-to-centre spacings with a volume loss of 2% and Soil 1

3.0

2.5

V1 = 1.3% V2 = 1.3% D = 4.0m V1 = 2.0% V2 = 2.0% D = 4.0m V1 = 1.3% V2 = 2.0% D = 4.0m

W2/W1

2.0

INCREASE 1.5

1.0

5.0 1

2

DECREASE 0.0 -105

-55

-5.0

45

95


Figure 5.30 Effect of volume loss and tunnel diameter on relative changes (W2/W1)

D.Hunt - 2004

- 165 -


3 (20m) (30m) (50m) (80m) (120m)

2.5

/

W1 W2

2

INCREASE

1.5

1

0.5

DECREASE

0 -105

-55

2


1

-5

45

95

145

195


Figure 5.31 Relative changes in surface settlement above Tunnel 2 (W2/W1) for a 4.0m diameter tunnels at various centre-to-centre spacings with a volume loss of 1.3% for Tunnel 1 and 2.0% for Tunnel 2

1.8

1.6

1.4

1.2

1 M 0.8

0.6 9.0m, V1=1.3% V2=1.3% 4.0m, V1=1.3%, V2=1.3% 4.0m, V1=2.0%, V2=2.0% 4.0m, V1=1.3%, V2=2.0%

0.4

0.2

0 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

d'/Z

Figure 5.32 Range of values of M with varying centre-to-centre tunnel spacing for 4.0m and 9.0m diameter tunnels

D.Hunt - 2004

- 166 -


0.6

0Z (9.0m) 0.26Z (9.0m) 0.44Z (9.0m)

0.5

0.60Z (9.0m)

Finite element (this study)

0z (4m) 0.26Z (4m) 0.44Z (4m)

0.4

0.60Z (4m)

e/d'

Cording and Hansmire (1975) Lafayette Park

0z (5.4m) 0.21z (5.4m)

0.3

0.55z (5.4m)

0.2

0.1

0 0

1

0.5

2

1.5

2.5

d'/Z0 (m)

Figure 5.33 Eccentricity of Wmax normalised by centre-to-centre spacing (e/d') for surface (0Z) and sub-surface (0.21, 0.26, 0.44, 0.55 and 0.60Z) depths (tunnel diameter shown in brackets) i/ii/i g (near) g(Near)

1.5 1.4 1.3 1.2 1.1

1

i/i i/igg(remote) (Remote)

eccentricity of U=0/d'

0.9 0.8 0.7 0.6 0.5

-0.5 -0.4 -0.3 -0.2 -0.1

0

0.1

0.2

0.5 0.6 0.7 0.8 0.9

0.3

1

1.1 1.2 1.3 1.4 1.5

0

0 i/ig(Near)

i/ig (Remote)


-0.1 1.5 1.4 1.3 1.2 1.1 1 0.9 0.8 0.7 0.6 0.5

-0.5 -0.4 -0.3 -0.2 -0.1

0

0.1

0.2

0.5 0.6 0.7 0.8 0.9

0.3

1

-0.1

1.1 1.2 1.3 1.4 1.5

0

0

-0.2

-0.2

-0.1

1

-0.3

-0.2

0 i/ig (Near)

-0.1

1.5 1.4 1.3 1.2 1.1

1

0

-0.4

Z/Z -0.3 0.9 0.8 0.7 0.6 0.5

-0.3

-0.4

0

-0.5 -0.4 -0.2 -0.1 -0.5 -0.6

-0.3 -0.2

Increase

Decrease

-0.6 -0.7 0

Z/Z -0.3

Increase

-0.4

-0.5

0

Z/Z

Z/Z0

-0.3 0.9 0.8 -0.2 0.7 0.6 0.5

Z/Z0

1.5 1.4 1.3 1.2 1.1

-0.1

Decrease

-0.7 -0.4

-0.5

-0.6 -0.6

-0.7

Increase Increase

-0.7

Decrease Decrease

15.9m spacing (9m) 20m spacing (9m) 15.9m 30m spacing spacing(9.0m) (9m) 20.0m spacing (9.0m) 36.8m spacing (9m) 30.0m spacing (9.0m) 50m spacing (9m) 36.8m spacing (9.0m) 20m spacing (4m) 50.0m spacing (9.0m) 30m spacing (4m) 20.0m spacing (4.0m) 30.0m spacing (4.0m)

15.9m spacing (9m) 20m spacing (9m) 30m spacing (9m) 36.8m spacing (9m) 50m spacing (9m) 20m spacing (4m) 30m spacingU(4m) max (near) U=0

Umax (near)

Umax (near)

Decrease

Increase

U max (remote)

Free surface

U=0 Umax (remote)

Umax (remote)

Free surface

Free surface

Z

Z

Z0

1

1

d’

2

( Z0-Z)

( Z0-Z)

2

d'

-0.6

Increase

( Z0-Z)

1

-0.5

U=0

Z

d’

-0.5

-0.6 Decrease

Z0

Z0

-0.4

2

Figure 5.34 Deviation of position of U=0 and Umax, i.e. i (near) and i (remote)

D.Hunt - 2004

-0.7

-0.7

15.9m spacing 20m spacing 30m spacing 36.8m spacing 50m spacing 20m spacing (4m) 30m spacing (4m)

- 167 -


Distance from centreline of Tunnel 1 and 2 (m) -105

Comparison of twin piggyback 9m diameter tunnels driven 33.4m and 16.4m below ground at 17m C-C spacing Measured at 0.0 m below ground level (Soil 1).

-55

-5

45

95 Depth (m)

5.00E-03

-5

0.0

0.00E+00

0

Settlement (mm)

-5.00E-03

5

-1.00E-02 10

Wmax = -3.3mm at 0.0m

-1.50E-02 15

Comparison of twin piggy back 9m diameter tunnels driven 33.4m andW 16.4m below ground at 0.0m max = 15mm at 17m C-C spacing Measured at 2.9 m below ground level (Soil 1). T2

-2.00E-02

-5

5.00E-03 T1

-2.50E-02 0.00E+00 -1.05E+02

0

Settlement (mm)

5

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

-2.9

Chainage (m)

-5.00E-03

10

-1.00E-02

15

-1.50E-02

Comparison of twin piggyback 9m diameter tunnels driven 33.4m and 16.4m below ground Wmax = -2.6mm at 0.0m at 17m C-C spacing Measured at 5.9 m below ground level (Soil 1).


5.00E-03

0

T2

0.00E+00 -2.50E-02

-5.9

T1

5

-3.00E-02 -1.05E+02

-5.00E-03

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

Chainage (m)

10

Settlement (mm)

Displacement (mm)

-2.00E-02

15

-1.00E-02


-1.50E-02

20


-2.00E-02

0

Comparison of twin piggyback 9m diameter tunnels driven 33.4m and 16.4m below ground at 20m C-C spacing Measured at 7.9 m belowT2 ground level (Soil 1).

-2.50E-02 0.00E+00

-7.9 T1

-3.00E-02

5 -5.00E-03 -1.05E+02

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

Chainage (m)

10 -1.00E-02

Settlement (mm)

15

20

-1.50E-02

Wmax =0.9mm at 0.0m Wmax =24.0mm at 0.0m

25 -2.00E-02 30

-2.50E-02

-3.00E-02 -1.05E+02

T1

Tunnel 2 -5.50E+01

-5.00E+00

Figure 5.35

4.50E+01

Chainage (m)

Tunnel 1

Symbols:

Tunnel axis


-16.4

9.50E+01

-33.4


Surface and sub-surface vertical displacements above Tunnel 2 when considering piggyback 9.0m diameter tunnels at depths of 16.4m and 33.4m (V1 & V2 = 1.3%); lower tunnel constructed first

D.Hunt - 2004


- 168 -

Chapter 5 - Movements above twin tunnels 1.50E-02

1.00E-02

10

8.5mm at 14.0m 7.1mm at 29.0m

55.00E-03

Settlement (mm)

00.00E+00

Comparison of twin piggy back 9m diameter tunnels driven 33.4m and 16.4m below ground at 17m C-C spacing Measured at 2.9 m below ground level (Soil 1).

Depth (m) 0.0

101.00E-02

-5.00E-03

55.00E-03

-1.00E-02

0 0.00E+00

Displacement (mm)

-1.50E-02

Settlement (mm)

7.9mm at 12.5m 7.0mm at 26.0m

1.00E-02 2-5.00E-03 -2.00E-02 5.00E-03 1-1.00E-02

-2.50E-02 -1.05E+02

Comparison of twin piggyback 9m diameter tunnels driven 33.4m and 16.4m belowHorizontal grounddisplacement above Tunnel 1 at 17m C-C spacing Measured at 5.9 m below ground level (Soil 1). Settlement above tunnel 2 T2

(No tunnel 1) 7.6mm at 12.5m

7.5mm atdisplacement Comparison of twin piggyback 9m diameter tunnels ground 20.0m T1 driven 33.4m and 16.4m belowHorizontal above Tunnel 2 (No tunnel at 20m C-C spacing 1) Measured at 7.9 m below ground level (Soil 1).

-5.50E+01

-5.00E+00

1.50E-02 0.00E+00

4.50E+01

-5.9

Horizontal displacement

1.00E-02

8.3mm at 14.0m above Tunnel 2 (No 8.0mm at 11.0m

Settlement (mm)

-5.00E-03 -2.00E-02 1

tunnel 1)

5.00E-03

T2

0.00E+00

T1

Horizontal displacement above Tunnel 2 after tunnel 1

-1.00E-02 -2.50E-02 0

S ettlement (mm)

-1.50E-02 -105 -3.00E-02 -1.05E+02

-5.00E-03

-2.00E-02

-1.00E-02 -2.50E-02

-1.50E-02 Symbols: -3.00E-02 -1.05E+02

-2.00E-02

9.50E+01

Chainage (m)

0-1.50E-02 2

-2.9

-55

-5

45

-5.50E+01 from centreline -5.00E+00of Tunnel 1 & 24.50E+01 Distance (m) Chainage (m)

Tunnel 2


-5.50E+01

95

9.50E+01 Tunnel axis

T2

Tunnel 1

T1

-16.4 -33.4


-5.00E+00

4.50E+01

9.50E+01

Chainage (m)

Figure 5.36

-7.9

Surface and sub-surface horizontal displacements above Tunnel 2 when considering piggyback 9.0m diameter tunnels at depths of 16.4m and 33.4m -2.50E-02 (V1 & V2 = 1.3%); lower tunnel constructed first T1

-3.00E-02 -1.05E+02

-5.50E+01

D.Hunt - 2004

-5.00E+00

Chainage (m)

4.50E+01

9.50E+01

- 169 -


Distance from centreline of Tunnel 1 and 2 (m) Comparison of twin piggyback 9m diameter tunnels driven 33.4m and 16.4m below ground at 17m C-C spacing Measured at 0.0 m below ground level (Soil 1).

-105

-55

-5

45

95

0.0

0

0.00E+00

Comparison of twin offset 4m diameter tunnels driven 30.4m and 16.4m below ground at 17m C-C spacing Measured at 2.9 m below ground level (Soil 1).

1

-1.00E-03

Settlement (mm)

2

-2.00E-03

3.00E-03

3

-3.00E-03


2.00E-03

4


-4.00E-03

1.00E-03

Settlement above tunnel 1 Settlement above tunnel 1 (1.3% loss)

T1 -5.00E-03 -105

00.00E+00

-55

-5

45

95

-2.9

Chainage (m)


1-1.00E-03 Settlement (mm)

Depth (m)

2-2.00E-03 3.00E-03

3-3.00E-03 Wmax = 2.6mm at 0.0m

2.00E-03

4-4.00E-03


1.00E-03

-5.00E-03

-5.9

T2

-6.00E-03


Displacement (mm)

00.00E+00

Comparison of twin offset 4m diameter tunnelsT1driven 33.4m and 16.4m below ground at 17m C-C spacing Measured at 7.9 m below ground level (Soil 1).

-7.00E-03

2-2.00E-03

-8.00E-03

3-3.00E-03 -1.05E+02 3.00E-03

-5.50E+01

-5.00E+00

4.50E+01

4-4.00E-03 2.00E-03

9.50E+01


Chainage (m)


5-5.00E-03 1.00E-03 -6.00E-03

T2

00.00E+00

-7.00E-03

Settlement (mm)

1-1.00E-03

-7.9

T1

-8.00E-03

2-2.00E-03 -1.05E+02

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

Chainage (m)

3-3.00E-03 4-4.00E-03


5-5.00E-03 6-6.00E-03 T1

-7.00E-03 -8.00E-03 -1.05E+02

Symbols:

Figure 5.37

-5.50E+01

Tunnel 1

-5.00E+00

4.50E+01

Chainage (m)


-16.4

Tunnel axis

Tunnel 2

9.50E+01

-33.4


Surface and sub-surface vertical displacements above Tunnel 2 when considering piggyback 4.0m diameter tunnels at depths of 16.4m and 33.4m (V1 & V2 = 1.3%); lower tunnel constructed first D.Hunt - 2004


- 170 -


3.00E-03

2 2.00E-03

1 1.00E-03

1.9mm at 12.5m Comparison of twin offset 4m diameter tunnels driven 30.4m and 16.4m below ground 1.5mm at 18.0m at 17m C-C spacing Measured at 2.9 m below ground level (Soil 1).

Depth (m) Settlement (mm)

00E-03 03.0.00E+00 22.00E-03

-1.00E-03

11.00E-03

-2.00E-03

0.0

1.7mm at 12.5m Comparison of twin offset 4m diameter tunnels driven 30.4m and 16.4m below ground 1.5mm at 18.0m at 17m C-C spacing Measured at 5.9 m below ground level (Soil 1).

0.03.000E+00 0E-03

-2.9

Settl ement (mm)

2-1.2.00E-03

Settl ement (mm)

S ettlement (mm)

Displacement (mm)

-3.00E-03

-4.00E-03

1-2.1.00E-03

-5.00E-03 -105

Comparison of twin offset 4m diameter tunnels driven 33.4m and 16.4m below ground 1.7mm at 10.0m 1.6mm at 12.5m at 17m C-C spaci n g T1 Measured at 7.9 m below ground level (Soil 1).

0E-03 0E-03 0-3. 0.3.0000E+00

-55

-5

45

95 -5.9

Chainage (m)

22.000E-03 0E-03 -4.-1.00E-03

1.8mm at 8.6m 1.7mm at 8.6m

11. -5.-2.00E-03 00E-03

T2 00.00E+00 -6.-3.00E-03 0E-03

-105

-1.00E-03 -7.-4.00E-03

-7.9 -55

-5

45

95

Distance from centreline T1 of Tunnel 1 & 2 (m) Tunnel axis

Tunnel 2

-2.00E-03 -8.-5.00E-03 -1.05E+02 -3.00E-03Symbols: -6.00E-03

Tunnel 1

-5.50E+01

-16.4 -33.4

-5.00E+00

Greenfield displacement Chainage (m)

T2

4.50E+01

9.50E+01


-4.00E-03

-7.00E-03 Surface and sub-surface horizontal displacements above Tunnel 2 when Figure 5.38 Settlement above tunnel 2 T1 considering piggyback 4.0m diameter tunnels at depths (No tunnel 1)of 16.4m and 33.4m -5.00E-03 (V1 & V2 = 1.3%); lower tunnel constructed first -8.00E-03 -1.05E+02 -6.00E-03 -7.00E-03

-5.50E+01

-5.00E+00 D.Hunt Chainage (m)- 2004

T1

4.50E+01

Horizontal displacement above tunnel 29.(No50E+01 tunnel 1) Settlement above tunnel 2 after tunnel 1

- 171 -

Comparison of twin offset 9m diameter tunnels driven 33.4m and 16.4m below ground Chapter 5 - Movements above twin tunnels at 17m C-C spacing Measured at 0.0 m below ground level (Soil 1). 1.00E-02

Distance from centreline of Tunnel 1 and Tunnel 2 (m) 5.00E-03

-105

-55

-5

45

95

0.0

00.00E+00 Settlement (mm)

Depth (m)

5-5.00E-03

10-1.00E-02


-1.50E-02

-2.00E-02

Comparison of twin offset 9m diameter tunnels driven 30.4m and 16.4m below ground at 17m C-C spacing Measured at 2.9 m below ground level (Soil 1). T1

-2.9

0.00E+00 0-2.50E-02

T2

-3.00E-02 5-5.00E-03 -1.05E+02

-5.50E+01

-5.00E+00

4.50E+01

Settlement (mm)

10-1.00E-02

Wmax = 51.3 mm at 0.0m

15-1.50E-02


20

Comparison of twin offset 9m diameter tunnels driven 30.4m and 16.4m below ground Settlement above tunnel 2 at 17m C-C spacing (No tunnel 1) Measured at 5.9 m below ground level (Soil 1).

-2.00E-02

0.00E+00 0 -2.50E-02

-5.9

T1

Settlement above tunnel 2 after tunnel 1

T2

5 -5.00E-03

-3.00E-02 -1.05E+02

-5.50E+01

-5.00E+00

10 -1.00E-02

4.50E+01

9.50E+01

Chainage (m)

Settlement (mm)

Displacement (mm)

9.50E+01

Chainage (m)

15 -1.50E-02 Wmax = 4.7mm at 0.0m -2.00E-02

Comparison of twin offset 9m diameter tunnels driven 30.4m and below ground Settlement above tunnel 2 W16.4m at 0.0m max = 12.0mm (No tunnel 1) at 17m C-C T1 spacing Measured at 7.9 m below ground level (Soil 1).

-2.50E-02

T2


-7.9

0.00E+00

0 -3.00E-02 -1.05E+02

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

Chainage (m)

5 -5.00E-03

15

Settlement (mm)

10 -1.00E-02 -1.50E-02


-2.00E-02


T1

Settlement above tunnel 2 (No tunnel 1) -2.50E-02


T2

-3.00E-02 -1.05E+02

Chainage (m) -5.00E+00

-5.50E+01

Tunnel 1

4.50E+01

Tunnel axis

Figure 5.39

-16.4 -33.4

Tunnel 2

Symbols:

9.50E+01



Surface and sub-surface vertical displacements above Tunnel 2 when considering piggyback 9.0m diameter tunnels at depths of 16.4m and 33.4m (V1 & V2 = 1.3%); upper tunnel constructed first

D.Hunt - 2004

- 172 -



10

1.00E-02 5.2mm at 23.0m 5.1mm at 33.0m

5 5.00E-03

0 0.00E+00

Depth (m)


0.0

Settl emen t (mm)

10 1.00E-02

-5.00E-03

4.7mm at 20.0m 4.9.mm at 33.0m

5 5.00E-03

-1.00E-02

0 0.00E+00

Comparison of twin offset 9m diameter tunnels driven 30.4m and 16.4m below ground at 17m C-C spacing Settlement above tunnel 2 Measured at 5.9 m below ground level (Soil 1).

1.00E-02 -2.00E-02

5 -1.00E-02 5.00E-03

-2.50E-02

0 -1.50E-02 0.00E+00

Horizontal displacement above Tunnel 2 (No tunnel 5.1mm at 29.0m Comparison of twin offset 9m diameter tunnels 1) ground T1 driven 30.4m and 16.4m below 4.5mm at 23.0m Settlement above tunnel 2 at 17m C-C spacing after tunnel 1 Measured at 7.9 m below ground level (Soil 1). T2 Settlement above tunnel 2 Horizontal displacements (No tunnel 1) above tunnel 2 after tunnel 1Horizontal displacement -5.50E+01

Settlement (mm)

-3.00E-02 -1.05E+02 1.00E-02 10 -2.00E-02 -5.00E-03

-5.00E+00

4.50E+01

Chainage (m) T1

9.50E+01 above Tunnel 2 (No tunnel 1) Settlement above tunnel 2 5.0mm at 26.0m after4.3mm tunnel 1at 23.0m

T2

Horizontal displacements above tunnel 2 after tunnel 1

5 -2.50E-02 5.00E-03 -1.00E-02

0 -3.00E-02 -1.50E-02 0.00E+00

-1.05E+02 -105

Settlement (mm)

-2.00E-02 -5.00E-03

-5.50E+01 -55

-3.00E-02 Symbols: -1.50E-02 -1.05E+02

-5.00E+00 -5

4.50E+01 45

Chainage (m)

T1 Tunnel 1 & 2 (m) Distance from centreline of Tunnel 1

-2.50E-02

-1.00E-02

-2.9

(No tunnel 1)

10 -5.00E-03 Settlement (mm)

Displacement (mm)

-1.50E-02

T2

Tunnel 2

Settlement above tunnel 2 (No tunnel 1) 959.50E+01 Horizontal displacement above Tunnel 2 (No tunnel 1) Tunnel axis Settlement above tunnel 2 after tunnel 1

Horizontal displacements above tunnel 2 after tunnel 1 Predicted displacement 4.50E+01 9.50E+01

Greenfield -5.50E+01displacement -5.00E+00

-5.9

-7.9

-16.4 -33.4

Settlement above tunnel 2 (No tunnel 1)

Chainage (m)

Horizontal displacement above Tunnel 2 (No

T1

-2.00E-02 Figure 5.40 Surface and sub-surface horizontal displacements Tunnel 2 when tunnelabove 1) considering piggyback 9.0m diameter tunnels atSettlement depths of above tunnel 16.4m 2 after tunnel 1 and 33.4m T2 (V1 & V2 = 1.3%); upper tunnel constructed first -2.50E-02

-3.00E-02 -1.05E+02

Horizontal displacement above tunnel 2 after tunnel 1

D.Hunt - 2004 -5.50E+01

Chainage (m) -5.00E+00

4.50E+01

9.50E+01

- 173 -

Chapter 5 - MovementsComparison above twin of twintunnels piggyback 9m diameter tunnels driven 33.4m and 16.4m below ground at 17m C-C spacing Measured at 0.0 m below ground level (Soil 1). 2.00E-03


-105

-55

-5

45

95

Depth (m) 0.0

Settlement (mm)

00.00E+00 1-1.00E-03 2-2.00E-03

1.0mm at 0.0m max =below Comparison of twin piggy back 9m diameter tunnels driven 33.4m and W 16.4m ground at 17m C-C spacing Measured at 2.9 m below ground level (Soil 1). Wmax = 1.9mm at 0.0m

-3.00E-03 2.00E-03

T1

-4.00E-03 1.00E-03

T2

-5.00E-03

-1.05E+02 0 0.00E+00

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

-2.9

9.50E+01

-5.9

Settlement (mm)

Chainage (m)

1 -1.00E-03 2 -2.00E-03 Comparison of twin piggyback 9m diameter tunnels driven 33.4m and 16.4m below ground Wmax = 1.3 mm at 0.0m at 17m C-C spacing Measured at 5.9 m below ground level (Soil 1).

3 -3.00E-03 2.00E-03


T1

-4.00E-03 T2

1.00E-03

Settlement (mm)

Displacement (mm)

0.00E+00 0 -5.00E-03 -1.05E+02

-5.50E+01

-5.00E+00

4.50E+01

Chainage (m)

1 -1.00E-03 2 3

-2.00E-03

Settlement above tunnel 2 Comparison of twin piggyback 9m diameter tunnels driven 33.4m and 16.4m below ground (No tunnel 1) at 20m C-C spacing T1 Measured at 7.9 m below ground level (Soil 1).

-3.00E-03

-4.00E-03

2.00E-03

Wmax = 1.5mmSettlement at 0.0m above tunnel 2

T2

-5.00E-03 -1.05E+02

-5.50E+01

after tunnel 1


-5.00E+00

1.00E-03

4.50E+01

9.50E+01

Chainage (m)

-7.9

Settlement (mm)

0 0.00E+00 1 -1.00E-03 2 -2.00E-03 3

-3.00E-03 T1

Wmax =1.7mm at 0.0m

T2

Wmax =2.5mm at 0.0m

-4.00E-03

-5.00E-03 -1.05E+02

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

Chainage (m)

Tunnel axis

Tunnel 1

-33.4

Tunnel 2

Symbols:

Figure 5.41

-16.4



Surface and sub-surface vertical displacements above Tunnel 2 when considering piggyback 4.0m diameter tunnels at depths of 16.4m and 33.4m (V1 & V2 = 1.3%); upper tunnel constructed first

D.Hunt - 2004

- 174 -

Chapter 5 - MovementsComparison above twin of twintunnels piggyback 9m diameter tunnels driven 33.4m and 16.4m below ground at 17m C-C spacing Measured at 0.0 m below ground level (Soil 1). 2.00E-03


-105

-55

-5

45

95

Depth (m) 0.0

Settlement (mm)

00.00E+00 1-1.00E-03 2-2.00E-03

1.0mm at 0.0m max =below Comparison of twin piggy back 9m diameter tunnels driven 33.4m and W 16.4m ground at 17m C-C spacing Measured at 2.9 m below ground level (Soil 1). Wmax = 1.9mm at 0.0m

-3.00E-03 2.00E-03

T1

-4.00E-03 1.00E-03

T2

-5.00E-03

-1.05E+02 0 0.00E+00

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

-2.9

9.50E+01

-5.9

Settlement (mm)

Chainage (m)

1 -1.00E-03 2 -2.00E-03 Comparison of twin piggyback 9m diameter tunnels driven 33.4m and 16.4m below ground Wmax = 1.3 mm at 0.0m at 17m C-C spacing Measured at 5.9 m below ground level (Soil 1).

3 -3.00E-03 2.00E-03


T1

-4.00E-03 T2

1.00E-03

Settlement (mm)

Displacement (mm)

0.00E+00 0 -5.00E-03 -1.05E+02

-5.50E+01

-5.00E+00

4.50E+01

Chainage (m)

1 -1.00E-03 2 3

-2.00E-03

Settlement above tunnel 2 Comparison of twin piggyback 9m diameter tunnels driven 33.4m and 16.4m below ground (No tunnel 1) at 20m C-C spacing T1 Measured at 7.9 m below ground level (Soil 1).

-3.00E-03

-4.00E-03

2.00E-03

Wmax = 1.5mmSettlement at 0.0m above tunnel 2

T2

-5.00E-03 -1.05E+02

-5.50E+01

after tunnel 1


-5.00E+00

1.00E-03

4.50E+01

9.50E+01

Chainage (m)

-7.9

Settlement (mm)

0 0.00E+00 1 -1.00E-03 2 -2.00E-03 3

-3.00E-03 T1

Wmax =1.7mm at 0.0m

T2

Wmax =2.5mm at 0.0m

-4.00E-03

-5.00E-03 -1.05E+02

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

Chainage (m)

Tunnel axis

Tunnel 1

-33.4

Tunnel 2

Symbols:

Figure 5.42

-16.4



Surface and sub-surface horizontal displacements above Tunnel 2 when considering piggyback 4.0m diameter tunnels at depths of 16.4m and 33.4m (V1 & V2 = 1.3%); upper tunnel constructed first

D.Hunt - 2004

- 175 -


i/ig 0

0.5

1.5

1

2

2.5

0

0.1

0.2 Z/Z0 0.3

9.0m (lower first)

0.4

4.0m (lower first) 9.0m (upper first) 4.0m (upper first)

0.5

0.6

Decrease

Increase

Figure 5.43 Deviation in position of Umax due to the construction of piggyback tunnels at depths of 33.4m depth and 16.4m with a volume loss of 1.3%. For 4.0m and 9.0m diameter tunnels construction sequence Tunneland 1 Linerchanging deformation

2

20mm displa cement

0

Origi nal liner shape Depth -2

Deform ation of liner after construction of Tunnel 2

-4

-6

-8 -5

-3

1

-1

3

Chainage

5

Figure 5.44 Displacement of upper tunnel lining (Tunnel 2) when considering the construction of 9.0m diameter piggyback tunnels at depths of 16.4m and 33.4 m (lower tunnel driven first) D.Hunt - 2004

- 176 -


Distance from centreline of Tunnel 2 (m) -125 0


-75

-25

25

75

Depth (m) 0.0

0.00E+00


10-1.00E-02 Wmax = 12.0mm at -20.0m

15-1.50E-02

Wmax = 14.5mm at 0.0m -2.00E-02

Comparison of twin offset 9m diameter tunnels driven 30.926m and 17.41m below ground at 20m C-C spacing2 Measured at 2.9 m below ground level (Soil 1).

-2.50E-02

0 5

0.00E+00

-3.00E-02 -5.00E-03 -105

15

-1.50E-02

Settlement (mm)

-1.00E-02


-1.00E-02


T1

0.00E+00

10 Settlement (mm)

Displacement (mm)

95

Comparison of twin offset 9m diameter tunnels driven 30.926m and 17.41m below ground at 20m C-C spacing T2 Settlement above tunnel 2 Measured at 5.9 m below ground level (Soil 1).

-3.00E-02 -105

-5.00E-03

20

45

-2.00E-02

5

15

-5

Wmax = 12.4 mm at -15.0m

-2.50E-02

0

-55

Chainage (m)

10

20

-2.9

1

-55

-5

45

-5.9

95

Chainage (m)


-1.50E-02

Wmax = 13mm at -12m

1.50E-02

Wmax = 20mm at 0.0m

-2.00E-02

1.00E-02 -2.50E-02


T2

5.00E-03


T1

Settlement (mm)

0 5 10

-3.00E-02 -105

0.00E+00

-55

-5

45

95

-8.9

Chainage (m)

-5.00E-03

-1.00E-02

-1.50E-02

15 -2.00E-02

20 25

Wmax =14.2mm at -3.7m -2.50E-02

Wmax =24.3mm at 0.0m -3.00E-02 -105

-55

-5

45

95

Chainage (m)

Tunnel axis

Tunnel 2

-30.9

Tunnel 1

Symbols:

Figure 5.45

-17.4



Surface and sub-surface vertical displacements above Tunnel 2 when considering offset 9.0m diameter tunnels at depths of 17.4m and 30.9m with a centre-to-centre spacing of 20.0m (V1 & V2 = 1.3%), lower tunnel constructed first

D.Hunt - 2004

Chapter 5 -

Comparison of twin offset 9m diameter tunnels driven 30.926m and 17.41m below ground at 20m C-C spacing Movements above twinMeasured tunnelsat 0.0 m below ground level (Soil 1).

- 177 -

1.50E-02 11.0mm at –23.6m

10 1.00E-02

5 5.00E-03

8.2mm at –15.6m

8.2mm at 15.6m Comparison of twin offset 9m diameter tunnels driven 30.926m and 17.41m below ground at 20m C-C spacing 2.6mm at 18.6m Measured at 2.9 m below ground level (Soil 1).

1.50E-02 00.00E+00

Depth (m)

U = 0 at +5.0m

0.0

S ettlement (mm)

11.0mm at –19.9m

1.00E-02 10-5.00E-03 5-1.00E-02 5.00E-03

7.6mm at –15.6m

7.6mm at 15.6m

Comparison of twin offset 9m diameter tunnels driven 30.926m and 17.41m below ground 2.6mm at 18.6m at 20m C-C spacing +6.8m Measured atU5.9= m0 atbelow ground level (Soil 1).

0-1.50E-02 0.00E+00

-2.9

Settlement (mm)

Displacement (mm)

1.50E-02 7.5mm at –13.4m

10 -2.00E-02 -5.00E-03

1.00E-02

2

5.7mm at –13.4m

5 -2.50E-02 -1.00E-02

-1.50E-02 -105

15 1.50E-02 S ettlement (mm)

1

5.00E-03

0 -3.00E-02 0.00E+00

2.7mm at 22.6m

Comparison of twin offset 9m diameter tunnels driven 30.926m and 17.41m below ground U 0 atC-C +6.8m at =20m spacing Measured at 8.9 m below ground level (Soil 1). -55 -5 45 95 14.6mm at –10.6m

-2.00E-02

7.8mm at –10.6m

Settle7.8mm ment aboveattunnel 2 10.6m Horizontal displacements 3.1mm at 20.5m Settlement above tunnel 1 (1.3% loss) Horizontal displacement above Tunnel 1

T2

5.00E-03 5-1.00E-02

-2.50E-02

00.00E+00 -1.50E-02

-3.00E-02 -5.00E-03-105 -2.00E-02

-1.00E-02

-2.50E-02 -1.50E-02

-3.00E-02 -105

Symbols: -2.00E-02

-5.9

Chainage (m)

-5.00E-03

10 1.00E-02

Settlement (mm)

7.5mm at 13.4m

U = 0 at +6.8m T1

-95

-45

-55

5

55

Distance from centreline of Tunnel45 2 (m) -5

Chainage (m)

Tunnel 2

95

Horizontal displacements Tunnel axis

T2

-8.9

105

-17.4

Horizontal displacement above Tunnel 1 -30.9

Tunnel 1

T1 Greenfield displacement

-55

Predicted displacement 95 1 Settlement above tunnel

-5

45


Chainage (m)

-2.50E-02 Surface and sub-surface horizontal displacements above Tunnel 2 when Figure 5.46 Settlement above tunnel 1 (1.3% loss) T2 T1 considering offset 9.0m diameter tunnels at depths of 17.4m and1 30.9m with a Horizontal displacement above Tunnel -3.00E-02 centre-to-centre spacing of 20.0m (V1 & V2 = 1.3%), lower tunnel constructed first -105

-55

-5

45 Chainage (m)

D.Hunt - 2004

95


- 178 -

Chapter 5 - Movements above twin tunnels 1.50E-02

1.00E-02


-120

-90

-60

-30

0

30

60

Depth (m)

80

0.0

0.00E+00

Settlement (mm)

0

-5.00E-03

5

-1.00E-02

10

-1.50E-02

Wmax = 10.8mm at -15.0m

-2.00E-02


15

-2.50E-02 -105

0

0.00E+00

5

-5.00E-03

-1.00E-02

15

-1.50E-02

20

-2.00E-02

Settlement (mm)

10

120

135

Chainage (m)

-2.9

Wmax = 11.5 mm at -10.2m Wmax = 18.0mm at 0.0m Comparison of twin offset 9m diameter tunnels drivenT2 30.926m and 17.41m below ground Settlement above tunnel 2 at 30m C-C spacing Settlement above tunnel 1 (1.3% loss) T1 Measured at 5.9 m below ground level (Soil 1).

-2.50E-02 0.00E+00 -105

-90

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

105

120

135

-5.9

Chainage (m)

5

-5.00E-03

10

-1.00E-02

Settlement (mm)

Displacement (mm)

0

Comparison of twin offset 9m diameter tunnels driven 30.926m and 17.41m below ground at 30m C-C spacing Measured ground level -75 -60 -45 -30 -15 at 2.9 0 m below 15 30 45 (Soil 60 1). 75 90 105

-90

15

-1.50E-02

20

-2.00E-02

Wmax = 12.7mm at -5.1m Wmax = 21.0mm at 0.0m Comparison of twin offset 9m diameter tunnels driven 30.926m and 17.41m below ground Settlements above tunnel 1 at 30m C-C spacing T2 Settlement above tunnel 1 (1.3% loss) Measured at 8.9 m below ground level (Soil 1).

-2.50E-02

T1

0

0.00E+00 -3.00E-02 -105

5

-5.00E-03

-8.9 -90

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

105

120

135

Chainage (m)

Settlement (mm)

10 -1.00E-02 15 -1.50E-02 Wmax =15.3mm at -1.3m

20 -2.00E-02

Wmax =24.3mm at 0.0m

25 -2.50E-02


T2 T1 -3.00E-02 -105

-90

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

105

120

135

Chainage (m)

Tunnel axis

Tunnel 2

-30.9

Tunnel 1

Symbols:

Figure 5.47

-17.4



Surface and sub-surface vertical displacements above Tunnel 2 when considering offset 9.0m diameter tunnels at depths of 17.4m and 30.9m and a centre-to-centre spacing of 30.0m (V1 & V2 = 1.3%), lower tunnel constructed first

D.Hunt - 2004

Comparison of twin offset 9m diameter tunnels driven 30.926m and 17.41m below ground at 30m C-C spacing Measured at 0.0 m below ground level (Soil 1). Chapter 5 - Movements above twin tunnels

- 179 -

1.50E-02 11.0mm at –19.8m

101.00E-02

8.2mm at 15.6m

8.2mm at –15.6m

Comparison of twin offset 9m diameter tunnels driven 30.926m and 17.41m below ground 3.4mm at 22.6m at 30m C-C spacing Measured at 2.9 m below ground level (Soil 1).

55.00E-03

Depth (m)

Settlement (mm)

U = 0 at +5.0m

1.50E-02 00.00E+00

0.0 11.0mm at –19.2m

10 1.00E-02 -5.00E-03

7.6mm at 15.6m

7.6mm at –15.6m

Comparison of twin offset 9m diameter tunnels driven 30.926m and 17.41m below ground at 30m C-C spacing 3.2mm at 22.6m Measured at 5.9 m below ground level (Soil 1). Horizontal displacements

5 5.00E-03

-1.00E-02

U = 0 at +6.8m

for tunnel 2

0 0.00E+00 1.50E-02

-2.9

Settlement (mm)

Displacement (mm)

-1.50E-02

11.6mm at –13.4m

T2

-5.00E-03 10-2.00E-02 1.00E-02


T1

7.5mm at –13.4m

7.5mm expected atfor13.4m Tunnel 2

-1.00E-02

5-2.50E-02 5.00E-03

3.3mm at 20.0m

-105 Comparison -90 -75 of twin -60 offset -45 9m-30diameter -15 tunnels 0 driven 15 30.926m 30 45and 17.41m 60 75below90ground 105 U= 0 spacing at +6.8m at 30m C-C -1.50E-02 Chainage (m)


135

Measured at 8.9 m below ground level (Soil 1).

1.50E-02

T2

-2.00E-02

12.7mm at –10.2m

-5.00E-03

-5.9

Horizontal displacements Horizontal displacement above Tunnel 1

T1

7.8mm at –10.6m

1.00E-02 10

7.8mm at 10.6m

-2.50E-02 5-1.00E-02-105 5.00E-03

-90

-75

-60

-45

-30

-15

0

15

30

45

60

75 3.7mm 90 at 15.6m 105 120

135

Chainage (m)

U = 0.0 at +5.0m

0 0.00E+00

-1.50E-02

Settlement (mm)

120

-120

-90

-60

-2.00E-02

30

60

80


T2

-2.50E-02

-17.4

Tunnel axis

Tunnel 2

-1.00E-02


Tunnel 1

-1.50E-02

-30.9

T1

Symbols: -2.00E-02 -3.00E-02


-105 -90

-3.00E-02 -105

0


-5.00E-03

Figure-2.50E-02 5.48

-8.9

-30

-75

-60

-45

-30

-15


0

15

30

45

60

75

90

105 120 135


Surface and sub-surface horizontal aboveabove Tunnel Horizontal displacement Tunnel 1 2 when Chainage (m)T2 displacements considering offset 9.0m diameter tunnels at depths of 17.4m and 30.9m and a T1 centre-to-centre spacing of 30.0m (V1 & V2 = 1.3%), lower tunnel constructed first -90

-75

-60

-45

-30

-15

0

15

30

45

Chainage (m)

D.Hunt - 2004

60

75

90

105

120

135

- 180 -


Distance from centreline of Tunnel 2 (m) Comparison of settlements above twin offset 9m diameter tunnels at 50m spacing (Tunnel Tunnel 2-17.41m) Measured -115 1-31.926m, -95 -75 -55 -35 -15at 0.00m below 15 ground 35 level.55

-135

75

Depth (m)

95

0.0

00.00E+00 5 -5.00E-03

10 W = 4.9mm

Settlement (mm)

15-1.00E-02

Wmax = 10.8mm at 15.0m Wmax = 14.5mm at 0.0m Comparison of settlements above twin offset 9m diameter tunnels at 50m spacing (Tunnel 1-17.5m, Tunnel 2-31m) Measured at 2.9 m below ground level

-1.50E-02

0 5

Se ttl e m en t (m m)

-2.9

0.00E+00

-2.00E-02 -5.00E-03

T1

10 15 20

-1.00E-02

W = 4.5mm

-2.50E-02 -105 -95 -85 -75 -65 -55 -45 -35 -25 -15

5

15

25

35

45

55

65

Chainage (m)

75

85 95 105 115 125 Wmax = 13 mm at 0.0m

135 145 155

Wmax = 18mm at 0.0m -2.00E-02

Comparison of settlements aboveT1twin offset 9m diameter tunnels at 50m spacing (Tunnel 1-17.5m, Tunnel 2-31m) Measured at 5.9 m below ground level

-2.50E-02

0 0.00E+00

-105

-95

-85

-75

-65

-55

-45

-35

-25

-15

-5

5

15

25

35

45

55

65

75

85

95

105

115

125

135

145

155

145

155

145

155

Chainage (m)

-5.9

5 -5.00E-03 10 -1.00E-02

W = 4.0mm

Settlement (mm)

Displacement (mm)

-5

-1.50E-02

15 -1.50E-02


20 -2.00E-02

Wmax = 21mm at 0.0m

-2.50E-02

T2

Comparison of settlements above twin offset 9m diameter tunnels at 50m spacing T1 (Tunnel 1-17.5m, Tunnel 2-31m) Measured at 8.9 m below ground level -3.00E-02 0.00E+00 -105 -95

-85

-75

-65

-55

-45

-35

-25

-15

-5

5

15

25

35

45

55

65

75

85

95

105

115

125

135

-8.9

Chainage (m)

5

-5.00E-03

10

-1.00E-02

Settlement (mm)

0

15

-1.50E-02

20

-2.00E-02

25

-2.50E-02

W = 3.6mm

Wmax =18.6mm at 0.0m Wmax =24.3mm at 0.0m T2

T1 -3.00E-02 -105

-95

-85

-75

-65

-55

-45

-35

-25

-15

-5

5

15

25

35

45

55

65

75

85

95

105

115

125

135

Chainage (m)

Tunnel axis

Tunnel 2

-30.9

Tunnel 1

Symbols:

Figure 5.49

-17.4



Surface and sub-surface vertical displacements above Tunnel 2 when considering offset 9.0m diameter tunnels at depths of 17.4m and 30.9m and a centre-to-centre spacing of 50.0m (V1 & V2 = 1.3%), lower tunnel constructed first

D.Hunt - 2004

Comparison of settlements above twin offset 9m diameter tunnels at 50m spacing (Tunnel 1-31.926m, Tunnel 2-17.41m) Measured at 0.0 m below ground level.

- 181 -

Chapter 5 - Movements above twin tunnels 1.50E-02 10.0mm at –19.6m

10 1.00E-02

8.2mm at 15.6m

8.2mm at –15.6m

6.0mm at 17.6m Comparison of settlements above twin offset 9m diameter tunnels at 50m spacing (Tunnel 1-17.5m, Tunnel 2-31m) Measured at 2.9 m below ground level

5 5.00E-03

Settlement (mm)

Depth (m)

U = 0 at +2.2m

1.50E-02 0 0.00E+00

0.0 9.6mm at –18.6m

10 1.00E-02 -5.00E-03

7.6mm at 15.6m

7.6mm at –15.6m

Comparison of settlements above twin offset 9m diameter tunnels at 50m spacing5.5mm at 17.6m Centre line of tunnel 1 Centre line of tunnel 2 (Tunnel 1-17.5m, Tunnel 2-31m) Measured at 5.9 m below ground level

5 5.00E-03

-1.00E-02


U = 0 at +2.2m Settlement (mm)

-1.50E-02


T2

9.7mm at –15.2m

-2.00E-02

7.5mm at –13.4m

T1

Horizontal displacement above

Centre line of tunnel 1above twin offset 9m diameter tunnels atCentre line ofTunnel tunnel Comparison of settlements 50m spacing 5.4mm at 15.6m 2 2(No tunnel 1) (Tunnel 1-17.5m, Tunnel 2-31m) Measured at 8.9 m below ground level

5 5.00E-03 -1.00E-02

-2.50E-02 Settlement above tunnel 2 -105 -95 -85 -75 -65 -55 -45 -35 -25 -15 -5 5 15 25 35 45 55 65 75 85 95 105 after 115 tunnel1251 135 145 155 U = 0 at +2.2m 1.50E-02 Chainage (m) 0 0.00E+00 -1.50E-02 Horizontal displacements above tunnel 2 after tunnel 10.5mm at –10.6m 1 10 1.00E-02 T2 Settlement above tunnel 1 7.8mm at 10.6m 7.8mm at –10.6m -2.00E-02 -5.00E-03 (No tunnel 1) T1 6.0mm at 12.0m Horizontal displacement 5 5.00E-03 above Tunnel 2 (No tunnel -2.50E-02 -1.00E-02 1) -105 -95 -85 -75 -65 -55 -45 -35 -25 -15 -5 5 15 25 35 45 55 65 75 85 95 105 115 125 135 145 155 U = 0 at +2.2m


-1.50E-02 -5.00E-03

-2.00E-02 -1.00E-02

-2.50E-02

-1.50E-02 Symbols:

-2.9

Settlement above tunnel 2 (No 7.5mm at 13.4m tunnel 1)

-5.00E-03 10 1.00E-02

S ettlement (mm)

Displacement (mm)

0 1.50E-02 0.00E+00

Chainage (m)

-135

-115

-95

-75

-55

-35

-15

0 15

35

Distance from centreline of Tunnel 2 (m) Tunnel 2

T2 Tunnel 1

T1

Settl above tunnel 55ements75 952 after tunnel 1

-5.9

-8.9

Horizontal displacements above tunnel 2 after tunnel Tunnel axis1

-17.4

Settlement above tunnel 1 (Not tunnel 1)

-30.9

Horizontal displacement above Tunnel 2 (No tunnel 1)



Settlement above tunnel 2 -3.00E-02 after tunnel 1 -105 -95 -85 -75 -65 -55 -45 -35 -25 -15 -5 5 15 25 35 45 55 65 75 85 95 105 115 125 135 145 155

Figure 5.50 Surface and sub-surface horizontal displacements above 2 when Horizontal disTunnel placement -2.00E-02 Chainagetunnels (m) considering offset 9.0m diameter at depths ofabove17.4m and tunnel 2 after tunnel 1 30.9m and a centre-to-centre spacing of 50.0m (V1 & V2 = 1.3%), lower tunnel constructed first Settlement above tunnel 1 (Tunnel 1)

-2.50E-02 T2

Horizontal displacement above Tunnel 2 (No tunnel D.Hunt - 2004 -3.00E-02 1) -105 -95 -85 -75 -65 -55 -45 -35 -25 -15 -5 5 15 25 35 45 55 65 75 85 95 105 115 125 135 145 155 T1

Chainage (m)

- 182 -


1.2

1 0Z (9m) 0.26Z (9m) 0.44Z (9m)

0.8

0.6Z (9m) e/d'

0.6

0.4

0.2

0 0

0.5

1

1.5

2

2.5

3

3.5

d'/Z0 (m)

1

Figure 5.51 d'Eccentricity of Wmax when constructing offset 9.0m diameter tunnels with various centre-to-centre spacings at depths of 17.4m and 30.9m (V1 & V2 = 1.3%), lower tunnel constructed first

i/ig(Near) 0

i/ig (Remote)


(Near) 1.6 1.5 1.4 1.3 1.2 1.1 1 0.9 0.8 0.7 0.6i/i g0.5 1.6 1.5 1.4 1.3 1.2 1.1

1

0

0.1

eccentricity of U=0/d' 0.3 0.4

0.2

0.9 0.8 0.7 0.6 0.5

0

0.1

0.2

1 0.3

(Remote) 1.1 1.2 1.3 1.4 1.5 1.6i/i g1.7 1.8 1.9 0.4

1

2

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 0 1.9

2

0

Z/Z 0

-0.2

i/ig(Near)

-0.1

-0.1

-0.2

-0.2

-0.3

-0.3

-0.3

-0.4

-0.4

-0.4

0 Z/Z

i/i g(Near)

1.50.7 1.4 0.6 1.3 0.5 1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 5 1.4 1.3 1.2 1.1 1 0.91.60.8

-0.1

-0.2

Z/Z 0

-0.1

0

0 Z/Z

-0.3

0 -0.4

-0.1 20m spacing (9m)

-0.2

Increase

Increase

0 Z/Z

20m spacing (9m) 30m spacing (9m) 30m spacing (9m) 50m spacing (9m) 50m spacing (9m)

-0.5

-0.5

-0.6

Decrease

U=0 ig (remote) ig (near)

ig (near)

-0.4

U=0 ig (remote)

Free surface

20.0m spacing (9.0m) -0.5 Increase

-0.6 Increase

Decrease

Increase

Decrease

-0.6

-0.3

-0.5

20m spacing (9m) 30m spacing (9m) 50m spacing (9m)

Free surface Z

Zo

50.0m spacing (9.0m)

Zo

Decrease

2

d’

2

1

d’

1

Figure 5.52 Deviation of Umax and U=0 when constructing offset 9.0m diameter tunnels at depths of 17.4m and 30.9m with various centre-to-centre spacings (V1 & V2 = 1.3%), lower tunnel constructed first D.Hunt - 2004

-0.6

-0.6

Z

30.0m spacing (9.0m)

-0.5

Increase

- 183 -


Distance from centreline of Tunnel 2 (m) Comparison of twin offset 9m diameter tunnels driven 30.926m and 17.41m below ground at 20m C-C spacing Measured at 0.0 m below ground level (Soil 1).

-105 0

-5.00E-03

10

-1.00E-02

Settlement (mm)

-5

45

-5.00E-03

10

-1.00E-02

15

-1.50E-02

20

-2.00E-02

Settlement (mm)


T1

Comparison of twin offset 9m diameter tunnels driven 30.926m and 17.41m below ground at 20m C-C T2 spacing Measured at 2.9 m below ground level (Soil 1). -55

-5

45

95

Chainage (m)

5

0.0


-1.50E-02

-2.50E-02 0.00E+00 -105

Depth (m)


-2.00E-02

0

95

0.00E+00

5

15

-55

-2.9

Wmax = 12.0 mm at 0.0m Wmax = 14.5mm at 0.0m

T1 30.926m and 17.41m Comparison of twin offset 9m diameter tunnels driven belowabove ground Settlement tunnel 2 at 20m C-C spacing Settlement above tunnel 1 (1.3% loss) T2 Measured at 5.9 m below ground level (Soil 1).

-2.50E-02 0.00E+00 -105

-55

-5

45

95

-5.9

Chainage (m)

5

-5.00E-03

10

-1.00E-02

15

Settlement (mm)

Displacement (mm)

0


Wmax = 13.3mm at 0.0m 1.50E-02

-1.50E-02

W

20

= 15.4mm at 0.0m

max Centreline of tunnel 2

Centreline of tunnel 1

1.00E-02

-2.00E-02

T1

Settlements above tunnel 1 Settlement above tunnel 1 (1.3% loss)

T2

5.00E-03

-2.50E-02 -105

-55

-5

45

95

0 5 10

Settlement (mm)

Chainage (m)

-8.9

0.00E+00

-5.00E-03

-1.00E-02

15

-1.50E-02

20

-2.00E-02

25

-2.50E-02 -105


-55

-5

45

95

Chainage (m)

Tunnel axis

Tunnel 1

-30.9

Tunnel 2

Symbols:

-17.4



Figure 5.53 Surface and sub-surface vertical displacements above Tunnel 2 when considering offset 9.0m diameter tunnels at depths of 17.4m and 30.9m and a centre-to-centre spacing of 20.0m (V1 & V2 = 1.3%), upper tunnel constructed first

D.Hunt - 2004

- 184 -


Comparison of twin offset 9m diameter tunnels driven 30.926m and 17.41m below ground at 20m C-C spacing Measured at 0.0 m below ground level (Soil 1). 10

1.00E-02 7.5mm at –17.6m 5.8mm at 22.2m

5.8mm at –23.2m

5 5.00E-03

2.5mm at 23.2m

0 0.00E+00

Settlement (mm)

10 1.00E-02

5.5mm at 23.6m 5.5mm at –23.6m

Comparison of twin offset 9m diameter tunnels driven 30.926m and 17.41m bel2.6mm ow ground at 18.6m

-1.00E-02

Comparison of twin U= offset0 at9m+13.2m diameter tunnels driven 30.926m and 17.41m below ground at 20m C-C spacing at 20m C-C spacing Measuredatat5.97.9mmbelow belowground groundlevel level(Soil (Soil1).1). Measured

Settlement (mm)

Displacement (mm)

0 0.00E+00

-1.50E-02 1.00E-02

6.4mm at –17.6m

T1

5.1mm at –23.6m

5.00E-03 5 -1.00E-02

1.50E-02

T2

1.00E-02

10

-55

U = 0 at +15.0m


-5

45

Settlement (mm)

5.00E-03

4.9mm at –21.0m

-2.50E-02 -105 S ettlement (mm)

0

-1.00E-02

0.00E+00

-105

-1.50E-02

-5.00E-03

Horizontal displacements Settlement4.9mm above tunnel 1 (1.3% loss) at 21.0m

T2

Horizontal displacement above Tunnel 1 1.8mm at 45.6m

-55

-5

45

U = 0 at +15.0m

Centreline -55 of tunnel 1

45Centreline of tunnel 2

-5

-8.9 95



T1

Tunnel 1

Tunnel axis



Tunnel 2


T2

-1.00E-02 -105

95

Chainage (m)

-2.00E-02

-2.50E-02 Symbols:

-5.9


6.2mm at –15.6m

T1

-5.00E-03

95

Chainage (m)

-2.00E-02

5

1.8mm at 42.6m


-2.50E-02 -105 0 -1.50E-02 0.00E+00

-2.9

Settlement above tunnel 2 Horizontal displacements at 23.6m Settlement5.1mm above tunnel 1 (1.3% loss) Horizontal displacement above Tunnel 1

-5.00E-03

-2.00E-02

0.0

6.8mm at –17.6m

-5.00E-03

5 5.00E-03

10

Depth (m)

Comparison of twin offsetU 9m tunnels driven 30.926m and 17.41m below ground = 0 diameter at +10.0m at 20m C-C spacing Measured at 2.9 m below ground level (Soil 1).


-55

-17.4 -30.9


-5

45

95

Chainage (m) Figure 5.54-1.50E-02 Surface and sub-surface horizontal displacements above Tunnel 2 when considering offset 9.0m diameter tunnels at depths of 17.4m and 30.9m and a centre-to-centre spacing of 20.0m (V1 & V2 = 1.3%), upper tunnel constructed first

-2.00E-02 D.Hunt - 2004

-2.50E-02

- 185 -


Distance from centreline of Tunnel 2 (m) Comparison of twin offset 9m diameter tunnels driven 30.926m and 17.41m below ground at 30m C-C spacing Measured at 0.0 m below ground level (Soil 1).

-105

5

45

95

Depth (m) 0.0

-5.00E-03

Settlement (mm)

15

-5

0.00E+00

0

10

-55

-1.00E-02


-1.50E-02

-2.00E-02

T1

Comparison of twin offset 9m diameter tunnels driven 30.926m and 17.41m below ground T2 at 30m C-C spacing Measured at 2.9 m below ground level (Soil 1).

0

-2.50E-02 0.00E+00 -105

-55

-5

45

95

-2.9

Chainage (m)

5

15

Settlement (mm)

10

-5.00E-03

20

-1.00E-02

Wmax = 12 .0mm at 0.0m Wmax = 13.8mm at 2.0m

-1.50E-02

-2.00E-02 T1

Comparison of twin offset 9m diameter tunnels driven 30.926m and 17.41m below ground at 30m C-C spacing T2 Measured at 5.9 m below ground level (Soil 1). -2.50E-02 0.00E+00

-105

-55

-5

45

95

-5.9

Chainage (m)

5

-5.00E-03

10

-1.00E-02

15

Settlement (mm)

Displacement (mm)

0

20

Wmax = 13.3mm at 0.0m -1.50E-02


-2.00E-02

T2 T1

-2.50E-02 -105

0

-8.9

0.00E+00

-5.00E-03

10

-1.00E-02

Settlement (mm)

5

15

-5 45 17.41m below ground 95 Comparison of twin-55 offset 9m diameter tunnels driven 30.926m and Chainage (m) at 30m C-C spacing Measured at 8.9 m below ground level (Soil 1).

Wmax =14.6mm at 0.0m

-1.50E-02

Wmax =15.3mm at 1.0m -2.00E-02 T1 T2 -2.50E-02 -105

-55

-5

45

95

Chainage (m)

Tunnel axis

Tunnel 1

-30.9

Tunnel 2

Symbols:

-17.4




D.Hunt - 2004

- 186 -

Chapter 5 - Movements above twin tunnels Comparison of twin offset 9m diameter tunnels driven 30.926m and 17.41m below ground at 30m C-C spacing Measured at 0.0 m below ground level (Soil 1). 1.00E-026.2mm at –20.0m

10

5.8mm at 23.2m

5.8mm at –23.2m

5.00E-03

5

Settlement (mm)

5

Comparison of twin offset diameter tunnels driven 30.926m and 17.41m below ground U = 09m at +8.5m at 30m C-C spacing Measured at 2.9 m below ground level (Soil 1).

0.00E+00

0

10

3.0mm at 27.8m

Depth (m) 0.0

1.00E-02 -5.00E-035.6mm at –20.0m 5.5mm at 23.6m 5.5mm at –23.6m

5.00E-03 -1.00E-02

2.2mm at 30.0m U = 0 at +10.0m

5

Settlement (mm)

10


0.00E+00 -1.50E-02

-2.9

T1

-5.00E-03 1.00E-02 -2.00E-025.3mm at –20.0m

T2

5.1mm at –23.6m

5.1mm at –23.6m 1.8mm at 33.0m 5.00E-03 -1.00E-02 -2.50E-02 -105 Comparison of twin-55offset 9m diameter tunnels -5 driven 30.926m and 45 17.41m below ground95

at 30m C-C spacing Chainage (m) Measured at 8.9 m below ground level (Soil 1). U = 0 at +10.0m

0

0.00E+00 -1.50E-02

10

1.00E-02

5

Settlement (mm)

Displacement (mm)

0

-5.9

5.0mm at –20.0m

T1

-5.00E-03 -2.00E-02

4.9mm at 21.0m

4.9mm at –21.0m

T2

5.00E-03

1.5mm at 40.0m

-1.00E-02 -2.50E-02

-105

0

-55 U = 0 at +10.0m

-5

45

0.00E+00

-1.50E-02 -105

95

Chainage (m) -55

-8.9

-5

45

95

Settlement (mm)

Settlements above tunnel 2 after tunnel 1

-5.00E-03 -2.00E-02

Distance from centreline of Tunnel 2 (m) T2 Settlement above tunnel 1 (No tunnel 1)

-2.50E-02 -1.00E-02 -105

Symbols:

Horizontal displacements Tunnel axis Horizontal displacement above Tunnel 1

T1

Tunnel 1

-30.9

Tunnel 2 -55

-17.4

-5

45

Chainage (m)


95

Settlement above tunnel 2 after tunnel 1 Predicted displacement

-1.50E-02

Horizontal displacement above tunnel 2 after tunnel 1

Figure 5.56 Surface and sub-surface horizontal displacements above Tunnel Settlement above tunnel 1 2 when T1 1) considering offset 9.0m diameter tunnels at depths (No oftunnel 17.4m and 30.9m and a -2.00E-02 centre-to-centre spacing of 30.0m (V1 & V2 = 1.3%), upper tunnel constructed first Horizontal displacement T2

-2.50E-02 -105

-55

-5 45 D.Hunt - 2004 Chainage (m)

above Tunnel 2 (No tunnel 1) 95

- 187 -

Chapter 5 - Movements above twin tunnels Comparison of settlements above twin offset 9m diameter tunnels at 50m spacing (Tunnel 1-17.5m, Tunnel 2-31m) Measured at 0.0 m below ground level. 1.00E-02

5.00E-03

-105

0

10

-55

-5

45

Depth (m)

95

0.0

0.00E+00

Settlement (mm)

5


-5.00E-03

-1.00E-02

W = 3.8mm

Wmax = 11.0mm at 0.0m -1.50E-02

15


T1

-2.00E-02 T2 Sett lem ent (m m)

0

-2.50E-02 -105

Comparison of settlements above twin offset 9m diameter tunnels at 50m spacing (Tunnel -55 1-17.5m, Tunnel 2-31m) Measured at 2.9-5 m below ground level.

5

-5.00E-03

10

-1.00E-02

15

-1.50E-02

45

95

145

-2.9

Chainage (m)

0.00E+00

W = 3.6mm

Wmax = 12.0 mm at 0.0m Centre line of tunnel 1



Settlement above tunnel 2 after tunnel 1 -2.00E-02

20

T1

5

-5.00E-03

15

Comparison of settlements above twin offset 9m diameter tunnels at 50m spacing (Tunnel 1-17.5m, Tunnel 2-31m) Measured at 5.9 m below ground level. -55

-5

45

95

145

Chainage (m)

0.00E+00

Settlement (mm)

Displacement (mm)

-105

0

10

Settlement above tunnel 1 (No tunnel 2)

T2 -2.50E-02

-5.9

W = 3.3mm

-1.00E-02

Wmax = 13mm at 0.0m -1.50E-02


20

T2

-2.00E-02 T1

-2.50E-02 -105

Comparison of settlements above twin offset 9m diameter tunnels at 50m spacing (Tunnel Measured at 8.9 -55 1-17.5m, Tunnel 2-31m) -5 45 m below ground level. 95

145

Chainage (m)

5

-5.00E-03

10

-1.00E-02

15

Settlement (mm)

0

0.00E+00

-1.50E-02

-2.00E-02

-8.9

W = 3.0mm Wmax =14.0mm at 0.0m Wmax =14.6mm at 0.0m

T1

Settlement above tunnel 1 T2

-2.50E-02 -105

-55


-5

45

95

145

Chainage (m)

Tunnel axis

Tunnel 1

-30.9

Tunnel 2

Symbols:

-17.4




D.Hunt - 2004

- 188 -

Chapter 5 - Movements above twin tunnels Comparison of settlements above twin offset 9m diameter tunnels at 50m spacing (Tunnel 1-17.5m, Tunnel 2-31m) Measured at 0.0 m below ground level. 10

1.00E-026.2mm at –23.2m 5.8mm at 23.2m

6.1mm at –23.2m

5

5.0mm at 30.0m

5.00E-03

Comparison of settlements above twin offset 9m diameter tunnels at 50m spacing U = 0 at 0.0m (Tunnel 1-17.5m, Tunnel 2-31m) Measured at 2.9 m below ground level. 0.00E+00

5

Settlement (mm)

0

10

Depth (m) 0.0

1.00E-02 -5.00E-03

5.6mm at –23.6m

5.00E-03 -1.00E-02

U = 0 at 1.0m

Comparison of settlements above twin offset 9m diameter tunnels at 50m spacing (Tunnel 1-17.5m, Tunnel 2-31m) Measured at 5.9 m below ground level.

-1.50E-02

0

5.5mm at 23.6m 4.7mm at 30.0m

5.5mm at –23.6m

0.00E+00

-2.9

10

5

-2.00E-02

Settlement (mm)

Displacement (mm)

T1

1.00E-02 -5.00E-03 5.3mm at –23.6m

5.1mm at 23.6m

5.2mm at –23.6m

-2.50E-02 -105 5.00E-03

0

T2

-1.00E-02

-55

-5

4.5mm at 28.0m 95

45

0.00E+00

line of tunnel 1above twin offset 9m diameter tunnelsCentre line ofspacing tunnel 2 ComparisonCentre of settlements at 50m U = 0 at Tunnel +2.2m 2-31m) Measured at 8.9 m below ground level. (Tunnel 1-17.5m,

Settlement (mm)

5

0

1.00E-02 5.0mm at –21.0m

4.9mm at 21.0m

4.9mm at –21.0m

5.00E-03

-1.00E-02

-2.50E-02 -105

0.00E+00

-1.50E-02 -105

Settlement (mm)

T1

-5.00E-03

-2.00E-02

-5.00E-03 -2.00E-02 -1.00E-02 -2.50E-02 -105

Symbols: -1.50E-02

-5.9


-1.50E-02

10

145

Chainage (m)

4.5mm 26.0m above Horizontalatdisplacement

T2

Tunnel 2 (No tunnel 1)



U = 0 at +2.2m

-55

-55

-5

45

-5

45

Chainage (m) T2 Distance from centreline of Tunnel 2 (m) Tunnel 1

45 Chainage (m)


95

-17.4 -30.9


-5

-8.9

95 tunnel 2 after tunnel 1

Tunnel axisabove Horizontal displacement Tunnel 1(No tunnel 1)

T1

TunnelCentre 2 line of tunnel 1

-55

95Horizontal displacements above 145

145

Predicted displacement T1

-2.00E-02


Figure 5.58 Surface and sub-surface horizontal displacements above Tunnel 2 when T2 Horizontal displacement above Tunnel 1 considering offset 9.0m diameter tunnels at depths of 17.4m and 30.9m and a centre-to-centre spacing of 50.0m (V1 & V2 = 1.3%), upper tunnel constructed first -2.50E-02 -105

-55

-5

45 Chainage (m)

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145

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Chapter 6 - Movements above triple tunnels

Chapter Six MOVEMENTS ABOVE TRIPLE TUNNELS

6.1 INTRODUCTION Chapter 6 extends the concept of a twin side-by-side tunnel alignment reported in Chapter 5 to include a third tunnel. The short term movements above consecutively constructed triple tunnels in London clay are reported. The chapter builds on the improved understanding of soil behaviour found when analysing side-by-side tunnels using the finite element analyses, where it was shown that a relative increase in settlement of approximately 60% always occurred above the centreline of the first tunnel driven. This chapter considers the numerical modelling of a triple tunnel geometry which is representative of actual 9.0m diameter tunnels constructed as part of the Heathrow Express Tunnels at 26m below ground level at the Central Terminal Station (U.K.); further details can be found in Cooper and Chapman (1998). This chapter reports the changes to the settlement profile above a second and third tunnel, caused through stiffness changes, when considering two different construction sequences. It is important to note that the second tunnel is only constructed once the first tunnel is completed and that the third tunnel is only constructed once the second tunnel is completed. Due to this reason and due to the geometries chosen for these analyses it is possible to generate additional data for the side-by-side tunnels. These data include side-by-side tunnels at a centre-to-centre spacing of 15.9m, 20.9 and 36.8m. The chapter compares these results with those found in Chapter 5 and draws conclusions relating to the importance of construction sequence when assessing the possible effects of previously strained soil for triple tunnels in a side-by-side alignment. 6.2 FINITE ELEMENT MODEL The finite element analyses considered in this chapter use the same geometry as the tunnels constructed for the Heathrow Express at the CTA (described in Section 6.3) using three types of construction sequence. Figure 6.1 shows Construction Sequence 1, where the middle

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tunnel is constructed first followed by the second outer tunnel, which provided extra data for the twin side-by-side tunnel analyses conducted in chapter 5 with a centre-to-centre spacing of 15.9m (0.77D), followed by the third outer tunnel. The displacements are reported at the same sub-surface levels as those reported in Chapter 5. The second construction sequence shown in Figure 6.2 shows Construction Sequence 2, where the outer tunnels are constructed first followed by the middle tunnel. Once again this produced extra data for the twin side-byside tunnel analyses conducted in chapter 5 with a centre-to-centre spacing 36.8m (1.22D). Figure 6.3 shows Construction Sequence 3, which was used for the Heathrow Express tunnels (although the use of pilot tunnels for the outer tunnels is not included). The triple tunnel mesh used in all the triple tunnel analyses is shown in Figure 6.4. The boundary conditions are the same as those specified in Chapters 4 and 5 for single and twin tunnels. The minimum distance from the centreline of the outermost tunnels to the vertical boundary was again taken to be 105m. The soil properties are assumed to be Soil 1 and the constitutive model was the small strain stiffness model proposed by Jardine et al. (1986) (see Section 5.2.2). The tunnels were constructed using the same gap parameter method, (see Section 4.3.4) for each tunnel, and using a prescribed volume loss of 1.3%. (N.B. In order that the volume loss did not become a variable in the finite element analyses reported herein a constant value of 1.3% was prescribed for each of the three tunnels. In practice Cooper and Chapman (1998) estimated the values of volume loss for Tunnel 2 and Tunnel 3 to be 1.7% and 1.5% respectively.) The inclusion of a third tunnel necessitated two further analyses, in addition to the four analyses previously reported in Section 5.2.4, referred to as analysis 5 and 6, analysis 5 and analysis 6 being analogous to analysis 3 and analysis 4 reported in Section 5.2.4. Analysis 4 was modified in order to find the movements of the nodes around the boundary for excavation of Tunnel 3, which were used to define a new mesh for analysis 5. The reaction forces found from analysis 5 were used to prop open the periphery nodes for Tunnel 3, which were subsequently reduced in a stepped manner (as previously performed for Tunnel 1 and 2). Analysis 6 includes the information gathered from analyses 1 to 5 in order to perform a full representation of the construction of all three tunnels. The tunnel linings were assumed to be 9.0m diameter and 200mm thick, with the same anchorage system as those reported for single and twin tunnels in Chapters 4 and 5. The same contact elements were used as those reported in Chapter 4.

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6.3 FINITE ELEMENT RESULTS 6.3.1 Construction Sequence 1 For Construction Sequence 1, the movements above the first 9.0m tunnel constructed 26.0m below ground level are identical to those reported in Chapter 4 for a single tunnel and hence are not reported again. Figure 6.5 shows the vertical displacements above Tunnel 2 which was constructed at a centre-to-centre spacing of 15.9m on the left side of Tunnel 1. The displacement profile above the first tunnel is superimposed over the second tunnel and is referred to as the greenfield profile. At the ground surface the maximum vertical displacement above the second tunnel has increased from 11.9mm to 14.2mm compared to the greenfield case (i.e. an increase of 19%). This new value is the same as that found for the side-by-side twin tunnels at a centre-to-centre spacing of 20m reported in Chapter 5. The position of this maximum is eccentrically displaced 8.0m towards Tunnel 1, which is less than the value of 8.5m found for tunnels with a 20m centre-to-centre spacing previously reported in Chapter 5. This reduction in eccentricity of Wmax at close spacing can be seen in the results reported by Addenbrooke (1996), for example see Figure 2.24 (Chapter 2) in which the eccentricity is smaller for a centre-to-centre spacing of 8m than it is for the 12m, 16m and 32m spacings. At 15.4m below ground surface the maximum vertical displacement has increased from 22.0mm to 23.0mm and is displaced 3.6m towards Tunnel 1 (both values being larger than those for a spacing of 20m). The corresponding horizontal movements are shown in Figure 6.6. When compared to the greenfield surface profile the value of Umax is increased on the near limb from 6.8mm to 7.2mm and reduced on the remote limb from 6.8mm to 5.2mm. These values are slightly larger than the values found for tunnels at a centre-to-centre spacing of 20m shown in Figure 5.6. At 15.4m below the surface the value of Umax on the near limb has increased from 6.7mm to 9.0mm (an increase compared to 20m spacing) and reduced from 6.7mm to 3.2mm on the remote limb (a decrease compared to the 20m spacing). The changing position of Umax and U=0 are very similar to those at a centre-to-centre spacing of 20m. Figures 6.7 and 6.8 show the vertical and horizontal displacements above Tunnel 3 which is constructed at 20.9m from Tunnel 1 and 36.8m from Tunnel 2. The size and shape of the vertical and horizontal displacement profiles are very similar to those found above twin tunnels at a centre-to-centre spacing of 20m (see Figure 5.5). In other words, it appears that

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the displacement profile above Tunnel 3 is being influenced more by the stiffness changes that occurred in the soil above Tunnel 1, which is only 20.9m away, rather than those above Tunnel 2 which is 36.8m away. For all analyses the tunnel liners deformed in a similar manner to those reported in chapter 5 with the nearer tunnel deforming more than the further tunnel. 6.3.2 Construction Sequence 2 The second construction sequence considered driving an initial tunnel at 26m below ground surface level followed by a second tunnel at a centre-to-centre spacing of 36.8m from the first. The vertical displacements above the second tunnel can be seen in Figure 6.9 and the corresponding horizontal displacements can be seen in Figure 6.10. As expected the behaviour is somewhere between that for tunnels observed at a centre-to-centre spacing of 30m and 50m reported in Chapter 5. At the surface the value of Wmax is 11.9mm, which is identical to the greenfield value and its position is eccentrically offset 8.6m towards the first tunnel (i.e. away from Tunnel 2), whereas at 15.4m below ground surface level it is close to the centreline of Tunnel 2. At the surface the position of U=0 is positioned over the centreline of the second tunnel and is positioned further away from Tunnel 1 (i.e. it is on the remote limb) for sub-surface levels. The third tunnel was constructed in between the first and second tunnels, i.e. 15.9m from Tunnel 1 and 20.9m from Tunnel 2. At the ground surface the vertical and horizontal displacements above the third tunnel (Figures 6.11 and 6.12 respectively) show the vertical displacement profile to be approximately symmetrical. The maximum vertical displacement of 16.0mm occurred above the centreline of Tunnel 3, this value being almost 50% larger than the greenfield value and 12% larger than the 14.2mm value reported above Tunnel 3 for the previous construction sequence. At 15.4m below ground Wmax has increased from 22.0mm to 23.5mm and is eccentrically placed 1.0m towards the nearer Tunnel 1. This behaviour shows the cumulative effect on the vertical displacement profile due to the previous straining of the soil above Tunnel 3 caused by Tunnel 1 and Tunnel 2. The corresponding horizontal movements above Tunnel 3 show a reduction compared to the greenfield values on both trough limbs. At the surface, the shape of the profile is almost symmetrical, the values of Umax being similar on both limbs of the trough with some bias in the position of U=0 towards the closer spaced Tunnel 1. With increasing depth the shape

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becomes less symmetric with greater values being apparent on the limb nearest to Tunnel 1 when compared to the limb nearest Tunnel 2. There are small changes in the position of Umax, although these are less than those found when using the previous construction sequence. 6.4.3 Relative Changes in Displacement Figures 6.13 and 6.14 shows the relative changes in settlement for Construction Sequence 1 and Construction Sequence 2 respectively. Two lines are shown on each figure, one representing the predicted vertical displacements above Tunnel 2 divided by the greenfield displacement (i.e. W2/W1) and the other represents the predicted vertical displacements above Tunnel 3 divided by the greenfield displacement (i.e. W3/W1). In Figure 6.13 the line W2/W1 is similar to those reported in Chapter 5, where 60% relative increase in settlement was found above the centreline of Tunnel 1. However, by looking at the line of W3/W1 it becomes apparent that large relative increases in settlement have occurred above both Tunnel 2 and Tunnel 1. The maximum relative increases were found to be 60% above Tunnel 2 and around 50% above Tunnel 1, and thus larger increases occurred over Tunnel 2 even though it is further away from Tunnel 3 than Tunnel 1. This behaviour would have been missed if one was to simply look at the displacement profile where the movements appear to be the same as for a twin tunnel with a centre-to-centre spacing of 20m. This indicates that even though the relative increases above Tunnel 2 are larger, due to the tunnel spacing the effect is less apparent. In Figure 6.14 the line W2/W1 once again shows a relative increase in settlement of approximately 60% above the centreline of Tunnel 1. The line W3/W1 shows a maximum relative increase of 40% above the centreline of Tunnel 3 with increases of 30% and 20% above the centrelines of Tunnel 1 and Tunnel 2 respectively. In other words a cumulative effect of the previous straining of soils above Tunnel 1 and Tunnel 2 is apparent. There are larger relative increases in settlement above Tunnel 1 compared to Tunnel 2 which is in direct contrast to that for Construction Sequence 1 described previously. Based on the findings of this analysis it would be plausible to assume that if Tunnel 1 and Tunnel 2 were constructed at a separation of d’ and a third tunnel was driven halfway between them (i.e. at d’/2) the profile above Tunnel 3 for surface and sub-surface regions, i.e. the settlement profile above the third tunnel being equally influenced by the stiffness changes which occurred above Tunnel 1 and Tunnel 2. This cumulative effect would produce an

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exaggerated maximum above the centreline of Tunnel 3 which would occur for surface and sub-surface displacements. This would be accompanied by increases in displacement above Tunnel 1 and Tunnel 2. The effects would be increased if the spacing of the tunnels was decreased and if larger volume losses were allowed for Tunnel 2 and 3. 6.3.3 Construction Sequence 3 (Heathrow Express) There was found to be little effect on the settlement profiles when using this Construction Sequence 3 compared to Construction Sequence 1 (Section 6.3.1), hence the full set of results are not included in this thesis. Figures 6.15 show the sub-surface settlement profile 13.0m above Tunnel 2, constructed at a centre-to-centre spacing from Tunnel 1 of 20.9m. The settlement profile is compared to the profile which would have occurred if Tunnel 1 was not present (i.e. the ‘greenfield’ profile). The settlement profile has changed significantly from the greenfield profile, the maximum settlement being increased from 18.1mm to 18.6mm with its position being drawn towards the centreline of Tunnel 1 (i.e. positioned 5.9m away from the centreline of Tunnel 2). Figure 6.16 shows the sub-surface settlement profile above Tunnel 3, which is only 15.9m from Tunnel 1, the maximum settlement is now increased to 19.6mm (i.e. much larger than that for Tunnel 2) although the eccentricity is now only 5.0m (less than the further spaced tunnel). Although not shown here the results for Tunnel 3 are almost identical to those that would have been obtained if Tunnel 2 had not been constructed (i.e. a twin tunnel result). The results closely resemble the behaviour of real tunnels (see Section 6.4). The data have not been plotted together due to the fact that the finite element method under-predicts the magnitude of settlement compared to that observed in the field. For example at 13m below ground surface the measured maximum vertical displacement on the centreline of the concourse Tunnel 1 (measured at track level) is reported to be 28mm, whereas the results from the finite element analyses showed a maximum of only 18.1mm for the Concourse tunnel. For both the measured case history displacements and the predicted finite element displacements an increased value of Wmax was found for the nearer tunnel (i.e. 15.9m spacing) compared to the more distant tunnel (i.e. 20.9m spacing). The finite element analysis and the case history data both show similar shaped profiles with large increases in settlement occurring above the centreline of the first tunnel driven with asymmetry being present in both cases.

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6.4 HEATHROW EXPRESS CASE HISTORY Cooper and Chapman (1998) reported the movement of existing 3.81m diameter twinrunning Piccadilly Line Tunnels at the Heathrow Express Central Area Station during the construction of three 9.0m diameter tunnels 13.0m below. The overlying Piccadilly tunnels, referred to as the Inner and Outer tunnels, were constructed 13m below ground level in London Clay between 1971 and 1976. Ground movements were expected to affect these tunnels and therefore extensive monitoring was carried out during the construction of the new tunnels below. The three new tunnels referred to as Upline, Downline and Concourse were constructed 26m below ground level at a 700 skew to the Piccadilly line tunnels. The Concourse tunnel was constructed using NATM, however, due to the collapse of a small section of the tunnel in October 1994, the Upline and Downline tunnels were subsequently constructed using 9.0m diameter segmental liners, using 3.9m pilot tunnels. The Upline tunnel (completed in February 1996) was the second tunnel to be constructed with a tunnel separation of 20.9m from the Concourse tunnel. The Downline tunnel (finished in May 1996) was constructed at a distance of 15.9m from the concourse tunnel on the opposite side to the Upline tunnel (i.e. 36.8m from Upline). Further details relating to the sub-surface ground movements measured within the Piccadilly Line tunnels can be found in Cooper and Chapman (1998) and Cooper (2003). Figure 6.17 shows recorded data for the sub-surface settlement profile after each stage of construction measured from within the Inner Piccadilly Line tunnel. The profile recorded above the first Concourse tunnel is almost Gaussian in shape with a maximum settlement of 28mm occurring above the tunnel centreline and a volume/unit length of 1.3%. The settlement profile above the Concourse tunnel is superimposed over the individual displacements which occurred above the Upline (Figure 6.17b) and Downline tunnels (Figure 6.17c). The concourse profile is used as an approximation to the greenfield settlement profile that would have most likely occurred above these tunnels. By comparing the settlement profile above the Upline tunnel with the greenfield profile it becomes evident that the curve is no longer Gaussian. Increases in displacement have occurred on both the remote and near limbs with larger increases being present on the near limb. The maximum displacement has increased to 32mm and the volume/unit length of the displacement profile has increased from 1.3% to 1.5% when compared to the Concourse profile. The profile for the construction of the Downline tunnel also shows an increase in displacement compared to

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the greenfield profile. However, large increases are mostly found on the near limb with small reductions in displacement occurring on the remote limb. The maximum settlement increased to 37mm and the volume/unit length of the displacement profile increased to 1.7%, both these values are larger than those reported above the Concourse tunnel and the Upline tunnel which has a greater centre-to-centre spacing. The maximum settlement is also eccentrically displaced towards the first tunnel driven. The maximum relative increase in settlement for both the Upline and Downline tunnels occurs above the centreline of the first tunnel driven, although the value is larger for the Upline tunnel. 6.5 CONCLUSIONS This chapter has shown the role of previous straining of the soil to be vitally important when considering the movements above triple tunnels. The effect of using a different construction sequence for closely-spaced multiple tunnels has also been shown to have dramatic consequences on the settlement profile above each tunnel: 

Constructing a tunnel followed by consecutive construction of a tunnel on either side results in almost identical behaviour to that found when analysing two separate twin tunnel analyses (i.e. Tunnel 1 & Tunnel 2 and Tunnel 1 & Tunnel 3).



The effect of constructing a third tunnel in between a first and second tunnel results in a cumulative effect where Tunnel 3 is influenced by the changes in soil stiffness above Tunnel 1 and Tunnel 2. The profile will be more influenced by the nearest tunnel.

This research has shown that the construction sequence adopted for the triple Heathrow Express tunnels at CTA was the best option when attempting to minimise vertical displacements. There was good agreement between the shape of individual settlement profiles obtained from the finite element analyses and the case history data reported for the Heathrow Express tunnels. By keeping the volume loss constant the changing shape of the profiles due to previous straining has been highlighted. Increases in volume loss for Tunnel 2 and Tunnel 3 have not been considered here, however, although it would be expected that increasing the value would only exaggerate the effects highlighted here. D.Hunt - 2004

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26.0m

2

3

1 15.9m


20.9m

Diameter = 9.0m

Figure 6.1

Geometry of triple tunnel analyses showing the construction sequence (Construction Sequence1).

15.9m

20.9m

26.0m

1

2

3

London Clay C’ = 5kPa 0  ’ = 25

Diameter = 9.0m

Figure 6.2

Geometry of triple tunnel analyses showing an alternative construction sequence. (Construction Sequence 2).

13.0m Case history data 26.0m

Downline

Concourse

3

Upline

2

1 15.9m

20.9m


Diameter = 9.0m

Figure 6.3

Geometry of triple tunnel analyses showing the construction sequence employed for the Heathrow Express Tunnels (Construction Sequence 3).

________________________________________________________________________________________________________

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105.0m

Figure 6.4 Finite element Mesh for side by side 9m and 4m diameter triple tunnels analysis (Z = 26.0m shown).


20.9m


15.9m




40.0 m

26.0m

105.0m


________________________________________________________________________________________________________

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Chapter 6 - Movements above triple tunnels Settlement above 25 m deep triple 9m diameter tunnels at 15 and 20m spacing from tunnel 1 Measured at 0.0 m below ground level (fixed).

Se ttl e m en t (m m)

1.00E-02

5.00E-03


-55

-5

45

Depth (m)

95

0.0

00.00E+00 5-5.00E-03 10-1.00E-02 15-1.50E-02


Settlement above 25 m deep triple 9m diameter tunnels at 15 and 20m spacing from tunnel 1 Measured at 7.9 m below ground level. T2

T3


1.00E-02 -2.00E-02 Se ttl e m en t (m m)

-1.05E+02

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

Chainage (m) 5.00E-03

0

-6.9

0.00E+00

5

-5.00E-03

10 -1.00E-02

Settlement above 25 m deep triple 9m diameter tunnels at 15 and 20m spacing from tunnel 1 Measured at 14.4 m below ground level.

Displacement (mm)

1.00E-02 15 -1.50E-02 Se 5.00E-03 ttl -2.00E-02 e m 0.00E+00 en -2.50E-02 t (m m) -5.00E-03

0


-11.4 -105

-55

-5

45

95

Chainage (m)

5

10-1.00E-02 15-1.50E-02


1.00E-02 20-2.00E-02 Se -2.50E-02 5.00E-03 ttl e m en 0.00E+00 t (m m) -5.00E-03

Wmax = 19.0mm at 0.0m Wmax = 21.0mm at 5.0m -105

-55

-5

45

95

Chainage (m)

0

-15.4

5

10-1.00E-02 15-1.50E-02 20-2.00E-02 25-2.50E-02

Wmax =22.0mm at 0.0m -105

-55

-5

45 Chainage (m)

95 Wmax =23.0mm at 3.6m

Tunnel axis

2 1 Symbols:

Figure 6.5

-26.0

Construction sequence



Surface and sub-surface vertical displacements due to the construction of Tunnel 2, using Construction Sequence 1 with a 9.0m diameter tunnel at 26.0m depth (V1 = V2 = 1.3%).

________________________________________________________________________________________________________

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Settlement above 25 m deep triple 9m diameter tunnels at 15 and 20m spacing from tunnel 1 Measured at 0.0 m below ground level (fixed). 10 1.00E-02

6.8mm at –20.0m 5.2mm at –12.0m

6.8mm at 20.0m 7.2mm at 22.4m

5 5.00E-03 Depth (m)

Settlement (mm)

0 0.00E+00

101.00E-02

-5.00E-03

U = 0.0 at +6.5m

Settlement above 25 m deep triple 9m diameter tunnels at 15 and 20m spacing from tunnel 1 Measured at 7.9 m below ground level. 5.7mm at –18.0m 5.7mm at 18.0m

3.6mm at –15.6m

5.7mm at 18.0m

55.00E-03

T2-U-act

-1.00E-02

U = 0.0 at +2.2m

00.00E+00

Settlement (mm)

Displacement (mm)

-1.50E-02

0.0

-6.9

Settlement above 25 m deep triple 9m diameter tunnels at 15 and 20m spacing from tunnel 1 T2-U-exp Measured at T2 14.4 m below ground T1 T3 level.

10-5.00E-03 0.01

5.9mm at –15.0m -2.00E-02 -1.05E+02 -5.50E+01 3.1mm at –15.0m

-5.00E+00

6.8mm at 11.0m

4.50E+01

9.50E+01

5.9mm at 15.0m

Chainage (m)

5-1.00E-02 0.005

0-1.50E-02 0

Settlement (mm)

10 1.00E-02 -0.005 -2.00E-02

U = 0.0 at -2.2m

T2-U-act

Settlement above 25 m deep triple 9m diameter tunnels at 15 and 20m spacing from tunnel 1 Measured at 15.4 m below ground level. 3.2mm at –13.6m 6.7mm at –11.3m T2-U-exp

-11.4

9.0mm at 8.0m

T2

T1

T3

6.7mm at 11.3m

5 5.00E-03 -0.01 -2.50E-02

-105

Settlement (mm)

00.00E+00 -0.015 -105

-55

-1.50E-02Symbols:

45

-55

95

U = 0.0 at -2.2m

Chainage (m) -5

45

-15.4 95


-5.00E-03 -0.02

-1.00E-02 -0.025 -105

-5

Tunnel axis

2 1 -55


-5


-26.0

45 Chainage (m)

95


-2.00E-02

Figure 6.6

Surface and sub-surface horizontal displacements due to the construction of Tunnel 2, using Construction Sequence 1 with a 9.0m diameter tunnel -2.50E-02 at 26.0m depth (V1 = V2 = 1.3%). -105

-55

-5

45

95

Chainage (m) ________________________________________________________________________________________________________

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Chapter 6 - Movements triple tunnels Settlement above 25 m above deep triple 9m diameter tunnels at 15 and 20m spacing from tunnel 1 Measured at 0.0 m below ground level (fixed). Se ttl e m en t (m m)

1.00E-02


-105

-55

-5

45

Depth (m)

95

0.0

00.00E+00 5-5.00E-03 10-1.00E-02 Sett lem ent (m m)

15

Settlement above 25 m deep triple 9m diameter tunnels at 15 and 20m spacing from tunnel 1

-1.50E-02


Measured at 7.9 m below ground level.

1.00E-02


-2.00E-02 5.00E-03

-1.05E+02

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

Chainage (m)

00.00E+00

-6.9

5

-5.00E-03

Sett lem ent (m m)

-1.00E-02 10


-1.50E-02 1.00E-02 15


-2.00E-02 5.00E-03

-11.4

Displacement (mm)

-2.50E-02

00.00E+00

-1.05E+02

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

Chainage (m)

5-5.00E-03 10-1.00E-02 15-1.50E-02


1.00E-02 20-2.00E-02


5.00E-03 Se -2.50E-02 -1.05E+02 ttl e m 0.00E+00 en t (m m) -5.00E-03

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

Chainage (m)

-15.4

0 5

10-1.00E-02 15-1.50E-02 20-2.00E-02 Wmax =22.0mm at 0.0m

25-2.50E-02

-1.05E+02

-5.50E+01

-5.00E+00

4.50E+01 Chainage (m)

9.50E+01 Wmax =21.5mm at -1.0m

Tunnel axis

2 1 Symbols:

Figure 6.7

3


-26.0



Surface and sub-surface vertical displacements due to the construction of Tunnel 3, using Construction Sequence 1 with a 9.0m diameter tunnel at 26.0m depth (V1, V2 and V3 = 1.3%).

________________________________________________________________________________________________________

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Settlement above 25 m deep triple 9m diameter tunnels at 15 and 20m spacing from tunnel 1 Measured at 0.0 m below ground level (fixed). 10 1.00E-02

6.8mm at –20.0m 6.7mm at –26.0m

6.8mm at 20.0m 4.4mm at 14.0m

5 5.00E-03 Depth (m)

Settlement (mm)

00.00E+00

U = 0.0 at -5.0m


101.00E-02

-5.00E-03

55.00E-03

5.7mm at –18.0m

5.7mm at 18.0m

5.7mm at –22.2m

3.2mm at 16.0m

T3-U-exp

-1.00E-02

U = 0.0 at 0.0m

00.00E+00

Settlement (mm)

Displacement (mm)

-1.50E-02

6.8mm at –9.6m

-2.00E-02 -1.05E+02

-5.50E+01

5.9mm at -15.0m

5.9mm at 15.0m

-5.00E+00

Settlement (mm)

9.50E+01

2.9mm at 19.4m

T3-U-exp

U = 0.0 at +3.0m

Settlement above 25 m deep triple 9m diameter tunnels at 15 and 20m spacing from tunnel 1 Measured at 15.4 m below ground level. 8.7mm at –8.6m

T2-W-act

T2

T1

T3

5-2.50E-02 5.00E-03 -1.00E-02 -1.05E+02

-5.50E+01

3.1mm at 14.8m

-5.00E+00

T3-U-exp

-5.00E-03 -2.00E-02

-11.4

6.7mm at 11.3m

6.7mm at –11.3m

4.50E+01

9.50E+01

Chainage (m) U = 0.0 at +3.0m

00.00E+00 -1.50E-02 -105 Settlement (mm)

4.50E+01 Chainage (m)

5-1.00E-02 5.00E-03

10-2.00E-02 1.00E-02 -5.00E-03

-6.9

Settlement above 25 m deep triple 9m diameter tunnels at 15 and 20m spacing from tunnel 1 T3-U-act Measured at 14.4 m below ground level. T2 T1 T3

10-5.00E-03 1.00E-02

-1.50E-02 00.00E+00

0.0

-55

-5

45

-15.4 95

Distance from centreline of Tunnel 2 (m) T3-W-act

Tunnel axis

2

-1.00E-02 -2.50E-02 -1.05E+02

-5.50E+01

T2-U-exp -1.50E-02Symbols:

1

-5.00E+00

3


4.50E+01

Chainage (m) Greenfield displacement

-26.0

9.50E+01


-2.00E-02 Surface and sub-surface vertical displacements due to the construction of Figure 6.8 T3-U-exp Tunnel 3, using Construction Sequence 1 with a 9.0m diameter tunnel at 26.0m depth (V1, V2 and V3 = 1.3%). -2.50E-02 -1.05E+02 -5.50E+01 -5.00E+00 4.50E+01 9.50E+01 ________________________________________________________________________________________________________ Chainage (m)

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Chapterm 6 - Movements above triple tunnels en t (m m)

Settlement above 25 m deep triple 9m diameter tunnels at 15 and 20m spacing from tunnel 1 Measured at 0.0 m below ground level (fixed).


-55

-5

5

55

Depth (m)

105

0.0

0 5 10 15 T1

Settlement above 25 m deep triple 9m diameter tunnels at 15 and 20m spacing from tunnel 1 Measured at 7.9 m below ground level. Se ttl e m en t (m m)

1.00E-02

-1.0 5E+ 02

-9.5 0E+ 01

-8.5 0E+ 01

-7.5 0E+ 01

-6.5 0E+ 01

-5.5 0E+ 01

-4.5 0E+ 01

-3.5 0E+ 01

-2.5 0E+ 01

-1.5 0E+ 01

-5.0 0E+ 00


T2 5.00 E+0 0

5.00E-03

1.50 2.50 E+0 E+0 1 1 Chainage (m)

3.50 E+0 1

4.50 E+0 1

5.50 E+0 1

6.50 E+0 1

Wmax = 11.9mm at –8.6m 7.50 E+0 1

8.50 E+0 1

9.50 E+0 1

1.05 E+0 2

1.15 E+0 2

1.25 E+0 2

1.35 E+0 2

0

-6.9

0.00E+00

5

-5.00E-03

10


Sett -1.00E-02 lem ent (m 1.00E-02 m)

15 -1.50E-02


Displacement (mm)

5.00E-03 -2.00E-02

0-2.50E-02

-11.4 -105

-55

-5

45

95

Chainage (m)

5 10 15 20

Settlement above 25 m deep triple 9m diameter tunnels at 15 and 20m spacing from tunnel 1 Measured at 15.4 m below ground level. 1.00E-02


5.00E-03 Se ttl e m 0.00E+00 en t (m -5.00E-03 m)

-105

-55

-5

45

Wmax = 16.0mm at -3.0m 95

Chainage (m)

-15.4

0 5

10 -1.00E-02 15 -1.50E-02 20 -2.00E-02 Wmax =22.0mm at 0.0m -2.50E-02 -105

-55

-5

45

Wmax =18.0mm at -1.0m 95

Chainage (m)

Tunnel axis

1 Symbols:

Figure 6.9

2


-26.0



Surface and sub-surface vertical displacements due to the construction of Tunnel 2, using Construction Sequence 2 with a 9.0m diameter tunnel at 26.0m depth (V1 = V2 = 1.3%).

________________________________________________________________________________________________________

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10

6.8mm at –20.0m 6.1mm at –27.5m

1.00E-02

6.8mm at 20.0m 4.3mm at 22.4m

5 5.00E-03 Depth (m)

U = 0.0 at 0.0m

00.00E+00Settlement above 25 m deep triple 9m diameter tunnels at 15 and 20m spacing from tunnel 1 Settlement (mm)

Measured at 7.9 m below ground level.

1.00E-02 10-5.00E-03

0.0

5.7mm at –18.0m 5.6mm at –23.1m

5.7mm at 18.0m

T2-U-act

5.00E-03 5-1.00E-02

3.7mm at 20.0m

U = 0.0 at 3.4m

Se ttlement (mm)

Displacement (mm)

0-1.50E-02 0.00E+00

-2.00E-02 10-5.00E-03 0.01

-1.05E+02

6.1mm -5.50E+01 at –15.0m

-5.00E+00

4.50E+01

9.50E+01 5.9mm at 15.0m

Chainage (m)

5.9mm at -15.0m

3.6mm at 19.0m

5 0.005 -1.00E-02

Settlement (mm)

0 0 -1.50E-02 101.00E-02 -0.005 -2.00E-02

Settlement (mm)

-6.9

T3-U-exp

Settlement above 25 m deep triple 9m diameter tunnels at 15 and 20m spacing from tunnel 1 T1 Measured at 14.4 m below ground level.

U = 0.0 at +3.4m

Settlement T2-U-act above 25 m deep triple 9m diameter tunnels at 15 and 20m spacing from tunnel 1 Measured at 15.4 m below ground level. 7.4mm at –12.3m

T3-U-exp6.7mm at –11.3m

T1

T3

6.7mm at 11.3m

T2

3.4mm at 13.3m

55.00E-03 -0.01

-2.50E-02 -105 0 0.00E+00 -0.015

-55

-105

-55

-5

45 Chainage (m)

-5

U = 0.0 at +1.6m

45

95 -15.4 95


-0.02 -5.00E-03

T1 -0.025 -1.00E-02 -105

-55

T2-U-act -1.50E-02Symbols:

-2.00E-02

-11.4

-5

T3

1

Tunnel axis

T2

2

45

-26.0

Construction sequence 95

Chainage (m)



T3-U-exp

Figure 6.10 Surface and sub-surface horizontal displacements due to the construction of Tunnel 2, using Construction Sequence 2 with a 9.0m diameter tunnel -2.50E-02 at 26.0m depth (V1 = V2 = 1.3%).

-105 -55 -5 45 95 ________________________________________________________________________________________________________ Chainage (m)

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Chapter 6 - Movements above triple tunnels Settlement above 25 m deep triple 9m diameter tunnels at 15 and 20m spacing from tunnel 1 Measured at 0.0 m below ground level (fixed). Sett lem ent (mm )

1.00E-02


5.00E-03

-105

-55

-5

5

55

105

Depth (m) 0.0

00.00E+00 5-5.00E-03 10-1.00E-02 15-1.50E-02 Se ttl e m en t (m m)

Wmax = 11.9mm at 0.0m Settlement above 25 m deep triple 9m diameter tunnels at 15 and 20m spacing from tunnel 1 Measured at 7.9 m below ground level.

-2.00E-02

1.00E-02 -1.05E+02

-5.50E+01

-5.00E+00

4.50E+01

Wmax = 16.0mm at 0.0m 9.50E+01

Chainage (m)

5.00E-03

0

-6.9

0.00E+00

5-5.00E-03 10-1.00E-02


1.00E-02 15-1.50E-02


Displacement (mm)

20

5.00E-03 Se -2.00E-02 ttl e m 0.00E+00 -2.50E-02 en -1.05E+02 t (m m) -5.00E-03

-11.4

0

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

Chainage (m)

5

10 -1.00E-02 15 -1.50E-02


-2.00E-02 20 1.00E-02


5.00E-03 -2.50E-02 25 Se

-1.05E+02 ttl e m 0.00E+00 en t (m m) -5.00E-03

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

Chainage (m)

-15.4

0 5

10-1.00E-02 15-1.50E-02 20-2.00E-02 Wmax =22.0mm at 0.0m

25-2.50E-02 -1.05E+02

-5.50E+01

-5.00E+00

4.50E+01

Wmax =23.5mm at -1.0m 9.50E+01

Chainage (m)

Tunnel axis

1 Symbols:

Figure 6.11

3

2


-26.0



Surface and sub-surface vertical displacements due to the construction of Tunnel 3, using construction sequence 2 with a 9.0m diameter tunnel at 26.0m depth.(V1, V2 and V2 = 1.3%).

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Sett lem ent 1.00E-02 10 (mm )

6.8mm at –20.0m 6.2mm at –22.5m

6.8mm at 20.0m 6.1mm at 18.4m

5 5.00E-03 Depth (m)

U = 0.0 at -3.6m

0

Sett 0.00E+00 lem ent (m m)101.00E-02

0.0


-5.00E-03

5.7mm at –18.0m

5.7mm at 18.0m

4.1mm at -18.0m

3.8mm at 16.0m

55.00E-03 -1.00E-02

U = 0.0 at -3.6m

00.00E+00

Displacement (mm)

-6.9


-1.50E-02

Sett lem ent (m -5.1.000E-03 0E-02 10 m) -2.00E-02

5.9mm at -15..0m -1.05E+02

-5.50E+01 3.8mm at -15.0m

-5.00E+00 Chainage (m)

5-1.5.000E-02 0E-03

T2-U-exp

0E-02 0-1.0.050E+00


Sett lem ent10 -2.1.00E-02 0E-02 (m -5.00E-03 m)

T2-W-act

5.9mm at 15.0m 9.50E+01 2.5mm at 15.0m

4.50E+01

6.7mm at –11.3m

T1

T3

U = 0.0 at 0.0m

-11.4

6.7mm at 11.3m

T2

4.8mm at –9.6m

3.4mm at 8.6m

5-2.5.500E-02 0E-03 -1.00E-02

-1.05E+02

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

Chainage (m)

00.00E+00 -1.50E-02

-15.4

U = 0.0 at 0.0m

-105

-55

-5

45

95


-5.00E-03

-2.00E-02

Tunnel axis T1

-1.00E-02

1

-2.50E-02 -1.05E+02 -1.50E-02

T2-U-exp

Symbols:

-2.00E-02

-5.50E+01

T3

3

T2

2

-5.00E+00

4.50E+01

Greenfield displacementChainage (m)

-26.0

Construction sequence 9.50E+01


T3-U-exp

Figure 6.12 Surface and sub-surface horizontal displacements due to the construction of Tunnel 3, using construction sequence 2 with a 9.0m diameter tunnel at -2.50E-02 26.0m depth.(V1, V2 and V2 = 1.3%). -1.05E+02

-5.50E+01

-5.00E+00

4.50E+01

9.50E+01

________________________________________________________________________________________________________ Chainage (m)

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2 W 2/W 1 W 3/W 1

1.8

W (Predicted) / W (Greenfield)

1.6 1.4 1.2 INCREASE 1 DECREASE 0.8 0.6 0.4 1

2

0.2 0 -105

-55

3

-5

45

95


Figure 6.13

Relative changes in surface settlement above Tunnel 2 and Tunnel 3 when constructing 9.0m diameter triple tunnels at 26.0m below ground level using Construction Sequence 1. (V1, V2, V3 = 1.3%)

2 W 2/W 3 W 3/W 1

1.8

W (Predicted) / W (Greenfield)

1.6 1.4 1.2 INCREASE 1 DECREASE 0.8 0.6 0.4 1

0.2

3

2

0 -105

-55

-5

45

95


Figure 6.14

Relative changes in surface settlement above Tunnel 2 and Tunnel 3 when constructing 9.0m diameter triple tunnels at 26.0m below ground level using Construction Sequence 2. (V1, V2, V3 = 1.3%)

________________________________________________________________________________________________________

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0

10

15

(mm)

Settlement (mm)

5

20

25 - 105

18.6mm at 31.7m (5.9m) Predicted

18.1mm at 36.8m (0.0m)

Greenfield

- 55

eccentricity shown in bracket

2

1 -5

45

95

Chainage (m)

Figure 6.15 Sub-surface displacements above Tunnel 2 (Upline) at 13.0m below ground surface (Construction Sequence 3)

0

10 (mm)

Settlement (mm)

5

15

20

18.1mm at 0.0m (0.0m) 19.6mm at 5.0m (5.0m) eccentricity shown in bracket

25 - 105

- 55

Predicted 3

1

Greenfield

2

-5

45

95

Chainage (m)

Figure 6.16 Sub-surface displacements above Tunnel 3 (Downline) at 13.0m below ground surface (Construction Sequence 3) ________________________________________________________________________________________________________

D.Hunt - 2004

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Chapter 6 - Movements above triple tunnels Chainage - m 0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

110.0

120.0

-30

Downline

CL Downline

Settlement - mm

-20

Upline

CL Upline

-10

Concourse

CL Concourse

0

-40

-50 After Concourse After Upline After Downline After Ancillaries

-60

- 9/1/95 - 2/3/96 - 31/05/06 - 20/12/96

-70

(a) Total settlement profile after each stage of construction Chainage - m 0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

110.0

120.0

CL Upline

0

-20

CL Concourse

CL Downline

Settlement - mm

-10

-30

-40

-50

(b) Contribution of Upline, (Concourse displacements superimposed) -60

0.0

Chainage - m 10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

110.0

120.0

-30

-40

CL Upline

-20

CL Concourse

Settlement - mm

-10

CL Downline

0 -70

-50

(c) Contribution of Dowline (Concourse displacements superimposed) -60

Figure 6.17 Sub-surface vertical displacements caused by the construction of triple -70 9.0m diameter tunnels as part of the Heathrow Express project recorded at 13.0m below ground level (Inside the Inner Piccadilly Line tunnel). (modified after Cooper and Chapman,1998) ________________________________________________________________________________________________________

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Chapter 7 - Small scale laboratory modelling of twin tunnels

- 210 -

Chapter Seven

SMALL SCALE LABORATORY MODELLING OF TWIN TUNNELS

7.1 INTRODUCTION

This chapter describes the apparatus used, the experimental procedure involved, the difficulties encountered and the results obtained from small-scale laboratory modelling of twin tunnels. The aims of the physical modelling were:

•

to assess the applicability of modelling twin-tunnel behaviour at small scale in a laboratory under gravity alone (i.e. 1g), including an assessment of the surface and subsurface displacements.

•

On successful completion of the first aim, to monitor the changes in surface and subsurface displacements above twin-tunnels at varying centre-to-centre spacing. Any data produced would be compared with the results of the finite element work reported in Chapter 5 and subsequently used to improve the existing empirical predictive methods which are proposed in Chapter 8.

The small-scale model tests reported here were carried out in heavilly over-consolidated Speswhite Kaolin clay. The sample was prepared by consolidating clay slurry from a water content of 90% down to 55% in a consolidation tank. The subsequent shear strength of the clay was found to be approximately 10kPa at a water content of 55%. Once primary consolidation was complete 83mm diameter ‘tunnels’ were constructed at a depth of 300mm. Various methods for constructing the tunnels were trialled. However, for the main tests the tunnels were excavated using an auger type cutter within a shield. Once the excavation had been completed, an 80mm diameter steel tunnel liner was placed within the tunnel. The diameter of the tunnel included a

D.Hunt - 2004


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specific over-cut (3mm) to create a volume loss of 6% for each liner placed. Once the first tunnel was constructed a second parallel tunnel was constructed at a centre-to-centre spacing of 140mm (1.5D), using the same tunnelling technique sequence and liner diameter. The liner used in these tests represents a 4.0m diameter tunnels at a scale of 1/50. The tests were not expected to reproduce the stress levels found in real tunnels having the same geometry. The ‘true’ stress behaviour around the tunnels can only be reproduced at small scale in a centrifuge (e.g. Mair 1979, Taylor 1984). In order to obtain the full-scale stresses in a 1/50th scale model the centrifuge would increase the value of gravity by 50 times (i.e. 50g). However such a centrifuge facility was not available. In addition Kim (1996), who previously modelled the behaviour of multiple tunnels (under gravity alone) reported that the additional complexities of using a centrifuge, in addition to the costs involved, outweighed the possible advantages. It should be noted that centrifuge modelling of twin-tunnels has recently been reported by Ng et al. (2004), although these tests were in sand. This chapter concludes by commenting on the use of small-scale modelling under gravity with respect to tunnelling induced ground movements. It should be noted that before the commencement of this project that the University of Birmingham did not have the facilities for consolidating large clay samples from a slurry. Therefore in order to prepare an overconsolidated sample, a consolidation tank was manufactured and loading arrangement constructed and proof tested. This chapter reports how this type of facility was created and used over a period of 12 months (October 2002 to October 2003).

7.2 APPARATUS DESIGN

The design of the consolidation tank was undertaken by first considering the various tank designs reported by previous authors (e.g. Love, 1984 and Kim, 1996) who used tanks that were 300mm wide, 1000mm long and 450mm high. The tank used in this research project has the same depth as the previously reported tanks (450mm) and a plan area of 1800 x 600mm (i.e. nearly four times greater). This plan dimension was chosen in order that a wide range of centreto-centre spacing for the tunnels could be used and to ensure full development of the surface settlement trough in the longitudinal plane. In order to reduce the influence of boundary effects the distance between the tunnel centreline and boundary wall must also be at least 3i (i.e. the

D.Hunt - 2004


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extent of bounds to movement on one side of tunnel). The largest centre-to-centre distance likely to be used in these tests would be where the bounds to movement for each of the tunnels stopped overlapping (i.e. a distance of 6i between centrelines). When constructing an 80mm diameter tunnel at 300mm depth, the trough width parameter is 150mm (i.e. i = 0.5 x 300) hence the full surface trough width (6i) is 900mm for a single tunnel. For two tunnels to have no interaction the minimum tank length required was 12i or 1800mm. For each tunnel the cover to diameter ratio (C/D) was 3.8 (i.e. 300/80) which equates to a deep tunnel if C/D > 2.0. Oteo and Sagaseta (1982), on the basis of numerical analyses suggested that the boundary should ideally be situated at (9.0D) away from the tunnel axis, where D is the tunnel diameter. However, earlier centrifuge models conducted by Mair (1979) and Taylor (1984) were based upon a boundary distance of 3.0D. The minimum boundary distance considered here was 5.6D.

7.2.1

Consolidation Tank

The consolidated clay samples were prepared in a consolidation tank, the design and development of which was undertaken as part of this research programme. The general design concept of the tank was similar to that reported by Love (1984) and later modified by Kim (1996) for testing of twin tunnels. The tank design consisted of Three main sections (Figure 7.1) which were all were fabricated in the Civil Engineering workshop at the University of Birmingham, they are known as:

•

The tank section

•

The extension section

•

The loading plate

•

The cover plate

The tank section was constructed in a slightly different manner from the extension section. The front and rear faces were made of 15mm clear Perspex which needed to be removed for placement of marker beads after consolidation. The side walls of the tank and bottom plate were constructed from 6mm mild steel plate connected together on the inside face by a 60x60x4mm mild steel angle (supplied by Warden Steel Ltd) frame. The steel frame incorporated recesses on

D.Hunt - 2004


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the front and back faces into which Perspex faces could be placed, the Perspex being thinner than that used by Kim (1996). The Perspex allowed the movement of marker beads in the clay to be monitored during the tunnelling procedure. Mair (1979) reported the use of 70mm thick Perspex in centrifuge tests, through which the displacements were monitored. However, due to concerns of problems with refraction of light within the Perspex (which would distort the displacements) the thinner Perspex was preferred. The Perspex would not have withheld the lateral stress during consolidation alone and hence was held in place by a restraining gate that was bolted through the frame of the tank.

The extension section has the same plan area as the tank section. It consists of a steel front plate, rear plate and two side plates held together by 60x60x4mm angle welded on its outer surfaces (i.e. so that the inner wall could be kept smooth to allow the free, unobstructed movement of the loading plate against the inner wall and facilitate the subsequent seal between them during the consolidation phase). The tank section and extension section which were initially rigidly bolted together using 15mm grade 8.8 bolts and forming a complete structure, which provided sufficient height to accommodate the unconsolidated clay slurry. Once consolidation had taken place the extension section was no longer required and was removed. The loading plate was used to apply the consolidation pressure to the clay slurry and was designed to withstand a stress of 160kPa (well in excess of the 120kPa stress required during the consolidation process). The loading plate consisted of a 6mm plate reinforced with 40x40x6mm square hollow section and 40x40mm solid steel sections under each jack. The construction details and the locating lugs for each jack can be seen can be seen in Figure 7.2. One of the essential requirements for the loading plate was for it to form a watertight seal with the edge of the tank during the consolidation process. Two different methods were tried, a tubular rubber seal and a high density plastic coated Armourflex foam. The latter was found to be more reliable and was consequently used in the tests (Figure 7.2). The cover plate was bolted on to the tank section once consolidation has occurred (i.e. after previous removal of the top extension section). It serves not only to keep the tank rigid during lifting but also to prevent the clay from drying out.

D.Hunt - 2004


7.2.2

- 214 -

Drainage

Consolidation was achieved by allowing drainage to occur from both the upper and lower surfaces of the sample, 8 taps being fitted to the underside of the bottom tank and 8 to the top of the loading plate. The taps were connected together by 8mm tubing, which was used to convey the water back to the surface of the loading plate with any excess water being transferred to a separate measuring tank. In order to prevent blockages occurring in the taps, Vyon sheet (PSHF030200-Vyon F, supplied by Power Utilities Ltd) was placed over the inside surface of the drainage taps (i.e. in the bottom of the tank and on the under side of the loading plate). A 20mm layer of evenly compacted Leighton Buzzard sand was placed in the bottom of the tank, on top of which a sheet of Vyon covering the full plan area of the tank was placed. The same drainage layer was created above the clay sample i.e. Vyon sheet and 20mm of sand above. The loading plate was then placed on top of this (Figure 7.2).

7.2.3

Reaction Frame

The reaction frame shown in Figure 7.3 was used to consolidate the clay slurry in the tank. The free-standing frame was constructed out of pre-drilled steel channel section, rigidly connected together with 16mm grade 8.8 steel bolts. The frame consisted of two supporting columns, four beams and a reaction plate for the jacks. The weight of the tank was taken by two beams at a centre-to-centre spacing of 300mm. The beams were bolted to the flanges of the column section at both ends. The 300mm gap between the beams allowed unobstructed access to the taps and the monitoring equipment below the tank.

7.2.4

Pressure System

In order to attain the pressures required for consolidation of the slurry, a pressure system was required. Three hydraulic jacks were individually located at the central location of a 600x600mm section of the full plan area in to apply the load evenly. The pressure system needed to be able to supply a pressure for long periods of time during the consolidation process. For this reason a ‘booster’ system was used to convert compressed air power (pneumatic) to hydraulic power. The

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- 215 -

use of compressed air meant that there was no danger of heat build up or fire from electrical sources. It was also the cheapest method with very low energy consumption (Figure 7.3).

7.2.4.1 Pneumatic system

The compressed air was supplied via a mains connection in the laboratory. This mains pressure was supplied by a Plusair SM11 electric compressor (Redhouse Eng. Co.) which can maintain a constant output pressure of 7.5 bar. The compressed air was connected to the power booster via a pneumatic control system as shown in Figures 7.3 and 7.4. The mains input pressure was controlled by a separate tap and monitored via the input air pressure gauge. The output air pressure (i.e. the pressure to the booster) was adjusted by the air pressure regulator and the subsequent input air pressure to the power booster was shown on a separate gauge. In order to protect the booster from pressures in excess of 6-bar a safety valve was fitted. The air pressure entered the power booster via an air filter, which removed particulates and water vapour. A manual pressure release tap was also attached to the pressure regulator system for safety purposes.

7.2.4.2 Pressure booster

Two types of pressure booster were used during the trial. The first to be used was a Spencer Franklin SF-2640 booster with a 54cc oil output capacity (Figure 7.5). The maximum possible oil output (hydraulic) pressure was 40 x the air input (pneumatic) pressure. The maximum capacity of the booster was 320 bar when using an air input pressure of 8 bar. In static tests the booster was found to be more than adequate for applying the magnitude of stress required for consolidating the clay slurry. However, during an initial trial run it was found that the 54cc internal oil capacity of the booster was too small for the requirements of the test. This was noticeable during the consolidation process: as water was squeezed out of the sample, the loading plate and jacks obviously move downwards. During this process the air pressure forces the piston inside the booster upwards and forces more oil into the hydraulic system. The amount of oil that can be forced into the system is dependent on the capacity of the booster. Once all the oil has been forced into the system the taps to each jack had to be closed (in order to maintain the

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pressure on the sample), the air pressure reduced to zero and the oil reservoir topped up. Upon reapplying the air pressure the oil was drawn into the booster, once this was done the taps could be opened up and the same initial pressure reapplied. Thus while this system worked, it needed constant 24hr monitoring of the pressure gauges. This proved physically impossible and hence a new type of booster system was required. For the test programme a HEYPAC GX 30 BSV R2M booster supplied by A1 hydraulics U.K. was used (Figure 7.6). The Heypac pump uses a large area air drive piston connected to a smaller area hydraulic piston to convert compressed air power to hydraulic power (in the same manner as the Spence Franklin booster pump). However, the fundamental difference lies in the reciprocating action of a differential area piston. This does what the Spencer Franklin compressor could not do and constantly draws oil into the system as the jacks move down via the reciprocating action of the piston. This reciprocating action in combination with the additional 5 litre oil reservoir meant that a specified stress could be applied to the sample and maintained as the sample consolidated, thus minimising the amount of intervention required. The booster had a maximum input pressure of 7 bar and a maximum output pressure of 210 bar (i.e. 30x multiplier). The maximum input air flow rate was 7.5l/min with a maximum cycle speed of 500 cycles/min (set to 50-60 cycles/min for these tests). The booster was bolted to the side of the loading frame and was slightly elevated from the base of the jacks in order to aid with bleeding air out of the system.

7.2.4.3 Hydraulic System

The three jacks, which required a stroke length of 500mm, were manufactured specifically for the project by The Fairway Hydraulics Company, Worcester, U.K. The acting diameter on the inside of the piston on the jack was 50mm. In order to minimise the cost of the jacks they were manufactured as single action (i.e. one way), the only drawback being that the oil has to be drained from the system in order to push the jacks back to their starting position. Four hydraulic taps were included in the hydraulic system, as shown in Figure 7.3. One tap was situated next to the booster for isolating the whole hydraulic system and the other three taps were included in order that each of the three jacks could be isolated. An oil pressure gauge was also included in the system (Figure 7.3).

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7.2.5

Speswhite Kaolin

Speswhite Kaolin has been used by many researchers for various types of small scale modelling (e.g. Mair 1979, Love 1984, Kim 1996, Lognathon and Poulos 2000, Poulos et al 2000) and consequently its properties are very well established and importantly its engineering properties are widely known. For this project the Speswhite Kaolin which had been mined by the English China Clay Company in St Austel, Cornwall was supplied by Whitchem Ltd, Newcastle, U.K. The properties of the material, compiled from papers by various authors, are shown in Table 7.1.

Table 7.1 Properties of Speswhite Kaolin clay obtained from various references

PL

MC at Plastic Limit (%)

Clegg (1981) 38

Material Properties

Airey (1984) 38

Elmes (1986) -

Fannin (1986) -

Al Tabaa (1987) -

Phillips (1988) 31

Smith (1993) -

LL

MC at Liquid Limit (%)

69

69

-

-

-

64

-

Gs

Specific gravity

2.61

-

2.61

-

2.64

-

-

γ

Bulk unit weight

-

-

-

-

-

-

-

-

-

0.5 mm2/s

-

-

-

-

-

-

0.82 (comp)

0.88

0.90 (comp) 0.68 (ext)

-

0.80 (comp)

-

-

0.03

0.04

0.03-0.06

3.44

-

2.87

3.51

3.00

-

3.34

0.3100.210

-

0.140

0.250

0.187

0.187

0.174

-

0.69

-

0.64

0.69

-

-

Coefficient of

Cv

consolidation Slope of critical state

M

line (csl) in q’ p’ plane slope of unload

κ

reload line

0.05

Intercept of csl at

Γ

p’=1kPa slope of normal

λ

consolidation line

Konc

Ko for normally consolidated clay

Table 7.2 Properties of Speswhite Kaolin (Imerys Minerals Co, 2003) Mineralogy

%

Feldspar and quartz

1

Montmorillonite

1

Mica

4

Speswhite Kaolin

94

Other Surface area (m2 g-1)

Moisture

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Particle distribution 14.0

1.5%

+ 300 mesh

% 0.02

10 micron

0.5

2 micron

80+/-3

1 micron

-

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Table 7.2 shows details of the Speswhite clay as provided by Imerys Mineral Co. Many researchers have considered the consolidation and strength parameters of Speswhite clay with a wide variation in reported values (Kim, 1996). The study by Al-Tabaa (1987) appears to be the most comprehensive of those found for the U.K.

7.2.6

Consolidation Theory and Soil Strength Calculation

At the start of the physical modelling two types of samples were considered:

•

Heavily over-consolidated (HOC) sample

Without surchage

•

Lightly over-consolidated (LOC) sample

With surcharge

Based on the earlier research of Love (1984) it was expected that the HOC sample (i.e without surcharge) would have an over-consolidation ratio OCR of around 12. Newson et al (2002) reported the shear strength of a Speswhite sample, consolidated at 100kPa, with a final water content of 50-52 % and without a surcharge pressure, to be 12.5 kPa when tested with a Pilcon mini vane. This value is in agreement with that reported by Kim (1996). Use of clay in this state would allow monitoring of the surface settlement profile during tunnelling by the use of LVDTs, dial gauges and marker beads (i.e. the surface would be freely available. The LOC yet stiff clay samples could be achieved by applying a surcharge to the clay. Although these tests were never conducted, they would have required measurement of displacements through the use of marker beads alone. Kim (1996) reported that the OCR should be approximately 3 and the value of su should be around 20 kPa (assuming su 12). As far as the author is aware this is the first time that twin tunnels have been constructed at this scale with measurable displacements reported, Kim (1996) only reported the tunnel lining displacements. The two tests conducted as part of this research are not conclusive and many more tests will be run as part of ongoing research. For these reasons they have not currently been used to improve the available predictive method for twin tunnel constructions. Valuable lessons were learnt about

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producing large-scale consolidated samples using a very successful consolidation process within a tank which performed very well. Several methods for constructing a small scale tunnel were trialled and it was concluded that the simple ‘augering’ method (using a specially designed shield) was the best method for construction. There are many factors which make the modelling of tunnel constructions in clays in the laboratory very difficult. These are addressed and recommendations made as follows: (1) A vibrating rod was used to disperse air from the mix. However, there was still evidence of air entrapment in the samples. The causes of the air entrapment were thought to be due to mixing the clay without a vacuum and subsequently placing it by hand. Any future testing should involve the use of a mixer with a vacuum and slurry pipe for transfer. (2) The whole process of sample preparation was very time consuming and labour intensive. This was mainly due to the size of the tank and the quantities of material preparation required. A larger capacity mixer would be essential for any further testing and would alleviate some of the workload. (3) The trimming of the clay and the removal of the Perspex face meant that the clay was exposed to the air for a ‘short’ period of time. (4) Kim (1996) conducted subsequent tests while applying a surcharge pressure on the surface via a water balloon. However, this meant that the displacements of the clay were not measured. Tests are currently being performed at the University of Birmingham where sub-surface displacements are being measured while applying a surcharge pressure. (5) When measuring sub-surface displacements, the use of marker beads is very time consuming and requires great precision in order to obtain good results. This is even more important when the magnitudes of displacements are small. Any disturbance to the camera will lead to inaccurate measurements. An improved method for measuring displacements within the clay which does not involve the use of marker beads or a camera would be preferable (i.e. nanosensors). (6) The use of high pressure water jets for removing clay from the cutting face (i.e. Type 4) in preliminary trials was shown to be unsuccessful. For its successful application rapid removal of this water is necessary to avoid mixing occurring at the tunnel face. It is difficult to imagine how this was actually achieved in the model described by Kim (1996).

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450mm

450mm

600mm

p

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Removable gate (Front and rear)

Figure 7.1 Consolidation tank details

1800mm

A

A

140mm

Removable ports

Tank section

Extension section

Loading plate

Section A--A

Perspex panel

85mm


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A

A

(Loading plate) 20mm (sand) 1mm (Vyon)

Hi 600mm (clay)

Plan View

Hf

1mm (Vyon) 20mm (sand)

B B

10

15

15

Section A-A C

C

30

30

40

40

40

30

30

Section B-B 15

15

Jack location

•

Armourflex

Drainage tap Pore Pressure Transducer

Section C-C

Total Pressure Transducer

Figure 7.2 Sections of tank showing taps and instrumentation (all dimensions in cm unless otherwise stated). D.Hunt - 2004

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Tap

Pressure gauge

Oil line

Air line

Output air pressure

Pressure regulator

Input air pressure

Pneumatic input (Max 6 bar) via mains

Output oil pressure

Figure 7.3 Hydraulic and pneumatic system for consolidation

Power booster

Oil Tank

Air filter

Pressure release valves

Clay

Hydraulic output (30X input air pressure) via rams


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Chapter 7 - Small scale laboratory modeling of twin tunnels

Figure 7.4 Air pressure control unit

Figure 7.5 Spencer Franklin booster

Figure 7.6 Heypac power booster

Figure 7.7 Jacking system

Figure 7.8 Trial of tunnelling machine in test tank

Figure 7.9 Trial of concrete corer (machine Type 1)

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Figure 7.10 Resulting heave from Type 1 tunnelling machine

Figure 7.11 Dispersion of lubrication on Type 2 tunnelling machine

Figure 7.12 Unsupported tunnel after using Type 2 tunnelling machine

Figure 7.13 Type 3 tunnelling machine

Figure 7.14 Front cutting blade (Type 4)

Figure 7.15 Water jet system (Type 4)

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(c) (a)

(e)

(a) Auger (b) Shield

(b)

(d)

(c) Test tank (d) Guide track

(e) Shield restraint

1

2

3

4

Figure 7.16 Drilling system and procedure

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•

PC1

•

•

00000

00000

•

•

AT2000

•

•

LVDT: 1 -12

PC2

LC1

•

DT615

TPT1

•

•

00000

PPT1-3

•

Figure 7.17 Monitoring Equipment Dial gauges LVDTs

Camera

Image

Guide track

Figure 7.18 Position of camera equipment, LVDTs and dial gauges D.Hunt - 2004

TPT2

•


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Figure 7.19 Bottom tank section (no side walls or top extension section)

Figure 7.20 Instrumentation and Vyon covered drainage holes

Figure 7.21 Layer of Leighton Buzzard sand

Figure 7.22 Layer of Vyon sheet over sand layer

Figure 7.23 Lifting mixed clay into place

Figure 7.24 Tank filled with clay showing top layer of Vyon and sand

________________________________________________________________________________________________________

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Figure 7.25 Day 1 - loading plate and load cell in place (prior to consolidation)

Figure 7.26

Side restraints for Tank

Figure 7.27 Day 23 - After consolidation (water removed from top plate)

Figure 7.28 removed

Figure 7.29 Loading plate removed exposing sand layer

Figure 7.30 Sand removed exposing Vyon sheet

Extension section being

________________________________________________________________________________________________________

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Figure 7.31 Top of clay sample being trimmed

Figure 7.32 Cover plate in place

Figure 7.33 Tank lifted out of reaction frame (prior to turning)

Figure 7.34 Tank turned on side. Side restraints and perspex face removed

Figure 7.35 Marker beads being positioned in clay surface

Figure 7.36 Front face: Tank back in reaction frame. LVDTs and camera track in place.

________________________________________________________________________________________________________

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Figure 7.37 Rear face: dial gauges in place

Figure 7.38 Tunneling machine in position (guide track visible)

Figure 7.39 Prior to drilling first 100mm (Tunnel 2 shown)

Figure 7.40 Tunneling 450mm through clay (spoil removal shown)

Figure 7.41 Tunnel after jacking complete (Tunnel 2 shown)

Figure 7.42 Shear vane testing of clay

________________________________________________________________________________________________________

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80

0

70

60

4

6 50 8 40 10 30 12 20 14

10

16

18

0 0

5

10

15

20

25

Time (Days)

Figure 7.43 Consolidation Results (Test 2) 62 60

Test 1

58

Test 2

Moisture Content W c (%)

56 54 52 50 48

KIM (1996)

46 44 42 40 0

2

4

6

8

10

12

14

16

18

Undrained Shear Strength, Su (kPa)

Figure 7.44 Undrained shear strength and corresponding moisture content

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20

Settlement (cm)

Total and Pore Water Pressures (kPa)

2

Consolidation pressure Pore water pressures Total pressure Settlement


Coordinate for centre of marker

Coordinate for centre of marker

Figure 7.45 Target selection method for monitoring displacements

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D.Hunt - 2004

2

1

800

750

700

650

Figure 7.46 Displacements above Tunnel 1 and Tunnel 2

Sub-surface (150mm) Tunnel 2 after 24 hours

Sub-surface (150mm) Tunnel 1 after 1 hour

Surface Tunnel 2 after 24 hours

Surface Tunnel 1 after 1 hour

Chainage (m) 1500 1450 1400 1350 1300 1250 1200 1150 1100 1050 1000 950 900 850 600

550

500

450

400

350

-2.5

-2

-1.5

-1

-0.5

0

300 0.5


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Displacement (mm)

Chapter 8 - Improving currently available predictive techniques for multiple tunnel constructions

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Chapter Eight IMPROVING CURRENTLY AVAILABLE PREDICTIVE TECHNIQUES FOR MULTIPLE TUNNEL CONSTRUCTIONS

8.1 INTRODUCTION The currently available empirical methods for predicting movements above a single tunnel and twin-tunnels in greenfield conditions have been reported in Chapter 2. The movements above a second tunnel, in close proximity to the first, are currently predicted assuming exactly the same parameter values as the first (i.e the settlement profiles are identical). However, when considering case histories, previous numerical studies (Chapter 2) and the extensive finite element analyses conducted during this current research programme (Chapter 5), significant differences in the predicted profile for the second tunnel when compared to the greenfield profile have been reported. These differences are: 1. Increases /decreases in Umax; 2. Change in position of Umax; 3. Change in position of U=0; 4. Increases/decreases in Wmax; 5. Increase in volume losses for Tunnel 2 ; 6. Eccentricity of Wmax; 7. Asymmetric settlement profile with bigger movements on the near limb compared to the remote limb (V2n >V2r); 8. Greater horizontal movements on the near limb compared to the remote, with maximum values being drawn towards Tunnel 1. The aim of this chapter is to show how these reported differences can be incorporated into the currently available predictive methods through the use of:

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

Parameter selection;



A modification factor.

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The chapter shows how some of the changes to the settlement profile reported above a second tunnel can be achieved through changes to the following parameters: 

Trough width parameter, K (hence i);



Near and remote limb lengths (related to K);



Position of the vector focus for movements;



Volume loss.

The chapter also considers the changes that can be achieved with using a ‘Modification Factor’ for altering the greenfield settlement profile above a second tunnel. The ‘Modification Factor’ modifies the profile in an ‘overlapping zone’ formed by the bounds to movement of each tunnel (assuming that the bounds to movement are unchanged for each tunnel driven). The application of the method is demonstrated through the modification of surface and subsurface movements above twin 4m diameter tunnels at 26m depth with various centre-tocentre spacings. The method is subsequently shown to reproduce the same shape of settlement profile above a second tunnel in a side-by-side alignment as some of the case history data. This chapter demonstrates how the modification method, when used in combination with careful parameter selection, can be used to match case history data for twin tunnels in London Clays with good accuracy (i.e. Nyren, 1998, Cording and Hansmire, 1975, Bartlett and Bubbers, 1970 and Cooper and Chapman, 1998). The reported methods can be easily programmed into a spreadsheet and used for predictions of vertical and horizontal movements for surface and sub-surface regions. The method provides a quick, cheap and reasonably accurate alternative to current finite element analyses for predicting settlements above a second tunnel driven at an early stage in the design process. The chapter proposes a valuable framework for predictive methods for displacement above twin tunnels. Future research combined with more case history data (as it becomes available) can be used to quantify more accurately the parameters involved in these predictive methods and thereby improve them.

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8.2 USING FINITE ELEMENT ANALYSES AND CASE HISTORY DATA TO ESTABLISH A VIABLE IMPROVED METHOD One of the currently available semi-empirical method for the prediction of movements above twin side-by-side tunnels was proposed by New and O’Reilly (1991). They assumed that the settlement profile above a second tunnel should take the same shape and form as that above a first tunnel driven (Section 2.7.2). The proposed improvement to the methods has been achieved by taking into account the role of parameter selection (Chapter 2), the findings from previous research (i.e. case histories and numerical analyses) and the results of this current research (Chapter 5). As far as the author is aware this study is the first to consider a way of incorporating all these findings into an existing predictive method. This chapter shows how the methods can replicate specific changes to the settlement profile (detailed below) occurring above twin tunnels. One important finding from previous research was the role of soil stiffness when considering the movements above single tunnels using finite elements. Addenbrooke (1996), through the results of numerical analyses, suggested that the changes to the settlement profile prediction were the direct cause of changes to soil stiffness. The incorporation of a smallstrain stiffness model led to the improvement of settlement prediction with further improvements found through changes to the value of Ko. Grant (1998) highlighted the importance of soil stiffness when considering the magnitude of the trough width, showing that the trough width (angle of draw) in each layer (sand overlain by clay) was directly related to the stiffness when modelling tunnel movements in a centrifuge. In this research (Chapter 5) the greenfield settlement trough widths were compared with the predicted trough widths in order to determine how they deviate for a second tunnel driven. Any change to the soil stiffness will change the shear strength of the soil, thus affecting the stability number for the soil, which will subsequently alter the volume loss for a second tunnel construction. When considering side-by-side tunnels in close proximity the changes to soil stiffness caused by constructing Tunnel 1 must therefore have an effect on the volume loss for Tunnel 2. Mair and Taylor (1997) stated that when a twin tunnel construction occurs the soil will have been previously strained by Tunnel 1 and bigger volume losses would be expected for Tunnel 2. Increased volume losses have been reported via field data (e.g. Cording and Hansmire, 1976, Perez Saiz et al, 1981 and Lo et al, 1987), and finite element

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analysis results (e.g. Addenbrooke, 1996, Ottavano and Pelli, 1983). This increase in volume loss will also lead to increases in the values of horizontal and vertical displacement for the second tunnel. Initially, prior to any tunnel construction, the stiffness of the soil was assumed to vary linearly with depth and remain constant for any given depth. However, once the construction of a first tunnel has occurred the ground stiffness will have changed, and will no longer be constant for any given depth. When considering twin tunnels, in close proximity, with a construction delay between each, the change in soil stiffness caused by the first tunnel must therefore have an influence on the trough width and displacement profile for the second tunnel. This is confirmed through field data and finite element results where larger increases to the vertical and horizontal displacement occur on the near limb compared to the remote limb of the settlement trough. These increases in displacement were also accompanied by an eccentrically positioned maximum vertical displacement set further towards the first tunnel driven (Chapter 2). The changes to the volume loss and the vertical and horizontal displacement were found to decrease with increased tunnel spacing, and also for sub-surface levels. This then indicates that the changes to the soil must also reduce with increased tunnel spacing and depth. By further inspection of Figure 2.27 shown in Chapter 2, it may be possible to quantify the bounds to this zone of previously strained soil where stiffness changes will have taken place. This zone of previously strained soil must be the region outlined by the overlapping bounds to movement for the first and second tunnels (Figure 8.1). The size of the zone will be dependent on the draw angles (i.e. trough width parameters) for the first and second tunnel, the tunnel spacing and depth. By making this initial assumption on the trough width parameters it is now possible to quantify a region over which changes in soil behaviour would be expected. If it is possible to characterise further the behaviour of the soil in this zone it may be possible to modify the shape of the profile given by the existing empirical model using a modification method. It will be shown later in the chapter that by considering the relative changes in displacement (W2/W1) shown in Figures 5.26, 5.27, 5.28 and 5.29 obtained from the finite element analyses conducted during this study, a possible shape for the modification factor can be defined. Incorporating this factor within the currently available predictive method is described in Section 8.4, where it is used to modify only the movements which occur in the overlapping zone.

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An indication is provided for a method of improving the prediction of movements above piggy-back tunnels based soley on parameter selection. 8.3 PARAMETER SELECTION The initial prediction of the shape of the settlement profile for surface and sub-surface regions in most cases can be assumed to be Gaussian. The values of Wmax, and hence W, are based upon an initial assumption of the volume loss, which in turn is based upon tunnelling method and tunnel depth. Sub-surface values of displacement are then found by assuming no volume change with depth (i.e. each sub-surface settlement profile has the same volume/unit length as the surface profile) and by assuming sub-surface values of i. For single tunnels the position of i is assumed to be equidistant on either side of the tunnel centreline. Wmax is coincident with the tunnel centreline and the position of Umax is coincident with the position of i. By careful consideration of the available equations it soon becomes apparent that some of the reported changes to the settlement profile, which occur above a second tunnel, can be accommodated by small changes to parameter selection. The influence of parameter selection on the settlement profile above as second tunnel are considered in this chapter. The finer details relating to these parameters can be found in Chapter 2. 8.3.1 Trough Width Parameter The full trough width is usually defined as 2.5 to 3.0 multiples of the distance to point of inflection. When considering the movements above a second tunnel it is apparent that the changes to soil stiffness may cause deviations in the angle of draw (i.e. trough width). Figure 8.1 shows possible mechanisms for increases/reductions in trough width (hence i) that could occur on the near limb, remote limb or both limbs above a second tunnel driven. In the empirical model the effect on the displacement profile of changing the trough width parameter is dependent on the volume loss. Figure 8.2 shows the effect on W when changing the values of K from 0.6 to 0.5 and then to 0.4, whilst assuming a constant volume loss. If it is assumed that 1.0Wmax relates to a K value of 0.5, as K is decreased from 0.6 to 0.5 and then to 0.4, Wmax increases from 0.8Wmax to 1.0Wmax and then to 1.2Wmax respectively. This is due to the fact that Wmax has an inverse relationship with K, hence as i decreases both Wmax and W must increase. When increasing K D.Hunt - 2004


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and keeping Vl constant the magnitude of Umax remains unchanged, however the position of Umax changes directly with K. It should be noted that the size of the zone of previously strained soil (shaded in grey in Figure 8.1) will be dependent on the value of K chosen. The effect of increasing the volume loss is described in Section 8.3.2. 8.3.2 Volume Loss Figures 8.3 demonstrates the effect of changing the value of K from 0.4 to 0.6 (Figure 8.1) whilst maintaining a constant value for Wmax. These increases in K cause an increase in the volume loss from 0.8Vl to 1.2Vl (where 0.8Vl refers to a K value of 0.4) and an increase in W along the limb length. For this case the position and magnitude of Umax increase relative to K. Figure 8.4 shows the effect of doubling or halving the volume loss while keeping K and vector focus constant. It can be seen that the magnitudes of W and U are directly dependent on the value of the volume loss, being doubled or halved respectively. 8.3.3 Vector Focus By assuming a position of vector focus (the bottom term in the fraction shown in Equation 2.36) U is directly dependent on the value of W. O’Reilly and New (1982) reported this vector focus to be situated at the exact centre of the tunnel (i.e. at depth Z0, highlighted as position 2 in Figure 8.5). The maximum horizontal displacement, Umax, occurs at the point of inflection, i. Hence, by combining Equation 2.8 and Equation 2.36, Umax can be given in terms of Wmax. When assuming a vector focus at depth Z0, Umax=0.202 Wmax as shown in Figure 8.6. The location of this point of vector focus is an important parameter which directly affects the magnitudes of horizontal displacement. Based on the work of Mair et al (1993) improved predictions for horizontal movements were reported after assuming a vector focus at 0.175Zo/0.325 below the tunnel axis (highlighted as position 3 in Figure 8.5). Using this new point of focus it can be shown that Umax=0.131 Wmax. The magnitude of horizontal displacements predicted by assuming a vector focus at position 3 are lower than those predicted by the vector focus at the tunnel axis (2). Interestingly, if a point of vector focus were now assumed to be located at a depth of 0.5Zo (highlighted as position 1 in Figure 8.5), the magnitude of U would be higher than those predicted at positions 2 and 3, consequently Umax = 0.404 Wmax. The changes in W and U and their corresponding maxima can be seen in Figure 8.6. In conclusion, using a vector focus below or above the tunnel centreline will D.Hunt - 2004


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decrease or increase the horizontal movements above the tunnel respectively. Grant and Taylor (2000) reported that the use of three separate points of vector focus for three distinct sub-surface regions led to improvements in the prediction of U for these regions. The focal points were assumed to be coincident with the intersection of the tangents to i with depth. 8.4 MODIFICATION METHOD 8.4.1 Defining the Method This section details how a more realistic vertical displacement profile can be found by using a modification factor, defined as a result of the finite element analyses which showed that: Irrespective of the tunnel spacing a maximum relative increase in settlement of 60-80% always occurred over the centreline of Tunnel 1 for surface and sub-surface regions and was almost independent of tunnel diameter. These relative increases in settlement found from the finite element analyses could not be applied directly into an empirical model due to the fact that the finite element analyses over predicted the trough widths for surface and sub-surface regions above a single greenfield tunnel. This meant that the zone of soil being disturbed above this tunnel was too large. Consequently, if a second tunnel were to be constructed, in close proximity to the first tunnel, the zone of previously strained soil being drawn from would be too large. This was particularly evident when considering the large tunnel spacing of 120m. The empirical method suggests that there would be no overlap to the bounds to movement at such a wide tunnel spacing and hence there should be no evidence of interaction due to the role of previously strained soil; however these effects were still evident. This necessitated adapting these factors before they could be applied directly to the empirically predicted greenfield settlement curves above a second tunnel driven. In so doing, careful assumptions were made with respect to the shape of the ‘Modification Factor’ and the region over which it should be applied (Figure 8.7). As a first approximation the region for application of the factor is defined by assuming: 1. The same bounds to movement for Tunnel 2 as Tunnel 1; 2. The same initial vertical displacement profile for Tunnel 2 as Tunnel 1; D.Hunt - 2004


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3. The increases in settlement above Tunnel 2 only occur in the ‘overlapping zone’, defined by the overlap of the bounds to movement for each tunnel. There are no changes in settlement outside the overlapping zone, i.e. the settlement profile is unchanged. Assumption 1 states that the bounds to movement (i.e. the trough width or draw angle) are unchanged, whereas there is evidence from the the finite element analyses that deviations in draw angle may occur. Due to the fact that quantification of these changes cannot be made at this stage, an initial assumption is made that they remain unchanged. Deviations in trough width are highly likely for a second tunnel driven, and could be implemented into the method easily. More case history data are required to quantify the effect. As mentioned in assumption 3, the increases in vertical displacement above Tunnel 2 are incorporated into the predictive model by the application of a modification factor in an overlapping zone of the bounds to movement. The size of this zone, and hence the effect on the settlement profile, decreases for sub-surface regions and increased tunnel spacing which is consistent with case history data and finite element results conducted during this study and by Addenbrooke (1996). This modification factor assumes that: 1. The maximum relative increase in settlement (M) occurs above the centreline of Tunnel 1 and reduces linearly with distance from this maximum to a value of zero at the bounds to movement for Tunnel 1. 2. There are no relative decreases in settlement assumed for Tunnel 2. The M factor described in (1) is based on the results of the finite element analyses (Figures 5.26, 5.27, 5.28 and 5.29) and for simplicity the influencing function above Tunnel 1 is assumed to vary linearly and to be symmetrical. Intuitively the changes to soil stiffness occurring above Tunnel 1 will also be symmetrical, having a maximum above the centreline and remaining unchanged at the outer extent of the trough. Although, its variation is more likely to be non-linear than suggested above, the linear relationship is simpler to apply at this stage. A non-linear function could easily be applied in future if necessary. The second assumption states that no relative decreases in settlement were assumed above Tunnel 2, even though these reductions in displacement were reported for the finite element analyses found in Chapter 5 (Figures 5.26, 5.27, 5.28 and 5.29). This is due to the fact that these reductions in displacement were occurring to very small displacements. These D.Hunt - 2004


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reductions in relative displacements were found to be more apparent when the volume losses for each tunnel remained unchanged and found to be less significant when the volume loss above the second tunnel was increased. 8.4.2 Surface Settlement Figure 8.7 shows the mathematical interpretation of the ‘Modification Factor’ function. The ‘Modification Factor’ for the settlements above Tunnel 2 (showing the influence of Tunnel 1) and the zone in which it is applied are shown. The influence of the changes to soil stiffness on the displacement profile above Tunnel 2 are directly related to the amount of modification applied. The maximum value of modification (M) could lie anywhere between 60% and 150% (Figures 5.26, 5.27, 5.28 and 5.29) depending on the change in volume loss for Tunnel 2. The equation for the modified settlement above a second tunnel is shown in Equation 8.1:

W

where Wmod =

   d ' x     W ( x)  1   M 1    Ai      

mod

max

 x2 exp   2  2i

  

Eqn 8.1

Settlement at distance x from the centreline of Tunnel 2 (mm)

Wmax =

Maximum settlement above centreline of Tunnel 1 (mm)

M

=

Maximum modification (e.g. 60% = 0.6)

d'

=

Centre-to-centre spacing of tunnels (m)

i

=

Trough width parameter (m)

A

=

Multiple of (i) for full trough width ( typically 2.5 or 3.0)

The value of M is based on the finite element results and is assumed to be the same magnitude for surface regions whatever the centre-to-centre spacing of the tunnels. The effect of increasing the centre-to-centre spacing reduces the size of the overlapping zone and hence reduces the size of the settlement profile which is modified, i.e. its influence decreases (Section 8.5.). The term Wmax exp(-x2/2i2) could be substituted for any expression relating to settlement profile shape, such as the ribbon sink predictive method reported by New and Bowers (1994). The term i, although defined by Equation 2.31 in the latter examples, can be defined by alternative predictive methods such as those found in Section 2.4 and 2.5. D.Hunt - 2004


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8.4.3 Sub-Surface Settlements The effects of previously strained soil were found to decrease with depth according to the Finite Element results reported in Section 5.3.3. The surface settlements above a second tunnel were found to have large increases in the maximum settlement combined with an eccentricity towards Tunnel 1. These increases in maximum settlement were found to decrease with increasing depth, accompanied by less eccentricity. At regions close to the tunnel the maximum settlements were almost the same as the greenfield predictions. The proposed method is good at replicating these types of sub-surface movements. Figure 8.7 shows how the overlapping zone decreases with depth due to the decrease in trough width that occurs. Intuitively, this indicates that the region of modification (due to the role of previous strained soil) as is the influence reduced with depth, as is the influence on the settlements above Tunnel 2. The sub-surface settlements can be found in exactly the same way as the surface settlements by modifying Equation 8.1 as shown in Equation 8.2.

W

Where Z*

   d ' x     W ( x)  1   M 1     AKZ *    

mod

max

 x2 exp   2  2 ( K Z *)

  

Eqn 8.2

= (Zo – Z), i.e. the distance from the tunnel axis to the sub-surface level of interest (m)

Wmax = Maximum settlement calculated for the sub-surface region (mm) K

= Sub-surface trough width parameter

The results of the finite element analyses have shown M to be relatively independent of depth, hence its value for all sub-surface movements is taken as the surface value. K is the sub-surface value of the trough width parameter and can be calculated according to the equations proposed by Mair at al (1993) and shown in Equation 2.31. The bounds to movement have been calculated assuming a full trough width of 3.0i for all sub-surface regions. The bounds to movement for both tunnels can be predicted by alternative methods such as the one proposed by Heath and West (1996) using Equation 2.35 or any method which includes a relationship between the trough width parameter (i) and the depth (Z). These D.Hunt - 2004


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relationships can be substituted directly into Equation 8.2. Typically the surface settlements will be the same whatever method is used; the main differences would occur in the prediction of movements for the sub-surface regions. 8.4.4 Changes to Trough Width Parameter, K Cording and Hansmire (1975) suggested that the trough width could possibly increase for the second tunnel on the side nearest to the first tunnel driven. Cooper and Chapman (2002) provided methods of estimating the relative increases in trough width based on an increase in the volume of the near limb, V2n, relative to the remote limb, V2r. A trend line for the ratio of V2r/V2n was given for varying tunnel spacing. The volume and hence the half trough width of the near limb were assumed to be greater than that for the remote limb, i.e. Kn > Kr. Changes to K have been noted in Section 2.4. When considering the settlements above a second tunnel, any increases made to the trough width while keeping Wmax constant would achieve an increase in the total volume per unit length of the settlement profile, and hence would assume an increase in volume loss. However, the changes in trough width alone do not account for the increases in Wmax that occur, or its eccentric placement towards Tunnel 1 (see Section 8.5.3). Similar patterns of V2r/V2n could be found by using Equation 8.1 when assuming no changes to K (i.e. Kn = Kr). If the changes in K could be exactly quantified their inclusion into Equation 8.2 could easily be facilitated by assuming different values of K when considering movements on the near and remote limbs as shown in Equation 8.3:

  x2  W  Wmax exp   2   2 (K 2 Z*) 

Eqn 8.3

where K2 represents the value of K for Tunnel 2 with separate values being used for Kn and Kr. Figure 5.34 shows typical values of i/ig (near and remote) found from the finite element analyses, which could in theory be used to find values of Kn and Kr for the surface and subsurface depths when assuming the relationship i=K2(Zo – Z).

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8.4.5 Changes in U Cording and Hansmire (1975), Addenbrooke (1996) and Chapman and Cooper (2002) have all reported higher horizontal displacements on the near limb compared to the remote limb. As far as the author is aware no methods are currently available for predicting these horizontal movements. One would expect that if improvements could be made to the prediction of W, such as that given by Equation 8.3 (whilst assuming the relationship given by Equation 2.36 for the horizontal movements to be still valid) it should be possible to improve the predictions of U. As far as the author is aware little attention has also been given to changes in the position of the vector focus for a second tunnel driven. The depth of the vector focus (Zf) has been highlighted in Section 8.3.3 as being a significant influence on the magnitude of U. By considering field data reported by Cording and Hansmire (1975) (Section 4) and the results of the finite element analyses, it may be possible to identify changes in horizontal position of U=0. This change in position can be incorporated into an empirical model by offsetting the horizontal coordinate of the vector focus (Xf) from its position on the centreline of Tunnel 2. Figure 8.8 shows the possible horizontal shift (Xf) in the position of the vector focus. It must be noted that xf is now used instead of x, where xf is the horizontal distance from the point of vector focus Xf. The effect of offsetting the vector focus, while keeping the depth constant (Zf =1 + 0.175/0.325 Zo), is seen in Figure 8.9. By offsetting the focal point on the left hand side of the tunnel the profile above the tunnel is changed considerably. The magnitude of the displacement on the left side of the tunnel is decreased and the distance to the point of Umax is increased. On the right side the magnitude of the displacement is increased with the distance to the point of Umax being decreased. The effect of increasing this offset further increases these effects. In conclusion a modified equation for prediction of horizontal displacements for movements above a second tunnel could look something like Equation 8.4.

W x U( x )   mod f  Zf

where

Wmod xf

  

= the modified settlement above Tunnel 2 (Equation 8.2); = the horizontal distance from vector focus at coordinate (Xf, Zf), Zf; and Xf have been previously defined

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Eqn 8.4


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8.5 APPLICATION OF THE METHOD TO TYPICAL EXAMPLES 8.5.1 Surface Settlements Equations 8.2 and 8.4 are used in this section to predict movements above twin 4.0m diameter tunnels situated at 26m below ground level with the tunnel spacing varying from 10m to 50m. The bounds to movement for each tunnel were found from the equations proposed by Mair et al (1993) with a volume loss of 1.3% assumed for Tunnel 1 (this value being typical of the losses found in London Clays using conventional mining methods). These tunnel dimensions and spacings were consistent with those used for the finite element analyses undertaken in this research project, allowing direct comparisons between the general behaviour. The settlements are shown using a maximum modification factor (M) of 0.6, 1.0 and 1.5 (i.e. 60%, 100% and 150% respectively). Figure 8.10 shows the surface settlement profiles for tunnels at a spacing of 10m. The graph shows the greenfield settlements for the first tunnel driven (1) and the second tunnel driven (2). The corresponding modification factors are shown for the overlapping regions indicating where the settlements have been modified. The unmodified greenfield settlement is 5.2mm. Including a maximum modification factor (M) of 0.6 for the settlement over Tunnel 2 increases the maximum settlement to 7.6mm and places it eccentrically 1.7m towards Tunnel 1. Increasing the modification factor to 1.0 and 1.5 increases both the offset and value of the maximum settlement in each case. Figure 8.11 shows the settlement at a spacing of 20m. The region over which the modification is applied has decreased and the magnitudes of the settlement over which they will be applied are smaller than those at a spacing of 10m. When taking a value of M to be 0.6 the maximum settlement is 6.8mm, less than the value at 10m spacing. The settlement is eccentrically placed 1.9mm towards Tunnel 1, which is 2mm more than the offset found for the 10m tunnel spacing. Increasing the tunnel separation to 30m increases the eccentricity to 2.2mm (Figure 8.12). For a spacing of 40m, the region for modification decreases and the magnitude of the settlements to be modified reduces (Figure 8.13). The general decrease in eccentricity (e) of Wmax, normalised by the spacing (d') can be seen in Figure 8.14. Field data points from the Heathrow Express tunnels (U.K.) reported by Cooper and Chapman (1998) involving two tunnels driven at different spacing from an existing tunnel are also shown on Figure 8.14. Field data reported by Bartlett and Bubbers

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(1970) for the second of twin tunnels driven on the Victoria lines, UK) have also been plotted on the graph. It should be noted that for this data point the value of e was obtained by assuming a Gaussian curve for displacements above Tunnel 2. Finite element data reported as part of the current research show similar behaviour to the field data. The x-axis shows tunnel separation normalised with respect to the distance to Umax. This has been done to account for the differences in behaviour between the finite element analyses and the empirical methods (the finite element analyses predicted a much greater distance to Umax compared to the field data or empirical methods). As far as the author is aware the inclusion of an eccentrically placed maximum settlement into an empirical method has not been included in any previous predictive method. The decrease in eccentricity is well predicted by the proposed method and reaches zero with a tunnel spacing of 40m (or a separation of around 3i) as shown in Figure 8.14. The predictive method also matches the general behaviour indicated by finite element analyses. 8.5.2 Horizontal Movements Figure 8.15 shows the greenfield and three modified horizontal displacements for a 4.0m diameter tunnel at centre-to-centre spacing of 20m determined using Equation 8.4. The values of Wmod are the same as those shown in Figure 8.12 predicted using Equation 8.2 assuming M values of 0.6, 1.0 and 1.5. The vector focus for the movements was assumed to be at 0.175Zo/0.325 below the tunnel axis and on the centreline of Tunnel 2. The maximum unmodified horizontal displacement is 1.0mm and positioned at 12.5 m from the centreline of Tunnel 2. By using Wmod relating to an M value of 0.6, the displacement on the near limb is increased to1.5mm and positioned 0.9m away from the greenfield maximum towards Tunnel 1. The remote limb shows a smaller increase in settlement from 1.0 to 1.1mm again with an offset of 1.0m towards Tunnel 1. The value of Umax is further increased and offset towards Tunnel 1 when using, an increased value of M to predict Wmod. 8.5.3 Volume Loss The volume loss for the modification method is controlled by the modification factor. Figure 8.16 shows how the volume loss for the second tunnel (V2) expressed as a ratio of the volume loss into the first tunnel (V1) varies with increasing tunnel spacing. When using an M

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factor of 0.6 and a tunnel spacing of 10m, the volume loss into the second tunnel is increased by a ratio of 1.4 compared to the first. An increase in M to 1.0 and 1.5 at this spacing increases the ratio to 1.7 and 2.0 respectively. Whatever M factor is used the general trend is for the volume loss to decrease with increasing tunnel spacing with no relative increases in volume loss at a tunnel separation equal to the full trough width (i.e 2Ai). The line created using an M factor of 0.6 shows a close correlation with the finite element data reported by Addenbrooke (1996). The data refer to twin 4.0m diameter tunnels driven at 34m depth in London Clay. The increased volume loss produced by modifying the greenfield settlements are distributed unevenly either side of the centreline of Tunnel 2, i.e. the value of V2r/V2n (where the symbols refer to the volumes of the near and remote limbs respectively) are no longer equal to 1.0 which is the case for the greenfield profile (Figure 8.17). For all spacings the remote limb appears to have a smaller volume than the near limb. The figure shows changes to the V2r/V2n ratio when considering changes to the tunnel spacing when using different values of M. The ratio is lowest when d'/Zo is approximately 1 for all values of M. At a tunnel spacing of d'/Zo=3 (i.e. d'=6i) the ratio can be seen to increase to 1.0. (i.e. the volumes of the near and remote limb are identical). At smaller spacings (i.e. d'/Zo 12) under gravity alone. The results obtained from the two tests conducted as part of this research have provided an invaluable insight into the inherent complexities of modelling at small scale within a laboratory when using Speswhite clay. At this time the results could not be used to improve the predictive method for twin tunnel constructions. 9.4 IMPROVING CURRENTLY AVAILABLE PREDICTIVE TECHNIQUES FOR MULTIPLE TUNNEL CONSTRUCTIONS Chapter 8 showed how the changes to the displacements (both vertical and horizontal), which were seen in Chapter 5 above a second tunnel, could be incorporated into an empirical model. The chapter showed how many of the changes to the settlement profile occurring above a second tunnel could be achieved through careful parameter selection alone and how the changes to the distribution of W and the eccentricity of Wmax could be achieved through the use of a Modification Factor:

W

   d ' x     W ( x)   1   M  1     AKZ *    

mod

max

 x2 exp   2  2 ( K Z *)

  

The Modification Factor appeared to give results that were consistent with both field data and finite element data when using a value of M of 0.6 and assuming the bounds to movement above a second tunnel to be unchanged. The method picked up general trends in behaviour for surface and sub-surface regions (i.e. changes in W, U, V2/V1, V2r/V2n, and e) for increased centre-to-centre spacing. While the method uses Equation 2.8 and hence has a dependency on K, due to the simplicity of the assumptions involved it can be easily adapted to any empirical predictive method.

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Chapter 9 – Conclusions

This chapter has shown how the best matches to case history data can be found when using the Modification Factor in conjunction with carefully selected parameters. The chapter has set in place a framework which incorporates an innovative method for predicting both the vertical and horizontal displacements above a second tunnel in a side-by-side alignment. The method can cautiously be extended to include a third tunnel in a side-by-side alignment or a second tunnel in an offset alignment. While possible explanations were given for the case of piggyback tunnels, further work is required to validate these claims. A flow chart showing how the method can be incorporated into current predictions is presented in Figures 8.26, 8.27 and 8.28. Further case history data are required in order to quantify more precisely the parameters involved (particularly the role of K for near and remote limbs) and hence improve the proposed predictive method. The current method has been developed into a spreadsheet for tunnel displacement prediction of multiple tunnels and if adopted as a method for prediction could easily be adopted into software packages such as TUNSET. 9.5 FUTURE RESEARCH This research has highlighted many potential areas for future research when considering multiple tunnels, which are as follows: 

The current research considered two-dimensional (2D) modelling for the twin tunnels only although a three dimensional (3D) mesh, based upon the 2D mesh, was set up (Figure 9.1). However due to the amount of elements and the lack of computational resources at the time it could not be used. Future research should implement this 3D model for direct comparison with the results obtained during this research. The author is aware that 3D finite element modelling of twin tunnels is due (circa 2004) to be conducted at The University of Dundee.



It would be interesting to find out what stiffness changes actually occur in the ground above a single tunnel driven and subsequently a second tunnel. These changes in stiffness will be different for regions where there is vertical extension to regions in which there is compression. These zones will undoubtedly affect the volume loss and the profile shape for a second tunnel in different ways. This behaviour could be modelled in the laboratory using a Triaxial cell. D.Hunt - 2004

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

Based on the proposed work above it could subsequently be possible to improve the currently existing constitutive soil model for London clay.



The physical model conducted as part of this study will now be considering increased stress levels through use of a water bag. True stress behaviour, however will only be achieved by conducting a twin tunnel test in a centrifuge.



This research has focused on the behaviour of clays for both the numerical work and the laboratory work. Future research work could consider the use of sands for both types of work.



The best way to improve understanding and hence prediction of the displacements above twin tunnels is from good quality case history data. Therefore it is necessary to monitor extensively any new tunnel construction for both horizontal and vertical displacements.



Further improvement to the modification factor, such as the use of a non-linear function rather than the current linear function, are now required. Initial trials using non-linear methods are currently showing improvements to the shape of the settlement curve, especially in regions close the edges of the modified zone.

Based on these recommendations it would be possible to improve the modification method reported in this thesis further and provide a more accurate value for the parameters contained therein.

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Figure 9.1 Three dimensional mesh constructed within ABAQUS

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References

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Predicting the movements

Predicting the movements

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