Behaviour of soldier piles and timber lagging support systems

BEHAVIOUR OF SOLDIER PILES AND TIMBER LAGGING SUPPORT SYSTEMS HONG SZE HAN B.Eng.(Hons.), NUS A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CIVIL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2002 .Let us run with perseverance the race that is set before us, looking to Jesus the pioneer and perfecter of our faith . - Hebrews 12:1 ii ABSTRACT ABSTRACT This thesis discusses the significance of three-dimensional (3D) effects arising from arching of soil behind retaining wall on wall deflection and ground surface settlement. Results from literature survey are not applicable to soldier piles retaining system owing to the added complexities of soil arching, movement between piles and anisotropy of lagging. A customised version of the CRISP 90 finite element program, with additional beams and reduced-integration elements incorporated, was used in the back-analysis. This is necessary in order to account for the local three-dimensional effects arising from the interaction of the soldier piles and the intervening soils. Strutted excavations, including soldier-piled excavations, are often analysed using two-dimensional (2D) finite element (FE) analyses with properties that are averaged over a certain span of the wall. In this thesis, the effects of “smearing” the stiffness of the soldier piles and timber laggings into an equivalent uniform stiffness are examined, based on comparison between the results of 2D and 3D analyses. The ability of the 3D analyses to model the flexural behaviour of the soldier piles and timber laggings is established by comparing the flexural behaviour of various FE beam representations to the corresponding theoretical solutions, followed by a reality check with an actual case study. Finally, the results of 2D and 3D analyses on an idealized soldier piled excavation are compared. The findings show that modelling errors can arise in several ways. Firstly, a 2D analysis tends to over-represent the coupling to pile to the soil below excavation level. Secondly, the deflection of the timber lagging, which is usually larger than that of the soldier piles, is often underestimated. For these reasons, the overall volume of ground loss is, in reality, larger than those given by a 2D analysis. Thirdly, a 2D analysis cannot replicate the swelling, and therefore iii ABSTRACT softening, of the soil face just behind the timber lagging. Increasing the inter-pile spacing will tend to accentuate the effects of these modelling errors. Some results of a comparative study into the effects of different constitutive models in simulating soldier-piled excavations in medium to stiff soils will be discussed. The field data, which were used as reference in this comparative study, came from the excavation for the Serangoon station of the North-East Line (NEL) contract 704. The subsoil at the site is generally residual Bukit Timah Granite. The temporary retaining structures for the excavation consisted of driven soldier piles and timber lagging supported by steel struts. The methods of modelling retaining system, boundary and groundwater conditions and excavation sequence are demonstrated. The models compared in this thesis include Mohr Coulomb, modified Cam-clay and hyperbolic Cam-clay. The results of the study indicates that deflection of the soldier pile may not necessarily be an accurate reflection of the soil face movement behind the timber lagging, and thereby the ground loss. Furthermore, modelling the soil with a hyperbolic Cam-clay model results in smaller initial deflection and better agreement with progressive field measurement compared to the linear elastic Mohr Coulomb criterion or modified Cam-clay models. Keywords: deep excavation, finite element method, 3D, soldier piles, piles spacing, timber lagging, arching effect, Mohr Coulomb, modified Cam-clay, hyperbolic Cam-clay, beam element iv ACKNOWLEDGEMENT ACKNOWLEDGEMENTS The Author is especially grateful to Professor Yong Kwet Yew for introducing him to this fascinating and active field of research and to Associate Professor Lee Fook Hou for his many most valuable and critical comments during their long discussions. The Author would like to acknowledge the research scholarship and scholarship augmentation provided by the National University of Singapore and Econ Piling Pte. Ltd. respectively. Thanks are due to Econ Piling Pte. Ltd. for their provision of site instrumentation and monitoring data. The equipment and software support provided by the Centre for Soft Ground Engineering at the National University of Singapore is also gratefully acknowledged. The Author also remembers most stimulating and valuable discussions with Chan Swee Huat, Chee Kay Hyang, Gu Qian, How You Chuan, Lim Ken Chai, Wong Kwok Yong and numerous other people which he would like to acknowledge collectively in order not to forget anyone. Most of all, he would like to thank all of his family for their love and understanding throughout his entire life and for their continuing belief in him. v TABLE OF CONTENTS TABLE OF CONTENTS ABSTRACT iii ACKNOWLEDGEMENTS v TABLE OF CONTENTS vi LIST OF TABLES viii LIST OF FIGURES ix LIST OF SYMBOLS xvi CHAPTER INTRODUCTION 1.1 BACKGROUND 1.2 SOLDIER PILE WALLS 1.3 DEFORMATIONS 1.4 OBJECTIVE 1.5 SCOPE OF WORK CHAPTER LITERATURE REVIEW 2.1 DESIGN APPROACHES FOR RETAINING SYSTEMS 2.2 VARIOUS METHODS FOR EVALUATING RETAINING SYSTEMS 2.2.1 EMPIRICAL APPROACHES 2.2.2 1-D BEAM AND SPRING MODELS 17 2.2.3 2D FINITE ELEMENT ANALYSIS 18 2.2.4 3D FINITE ELEMENT ANALYSIS 24 2.3 SOIL ARCHING 31 2.3.1 DESIGN PROCEDURES FOR SOLDIER PILE WALL 31 2.3.2 RESEARCH ON ARCHING EFFECT 32 2.4 REVIEW SYNOPSIS CHAPTER IDEALISED ANALYSIS OF PILE-SOIL INTERACTION 35 37 3.1 MODELLING OF SOLDIER PILES IN 2D AND 3D ANALYSES 38 3.2 COMPARISON WITH CASE HISTORY 47 vi TABLE OF CONTENTS 3.3 3D AND 2D COMPARISONS 54 3.3.1 IDEALISED EXCAVATION 54 3.3.2 WALL DEFLECTION 56 3.3.3 STRESS CHANGES 59 3.4 SYNOPSIS ON 3D AND 2D ANALYSES CHAPTER GEOTECHNICAL STUDY OF SERANGOON MRT SITE 65 66 4.1 SERANGOON MRT SITE GEOLOGY 66 4.2 RETAINING SYSTEM 76 4.3 CONSTRUCTION SEQUENCE 78 CHAPTER FEM STUDY OF SERANGOON MRT SITE 81 5.1 GEOMETRY OF FINITE ELEMENT MODEL 81 5.2 MODELLING OF EXCAVATION SEQUENCE 84 5.3 PARAMETRIC STUDIES FOR VARIOUS MODELS 85 5.3.1 ELASTIC-PERFECTLY PLASTIC MOHR COULOMB 86 5.3.2 MODIFIED CAM-CLAY 103 5.3.3 HYPERBOLIC CAM-CLAY 123 5.4 SUMMARY OF FINDINGS CHAPTER CONCLUSION AND RECOMMENDATIONS 142 144 6.1 CONCLUDING REMARKS 144 6.2 RECOMMENDATIONS FOR FUTURE WORK 145 REFERENCES 147 APPENDICES 159 APPENDIX A TRANSFORMATION MATRIX FOR 3D BEAM APPENDIX B EVALUATING BENDING MOMENTS FROM LINEAR-STRAIN 159 BRICK ELEMENTS 163 APPENDIX C STRESS REVERSAL IN NON-LINEAR SOIL MODEL 166 APPENDIX D PROPERTIES OF TIMBER LAGGING (CHUDNOFF, M., 1984) 168 vii LIST OF TABLES LIST OF TABLES Table 2.1: Empirical approaches contribution by various researchers. 10 Table 2.2: 2D finite element analyses contribution by various researchers. 19 Table 2.3: 3D finite element analyses contribution by various researchers. 25 Table 3.1: Idealised soil and soldier pile properties for beam and brick soldier piles study. 45 Table 3.2: Idealised soil and soldier pile properties for O’Rourke’s case study. 49 Table 3.3: Idealised soil and soldier pile properties for idealised study. 55 Table 3.4: Summary of effective stress analyses for the idealised excavation at OCR = and k = 1× ×10-8m/s. 55 Table 4.1: Soil properties of Serangoon MRT site. 75 Table 4.2: Struts details for Serangoon MRT retaining system. 76 Table 5.1: Soil properties of Serangoon MRT site. 86 Table 5.2: Soil properties for Layers 1, and for Mohr Coulomb analyses. 89 Table 5.3: Comparison of strut forces at various levels between daily average instrumented and FEM result for MC2, MC3, MC4 and MC5. Table 5.4: Soil properties for Layer and Layer for modified Cam-clay. 100 109 Table 5.5: Comparison of strut forces at various levels between instrumented and FEM result for the best-fit deflection profile for MCC1. 121 Table 5.6: Modification to 3.5m of topsoil to Mohr Coulomb properties. 122 Table 5.7: Soil properties for Layer and Layer for hyperbolic Cam-clay. 129 Table 5.8: Comparison of strut forces at various levels between instrumented and FEM result for the best-fit deflection profile for HCC4. 135 viii LIST OF FIGURES LIST OF FIGURES Figure 1.1: Components of soldier piles and timber lagging systems. Figure 2.1: Observed settlements behind excavations (after Peck, 1969). 10 Figure 2.2: Summary of settlements adjacent to strutted excavation in Washington, D.C. (after O’Rourke et al., 1976). 11 Figure 2.3: Summary of settlements adjacent to strutted excavation in Chicago (after O’Rourke et al., 1976). 12 Figure 2.4: Effects of wall stiffness and support spacing on lateral wall movements (after Goldberg et al., 1976). 13 Figure 2.5: Calculation of embedment depth of sheet pile wall in relatively uniform competent soil conditions (after Goldberg et al., 1976) 14 Figure 2.6: Relationship between maximum settlement and stability number for different batters (after Clough & Denby, 1977). 15 Figure 2.7: Relationship between factor of safety against basal heave and non-dimensional maximum lateral wall movement for case history data (after Clough et al., 1979). 16 Figure 2.8: Relationship between maximum ground settlements and maximum lateral wall movements for case history data (after Mana & Clough, 1981). 17 Figure 3.1: Comparison of deflection profiles under distributed load for 2D 43m-cantilever beam. (a) 32-bit precision. (b) 64-bit precision. 41 Figure 3.2: Comparison of bending moments under distributed load for 2D 43m-cantilever beam. (a) 32-bit precision. (b) 64-bit precision. 41 Figure 3.3: Effect of aspect ratios for 2D 43m-cantilever beam in 64-bit precision using RIQUAD elements. (a) Deflection. (b) Bending moment. 42 Figure 3.4: Comparison of deflection profiles under distributed load for 3D 43m-cantilever beam. (a) 32-bit precision. (b) 64-bit precision. 42 Figure 3.5: Comparison of bending moments under distributed load for 3D 43m-cantilever beam. (a) 32-bit precision. (b) 64-bit precision. 43 Figure 3.6: Locations of beams and linear strain bricks for modelling soldier piles in the finite element model of an idealistic excavation. (a) Plan view of beam element as soldier pile in section A-A. (b) Plan view of RIBRICK element as soldier pile ix LIST OF FIGURES in section A-A. (c) Cross-sectional view in x-y plane of the FEM model. (d) Soil layers, struts and excavation levels. 44 Figure 3.7: (a) Deflection profile of soldier pile and soil at the center between adjacent piles. (b) Bending moment profile of soldier piles. 46 Figure 3.8: Plan view of lateral deflection retaining system 9m depth after final excavation stage. 46 Figure 3.9: Lateral stress contours for at 9.3m below ground level for excavation to 11.5m. (a) Beam soldier pile elements. (b) RIBRICK soldier pile elements. 47 Figure 3.10: Plan view of retaining system after O’Rourke (1975). 48 Figure 3.11: Finite element mesh used for reality check with O’Rourke (1975). 48 Figure 3.12: Comparison of a series of 2D and 3D analyses from O’Rourke (1975). (a) Soldier pile deflection. (b) Bending moments. 50 Figure 3.13: Deflection of soldier pile and soil at mid-span with respect to excavation sequence. (a) Excavation depth at 6.1m. (b) Excavation depth at 11.9m. (c) Excavation depth at 18.3m. 51 Figure 3.14: Effect of ‘smearing’ on rotational fixity below excavation level. 52 Figure 3.15: Modelling the S-shaped deflection profile of the soldier pile in 3D. 53 Figure 3.16: Construction sequence for idealized excavation from stage A through G. 56 Figure 3.17: Comparison of wall deflection between 2D and different pile spacing for cases without preloading at final stage of construction. 57 Figure 3.18: Comparison of wall deflection between 2D and different pile spacing for cases with preloading at final stage of construction. 58 Figure 3.19: Comparison of effects of preloading on wall deflection for 3D-4 at 4.5m below ground level with stages B, C and D shown in Figure 3.16. 58 Figure 3.20: Location of stress paths plotted for soil behind first level of strut at 4.22m below ground level in x-z plane. 59 Figure 3.21: Stress path plot for 2D-1 without preload. Stages A to G are shown in Figure 3.16. 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These series of rotations about the y-, z- and x-axes, can be resolved into their respective vector components through the following transformations, [T '] = [Tα ][Tγ ][Tβ ] (A.1) where  cos β Tβ =  − sin β sin β   cos β   cos γ Tγ = − sin γ  sin γ [ ] [ ] cos γ 1  [Tα ] = 0 cosα 0 − sin α 0 0 1  sin α  cos α  thus, 159 APPENDICES (cos β cos γ ) (sin γ ) (cos γ sin β )    [T '] = − (sin β sin α + cos β sin γ cosα ) (cos γ cosα ) (sin α cos β − sin β sin γ cos α )  − (sin β cos α − cos β sin γ sin α ) − (cos γ sin α ) (cos β cos α − sin β sin γ sin α ) (A.2) where β is the rotation of global y-axis γ is the rotation of global z-axis α is the rotation of global x-axis (angle of tilt) The vector components can be expressed in terms of the direction cosines of the member, we get:   Cx   − C C cos α − C z sin α [T '] =  x y 2 Cx + Cz   C x C y sin α − C z cosα  2 Cx + Cz  Cy C x + C z cosα     − C y C z cos α + C x sin α  (A.3) 2  Cx + C z  C y C z sin α + C x cos α   2 Cx + C z  Cz − C x + C z sin α where Cx = x j − xi L , Cy = y j − yi L , Cz = z j − zi L and L = ( x j − xi ) + ( y j − yi ) + ( z j − zi ) 160 APPENDICES When the element lies vertical, i.e., when local x-axis coincides with the global y-axis, Cx = Cz = 0. This makes some of the terms in the transformation matrix indeterminate. Thus the above procedure breaks down. In a general case of a vertical member, β = 0° and γ = 90° or 270°. The rotation matrix for either case can be written as:   [T 'vert ] = − C y cosα  C y sin α  Cy 0   sin α  cosα  (A.4) As there are eighteen degrees of freedom for a three-dimensional beam element the rotation transformation matrix can now be expressed as [T ']  [0]   [0] [T ] =   [0]  [0]   [0] [0] [T '] [0] [0] [0] [0] [0] [0] [T '] [0] [0] [0] [0] [0] [0] [T '] [0] [0] [0] [0] [0] [0] [T '] [0] [0]  [0]  [0]  [0]  [0]   [T '] (A.5) 161 APPENDICES y ym α xm LCy γ x β L Cx + Cz LCz LCx z zm Figure A-1: Rotation transformation of axes for a 3D beam element 162 APPENDICES Appendix B Evaluating Bending Moments from Linear-strain Brick Elements For quadrilateral models, the bending moments were evaluated using the method suggested by Rahim and Gunn (1997). For a plane strain quadrilateral element representing part of a structure, the bending moment in x-y plane in Figure B-1 is found from the integral: h2 M = ∫σ x y.dy (B.1) −h where h is the depth of the beam and σx is the stress normal to the cross section. η +1 I h II M +1 -1 ξ III y -1 x Global coordinate system Local coordinate system Figure B-1: A full-integration 8-noded quadrilateral element forming part of a beam. For reason associated with numerical integration, it is convenient to work with a ‘normalised’ local coordinate system shown in Figure B-2 based on the following relationship: dy h = dη (B.2) This leads to 163 APPENDICES h y= η (B.3) Using the local coordinates, we obtain +1  h2  M = ∫ σ x  η.dη   −1 (B.4) The above integral can be evaluated using a three-point, one-dimensional Gauss integration rule. Thus:  h  III M =  ∑ σ xi × ηi × ϖ i   i=I (B.5) Similarly for reduced-integration 8-noded quadrilateral element,  h  II M =  ∑ σ xi × ηi × ϖ i   i=I (B.6) In the case of 3D, which was considered in analyses of Chapter 3, we obtain the following integral: hz h y M= ∫ ∫σ x y.dydz (B.7) − hz − h y η hz +1 I hy z II III y x -1 Global coordinate system Mzz +1 ζ ξ -1 Local coordinates system Figure B-2: A full-integration 20-noded linear strain brick element forming part of a beam. 164 APPENDICES In local coordinates as defined in Figure B-2, the integral is  hy  hz   M = ∫ ∫σ x  η.dηdζ    −1 −1   +1 +1 (B.8) Thus for full-integration 20-noded linear strain brick, M zz  h y hz =    III  σ xik × η i × ϖ i × ϖ k ∑∑ k =1 i = I  (B.9) and reduced-integration 20-noded linear strain brick M zz  h y hz =    II  σ xik × η i × ϖ i × ϖ k ∑∑ k =1 i = I  (B.10) where h is the dimension of the element in x-, y- or z- direction η is the normalised local coordinate ω is the weight at respective local coordinates for the element 165 APPENDICES Appendix C Stress Reversal in Non-linear Soil Model 200 Dasari (1996) Deviator stress, q (kPa) Stallebrass (1990) FEM modelling Dasari (1996) 150 FEM modelling Stallebrass (1990) 100 50 0.000 0.002 0.004 0.006 0.008 0.010 Deviator strain, εs Figure C-1: Comparison of FEM modelling of stress reversal with laboratory test results done by Stallebrass (1990) and Dasari (1996). The stiffness of soil on unloading is not the same as the stiffness in loading at the same strain level. During unloading, the rate of decay of soil stiffness is slower. This effect can be seen in a strutted excavation where the soil is first excavated and the subsequent strutting will cause some stress reversal. Further excavation will again trigger the stress reversal process. This behaviour can be approximately modelled by Massing’s rule (1926): q − qur  ε − ε ur  = F s    (C.1) From Equation 5.11, assuming S=3G and G∞=0,  ε − ε ur  3G0  s  q − qur   = 3G  ε − ε ur  1+  s q f   (C.2) 166 APPENDICES   3G  ε − ε     ε − ε ur  3G0 ur  s   − 3G0  s  G0 1 +  q f       qf dq   = 3G  ε − ε ur  dε s 1+  s q f   = G0  3G0  ε s − ε ur    1 + q f           (C.3) Simplify, 3G0 dq = dε s  3G  ε − ε ur  s 1 + qf      (C.4) Variation of G can be rewritten as: G= G0  3G0  ε s − ε ur  1 + qf       (C.5) Tests from Stallebrass (1990) and Dasari (1996) are used to verify the rule as shown in Figure C-1. Figure C-1 shows good approximation of Massing’s rule with stress-strain behaviour of real soil in laboratory tests. 167 APPENDICES Appendix D Properties of Timber Lagging (Chudnoff, M., 1984) STANDARD NAME: KEMPAS (Medium Hardwood) BOTANICAL NAME: Koompassia malaccensis FAMILY Leguminosae DISTRIBUTION Very abundant in all lowland forests and in the mountains, often growing on moist, peaty or fresh water swamp soils and on low ridges. GENERAL DESCRIPTION Sapwood is well-defined and yellow in colour. Heartwood is pinkish when fresh and darkening to a bright orange-red or deep brown. Grain is interlocked, often very interlocked. Texture is coarse and even. Vessels are large and with simple perforations, few or very few, mostly solitary, but also in radial groups of to and evenly distributed. Wood parenchyma is abundant and predominantly paratracheal, as conspicuous aliform type; apotracheal type may occur as narrow terminal bands. Rays are moderately fine, just visible to the naked eye on the cross- section. Ripple marks are generally distinct. Concentric bands of included phloem are often present. PHYSICAL PROPERTIES Air-Dry Density: 770.00 - 1120.00 kg/m3 Shrinkage Radial: 2.00 % Shrinkage Tangential: 3.00 % Seasoning: Seasons fairly slowly with little or no defects Recommended Kiln Schedule: E MECHANICAL PROPERTIES Strength Group: A 168 APPENDICES Static Bending MOE: 18600.00 N/mm2 Static Bending MOR: 122.00 N/mm2 Compression perpendicular to grain: 7.52 N/mm2 Compression parallel to grain: 65.60 N/mm2 Shear Strength: 12.40 N/mm2 DURABILITY Moderately durable TREATABILITY Easy WORKING PROPERTIES Planing: Easy Planing Finish: Smooth Boring: Slightly difficult Boring Finish: Rough Turning: Slightly difficult Turning Finish: Rough Nailing: Poor USES Heavy construction, railway sleepers, posts and cross arms (telegraphic and power transmission), beams, joists, rafters, piling, columns (heavy duty), fender supports, pallets (permanent, heavy duty), doors, window frames and sills, tool handles (heavy duty) and marine construction. Untreated the timber is suitable for parquet and strip flooring, flooring (medium to heavy traffic), panelling and vehicle bodies (framework and floor boards) 169 [...]... deflection profile of soldier pile and timber lagging for HCC1 and HCC2 130 Figure 5.39: Final deflection profile of soldier pile and timber lagging for HCC1 and HCC3 131 Figure 5.40: Final deflection profile of soldier pile and timber lagging for HCC1 and HCC4 132 Figure 5.41: Deflection profile of soldier pile for HCC4 (a) Before installation of first level struts (b) After installation of forth level... Location II Locations I and II for each case are defined in Figure 5.6 Units of stresses in kPa 114 Figure 5.26: Final deflection profile of soldier pile and timber lagging for MCC1, MCC3 and MCC4 115 Figure 5.27: Final deflection profile of soldier pile and timber lagging for MCC4 and MCC5 116 Figure 5.28: Final deflection profile of soldier pile and timber lagging for MCC1, MCC6 and MCC7 117 Figure 5.29:... certain span of the wall In chapter 3, the effects of “smearing” the stiffness of the soldier piles and timber laggings into an equivalent uniform stiffness are examined, based on comparison between the results of 2D and 3D analyses The ability of the 3D analyses to model the flexural behaviour of the soldier piles and timber laggings is established by comparing the flexural behaviour of various FE... using soldier pile and timber lagging support system (Coutts and Wang, 2000) The retaining system for Harbour Front MRT station consists of soldier pile wall scheme with sheet pile lagging in the upper soil and shotcrete lagging in the weathered rock (Chen et al., 2000) 1.2 Soldier pile walls Soldier Pile Soil Arch Formation Timber Lagging Waler King Post Strut Figure 1.1: Components of soldier piles and. .. Stiffness of support system Passive soil resistance Effects of passive soil buttress Factor of safety against basal heave Goldberg (1976) Soldier pile and lagging Soil type Dense sand and interbedded stiff clay - Goldberg (1976) Soldier pile and lagging Clough & Denby (1977) Sheet pile Soft to medium clay Clough et al (1979) Mana & Clough (1981) - Soldier pile and lagging Soldier pile and lagging Settlement... deflection profile of soldier pile and timber lagging for MC2, MC4 and MC5 Locations I and II for each case are defined in Figure 5.6 93 Figure 5.11: Stress path plots for MC2, MC4 and MC5 at 12.3m below ground (a) Location I (b) Location II Locations I and II for each case are defined in Figure 5.6 Units of stresses in kPa 94 Figure 5.12: 2D final deflection profile of soldier pile and timber lagging for... least some cohesion and homogeneous, free-draining soils that can be effectively dewatered provide suitable conditions for the use of soldier pile walls Advantages of soldier pile walls are (1) soldier- piles and timber lagging are easy to handle, (2) low initial cost and (3) can be driven or augured Furthermore, since the soldier piles are not contiguous, much fewer soldier piles are often needed to be... separation between two soldier piles allows the soil to move between them especially below the excavation level in the absence of lagging The lagging serves as a secondary support to the soil face and prevents progressive deterioration of the soil arching between the piles It is often installed in lifts of 1 to 1.5 metres, depending on the soil being supported and on the convenience of working Overconsolidated... of soldier piles and timber lagging systems Soldier piles with timber laggings have been used extensively as an excavation support system, particularly in stiff soil conditions and where ground water ingress into the excavated area is not problematic (e.g GCO, 1990 Tomlinson, 1995; O’Rourke, 1975) Soldier pile walls have two basic components, soldier piles (vertical component) and lagging (horizontal... MC2, MC4 and MC5 95 Figure 5.13: Final deflection profile of soldier pile and timber lagging for MC2, MC6 and MC7 Locations I and II for each case are defined in Figure 5.6 96 Figure 5.14: Stress path plots for MC2, MC6 and MC7 at 12.3m below ground (a) Location I (b) Location II Locations I and II for each case are defined in Figure 5.6 Units of stresses in kPa 98 Figure 5.15: Deflection profiles at . Final deflection profile of soldier pile and timber lagging for MCC1, MCC3 and MCC4. 115 Figure 5.27: Final deflection profile of soldier pile and timber lagging for MCC4 and MCC5. 116 Figure. Depth of sample is 20m. 129 Figure 5.38: Final deflection profile of soldier pile and timber lagging for HCC1 and HCC2. 130 Figure 5.39: Final deflection profile of soldier pile and timber lagging. Units of stresses in kPa. 94 Figure 5.12: 2D final deflection profile of soldier pile and timber lagging for MC2, MC4 and MC5. 95 Figure 5.13: Final deflection profile of soldier pile and timber