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 1 INTRODUCTION 1
1.1 BACKGROUND 1 1.2 SOLDIER PILE WALLS 2 1.3 DEFORMATIONS 4 1.4 OBJECTIVE 5 1.5 SCOPE OF WORK 5
CHAPTER 2 LITERATURE REVIEW 8
2.1 DESIGN APPROACHES FOR RETAINING SYSTEMS 8 2.2 VARIOUS METHODS FOR EVALUATING RETAINING SYSTEMS 9 2.2.1 EMPIRICAL APPROACHES 9 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 35
CHAPTER 3 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION 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 65
CHAPTER 4 GEOTECHNICAL STUDY OF SERANGOON MRT SITE 66
4.1 SERANGOON MRT SITE GEOLOGY 66 4.2 RETAINING SYSTEM 76 4.3 CONSTRUCTION SEQUENCE 78
CHAPTER 5 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 142
CHAPTER 6 CONCLUSION AND RECOMMENDATIONS 144
6.1 CONCLUDING REMARKS 144 6.2 RECOMMENDATIONS FOR FUTURE WORK 145
REFERENCES 147
APPENDICES 159
APPENDIX A TRANSFORMATION MATRIX FOR 3D BEAM 159 APPENDIX B EVALUATING BENDING MOMENTS FROM LINEAR-STRAIN 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 = 3 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, 2 and 3 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. 100
Table 5.4: Soil properties for Layer 1 and Layer 2 for modified Cam-clay. 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 1 and Layer 2 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. 2
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.
Units of stresses in kPa. 60
Figure 3.22: Stress path plot for 2D-2 with preload. Stages A to G are shown in Figure 3.16.
Units of stresses in kPa. 61
x LIST OF FIGURES
Figure 3.23: Stress path plots for 3D-1 and 3D-2 at point I without preload. Stages A to G are
shown in Figure 3.16. Units of stresses in kPa. 62
Figure 3.24: Stress path plots for 3D-1 and 3D-2 at point II without preload. Stages A to G are
shown in Figure 3.16. Units of stresses in kPa. 63
Figure 3.25: Stress paths plots for 3D-3 and 3D-4 at point I with preload. Stages A to G are
shown in Figure 3.16. Units of stresses in kPa. 63
Figure 3.26: Stress path plots for 3D-3 and 3D-4 at point II with preload. Stages A to G are
shown in Figure 3.16. Units of stresses in kPa. 64
Figure 4.1: Singapore north-east MRT line with location plan. 66
Figure 4.2: Soil profile of Serangoon MRT site at section A-A. 69
Figure 4.3: Soil profile of Serangoon MRT site at section B-B. 69
Figure 4.4: Plan view of Serangoon MRT station. 70
Figure 4.5: Variation of physical properties at Serangoon MRT site. (a) Bulk unit weight.
(b) Atterberg Limits. 71
Figure 4.6: Plasticity chart of G4 soil at Serangoon MRT station. 71
Figure 4.7: Grain size distribution of G4 soil at Serangoon MRT station. 72
Figure 4.8: Variation of soil properties with depth at Serangoon MRT site. (a) SPT values.
(b) Undrained Young’s modulus. (c) Undrained shear strength. (d) Effective
cohesion. (e) Effective friction angle. (f) Over-consolidation ratio. 74
Figure 4.9: Variation of soil permeability with depth at Serangoon MRT site. 75
Figure 4.10: Soldier pile and timber lagging retaining system of Serangoon station. 77
Figure 4.11: Plan view of retaining system for Serangoon MRT station. 77
Figure 4.12: Cross sectional view of retaining system for Serangoon MRT station. 78
Figure 5.1: Finite element model for Serangoon MRT site excavation. 82
Figure 5.2: Plan view of Serangoon MRT station indicating the section B-B’ modelled. 83
Figure 5.3: Excavation with strut and timber lagging installation sequence. 85
Figure 5.4: Assumed piecewise linear variation of E’ with depth for different soil layers. 87
Figure 5.5: Drained Poisson’s ratio versus plasticity index for several lightly overconsolidated
soils after Wroth (1975). 88
Figure 5.6: Plan view of FEM model of retaining system. 89
xi LIST OF FIGURES
Figure 5.7: Final deflection profile of soldier pile and timber lagging for MC1, MC2. Locations
I and II for each case are defined in Figure 5.6. 90
Figure 5.8: Final deflection profile of soldier pile and timber lagging for MC2, MC3 and ELAS.
Locations I and II for each case are defined in Figure 5.6. 91
Figure 5.9: Apparent Mohr Coulomb yield envelopes at the limits of the effective stress range
of interest. (a) At 6m below EGL. (b) At 12m below EGL. 92
Figure 5.10: Final 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 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 various stages of excavation for MC5. (a) Stage B. (b) Stage
C. (c) Stage D. (d) Stage E. (e) Stage F. (f) Stage G. (g) Stage H. (h) Stage I. 101
Figure 5.16: Deflection profile of soldier pile for MC5. (a) Before installation of first level
struts. (b) After installation of forth level struts. 102
Figure 5.17: Ground settlement behind Location I of the retaining wall for MC2, MC3, MC4
and MC5. 103
Figure 5.18: Critical state friction angle estimated from triaxial compression tests. (a) At 6m
below EGL. (b) At 12m below EGL. 105
Figure 5.19: Variation of deformability indices with depth at Serangoon MRT site. (a)
Compression index. (b) Swelling index. 106
Figure 5.20: Comparison of laboratory’s odeometer test with MCC soil models. 107
xii LIST OF FIGURES
Figure 5.21: Axisymmetric FEM undrained (CU) triaxial test model with 9-integration points
eight noded quadrilateral elements. (a) Plane view. (b) Isometric view. 109
Figure 5.22: Comparison of laboratory’s CU triaxial tests with MCC soil models. (a) Depth of
sample is 11m. (b) Depth of sample is 20m. 110
Figure 5.23: Final deflection profile of soldier pile and timber lagging for MCC1 and MCC2. 111
Figure 5.24: Yield zones behind retaining wall at 12.3m below ground at instance when first
yield was detected in MC5 (Between stage C and D of Figure 5.3). (a) MC2.
(b) MC4. (c) MC5. 112
Figure 5.25: Stress path plots for MCC1 and MCC2 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. 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: Stress path plots for MCC1, MCC6 and MCC7 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. 118
Figure 5.30: Deflection profiles at various stages of excavation for MCC1-M. (a) Stage B.
(b) Stage C. (c) Stage D. (d) Stage E. (e) Stage F. (f) Stage G. (g) Stage H.
(h) Stage I. 120
Figure 5.31: Deflection profile of soldier pile for MCC1. (a) Before installation of first level
struts. (b) After installation of forth level struts. 121
Figure 5.32: Ground settlement behind Location I of the retaining wall for MCC1, MCC2,
MCC3, MCC4 and MCC5. 122
Figure 5.33: 2D and 3D ground settlement behind Location I of the retaining wall for
MCC1-M. 123
Figure 5.34: Parameters for G0. (a) Coefficient m. (b) Coefficient n. (Viggiani & Atkinson,
1995) 126
xiii LIST OF FIGURES
Figure 5.35: Variation of K’ and G with volumetric strain and deviator strain respectively in a
simulated FEM drained triaxial test. 128
Figure 5.36: Variation of K’ and G with mean effective stress, p’, and deviator stress, q,
respectively in a simulated FEM drained triaxial test. 128
Figure 5.37: Comparison of laboratory’s triaxial tests with HCC soil models. (a) Depth of
sample is 11m. (b) 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 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 struts. 133
Figure 5.42: Deflection profiles at various stages of excavation for HCC4-M. (a) Stage B.
(b) Stage C. (c) Stage D. (d) Stage E. (e) Stage F. (f) Stage G. (g) Stage H.
(h) Stage I. 134
Figure 5.43: Ground settlement behind Location I of the retaining wall for HCC1, HCC2,
HCC3 and HCC4. 136
Figure 5.44: Normalised ground settlement behind Location I of the retaining wall for MCC1,
MCC2, MCC3, MCC4 and MCC5. 136
Figure 5.45: Normalised ground settlement behind Location I of the retaining wall for HCC1,
HCC2, HCC3 and HCC4. 137
Figure 5.46: 2D vs 3D wall deflections behind Location I of the retaining wall for MCC1 and
HCC4. 138
Figure 5.47: 2D vs 3D ground settlements behind Location I of the retaining wall for MCC1
and HCC4. 138
Figure 5.48: Comparison of effect of kingpost modelling on 2D and 3D soldier pile deflection
for HCC4-M. 139
Figure 5.49: Comparison of effect of kingpost modelling on 2D and 3D soldier pile deflection
for MCC1-M. 140
Figure 5.50: 2D and 3D displacement vectors behind Location I of the retaining wall for
HCC4-M. 141
xiv LIST OF FIGURES
Figure 5.51: 2D and 3D ground settlement behind Location I of the retaining wall for
HCC4-M. 141
Figure A-1: Rotation transformation of axes for a 3D beam element 162
Figure B-1: A full-integration 8-noded quadrilateral element forming part of a beam. 163
Figure B-2: A full-integration 20-noded linear strain brick element forming part of a beam. 164
Figure C-1: Comparison of FEM modelling of stress reversal with laboratory test results done
by Stallebrass (1990) and Dasari (1996). 166
xv LIST OF SYMBOLS
LIST OF SYMBOLS
Upper case
A cross-sectional area of soldier pile
A pore pressure coefficient
B soldier pile width
C undrained cohesion
C’ effective cohesion
Cc compression index
Cs swelling index
Cub undrained cohesion at base of excavation
E Young’s modulus
Eh Young’s modulus in the horizontal direction
Eu undrained Young’s modulus
Ev Young’s modulus in the vertical direction
G shear modulus
G0 initial shear modulus
Ghv shear modulus representing the coupling between the horizontal and vertical
directions
H excavation depth
I second moment of area of cross section
Ixx second moment of area of cross section about x axis
Iyy second moment of area of cross section about y axis
K’ effective bulk modulus
K0 coefficient of earth pressure at rest
Ka coefficient of active earth pressure
Kmin’ minimum effective bulk modulus
Knc coefficient of earth pressure at rest in normally consolidated soil
xvi LIST OF SYMBOLS
Kp coefficient of passive earth pressure
LL liquidity index
M critical state frictional constant
N number of blows on sampling spoon during performance of standard
penetration test
OCR overconsolidation ratio
Pa active earth pressure
PI plasticity index
Pp passive earth pressure
Pt apparent earth pressure
S∞ tangential stiffness at very large strain
S0 initial tangential stiffness
Lower case
c cohesion
c’ effective cohesion
cc compression index
cs swelling index
e void ratio
ecs void ratio on the critical state line for p’=1
k coefficient of permeability
kx coefficient of permeability in the x-direction
ky coefficient of permeability in the y-direction
m overconsolidation ratio, OCR, exponent
n effective stress, p’, exponent
p’ mean effective stress
pc’ preconsolidation pressure
q deviator stress xvii LIST OF SYMBOLS
qˆ modified deviator stress
qf deviator stress at failure
su undrained shear strength
ln a Naperian (natural) logarithm of a
Greek symbols
∆hmax maximum wall deflection
∆vmax maximum ground settlement
εs deviator or shear strain
εv volumetric strain
εy deviator or shear strain at yielding
γs bulk unit weight of soil
γw unit weight of water
κ slope of swelling line in e-ln p’ space
κ0 slope of swelling line in e-ln p’ space for isotropic loading
κi slope of swelling line in e-ln p’ space for one-dimensional loading
λ slope of compression line in e-ln p’ space
λ0 slope of compression line in e-ln p’ space for isotropic loading
λi slope of compression line in e-ln p’ space for one-dimensional loading
υ specific volume
φ angle of friction
φ’ effective angle of friction
φcs critical state angle of friction
ν Poisson’s ratio
ν’ drained Poisson’s ratio
νhh Poisson’s ratio representing the coupling between the horizontal directions
xviii LIST OF SYMBOLS
νhv Poisson’s ratio representing the coupling between the horizontal and vertical
directions
σh’ effective horizontal stress
σv’ effective vertical stress
σx’ effective stress in x-direction
σy’ effective stress in y-direction
xix INTRODUCTION
CHAPTER 1 INTRODUCTION
1.1 Background
In 1930’s, an entire section of the Berlin subway collapsed because the bracing was designed for earth pressures calculated in accordance with an inappropriate theory
(Terzaghi et al., 1996). On the other hand, ground movements damaging to a sensitive monumental structure occurred adjacent to a deep cut in Washington, D. C., even though the bracing experienced no structural distress (O’Rourke et al., 1976). The retaining systems used in the above cases were a combination of soldier piles, lagging, walers and struts. Similar retaining systems were used in excavations for Munich and
New York subways (Terzaghi & Peck, 1948), excavations for the 12th and 19th Street
Stations of the BART system (Armento, 1972), the Downtown Seattle Transit Project
(Borst et al., 1990), eight project sites in Chicago Area (Gill & Lukas, 1990) and the
Bad Creek pumped storage facility near Salem, South Carolina (Pearlman & Wolosick,
1990).
In Singapore, soldier pile walls are used mainly for excavations in residual soils and where water drawdown is not a problem. They are less popular than sheet pile walls, although soldier piles installed in predrilled holes are often used to overcome the problem of inadequate penetration of sheet piles in areas where rock is encountered at shallow depths below excavation. In hard driving conditions caused by boulders or other obstructions, soldier piles can be predrilled if necessary, or relocated to avoid the obstruction, which gives them an advantage over sheet pile walls. Predrilling is often used in urban areas to avoid the noise and vibrations of pile driving. Soldier pile walls were used in basement excavations of Boulevard Hotel and Four Season Hotel along
1 INTRODUCTION
Orchard Boulevard. Serangoon and Woodleigh MRT stations along the north-east line were excavated 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
Soil Arch Formation Soldier Pile
Timber Lagging
Waler
King Post
Strut
Figure 1.1: Components 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 component) as indicated in Figure 1.1. Soldier
2 INTRODUCTION piles provide intermittent vertical support and are installed before excavation commences.
The behaviour of discrete piles in the retaining wall gives rise to complexities in design. Due to their relative rigidity compared to the lagging, the piles provide the primary support to the retained soil as a result of the arching effect which will be described in details in later section. The arching of soil behind the soldier piles is a local 3D effect (Figure 1.1) that cannot be analysed using 1D or 2D analyses. Spacing of the piles is chosen to suit the arching ability of the soil and the proximity of any structures sensitive to settlement. A spacing of 2 to 3 metres is commonly used in strong soils, where no sensitive structures are present. The spacing is reduced to 1 to 2 metres in weaker soils or near sensitive buildings. The 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 clays, all soils above the water table if they have at 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 driven in comparison to
3 INTRODUCTION sheet piles, thereby yielding significant savings in time and cost of installation and thus allowing excavation to commence with a minimum of lead time.
The design approaches on discrete pile retaining wall systems are laid out in numerous code of practices, e.g. BS8002 (1994), GCO (1990), Trada (1990) and
NAVFAC (1982). The details will be reviewed in Chapter 2. The design of retaining systems using soldier piles and timber lagging for deep excavation are becoming more demanding because of the increasing depth for which they are designed. Soldier piles retaining systems are used extensively for excavation in residual soil owing to its low construction cost as compared with diaphragm wall and bored pile retaining systems.
1.3 Deformations
In the frontispiece to his PhD thesis, Professor John Burland wrote (Burland,
1967):
“Stress is a philosophical concept - deformation is the physical reality.”
Engineers are familiar with concepts and calculations involving stresses in materials but what really matters – what the public sees – is movement and deformation which lead to damage and danger. Designers are particularly interested in making reliable predictions of the magnitudes of movements in the surrounding soil; and then estimating the effects of these movements on adjacent structures and facilities. In principle, these predictions can be achieved using powerful numerical methods such as finite element analyses.
4 INTRODUCTION
1.4 Objective
The objective of this study is to investigate the mechanism of soil support in a retaining system consisting of soldier piles and timber lagging.
In particular, the research will attempt to clarify the role of soil arching in discrete pile retaining walls and to provide an information base for rational design.
The effect of pile spacing and timber lagging stiffness on soil arching will also be investigated.
1.5 Scope of Work
Chapter 2 reviews the current design procedures and various methods for evaluating retaining systems. These include the different aspects of retaining wall that were investigated by researchers using simple beam and spring models to the state of the art 3D finite element analysis. A definition and behaviour of soil arching and will also be surveyed.
Chapter 3 had been contributed to journals Computers and Geotechnics entitled
“Three-dimensional pile-soil interaction in soldier-piled excavations” (Hong et al.,
2003). Strutted excavations, including soldier-piled excavations, are often analysed using two-dimensional (2D) finite element (FE) analyses with properties, which are averaged over a 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 beam representations to the corresponding theoretical solutions, followed by a reality check 5 INTRODUCTION with an actual case study. Finally, the results of 2D and 3D analyses of 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 this 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 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.
Chapter 4 begins by drawing attention to a case study of Serangoon MRT (Mass
Rapid Transit) site. The subsoil at the site consists of residual soil of a local granite formation known as Bukit Timah Granite. The temporary retaining structures for the excavation consisted of driven soldier piles and timber lagging supported by steel struts. In this chapter, the soil properties of Serangoon station’s geological formation and construction sequence of the retaining system are presented as a prelude to the subsequent chapter.
Chapter 5 discusses some results of a comparative study into the effects of different constitutive models in simulating soldier-piled excavations in medium to stiff soils. 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 methods of modelling retaining system, boundary and groundwater conditions and excavation sequence are described in this thesis. The behaviour in 2D and 3D for each soil model, Mohr Coulomb criterion, modified Cam-clay and hyperbolic Cam-clay, is investigated.
6 INTRODUCTION
Chapter 6 concludes the report by emphasising the complexity and importance of conducting a 3D analysis for soldier pile retaining system. A brief recommendation for future research work is also given.
7 LITERATURE REVIEW
CHAPTER 2 LITERATURE REVIEW
Reliable predictions of ground deformations are essential in the design process for (1) assessing the effects of excavation on adjacent facilities; and (2) identifying sections where special remedial construction measures are required. Available techniques for estimating wall deflections and soil settlements involve either interpolation from existing empirical databases or numerical analyses using finite element methods.
2.1 Design approaches for retaining systems
‘Limit analysis approach’ is often used as a preliminary tool to determine the component sizes of a retaining structure. In this approach, the equilibrium of the retaining structure with an assumed failure mechanism or some active earth pressure distribution is considered to evaluate the restoring forces or moments required.
Comparison of the available restoring forces with the required restoring forces yields a
‘factor of safety’. This is taken to be an indication of the available margin for diaphragm walls, which are now commonly used in basement construction, gives rise to several problems.
Firstly, whereas unstrutted walls can be treated as statically determinate problems once a failure mechanism is assumed for the surrounding soil, the same cannot be done for strutted walls. For single-strutted walls, using the ‘free earth support’ or ‘fixed earth support’ assumption can simplify the problem. Multi-strutted walls, on the other hand, are often difficult to reduce the degree of freedoms to the point where they can be solved as static problems.
8 LITERATURE REVIEW
Secondly, the requirement to limit ground movement often leads to the usage of fairly stiff strutting systems. Under such circumstances, ground deformation is often not large enough to allow full active or passive pressures to be developed around the wall. Thus, the assumption of active or passive condition usually does not accurately reflect reality.
Thirdly, even if the factor of safety can be evaluated, this parameter offers no information on the ground movement that is likely to be incurred. Because of these limitations, it is often difficult to apply conventional design approaches to multi- strutted excavations.
2.2 Various methods for evaluating retaining systems
A number of methods are available in practice to evaluate the soundness of retaining systems. They are empirical approaches based on proposed relations and charts, beam and springs model and 2 and 3D numerical analyses.
2.2.1 Empirical approaches
Various researchers (e.g. Peck, 1969; Goldberg et al., 1976; O’Rourke et al.,
1976; Clough & Denby, 1977; Clough et al., 1979 and Mana & Clough, 1981) have proposed empirical relations and charts for the evaluation of strut loads and ground movements in deep excavations. Table 2.1 summarises some of the empirical approaches available for retaining system evaluation.
9 LITERATURE REVIEW
Table 2.1: Empirical approaches contribution by various researchers. Scope Author Retaining system Soil type Settlement Peck (1969) Soldier pile and lagging - O’Rourke (1976) Soldier pile and lagging Dense sand and interbedded stiff clay Stiffness of support Goldberg (1976) Soldier pile and lagging - system Passive soil resistance Goldberg (1976) Soldier pile and lagging - Effects of passive soil Clough & Denby (1977) Sheet pile Soft to medium clay buttress Factor of safety against Clough et al. (1979) Soldier pile and lagging - basal heave Mana & Clough (1981) Soldier pile and lagging -
Settlement
Ground movements and strut loads in excavations are highly dependent upon the stress histories, soil properties, ground condition and the support system.
Settlement behind excavations can be estimated based on data obtained from previous excavations in similar conditions.
Figure 2.1: Observed settlements behind excavations (after Peck, 1969).
Peck (1969) summarised data on settlements behind excavations to produce the useful chart shown in Figure 2.1. Settlements presented as a percentage of the excavation depth were plotted against distance from the excavation divided by
10 LITERATURE REVIEW excavation depth. Three different zones, as defined in Figure 2.1, were identified. It should be noted that construction technique has a strong influence on movements of strutted systems.
Figure 2.2: Summary of settlements adjacent to strutted excavation in Washington, D.C. (after O’Rourke et al., 1976).
O’Rourke et al. (1976) compiled settlement data associated with soldier pile and lagging excavation in dense sand and interbedded stiff clay of Washington, U.S.A.
(Figure 2.2). Expressed as a percentage of the excavation depth, the surface settlements were equal to or less than 0.3% near the edge of the cut and 0.05% at a distance equal to 1.5 times the excavation depth. O’Rourke et al. (1976) carried out a comparative study of strutted excavations in the soft clay of Chicago using temporary berms and raking struts. The data are plotted in dimensionless form in Figure 2.3.
Three zones of ground displacement can be distinguished and related to the salient
11 LITERATURE REVIEW characteristics of construction. These zones approximate to the three zones of settlement delineated by Peck (1969), with the exception that the widths of the settlement zones are notably shorter. This indicated that the settlements associated with the Chicago excavations are confined to areas that are comparatively nearer to the edges of the excavation.
The charts provided by Peck (1969) and O’Rourke et al. (1976) took into account the construction and support systems in a general and qualitative manner. It is doubtful whether these curves, which were compiled from data obtained in North
America, are directly applicable to Singapore soil. The stiffness of the support systems is not quantitatively accounted for. Peck’s chart also overestimates the settlement due to the lower stiffness of struts in the 60’s. These empirical tools lack universal applicability as none of them considered all these factors.
Figure 2.3: Summary of settlements adjacent to strutted excavation in Chicago (after O’Rourke et al., 1976).
12 LITERATURE REVIEW
Stiffness of support system
The support system stiffness depends on the stiffness of the wall and its supports, the spacing between supports, and the length of wall embedded below excavation level. Goldberg et al. (1976) conducted a valuable study into the effect of wall stiffness and support spacing, and the results are presented in Figure 2.4.
Figure 2.4: Effects of wall stiffness and support spacing on lateral wall movements (after Goldberg et al., 1976).
Passive soil resistance
Goldberg et al. (1976) provided the method, illustrated in Figure 2.5, for determining the depth of penetration in ‘competent’ soils, which are capable of developing adequate passive resistance. The practicality of using this method on soldier pile walls is doubted, as the piles do not provide adequate contact surface
13 LITERATURE REVIEW below excavation level and the passive resistance between the soldier piles is non- existence.
Pt: Apparent earth
Figure 2.5: Calculation of embedment depth of sheet pile wall in relatively uniform competent soil conditions (after Goldberg et al., 1976)
Effect of passive soil buttresses.
The effectiveness of these in controlling movements in excavation in soft to medium clay was studied by Clough & Denby (1977). Figure 2.6 shows the theoretical relationships between settlements behind bermed sheet pile walls and the
γH stability number, , for the condition of excavation after the berm has been Cub removed and the rakers installed.
14 LITERATURE REVIEW
Figure 2.6: Relationship between maximum settlement and stability number for different batters (after Clough & Denby, 1977).
15 LITERATURE REVIEW
Factor of safety against basal heave
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).
Clough et al. (1979) and Mana & Clough (1981) reviewed case histories of sheet pile and soldier pile walls in clays supported primarily by cross-lot struts. The results are summarised in Figures 2.7 and 2.8, which show that the maximum lateral movement can be correlated with the factor of safety against basal heave defined by
Terzaghi (1943). The movement increases rapidly below a factor of safety of 1.4 and
1.5, while at higher factors of safety the non-dimensional movements lie within a narrow range of 0.2% and 0.8%. Moreover, there do not appear to be any significant differences in lateral movements between sheet pile walls whose tips are embedded in an underlying stiff layer and those whose tips remain in the moving clay mass. Wall deflection is sometimes correlated to and used as a control parameter for ground movement (e.g. Mana & Clough, 1981). For example, Mana & Clough (1981) reported that the maximum ground settlement ∆vmax typically lies between 0.5 and 1 times the maximum wall deflection ∆hmax for sheet-piled and soldier piled excavations.
This suggests that the ground loss arising from the inward movement of the wall is closely correlated to that due to ground settlement. 16 LITERATURE REVIEW
Figure 2.8: Relationship between maximum ground settlements and maximum lateral wall movements for case history data (after Mana & Clough, 1981).
2.2.2 1-D beam and spring models
Multi-strutted wall in a deep excavation is a statically indeterminate structure.
This has led to the development of computer models, which are based on treating the wall as a beam and the soil around the wall as equivalent generalised springs. An example is the classical Winkler solution of about 1867, in which the foundation is considered as a bed of springs.
Hetenyi (1946) developed solutions for a load at any point along a beam. Based on these equations, a load is applied at the strutted location to simulate the effect of strutting. The soil stiffness is reflected as the spring constant.
Bowles (1988) also modelled the sheet pile wall as beam elements, but utilised the concept of subgrade reaction for soil below the excavation level. The matrix stiffness method of analysis was used to obtain the solution. Pearlman & Wolosick
17 LITERATURE REVIEW
(1990) modelled soldier piles and diaphragm wall using beam on elastic foundation analysis to study the soil-structure interaction.
An advantage of the beam and spring approach over limit analysis is its ability to account for structure flexibility and soil stiffness. Thus, the effects of stress redistribution in soil because of differential structural deflections are accommodated.
Unfortunately, there are some limitations to this approach. There is inherent difficulty in determining the appropriate spring stiffness of the soil for analysis, as these are not fundamental soil properties. This method cannot directly simulate construction sequence, unusual initial soil stresses and development of wall friction. The Winkler solution did not account for the shear between the soil particles, which is a great disadvantage to this model. The analytical treatment of the soil continuum as a series of generalised springs implies that ground movement cannot be directly obtained from the computation.
2.2.3 2D finite element analysis
A summary of the contribution by various researchers in the area of 2D finite element simulation of excavation is presented in Table 2.2.
Prediction of excavation wall deformation or ground surface settlement in the centre section of an excavation has been studied using plane strain finite element analysis by many researchers (e.g., Clough & Denby, 1977; Clough & Hansen, 1981;
Clark & Wroth, 1984; Borja, 1990; Finno et al., 1991; Whittle et al., 1993). Apart from wall deflection and ground settlement, other researchers undertook a number of excavation-related studies.
18 LITERATURE REVIEW
Table 2.2: 2D finite element analyses contribution by various researchers. Scope of Study Author Retaining system Soil type Installation effect Finno et al. (1991) Sheet pile wall Chicago clay and Niagaran limestone Gunn et al. (1992) Diaphragm wall London clay De Moor (1994) Diaphragm wall London clay Ng et al. (1995) Diaphragm wall Gault clay Effect of wall length Hashash & Whittle Diaphragm wall Boston blue clay (1996) Bica & Clayton (1998) Cantilever Wall Sand (Experimental) Richards & Powrie Diaphragm wall Kaolin clay (1998) Earth pressures Fourie & Potts (1989) Cantilever Wall London clay Ling et al. (1993) Diaphram Wall Gault clay Bica & Clayton (1998) Cantilever Wall Sand (Experimental) Factor of safety against Mana & Clough (1981) Sheet piles and soldier Clay basal heave piles Clough & O’Rourke Sheet piles and soldier Clay (1990) piles Effect of water table Hsi & Small (1992) Diaphragm wall Sandy and clayey soil drawdown Effect of consolidation Yong et al. (1989) Diaphragm wall Singapore marine clay in Singapore Lee et al. (1989) Tieback sheet pile wall Singapore marine clay Parnploy (1990) Diaphragm wall Singapore marine clay Excavation in residual Lee et al. (1993) Bored pile wall Bukit Timah granite soils formation Discrepancies between Lee et al. (1989) Diaphragm wall Singapore marine clay computed and predicted results
Installation effect
The effect of wall installation on the lateral stresses in overconsolidated soil strata and on the behaviour of retaining walls is commonly recognised. It is featured in many discussions of retaining wall analyses and performance (e.g. Finno et al., 1991;
Gunn et al., 1992; De Moor, 1994 and Ng et al., 1995).
Finno et al. (1991) noted that the computed sheet pile displacements are slightly greater for the case of no sheet pile installation after initial excavation stage due to the preloading effect of sheet pile installation. These trends are reversed by the end of excavation because of the reduction of available passive resistance caused by the installation procedure.
19 LITERATURE REVIEW
Gunn et al. (1992) found that installation effects do seem to be significant when walls are propped. This can be understood as the propping action ‘locking in’ the reduction in lateral stresses associated with wall installation – the soil around the wall does not have the same freedom to strain and approach the classical stress distributions. However, the magnitude of installation effects depends strongly on the initial position of the ground water table. Installation effects are relatively minor when ground water table is high, and become more significant as it falls below excavation level.
De Moor (1994) showed that non-dimensional graphs could be produced that allow the change in lateral stress in the ground adjacent to the wall to be estimated for any given applied change in lateral stress at the wall excavation boundary, for a range
σ ' of wall panel widths. These estimates may provide more realistic h σ values than the v ' in situ conditions often used at present for analysis of diaphragm walls.
Ng et al. (1995) proposed that the stress changes in the ground are dominated by two distinct mechanisms: horizontal arching and downward load transfer.
Approximate analyses of the three-dimensional effects of diaphragm wall installation had been carried out using two simplified horizontal and vertical plane strain sections.
The analyses showed the horizontal arching results only in lateral stress redistribution, whereas downward load transfer can result in substantial stress reductions by shedding load downwards beneath the toe through the action of shear stresses in the vertical plane. However, the effects do not appear to be readily quantified. The authors recognised that techniques used to simulate the effects of wall installation by a general reduction in horizontal stresses in all soil above the toe level of the wall is less satisfactory than those that permit stress redistribution.
20 LITERATURE REVIEW
Effect of wall length
Hashash & Whittle (1992) demonstrated that wall length has a minimal effect on the pre-failure deformations for excavations in deep layers of clay, but does have a major influence on the location of failure mechanisms within the soil. Base stability is controlled by the location of the failure mechanism, which is constrained by the wall length.
Hashash & Whittle (1996) and Bica & Clayton (1998) also observed the trend of increasing bending moment with depth of embedment. This conflicts with the design recommendation that maximum bending moment should be evaluated with a safety factor of 1. This factor must instead be greater than 1 when evaluating the maximum bending moment.
Richards & Powrie (1998) showed that an increase in embedment depth will lead to an increase in wall bending moment and a reduction of bottom prop load.
There is no real advantage in terms of limiting ground movements in increasing the embedment depth without increasing the wall stiffness. The additional movement due to bending counteracts the reduction in the component of movement due to wall rotation.
Lateral earth pressures
Fourie & Potts (1989) examined the lateral earth pressures in front and behind the wall and found that the earth pressures measured near the cantilever wall bottom correspond to a value of Kp which is significantly lower than just below the excavation level.
21 LITERATURE REVIEW
Bica & Clayton (1998) showed experimentally that some cantilever wall design methods that use the same value of passive earth pressure both above and below the centre of rotation of the wall could be unsafe unless some conservative assumptions are made.
Ling et al. (1993) studied the reliability of the earth pressure measurements adjacent to a multi-propped diaphragm wall. It appeared that the earth pressure cells do not indicate changes in earth pressure with any great accuracy, although the direction of change is consistent with the derived earth pressures. Back analysis of earth pressure for final stage of excavation showed stress redistribution (arching) that was consistent with the changes in earth pressure recorded by instrumentation.
Basal heave
Mana & Clough (1981) and Clough & O’Rourke (1990) showed that measurement of maximum lateral wall deflection could be correlated with factor of safety against basal heave, as defined by Terzarghi (1943). The movements increase rapidly below a factor of safety of 1.4 to 1.5. At higher factor of safety, the non- dimensional movements lie within a narrow range of 0.2% to 0.8%. Moreover, there do not appear to be any significant differences in lateral movements between sheet piles walls whose tips are embedded in an underlying stiff layer and those whose tips remain in the moving clay mass.
Effects of water table drawdown
Hsi & Small (1992) developed a fully coupled finite element method for evaluating the deformations and pore pressures in a soil during excavation taking into account the drawdown of the free surface. This method is implemented in a finite
22 LITERATURE REVIEW element program, EXCA2 that is able to solve plane strain and axisymmetric problems. It can be used for elastic or elasto-plastic soils. To ensure the equilibrium of stresses within each increment of excavation and determine the location of the free surface, iterations using implicit Euler backward method, are required within each time step so that equilibrium can be achieved.
Singapore soil
A number of researchers, (e.g. Yong et al., 1989; Lee et al., 1989 and Parnploy,
1990) had analysed excavation in local Singapore Marine Clay. Lee et al. (1993) investigated the behaviour of excavation in both marine clay and residual soil.
Yong et al. (1989) indicates that an undrained analysis could not account for the progressive increase in lateral sheet pile movement and build-up of strut loads with time. The sheet pile movement may be substantially underestimated.
Lee et al. (1989) suggested a design method that uses movement control. It is based on the idea that reasonable estimates of support system movements can be made, including effects of soil conditions, structural components and construction process.
The design method is iterative in that trials are needed to adjust the estimated expected movements to the allowable values.
Parnploy (1990) studied the time-dependent behaviour of excavations in
Singapore marine clay. The author reported that the time-dependent change in ground movement is associated with the dissipation of negative pore-water pressure. Excess pressure begins to dissipate immediately and typically continues well beyond the completion of the excavation, resulting in progressive movements and increase in strut loads even when no excavation is being carried out. Parnploy (1990) also reported that
23 LITERATURE REVIEW piles installed prior to the excavation work would increase the stiffness of the soil in front of the wall and help to reduce the wall deflection.
Lee et al. (1993) proposed two mechanisms for the ground movement namely dissipation of excess negative pore pressure and drawdown-cum-seepage. For marine clay formations, pore pressure dissipation is sufficient to account for the observed ground movement. The low permeability of the soil formation is probably sufficient to limit the effects of drawdown and seepage over the duration of excavation. On the other hand, the much higher permeability of granitic residual soil formations ensures that the first mechanism is completed much more rapidly than the excavation duration.
Observable ground movement is thus likely to be the result of drawdown and seepage.
Among the researchers, only Mana & Clough (1981) and Clough & O’Rourke
(1990) studied the behaviour of soldier piles. They invoked the plane strain assumption so that problem simplifies drastically to 2D. Owing to arch formation in the retained soil, anisotropic behaviour of lagging and movement of soil between the soldier piles, 2D analysis over simplifies the mechanism of basal heave. Plane strain assumption is not strictly true because the strut loads are discrete point loads, not a line load as the load redistribution by the walers is not uniform. The plane strain assumption will lead to unrealistically large lateral stress reductions.
2.2.4 3D finite element analysis
A summary of the contribution by various researchers in the area of 3D finite element simulation of excavation is presented in Table 2.3.
Three-dimensional effects in excavation were observed in many field measurements. Dysli & Fontana (1982) observed the corner effects in a well-
24 LITERATURE REVIEW instrumented excavation and explore it further in a 3D non-linear analysis of an excavation in clayey soil using the program ADINA on VAX11-780. They failed to get any meaningful result because of the expensive cost, limitation of computer hardware and the unavailability of pre/post processor.
Table 2.3: 3D finite element analyses contribution by various researchers. Scope Author Retaining system Soil type Installation effect Ng & Yan (1999) Diaphragm wall Gualt clay Gourvenec & Powrie Diaphragm wall Lias clay (1999) Corner effect Giger & Krizek (1975) Unsupported Coulomb yield criterion (Analytical) Cardoso (1987) Tieback diaphragm wall Granitic residual soil Borja et al. (1989) Unsupported Elastoplastic (Numerical) Ou & Chiou (1993) Diaphragm wall Silty clay Matos Fernandes et al. Strutted diaphragm wall Silty clay (1994) Ou et al. (1996) Diaphragm wall Silty clay Ou & Shiau (1998) Diaphragm wall Silty clay Point load effect Tsui & Clough (1974) Tie-back diaphragm wall - Matos Fernandes (1986) Strutted diaphragm wall Silty clay Liu (1995) Diaphragm wall Singapore marine clay Wall deflection Briaud & Lim (1999) Tieback soldier pile Silty sand Small strain effect Nasim (1999) Strutted diaphragm wall Singapore marine clay Arching effect Vermeer et al. (2001) Tieback soldier pile - Axisymmetric analyses St. John (1975) Unsupported London clay Britto & Kusakabe Unsupported Clay (1983) Simpson (1992) Bored pile London clay
Installation effect
Ng & Yan (1999) confirms the roles of two stress transfer mechanisms: the horizontal arching and downward load transfer mechanisms during diaphragm wall installation. A three-dimensional analysis was carried out. The difference in the computed behaviour between the true and pseudo three-dimensional analyses is that the downward load transfer and the horizontal arching mechanism were uncoupled in the pseudo three-dimensional analyses.
Gourvenec & Powrie (1999) clarified the sequence of stress changes and displacements that takes place during the installation of a diaphragm wall in panels.
25 LITERATURE REVIEW
Their analyses showed that the magnitude and extent of lateral stress reduction near a diaphragm wall during construction depends on the panel length and are over-predicted in analyses assuming condition of plane strain. The analyses also showed that three- dimensional effects tend to reduce lateral soil movements during installation of a diaphragm wall in panels compared with the plane strain case, but soil movements increase markedly with panel length at aspect ratios (panel depth : panel length) of less than three.
Corner effect
Giger & Krizek (1975) analysed the stability of a vertical cut with a variable corner angle. Subsequently, Cardoso (1987), Borja (1989), Ou & Chiou (1993), Liu
(1995), Ou et al. (1996) and Ou & Shiau (1998) investigated corner effect of a 3D excavation.
Cardoso (1987) found out that settlements and horizontal deflections are smaller in the 3D case, especially at the corner, because of the soil arching and mutual support between intersecting walls. The lateral deflections for 2 and 3D case are almost the same at midsection, but settlements are overestimated in the 2D case. The reason being that the intermediate principal stresses in 3D case experience less reduction than in 2D case during excavation.
Ou & Chiou (1993) reported that for excavations with shorter sides, 3D analyses might be required to obtain a more realistic prediction of wall behaviour.
The significance of corner constraint was also studied by Matos Fernandes et al.
(1994). The authors also suggested that, near the corners, the structural behaviour is
26 LITERATURE REVIEW considerably influenced by the stress distribution due to soil arching as well as by the mutual support between the intersecting walls.
From the above reviews, it was noted that 3D geometrical considerations were essential in capturing the soil-structure interaction for retaining systems.
Unfortunately, the arching effect afforded by the soldier piles could not be captured in these literatures.
Point load effect
Tsui & Clough (1974) compared the earth pressure acting on a 0.3m thick concrete laterally supported by tie backs spaced 1m apart in clay. It was shown that the assumption of plane strain usually adopted in finite element analysis of strutted and anchored walls cannot be arbitrarily extrapolated to many practical problems, particularly those involving soldier pile walls or light sheet pile walls. Diaphragm walls, however, were shown to approximately satisfy the conditions assumed in a plane strain analysis. In general, discrepancies increase with wall flexibility, soil stiffness and tie back spacing.
Matos Fernandes (1986) concluded that 3D effects arising from strut loads are only significant near the struts and do not play an important role in the behaviour of the wall.
Liu (1995) simulated the struts in an excavation using springs. The disadvantage of this simulation is that the stiffness of the springs is a constant throughout the excavation process. Furthermore, it is difficult to obtain the stiffness of the raking struts.
27 LITERATURE REVIEW
Wall deflection
Briaud & Lim (1999) studied the influence of various design decision for tieback walls. One-dimensional beam elements were used to simulate soldier piles and tendons. The analyses used isotropic shell elements to model the timber lagging. The authors recommended that the first anchor be installed between 1.2m and 1.5m below the top of the wall. Deflections accumulated during this period are very difficult to eliminate by further tieback installation.
Small strain effect
Nasim (1999) showed that non-linear effect is likely to be more dominant away from the corners whereas, at the corners, the effects may be more important. Other situations where the non-linear effect is important are in the prediction of the response of piled and shallow foundations.
Several methods have been used to represent the non-linear behaviour of soils below the yield locus. The simplest, but not necessarily the best is to use variable shear modulus, G. For instance, Dasari (1996) developed a “strain-dependent Cam- clay model” by assuming that
G = Bp'n OCR mε b s (2.1) in the non-linear region, in which B, n, m and b are parameters to be measured from tests. Similarly, Nasim (1999) assumed that G decreases hyperbolically with εs.
Arching effect
Vermeer et al. (2001) studied both horizontal and vertical arching behind soldier piled retaining wall using finite elements. Horizontal arching was promoted by 28 LITERATURE REVIEW means of flexible horizontal lagging timbers and solid contact between the piles and the surrounding soil. A simple 2D analysis was performed to assess the amount of arching. As a result, lighter timber laggings could be used and the economy of the wall construction could be increased. High pre-stress forces in the upper ground anchors induced vertical arching.
Axisymmetry
St. John (1975) studied the differences between 2 and 3D analyses of square, unsupported excavation in London Clay using linear elastic finite element analyses.
His results showed that good agreement was obtained between the 2D axisymmetric and 3D analyses.
Britto & Kusakabe (1983) found that the width of the settlement zone adjacent to the excavation is approximately equal to 0.4 times the depth of excavation in 2D axisymmetric analysis. Burland et al. (1979) also suggested that an assumption of axial symmetry is more appropriate to computations for square excavations than is plane strain. This assumption is often difficult to apply to excavations that are irregularly shaped or supported by strutting system. The geometry of the analysis will induce large compressive hoop stresses in the wall resulting in unrealistically small deflection.
Simpson (1992), in his study of British Library excavation, reported that the differences between axisymmetric and plane strain analyses are negligible and attributed this to the shallow depth to a relatively rigid stratum.
Axisymmetric analyses are simple and intuitively reasonable for unsupported excavations, it is often difficult to apply to excavations that are irregularly shaped or
29 LITERATURE REVIEW supported by strutting systems. There is also a possibility that, if the stiffness of the strutting system is sufficiently high, corner effects may be suppressed to the point that the excavation behaves in a largely 2D plane strain manner.
Furthermore, if a soldier pile wall supports the excavation, the use of axisymmetric analysis will require the lateral modulus of the wall to be artificially reduced in order to avoid large compressive hoop stresses that would render the computed wall deflection unrealistically small. Finally, it also does not replicate the lateral flexural action of the walers system.
With the exception of works done by Briaud & Lim (1999) and Vermeer et al.
(2001), most research mentioned are not applicable to soldier piles retaining system owing to the added complexities of soil arching, movement between piles and anisotropy of lagging. Matos Fernandes (1986) simulated the soil and wall using linear elastic elements and the strut with spring. This will hardly reflect the complex behaviour of the soil that is more likely to be elastoplastic in nature. The work by Ng et al. (1995) and Ng & Yan (1999) highlighted the importance of using three- dimensional analyses in the investigation of horizontal arching. Beam elements used by Briaud & Lim (1999) may not realistically represent the interaction between the soldier piles and surrounding soil, owing to their inability to replicate the finite cross- sectional dimensions of real soldier piles. Vermeer et al. (2001) did not investigate the effect of pile spacing on arching, which will further determine the economy of the retaining system. The 2D analysis in a horizontal cross section may not give a realistic view of arching, which occurs in 3 dimensions. Axisymmetric analyses are strictly applicable to a circular unsupported excavation only. Research with this level of
30 LITERATURE REVIEW complexity in modelling has never been attempted from the literature survey conducted.
2.3 Soil arching
In addition to the above research, soldier pile retaining systems have added complications, viz. (1) soil arching and discrete piles, (2) interaction with timber lags.
Little has been published on the arching effect of soil for the design of retaining walls using discrete piles spaced some distance apart. As defined by the Committee on the
Glossary of Terms and Definitions in Soil Mechanics (1958), arching is the phenomenon of the transfer of stress from a yielding part of a soil mass to adjoining less yielding or restrained parts of the mass.
Terzaghi (1936) and Bosscher (1981) used the trap door testing apparatus and not discrete piles to quantify arching effect and draw parallelism between the two.
Nevertheless, the assumption that arching produces relieving effect is widely used in practice where the retaining systems consist of discrete piles and flexible timber lagging. Numerous uses of this assumption on discrete pile retaining wall systems exist in current geotechnical practice, BS8002 (1994), GCO (1990), Trada (1990) and
NAVFAC (1982).
2.3.1 Design procedures for soldier pile wall
Soldier piles are often designed and analysed as a contiguous wall systems even though they are, in reality, not so (e.g. Peck, 1969). Nonetheless, designers have long recognized that the soldier pile retaining system is not only often more flexible than other systems but the stiffness of the system is non-uniform in that the piles are much stiffer than the timber lags. To address this characteristic, Trada (1990) and BS8002
31 LITERATURE REVIEW
(1994) recommended a 20% to 25% reduction of Peck’s earth pressure for the soldier piles and 50% reduction for the timber lagging. It also indicates that relieving effect of the arching is much reduced with the use of stiffer lagging materials, for example concrete, due to lower relative flexibility of the concrete. Armento (1972) also proposed a similar reduction based on measurements from the excavations for the 12th and 19th Street Stations of the BART system. This is a simplifying assumption for a hinge at formation level. It makes an allowance for the difficulty of assessing the degree of fixity at the toe of the pile. Broms (1964), Teng (1975), NAVFAC (1982) and the Canadian Geotechnical Society (1992) proposed that the soldier pile of width
B be designed to support the passive earth pressure imposed by an extent of ground of span 3B (i.e. 1.5B on both sides of the pile) below the bottom of excavation. This is because the failure in soil due to individual pile elements is different from that of continuous walls for which pressure distributions are derived. All the above has made it difficult for designers to quantify the relieving effect of arching in soil.
2.3.2 Research on arching effect
If a portion of an otherwise rigid support of a granular mass yields, the adjoining particles move with respect to the remainder of the granular mass. This movement is resisted by shearing stresses that reduce the pressure on the yielding portion of the support while increasing the pressure on the adjacent rigid zone. This phenomenon is called the “Arching Effect”. “Arching” derives from the Latin archus, as in archery, for flight of an arrow. Lusher & Hoeg (1964) suggested arching as a
“thrust ring action” in soil surrounding an opening, and noted the existence of self- supporting soil arches or domes.
32 LITERATURE REVIEW
Terzaghi (1936) studied arching effect using the trap door testing apparatus. In
1943, Terzarghi described arching action in soils as “one of the most universal phenomena encountered in soils both in fields and in laboratory,” and devoted a chapter to the subject. However, he did not actually draw an arch, but used the term qualitatively to explain observed non-hydrostatic pressure distributions of soils against retaining walls. Getzler et al. (1968) described earth pressure distributions in terms of arching action but the authors rarely draw an arch.
Krynine (1945) proved by using Mohr’s circle that the stresses along the wall at the two ends are not the principal stresses but the rotation of the principal stresses.
Handy (1985a) extended this concept and concluded that soil-arching action may be depicted as a trajectory of minor principal stress that approximates a catenary. The concept of the dipping downward catenary arch was further discussed by Kingsley
(1989). He used the force equilibrium to prove that the shape of soil arch behind the wall can be, theoretically, very close to catenary or circular. This gives strong support to the assumption made by Handy (1985a) that both minor and major principal stresses are constant along the arch.
Handy (1985b) further that the self-supported arch must assign its continuous stress trajectory to the major rather than the minor principal stress. The soil arching actions features the continuous stress trajectory of minor principal stress for downward catenary type of soil arch and major principal stress for supportive soil arch.
Al-Hussaini & Perry (1978) found that, as a reinforced earth wall was surcharged to failure, wall pressures increased markedly above Rankine stresses near the centre of the wall while horizontal stresses in soil only a foot away were much lower. These changes are indicative of an arching action near the wall.
33 LITERATURE REVIEW
Bosscher (1981) investigated the role of soil arching in sandy slope using the trap door apparatus. His findings show that arching can occur in both loose and dense sand. The density of the soil at the slip surface may have contracted or dilated to the critical void ratio. Therefore, the soil stress transfer capability is the same in the loose and dense deposit.
Handy (1985a) explained soil arching in terms of rotation of principal stresses at the wall thereby producing appreciably higher wall pressure than those predicted by
Rankine or Coulomb analyses. The subsequent lateral wall yielding initiates active- state soil conditions, and reduces pressures on the lower wall. Nakai (1985) also noted this behaviour behind retaining wall in his 2D analyses.
As mentioned in previous section, Ng et al. (1995) and Ng & Yan (1999) studied soil arching as one of the mechanism during diaphragm wall installation. The horizontal arching mechanism transfers lateral stress (via the shear stress, τyx) from the center to the edge of the panel.
The discussion made by Handy (1985a & b) and Kingsley (1989) is limited to vertical arching in soil behind the wall. Horizontal arching was not explained.
Investigations on soil arching were done using trap door testing apparatus in experiments and 2D finite element analysis to explain the appreciably higher wall pressure than those predicted by Rankine or Coulomb analyses. Arching was never explained in terms of pressure distribution on the soldier piles and timber lagging in a
3D finite element analysis.
Due to their relative rigidity compared to the lagging, the piles provide the primary support to the retained soil as a result of the arching effect. The arching of
34 LITERATURE REVIEW soil behind the soldier piles is a local 3D effect that cannot be analysed using 1D or 2D analyses.
2.4 Review synopsis
The descriptions so far have shown that numerical analysis can play an important role as a research tool in studying earth-retaining structures. Its use as a design tool, however, is somewhat limited in the past owing to reasons stated by
Clough & Tsui (1977), namely (1) satisfaction with conventional methods; (2) difficulties with older numerical methods; (3) cost; (4) character of the geotechnical engineer. The last reason can be explained by the fact that most geotechnical engineers enjoy their work precisely because they often design using considerable
‘engineering judgment’ and less reliance on theoretical tools. In recent years, engineers have had the possibility to routinely use advance numerical methods in design. The possibility to do so is largely due to the increased availability of such programs, combined with the rapid pace of hardware development (Potts &
Zdravković, 2001).
Results from literature survey are not applicable to soldier piles retaining systems owing to the added complexities of soil arching, movement between piles and anisotropy of lagging.
Mana & Clough (1981) and Clough & O’Rourke (1990) studied the behaviour of soldier piles using 2D analysis. Owing to arch formation in the retained soil and movement of soil between the soldier piles, 2D analysis tends to oversimplify the mechanism of basal heave. Plane strain assumptions are not strictly true because the strut loads are discrete point loads, not a line load as the load redistribution by the
35 LITERATURE REVIEW walers is non-uniform. Matos Fernandes (1986) studied the effect of anchors and struts applied to a diaphragm wall at discrete points. The interaction between soil and soldier piles, as discrete elements is still unknown.
36 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION
CHAPTER 3 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION
Soldier piles with timber lags 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). The main advantage of using soldier piles is their relatively low cost and ease of installation, compared to other forms of support systems such as diaphragm walls and bored piles. Since the soldier piles are not contiguous, fewer soldier piles are needed in comparison to sheet piles, thereby yielding significant savings in time and cost of installation and thus allowing excavation to commence with a minimum lead time.
Soldier piles are often designed and analysed as a contiguous wall systems even though they are, in reality, not so (e.g. Peck, 1969, Potts & Zdravković, 2001). The fact that the soldier piles and timber laggings are of vastly different construction and have very different stiffnesses means that the interaction between the retaining system and the soil is three-dimensional (3D) in nature. However, most of the finite element
(FE) analyses on soldier pile walls to date are two-dimensional (2D) and based on the assumption of plane strain (e.g. O’Rourke, 1975; Clough et al., 1972; Tsui and Clough,
1974 and Gomes Correia and Guerra, 1997). The differences in pile and timber lagging stiffnesses cannot be modelled by these analyses, which necessarily assume a
“smeared” uniform stiffness for the entire span of the retaining wall. Briaud and Lim
(1999) used 3D FE analyses to study tieback soldier pile walls. However, their study focuses more on the parameters of the tiebacks and depth of soldier pile embedment rather the effects of different types of analyses. Furthermore, Briaud and Lim (1999)
37 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION modelled the soldier piles with beam elements. As will be discussed later, beam elements may not realistically represent the interaction between the soldier piles and surrounding soil, owing to their inability to replicate the finite cross-sectional dimensions of real soldier piles.
In this chapter, 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. “Smeared” uniform stiffness is used for the retaining systems in the 2D analyses. On the other hand, in the 3D analyses, different elements and material types represent the soldier piles and timber laggings. In the first part of this chapter, the ability of the 3D analyses to model the flexural behaviour of the soldier piles and timber laggings is examined. This is accomplished by comparing the flexural behaviour of various FE beam representations to the corresponding theoretical solutions. A reality check is then conducted using
O’Rourke’s study on the G Street test section as a reference. Finally, the results of a comparative study between 2D and 3D analyses on an idealized soldier piled excavation will be discussed to highlight the effects of using “smeared” uniform stiffnesses in 2D analyses. All of the analyses reported herein were conducted using an in-house version of CRISP (Britto and Gunn, 1990), with 3D beam and reduced- integration brick elements incorporated.
3.1 Modelling of soldier piles in 2D and 3D analyses
In this section, the modelling of soldier piles in 2D and 3D analyses is first addressed. Soldier piles act essentially in flexure, and it is well-known that 4-noded quadrilaterals with high aspect ratios do not model flexural behaviour well, the strain energy due to the transverse shear stress and strain becomes artificially large, which
38 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION causes shear-locking (e.g. Livesley, 1983; Reddy, 1993). The 8-noded quadrilateral element suffers from the same problem, albeit to a lesser extent (e.g. Reddy, 1993). It has been shown (e.g. Zienkiewicz and Taylor, 1988; Day and Potts, 1993) that, by using reduced-integration eight-noded quadrilaterals, flexural behaviour in 2D can be readily modelled. The same may presumably be true for the 20-noded brick element.
In order to assess the ability of various elements to represent the soldier pile, the idealized problem of a long cantilever beam subjected to a triangular load distribution, the latter representing an idealized earth pressure profile, was studied using various 2D and 3D representations, as shown in Figures 3.1 to 3.5. The 2D representations were achieved using beam elements as well as full- and reduced-integration 8-noded quadrilateral elements, hereafter termed FIQUAD and RIQUAD, respectively. The 3D representations were achieved using beam element as well as full- and reduced- integration 20-noded brick elements, hereafter termed FIBRICK and RIBRICK, respectively. For each type of element, two different cases were studied. In the first case, one element was used to model the whole length of cantilever beam. In the second, the cantilever was modelled using 18 elements of equal length. For the quadrilateral elements, the element aspect ratios for the 1- and 18-element representations are 1:70.5 and 1:3.9, respectively.
Figure 3.1a compares the deflected shape computed using 32-bit precision with the theoretical value from Euler-Bernoulli beam theory. As can be seen, all of the 8- noded quadrilateral representations show significantly smaller deflection than the theoretical value. The only representations that come close to the theoretical value are predictably, those using beam elements. Figure 3.2a shows the corresponding bending moment profiles obtained from the various representations. For beam elements, the bending moment profile was interpolated from the integration point values using a
39 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION spline function. For quadrilateral elements, the bending moments were evaluated using the method suggested by Rahim and Gunn (1997). As can be seen, the discrepancy in the deflection is also reflected in the bending moment profiles.
Figures 3.1b and 3.2b show the corresponding deflected shapes and bending moment profiles computed using 64-bit precision. As can be seen, a dramatic improvement in accuracy is now achieved in deflection and bending moment in the 18- element quadrilateral representations. On the other hand, both 1-element quadrilateral representations show little or no improvement in accuracy. In summary, flexural behaviour of the cantilever is well represented by single and multiple beam elements, in both 32- and 64-bit precision. The 18-element quadrilateral representations adequately represent the cantilever behaviour if they are used with 64-bit precision. In practice, this is unlikely to be a major constraint since 64-bit precision may be needed, in any case, to capture the large difference in stiffness between soil and pile (Britto &
Gunn, 1990). Between the two 18-element quadrilateral representations tested, the
RIQUAD representation produces a smoother bending moment profile whereas the
FIQUAD representation produces a rather jagged bending moment profile. The 1- element quadrilateral representations are unable to adequately replicate the deflection and bending moment profiles, regardless of whether 32- or 64-bit precision is used. In other words, the representations, which model cantilever flexure well, are the beam element and the RIQUAD element with 64-bit precision. Figure 3.3 shows the effect of using different number of RIQUAD elements, and therefore aspect ratios. As can be seen, reasonably good bending moment representation can be achieved for aspect ratio less than about 14. Figures 3.4 and 3.5 show the corresponding deflection and bending moment plots for the 3D representations. As can be seen, the performance trends of the various 3D representations closely mirror those of their 2D counterparts,
40 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION with the beam elements being the most reliable and the FIBRICK element being the least.
45 (a) 45 (b)
40 40
35 35
30 30
25 25
20 20 Height (m) Height (m)
15 15 Euler-Bernoulli beam theory Beam (1 element) Beam (18 elements) 10 10 Types of Quad Elements Aspect Ratio Full-integration 1:70.5 5 5 Full-integration 1:3.9 Reduced-integration 1:70.5 Reduced-integration 1:3.9 4.3kN 0 0 0123401234 Deflection (m) Deflection (m) Figure 3.1: Comparison of deflection profiles under distributed load for 2D 43m-cantilever beam. (a) 32-bit precision. (b) 64-bit precision.
45 45 Euler-Bernoulli beam theory Beam (1 element) 40 40 Beam (18 elements) Types of Quad Elements Aspect Ratio Full-integration 1:70.5 35 35 Full-integration 1:3.9 Reduced-integration 1:70.5 30 30 Reduced-integration 1:3.9
25 4.3kN 25
20 20 Height (m) Height (m)
15 15
10 10
5 5 (a) (b) 0 0 0 400 800 1200 1600 0 400 800 1200 1600 Bending Moment (kNm) Bending Moment (kNm) Figure 3.2: Comparison of bending moments under distributed load for 2D 43m-cantilever beam. (a) 32-bit precision. (b) 64-bit precision.
41 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION
45 (a) 45 (b)
40 40
35 35
30 30
25 25 1:7.0 1:70.5 1:3.9 1:35.2 1:14.1 20 20 Height (m) Height (m) Height Aspect ratio 15 15 1:70.5 1:35.2 1:14.1 10 10 1:7.0 1:3.9
5 4.3kN 5
0 0
012340 400 800 1200 1600 Deflection (m) Bending Moment (kNm) Figure 3.3: Effect of aspect ratios for 2D 43m-cantilever beam in 64-bit precision using RIQUAD elements. (a) Deflection. (b) Bending moment.
45 (a) 45 (b)
40 40
35 35
30 30
25 25
20 20 Height (m) Height (m)
15 15
10 10 Euler-Bernoulli beam theory Beam (1 element) Beam (18 elements) Types of Brick Elements Aspect Ratio 5 4.3kN 5 Full-integration 1:3.9 Reduced-integration 1:3.9 0 0 0123401234 Deflection (m) Deflection (m) Figure 3.4: Comparison of deflection profiles under distributed load for 3D 43m-cantilever beam. (a) 32-bit precision. (b) 64-bit precision.
42 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION
45 45
40 40 Euler-Bernoulli beam theory Beam (1 element) Beam (18 elements) 35 35 Types of Brick Elements Aspect Ratio Full-integration 1:3.9 Reduced-integration 1:3.9 30 30
25 25 4.3kN
20 20 Height (m) Height (m)
15 15
10 10
5 5
(a) (b) 0 0 0 400 800 1200 1600 0 400 800 1200 1600 Bending Moment (kNm) Bending Moment (kNm) Figure 3.5: Comparison of bending moments under distributed load for 3D 43m-cantilever beam. (a) 32-bit precision. (b) 64-bit precision.
In soldier-piled excavations, the soldier piles not only act in flexure but also attract earth pressures from the retained soil. Although this phenomenon is not modelled, and thus irrelevant, in 2D analyses, it is relevant to a 3D analysis wherein soldier piles and timber laggings are modelled explicitly. In this section, the ability of the beam and brick representations of the soldier piles to capture the interaction between pile and soil in a 3D analysis will be studied using a typical section of an idealized unstrutted, soldier-piled excavation shown in Figure 3.6. As can be seen, the chosen section consists of one half-soldier pile and the ground in front of and behind it.
The soldier piles are modelled using 64-bit precision and are spaced at an interval of six times the width of the soldier pile, center-to-center.
43 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION
(a) A' (b) A'
Soldier piles Soil layer 1 Soldier piles x x (brick element) (beam element) Soil layer 2
z z Excavation levels A A
15m AA' Soldier piles (c) (d) 0.0m -4.5m -7.5m -11.5m
-24.0m y
x -37.0m
100m
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 in section A-A. (c) Cross- sectional view in x-y plane of the FEM model. (d) Soil layers, struts and excavation levels.
In this analysis, the outer cross-sectional dimensions and flexural rigidity EI of the soldier are based on the properties of the 610 mm × 305 mm × 149 kg/m H-pile
(BSI, 1996). The outer cross-sectional dimensions are only simulated in the RIBRICK elements, not beam element. Nodes on the four vertical faces of the mesh are only allowed to move in-plane. The bottom face is fixed in all directions. Timber laggings are not modelled, as the objective of this exercise is to study the ability of various soldier pile representation to model the pile-soil interaction. Soil Layer 1 is underlain by Layer 2 at 22.5m depth to model the increasing stiffness of real ground. Each soil layer is assumed to be elastic and uniform. The soldier pile is socketed 1.5m deep into
Layer 2. A Poisson’s ratio of 0.02 is used for RIBRICK soldier pile elements as pure
44 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION bending behaviour is only achieved if Poisson’s ratio is zero (MacNeal, 1994). The properties of the soldier piles and soil are shown in Table 3.1.
Table 3.1: Idealised soil and soldier pile properties for beam and brick soldier piles study. 3 Soil layer 1 (Depth: 0-22.5m) γs = 19.5 kN/m Elastic model E = 50000 kN/m2 ν = 0.3 K0 = 0.94 -9 kx = 1.0×10 m/s -9 ky = 1.0×10 m/s 3 Soil layer 2 (Depth: 22.5-37m) γs = 19.5 kN/m Elastic model E = 120000 kN/m2 ν = 0.3 -9 kx = 1.0×10 m/s -9 ky = 1.0×10 m/s Half soldier pile modelled with beam at 6B pile spacing E = 1×108 kN/m2 -3 4 Ixx = 1.259×10 mm -5 4 Iyy = 9.308×10 mm ν = 0.29 A = 0.019 m2 Half-soldier pile modelled with RIBRICKs at 6B pile spacing E = 4.36×107 kN/m2 (610×152.5mm) ν = 0.02 G = 2.14×107 kN/m2
The soldier pile is assumed in-place at the start of the analysis. The excavation process is assumed to occur in three lifts with pore pressure dissipation being modelled using the Biot’s (1941) consolidation formulation. The final depth of excavation is
11.5m.
As shown in Figure 3.7a, the solid and beam elements give similar results and the differences appear to be minor. The differences are more clearly reflected in
Figure 3.7b, where the bending moment of the solid elements is clearly larger than that of the beam element, although the differences are still not substantial. This can be attributed to the finite cross-sectional dimensions of the RIBRICK element, which enables it to attract a larger proportion of the earth pressure through the arching process than the beam elements.
45 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION
0 0
5 5
10 10
Depth (m) 15 Depth (m) 15 Soldier pile location Beam RIBRICK 20 Mid-span location 20 Beam RIBRICK
(a) (b) 25 25 0.00 0.02 0.04 0.06 -200 0 200 400 Deflection (m) Bending Moment (kNm) Figure 3.7: (a) Deflection profile of soldier pile and soil at the center between adjacent piles. (b) Bending moment profile of soldier piles.
0.037
Beam 0.036 RIBRICK
0.035 Beam element CL (m) Deflection Brick element Mid-span of lagging 0.034 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Lateral distance from soldier pile (m) Figure 3.8: Plan view of lateral deflection retaining system 9m depth after final excavation stage.
Figure 3.8 shows the local deflection of soldier pile and soil face, in plan view, at 9m depth below ground surface for half-span between adjacent soldier piles. As can be seen, the differential movement between pile and soil is clearly larger with the beam representation than the RIBRICK representation of the soldier pile. Furthermore, as shown in Figures 3.9a and 3.9b, although the development of stress arch in the soil is evident in both representations, the local stress distribution is very different. The brick
46 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION representation results in a much higher concentration of stresses in the vicinity of the soldier pile than the beam representation, owing to its finite dimensions. In addition, the stress arch spans over a shorter distance but extends deeper into the retained soil in the case of the brick representation. This allows the soil movement to be better coupled to the pile movement than the beam representation. Thus, although a beam element is slightly more accurate in replicating the flexural behaviour of the soldier pile, local pile-soil interaction is better represented using solid elements. For this reason, subsequent 3D analyses discussed herein will model the soldier piles using reduced-integration 20-noded bricks with 64-bit precision, unless otherwise stated. 0.915 0.732
0.549 0.366 (a) 0.183 0.000 0.00 1.00 2.00 3.00 0.915 Span (m) 0.732 0.549 0.366 (b) 0.183 0.000 0.00 1.00 2.00 3.00 Distance from retaining wall (m) 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.
3.2 Comparison with case history
In this section, a comparison is made with O’Rourke’s (1975) field measurement of an 18.3m-deep braced excavation in the G Street test section (Panel
158). Figure 3.10 shows the plan view of the retaining system. The modelled geometry and excavation sequence follows closely that of O’Rourke’s. Figure 3.11 shows the 2D and 3D FE meshes used in the current analyses. The 2D mesh follows
47 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION that of O’Rourke’s, whilst the 3D mesh is merely an “extrusion” of the 2D mesh in the third dimension.
Strut
Reaction Plates
Waler
Soldier Pile
3’-9” 12’-6” 6’-3”
Figure 3.10: Plan view of retaining system after O’Rourke (1975).
Plan view Upper Brown Sand Middle Gray Clay Gray Sands and Interbedded Stiff Clay strut Lower Orange Sand Hard Cretaceous Clay Cretaceous Sands, Gravels, Clays timber Excavation levels soldier pile lagging 0.0m EE == 48263.3kPa48300kPa νν == 0.30.3 φ ° CC == 12.4kPa φ = 3333° 4.18m 7.60m EE == 13789.5kPa13800kPa νν == 0.49 CC == 48.3kPa φ = 00°° 10.62m EE == 103421.4kPa10300kPa νν == 0.30.3 14.33m CC == 20.7kPa φ = 3333°° EE == 137895.2kPa13800kPa νν == 0.30.3 CC == 10.3kPa φ = 3535°°
ν EE == 241316.5kPa24100kPa ν == 0.49 CC == 289.6kPa φ = 00°°
EE == 344737.9kPa34500kPa νν == 0.30.3 CC == 48.3kPa φ = 3535°° 39.40m Soil properties Cross sectional view Figure 3.11: Finite element mesh used for reality check with O’Rourke (1975).
Figure 3.11 shows the soil parameters from O’Rourke (1975), which were adopted in this comparative study. Since O’Rourke only presented total stress
48 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION parameters, only a total stress analysis was performed. Furthermore, following
O’Rourke, the Drucker-Prager soil model is used for all soil layers.
Table 3.2: Idealised soil and soldier pile properties for O’Rourke’s case study. Soldier piles E (kPa) ν Ghv (kPa) 5.09×107 0.02 2.5×107 4 4 2 Struts E (kPa) Ixx (m ) Iyy (m ) Area (m ) Level 1 (36 WF 260) 1×108 0.0072 4.54×10-4 0.0623 Level 2 1×108 1.19×10-6 1.19×10-6 0.0296 Level 3 1×108 0.55×10-6 0.55×10-6 0.0238 Level 4 1×108 1.19×10-6 1.19×10-6 0.0296 Level 5 1×108 1.19×10-6 1.19×10-6 0.0296 Timber lagging Eh (kPa) Ev (kPa) νhh νvh Ghv (kPa) 12×103 1 0.02 3×10-13 0.3676
In the 2D analysis, the soldier pile wall was modelled using beam elements with a “smeared” wall stiffness derived by scaling the bending stiffness of individual soldier piles over the distance separating them and neglecting the effects of the timber lags; this also follows O’Rourke’s (1975) procedure. In the 3D analyses, the soldier piles and timber lags are modelled using RIBRICK elements, the properties of which are shown in Table 3.2. The soldier pile properties were derived from the section properties of the 24 WF 100 H-piles used in the excavation. Less is known about the timber lags apart from the fact that they were made from oak wood. Back-calculation using BS8002 (1994) guidelines and AITC (1994) suggest that the required thickness of the timber lags is likely to be about 100mm, which falls within the common range of timber lagging thickness (Tomlinson, 1995). Because of the uncertainty over the thickness of the timber lagging, the analysis was repeated with timber lagging thickness of 50mm and 100mm. Since timber lagging is normally installed in the form of long, narrow planks slotted horizontally in between the flanges of the soldier piles
(e.g. Tomlinson, 1995; BS8002, 1994), the flexural rigidity of the timber lagging to bending in the vertical direction is likely to be very small. To model this behaviour, an anisotropic elastic material model is used for the timber lagging, with the Young’s modulus in the vertical direction being set much lower than that in the horizontal
49 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION direction, Table 3.2. This differs from Briaud and Lim’s (1999) analyses, which used isotropic shell elements to model the timber lagging. The braces and walers were modelled using beam elements, with properties adjusted to replicate those in the field.
0 0
5 5
10 10
Depth (m) 15 Depth (m) 15
Field (O’Rourke, 1975) IN4B 20 IN5B 20 Soldier pile models RIQUAD 2D beam (a) RIBRICK (b) 25 25 0.000 0.005 0.010 0.015 0.020 0.025 -300 -100 100 300 500 Deflection (m) Bending moment (kNm) Figure 3.12: Comparison of a series of 2D and 3D analyses from O’Rourke (1975). (a) Soldier pile deflection. (b) Bending moments.
Figure 3.12a compares the computed wall deflection to the O’Rourke’s measured final deflection. As can be seen, all the computed deflections agree reasonably well with one another and with the field measurements. The same can be said of the bending moment diagrams in Figure 3.12b. This indicates that the results of the FE analyses are reasonably realistic. Nonetheless, it is interesting to note that the
3D FE analysis predicts a slightly larger maximum soldier pile deflection than the 2D analyses; in spite of the fact that the “smeared” stiffness of the soldier pile wall in the
2D analysis does not take into account the contribution from the timber lagging. In other words, if the 3D analysis is taken as a reasonably accurate representation of reality, then the wall deflection from the 2D analysis represents an optimistic, rather
50 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION than average, estimate of the soldier pile and timber lagging deflection. The reason for this will be examined in greater detail later.
0 0 0
5 5 5
10 10 10
Depth (m) Depth (m) Depth (m) Depth 15 Field (O’Rourke, 1975) 15 15 IN4B IN5B Soldier pile location 100mm lagging 20 50mm lagging 20 20 Mid-span location 100mm lagging 50mm lagging 25 25 25 0.00 0.01 0.02 0.03 0.00 0.01 0.02 0.03 0.00 0.01 0.02 0.03 Deflection (m) Deflection (m) Deflection (m) (a) (b) (c) 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.
Figures 3.13a – c show the deflection profiles leading to various excavation levels. As can be seen, more substantial differences between measured and predicted wall deflection are present in the earlier stages. This may be attributed to the fact that soil behaviour is not truly linearly elastic prior to yielding. The lower strain levels, which are incurred in the early stages, could have allowed higher soil stiffness to be mobilised than in the final stages. The timber lagging thickness of 50mm and 100mm leads to nearly the same result, thus indicating that the results are not heavily contingent upon the assumed thickness of timber lagging. In both cases, the computed deflection of the timber lagging is significantly larger than that of the soldier pile deflection. This is to be expected, since the timber lagging is much more flexible than the soldier piles and thus expected to deflect more. In other words, significant
51 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION differences can arise between the soldier pile deflection and that of the intervening soil.
0
5
10
Depth (m) 15
20 2D RIQUAD 3D RIBRICK no smearing 3D RIBRICK smeared stiffness 25 0.000 0.005 0.010 0.015 0.020 0.025 Deflection (m) Figure 3.14: Effect of ‘smearing’ on rotational fixity below excavation level.
Figure 3.13 also shows that, just below excavation level, there is a short segment of the soldier pile that moves ahead of the soil. This is to be expected; the soldier pile wall is not a continuous wall below excavation level. The presence of soil between adjacent soldier piles allows the piles to move relative to the intervening soil; this movement being accentuated if the soil yields. In 2D analysis, the discontinuous nature of the wall cannot be modelled since a uniform wall with a reduced “smeared” stiffness is assumed instead. This suppresses the relative pile-soil movement, thus exaggerating the degree of rotational fixity afforded by the pile embedment. As shown in Figure 3.14, using a “smeared” stiffness for the soldier pile and the intervening soil in a 3D analysis leads to a deflection profile that is virtually identical with that from a
2D analysis, thus indicating that the difference in deflection between 2D and 3D
52 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION analyses noted earlier arises from the representation of the non-uniform stiffness of the soldier pile and intervening soil.
0
5
10 Field (O’Rourke, 1975) IN4B IN5B φ = 33° Depth (m) 15 c = 12.41kPa c = 5.0kPa φ = 30° c = 5.0kPa c = 2.0kPa 20 c= 0.1kPa
25 0.000 0.005 0.010 0.015 0.020 0.025 Deflection (m) Figure 3.15: Modelling the S-shaped deflection profile of the soldier pile in 3D.
It is interesting to note that the S-profile present in O’Rourke’s field data was not predicted in the FE analyses. One possible reason for this is the high values of cohesion and friction angle prescribed by O’Rourke (1975) for the top layers of soil.
O’Rourke reported significant variation in the modulus of the Upper Brown sand from about 41MPa to about 97MPa. This is suggestive of significant variation in soil properties with location, which is not considered in the analysis wherein uniform soil properties are assumed. As shown in Figure 3.15, progressive reduction in c and φ values does lead to an S-shape soldier pile deflection profile.
53 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION
3.3 3D and 2D comparisons
3.3.1 Idealised excavation
The complexity of the soil profile and multi-level bracing at the G Street excavation renders an in-depth study of pile-soil interaction difficult. For this reason, an idealized excavation involving two levels of bracing in a single soil type is studied, as shown in Figure 3.6. To enhance the long-term stability of the soil face, 3-inch thick timber laggings were used. As can be seen, the two levels of bracing were set at
4.5m and 7.5m below the original ground level. The two-levels bracing’s configuration is suggested to study the stress changes due to strutting at different depths. Boundary conditions are similar to those used in the back-analysis of the G
Street excavation. Initial groundwater table is assumed to be 2m below original ground level, this being a typical groundwater table depth in Singapore conditions.
The corresponding 2D mesh is not shown since it is merely a vertical section of the 3D mesh.
Table 3.3 shows the properties of soil and structural components used in the analyses. The analyses conducted are effective stress analyses and the soil properties prescribed are representative of granitic sapprolites. Such geologic material occurs widely in Singapore (Dames and Moore, 1983) and can be described as a silt of intermediate or high plasticity (BS5930, 1999). Soldier piles have been used as a retaining system in such soils (e.g. Wong et al., 1997). The modified Cam-clay model is used to describe the behaviour of the soil skeleton since it allows soils with different over-consolidation ratios (OCRs) to be modelled while requiring relatively few parameters compared to other, more complex models. The lack of detailed
54 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION information about the soil to be modelled does not justify the use of more sophisticated models in such an idealized study.
Table 3.3: Idealised soil and soldier pile properties for idealised study. 3 Soil layer 1 (Depth: 0-22.5m) γs = 19.5 kN/m Modified Cam-clay cc = 0.1 cs = 0.01 M = 1.2 ecs = 1.47 ν = 0.3 K0 = 0.94 3 Soil layer 2 (Depth: 22.5-37m) γs = 19.5 kN/m Elastic E = 120000 kN/m2 ν = 0.3 3 2 Timber lagging at 3in thickness Eh = 16.3×10 kN/m 2 Elastic Ev = 1 kN/m νhh = 0.02 -5 ν vh= 2.2×10 2 Ghv = 0.37 kN/m Soldier pile modelled with 2D beam element E = 1.09×108 kN/m2 -3 4 Ixx = 1.259×10 mm ν = 0.29 A = 0.019 m2 Half soldier pile modelled with RIBRICK at 3B pile spacing E = 2.18×107 kN/m2 (610×152.5mm) ν = 0.02 G = 1.07×107 kN/m2 Half soldier pile modelled with RIBRICK at 6B pile spacing E = 4.36×107 kN/m2 (610×152.5mm) ν = 0.02 G = 2.14×107 kN/m2 Strut at 3.75m spacing modelled with beams E = 2.67×107 kN/m2 -3 4 Level 1 at 165.0kN/m Ixx = 1.259×10 mm Level 2 at 441.1kN/m ν = 0.29 A = 0.019 m2 Half strut with stiffness equivalent to 3.75m spacing modelled with E = 1.22×107 kN/m2 -3 4 beams for cases of 3B pile spacing Ixx = 1.259×10 mm -5 4 Level 1 at 75.5kN Iyy = 9.308×10 mm Level 2 at 201.8kN ν = 0.29 A = 0.019 m2 Half strut with stiffness equivalent to 3.75m spacing modelled with E = 2.44×107 kN/m2 -3 4 beams for cases of 6B pile spacing Ixx = 1.259×10 mm -5 4 Level 1 at 151.0kN (30-60%) (Wong et al., 1997) Iyy = 9.308×10 mm Level 2 at 403.6kN (40-70%) ν = 0.29 A = 0.019 m2 Note: Walers are assumed to be sufficiently stiff and able to distribute the load evenly to all soldier piles and thus not modelled in the idealized analyses.
Table 3.4: Summary of effective stress analyses for the idealised excavation at OCR = 3 and k = 1×10-8m/s. Analysis Geometric representation Preloading 2D-1 Plane strain No 2D-2 Plane strain Yes 3D-1 3B No 3D-2 6B No 3D-3 3B Yes 3D-4 6B Yes Note: B is the width of the soldier pile.
55 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION
Figure 3.16 shows the excavation and wall installation sequences of the idealized excavation. For the non-preloaded cases, the preloading stage is simply omitted in the analyses. As shown in Table 3.4, the effects of preloading and centre- to-centre inter-pile spacing on the discrepancy between 2D and 3D analyses are examined.
Excavation stage ABC DE F G 0 1 2 3 Install strut level 1 4 5 6 Install strut level 2
Depth (m) 7 Preload strut level 1 8 9 10 Preload strut level 2 Lull period 11 (20 days) 12 0 102030405060708090100110120 Time (days) Figure 3.16: Construction sequence for idealized excavation from stage A through G.
3.3.2 Wall deflection
Figure 3.17 compares the 2D and 3D computed wall deflection profiles for the non-preloaded soldier piles at the final stage of construction. As can be seen, for inter- pile spacings of 3 and 6 times the soldier pile width B, the 3D analyses predict slightly larger maximum soldier pile deflection than the 2D analysis, this being consistent with the trend indicated for the G-Street excavation. The deflection profile at the mid-span of the timber lagging is more variable. For an inter-pile spacing of 3B, the timber lagging deflection remains reasonably well coupled to the soldier pile deflection. For an inter-pile spacing of 6B, the timber lagging deflection becomes much larger than
56 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION the soldier pile deflection. It should be noted that an inter-pile spacing of 6B is not unrealistic; in the G-Street excavation (O’Rourke, 1975), the inter-pile spacing was approximately 6.5B. Comparison of the soldier pile and timber lagging deflection profiles shows that, above excavation level, the mid-span deflection is larger than the soldier pile deflection, which is consistent with the fact that the soldier pile is supporting the soil face through the timber lagging and the soil arch spanning across adjacent piles. On the other hand, the reverse is the case just below excavation level.
This occurs because, whereas the soil face at the mid-span can adopt rather sharp curvature, the soldier pile cannot, owing to its much higher flexural stiffness. Thus, soldier pile deflection can only decrease gradually below excavation level thereby resulting in higher deflection in the pile than the mid-span soil. This is similar to the
3D FE results on the deflection of pile groups adjacent to surcharge, reported by
Bransby and Springman (1996).
0
5
10
Depth (m) Depth 15 2D-1 Soldier pile location 3D-1 3D-2 20 Mid-span location 3D-1 3D-2
25 0.00 0.01 0.02 0.03 0.04 0.05 Deflection (m) Figure 3.17: Comparison of wall deflection between 2D and different pile spacing for cases without preloading at final stage of construction.
57 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION
Figure 3.18 shows the wall deflection profiles of the preloaded cases at the final stage of construction. As can be seen, preloading pushes the soldier pile backwards into the retained soil, this combining with the excavation below strut level to produce the S-shape profile that is also present in O’Rourke’s measurement, but not in the idealised non-preloaded case discussed in the previous section.
0
5
10
Depth (m) 15
2D-2 Soldier pile location 3D-3 20 3D-4 Mid-span location 3D-3 3D-4 25 0.00 0.01 0.02 0.03 0.04 0.05 Deflection (m) Figure 3.18: Comparison of wall deflection between 2D and different pile spacing for cases with preloading at final stage of construction.
0.030 Stage B 0.025 D 0.020
0.015 Deflection (m) C
0.010 0.0 0.2 0.4 0.6 0.8 1.0 Span (m) 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 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION
Figure 3.19 compares the differences in deflection at the excavation face 4.5m below ground level before and after preloading. As shown in Figure 3.16, in stage B, excavation just reaches a depth of 4.5m. At this point, the deflection of the soldier pile is larger than that of the intervening soil, owing to the large flexural stiffness of the wall, as discussed earlier. In stage C, the process of preloading pushes soldier pile and the soil rearwards, but with the soldier pile displacing more. Subsequent excavation
(stage D) allows the soil to move forward more than the soldier pile as the latter is restrained by the strut and waler system.
3.3.3 Stress changes
This interaction between soil and soldier pile is illustrated in Figures 3.21 to
3.26, which show the stress paths for two points in the retained soil at the upper strut level, which is located at a depth of 4.22m below ground surface. As shown in Figure
3.20, one point (marked I) is located just behind a soldier pile whereas the other
(marked II) is located just behind the mid-span of the timber lagging. Results for a corresponding point at the same depth from a corresponding 2D analysis are also plotted for comparison.
(I)
x
z (II)
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 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION
The deviator stress q is strictly a positive quantity. In Figure 3.21, a modified quantity qˆ is instead plotted, such that
()σ' − σ' qˆ = y x q (3.1) ' − ' σ y σ x
where σx’ and σy’ are the horizontal and vertical effective stresses
The use of qˆ in place of q allows an active stress state (σy’ > σx’) to be distinguished from a passive stress state (σx’ > σy’).
120
100
80 I nitia l yie 60 ld lo G cus D,E,F 40 ^ q 20
0 A
-20 Deviator stress, stress, Deviator -40 B,C
-60
-80
-100 C SL -120
0 102030405060708090100110120 Mean effective stress, p' Figure 3.21: Stress path plot for 2D-1 without preload. Stages A to G are shown in Figure 3.16. Units of stresses in kPa.
As Figure 3.21 shows, for the 2D analysis, initial excavation leads to an increase in mean effective stress due to the drag from the soil flow above the monitored point. However, this quickly fades away as the formation level approaches the monitored level [end point B] and lateral effective stress starts to decrease.
60 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION
Meanwhile, q continues to increase as shear stresses build up in the retained soil.
Further excavation below the formation level leads to a reversal in the sign of qˆ [end point D] as the lateral stress falls below the vertical stress, leading to an active stress state. Comparison of Figures 3.21 and 3.22 shows that preloading causes the stress state to remain in a passive, rather than active, state throughout the entire construction sequence, thereby eliminating the passive-active reversal predicted for the non- preloaded case.
120
100
80 I niti al y iel 60 d lo cus 40 ^ q 20
0 A
-20
Deviator stress, stress, Deviator C -40 B D E F,G -60
-80
-100 C SL -120
0 102030405060708090100110120 Mean effective stress, p' Figure 3.22: Stress path plot for 2D-2 with preload. Stages A to G are shown in Figure 3.16. Units of stresses in kPa.
As Figures 3.23 and 3.24 show, the initial stress changes behind the soldier pile
(point I) and the timber lagging (point II) are similar to that of the 2D prediction in
Figure 3.21. At both locations, initial excavation leads to an increase in mean effective stress and a passive stress state due to the drag from the soil flow above the monitored point. As excavation approaches the monitored level, the release in lateral stress due
61 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION to soil removal in front of the wall leads to an active stress state [end points B and C].
However, further excavation below the first strut level produces very different stress paths at the two monitored locations. As shown in Figure 3.23, the build-up of lateral stress at the base of the soil arch between adjacent soldier piles results in a passive stress state, which persists up to the end of the construction sequence. On the other hand, as negative pore pressure in front of the soil arch dissipates, the effective stress in the soil behind the timber lagging decreases as the soil approaches a state of incipient active failure at the end of the construction sequence. In physical terms, this suggests significant softening of the soil behind the timber lagging. These stress path differences are accentuated as the soldier pile spacing increases from 3B to 6B.
120
100
80 I niti al y 60 iel d lo cus [B,C] 3B,6B 40
^ q 20
0 A
-20 Deviator stress, stress, Deviator -40 [F,G] 3B [D,E] 3B,6B -60 [F,G] 6B -80 Spacing 3B -100 C SL 6B -120
0 102030405060708090100110120 Mean effective stress, p' Figure 3.23: Stress path plots for 3D-1 and 3D-2 at point I without preload. Stages A to G are shown in Figure 3.16. Units of stresses in kPa.
62 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION
120
100
80 [B,C] 6B In iti 60 al [B,C] 3B yie ld loc 40 us ^ q [D,E,F] 6B 20 [D,E,F] 3B 0 A
-20 Deviator stress, stress, Deviator -40
-60
-80 Spacing 3B -100 C 6B SL -120
0 102030405060708090100110120 Mean effective stress, p' Figure 3.24: Stress path plots for 3D-1 and 3D-2 at point II without preload. Stages A to G are shown in Figure 3.16. Units of stresses in kPa.
120 Spacing 100 3B 6B 80 I niti al y iel 60 d lo cus [B] 40 6B [B] 3B ^ q 20
0 A
-20 [C] Deviator stress, 6B -40 [C] 3B
[D] 3B [D] 6B -60 [E,F,G] 3B [E] 6B -80 [F,G] 6B -100 C SL -120
0 102030405060708090100110120 Mean effective stress, p' Figure 3.25: Stress paths plots for 3D-3 and 3D-4 at point I with preload. Stages A to G are shown in Figure 3.16. Units of stresses in kPa.
63 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION
120
100
80 [B,C] 6B In 60 itia l [B,C] 3B yie ld l oc 40 us ^ q [D,E,F] 6B 20 [D,E,F] 3B 0 A
-20 Deviator stress, stress, Deviator -40
-60
-80 Spacing 3B -100 C SL 6B -120
0 102030405060708090100110120 Mean effective stress, p' Figure 3.26: Stress path plots for 3D-3 and 3D-4 at point II with preload. Stages A to G are shown in Figure 3.16. Units of stresses in kPa.
Comparison of Figures 3.25 and 3.26 with Figures 3.23 and 3.24 shows that preloading does not have significant effect that it has on the 2D analysis. The only significance changes that arise from preloading occur behind the soldier pile and consist of an earlier reversal back to a passive stress state [before end point C] and a slightly larger mean effective stress at the end of the construction sequence. Both of these are directly attributable to the preload. There is no significant difference at location II.
Comparison of Figure 3.21 with Figures 3.23 and 3.24 as well as Figure 3.22 with Figures 3.25 and 3.26 shows that, at any given end point, the stress state predicted by the 2D analysis appears to lie somewhere between those of locations I and II in the
3D analysis. This is not surprising in view of the fact the retaining effect of the soldier pile and timber lagging is “smeared” in a 2D analysis. The large changes in the 2D
64 IDEALISED ANALYSIS OF PILE-SOIL INTERACTION stress paths between Figures 3.21 and 3.22 appears to be due to the fact that “smeared” stress path of the 2D analysis is affected by the small variations in the strongly divergent stress states of the two locations.
3.4 Synopsis on 3D and 2D analyses
Strutted excavations, including soldier-piled excavations, are often analysed using 2D FE analyses with properties that are averaged over a certain span of the wall.
The foregoing discussion shows that when such an approach is applied to soldier-piled excavations, modelling errors can arise in several ways. Firstly, by modelling the discrete soldier piles as a wall, a 2D analysis tends to over-predict the coupling of pile to the soil below excavation level. In instances where the pile is not embedded into stiff soil, this modelling error can give rise to discernible underestimation of soldier pile deflection. Secondly, the deflection of the timber lagging, which is usually larger than that of the soldier piles, is often underestimated. Thirdly, a 2D analysis cannot replicate the differences in stress paths taken by the retained soil at different locations at the same depth. In particular, it cannot model the softening of the soil face just behind the timber lagging. In instances where the timber lagging is insufficient or its delayed installation, this softening can give rise to local collapse, which may exacerbate the ground loss and therefore ground movement. Increasing the inter-pile spacing will tend to accentuate the effects of these modelling errors.
65 GEOTECHNICAL STUDY OF SERANGOON MRT SITE
CHAPTER 4 GEOTECHNICAL STUDY OF SERANGOON MRT SITE
The North-East Line is a new mass rapid transit line that will run from the
World Trade Centre in the south of the Singapore island towards the North-East. As shown is Figure 4.1, it passes through the Central Business District, and following the corridors of Serangoon Road and Upper Serangoon Road up to the new towns of
Hougang, Sengkang and Punggol. Outram Park and Dhoby Ghaut stations are two existing stations where the new North-East Line will criss-cross an existing line. The line is approximately 20 kilometres (km) long and it will be built primarily underground. It will consist of 16 stations and one depot when fully completed.
Figure 4.1: Singapore north-east MRT line with location plan.
4.1 Serangoon MRT site geology
The Serangoon Mass Rapid Transit (MRT) station will be located underground at the junction of Upper Serangoon Road and Serangoon Central. In order to study in detail the behaviour of soldier piles and timber lagging retaining system, field
66 GEOTECHNICAL STUDY OF SERANGOON MRT SITE measurements have been performed throughout the project. Inclinometers were installed around the perimeter of Serangoon station. Strain gauges were also installed at each layer of struts. The depth of excavation reaches 26m below existing ground level. The support system employed is strutted soldier piles and timber lagging.
The Serangoon MRT station is situated on a ridge of Bukit Timah Granite
Formation, which refers to an entire suite of igneous rocks, principally granite, adamellite and granodiorite (PWD, 1976). The Central Singapore Granite is a granitic intrusion which occupies an area in the centre of Singapore island extending some 8 km in the northerly direction and 7 km in the westerly direction where it forms hills and valleys of both high and low relief. In general, the granite revealed in the MRT projects had been of grades V and IV. Some limited volumes of grades III, II and I had been found. The gradation from V to II can be very sudden in the weathering profile. Weathering of granite is primarily due to chemical action involving the breakdown of its primary minerals. The resultant soil is mainly sandy and/or clayey silt. Figures 4.2 and 4.3 show the typical geological profiles at Serangoon station. The two profiles do not register abrupt changes across the sections. The layout of boreholes sunk at the Serangoon station site are shown in Figure 4.4.
The Dames & Moore’s report (1983) classified the Bukit Timah formation into four sublayers:
a) G1: refers to fresh to slightly weathered Bukit Timah Formation
(Weathering Grades I and II);
b) G2: refers to moderately to highly weathered Bukit Timah Formation
(Weathering Grades III and IV);
67 GEOTECHNICAL STUDY OF SERANGOON MRT SITE
c) G3: refers to bouldery soil with boulders exceeding 400mm average
dimension surrounded by completely weathered rock and residual soil
(Weathering Grades III and IV);
d) G4: refers to completely weathered rock or granitic sapprolites in the
form of residual soil (Weathering Grades V and VI);
Soil investigation results indicate that Serangoon Station is underlain by G4 soil up to a depth of 60m below existing ground level. The geological formation at
Serangoon station can be further divided into the following five sub-units:
a) Layer 1 (Fill & G4a): Stiff Silty Clay - fill is underlain by reddish
brown to light brown silty clay. The SPT N values range from zero to
15 blows/300mm.
b) Layer 2 (G4b): Medium dense Silty Clay to Clayey Silt - medium
dense whitish pink silty clay to clayey silt, with traces of sub-angular
to sub-rounded, fine medium size gravels. The SPT N values range
from 15 to 30 blows/300mm.
c) Layer 3 (G4c): Medium dense to dense Silty Sand - medium dense to
dense dark green silty sand with some fine quartz gravel. The SPT N
values ranges from 30 to 50 blows/300mm.
d) Layer 4 (G4d): Very dense Silty Sand - a layer of very dense greenish
grey silty sand with angular to sub-angular quartz gravel overlies the
weathered granite material. The SPT N values range from 50 to 100
blows/300mm.
68 GEOTECHNICAL STUDY OF SERANGOON MRT SITE
Figure 4.2: Soil profile of Serangoon MRT site at section A-A.
Figure 4.3: Soil profile of Serangoon MRT site at section B-B.
69 GEOTECHNICAL STUDY OF SERANGOON MRT SITE
Figure 4.4: Plan view of Serangoon MRT station. MRT station. of Serangoon view Plan 4.4: Figure Zone 1 Zone 2 Zone 3 Zone 4 Zone 5 30 20 10 5 Borehole Borehole borehole Additional Inclinometer 0
70 GEOTECHNICAL STUDY OF SERANGOON MRT SITE
e) Layer 5 (G4e): Weathered Granite - weathered granite is pinkish grey
to light grey with dip of joint ranging from 20-60 degrees. The SPT N
values are greater than 100 blows/300mm.
Figure 4.5 presents the variations of bulk unit weight and Atterberg Limits versus depth of G4 soil at Serangoon MRT site.
0 0 Plastic Limit Liquid Limit
-10 -10
-20 -20 Depth (m) Depth (m) -30 -30
-40 -40
(a) (b) -50 -50 16 18 20 22 0 20406080100 Unit Weight (kN/m3) Atterberg Limits (%) Figure 4.5: Variation of physical properties at Serangoon MRT site. (a) Bulk unit weight. (b) Atterberg Limits.
60
CH 50 LL = 50% = LL e in 40 L CL A
30
MH & OH 20 Plasticity index, PI
10
ML MH & OL 0 0 102030405060708090100 Liquid limit, LL Figure 4.6: Plasticity chart of G4 soil at Serangoon MRT station.
71 GEOTECHNICAL STUDY OF SERANGOON MRT SITE
Figure 4.7: Grain size distribution of G4 soil at Serangoon MRT station.
Figures 4.5 and 4.8 show the variation of some of the basic properties of the G4 soils with depth. The Atterberg limits of this soil put it in the class of medium plasticity inorganic silt as shown in Figure 4.6. This is consistent with the particle size distribution data in Figure 4.7, which shows a predominant particle size range varying from sand to silt. As shown in Figures 4.8a, b and c, the SPT blow counts N, undrained Young’s modulus and undrained shear strength show a gradually increasing trend with depth, rather than stepwise fashion, thus indicating that the transition from one layer to the next is often not abrupt. This is consistent with the c’ values, which do not show any significant increase that would suggest an increase in the degree of structure or bonding. The significant scatter in the values of effective cohesion c’ and friction angle φ’ can be explained by the fact that most of the Mohr Circle plots in the site investigation reports (OYO, 1996; Ove Arup & Partners, 1997) imply a slightly curved failure envelope, which has been noted by many researchers; e.g. Roscoe et al.
(1958), Roscoe et al. (1963) and Schofield & Wroth (1968), rather than the straight
72 GEOTECHNICAL STUDY OF SERANGOON MRT SITE line fit prescribed by the Mohr Coulomb envelope. Thus, the derived value of c’ and
φ’ depends somewhat on how the straight line is fitted to the curve.
The overconsolidation ratio values of G4 soil decrease from 4 near the ground surface to 1 at depth of 20m. In the site investigation for this project, the OCR was measured using oedometer test. Chong (1998) showed that sampling disturbance tends to cause a significant reduction in the values of parameters related to the yield surface of the soil, which includes the preconsolidation pressure pc’. Thus, it is possible that the measured values of the OCR represent a lower bound of the actual OCR in the field. It should also be mentioned that the presence of a preconsolidation pressure which is higher than existing overburden effective stress does not suggest overconsolidation in the actual sense of the word, since the soil is derived from weathering of rock rather than consolidation of deposited specimens. For this reason, the apparent OCR so measured may be more related to the structure of the soil, including bonds, rather than actual overconsolidation. Various authors (e.g. Terzaghi et al., 1996; Balasubramaniam & Brenner, 1981; Brumund et al., 1976; Bjerrum, 1973) have shown that naturally and artificially cemented soils do possess an elevated preconsolidation pressure.
73 GEOTECHNICAL STUDY OF SERANGOON MRT SITE
0 0 0
-10 -10 -10
-20 -20 -20 Depth (m) Depth (m) Depth (m) Depth -30 -30 -30
-40 -40 -40
(a) (b) (c) -50 -50 -50 0 20406080100 0 100 200 300 400 500 600 0 100 200 300 SPT (N) E (MPa) su (kPa)
0 0 0
-10 -10 -10
-20 -20 -20 Depth (m) Depth (m) Depth (m) Depth -30 -30 -30
-40 -40 -40
(d) (e) (f) -50 -50 -50 0 10203040 0 10203040 01234 c' (kPa) φ' (°) OCR Figure 4.8: Variation of soil properties with depth at Serangoon MRT site. (a) SPT values. (b) Undrained Young’s modulus. (c) Undrained shear strength. (d) Effective cohesion. (e) Effective friction angle. (f) Over-consolidation ratio.
Permeability assessment employing the variable head method was conducted for soil layer at track level (depth ranges from 14-20m). Figure 4.9 summarises the permeability of G4 soil with depth at the MRT site. At borehole NA124 (RL 101.5m) and BH11 (RL 85.63m), the permeability of Clayey Silt layer registered is 1.70×10-
7m/s and 2.81×10-8m/s respectively. At a borehole 1.7km away, the permeability in the
Silty Sand layer (RL 92.6m) is 2.42×10-7m/s. The permeability in the vicinity lies in
74 GEOTECHNICAL STUDY OF SERANGOON MRT SITE the order of 10-7m/s in the top two layers of soil. The values obtained from the site represent the upper bound permeability indicated in Dames & Moore (1983) for G4 soil. The average overall permeability recommended by Dames & Moore is 1×10-8m/s with a lower bound of 4×10-10m/s. Lee et al. (1993) reported the typical permeability of G4 materials to be between 10-7 and 10-9m/s. The water table exists at 5m below ground. The lowering of water head monitored ranges from 0.1m/day to 1.1m/day for all stages of excavation.
0
-10
-20 Depth (m) -30
-40
-50 0 5 10 15 20 k ( x10-7 m/s) Figure 4.9: Variation of soil permeability with depth at Serangoon MRT site.
Table 4.1 summarises the soil properties for the various sub-layer of G4 soil at
Serangoon MRT site.
Table 4.1: Soil properties of Serangoon MRT site.
Sub-layer γs E’ c’ φ’ k OCR (kN/m3) (MPa) (kPa) (m/s) G4a 18.5 5.0 + 5.5z 11 27° 1.4×10-7 2-4 G4b 19.0 80.0 + 5.0z 17 30° 2.1×10-7 1-2 G4c 19.5 500.0 + 4.5z 25 38° 9.7×10-8 1 G4d 20.0 2000.0 + 2.2z 30 38° 7.8×10-8 1 G4e 21.0 30000.0 + 2.2z 35 40° 4.0×10-8 1 Note: Young’s moduli are expressed as variation with depth, z.
75 GEOTECHNICAL STUDY OF SERANGOON MRT SITE
4.2 Retaining system
The retaining system used in this project is soldier piles with timber lagging.
Figure 4.10 shows the retaining system at the MRT site after installation of first layer of strut in Zone 2. The soldier piles are 610mm × 305mm × 149kg/m H-pile (BSI,
1996) driven at 1.5m centre to centre shown in Figure 4.11. The struts are located
7.5m apart at Zone 2. The first level of strut is 3.5m below ground level. The spacing between each level of struts varies from 3-4m as illustrated in Figure 4.12. The raking struts, 3.5m each, (250mm × 250mm × 64.4kg/m H-piles) are connected to the main strut, one on each side, inclined at 45° as shown in Figure 4.10. The walers consist of
610mm × 305mm × 149kg/m H-piles. No pre-stressing was applied to the struts. The timber lagging consists of 3in × 8in (76mm × 203mm) Kempas wood. Table 4.2 summarises the prop system from the excavation retaining system.
Table 4.2: Struts details for Serangoon MRT retaining system. Level Strut Vertical Spacing Waler Raking Strut 1 H610×305 0.5m – 3.5m to ground level H610×305 H250×250 149kg/m 1.2m – 3.15m to 2nd layer strut 149kg/m 64.4kg/m 2 2H610×305 1.2m – 3.15m to 1st layer strut 2H610×305 H250×250 149kg/m 4.0m to 3rd layer strut 149kg/m 64.4kg/m 3 2H610×305 4.0m to 2nd layer strut 2H610×305 H250×250 149kg/m 4.0m to 4th layer strut 149kg/m 64.4kg/m 4 2H610×305 4.0m to 3rd layer strut 2H610×305 H250×250 149kg/m 4.0m to 5th layer strut 149kg/m 64.4kg/m 5 2H610×305 4.0m to 4th layer strut 2H610×305 H250×250 149kg/m 3.0m to 6th layer strut 149kg/m 64.4kg/m 6 2H610×305 3.0m to 6th layer strut 2H610×305 H250×250 149kg/m 3.5m to excavation level 149kg/m 64.4kg/m
76 GEOTECHNICAL STUDY OF SERANGOON MRT SITE
Figure 4.10: Soldier pile and timber lagging retaining system of Serangoon station.
0 10 20 30 metres
EGL = 123.75m
EL = 106.35m
Figure 4.11: Plan view of retaining system for Serangoon MRT station.
77 GEOTECHNICAL STUDY OF SERANGOON MRT SITE
Depth H610×305×149kg/ 3.5m
2H610×305×149kg/m 6.5m
2H610×305×149kg/m 10.5m
2H610×305×149kg/m 14.5m
2H610×305×149kg/m 18.5m
2H610×305×149kg/m 21.5m
25.0m H610×305×149kg/m @ 1.5m c/c
42.0m
Figure 4.12: Cross sectional view of retaining system for Serangoon MRT station.
4.3 Construction sequence
The excavation depths are 15m at the concourse and approximately 25m at the platform. Propped soldier piles retaining walls were adopted to temporarily support the proposed excavation. Construction followed a “bottom-up” type sequence with steel frames providing temporary propping support as excavation proceeded downwards. As the permanent works slabs were casted from the bottom upward the temporary props were removed sequentially, with the floor slabs being used as permanent props to the permanent walls.
The soldier piles were firstly driven to the designed level. Upon completion of the soldier piles installation, excavation commenced cell by cell (zone by zone). The excavation commenced from two ends of the station toward the centre. On reaching
78 GEOTECHNICAL STUDY OF SERANGOON MRT SITE the designed level, strutting would follow, while excavation to the same level would continue in the next cell. Thus, strutting was also performed successively from two ends of station, i.e. Zones 1 and 5, towards the centre. This cycle was repeated until all of the zones have been excavated to the designed level, after which excavation to the next level would be carried out in a similar cycle. Timber lagging was installed after the exposed soil face of the excavation reaches a depth of 1 to 1.5m. Following the timber installation, further excavation up to another 1m to 1.5m below the installed timber lagging was carried out. This cycle was repeated until the full excavation completed. No back-filling of voids or dewatering was conducted in the retained ground behind the soldier piles with the exception of Zone 1 in Serangoon Station site, where problems of water ingress and local collapse of soil were encountered (Lee et al., 2001).
The construction details are as follows:
a) After the installation of kingposts and soldier piles, excavate from
EGL to a depth of 2m below and install timber lagging;
b) Excavate to 5m below EGL and install timber lagging. Install 1st
layer strut at a depth of 3.5m below EGL;
c) Excavate to 8m below EGL and install timber lagging. Install 2nd
layer strut at a depth of 6.5m below EGL;
d) Excavate to 12m below EGL and install timber lagging. Install 3rd
layer strut at a depth of 10.5m below EGL;
e) Excavate to 16m below EGL and install timber lagging. Install 4th
layer strut at a depth of 14.5m below EGL;
79 GEOTECHNICAL STUDY OF SERANGOON MRT SITE f) Excavate to 20m below EGL and install timber lagging. Install 5th
layer strut at a depth of 18.5m below EGL; g) Excavate to 23m below EGL and install timber lagging. Install 6th
layer strut at a depth of 21.5m below EGL; h) Excavate to 25m below EGL and install timber lagging.
80 FEM STUDY OF SERANGOON MRT SITE
CHAPTER 5 FEM STUDY OF SERANGOON MRT SITE
This chapter discusses the interaction between material and geometric modelling of soldier piled excavations, using the measured data from Serangoon MRT site as the reference. The computed behaviour of soldier piled excavations will be examined using 2D and 3D analyses and with 3 soil models, namely Mohr Coulomb criterion, modified Cam-clay and a hyperbolic Cam-clay model (Nasim 1999). Fitting attempts and sensitivity studies will be made on the wall deflection and ground settlement using the three models. By so doing, the performance of each type of soil model in finite element analysis will be assessed. Additionally, a set of soil parameters will be determined for each model that gives good agreement between computed and measured movements. With these sets of parameters, 2D and 3D analyses will be conducted to examine the stress changes and wall deflection development during excavation and its final settlement profile.
5.1 Geometry of finite element model
The finite element model for the Serangoon MRT Station excavation is shown in Figure 5.1. As shown in Figure 5.2 (section B-B’), the modelled section is located at 20.4m from the nearest corner. The soil domain was modelled using FIBRICK elements with pore-pressure degree of freedoms at vertex nodes. RIBRICK elements without pore-pressure degree of freedoms were used for soldier piles for reasons highlighted in Chapter 3. The struts and walers were modelled with beam elements.
As discussed in Chapter 3, the timber lagging is modelled using RIBRICK elements with anisotropic elastic material model. Kingposts installed within the excavated area are also modelled using beam elements as their cross-sectional dimensions are too
81 FEM STUDY OF SERANGOON MRT SITE small to be modelled viably using solid elements. As will be shown later, the presence of kingposts has a significant effect on the computed base heave.
As shown in the plan view of Figure 5.1, only half of the strutted section and half of the intervening soil domain were modelled to take advantage of symmetry.
Timber lagging Layer 1 Layer 2 Soldier pile Layer 3 Layer 4 Layer 5
Plan view of section A - A'
AA' Depth 0.0m Strut level 1 3.5m Strut level 2 6.5m Strut level 3 10.5m Strut level 4 14.5m Strut level 5 18.5m Strut level 6 21.5m 25.0m 28.5m King (KP Toe) Posts
Soldier 42.0m piles (SP Toe)
79.0m Cross sectional view Figure 5.1: Finite element model for Serangoon MRT site excavation.
The modelling of boundary and groundwater conditions is similar to that discussed in Chapter 3 and will not be repeated herein. The bottom boundary is located in weathered granite rock which is likely to undergo much less movement than the overlying strata (Britto and Gunn, 1990). Preliminary trials indicate that the results
82 FEM STUDY OF SERANGOON MRT SITE
B B’ Zone 1 Zone 2 Zone 3 Zone 4 Zone 5 Figure 5.2: Plan view of Serangoon MRT station indicating the section B-B’ modelled. modelled. B-B’ section the indicating MRT station of Serangoon view Plan 5.2: Figure 30 20 10 5 Borehole Borehole borehole Additional Inclinometer 0
83 FEM STUDY OF SERANGOON MRT SITE of the analyses are not unduly sensitive to the location of the bottom boundary. This is consistent with the findings of Potts & Zdravković, (2001), who attributed it to the fact that soil strength and stiffness usually increase with depth. Britto and Gunn (1990) suggested that the vertical end boundary be placed at a distance of between 4 to 5 times the final depth of the excavation from the retaining wall. Liu’s (1995) finding for Marine Clay using modified Cam-clay indicates that beyond a distance 3 times the depth of excavation, the far-field boundary will have little effect on the settlement. In the present analyses, the far-field vertical boundary was set at 4 times the depth of excavation. The water table for the subsequent analyses was set at 5m below ground surface in accordance with standpipes’ readings given in the soil investigation report.
5.2 Modelling of excavation sequence
As summarised in Figure 5.3, the excavation was simulated in 15 stages. Since fully coupled consolidation analyses were conducted, the increments also modelled the dissipation of pore pressure in the soil with time. As shown in Figure 5.3, the time duration for each stage of construction were also modelled in the analyses. The analyses were performed with the soldier piles already in place, as the driving of the piles cannot be simulated by CRISP. The installation of the pile was itself a complex process and its effects on the in-situ stress conditions could not be modelled into the analyses. The excavation process was simulated by the removal of appropriate soil elements from the finite element mesh.
84 FEM STUDY OF SERANGOON MRT SITE
Excavation stage ABCDEFGHI 0 Install timber lag Install strut level 1 and timber lag 5 Install strut level 2 and timber lag
10 Install strut level 3 and timber lag Install strut level 4 15 and timber lag Depth (m)Depth Install strut level 5 and timber lag 20 Install strut level 6 and timber lag Install timber lag 25
0 50 100 150 200 250 300 Time (days) Figure 5.3: Excavation with strut and timber lagging installation sequence.
5.3 Parametric studies for various models
Table 5.1 shows the soil properties used for each type of material model.
Comparison of Figure 5.1 and Table 5.1 shows that the entire excavation took place within Layers 1 and 2, which correspond to the fill and medium dense silty clay/clayey silt, the latter being residual soil derived from the weathering of the granitic rock. It is thus likely that the modelling of these two soil layers will significantly affect the computed results. For this reason, three types of soil model, namely the Mohr
Coulomb criterion, modified Cam-clay and strain-dependent hyperbolic Cam-clay
(Nasim, 1999) models, are considered for these two layers.
85 FEM STUDY OF SERANGOON MRT SITE
Table 5.1: Soil properties of Serangoon MRT site. 3 MC Depth (m) K0 γs (kN/m ) E’ (Mpa) c’ (kPa) φcs’ φp’ ν kx (m/s) ky (m/s) Layer 1 0.0-11.5 0.9 18.5 2.7z + 9.2 11 27° 33° 0.30 1.4×10-7 1.4×10-7 Layer 2 11.5-22.5 0.9 19.0 3.4z – 8.3 17 30° 36° 0.28 2.1×10-7 2.1×10-7 Layer 3 22.5-37.0 1.0 19.5 10.8z – 172.8 27 - 38° 0.30 9.7×10-8 9.7×10-8 Layer 4 37.0-55.0 1.0 20.0 2.2z + 2000.0 30 - 38° 0.30 7.8×10-8 7.8×10-8 Layer 5 55.0-79.0 1.0 21.0 2.2z + 30000.0 35 - 40° 0.33 4.0×10-8 4.0×10-8 3 e MCC Depth (m) K0 γs (kN/m ) κ λ cs M ν kx (m/s) ky (m/s) Layer 1 0.0-11.5 0.9 18.5 0.020 0.087 1.74 1.07 0.30 1.4×10-7 1.4×10-7 Layer 2 11.5-22.5 0.9 19.0 0.021 0.109 1.98 1.2 0.28 2.1×10-7 2.1×10-7 3 HCC Depth (m) K0 γs (kN/m ) C (kPa) n m qf (kPa) G∞ (kPa) Layer 1 0.0-11.5 0.9 18.5 155 0.8 0.23 177.5 0 Layer 2 11.5-22.5 0.9 19.0 131 0.8 0.23 369.2 0 Note: Young’s moduli are expressed as variation with depth, z. MC: Mohr Coulomb criterion MCC: Modified Cam-clay HCC: Hyperbolic Cam-clay
Based on the soil investigation reports by OYO (1996), Ove Arup & Partners
(1997) and Dames & Moore (1983), an initial estimate of soil parameters for the three different models are set out in Table 5.1. As discussed below, the hyperbolic Cam- clay model requires the use of the modified Cam-clay parameters as shown in Table
5.1, as well as five additional parameters, the value for which are shown in Table 5.1.
At larger depths, that is layers 3 to 5, where the soil consists of silty sand only the elastic-perfectly plastic Mohr Coulomb criterion model is used owing to the limited laboratory test data available for these deeper layers. Herewith, the elastic-perfectly plastic Mohr Coulomb criterion model will be known, in short, as the Mohr Coulomb model. All the three models assumed associated flow rule.
5.3.1 Elastic-perfectly plastic Mohr Coulomb
The Young’s modulus was estimated from Menard pressuremeter data obtained in this project (OYO, 1996; Ove Arup & Partners, 1997) as well as geotechnical reports on similar soil types by Dames & Moore (1983). The variation of the undrained Young’s modulus with depth has been presented in Chapter 4. As shown in
Figure 5.4, in the Mohr-Coulomb analyses which follows, the variation of E’ with depth for different soil layers were assumed to be piecewise linear. Following Lambe
86 FEM STUDY OF SERANGOON MRT SITE
and Whitman (1979), the effective Young’s modulus E’ is deduced from Eu using the expression:
E (1+ν ') E'= u (5.1) 1.5
10
Linear regression from field data used in MC1
0
-10
-20 Depth (m) Depth
-30
-40
-50 0 100 200 300 400 500 E' (MPa) Figure 5.4: Assumed piecewise linear variation of E’ with depth for different soil layers.
The other elastic deformability property is the Poisson’s ratio. Relatively little information is available in the literature on the Poisson’s ratio, ν’, of Singapore weathered granite. As noted by Kulhawy (1990), this parameter often does not vary greatly. For granular soils:
ν ≈ + φ ' 0.1 0.3 rel (5.2) with
()φ'−25 φ = ()0 ≤ φ ≤ 1 (5.3) rel ()45 − 25 rel
87 FEM STUDY OF SERANGOON MRT SITE
in which φrel is the relative friction angle.
For cohesive soils, the effective Poisson’s ratio has been related to plasticity index (PI) for several lightly overconsolidated soils (Wroth, 1975) as shown in Figure
5.5. For layers G4a and G4b, which consist of soils of clayey nature with plasticity indices in the region of 25 and 17 respectively, the effective Poisson’s ratio was estimated from PI using Figure 5.5. For layers G4c, G4d and G4e, where the soil is sandy, Equations 5.2 and 5.3 are used to determine the Poisson’s ratio.
0.6 ' ν
0.4
0.2 Drained Poisson's Ratio,
0.0 0 20406080 Plasticity Index, PI(%) Figure 5.5: Drained Poisson’s ratio versus plasticity index for several lightly overconsolidated soils after Wroth (1975).
Wall deflection
Figure 5.6 shows the plan view of the FEM model in the vicinity of the wall.
The wall deflection was computed at two points, the first marked I located at a rear corner of a soldier pile and the second marked II located behind the mid-span of the timber lagging.
88 FEM STUDY OF SERANGOON MRT SITE
Table 5.2: Soil properties for Layers 1, 2 and 3 for Mohr Coulomb analyses.
Analyses E’ (MPa) c’ (kPa) φ’ K0 MC1 Layer 1 2.7z + 9.2 11 27° 0.9 Layer 2 3.4z – 8.3 17 30° 0.9 Layer 3 10.8z – 172.8 27 38° 1.0 MC2 Layer 1 5.6z + 0.5 11 27° 0.9 Layer 2 4.9z + 80.0 17 30° 0.9 Layer 3 4.5z + 500.0 27 38° 1.0 MC3 Layer 1 5.6z + 0.5 11 27° 0.9 Layer 2 4.9z + 100.0 17 30° 0.9 Layer 3 4.5z + 500.0 27 38° 1.0 MC4 Layer 1 5.6z + 0.5 5 37° 0.9 Layer 2 4.9z + 80.0 5 40° 0.9 Layer 3 4.5z + 500.0 27 38° 1.0 MC5 Layer 1 5.6z + 0.5 30 27° 0.9 Layer 2 4.9z + 80.0 30 30° 0.9 Layer 3 4.5z + 500.0 27 38° 1.0 MC6 Layer 1 5.6z + 0.5 11 27° 0.7 Layer 2 4.9z + 80.0 17 30° 0.7 Layer 3 4.5z + 500.0 27 38° 0.7 MC7 Layer 1 5.6z + 0.5 11 27° 1.0 Layer 2 4.9z + 80.0 17 30° 1.0 Layer 3 4.5z + 500.0 27 38° 1.0 ELAS Layer 1 5.6z + 0.5 - - - Layer 2 4.9z + 80.0 - - - Layer 3 4.5z + 500.0 - - -
Timber lagging
II I Timber lagging
Figure 5.6: Plan view of FEM model of retaining system.
Figure 5.7 shows two computed deflection profiles at final excavation level.
Deflection profiles MC1 are computed by adopting a Young’s modulus variation with depth that is inferred from soil investigation using linear regression for each layer.
Deflection profiles MC2 are computed by adjusting the variation of Young’s modulus that gives a good fit to the measured wall deflection. Comparison of the parameters for MC1 and MC2 in Table 5.2 shows that, in order to match the field deflection using
Mohr Coulomb model, the Young’s modulus for the top three layers need to be
89 FEM STUDY OF SERANGOON MRT SITE increased. A more detailed discussion will be carried out on this observation in the next section together with modified Cam-clay model. Henceforth, the Mohr Coulomb properties for MC2 Layer 3 will be used for the rest of the analyses to give a realistic deflection below final excavation level.
0
5
10
15
20
25 Depth (m)
30 Field MC1-I 35 MC1-II MC2-I 40 MC2-II
45 0 100 200 300 400 Deflection (mm) Figure 5.7: Final deflection profile of soldier pile and timber lagging for MC1, MC2. Locations I and II for each case are defined in Figure 5.6.
Figure 5.8 shows the final deflection profile for two Mohr Coulomb cases designated MC2 and MC3, and one linear elastic case, designated ELAS using the same elastic parameters as MC2 (Table 5.2). Comparison of the results from MC2 and
ELAS shows that ELAS significantly underestimated the measured deflection of the soldier pile. Furthermore, there was no significant relative movement between the timber lagging and the soldier pile. This indicates that plastic deformation contributes substantially to the computed wall deflection, as well as the relative movement between soldier pile and timber lagging, in case MC2. Evidently, plastic deformation and outward movement of the soil was able to occur at the timber lagging between
90 FEM STUDY OF SERANGOON MRT SITE soldier piles in the Mohr-Coulomb model, whereas it was not allowed to occur in the elastic model. This point will be further discussed later.
0
5
10
15
20
25 Depth (m) Field 30 MC2-I MC2-II 35 MC3-I MC3-II ELAS-I 40 ELAS-II
45 0 40 80 120 160 Deflection (mm) Figure 5.8: Final deflection profile of soldier pile and timber lagging for MC2, MC3 and ELAS. Locations I and II for each case are defined in Figure 5.6.
To assess the sensitivity of the results to the modulus estimated from Menard pressuremeter data as well as geotechnical reports on similar soil types by Dames &
Moore (1983), the modulus of Layer 2 is increased in MC3 to investigate the effect of the Young’s modulus in this study. As presented in Figure 5.8, increasing the Young’s modulus between the depths of 11.5 and 22.5m reduces the wall deflection within this depth interval. The difference is quite significant for the timber lagging deflection but much less so for the soldier pile deflection.
Actual shear failure envelopes may exhibit slight curvature in certain cases
(Lambe & Whitman, 1979) but a straight line is often taken over the stress range of interest and the shear strength parameters determined for that range (Craig, 1996).
This can result in several combinations of fitted cohesion and angle of friction,
91 FEM STUDY OF SERANGOON MRT SITE depending upon the manner in which the fitting was conducted. As shown in Figure
5.9, a similar curvature exists for the soil at the Serangoon station. Furthermore, depending upon the method of fitting the linear envelope to the Mohr Circles, the fitted cohesion may range from 8kPa to 22kPa.
300 (a) c' = 8 kPa φ ° p' = 34 200 c' = 22 kPa ess (kPa)
r φ ° p' = 28 St r 100 Shea 0
0 100 200 300 400 500 Effective Stress (kPa)
480 (b) c' = 13 kPa 400 φ ° p' = 36.5 320 ess (kPa)
r 240 St r 160 80 Shea 0
0 200 400 600 800 Effective Stress (kPa) Figure 5.9: Apparent Mohr Coulomb yield envelopes at the limits of the effective stress range of interest. (a) At 6m below EGL. (b) At 12m below EGL.
Table 5.2 shows the cohesion and friction parameters for MC2, MC4 and MC5, with similar modulus for each layer. MC4 and MC5 represent the possible Mohr
Coulomb yield envelopes fitted at the two limits of the effective stress range of interest, in addition to MC2, as illustrated in Figure 5.9a. In the site investigation for this project, OYO (1996) considered the effective stress range of interest to be between
92 FEM STUDY OF SERANGOON MRT SITE
50 and 600kPa. The difference in effective cohesion between the upper bound and lower bound of the range seldom exceed 5% of the effective stress range. The effective friction angle at the two bounds is within the difference of 10°.
0
5
10
15
20
25 Depth (m) Field 30 MC2-I MC2-II MC4-I 35 MC4-II MC5-I 40 MC5-II
45 0 40 80 120 160 Deflection (mm) Figure 5.10: Final 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.
Figure 5.10 shows the final deflection of the retaining wall for MC2, MC4 and
MC5, all of which have the same values of elastic parameters. As this figure shows, at the soldier pile, that is location I, MC2 shows larger deflection compared to MC4 and
MC5. On the other hand, at the mid-span of the timber lagging, that is location II,
MC4 shows larger deflection than MC2 and MC5. This can be explained in terms of the differences in effective cohesion and angle of friction. Figure 5.11a and b show the effective p’-q stress paths for points I and II in analyses MC2, MC4 and MC5 at 12.3m below ground. In Figures 5.11, q is treated as a strictly a positive quantity in accordance with the definition of deviator stress. As can be seen, the effective stress increases to a much higher level for point I than for point II when excavation
93 FEM STUDY OF SERANGOON MRT SITE approaches the final level. This is attributable to stress arching across the soldier piles, which has been discussed in Chapter 3. Thus, for the effective stress range at point I,
150 Final excavation level q 100 ess, ess, r ic st ic r
50 Deviato
(a) 0 0 50 100 150 200 Mean effective stress, p' 3D - behind soldier pile
200
q 150 ess, ess, r Final
ic st ic 100 MC2 r excavation level MC4 MC5 MC2 yield locus 50 MC4 yield locus Deviato MC5 yield locus
(b) 0 -100 0 100 200 300 Mean effective stress, p' 3D - behind timber lagging 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 FEM STUDY OF SERANGOON MRT SITE
MC2 has the lowest failure envelope, and the readiness of the soil to yield is manifested as the largest deflection at the soldier pile. On the other hand, for the effective stress range at point II, MC4 has the lowest failure envelope. Thus, MC4 shows the largest timber lagging deflection.
0
5
10
15
20
25 Depth (m) 30 Field 35 2D-MC2 2D-MC4 40 2D-MC5
45 0 20406080100 Deflection (mm) Figure 5.12: 2D final deflection profile of soldier pile and timber lagging for MC2, MC4 and MC5.
Figure 5.12 shows the wall deflection for the three cases as computed by 2D analyses. As can be seen, the results from the 2D analyses show a similar trend as those of the soldier pile, but not the timber lagging, in the 3D analyses. However, for each case, the maximum deflection computed by the 2D analysis is slightly higher than that computed by the 3D analysis. Thus, three-dimensional analyses of soldier piled excavations highlights the presence of a much larger range of stress excursions over the ground domain than is manifested in two-dimensional analyses. In order to capture the appropriate relative behaviour between soldier pile and timber lagging in three- dimensional analyses, more care is needed in the choice of parameters.
95 FEM STUDY OF SERANGOON MRT SITE
0
5
10
15
20
25 Depth (m)
30 MC2-I K0 = 0.9 MC2-II K0 = 0.9 35 MC6-I K0 = 0.7 MC6-II K0 = 0.7 MC7-I K = 1.0 40 0 MC7-II K0 = 1.0 45 0 40 80 120 160 Deflection (mm) 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.
In the above analyses, the process of soldier pile installation was not modelled.
In reality, it is possible that installation of soldier piles may alter the initial stress state, which will then be reflected by changes in the K0-values in the vicinity of the soldier piles. It is likely that the changes in stress state will depend upon the method of soldier pile installation. For example, Symons & Carder (1993) suggest that total stress reductions of up to 10% may occur close to bored piles in stiff over-consolidated clay.
Ekström (1989) reported an approximately 20% increase of lateral earth pressure on the surface a square concrete driven pile from in-situ lateral earth pressure measured using a dilatometer before pile driving in non-cohesive soil.
In the Serangoon MRT Station excavation, the soldier piles were driven into the ground. It is therefore reasonable to expect an increase in lateral earth pressure in the vicinity of the pile. However, this increase is likely to be substantially less than that arising from driving square piles, since the amount of displacement inflicted on the
96 FEM STUDY OF SERANGOON MRT SITE surrounding soil due to the H-pile is much less. It is thus reasonable to assume an upper bound of K0 equals 1.0 due to H-pile driving.
Figure 5.13 compares the variation in final wall deflection profile as the K0- values changes from 0.7 to 1.0. As discussed above, this range of change is likely to emcompass the changes in K0-values arising from the installation of soldier piles. In the analyses, the variation in K0 is effected between the head and toe of the soldier piles.
As can be seen, there is a slight increase in soldier pile and timber lagging deflections with the increase in K0-value from 0.7 to 1.0. This is not surprising since an increase K0 leads to an increase in initial lateral earth pressure. However, as in the case of the other parameters, the changes are not significant. The fact that the mid- span deflection is much larger than soldier pile deflection remains unchanged.
Figure 5.14 demonstrates the stress paths for the various K0 conditions. The trend of stress paths for MC2 Mc6 and MC7 are almost similar. This shows that the wall deflection behaviour and stress paths of Mohr Coulomb model are not heavily contingent upon the initial stress state resulting from auguring of soil or the driving of pile into soil where K0 ranges from 0.7 to 1.0.
97 FEM STUDY OF SERANGOON MRT SITE
150 q 100 ess, ess, r Initial excavation ic st ic r
50 Deviato
(a) 0 0 50 100 150 200 Mean effective stress, p' 3D - behind soldier pile
200
Initial q 150 excavation ess, ess, r
ic st ic 100 MC2 K0 = 0.9 r MC6 K0 = 0.7 MC7 K0 = 1.0 yield locus 50 Deviato
(b) 0 -100 0 100 200 300 Mean effective stress, p' 3D - behind timber lagging 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.
Wall deflection from 2D vs 3D analyses
Figure 5.15 shows the measured and computed wall deflection 2D and 3D progressive movement of the retaining wall for MC5 from Stages B to I as illustrated
98 FEM STUDY OF SERANGOON MRT SITE in Figure 5.3 compared to the field results. The maximum deflection shown by the field measurement is approximately 50mm (0.20%H). This is close to the average of
0.18%H reported by Yoo & Kim (1999) for 145 cases of H-piled excavation. The
FEM soldier pile profile for 2D and 3D matches that of the field well in the initial stages (Stages B-D). From Stages E-I above excavation level, the 2D deflection profile takes an average value lies between the soldier pile profile and the timber lagging profiles. This can be attributed to the averaging effect implied by the smearing of the soldier piles and timber lagging, which prevents the effects of pile-soil interaction from being exhibited.
Strut forces
Table 5.3 compares the strut forces obtained from finite element analyses of
MC2, MC3, MC4 and MC5. In all of the cases, large discrepancies between the daily average field and analysed results are found in the first and fifth struts. Furthermore, the different combinations of parameters do not affect the strut forces significantly. As will be shown later, the same discrepancies arose with the use of the Cam Clay models.
This suggests that the discrepancies are unlikely to be due to the choice of parameters or models. In particular, the computed strut forces for the first level greatly exceeded the field measurement. Figures 5.16a shows the deflection of the soldier pile at an early stage of the excavation, before the installation of the first level struts. As can be seen, FEM analysis overestimates the measured soldier pile deflection. A possible reason is the presence of a 1 to 2m deep concrete pile cap beam which limited the movement at the initial stages of excavation and reduced the load transferred to the 1st level strut at 3.5m below EGL. As Loh et al. (1998) noted from centrifuge model tests, a stiff beam at the top of the wall can act as a strut to limit wall deflection.
99 FEM STUDY OF SERANGOON MRT SITE
Table 5.3: Comparison of strut forces at various levels between daily average instrumented and FEM result for MC2, MC3, MC4 and MC5. Strut level Instrumented (kN) FEM (kN) Instrumented/FEM × 100% MC2 MC3 MC4 MC5 MC2 MC3 MC4 MC5 1 173.1 427.0 429.0 439.1 410.4 40.5 40.3 39.4 42.2 2 692.3 822.7 825.7 813.3 824.8 84.1 83.8 85.1 83.9 3 836.5 836.6 834.2 811.9 877.5 100.0 100.0 103.0 95.3 4 865.4 839.2 843.6 828.8 839.6 103.1 102.6 104.4 103.1 5 1015.4 555.9 558.2 556.4 534.8 182.7 181.9 182.5 189.9 6 126.9 179.9 181.4 169.6 204.1 70.6 70.0 74.8 62.2
The discrepancy in the fifth level strut forces are unlikely to be caused by the ground surface activities. Figure 5.16b shows the wall deflection profile after the installation of the 4th level strut. As can be seen, the analysis significantly over- estimates the wall deflection at this stage. In other words, there is, in reality, a large increase in soldier pile deflection between the installation of the 4th and 5th level struts which is not captured in the analyses; this explains the under-estimation of the 5th level strut load. The cause of the large increase in wall deflection is unclear, but one possibility lies in the errors in modelling of the soil profile. As the previous chapter shows, the soil conditions at this site are quite variable. Since the nearest borehole to the matched section is about 10m, the interpolated soil profile may not truly reflect the actual soil profile at the matching section. Another possible reason is the presence of groundwater problems at this site. Lee et al. (2001) reported that groundwater problems experienced at the Serangoon Station excavation appear to cause quite significant softening of the soil, especially near the final formation level. The matched section is located roughly 30m from the location where groundwater problems were experienced. It is therefore plausible that some groundwater-induced softening of the
100 FEM STUDY OF SERANGOON MRT SITE
(d) (h) Deflection (mm)Deflection (mm)Deflection 0 20406080100 0 20406080100
0 5 0 5
10 15 20 25 30 35 40 45 10 15 20 25 30 35 40 45
Depth (m) Depth (m) Depth (c) (g) Deflection (mm)Deflection (mm)Deflection 0 20406080100 0 20406080100
0 5 0 5
25 30 35 10 15 20 40 45 10 15 20 25 30 35 40 45
Depth (m) Depth (m) Depth (b) (f) 60 80 100 Deflection (mm) Deflection Deflection (mm) Deflection 0 20406080100 02040
0 5 0 5
10 15 20 25 30 35 40 45 10 15 20 25 30 35 40 45
Depth (m) Depth (m) Depth (e) (a) ) mm ( Field 2D 3D-I 3D-II
Deflection (mm)Deflection Deflection 0 20406080100 0 20406080100 Figure 5.15: Deflection profiles at various stages of excavation for MC5. (a) Stage B. (b) Stage C. (c) Stage D. Stage (c) C. Stage B. (b) Stage (a) MC5. for of excavation stages at various profiles Deflection 5.15: Figure I. Stage (h) H. Stage (g) G. Stage F. (f) Stage E. (e) (d) Stage
0 5 0 5
25 30 35 10 15 20 40 45 10 15 20 25 30 35 40 45
Depth (m) Depth (m) Depth
101 FEM STUDY OF SERANGOON MRT SITE retained soil could have occurred towards the end of the excavation construction which led to a large increase in wall deflection.
0 0
5 5
10 10
15 15
20 20
25 25 Depth (m) Depth (m) 30 30 Field 35 35 MC2 MC3 40 40 MC4 MC5 45 45 0204060 0 204060 Deflection (mm) Deflection (mm) (a) (b) Figure 5.16: Deflection profile of soldier pile for MC5. (a) Before installation of first level struts. (b) After installation of forth level struts.
Ground settlement
Figure 5.17 shows the FEM settlement profile behind the retaining wall plotted against the field settlement. In order to match the wall deflection, the Young’s modulus of soil was raised beyond that inferred from field tests thus resulting in a much stiffer settlement profile. As shown in Figure 5.17, all of the Mohr-Coulomb cases predicted much smaller settlement than the measured values. Thus, in essence, while the Mohr-Coulomb model was able to match the wall deflection, and to some extent, the strut loads by increasing the values of the elastic parameters above the measured values, the settlement profile was significantly underpredicted. This point will be further discussed in a later section.
102 FEM STUDY OF SERANGOON MRT SITE
Distance from retaining wall (m) 0 102030405060708090
0
10 L215(G) L217(G) L214(G) 20 Field MC2 L222(G) MC3 30 L203(G)
Settlement (mm) Settlement MC4 MC5 40 Figure 5.17: Ground settlement behind Location I of the retaining wall for MC2, MC3, MC4 and MC5.
5.3.2 Modified Cam-clay
The Serangoon Station site is underlain by residual soil derived from the weathering of granitic rock. The material may range from highly fissured rock at depth to completely weathered residual soil with a clayey and silty constitution.
Although it is not strictly an over-consolidated soil, some aspects of its behaviour do resemble those of over-consolidated soil (Dames & Moore, 1983). For instance, the
Skempton’s pore pressure parameter A is typically about zero at failure, indicating a tendency to dilate and generate negative pore pressure. The deviator stress-strain curve also typically shows peak strength at failure, which is again typical of over- consolidated soil. Dames & Moore (1983) recommended an equivalent over- consolidation ratio of about 3 for this residual soil.
In Chapter 3 as well as the last section, it has been demonstrated that the transfer of stress from soil to soldier pile as a result of arching action may result in a significant increase in effective stress at localized region of the ground. At such locations, stresses may be sufficiently high to induce normally consolidated behaviour, even from over-consolidated soil. In such cases, the use of the Cam-clay model is
103 FEM STUDY OF SERANGOON MRT SITE advantageous compared to the Mohr-Coulomb model since it allows the transition from over-consolidated to normally consolidated state to be captured. In addition, the pile-soil interaction may give rise to high shear stresses in localised regions around the soldier piles. In such cases, the Cam-clay model has the advantage that it allows stress-induced dilatancy to cease as the critical state is approached, whereas the Mohr-
Coulomb model does not. Finally, as was demonstrated earlier, there is likely to be significant stress relief in the soil at the excavation face, especially behind the timber lagging. As the effective stress reduces, the soil is also likely to soften. In such an instance, the Cam-clay models the softening process to be modelled through the reduction in modulus of the soil with effective stress, whereas the Mohr-Coulomb model does not. In this section, the Serangoon Station excavation is back-analysed using a modified Cam-clay model.
Determination of modified Cam-clay parameters
The critical state frictional constant, M was evaluated using the relationship:
6sinφ ' M = cs (5.4) − φ 3 sin cs '
Figures 5.18a and b shows the critical state friction angles corresponding to the depth of 6m and 12m for the soil at the Serangoon station. Using typical φcs’ of 27° for soil
Layer 1 and 30° for soil Layer 2 leads to M equals 1.07 and 1.2 respectively.
104 FEM STUDY OF SERANGOON MRT SITE
300 φ ° cs' = 29
200 ess (kPa) ess r St r 100
Shea (a) 0
0 100 200 300 400 500 Mean Effective Stress (kPa)
480 φ ° cs' = 31 400 320 240 160 80 Shear (kPa) Stress (b) 0
0 200 400 600 800 Mean Effective Stress (kPa) Figure 5.18: Critical state friction angle estimated from triaxial compression tests. (a) At 6m below EGL. (b) At 12m below EGL.
Figures 5.19a and b show the compression and swelling indices respectively for soil up to 24m below EGL. The compression index, cc, and swelling index, cs, were estimated from odeometer tests. The cc and cs is related to λ and κ through Equations
5.5 and 5.6 respectively:
= λ cc o ln10 (5.5)
= κ cs o ln10 (5.6)
105 FEM STUDY OF SERANGOON MRT SITE
0 0
-2 -2
-4 -4
-6 -6
-8 -8
-10 -10
-12 -12 Depth (m) Depth (m) Depth -14 -14
-16 -16
-18 -18
-20 -20
-22 -22 (a) (b) -24 -24 0.00 0.20 0.40 0.60 0.00 0.05 0.10 0.15 cc cs Figure 5.19: Variation of deformability indices with depth at Serangoon MRT site. (a) Compression index. (b) Swelling index.
Bolton (1991) suggested λo and κo in one-dimensional (1D) loading and λi and
κi isotropic values may be approximately related through the relations
λ = λ i o (5.7)
κ ≈ κ i 1.5 o (5.8))
Goh (1995) showed from theory of elasticity, κi vary from 1.4-1.8 times κo.
The values of λ inferred for Layer 1 and Layer 2 are 0.087 and 0.109 respectively.
The corresponding values of κ Layer 1 and Layer 2 are 0.02 and 0.021.
The values of λ inferred for Layer 1 and Layer 2 are 0.087 and 0.109 respectively. The corresponding values of κ Layer 1 and Layer 2 are 0.02 and 0.021.
Another parameter which needs to be specified in CRISP is the critical state void ratio at mean effective stress of 1kPa, or ecs. In this study, ecs was inferred by simulating the 1D consolidation problem using CRISP and adjusting the critical state void ratio until the compression curve agrees with that from laboratory test, as depicted
106 FEM STUDY OF SERANGOON MRT SITE
in Figure 5.20. This iterative fitting process returns a value of 1.7 and 2.0 for the ecs of
Layer 1 and Layer 2 respectively.
1.30
1.20
1.10 e 1.00
0.90 Void ratio, ratio, Void 0.80 odeometer test FEM
0.70
0.60
1.0E+0 1.0E+1 1.0E+2 1.0E+3 1.0E+4 Axial load (Mpa)(MPa) Figure 5.20: Comparison of laboratory’s odeometer test with MCC soil models.
Determination of in-situ stress state
Apart from the compression and swelling indices, the initial state of the soil also needs to be specified. The initial earth pressure coefficient K0 was inferred from the over-consolidation ratio (OCR) determined from one-dimensional consolidation test data. Consolidation test data conducted on soil samples obtained from the top of the residual soil stratum indicate an OCR value of about 4. Dames and Moore (1983) suggested that 1.5 to 3, which was inferred from the ratio of the undrained Young’s modulus Eu to the undrained shear strength cu, using Duncan and Buchignani’s (1976) method. Dames and Moore’s (1983) Eu values were obtained as an average from the recompression curves in unconsolidated undrained (UU) triaxial tests and from the initial modulus of pressuremeter tests. Given the uncertainty involved in determining
Eu from UU triaxial and pressuremeter tests as well as that in determining OCR from
107 FEM STUDY OF SERANGOON MRT SITE
consolidation tests, the small discrepancy is not unreasonable. For this study, K0 was inferred using Mayne & Kulhawy (1982) relation that
= sinφ ' K 0 K ncOCR (5.9)
in which Knc is the earth pressure coefficient of the same soil in a normally consolidated soil and is determined by Jáky’s (1944) relation
= − φ Knc 1 sin ' (5.10)
For the top 11.5m of residual soil stratum, using Equations 5.9 and 5.10 with OCR ranging from 3 to 4 and φ’ between 30° and 35° leads to K0-values in the range of 0.8 to 1.0. This is also in agreement with Dames and Moore (1983) who recommended a value of between 0.8 and 1.0. At depths of between11.5-22.5 m, the OCR ranges from
2-4 with φ’ in the range of 27°-39°. This implies that the K0 ranges from 0.57-1.02, which is also in reasonable agreement with Dames and Moore’s (1983) recommended range of values.
Table 5.4 summarised the modified Cam-clay properties used in the analyses.
Analysis MCC1 uses the soil properties as inferred above. The OCR in Layer 1 and 2 of MCC2 is artificially raised to 200% of the inferred value so as to enforce predominantly elastic behaviour. MCC3 represents the upper bound of κ deduced from field measurement at 0.040 and 0.047 for Layers 1 and 2 respectively. MCC4 adopted the lower bound of κ at 0.013 and 0.014 for Layers 1 and 2 respectively.
108 FEM STUDY OF SERANGOON MRT SITE
Table 5.4: Soil properties for Layer 1 and Layer 2 for modified Cam-clay. Analyses κ OCR M (φ) K0 Layers 1 2 1 2 1 2 1 2 3 MCC1 0.020 0.021 4 2 1.07 (27°) 1.2 (30°) 0.9 0.9 1.0 MCC2 0.020 0.021 8 4 1.07 (27°) 1.2 (30°) 0.9 0.9 1.0 MCC3 0.040 0.047 4 2 1.07 (27°) 1.2 (30°) 0.9 0.9 1.0 MCC4 0.013 0.014 4 2 1.07 (27°) 1.2 (30°) 0.9 0.9 1.0 MCC5 0.013 0.014 4 2 1.5 (37°) 1.6 (39°) 0.9 0.9 1.0 MCC6 0.020 0.021 4 2 1.07 (27°) 1.2 (30°) 0.7 0.7 0.7 MCC7 0.020 0.021 4 2 1.07 (27°) 1.2 (30°) 1.0 1.0 1.0
Simulation of triaxial test behaviour
Axis of symmetry
σ1 35.25mm
Plane of symmetry
σ σ3 3
20.38mm
σ1
(a) (b) Figure 5.21: Axisymmetric FEM undrained (CU) triaxial test model with 9-integration points eight noded quadrilateral elements. (a) Plane view. (b) Isometric view.
As a precursor to simulating the behaviour of the excavation, a FE simulation of a consolidation undrained (CU) triaxial test was conducted and the results compared to the measured stress-strain curve in the same kind of test. As shown in Figure 5.21, an axisymmetric model with 9-integration-points, eight noded quadrilateral elements was preloaded isotropically to a level of confining stress that the soil is expected to be
109 FEM STUDY OF SERANGOON MRT SITE subjected to in the field. Strain-controlled axial loading is then simulated by progressively increasing the vertical displacement of the top boundary.
200 400 (a) (b)
150 300 (kPa) (kPa) q q
100 200
Triaxial test Triaxial test
50 MCC1 100 MCC1 Deviator stress, stress, Deviator MCC3 stress, Deviator MCC3 MCC4 MCC4
0 0 0.00 0.01 0.02 0.03 0.04 0.00 0.01 0.02 0.03 0.04 0.05 ε ε Deviator strain, s Deviator strain, s Figure 5.22: Comparison of laboratory’s CU triaxial tests with MCC soil models. (a) Depth of sample is 11m. (b) Depth of sample is 20m.
As can be seen from Figure 5.22, the FE model predicts linear elastic right up to the point of yield whereas the measured data indicate that a curve is more appropriate.
The reason for this is that modified Cam-clay model in CRISP does not model any shear-induced reduction in shear modulus within the yield surface. Thus, small strain non-linearity is not modelled. For the sample taken from 11m-depth, the elastic segments of the stress-strain curves from MCC3 and MCC4 appears to bind the measured curve. The elastic segment of MCC1 also appears to be a reasonable
“average” of the measured curve. For the sample taken from 20-m depth, the measured curve appears to imply an “average” stiffness that is closer to MCC3 and definitely lower than that of MCC1. One possible reason could be due bedding errors in conventional triaxial test sample. The ‘bedding down’ at the ends of the sample arises due to local irregularities or voids (Jardine et al., 1984). Therefore, the externally measured strain will often exceed those experienced locally on the sample.
Such errors will not be reflected in a FEM simulation. Notwithstanding the limitations
110 FEM STUDY OF SERANGOON MRT SITE of the soil model and modelling process, the predicted stress-strain curves appear to suggest that the computed range of stress-strain behaviour do represent the measured behaviour reasonably well. It should also be noted that samples taken from the field often suffer a certain amount of sampling disturbance which commonly leads to a reduction in the measured strength and modulus of the sample.
The fill properties tend to be highly variable and little or no investigation was conducted on the fill. Thus for the preliminary investigation, the properties of the fill were assumed to be the same as those of Layer 1 of residual soil
Wall deflection
0
5
10
15
20
25 Depth (m) 30 Field 35 MCC1-I MCC1-II 40 MCC2-I MCC2-II 45 0 20406080 Deflection (mm) Figure 5.23: Final deflection profile of soldier pile and timber lagging for MCC1 and MCC2.
Figure 5.23 shows the final deflection profiles for MCC1 and MCC2. As can be seen, analyses MCC1 and MCC2 predict very similar deflection profiles. Since the only difference between the two analyses is the larger initial yield surface assumed in
MCC2, the close similarity of the results imply the soil behaviour is likely to be
111 FEM STUDY OF SERANGOON MRT SITE predominantly elastic. This is also reflected in Figure 5.25, which shows that the stress paths plotted did not reach the yield surface.
Comparison of Figure 5.23 with Figures 5.8 and 5.10 also suggests that the modified Cam-clay model predicts a much smaller difference between soldier pile and timber lagging deflection than the Mohr-Coulomb model. This can be attributed to the manner in which the parameters for the Mohr-Coulomb and the modified Cam-clay models were derived. In the case of the Mohr-Coulomb model, the measured angle of friction was used to define the yield surface. On the other hand, in the modified Cam- clay model, the angle of friction was used to define the critical state line. This implies that, given the same angle of friction on the “dry” side of critical, the modified Cam- clay yield surface can sustain a higher q/p’ stress ratio than the Mohr-Coulomb yield surface. Thus, if the excavation behaviour is controlled by “dry” side yielding, the
Mohr-Coulomb model will yield more readily than the modified Cam-clay model.
7 - 9 IPs yielded
Soldier piles 4 - 6 IPs yielded
1 - 3 IPs yielded
No IPs yielded (a) MC1
(b) MC4 (c) MC5 Figure 5.24: Yield zones behind retaining wall at 12.3m below ground at instance when first yield was detected in MC5 (Between stage C and D of Figure 5.3). (a) MC2. (b) MC4. (c) MC5.
112 FEM STUDY OF SERANGOON MRT SITE
The presence of yielded zones in the MC cases discussed is illustrated in Figure
5.24, which shows widespread yielding of the soil just behind the soldier piles and timber lagging. For this reason, the Young’s modulus of the Mohr-Coulomb has to be raised in order to fit the measured wall deflection. As mentioned earlier, the modulus values needed to give a good fit to the measured soldier pile deflection significantly exceeds those derived by fitting the pressuremeter data in Figure 5.4. As the soil yields, dilatancy causes an expansion in soil volume, which helps to push the flexible timber lagging out further. This explains the large predicted differences between soldier pile and timber lagging deflection.
For the modified Cam-clay model, the Young’s modulus is controlled indirectly by κ and the Poisson’s ratio ν’. For the values of κ and ν’ used in the MCC-analyses, the implied E’ ranges from about 9MPa to 28MPa, with an average value of about
18MPa; this is in much better agreement with Dames & Moore’s (1983) data than the range of values for the Mohr-Coulomb model. As shown in Figures 5.25a and b, the soil remains predominantly elastic with the modified Cam-clay model. Thus dilatancy is not present in the MCC-analyses. Given the fact that the 30° friction angle is quite a commonly used value, it is possible that premature yielding may well be a common syndrome in many Mohr-Coulomb FE analyses of residual or over-consolidated soils in excavation problems, where localised stress concentration may be present.
113 FEM STUDY OF SERANGOON MRT SITE
150 MCC1 MCC2 MCC1 YL & CSL MCC2 YL & CSL ^ q 100 ess, ess, r ic st r CSL 50 Deviato
(a) 0 0 50 100 150 200 Mean effective stress, p' 3D - behind soldier pile
150 100 ^ q 50 ess, ess,
r 0 CSL
ic st ic -50 r -100 -150 Deviato -200 (b) -250 0 50 100 150 200 Mean effective stress, p' 3D - behind timber lagging Figure 5.25: Stress path plots for MCC1 and MCC2 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.
114 FEM STUDY OF SERANGOON MRT SITE
0
5
10
15
20
25 Depth (m) Field 30 MCC1-I MCC1-II MCC3-I 35 MCC3-II MCC4-I 40 MCC4-II
45 0 40 80 120 160 Deflection (mm) Figure 5.26: Final deflection profile of soldier pile and timber lagging for MCC1, MCC3 and MCC4.
Figure 5.26 compares the computed results for analyses MCC1, MCC3 and
MCC4. As can be seen, MCC3 shows a much larger wall deflection than MCC1 and
MCC4, this being attributable to its much higher value of κ. This further underlines the fact that, in the MCC-analyses, wall deflection is largely controlled by elastic parameters. On the other hand, as shown in Figure 5.27, changing the critical state angle of friction (from case MCC4 to MCC5) has a much smaller effect.
Figure 5.27 reflects the deflection profiles for MCC4 and MCC5. The angle implied in this friction constant, M, is the critical state friction angle. An increase in the M corresponding to an increase in critical state friction angles from 27° to 37° in
Layer 1 and 30° to 39° in Layer 2 does not change the profile as significantly as
MCC3.
115 FEM STUDY OF SERANGOON MRT SITE
0
5
10
15
20
25 Depth (m) 30 Field 35 MCC4-I MCC4-II MCC5-I 40 MCC5-II
45 0 20406080 Deflection (mm) Figure 5.27: Final deflection profile of soldier pile and timber lagging for MCC4 and MCC5.
Graham (1992) observed that modified Cam-clay predicts shear strains relatively poorly, especially when clay is heavily overconsolidated. However, the above discussion shows that, by using appropriate values for the Cam-clay parameters, meaningful results can still be obtained, notwithstanding the fact that small strain non- linearity is not modelled. To further assess the significance of small strain non- linearity, a hyperbolic Cam-clay model (Nasim, 1999) will be used to model the non- linearity of small-strain non-linearity of the residual soil in a later section.
116 FEM STUDY OF SERANGOON MRT SITE
0
5
10
15
20
25 Depth (m)
30 MCC1-I K0 = 0.9 MCC1-II K0 = 0.9 MCC6-I K = 0.7 35 0 MCC6-II K0 = 0.7 MCC7-I K0 = 1.0 40 MCC7-II K0 = 1.0
45 0 20406080 Deflection (mm) Figure 5.28: Final deflection profile of soldier pile and timber lagging for MCC1, MCC6 and MCC7.
As in the case of Mohr-Coulomb models, Figure 5.28 shows slightly increasing wall deflections with increasing K0-values. Furthermore, as Figure 5.29 shows the stress paths behind the soldier pile and timber lagging at 12.3m below ground follows almost parallel paths from initial points. This shows that the pile-soil interaction mechanism does not change greatly with different in-situ stress conditions. Thus, as in the case for the Mohr Coulomb models, the wall deflection behaviour and stress paths for the Modified Cam-clay models are not heavily contingent upon the initial stress state of K0 between 0.7 and 1.0 resulting from auguring of soil or the driving of H-pile into soil respectively.
117 FEM STUDY OF SERANGOON MRT SITE
150 q 100 ess, ess, r Initial excavation ic st ic r
50 Deviato
(a) 0 0 50 100 150 200 Mean effective stress, p' 3D - behind soldier pile
200
q 150 ess, ess, r
ic st ic 100 MCC1 K0 = 0.9 r MCC6 K0 = 0.7 MCC7 K0 = 1.0 50 Deviato Initial excavation (b) 0 0 100 200 300 Mean effective stress, p' 3D - behind timber lagging Figure 5.29: Stress path plots for MCC1, MCC6 and MCC7 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.
Wall deflection from 2D and 3D analyses
Figure 5.30 shows the 2D and 3D progressive wall deflection after replacement of the top 3.5m fill material to Mohr Coulomb’s properties. As observed from the
118 FEM STUDY OF SERANGOON MRT SITE timber lagging deflection in top 3.5m fill, there is a larger difference between soldier pile and timber lagging deflection. This is due to excavation behaviour being controlled by “dry” side yielding as discussed earlier. Otherwise, the soldier pile deflection did not change drastically after modification of the fill properties even though it made significant improvement to the ground settlement. The 2D profile takes an average value between the soldier pile and timber lagging deflections in the
Mohr Coulomb layer. In the modified Cam-clay layer above excavation level, the 2D takes after the soldier pile deflection profile closely.
Comparison of the computed and measured wall deflections at various stages of excavations shows that, although the final wall deflection is well-matched. The early- stage wall deflection is significantly over-predicted. The discrepancy appears to increase towards the initial stages of the excavation. One possible reason for this discrepancy is the fact that the modified Cam-clay model does not model the degradation in shear modulus as shear strain increases. Thus, the shear modulus which is appropriate for matching the final wall deflection is likely to be too low to match the initial wall deflection, where the shear strains are lower. For this reason, the initial wall deflection is over-predicted. The notion will be further examined when the hyperbolic Cam Clay cases are analysed below.
119 FEM STUDY OF SERANGOON MRT SITE
(d) (h) Deflection (mm)Deflection (mm)Deflection 0 20406080100 0 20406080100
0 5 0 5
10 15 20 25 30 35 40 45 10 15 20 25 30 35 40 45
Depth (m) Depth (m) Depth (c) (g) Deflection (mm) Deflection (mm) Deflection 0 20406080100 0 20406080100
0 5 0 5
10 15 20 25 30 35 40 45 10 15 20 25 30 35 40 45
Depth (m) Depth (m) Depth (b) (f) 60 80 100 Deflection (mm)Deflection Deflection (mm)Deflection 0 20406080100 02040
0 5 0 5
25 30 35 40 45 10 15 20 25 30 35 40 45 10 15 20
Depth (m) Depth (m) Depth (e) (a) ) mm ( Field 2D 3D-I 3D-II
Deflection (mm) Deflection Deflection 0 20406080100 0 20406080100 Figure 5.30: Deflection profiles at various stages of excavation for MCC1-M. (a) Stage B. (b) Stage C. (c) Stage D. Stage (c) C. Stage (b) Stage B. (a) MCC1-M. for of excavation stages at various profiles Deflection 5.30: Figure I. Stage (h) H. Stage (g) G. Stage F. (f) Stage E. (e) (d) Stage
0 5 0 5
25 30 35 10 15 20 40 45 10 15 20 25 30 35 40 45
Depth (m) Depth (m) Depth
120 FEM STUDY OF SERANGOON MRT SITE
Strut forces
Table 5.5 compares the strut forces obtained from the best-fit finite element analyses of the MCC1. Similar observation to MC5 can be inferred from Table 5.5 and Figure 5.31 where large discrepancies between the field and analysed results are found in the first and fifth struts. The reasons are as explained in the previous section.
Table 5.5: Comparison of strut forces at various levels between instrumented and FEM result for the best-fit deflection profile for MCC1. Strut level Instrumented (kN) FEM (kN) Instrumented/FEM × 100% 1 173.1 395.9 43.7 2 692.3 777.9 89.0 3 836.5 867.5 96.4 4 865.4 970.0 89.2 5 1015.4 503.2 201.8 6 126.9 182.4 69.6
0 0
5 5
10 10
15 15
20 20
25 25 Depth (m) Depth (m) 30 30
35 35
40 40 Field FEM 45 45 0 204060 0 204060 Deflection (mm) Deflection (mm) (a) (b) Figure 5.31: Deflection profile of soldier pile for MCC1. (a) Before installation of first level struts. (b) After installation of forth level struts.
Ground settlement
Figure 5.32 compares the computed and measured settlement profiles behind the retaining wall. As can be seen, in all cases, the ground settlement is over-estimated
121 FEM STUDY OF SERANGOON MRT SITE by the FE analyses. Examination of the variation of the settlement with depth indicates that much of the settlement occurs within the fill layer. Given the values of λ and κ assumed for the fill layer, the implied modulus is of the order of 2MPa at the mid- depth of the fill. Given that the fill is very heavily compacted, this value is unrealistically low. In addition, the modified Cam-clay model implies that, right at the ground surface, the modulus of the soil is zero, which is also unrealistic. In order to model the fill more realistically, a Mohr-coulomb model with properties as shown in
Table 5.6 was used for the fill. Note that, in order to forestall early yielding, a relatively high angle of friction of 35° has been adopted for this layer. As shown in
Figure 5.33, the agreement between the computed profile for MCC1-M and the field data is now much better.
Table 5.6: Modification to 3.5m of topsoil to Mohr Coulomb properties. 3 Depth (m) γs (kN/m ) E’ (MPa) c’ (kPa) φ’ ν kx (m/s) ky (m/s) 0.0-3.5 18.5 8.0 0 35° 0.30 1.0×10-5 1.0×10-5
Distance from retaining wall (m) 0 102030405060708090
0 L215(G) 20 L214(G) L217(G) L203(G) L222(G) 40
60
80
100 Field MCC1 120 Settlement (mm) Settlement MCC2 MCC3 140 MCC4 MCC5 160
180 Figure 5.32: Ground settlement behind Location I of the retaining wall for MCC1, MCC2, MCC3, MCC4 and MCC5.
122 FEM STUDY OF SERANGOON MRT SITE
Distance from retaining wall (m) 0 102030405060708090 0 L215(G) 10 L217(G) L214(G) 20
L222(G) Field 30 2D
Settlement (mm) 3D L203(G) 40 Figure 5.33: 2D and 3D ground settlement behind Location I of the retaining wall for MCC1- M.
5.3.3 Hyperbolic Cam-clay
It is now well-recognised that the shear modulus of most soils tends to decrease as the shear strain increases (e.g. Simpson et al., 1979; Jardine et al., 1986; Burland,
1989), even before the initiation of large-scale yielding. This phenomenon is evident also from Figure 5.22, in which the triaxial tests data indicate a progressive decrease in the tangent modulus of the soil that was not reflected by the highly linear pre-yield segments of the stress-strain curves prescribed by the modified Cam-clay model. This non-linear behaviour at relatively small shear strains has been variously represented by multi-nested surface models (e.g. Stallebrass 1990) and by non-linear hysteretic models (e.g. Dasari 1996; Nasim, 1999). In this and the following sections, the effect of small strain non-linearity is examined using Nasim’s (1999) hyperbolic Cam-clay model as a vehicle. More complicated multi-nested models are not used in this investigation as the emphasis of this discussion is on the influence of geometric and material factors on soldier-pile-soil interaction rather than the development of constitutive models for residual soils. In any case, since the triaxial tests in the soil investigation were not conducted using small strain measurements, the quality of the
123 FEM STUDY OF SERANGOON MRT SITE data and the knowledge of the soil derived from it is unlikely of a sufficiently high quality to justify the use of a more complex model.
Determination of hyperbolic Cam-clay’s parameters
Nasim’s hyperbolic Cam-clay model is based on the concept that the pre-yield non-linear behaviour of a soil can be represented by a hyperbolic function. The hyperbolic function used by Nasim (1999) is given by:
()S − S ε = 0 ∞ s + ε ( < ε < ε ) q S∞ s 0 s y (5.11) ()S − S ⋅ ε + 0 ∞ s 1 q f where
S0 is the initial tangential stiffness
S∞ is the tangential stiffness at very large strain
εs is the shear strain
εy is the shear strain at yielding
qf is the deviator stress at failure
Assuming Equation 5.12 and differentiating Equation 5.11 with respect to εs leads to a variation of shear modulus G with shear strain εs that is given by:
dq S = = 3G (5.12) ε d s
G − G = 0 ∞ + G 2 G∞ (5.13) 3()G − G ⋅ ε + 0 ∞ s 1 q f where
124 FEM STUDY OF SERANGOON MRT SITE
G0 is the initial shear modulus
G∞ is the shear modulus at very large strain
This allows the shear modulus G to decrease with increasing shear strain following the trend of the S-shaped curve which has been observed experimentally (e.g. Jardine et al., 1986; Dasari 1996). The initial shear modulus, G0, is in turn related to the current state of soil by the relation:
= n m G0 Cp' OCR (5.14) where
C is a constant
n is the effective stress, p’, exponent
m is the OCR exponent
The experimental results reported by Wroth et al. (1979) from both dynamic and static tests on sand indicated that the value of n varied from approximately 0.5 at small strain to about 1.0 at large strain.
Viggiani & Atkinson (1995) carried out bender element tests on reconstituted samples of a variety of different soils and observed that, for fine-grained soils, both the indices m and n increase with increasing plasticity index in the manner shown in
Figures 5.34a and b respectively. The values of m reported typically range from 0.2 to
0.3 whereas n typically ranged from 0.5 to 0.9. Using bender element tests, Coop &
Jovičić (1999) also reported similar m and n values for a variety of coarse-grained soils. They also suggested that, for coarse-grained soils, n could reasonably be approximated by 0.58, while the value of m depended on the history of over-
125 FEM STUDY OF SERANGOON MRT SITE consolidation or compaction. In this study, the values of m and n were determined from Figure 5.34.
0.4 1.0
0.9
0.3 n m 0.8 icient, f f 0.7 Coefficient, Coe 0.2
0.6
0.1 0.5 0 10203040506070 0 10203040506070 Plasticity index, PI Plasticity index, PI (a) (b)
Figure 5.34: Parameters for G0. (a) Coefficient m. (b) Coefficient n. (Viggiani & Atkinson, 1995)
Since the hyperbolic Cam-clay model is based purely on empirical relationship, thus matching with laboratory tests is essential in determining the soil parameters. The soil parameters of the hyperbolic Cam-clay model were determined by simulating a consolidated undrained triaxial test using finite elements. It is likely that some errors will be incurred in the fitting process since conventional triaxial tests with external strain measurements often tend to return lower soil stiffness than the true values.
Based on the CU triaxial tests conducted on Serangoon residual soil, the values of G0 determined are 9.3MPa and 10.4MPa at sample depths of 11m and 20m, respectively.
These benchmark values in turn allow the value of C to be estimated.
At very large strain, the soil is likely to be destructured. For this reason, the shear modulus at very large strain, G∞, is assumed to be zero. After commencement of yielding, the strain-dependent model would follow the behaviour of modified Cam- clay model.
126 FEM STUDY OF SERANGOON MRT SITE
The bulk modulus K’ is related to G through the following equation:
21()+ν ' K ' =⋅G (5.15) 31()− 2ν '
Stallebrass’s test data (1990) showed that K’ will ultimately reach a minimum value for swelling or if loaded in a constant-q stress path. Since the behaviour of the soil is assumed to be consistent with that prescribed by the modified Cam-clay at large strains, K’ is limited to be lower bounded:
υp' K '= (5.16) min κ where
Kmin’ is effective bulk modulus
υ is the specific volume
p’ is the mean effective stress
Figure 5.35 shows the variation of K’ with volumetric strain and G with deviator strain from FEM simulated drained triaxial test similar to the mesh in Figure 5.21. Figure
5.36 shows the variation of K’ with mean effective stress and G with deviator stress from FEM simulated drained triaxial test.
127 FEM STUDY OF SERANGOON MRT SITE
ε 2 Deviator strain, v x10 0.01 0.1 1 10 80000 40000
60000 30000 (kPa)
(kPa) Bulk Modulus, K G
K Shear Modulus, G 40000 20000 modulus, r 20000 10000 Bulk modulus, Bulk Shea
0 0 0.1 1 10 ε 3 Volumetric strain, v x10 Figure 5.35: Variation of K’ and G with volumetric strain and deviator strain respectively in a simulated FEM drained triaxial test.
Deviator stress, q (kPa) 0 50 100 150 200 250 300 80000 40000
60000 30000 (kPa)
(kPa) Bulk Modulus, K G K Shear Modulus, G 40000 20000 modulus, modulus, r 20000 10000 Bulk modulus, modulus, Bulk Shea
0 0 180 200 220 240 260 280 Mean effective stress, p' (kPa) Figure 5.36: Variation of K’ and G with mean effective stress, p’, and deviator stress, q, respectively in a simulated FEM drained triaxial test.
The parameter qf is taken to be the deviator stress at failure in an undrained triaxial test of the soil. The value of qf can be determined through the least square fitting of laboratory test data with the strain-dependent relation (Equation 5.11). This may not be strictly accurate for all soils, but for residual soils, it may not be a bad approximation since the in-situ effective stress state is likely to be fairly near to being isotropic, as indicated by K0 ~ 1.0.
128 FEM STUDY OF SERANGOON MRT SITE
Wall deflection
Table 5.7 shows the various hyperbolic Cam-clay cases studied whilst Figure
5.37 compares the measured stress-strain curve from conventional triaxial test with the predicted curves of the 4 analyses.
Table 5.7: Soil properties for Layer 1 and Layer 2 for hyperbolic Cam-clay. Analyses C n qf (kPa) Layer 1 Layer 2 Layer 1 Layer 2 Layer 1 Layer 2 HCC1 155 140 0.8 0.8 177.5 369.2 HCC2 596 524 0.8 0.8 177.5 369.2 HCC3 155 140 0.6 0.6 177.5 369.2 HCC4 250 140 0.8 0.8 250.0 300.0
The values of the properties used in HCC1 are obtained by back-fitting the the measured stress-strain curve in CU triaxial test in the laboratory, Figure 5.37. In
HCC2, G0 is increased several times above that measured by conventional triaxial test, in order to examine the effect of underestimating the initial stiffness, G0, due to errors in the triaxial test data. HCC3 studies the effect of lowering the parameter n to that which is representative of a low plasticity soil. Finally, the parameters of case HCC4 are determined by back-fitting the final deflection profile of the soldier pile.
175 300 (a) (b)
150 250
125
(kPa) (kPa) 200 q q 100 150 75 Triaxial test Triaxial test HCC1 100 HCC1 50 HCC2 HCC2
Deviator stress, stress, Deviator HCC3 stress, Deviator HCC3 25 50 HCC4 HCC4
0 0 0.00 0.01 0.02 0.03 0.04 0.00 0.01 0.02 0.03 0.04 0.05 ε ε Deviator strain, s Deviator strain, s Figure 5.37: Comparison of laboratory’s triaxial tests with HCC soil models. (a) Depth of sample is 11m. (b) Depth of sample is 20m.
129 FEM STUDY OF SERANGOON MRT SITE
Figure 5.38 shows computed final wall deflection profiles from analyses HCC1 and HCC2. As can be seen, the measured soldier pile deflection matches the HCC1 results better than HCC2 results. HCC2, with larger initial stiffness, appears to be overly stiff in the final stages of excavation. This suggests that the stress-strain curve determined from the triaxial test gives a reasonable representation of the “real” stress- strain curve in the stress range experienced in this study, for the purpose of prediction soldier pile deflection. Driving of soldier piles to the required depth could have resulted in remoulding of the surrounding soil thereby reducing the soil stiffness in the vicinity. The ‘real’ stress-strain relationship thus approaches that of the ‘disturbed’ sample used in the CU triaxial test.
0
5
10
15
20
25 Depth (m) 30 Field HCC1-I 35 HCC1-II HCC2-I 40 HCC2-II
45 0 20406080 Deflection (mm) Figure 5.38: Final deflection profile of soldier pile and timber lagging for HCC1 and HCC2.
130 FEM STUDY OF SERANGOON MRT SITE
0
5
10
15
20
25 Depth (m) Depth 30 Field 35 HCC1-I HCC1-II HCC3-I 40 HCC3-II
45 04080120160 Deflection (mm) Figure 5.39: Final deflection profile of soldier pile and timber lagging for HCC1 and HCC3.
Figure 5.39 shows the final deflection profiles for HCC1 and HCC3. As can be seen, HCC3 gives a much larger wall deflection that HCC1 and the measured wall deflection. This can be readily explained by the lower value of n used in analysis
HCC3, which reduces the initial modulus. Thus, n=0.8 appears to be better describe the variation of G0 with mean effective stress. This is not surprising since the residual soil encountered in the Serangoon Station site consists predominantly of fine-grained soils, with medium-high plasticity. Figure 5.40 compares the deflection profiles for
HCC 1 and HCC4. As can be seen, the results of the two analyses are quite close; the main difference being that HCC4 computes a smaller soldier pile deflection than
HCC1, in layer 1 of the soil near the ground surface. This is not surprising, given the higher modulus assigned to the layer 1 soil in HCC4.
131 FEM STUDY OF SERANGOON MRT SITE
0
5
10
15
20
25 Depth (m) 30 Field HCC1-I 35 HCC1-II HCC4-I 40 HCC4-II
45 0 20406080 Deflection (mm) Figure 5.40: Final deflection profile of soldier pile and timber lagging for HCC1 and HCC4.
Comparison of the performance of the three models in predicting wall deflection alone shows that the modified Cam-clay and the hyperbolic Cam-clay behaviour very similarly. With appropriate values of parameters, both models can reasonably predict the deflection of the soldier pile. Furthermore and in contrast to the
Mohr-Coulomb model, both the Cam-clay models predict relatively small differences between soldier pile and timber lagging deflection. This is due mainly to the shape of the Cam-clay yield surface. In other words, the relative performances of the two Cam- clay models are not readily differentiable by wall deflection at final excavation alone.
132 FEM STUDY OF SERANGOON MRT SITE
0 0
5 5
10 10
15 15
20 20
25 25 Depth (m) Depth (m) 30 30
35 35
40 40 Field FEM 45 45 0 204060 0 204060 Deflection (mm) Deflection (mm) (a) (b) Figure 5.41: Deflection profile of soldier pile for HCC4. (a) Before installation of first level struts. (b) After installation of forth level struts.
Some differences in wall deflection prediction may be observed in the early stages of excavation. Figures 5.41a shows the deflection of the soldier pile at an early stage of the excavation, before the installation of the first level struts for the case
HCC4. Comparison of Figures 5.41a and 5.31a shows that case HCC4 computes a smaller wall deflection profile than case MCC1. It is also much closer to the field result than case MCC1. This supports the earlier hypothesis that the over-prediction of wall deflection by the modified Cam-clay at the initial stages of excavation arises from its inability to capture the degradation in shear modulus with shear strain.
133 FEM STUDY OF SERANGOON MRT SITE
(d) (h) Deflection (mm) Deflection (mm) Deflection 0 20406080100 0 20406080100
0 5 0 5
25 30 35 10 15 20 40 45 10 15 20 25 30 35 40 45
Depth (m) Depth (m) Depth (c) (g) Deflection (mm) Deflection (mm) Deflection 0 20406080100 0 20406080100
0 5 0 5
25 30 35 10 15 20 40 45 10 15 20 25 30 35 40 45
Depth (m) Depth (m) Depth (b) (f) 60 80 100 Deflection (mm) Deflection Deflection (mm) Deflection 0 20406080100 02040
0 5 0 5
10 15 20 25 30 35 40 45 10 15 20 25 30 35 40 45
Depth (m) Depth (m) Depth (e) ) (a) mm ( Field 2D 3D-I 3D-II
Deflection (mm)Deflection Deflection 0 20406080100 0 20406080100 Figure 5.42: Deflection profiles at various stages of excavation for HCC4-M. (a) Stage B. (b) Stage C. (c) Stage D. Stage (c) C. Stage (b) Stage B. (a) HCC4-M. for of excavation stages at various profiles Deflection 5.42: Figure I. Stage (h) H. Stage (g) G. Stage F. (f) Stage E. (e) (d) Stage
0 5 0 5
25 30 35 10 15 20 40 45 10 15 20 25 30 35 40 45
Depth (m) Depth (m) Depth
134 FEM STUDY OF SERANGOON MRT SITE
Development of wall deflection with excavation depth
Figure 5.42 shows the 2D without kingposts and 3D progressive movement of the retaining wall for HCC4-M from Stage B–I as illustrated in Figure 5.3 compared to the field results. With almost the same final deflection profile as the MCC, the HCC soil model, with non-linear stiffness, shows a more gradual development of the soldier pile wall deflection compared to the former. It was noted the in all soil models, the 2D deflections below the excavation level are significantly larger than the 3D deflection.
Strut forces
Table 5.8 compares the strut forces obtained from the best-fit finite element analyses for HCC4. Similar to MC5 and MCC1, large discrepancies between the field and analysed results are found in the first and fifth struts. The reasons for these discrepancies have been presented earlier and will not be repeated here.
Table 5.8: Comparison of strut forces at various levels between instrumented and FEM result for the best-fit deflection profile for HCC4. Strut level Instrumented (kN) FEM (kN) Instrumented/FEM × 100% 1 173.1 386.7 44.8 2 692.3 746.5 92.7 3 836.5 850.7 98.3 4 865.4 947.6 91.3 5 1015.4 490.8 206.9 6 126.9 166.7 76.1
Ground settlement
Figure 5.43 shows the computed ground settlements behind the retaining wall after excavation to the final level. As for the modified Cam-clay model, the hyperbolic
Cam-clay model also predicts much larger settlement than the field data. This is also attributable to the fact that the moduli in the hyperbolic Cam-clay are also a function of the effective stress. As the effective stress approaches zero near the ground surface, so does the modulus. 135 FEM STUDY OF SERANGOON MRT SITE
Distance from retaining wall (m) 0 102030405060708090
0 L215(G) 20 L214(G) L217(G) L203(G) L222(G) 40
60 Field 80 HCC1
Settlement (mm) Settlement HCC2 100 HCC3 HCC4 120 Figure 5.43: Ground settlement behind Location I of the retaining wall for HCC1, HCC2, HCC3 and HCC4.
Distance from retaining wall (m) 0 102030405060708090
0
t 0.2
0.4
0.6 MCC1 MCC2 Settlement (mm) MCC3 0.8 MCC4
Normalised Settlemen MCC5 1 Figure 5.44: Normalised ground settlement behind Location I of the retaining wall for MCC1, MCC2, MCC3, MCC4 and MCC5.
Figure 5.44 and 5.45 compare the relative decay in settlements computed by the modified Cam-clay and the hyperbolic Cam-clay model respectively. In these figures, all the settlement values have been normalised by their respective maximum so that the maximum normalised settlement in all cases is 1. As can be seen, the hyperbolic Cam- clay cases predict a slightly higher rate of attenuation in settlement with distance, after
136 FEM STUDY OF SERANGOON MRT SITE the point of maximum settlement, than the modified Cam-clay cases. This effect is well-documented (e.g. Jardine et al., 1986).
Distance from retaining wall (m) 0 102030405060708090
0
t 0.2
0.4
0.6 HCC1
Settlement (mm) Settlement HCC2 0.8 HCC3
Normalised Settlemen HCC4 1 Figure 5.45: Normalised ground settlement behind Location I of the retaining wall for HCC1, HCC2, HCC3 and HCC4.
Figure 5.46 shows various cases of 2- and 3D analyses which explore the effects of some other factors on wall deflection. As can be seen, the results are also slightly dependent upon whether the analysis is 2- or 3D. Given the same parameters, the 3D analysis predicts a slightly smaller wall deflection than the 2D analysis, especially below excavation level. This is attributable to the mechanism of soil flow around the soldier piles, which have been discussed in Chapter 3. As discussed then, the flexural stiffness of the soldier piles tends to drag the retained soil into the excavated area, and this effect is accentuated in the 2D analysis which modelled the soldier piles as a wall with equivalent flexural rigidity. For this reason, the settlement predicted by the 2D analysis is also slightly larger than that predicted by the 3D analysis, Figure 5.47.
137 FEM STUDY OF SERANGOON MRT SITE
0
5
10
15
20
25 Depth (m) 30
35 MCC1-2D MCC1-3D 40 HCC4-2D HCC4-3D 45 0 20406080 Deflection (mm) Figure 5.46: 2D vs 3D wall deflections behind Location I of the retaining wall for MCC1 and HCC4.
Distance from retaining wall (m) 0 102030405060708090
0
20
40
60
80 MCC1-2D
Settlement (mm) Settlement MCC1-3D 100 HCC4-2D HCC4-3D 120 Figure 5.47: 2D vs 3D ground settlements behind Location I of the retaining wall for MCC1 and HCC4.
One factor which may have an effect on the settlement profile is the kingposts within the excavation area. Figure 5.48 illustrates the effect of modelling the kingposts in the analyses. As mentioned earlier, kingposts were modelled using beam elements.
Two 2D analyses were performed; the first without modelling the kingposts and the
138 FEM STUDY OF SERANGOON MRT SITE secondly modelling the kingposts as a kingpost wall with equivalent axial stiffness. As can be seen, the wall deflection predicted by the two 2D analyses bracket the prediction of the 3D analyses (with and without kingposts). If the kingposts were not modelled, the wall deflection of the 2D analysis is larger than that of the 3D analysis.
This arises from the soldier-pile-soil interaction discussed above. On the other hand, if the kingposts were modelled, the wall deflection of the 2D analysis is smaller than that of the 3D analysis. This is because the kingposts had to be modelled as an equivalent wall in the 2D analysis, which inhibits the flow of soil around the kingposts, thereby giving rise to a spurious stiffening effect. The effect of the kingpost is particularly evident in the wall deflection just below excavation level and in the attenuation of settlement just after the maximum settlement is reached. Similar observation is made in MCC1-M (Figure 5.49).
0
5
10
15
20
25 Depth (m) 30
35 2D without kingpost 2D with kingpost 40 3D without kingpost 3D with kingpost 45 0 20406080100 Deflection (mm) Figure 5.48: Comparison of effect of kingpost modelling on 2D and 3D soldier pile deflection for HCC4-M.
139 FEM STUDY OF SERANGOON MRT SITE
0
5
10
15
20
25 Depth (m) 30
35 2D without kingpost 40 2D with kingpost 3D with kingpost 45 0 20406080100 Deflection (mm) Figure 5.49: Comparison of effect of kingpost modelling on 2D and 3D soldier pile deflection for MCC1-M.
The above effects are also evident from the displacement field of the retained soil. Figure 5.50 depicts the displacement vectors for both 2D without kingpost and
3D with kingpost HCC4-M analyses. In 3D analysis, the slightly larger deflection of timber lagging allows for horizontal movement of soil towards the mid-span which is not possible in the case of 2D analysis as reflected in Figure 5.42. The continuous simulation of piles in the 2D causes deeper soil movement immediately behind the retaining wall. When there are no kingpost to restrain the swelling of soil at the excavation base, the larger upward movement in the excavation is likely to cause larger settlement a distance away from the retaining wall reflected in Figure 5.51.
When the kingposts are modelled in the 2D analysis, the settlement beyond 10m from the retaining wall approaches that of 3D analysis. The additional restraint to the lateral movement and swelling of soil below the excavation afforded by 2D modelling of kingposts reduces the ground settlement.
140 FEM STUDY OF SERANGOON MRT SITE
0
-10
-20 Depth (m) Depth
-30 2D 3D -40 0 102030405060 Distance from center of excavation (m) Figure 5.50: 2D and 3D displacement vectors behind Location I of the retaining wall for HCC4-M.
Distance from retaining wall (m) 0 102030405060708090 0 L215(G) 10 L217(G) L214(G) 20 Field 30 L222(G) 2D without kingposts
Settlement (mm) Settlement L203(G) 2D with kingposts 3D with kingposts 40 Figure 5.51: 2D and 3D ground settlement behind Location I of the retaining wall for HCC4- M.
In the immediate zone up to 10m, ground settlements for both 2D analyses are almost identical but larger than 3D profile. This can be attributed to the larger 2D deflection profiles than in 3D reflected by Figure 5.47 that affects the near field ground settlement in Figure 5.50. This shows that the effects of kingposts cannot be properly simulated in 2D analyses.
141 FEM STUDY OF SERANGOON MRT SITE
5.4 Summary of findings
In the Mohr-Coulomb model, the measured angle of friction was used to define the yield surface, on the other hand, the modified Cam-clay clay, the angle of friction was used to define the critical state line. This implies that, on the “dry” side of critical, the modified Cam-clay yield surface is larger than the Mohr-Coulomb yield surface. If the excavation behaviour is controlled by “dry” side yielding, the Mohr-Coulomb model will yield more readily than the modified Cam-clay model. For this reason, the
Young’s modulus of the Mohr-Coulomb has to be raised in order to fit the measured wall deflection. In this case study, the soil remains predominantly elastic with the modified Cam-clay model, thus, dilatancy is not observed in the MCC-analyses.
Given the fact that the 30° friction angle is not uncommonly used value, it is possible that premature yielding may well be a common syndrome in many Mohr-Coulomb FE analyses of residual or over-consolidated soils in excavation problems.
The modified Cam-clay model predicts linear elastic right up to the point of yield whereas the measured data indicate that a curve is more appropriate. The reason for this is that modified Cam-clay model in CRISP does not model any shear-induced reduction in shear modulus within the yield surface, thereby the stiffer initial tangent modulus of hyperbolic Cam-clay that is not reflected by the highly linear pre-yield segments of the stress-strain curves computed by the modified Cam-clay model.
The discussion above shows that all three models used are able to compute wall deflections which are in reasonable agreement with the measured deflection. This implies that wall deflection alone may not be sufficient to highlight the differences between the various models.
142 FEM STUDY OF SERANGOON MRT SITE
In the ground settlement studies, the discrepancy in the implied modulus is accentuated in both the MCC and HCC models for the shallow soil layers where the effective stresses are lower. Such discrepancy can be overcome by prescribing the fill as Mohr Coulomb material. It was also reflected in the modified and hyperbolic Cam- clays analyses that the attenuation of the settlement profile with distance is more pronounce in the latter. In the 2D analyses, the kingposts had to be modelled as an equivalent wall, which inhibits the flow of soil around the kingposts, thereby giving rise to a spurious stiffening effect.
143 CONCLUSION AND RECOMMENDATIONS
CHAPTER 6 CONCLUSION AND RECOMMENDATIONS
6.1 Concluding remarks
The findings arising from foregoing discussion can be summarised as follows:
1) When 2-D analysis is applied to soldier-piled excavations, modelling errors may
arise in several ways as follows:
a) Firstly, by modelling the discrete soldier piles as a wall, a 2D analysis tends to
over-predict the coupling of pile to the soil below excavation level. In
instances where the pile is not embedded into stiff soil, this modelling error can
give rise to discernible underestimation of soldier pile deflection.
b) Secondly, the deflection of the timber lagging, which is usually larger than that
of the soldier piles, is often underestimated.
c) Thirdly, a 2D analysis cannot replicate the differences in stress paths taken by
the retained soil at different locations at the same depth. In particular, it cannot
model the softening of the soil face just behind the timber lagging. In instances
where the timber lagging is insufficient or its installation, this softening can
give rise to local collapse, which may exacerbate the ground loss and therefore
ground movement. Increasing the inter-pile spacing will tend to accentuate the
effects of these modelling errors.
2) Comparison with field data from the Serangoon MRT site shows that using the
measured angle of friction to define the yield criteria in Mohr Coulomb and critical
state line in modified Cam-clay leads to very different predicted behaviour in the
vicinity in the soldier pile wall in the 3-D analysis, which is attributable to the
144 CONCLUSION AND RECOMMENDATIONS
differences in the “dry-side” yielding behaviour of the two models. These
differences in behaviour between soldier pile and timber lagging is not evident in
2-D analysis, which cannot explicitly predict the behaviour of the timber.
3) Comparison of the modified and hyperbolic Cam-clay models shows that while the
former may be able to fit the final deflection profile if assigned appropriate model
parameters, it tends to over-predict the wall deflection in the early stage of
excavation owing to its inability to model the reduction in the moduli of the soils
with increasing shear strain.
4) The kingposts have a discernible effect in reducing the wall deflection below
excavation level, which in turn affects the far-field settlement characteristics of the
retained soil.
5) In this study, soldier pile installation was not explicitly modelled but the sensitivity
of the analysis to the change of K0-values arising from pile installation was studied.
The range of K0-values varied is likely to encompass that incurred by the
installation of the H-piles. The results of these studies indicate that the broad trend
of behaviour was not altered.
6.2 Recommendations for Future Work
The knowledge gathered from this study pave way for further numerical studies to assess the effect of piles spacing and pile width on the arching action in the retained soil. The inter-pile spacing can be gradually increased from a fore-determined value, with constant equivalent stiffness of soldier piles, until the collapse of retained soil is observed. Effectiveness of timber lagging in preventing progressive deterioration of the soil arching between the piles can thus be examined. This will provide guidelines
145 CONCLUSION AND RECOMMENDATIONS to suitability of pile spacing used in mobilising the arching action in the retained soil based on 3D stress distribution in finite element analysis.
In reality, unsaturated soils are often encountered. The inability of Crisp90 to model unsaturated flow is widely recognised (Lee et al., 1993 and Hsi & Small, 1992).
The conductivity relation of a particular soil can be incorporated to modify Biot’s consolidation theory for analysing the unsaturated flow in residual soil. The drawdown effect of groundwater table can thus be more reasonably represented.
146 REFERENCES
REFERENCES
AITC (1994). Timber Construction Manual, 4th Edn. American Institute of Timber
Construction. Wiley, New York.
Al-Hussaini, M. and Perry, E.B. (1978). Field Experiment of Reinforced Earth Wall. Journal
of Geotechnical Engineering, Div., ASCE, Vol. 104, No. GT3, Mar., pp. 307-322.
Armento, W.J. (1972). Criteria for Lateral Pressures for Braced Cuts. Proceedings of the
Specialty Conference on Performance of Earth and Earth-Supported Structures. Vol 1,
Part 2, Purdue University, Indiana, pp. 1283-1302.
Balasubramaniam, A.S. and Brenner, R.P. (1981). Consolidation and Settlement of Soft Clay.
Soft Clay Engineering, (Eds. A.S. Balasubramaniam and R.P. Brenner), Elsevier, New
York, pp. 481-566.
Bica, A. V. D. and Clayton, C. R. I. (1998). An Experimental Study of Behaviour of
Embedded Lengths of Cantilever Walls. Geotechnique, Vol. 48, No. 1, pp. 731-745.
Biot, M.A. (1941). General Theory of Three Dimensional Consolidation. Journal of Applied
Physics, Vol. 12, pp. 155-164.
Bjerrum, L. (1973). Problems of Soil Mechanics and Construction on Soft Clays and
Structurally Unstable Soils. Proceedings of the 8th International Conference on Soil
Mechanics and Foundation Engineering, Vol. 3, pp. 111-159.
Bolton, M. (1991). A Guide to Soil Mechanics. Macmillan Education Ltd. London.
Borja, R.I., Lee, S.R. and Seed, R.B. (1989). Numerical Simulation of Excavation in
Elastoplastic Soils. International Journal for Numerical and Analytical Methods in
Geomechanics, Vol. 13, pp. 231-249.
Borst, A.J., Conley, T.L., Russell, D.P. and Boirum, R.N. (1990). Subway Design and
Construction for the Downtown Seattle Transit Project. Proceedings of Design And
Performance of Earth Retaining Structures, ASCE Special Conference, Ithaca, New
York, pp. 510-524.
147 REFERENCES
Bosscher, P.J. (1981). Soil Arching in Sandy Slopes. Ph.D. Thesis, The University of
Michigan, U.S.
Bowles, J.E. (1988). Foundation Analysis and Design. McGraw Hill, New York.
Bransby, M.F. and Springman, S.M. (1996). 3-D Finite Element Modelling of Pile Groups
Adjacent to Surcharge Loads. Computers and Geotechnics, Vol. 19, pp. 301-324.
Briaud J.-L. and Lim, Y (1999). Tieback Walls in Sand: Numerical Simulation and Design
Implications. Journal of Geotechnical and Geoenvironmental Engineering, Vol. 125,
No. 2, pp. 101-110.
Britto, A.M. and Gunn, M.J. (1990). CRISP 90 User's & Programmer’s Guide. Cambridge.
Britto, A.M. and Kusakabe, O. (1983). Stability of Axisymmetric Excavations in Clay. Journal
of Geotechnical Engineering, Div., ASCE, Vol. 109, No. 5, pp. 666-681.
Broms, B.B. (1964). Lateral Resistance of Piles in Cohesive Soils. Journal for Soil Mechanics
and Foundation Engineering, ASCE, Vol. 90, SM2, pp. 27-64.
Brumund, W.F., Jonas, E., and Ladd, C.C. (1976). Estimating In Situ Maximum Past
Preconsolidation Pressure of Saturated Clays from Results of Laboratory
Consolidometer Tests. Special Report 163, Transportation Research Board, pp. 4-12.
BS 5930 (1999). Code of Practice for Site Investigations. British Standards Institutions.
BS 8002 (1994). Code of Practice for Earth Retaining Structures. British Standards
Institutions.
BSI (1996). Steelwork Design Guide to BS 5950: Part 1: 1990, Vol.1, Section Properties,
Member Capacities, 4th Edn. British Standards Institutions.
Burland, J.B. (1967). Deformation of Soft Clay. Ph.D. Thesis, University of Cambridge, U.K.
Burland, J.B. (1989). ‘Small is Beautiful’-the Stiffness of Soils at Small Strains. Canadian
Geotechnical Journal, Vol. 26, pp. 499-516.
Burland, J.B., Simpson, B. and St. John, H.D. (1979). Movements around Excavations in
London Clay. Proceedings of 7th European Conference in Soil Mechanics, Brighton,
Vol. 1, pp. 13-30.
148 REFERENCES
Canadian Geotechnical Society (1992). Canadian Foundation Engineering Manual. Canadian
Geotechnical Society, Technical Committee on Foundations.
Cardoso, A.S. (1987). Soil Nailing Applied to Excavations. Ph.D. Thesis, University of Porto,
Portugal.
Chen, D.C., Osborne, N., Shim, J.D. and Hong, E. (2000). An Observational Approach to the
Monitoring of the Excavation at Harbour Front Station, Singapore. Tunnels and
Underground Structures, (Eds. J. Zhao, J.N. Shirlaw & R. Krishnan), Balkema,
Rotterdam, pp. 465-471.
Chong, P.T. (1998). Characterisation of Singapore Soils. Ph.D. Conversion Report, National
University of Singapore.
Chudnoff, M. (1984). Tropical Timbers of the World, Agriculture Handbook 607, U.S.
Department of Agriculture, Forest Service, Forest Products Laboratory, Madison, WI.
Clarke, B.G and Wroth, C.P. (1984). Analyses of the Dunton Green Retaining Wall Base on
Results of Pressuremeter Tests. Geotechnique, Vol. 34, No. 4, pp. 549-562.
Clough, G.W. and Denby, G.M. (1977). Stabilising Berm Design for Temporary Walls in
Clay. Journal of Geotechnical Engineering, Div., ASCE, Vol. 103, No. GT2, pp.75-90.
Clough, G.W. and Hansen, L.A. (1981). Clay Anisotropy and Braced wall Behaviour. Journal
of Geotechnical Engineering, Div., ASCE, Vol. 107, No. 7, pp. 893-913.
Clough, G.W. and O’Rourke, T.D. (1990). Construction-Induced Movements of In-situ Walls.
Proceedings of Design And Performance of Earth Retaining Structures, ASCE Special
Conference, Ithaca, New York, pp. 439-470.
Clough, G.W. and Tsui, Y. (1977). Static Analysis of Earth Retaining Structures. Numerical
Methods in Geotechnical Engineering, (Eds. C.S. Desai & J.T. Christian), McGraw
Hill, New York, pp. 506-527.
Clough, G.W., Hansen, L.A. and Mana, A.I. (1979). Prediction of Support Excavation
Movements Under Marginal Stability Conditions in Clay. Proceedings of 3rd
International Conference on Numerical Methods in Geomechanics, Aachen, Vol. 4, pp.
1485-1502.
149 REFERENCES
Clough, G.W., Weber, P.R. and Lamont, J. (1972). Design and Observation of a Tie-back
Wall. Proceedings of the Specialty Conference on Performance of Earth and Earth-
Supported Structures, Vol. 1, New York, pp. 1367-1389.
Committee on Glossary of Terms and Definitions in Soil Mechanics (1958). Glossary of
Terms and Definitions in Soil Mechanics. Journal of the Soil Mechanics and
Foundations. Div., ASCE, Vol. 84, No. 4, pp. 1-43.
Coop, M.R. and Jovičić, V. (1999). The Influence of State on the Very Small Strain Stiffness
of Soils. 2nd International Symposium for Pre-faliure Deformation of Geomaterials IS-
Torino ’99, Turin, pp 175-181.
Coutts, D.R. and Wang, J. (2000). The Monitoring and Analysis of Results for Two Strutted
Deep Excavations in Singapore using Vibrating Wire Strain Gauges. Tunnels and
Underground Structures, (Eds. J. Zhao, J.N. Shirlaw & R. Krishnan), Balkema,
Rotterdam, pp. 465-471.
Craig, R.F. (1996). Soil Mechanics, 5th Edn. Chapman & Hall. London.
Dames and Moore (1983). Detailed Geotechnical Study Interpretative Report, Submitted to
Singapore Mass Rapid Transit System.
Dasari, G. R. (1996). Modelling of the Variation of Soil Stiffness during Sequential
Construction. Ph. D. Thesis, University of Cambridge, U.K.
Day, R.A. and Potts, D.M. (1993). Modelling Sheet Pile Retaining Walls. Computers and
Geotechnics, Vol. 15, pp. 125-143.
De Moor, E.K. (1994). An Analysis of Bored Pile/Diaphragm Wall Installation Effects.
Geotechnique Vol. 44, No. 2, pp. 341-347.
Duncan, J.M. and Buchignani, A. L. (1976). An Engineering Manual for Settlement Studies.
Geotechnical Engineering Report, University of California, Berkeley.
Dysli, M. and Fontana, A. (1982). Deformations Around the Excavation in Clayey Soil. Proc.
Of the Int. Symposium on Numerical Models in Geomechanics, Zurich, Sept. pp. 634-
642.
150 REFERENCES
Ekström, J. (1989). Field Study of Model Pile Group Behaviour in Non-cohesive Soils –
Influence of Compaction due to Pile Driving. Ph. D. Thesis, Chalmers University of
Technology, Göteborg, Sweden.
Finno, R.J., Harahap, I.S. and Sabatini, P.J. (1991). Analysis of Braced Excavations with
Coupled Finite Element Formulations. Computers and Geotechnics, Vol. 12, pp. 91-
114.
Fourie, A.B. and Potts, D.M. (1989). Comparison of Finite Element and Limit Equilibrium
Analysis for an Embedded cantiliver Retaining Wall. Geotechnique, Vol. 39, No. 1,
pp. 175-188.
GCO (1990). Review of Design Methods for Excavations. Geotech. Control Office, Hong
Kong.
Getzler, Z., Komovnik, A. and Mazurik, A. (1968). Model Study on Arching Above Buried
Structures. Journal of the Soil Mechanics and Foundations. Div., ASCE, Vol. 94, No.
SM5, pp. 1123-1141.
Giger, M.W. and Krizek, R.J. (1975). Stability Analysis of Vertical Cut with Variable Corner
Angle. Soils and Foundations, The Japanese Society of Soil Mechanics and
Foundation Engineering, Vol. 15, No. 2, pp. 63-71.
Gill, S.A. and Lukas, R.G. (1990). Ground Movement Adjacent to Braced Cuts. Proceedings
of Design And Performance of Earth Retaining Structures, ASCE Special Conference,
Ithaca, New York, pp. 471-488.
Goh, S.H. (1995). Propagation and Attenuation of Ground Shock in Dry Soil. M. Eng. Thesis,
National University of Singapore, Singapore.
Goldberg, D.T., Jaworski, W.E. and Gordon, M.D. (1976). Lateral Support Systems and
Underpinning, Federation of Highway Administration. Rep. FHWA-RD-75-128, 3
volumes.
Gomes Correia, A. and Guerra, N.M. da C. (1997). Performance of three Berline-type
Retaining Walls. Proceedings of the 14th International Conference of Soil Mechanics
and Foundation Engineering, Hamburg, Vol. 2, pp. 1297-1300.
151 REFERENCES
Gourvenec, S. M. and Powrie, W. (1999). Three-dimensional Finite-element Analysis of
Diaphragm Wall Installation. Geotechnique, Vol. 49, No. 6, pp. 801-823.
Graham, J. (1992). The Key Material Properties in Geotechnical engineering need to be
measured, instead of being specified. Proceedings of the Wroth Memorial Symposium,
Oxford, pp. 1-18.
Gunn, M.J. Satkunananthan, A. and Clayton, C.R.I. (1992). Finite Element Modelling of
Installation Effects. Proceedings Conference on Retaining Structure by ICE,
Cambridge, pp. 46-55.
Handy, R.L. (1985a). The Arch in Soil Arching. Journal of Geotechnical Engineering, Div.,
ASCE, Vol. 111, No. 3, pp. 302-318.
Handy, R.L. (1985b). Discussion of “The Arch in Soil Arching”: Closure by Richard L.
Handy. Journal of Geotechnical Engineering, Div., ASCE, Vol. 111, No. 4, pp. 275-
277.
Hashash, Y.M.A. and Whittle, A.J. (1992). Analysis of Braced Diaphragm Walls in Deep
Deposits of Clay. Res. Rep. R92-19, Department of Civil Engineering, Massachusetts
Institute of Technology (MIT), Cambridge, Mass.
Hashash, Y.M.A. and Whittle, A.J. (1996). Ground Movement Prediction for Deep
Excavations in Soft Clay. Journal of Geotechnical Engineering, Div., ASCE, Vol. 122,
No. 6, June, pp. 474.-486.
Hentenyi, M. (1946). Beams on Elastic Foundations. The University of Michigan Press, Ann
Arbor, MI.
Hong, S.H., Lee, F.H. and Yong, K.Y. (2003). Three-dimensional Pile-soil Interaction in
Soldier-piled Excavations. Computers and Geotechnics, Vol. 30, pp. 81-107.
Hsi, J.P. and Small, J.C. (1992). Ground Settlements and Drawdown of the Water Table
around an Excavation. Canadian Geotechnical Journal, Vol. 29, pp. 740-754.
Jáky, J. (1944). The Coefficient of Earth Pressure at Rest. Journal of the Society of Hungarian
Architects and Engineers, Oct., Budapest, pp 355-358.
152 REFERENCES
Jardine, R.J., Symes, M.J. and Burland, J.B. (1984). The Measurement of Soil Stiffness in the
Triaxial Apparatus. Geotechnique, Vol. 34, No. 3, pp. 323-340.
Jardine, R.J., Potts, D.M., Fourie, A.B. and Burland, J.B. (1986). Studies of the Influence of
Non-linear Stress-strain Characteristics in Soil-structure Interaction. Geotechnique,
Vol. 36, No. 3, pp. 377-396.
Kingsley, H.W. (1989). Arch in Soil Arching. Journal of Geotechnical Engineering, Div.,
ASCE, Vol. 115, No. 3, March, pp. 415-419.
Krynine, D.P. (1945). Discussion of “Stability and Stiffness of Cellular Cofferdams” by Karl
Terzaghi. Transactions, ASCE, Vol. 110, pp. 1175-1178.
Kulhawy, F.H. (1990). Manual on Estimating Soil Properties for Foundation Design. Electric
Power Research Institute, Report no. EL-6800, Ithaca, New York.
Lambe, T.W. and Whitman, R.V. (1979). Soil Mechanics, SI Version. John Wiley & Sons, Inc.
New York.
Lee, F.H., Tan, T.S. and Yong, K.Y. (1993). Excavation in Residual Soils with High
Permeability. Proceedings of 11th Southeast Asian Geotechnical Conference,
Singapore, pp. 739-744.
Lee, F.H., Tan, T.S. and Wang, X.N. (2001). Groundwater Effects in Soldier-piled Excavation
in Residual Soils. Proceedings of Underground Singapore 2001, Singapore, pp. 249-
260.
Lee, F.H., Yong, K.Y., Lee, S.L. and Toh, C.T. (1989). Finite Element Modelling of Strutted
Excavation. Numerical Models in Geomechanics (NUMOG III), Niagra Falls, Canada,
pp. 577-584.
Lee, S.L., Parnploy, U., Yong, K.Y. and Lee, F.H. (1989). Time-dependent Deformation of
Anchored Excavation in Soft Clay. Symp. On Underground Excavations in Soils and
Rocks, Including Earth Pressure Theories, Buried Structures and Tunnels, Bangkok,
Thailand, pp. 377-384.
153 REFERENCES
Lings, M.L., Nash, D.F.T., Ng, C.W.W. (1993). Reliability of Earth Pressure Measurements
Adjacent to a Multipropped Diaphragm Wall. Proceedings of an International
Conference on Retaining Structures, Cambridge, U.K., pp. 258-269.
Liu, K.X. (1995). Three Dimensional Analyses of Deep Excavation in Soft Clay. M. Eng.
Thesis, National University of Singapore, Singapore.
Livesley, R.K. (1983). Finite Element: An Introduction for Engineers. Cambridge University
Press, Cambridge.
Loh, C. K., Tan T. S. and Lee F. H. (1998). Three-dimensional excavation tests. Proceedings
of International Conference Centrifuge 98, 23-25 September, Tokyo, Japan, pp. 649-
654.
Lusher, U. and Hoeg, K. (1964). The Beneficial Action of the Surrounding Soil on the Load
Carrying Capacity of Buried Tubes. Proceedings of the 1964 Symposium on Soil-
Structure Interaction, Tuscon, Arizona, pp. 393-402.
Macneal, R.H. (1994). Finite Elements: Their Design and Performance. Marcel Dekker, Inc.,
New York.
Mana, A.I. and Clough, G.W. (1981). Prediction of Movements for Braced Cuts in Clay.
Journal of Geotechnical Engineering, Div., ASCE, Vol. 107, pp.759-777.
Massing, G. (1926). Eigenspannungen und Verfesttigung beim Messing. Proceedings of 2nd
International Congress of Applied Mechanics.
Matos Fernandes, M.A. (1986). Three-dimensional Analysis of Flexible Earth Retaining
Structures. Proceedings of Second NUMOG (Eds. G.N. Pande & W.F. van Impe), M.
Jackson & Sons, UK.
Matos Fernandes, M.A., Cardoso, A.J.S.,Trigo J.F.C. and Marques J.M.M.C. (1986). Finite
Element Modelling of Supported Excavations. Soil-Structure Interaction: Numerical
Analysis & Modelling (Ed. J.W. Bull), E & FN Spon.
Mayne, P.W. and Kulhawy, F.H. (1982). Ko – OCR Relationships in Soil. Journal of the
Geotechnical Engineering Division, ASCE, Vol.108, No. GT6, pp. 851-872.
154 REFERENCES
Nakai, T. (1985). Finite Element Computations for Active and Passive Earth Pressure
Problems of Retaining Wall. Soil and Foundations, Vol. 25, No. 3, pp. 98-112.
Nasim, A. S. M. (1999). Numerical Modelling of Soil Profile and Behaviour in Deep
Excavation Analyses. M. Eng. Thesis, National University of Singapore, Singapore.
NAVFAC (1982). Design Manual 7.2: Foundations and Earth Structures, Department of the
Navy, Naval Facilities Engineering Command, Washington D.C.
Ng, C.W.W., Simpson, B., Lings, M.L. and Nash, D.F.T. (1995). An Approximate Analysis of
the Three-dimensional Effects of Diaphragm Wall Installation. Geotechnique, Vol. 45,
No. 3, pp. 497-507.
Ng, C.W.W. and Yan, R. W. M. (1999). Three-dimensional Modelling of a Diaphragm Wall
Construction Sequence. Geotechnique, Vol. 49, No. 6, pp. 825-834.
O’ Rourke, T.D. (1975). A Study of two Braced Excavations in Sands and Interbedded Stiff
Clay. PhD Thesis, University of Illinois, U.S.
O'Rourke, T.D., Cording, E.J. and Boscardin, M. (1976). The Ground Movements Related to
Braced Excavation and their Influence on Adjacent Buildings. U.S. Department of
Transportation, Report no. DOT-TST 76, T-23.
Ou, C.Y. and Chiou, D.C. (1993). Three-Dimensional Finite Element Analysis of Deep
Excavation. 11th Southeast Asian Geotechnical Conference, Singapore, pp. 769-774.
Ou, C.Y. and Shiau, B.Y. (1998). Analysis of the Corner Effect on Excavation Behaviours.
Canadian Geotechnical Journal, Vol. 35, pp. 532-540.
Ou, C.Y., Chiou, D.C. and Wu, T.S. (1996). Three-Dimensional Finite Element Analysis of
Deep Excavations. Journal of Geotechnical Engineering, Div., ASCE, Vol. 122, No. 5,
pp. 337-345.
Ove Arup and Partners, (1997). North East Line Contract 704: Additional Soil Investigation
for Proposed Serangoon Station. Ove Arup and Partners, Singapore.
OYO, (1996). Geotechnical Soil Investigation and Related Works (Serangoon to Kangkar):
Final Report. OYO Corporation Singapore Branch, Singapore.
155 REFERENCES
Parnploy, U. (1990). Time Dependent Behaviour of Excavation Support System in Soft Clay.
Ph. D. Thesis, National University of Singapore, Singapore.
Pearlman, S.L. and Wolosick, J.R. (1990). Anchored Earth Retaining Structures-Design
Procedures and Case Studies. Proceedings of Design And Performance of Earth
Retaining Structures, ASCE Special Conference, Ithaca, New York, pp. 525-539.
Peck, R.B. (1969). Deep Excavations and Tunnelling in Soft Ground. Proceedings of 7th
Conference on Soil Mechanics and Foundation Engineering, Mexico. State of the Art
Report, pp.225-290.
Potts, D. M. and Zdravković, L. (2001). Finite Element Analysis in Geotechnical Engineering:
Application. Thomas Telford, London.
PWD, (1976). Geology of the Republic of Singapore. Public Works Department, Singapore.
Rahim, A. and Gunn, M.J. (1997). Bending CRISP. CRISP NEWS, No.4, Sage Engineering
Ltd.
Reddy, J.N. (1993). An Introduction to the Finte Element Method, 2nd Edn. McGraw Hill, Inc.
New York.
Richards, D.J. and Powrie, W. (1998). Centrifuge Model Tests on Doubly Propped Embedded
retaining Walls in Overconsolidated Kaolin Clay. Geotechnique, Vol. 48, No. 6, pp.
833-846.
Roscoe, K.H., Schofield, A.N. and Thurairajah, A.H., (1963). Yielding of Soils in States
Wetter than Critical, Geotechnique, Vol. 13, pp. 211-240.
Roscoe, K.H., Schofield, A.N. and Wroth, C.P., (1958). On the Yielding of Soils.
Geotechnique, Vol. 8, pp. 22-53.
Schofield, A.N. & Wroth, C.P. (1968). Critical State Soil Mechanics, McGraw Hill, London.
Simpson, B. (1992). Retaining Structures: Displacement and Design. Geotechnique, Vol. 42,
No. 4, pp. 541-576.
Simpson, B., O'Riordan, N.J. and Croft, D.D. (1979). A Computer Model for the Analysis of
Ground Movements in London Clay. Geotechnique, Vol. 29, No. 2, pp. 149-175.
156 REFERENCES
St John, H.J. (1975). Field and Theoretical Studies of the Behaviour of Ground around Deep
Excavations in London Clay. PhD Thesis, University of Cambridge, U.K.
Stallebrass, S.E. (1990). Modelling the Effect of Recent Stress History on the Deformation of
Overconsolidated soils. PhD Thesis, The City University, U.K.
Symons, I.F. and Carder, D.R. (1993). Stress changes in stiff clay caused by the installation of
embedded retaining walls. Retaining Structures (Ed. C.R.I. Clayton), Thomas Telford,
London, pp. 227-236.
Teng, W.C. (1975). Soil Stresses for Design of Drilled Caisson Foundations Subjected to
Lateral Loads. ASCE, Conference on Analysis and Design in Geotechnical
Engineering.
Terzaghi, K. (1936). The Shearing Resistance of Saturated Soils and the Angles between the
Planes of Shear. 1st International Conference of Soil Mechanics and Foundation
Engineering., Cambridge, Vol. 1, pp. 54-56.
Terzaghi, K. (1943). Theoretical Soil Mechanics. John Wiley and Sons, Inc., New York.
Terzaghi, K. and Peck, R.B. (1948). Soil Mechanics in Engineering. Practice. John Wiley and
Sons, Inc., New York.
Terzaghi, K., Peck, R.B. and Mesri, G. (1996). Soil Mechanics in Engineering Practice, 3rd
Edn. John Wiley and Sons, Inc., New York.
Tomlinson, M.J. (1995). Foundation Design and Construction, 6th Edn. English Language
Book Society, London.
Trada (1990). Timber in Excavations. Thomas Telford Ltd, London.
Trautmann, C.H. and Kulhawy, F.H. (1987). CUFAD-A Computer Program for Compression
and Uplift Foundation Analysis and Design. Eletric Power Research Institute, Report
no. EL-4540-CCM, Vol. 16.
Tsui, Y. and Clough, G.W. (1974). Plane Strain Approximations in Finite Element Analyses of
Temporary Walls. Proceedings of Conference on Analysis and Design in Geotechnical
Engineering, University of Texas, Austin, 1, pp173.
157 REFERENCES
Vermeer, P.A., Punlor, A. and Ruse, N. (2001). Arching Effects behind a Soldier Pile Wall.
Computers and Geotechnics, Vol. 28, pp. 379-396.
Viggiani, G. and Atkinson, J.H. (1995). Stiffness of Fine-grained Soil at Very Small Strain.
Geotechnique, Vol. 45, No. 2, pp. 249-265.
Whittle, A.J., Hashash, Y.M.A. and Whitman, R.V. (1993). Analysis of Deep Excavation in
Boston. Journal of Geotechnical Engineering, Div., ASCE, Vol. 119, pp. 69-90.
Wong, I.H., Poh T.Y. and Chuah, H.L. (1997). Performance of Excavation for Depressed
Expressway in Singapore. Journal of Geotechnical & Geoenvironmental Engineering,
Div., ASCE, Vol. 123, No. 7, pp. 617-625.
Wroth, C.P. (1975). In-situ Measurement of Initial Stresses and Deformation Characteristics.
Proceedings of ASCE Specialty Conference on In-situ Measurement of Soil Properties,
Vol. 2, Raleigh, pp. 180-230.
Wroth, C.P., Randolph, M.F., Houlsby, G.T. and Faehy, M. (1979). A Review of the
Engineering Properties of Soils with Particular Reference to the Shear Modulus.
OUEL Report No. 1523/84. University of Oxford.
Yong, K.Y., Lee, F.H., Parnploy, U. and Lee, S.L. (1989). Elasto-Plastic Consolidation
Analysis for Strutted Excavation in Clay. Computer and Geotechnics, Vol. 8, pp. 311-
328.
Yoo, C.S. and Kim, Y.J. (1999). Measured Behaviour of In-situ Walls in Korea. Proceedings
of the 5th International symposium on Field Measurements in Geomechanics,
Singapore, pp. 211-216.
Zienkiewicz, O.C. and Taylor, R.L. (1988). The Finite Element Method, 4th Edn, Vol. 1.
McGraw-Hill, London.
158 APPENDICES
APPENDICES
Appendix A Transformation Matrix for 3D Beam
The stiffness matrix of a three dimensional beam element with reference to the member axes between the end nodes i and j has been derived in the earlier section.
The global axes are brought to coinside with the local member axes by sequence of rotation about y, z and x axes respectively. This is referred to as y-z-x transformation.
Figure A-1 shows the three rotations of the global axes. The angle of rotation are denoted as β, γ and α respectively.
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 0 sin β []= Tβ 0 1 0 − sin β 0 cos β
cosγ sinγ 0 []= − γ γ Tγ sin cos 0 0 0 1
1 0 0 []= α α Tα 0 cos sin 0 − sinα cosα thus,
159 APPENDICES
(cos β cosγ ) (sinγ ) (cosγ sin β ) []T' = − (sin β sinα + cos β sinγ cosα) (cosγ cosα) (sinα cos β − sin β sinγ cosα) − (sin β cosα − cos β sinγ sinα) − (cosγ sinα) (cos β cosα − sin β sinγ sinα) (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:
C C C x y z − α − α − α + α CxCy cos Cz sin 2 2 CyCz cos Cx sin []T' = C + C cosα (A.3) 2 + 2 x z 2 + 2 Cx Cz Cx Cz C C sinα − C cosα C C sinα + C cosα x y z − 2 + 2 α y z x Cx Cz sin 2 + 2 2 + 2 Cx Cz Cx Cz where
x − x y − y z − z C = j i , C = j i , C = j i x L y L z L and
= − 2 + − 2 + − 2 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:
0 C 0 y []= − α α (A.4) T'vert Cy cos 0 sin α α Cy sin 0 cos
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 []0 []0 []0 [] [ ] [] [] [] [] 0 T' 0 0 0 0 []0 []0 [T ' ] []0 []0 []0 []T= (A.5) []0 []0 []0 [T ' ] []0 []0 []0 []0 []0 []0 [T' ] []0 []0 []0 []0 []0 []0 [T' ]
161 APPENDICES
y
ym
α xm
LCy γ x β
LC 2 + 2 z L C x Cz
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:
h 2 = σ M ∫ x y.dy (B.1) −h 2
where h is the depth of the beam and σx is the stress normal to the cross section.
η
+1 I M ξ h II -1 +1 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 = (B.2) dη 2
This leads to
163 APPENDICES
h y = η (B.3) 2
Using the local coordinates, we obtain
+1 2 = σ h η η M ∫ x .d (B.4) −1 4
The above integral can be evaluated using a three-point, one-dimensional Gauss integration rule. Thus:
2 III = h σ ×η ×ϖ M ∑ xi i i (B.5) 4 i=I
Similarly for reduced-integration 8-noded quadrilateral element,
2 II = h σ ×η ×ϖ M ∑ xi i i (B.6) 4 i=I
In the case of 3D, which was considered in analyses of Chapter 3, we obtain the following integral:
hz 2 hy 2 = σ M ∫∫x y.dydz (B.7) −− hz 2 hy 2
η
hz +1 I -1 ξ Mzz +1 hy II ζ 3 -1 y III 2 1 x z Global coordinate system 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
+ + 2 1 1 h h M = ∫∫σ y z η.dηdζ (B.8) x −1−1 4 2
Thus for full-integration 20-noded linear strain brick,
2 h h 3 III = y z σ ×η ×ϖ ×ϖ M zz ∑∑ xik i i k (B.9) 8 k ==1 i I and reduced-integration 20-noded linear strain brick
2 h h 2 II = y z σ ×η ×ϖ ×ϖ M zz ∑∑ xik i i k (B.10) 8 k ==1 i I 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) Stallebrass (1990) 150 FEM modelling Dasari (1996)
(kPa) FEM modelling Stallebrass (1990) q
100
50 Deviator stress, stress, Deviator
0 0.000 0.002 0.004 0.006 0.008 0.010 ε Deviator strain, s
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 − q ε −ε ur = F s ur (C.1) 2 2
From Equation 5.11, assuming S=3G and G∞=0,
ε −ε s ur 3G0 q − q 2 ur = (C.2) 2 3G ε −ε 1+ 0 s ur q f 2
166 APPENDICES
3 3G ε −ε ε −ε 3G 1 + 0 s ur − s ur 0 G0 1 3G0 1 dq 2 q f 2 2 q f 2 = 2 dε 3G ε −ε s 1+ 0 s ur q f 2
3 G0 = 2 2 (C.3) 3G ε −ε 1+ 0 s ur q f 2
Simplify,
dq 3G = 0 (C.4) ε 2 d s 3G ε −ε 1+ 0 s ur q f 2
Variation of G can be rewritten as:
G = 0 G 2 (C.5) 3G ε −ε 1+ 0 s ur q f 2
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 2 to 6 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