The influence of bored piles on existing tunnels

Transcription

1 The influence of bored piles on existing tunnels A thesis submitted to the University of London for the degree of Doctor of Philosophy and for the Diploma of the Imperial College of Science, Technology and Medicine By Felix Christian Schroeder Department of Civil and Environmental Engineering Imperial College of Science, Technology and Medicine London, SW7 2BU November 2002

2 2 Abstract In the urban environment, deep foundations are often constructed in locations very close to existing tunnels. Many tunnels can often only tolerate minimal movements. Tunnel owners are concerned that the process of bored pile construction and/or the subsequent loading of the piles may cause intolerable movements or stress levels that might cause cracking of the tunnel linings. Over the last thirty years tunnel owners have developed restrictive guidelines based on their experience of the problem. This thesis investigates the influence of bored piles on existing tunnels using the finite element method and field measurements. In this thesis the finite element method was used to analyse the effects of bored pile construction and pile loading on existing tunnels in two separate analyses. The numerical results were supplemented with field measurement of the pile-tunnel interaction problem at a site in central London. It is shown that in order to adequately model the influence of bored pile construction on a nearby tunnel three dimensional analyses are required. Based on three dimensional analyses of the loading of rows of piles a plane strain approach is developed for the analyses of the influence of pile loading on existing tunnels. A general shell element for use in three dimensional finite element analyses has been developed from basic principals. The development, implementation and testing of this new element type in the Imperial College Finite Element Program (ICFEP) element library is presented and the element is then used to analyse the effects of a dry excavation of a pile bore in the close vicinity of an existing tunnel. The research presented in this thesis has led to a significantly improved understanding of the pile-tunnel interaction problem. It has been shown that there are many influential factors in the assessment of the influence of pile loading on nearby tunnels and that due to the number of influential factors it is not possible to produce simple design charts that are universally applicable. Therefore, it is concluded that universal guidelines based on just a single parameter, such as the specification of the minimum pile offset developed by the tunnel owners, are necessarily conservative with regards to pile loading and that job specific assessments of the influence of pile loading on adjacent tunnels may lead to economies in the design of building foundations.

3 3 Acknowledgements First and foremost I would like to thank my two supervisors Trevor Addenbrooke and Dave Potts for their tireless support, interest and enthusiasm for my research. Without their guidance, encouragement and assistance throughout this project I would not have been able to produce the thesis in its present form. The research presented in this thesis was funded by The Engineering and Physical Science Research Council (EPSRC), The Institution of Civil Engineers and The Department of Civil and Environmental Engineering at Imperial College. London Underground Limited (LUL) and the Geotechnical Consulting Group (GCG) were industrial collaborators in the research project. The funding and collaboration of all parties is gratefully acknowledged. Particular thanks are due to Ivan Chudleigh and Jon Austin of LUL and Kelvin Higgins, Nesha Kovačević, Hugh St John and Tony Bracegridle of GCG. All members of the academic staff in the Soil Mechanics Section have contributed to my work through suggestions at colloquia or at the tea table. I would like to thank them for this support. Special thanks are due to Lidija Zdravković for introducing me to the finer details of ICFEP in the early stages of my research and always having an open ear for any problem I might have encountered in my work. I believe no research can be completed without having the support of friends and colleagues in a research group. Being part of the Soil Mechanics research group was a great pleasure and indeed privilege. During my rather prolonged membership of the group I have met many colleagues and made many friends, too numerous to name. I would however like to mention Angeliki, Kostis, Niki, Reinaldo and Stuart who have become great friends hopefully for the rest of my life. Finally, I would like to thank my parents, my brother and my grandma for supporting me and giving me the confidence to complete the initially daunting task of a PhD thesis.

4 Contents 1 Introduction General Scope Layout Tunnels, bored piles and their interaction Tunnels Introduction Ground response to tunnel construction Modelling tunnel construction Short-term settlement behaviour Time dependent ground behaviour Typical grey cast iron tunnel lining capacities Lining response Summary Bored piles Introduction Pile construction Pile Loading Pile-tunnel interaction Introduction The influence of tunnel construction on existing piles

5 CONTENTS The influence of pile construction and loading on existing tunnels Restrictions commonly imposed by tunnel owners Comments The Finite Element Method Introduction Governing equations for geotechnical problems Formulation of the finite element method Element discretisation Primary variable approximation Element equations Global equations Boundary conditions Solution of global equations Calculation of secondary unknowns Geotechnical considerations Initial stress conditions Undrained analyses Excavation Construction Pore pressure boundary conditions Tied degrees of freedom Constitutive soil models Pre-yield models Mohr-Coulomb yield surface Permeability models Modelling segmental tunnel linings Pre- and Post-Processing

6 6 CONTENTS 4 Shell Elements Introduction Differential geometry of surfaces First fundamental form Normal to a surface Second fundamental form Principal curvature A right handed orthogonal coordinate system Fundamental shell element equations Strain-displacement relations Finite element implementation Force-strain relations Drilling degrees of freedom Selectively reduced integration, SRI Sign conventions The element In-plane strains Bending strains Transverse shear strains Verification Plates Shells Tunnels Summary and recommendations Field measurements at the Effra site Introduction EFFRA Introduction

7 CONTENTS Site Geometry Construction sequence Ground conditions Instrumentation Vibration Wire Strain Gauges Electrolevels Rod Extensometers Results The influence of pile construction on existing tunnels The influence of pile loading on existing tunnels Conclusions and recommendations Finite element analyses of the Effra site Introduction Axially symmetric analyses Introduction Analysis details Analysis results Summary Plane strain analyses Introduction Analysis details Analysis results Summary Conclusions The influence of pile construction on tunnels Introduction Analysis details Stratigraphy

8 8 CONTENTS Initial conditions Boundary conditions Constitutive models Modelling sequence Analysis results Summary and Conclusions The influence of pile loading on tunnels Introduction Justification of a 2-D plane strain approximation Introduction Analysis details Analysis results Conclusions Pile rows located on both sides of a tunnel Introduction Analysis details Results from a reference case Results from a parametric study Results from the analyses of a 15 storey building Conclusions Pile rows located on one side of a tunnel Introduction Analysis details Results from a reference case Results from a parametric study Conclusions The use of slip coatings as mitigating measure Introduction

9 CONTENTS Analysis details Analysis results Conclusions Conclusions and recommendations Conclusions and recommendations Introduction Analysing pile-tunnel interaction problems Shell elements for use in three dimensional finite element analyses The influence of pile construction on existing tunnels The influence of pile loading on existing tunnels Lessons learned from the field instrumentation Recommendations for further research References 431 A An anisotropic model for shell elements 443 B Radial heat conduction from a new pile 445 B.1 Governing equation for radial heat conduction B.2 Parameter determination for London Clay B.3 The finite difference scheme C Material parameters 449 C.1 Linear elastic parameters C.2 Non-linear elastic equations and parameters C.3 Mohr-Coulomb yield surface and plastic potential parameters C.4 Non-linear permeability equation and parameters D Working load calculation 455 E Interface elements used to model slip coatings 459

10 List of Figures 2.1 Sources of volume loss (example of a conventional shield tunnelling machine (Figure 2.4 of Potts & Zdravković (2001)) The gap method (Figure 2.9 of Potts & Zdravković (2001)) The convergence-confinement method (Figure 2.10 of Potts & Zdravković (2001)) The progressive softening method (Figure 2.11 of Potts & Zdravković (2001)) The effect of different pre-yield models on the predicted surface settlement trough (after Figure 2.28 of Potts & Zdravković (2001)) The effect of an anisotropic non-linear pre-yield model on the predicted surface settlement trough (after Figure 2.31 of Potts & Zdravković (2001)) The effect of kinematic hardening models on the predicted surface settlement trough (Figure 7 of Grammatikopoulou et al. (2002)) Local zone of reduced K 0 (Figure 2.29 of Potts & Zdravković (2001)) The effect of a zone of reduced K 0 on the predicted surface settlement trough (Figure 2.30 of Potts & Zdravković (2001)) Geometric layout and parameters used in the GCG parametric study (Figure 2.22 of Potts & Zdravković (2001)) The effect of tunnel lining permeability of a 25 m deep station tunnel on time dependent maximum surface settlement (Figure 2.25 of Potts & Zdravković (2001)) The effect of the pore water pressure profile on time dependent maximum surface settlement for permeable tunnels at a depth of 25 m (Figure 2.23 of Potts & Zdravković (2001)) The effect of a non-linear permeability model on the long-term pore water pressure profile above a tunnel (Figure 2.21 of Potts & Zdravković (2001)) The effect of different permeability models on the consolidation settlement profiles (Figure 4.52 of Addenbrooke (1996))

11 LIST OF FIGURES The effect of using of zone of reduced K 0 on the consolidation settlement profiles (Figure 4.53a of Addenbrooke (1996)) Typical stress-strain response of a grey cast iron Grade 150 test bar during a tensile test (after Figure 9 of Casting Development Centre (1997)) Circumferential force-moment of resistance interaction diagram for a typical cast iron running tunnel lining found on the LUL tunnel network Circumferential force - moment of resistance interaction diagram for a typical cast iron station tunnel lining found on the LUL tunnel network short-term lining load in segmental tunnel linings in London Clay (after Figure 58 of Mair & Taylor (1997)) long-term measurements of lining loads in a Jubilee Line tunnel underneath Regent s Park (after Figure 4 of Barratt et al. (1994)) Pressure envelope for the design of structural formwork (after Figure 3 of Clear & Harrison (1985)) Lateral concrete pressures against depth in steel cylinder (after Figures 8.5 & 8.6 of Bernal & Reese (1983)) Development of lateral concrete pressures with time (from Appendix D of Bernal & Reese (1983)) Comparison of measured and predicted concrete pressures for diaphragm walls (after Figure 2 of Ng (1993)) Predicted critical depth from CIRIA report for diaphragm walls (Figure 13 of Lings et al. (1994)) Total stress changes during contiguous bored pile wall installation (Figure 1 of Symons & Carder (1993)) Total stress distribution before and after contiguous bored pile wall installation (Figure 2 of Symons & Carder (1993)) Coefficient of permeability of cement paste (0.7 water/cement ratio) as a function of time (Figure 5 of Clayton & Milititsky (1983)) Pore pressures in fresh concrete as measured in cylindrical samples under isotropic confining pressure (Figure 6 of Clayton & Milititsky (1983)) The variation of K 0 with depth for London Clay extending to the surface (after Figure 4 of Burland (1973)) Pile movements and corresponding vertical displacement of the soil due to pile loading (after Figure 14 of Cooke et al. (1979) and Figure 6a of Cooke et al. (1980)) The extent of the Shell Centre basement excavation with respect to Bakerloo Line tunnels (after Figure 1 of Ward (1961))

12 12 LIST OF FIGURES 2.33 Cross section (A-A on Figure 2.32) of the Shell Centre showing the underreamed piles next to the Bakerloo Line tunnels (after Figure 4 of Measor & Williams (1962)) Foundation layout of Lee House and Air Rights Building with respect to 2 B.T. tunnels (Figure 3 of Benton & Phillips (1991)) Cross section 1-1 from Figure 2.34 (Figure 4 of Benton & Phillips (1991)) Foundation layout of the site development at 88 Wood Street with respect to the underlying tunnels (Figure 2 of Chapman et al. (2001)) Schematic representation of a section of the foundations of the site development at 88 Wood Street (Figure 3 of Chapman et al. (2001)) node isoparametric quadrilateral element (Figure 2.11 of Potts & Zdravković (1999)) Modified Newton-Raphson method for the solution of non-linear equations Accelerated Newton-Raphson method for the solution of non-linear equations Sub-stepping stress point algorithm (after Figure 2.3 of Kovačević (1994)) Tunnel excavation Special pore pressure boundary condition for the modelling of tunnel construction (after Figure of Potts & Zdravković (1999)) Typical London Clay unconsolidated undrained test data: (a) initial stressstrain behaviour; (b) stiffness-strain characteristics (Figure 3 of Mair (1993)) Trigonometric nature of pre-yield model (Figure 3.7 of Addenbrooke (1996)) Mohr-Coulomb failure criterion (Figure 3.11 of Addenbrooke (1996)) Modelling segmental tunnel linings using small shell elements (Figure 2.16 of Potts & Zdravković (2001)) A model for tunnel lining joints (after Figure 2.17 of Potts & Zdravković (2001)) a) Unrolled and b) rolled tunnel linings (Figure 2.18 of Potts & Zdravković (2001)) Shells; differential geometry Transformation of coordinates from parametric lines to lines of maximum and minimum curvature Definition of local displacements and rotations of the tangents to the reference surface

13 LIST OF FIGURES Transverse shear strain Sign convention for rotational degrees of freedom Checking for co-planar shell elements Direction of element normal Sign convention for the in-plane shear strain, γ Sign convention for bending strains, κ 1 and κ Sign convention for twisting strain, κ Sign convention for transverse shear strains, γ 1n and γ 2n Square plate (E = ; ν = 0.3) Performance of plate elements with varying L/t ratios; uniformly distributed load on square plate with simply supported edges and 4x4 mesh on one quarter Performance of plate elements with varying L/t ratios; uniformly distributed load on square plate with fully fixed edges and 4x4 mesh on one quarter Performance of a) quadratic serendipity (QS) and b) Lagrangian (QL) elements with varying L/t ratios, uniform load on a square plate with 4x4 normal subdivisions in a quarter (Figure 2.3 of Zienkiewicz & Taylor (1991)) Convergence of plate element results to theoretical solutions with varying L/t ratios; uniformly distributed load on square plate with simply supported edges Convergence of plate element results to theoretical solutions with varying L/t ratios; uniformly distributed load on square plate with fully fixed edges Comparison of ICFEP results with results published by Liu et al. (2000); uniformly distributed load on square plate with simply supported edges and L/t = Comparison of ICFEP results with results published by Liu et al. (2000); uniformly distributed load on square plate with fully fixed edges and L/t = Comparison of ICFEP results with results published by Wanji & Cheung (2001); uniformly distributed load on square plate with simply supported edges and L/t = Comparison of ICFEP results with results published by Wanji & Cheung (2001); uniformly distributed load on square plate with fully fixed edges and L/t = Comparison of ICFEP results with results published by Liu et al. (2000); uniformly distributed load on square plate with simply supported edges and L/t =

14 14 LIST OF FIGURES 4.23 Comparison of ICFEP results with results published by Liu et al. (2000); uniformly distributed load on square plate with fully fixed edges and L/t = Convergence of plate element results to theoretical solution with varying L/t ratios; central point load on square plate with simply supported edges Convergence of plate element results to theoretical solution with varying L/t ratios; central point load on square plate with fully fixed edges Comparison of ICFEP results with results published by Liu et al. (2000); central point load on square plate with simply supported edges and L/t = Comparison of ICFEP results with results published by Liu et al. (2000); central point load on square plate with fully fixed edges and L/t = Scordelis-Lo roof (R = 25; L = 50; thickness = 0.25; E = ; ν = 0) Convergence of 8-node shell element results to published solution for Scordelis- Lo roof problem Comparison of ICFEP results with results published by Liu et al. (2000), MacNeal & Harder (1985) and Belytschko et al. (1985) for the Scordelis-Lo roof problem Predictions of F 1 plotted against y-coordinate for 3x3 and 7x7 meshes; reduced integration Predictions of F 2 plotted against y-coordinate for 3x3 and 7x7 meshes; reduced integration Predictions of F 12 plotted against y-coordinate for 3x3 and 7x7 meshes; reduced integration Predictions of M 1 plotted against y-coordinate for 3x3 and 7x7 meshes; reduced integration Predictions of M 2 plotted against y-coordinate for 3x3 and 7x7 meshes; reduced integration Predictions of M 12 plotted against y-coordinate for 3x3 and 7x7 meshes; reduced integration Predictions of S 1 plotted against y-coordinate for 3x3 and 7x7 meshes; reduced integration Predictions of S 2 plotted against y-coordinate for 3x3 and 7x7 meshes; reduced integration Comparison of ICFEP results with results published by Ahmad et al. (1970) and Kanok-Nukulchai (1979) in terms of the longitudinal force F 1 in the middle of the Scordelis-Lo roof

15 LIST OF FIGURES Comparison of ICFEP results with results published by Ahmad et al. (1970) and Kanok-Nukulchai (1979) in terms of the bending moments in the middle of the Scordelis-Lo roof Comparison of ICFEP results with results published by Ahmad et al. (1970) in terms of the torsional moment M 12 at the support of the Scordelis-Lo roof Convergence of 4-node shell element results to published solution for Scordelis- Lo roof problem Pinched cylinder (R = 300; L = 600; thickness, t = 3; E = ; ν = 0.3) Convergence of 8-node shell element results to published solution for pinched cylinder problem Comparison of ICFEP results with results published by Liu et al. (2000), Belytschko et al. (1985) and Zhang et al. (2000) for the pinched cylinder problem The 5x5 nonuniformily skewed mesh for the pinched cylinder (after Figure 8 of Yang et al. (1990)) Pinched hemisphere (R = 10; thickness = 0.04; E = ; ν = 0.3) Convergence of 8-node shell element results to published solution for pinched hemisphere problem Comparison of ICFEP results with results published by Liu et al. (2000), MacNeal & Harder (1985), Belytschko et al. (1985) and Zhang et al. (2000) for the pinched hemisphere problem Mechanical model of a) the plate element developed by Phaal & Calladine (1992) and b) their shell element (Figure 5 of Augarde & Burd (2001)) Comparison of ICFEP results with results published by Phaal & Calladine (1992) for the Scordelis-Lo roof problem Comparison of ICFEP results with results published by Phaal & Calladine (1992) for the pinched cylinder problem Comparison of ICFEP results with results published by Phaal & Calladine (1992) for the pinched hemisphere problem Finite element mesh used for the analysis of a deep tunnel in a prestressed, elastic medium with no self-weight Comparison of ICFEP results with results published by Augarde & Burd (2001) for the normalised radial displacement at the tunnel springline Comparison of ICFEP results with results published by Augarde & Burd (2001) for the normalised radial displacement at the tunnel invert The influence of Poisson s ratio on radial tunnel liner displacements; analytical solution and ICFEP results (E/E l = & 0.005)

16 16 LIST OF FIGURES 4.58 The influence of Poisson s ratio on radial tunnel liner displacements; analytical solution and ICFEP results (E/E l = 0.05 & 0.5) The EFFRA riverside housing development in October Map showing the site location (Reproduced by permission of Geographers A-Z Map Co Ltd. This product includes mapping data licensed from Ordnance Survey. (C) Crown Copyright Licence number ) Outline of the LUL tunnels at Vauxhall station. Also indicated are the locations of tunnel lining monitoring equipment and piles of particular interest to the monitoring programme Foundation layout of the Effra riverside housing development in relation to the LUL Victoria line tunnels and location of monitoring equipment Cross section A-A (plan shown in Figure 5.4) indicating the stratigraphy at the site Location of vibrating wire strain gauges in a) station tunnel (Ring A) and b) running tunnel (Ring B). Note: the view is in a westerly direction Electrolevel strings; a) Positions of electrolevels and imaginary nodes; b) Calculation model The influence of heat changes on measurements made with electrolevel beams (after Figure 5.30 of Barakat (1996)) Daily cycle of electrolevel measurement in a LUL tunnel at Heathrow airport (after Figure 7.25 of Barakat (1996)) The influence of heat on electrolevels with different initial inclinations (after Figure 3 of Spalton (1995) Combined electrolevel and extensometer Indication of setup of string of electrolevels and rod extensometer Horizontal displacement measurements from tube A; a) from until ; b) from until Measurements of Probe EL A and EL 1A; a) from until ; b) from until Measurements of EL 2A; a) from until ; b) from until Measurements of EL 3A and 4A; a) from until ; b) from until Development of temperatures in a large diameter bored pile in Hong Kong (after Figure 4 of Pennington (1995))

17 LIST OF FIGURES Finite difference prediction of temperature development with time in the soil surrounding a large diameter bored pile (x = distance from pile surface) Measurements of VW A2 and A3; a) from until ; b) from until Measurements of VW A4 and A5; a) from until ; b) from until Measurements of VW A1 from until Measurements of VW B1 from until Measurements of VW B1 showing daily fluctuations Measurements of VW B1 from until Measurements of VW B2; a) from until ; b) from until Measurements of VW B3; a) from until ; b) from until Measurements of VW B4; a) from until ; b) from until Measurements of VW B5 from until Measurements of VW B5 showing daily fluctuations Measurements of VW B5 from until Horizontal movements measured in tubes A, D and F during and subsequent to pile loading (from until ) Horizontal movements measured in tube C during and subsequent to pile loading (from until ) Vertical movements of node N5 of tubes A, C, D and F during and subsequent to pile loading (from until ) Vertical movements of node N5 of tube E during and subsequent to pile loading (from until ) Vertical deformation of tube A at different times during and subsequent to pile loading (from until ) Rotations measured with electrolevels in tube A during and subsequent to pile loading (from until ) Rotations measured with electrolevels in tube C during and subsequent to pile loading (from until ) Vertical deformation of tube C at different times during and subsequent to pile loading (from until )

18 18 LIST OF FIGURES 5.39 Rotations measured with electrolevels in tube D during and subsequent to pile loading (from until ) Vertical deformation of tube D at different times during and subsequent to pile loading (from until ) Rotations measured with electrolevels in tube F during and subsequent to pile loading (from until ) Vertical deformation of tube F at different times during and subsequent to pile loading (from until ) Measurements of strain gauges in ring A during pile loading from until Measurements of strain gauges in ring B during pile loading from until Finite element mesh for the axially symmetric analysis of the construction of pile P27 at the Effra site Underdrained pore water pressure profile used in the analyses (labelled ICFEP) and measured in the field at Waterloo (Hight et al., 1993) and Effra (Section of Chapter 5) K 0 distributions under greenfield conditions, after tunnel construction and consolidation at a distance of 3.4 m from the tunnel and the conditions prescribes at the beginning of analysis EFFRA Wet concrete pressure distributions applied in the modelling of the construction of pile P27 on the Effra site Predicted (EFFRA 01A) and measured horizontal movements during the construction of pile P The stress path followed by an element between the pile bore and the geometric location of the tunnel during the construction of pile P27 as predicted with analysis EFFRA 01A The influence of zeroing the strains prior to the introduction of bentonite (EFFRA 01B) on the predicted horizontal movements Predicted (EFFRA 01A) and measured horizontal movements immediately after the completion of concreting of pile P Predicted (EFFRA 01A) horizontal movements until the end of the analysis (2 years after the end of the construction of pile P27) The influence of changing the initial stresses to allow for the presence of the tunnel (EFFRA 02) on the predicted horizontal movements

19 LIST OF FIGURES p distributions under greenfield conditions, after tunnel construction and consolidation at a distance of 3.4 m from the tunnel and the conditions prescribes at the beginning of analysis EFFRA Pore water pressure distributions under greenfield conditions, after tunnel construction and consolidation at a distance of 3.4 m from the tunnel and the conditions prescribes at the beginning of analysis EFFRA Predicted (EFFRA 01A) and measured vertical movements during the construction of pile P Predicted (EFFRA 01A) and measured vertical movements immediately after the completion of concreting of pile P Finite element mesh for the plane analysis of the pile loading at the Effra site The predicted distorted shape of the tunnel lining at the end of construction and prior to construction activities on the Effra site The predicted distorted shape of the tunnel lining due to different construction activities on the Effra site The distribution around the tunnel lining of the circumferential force expressed in absolute terms at key stages of the analysis of pile loading at the Effra site The distribution around the tunnel lining of the circumferential force expressed as a percentage of full overburden at the tunnel springline at key stages of the analysis of pile loading at the Effra site The distribution around the tunnel lining of the change of circumferential force due to pile loading at the Effra site The distribution around the tunnel lining of the bending moment at key stages of the analysis of pile loading at the Effra site The distribution around the tunnel lining of the change of bending moment due to pile loading at the Effra site The distribution around the tunnel lining of the change of the direct circumferential strain at the tunnel intrados due to pile loading The distribution around the tunnel lining of the change of the direct circumferential strain at the tunnel intrados from before pile loading until the end of pile loading and until the end of the analysis Comparison of predicted and measured direct circumferential strain at the tunnel intrados Vertical displacements relative to the tunnel lining for different pile loadings and at the end of the analysis Comparison of predicted and measured relative vertical displacements

20 20 LIST OF FIGURES 6.28 Comparison of predicted and measured relative horizontal displacements Finite element mesh for the three dimensional analysis Finite element mesh for the axially symmetric analysis Underdrained pore water pressure profile used in the analyses (labelled ICFEP) and measured in the field at Waterloo (Hight et al., 1993) and Effra (Section of Chapter 5) Comparison of the vertical effective stress profiles at a distance of 3.5 m from the tunnel extrados obtained with a coupled two dimensional analysis and a drained three dimensional analysis Comparison of the horizontal effective stress profiles obtained at a distance of 3.5 m from the tunnel extrados with a coupled two dimensional analysis and a drained three dimensional analysis Mean effective stress contours; a) coupled two dimensional analysis; b) drained three dimensional analysis Tunnel deformation due to pile excavation to the right of the tunnel for different positions along the tunnel axis Horizontal displacement in the x-direction along the right and left springline obtained from the three dimensional analysis and results from the axially symmetric analysis as a comparison Vertical displacement along the right and left springline obtained from the three dimensional analysis and results from the axially symmetric analysis as a comparison Horizontal displacements in the x-direction at tunnel axis level depth plotted against distance from the pile Vertical displacements at tunnel axis level depth plotted against distance from the pile The distribution around the tunnel lining of the circumferential force expressed in absolute terms at the end of tunnel construction and the end of pile excavation The distribution around the tunnel lining of the circumferential force expressed as a percentage of full overburden at the tunnel springline at the end of tunnel construction and the end of pile excavation The distribution around the tunnel lining of the change of circumferential force due to pile excavation The distribution around the tunnel lining of the bending moment at the end of tunnel construction and the end of pile excavation

21 LIST OF FIGURES The distribution around the tunnel lining of the change of the direct circumferential strain at the tunnel intrados at y = m due to pile excavation The distribution around the tunnel lining of the change of the direct circumferential strain at the tunnel intrados at y = 9.15 m due to pile excavation Geometric parameters in the modelling of pile-tunnel interaction problems Three dimensional mesh used for the modelling of pile rows Two dimensional mesh used for the modelling of walls equivalent to the pile rows shown in Figure Comparison of vertical displacements at a depth of 20 m from 3-D and 2-D analyses Comparison of horizontal displacements at a depth of 20 m from 3-D and 2-D analyses Comparison of vertical effective stress changes at a depth of 20 m from 3-D and 2-D analyses Comparison of horizontal effective stress changes at a depth of 20 m from 3-D and 2-D analyses The influence of S1 on the accuracy of the 2-D analyses compared with the 3-D analyses in terms of vertical displacements The influence of S1 on the accuracy of the 2-D analyses compared with the 3-D analyses in terms of horizontal displacements The influence of S1 on the accuracy of the 2-D analyses compared with the 3-D analyses in terms of vertical stress changes The influence of S1 on the accuracy of the 2-D analyses compared with the 3-D analyses in terms of horizontal stress changes The influence of S2 on the accuracy of the 2-D analyses compared with the 3-D analyses in terms of vertical displacements The influence of S2 on the accuracy of the 2-D analyses compared with the 3-D analyses in terms of horizontal displacements The influence of S2 on the accuracy of the 2-D analyses compared with the 3-D analyses in terms of vertical stress changes The influence of S2 on the accuracy of the 2-D analyses compared with the 3-D analyses in terms of horizontal stress changes Plane strain mesh used for the reference analysis of pile rows located on both sides of a tunnel

22 22 LIST OF FIGURES 8.17 Underdrained pore water pressure profile used in the analyses (labelled ICFEP) and measured in the field at Waterloo (Hight et al., 1993) and Effra (Section of Chapter 5) The deformed tunnel shape at the end of tunnel construction and at the end of consolidation with pile rows located on both sides of the tunnel The deformation of the tunnel due to the loading of pile rows located on both sides of the tunnel The distribution around the tunnel lining of the circumferential force expressed in absolute terms at key stages of the reference case with pile rows located on both sides of the tunnel The distribution around the tunnel lining of the circumferential force expressed as a percentage of full overburden at tunnel axis level at key stages of the reference case with pile rows located on both sides of the tunnel The distribution around the tunnel lining of the change of circumferential force due to loading of pile rows located on both sides of the tunnel The distribution around the tunnel lining of the bending moment at key stages of the reference case with pile rows located on both sides of the tunnel The distribution around the tunnel lining of the change of bending moment due to loading of pile rows located on both sides of the tunnel The influence of the spacing along the pile rows, S1, on tunnel distortions expressed in terms of diametrical changes The influence of the spacing along the pile rows, S1, on tunnel crown settlement The influence of the spacing along the pile rows, S1, on the maximum change of the circumferential lining force due to pile loading The influence of the spacing along the pile rows, S1, on the change of bending moment due to pile loading The influence of the clear distance between piles and tunnel, S3, on tunnel distortions; a) increase of horizontal diameter; b) reduction of vertical diameter The influence of the clear distance between piles and tunnel, S3, on tunnel crown settlement The influence of the clear distance between piles and tunnel, S3, on the maximum change of the circumferential lining force due to pile loading The influence of the clear distance between piles and tunnel, S3, on the change of bending moment due to pile loading; a) maximum decrease close to tunnel axis; b) maximum increase close to tunnel invert

23 LIST OF FIGURES Long-term tunnel distortion in response to pile loading Long-term crown settlements in response to pile loading Long-term circumferential lining forces in response to pile loading Long-term bending moments in response to pile loading The influence of not modelling the presence of the tunnel on predicted tunnel distortions The influence of not modelling the presence of the tunnel on predicted global tunnel movements The influence of matching the flexural as well as the axial wall stiffness on predicted tunnel distortions The influence of matching the flexural as well as the axial wall stiffness on predicted global tunnel movements The influence of the number of pile rows on tunnel distortions; a) increase of horizontal diameter; b) reduction of vertical diameter The influence of the number of pile rows on tunnel crown settlement The influence of the number of pile rows on the maximum change of the circumferential lining force due to pile loading The influence of the number of pile rows on the change of bending moment due to pile loading; a) maximum decrease close to tunnel axis; b) maximum increase close to tunnel invert The influence of the clear distance between piles and tunnel, S3, on tunnel distortions of a station tunnel (D tunnel = 6.9 m); a) increase of horizontal diameter; b) reduction of vertical diameter The influence of the clear distance between piles and tunnel, S3, on tunnel crown settlement of a station tunnel (D tunnel = 6.9 m) The influence of the clear distance between piles and tunnel, S3, on the maximum change of the circumferential lining force due to pile loading in a station tunnel (D tunnel = 6.9 m) The influence of the clear distance between piles and tunnel, S3, on the change of bending moment due to pile loading in a station tunnel (D tunnel = 6.9 m); a) maximum decrease close to tunnel axis; b) maximum increase close to tunnel invert A 15 storey building bridging an underlying tunnel Different foundation layouts for the 15 storey building with varying clear distance between the pile rows and the tunnel

24 24 LIST OF FIGURES 8.51 Different foundation layouts for the 15 storey building with varying pile diameter The influence of the clear distance between piles and tunnel, S3, on tunnel distortions in response to the construction of a 15 storey building; a) increase of horizontal diameter; b) reduction of vertical diameter The influence of the clear distance between piles and tunnel, S3, on tunnel crown settlement in response to the construction of a 15 storey building The influence of the clear distance between piles and tunnel, S3, on the maximum change of the circumferential lining force due to the construction of a 15 storey building The influence of the clear distance between piles and tunnel, S3, on the change of bending moment due to the construction of a 15 storey building; a) maximum decrease close to tunnel axis; b) maximum increase close to tunnel invert The influence of the pile diameter on tunnel distortions, expressed in terms of the increase of the horizontal diameter and the reduction of the vertical diameter The influence of the pile diameter in the foundation layout of a 15 storey building on tunnel crown settlement The influence of the pile diameter in the foundation layout of a 15 storey building on the maximum change of the circumferential lining force due to pile loading The influence of the pile diameter in the foundation layout of a 15 storey building on the change of bending moment due to pile loading; a) maximum decrease close to tunnel axis; b) maximum increase close to tunnel invert Plane strain mesh used for the reference analysis of pile rows located on one side of a tunnel The deformed tunnel shape at key stages of the reference case with pile rows located on the right hand side of the tunnel The distribution around the tunnel lining of the circumferential force expressed in absolute terms at key stages of the reference case with pile rows located on one side of the tunnel The distribution around the tunnel lining of the circumferential force expressed as a percentage of full overburden at tunnel axis level at key stages of the reference case with pile rows located on one side of the tunnel The distribution around the tunnel lining of the change of circumferential force due to pile loading expressed in absolute terms at key stages of the reference case with pile rows located on one side of the tunnel