analytical and numerical study of soil disturbance associated wit
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University of Wollongong
Research Online
University of Wollongong Thesis Collection University of Wollongong Thesis Collections
2010
Analytical and numerical study of soil disturbanceassociated with the installation of mandrel-driven
prefabricated vertical drainsAli GhandeharioonUniversity of Wollongong
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Repository Services: [email protected].
Recommended CitationGhandeharioon, Ali, Analytical and numerical study of soil disturbance associated with the installation of mandrel-drivenprefabricated vertical drains, Doctor of Philosophy thesis, Department of Civil Engineering, University of Wollongong, 2010.
http://ro.uow.edu.au/theses/3338
http://ro.uow.edu.au/http://ro.uow.edu.au/theseshttp://ro.uow.edu.au/thesesuowhttp://ro.uow.edu.au/http://ro.uow.edu.au/thesesuowhttp://ro.uow.edu.au/theseshttp://ro.uow.edu.au/http://ro.uow.edu.au/http://ro.uow.edu.au/ -
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ANALYTICAL AND NUMERICAL STUDY OF SOIL
DISTURBANCE ASSOCIATED WITH THE
INSTALLATION OF MANDREL-DRIVEN
PREFABRICATED VERTICAL DRAINS
A thesis submitted in fulfilment of the requirements
for the award of the degree of
Doctor of Philosophy
from
UNIVERSITY OF WOLLONGONG, AUSTRALIA
by
ALI GHANDEHARIOON, B.Sc., M.Sc.
Department of Civil Engineering
2010
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ii
CERTIFICATION
I, Ali Ghandeharioon, declare that this thesis, submitted in fulfilment of the
requirements for the award of Doctor of Philosophy in the Department of Civil
Engineering at the University of Wollongong, is wholly my own work unless
otherwise referenced or acknowledged. The document has not been submitted for
qualifications at any other academic institution.
Ali Ghandeharioon
October 2010
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Abstract
Prefabricated vertical drains (PVDs) combined with preloading have gained in
popularity among the most effective ground improvement techniques available to
mitigate the unacceptable differential settlements caused by the heterogeneity and
high compressibility of soft soil deposits. In this thesis the installation of
mandrel-driven PVDs and associated disturbance in cohesive soils were studied by
conducting analytical investigations, laboratory experiments, and numerical
modelling. The pattern of disturbed regions surrounding the mandrels and the
distribution of stresses in soils obtained from the analytical and numerical predictions
agreed with the results of the laboratory tests. A number of case histories taken from
Malaysia, Australia and Thailand were also analysed to evaluate the associated soil
disturbance during installation of prefabricated vertical drains.
An analytical study of mandrel penetration and the resulting disturbance in soft
saturated clays was carried out with a new elliptical cavity expansion theory (CET).
This research postulated that installing PVDs in the field with commonly used
mandrels would create elliptical cavities with a concentric progression in the
horizontal plane. An elliptical CET was developed using modified Cam clay
parameters for undrained analysis with a formulation based on polar coordinates that
accounts for the rate of mandrel penetration and the time for predicting internal
pressure in the cavity, corresponding stresses and excess pore pressure in the soil
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while driving the mandrel. The pattern of distribution calculated for the excess pore
pressure was verified using data available in the literature. A more realistic elliptical
smear zone based on the elliptical CET was introduced while the disturbed soil
surrounding the mandrel was characterised by the plastic shear strain normalised by
the rigidity index.
A number of large-scale laboratory tests that incorporated the field conditions and
effects of confining pressures were performed. A consolidometer specifically
designed for the purpose, and a machine capable of driving mandrels at realistic rates
were used in these experiments. The variations of pore water pressure during
installation of a mandrel-driven PVD and withdrawal of the mandrel were monitored
by fast response pore pressure transducers connected to a digital data logger. The
extent of smear zone in the large-scale consolidometer was determined using the
results of moisture content tests on samples, which in relation to the installed PVD
were cored along different polar axes from various locations. The smear zone was
then analysed to establish a relationship between its size and the in-situ effective
stresses.
The installation of a mandrel was simulated numerically using a commercial finite
element software package, ABAQUS. The finite element models included coupled
analyses with a large-strain formulation. Coulombs law of friction and the penalty
method were incorporated into the numerical technique. It was shown that the soil
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surrounding the mandrel moved radially and downwards as the mandrel was installed.
The variations of pore water pressure at different locations during the installation of a
mandrel-driven PVD and withdrawal of the mandrel were illustrated. There was an
agreement between the pore pressures measured in the laboratory and the finite
element predictions. The extent of smear zone was studied according to a numerical
simulation of the mandrel installation.
The analytical formulation incorporating the elliptical CET presented in this thesis
was applied to case histories from the Muar clay region in Malaysia and the Sunshine
Motorway in Australia. The ratio of plastic shear strain to the rigidity index was
found useful for estimating the extent of the smear zone in the field because in
practical situations the basic soil parameters may be used without sophisticated
large-scale testing.
Moreover, the numerical model of mandrel installation was specifically developed to
study a case history from the Second Bangkok International Airport in Thailand. The
variations of pore pressure while installing a vertical drain and withdrawing the
mandrel were obtained. The plastic shear strain was evaluated to indentify different
aspects of disturbance in the soil elements. The results of this analysis indicated that
the model developed can be applied to field conditions.
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ACKNOWLEDGMENTS
vi
ACKNOWLEDGMENTS
The writer would like to express his profound gratitude to
Professor Buddhima Indraratna and Dr. Cholachat Rujikiatkamjorn for their
enthusiasm, invaluable help, and constructive criticism throughout the supervision
of this thesis. Their patience and suggestions regarding any inquiry were greatly
appreciated. Professor Buddhima Indraratna and Dr. Cholachat Rujikiatkamjorn
were the source of novel ideas during the twists and turns of this research, and
actively encouraged the writer in every aspect of his Ph.D. career.
Sincere appreciation is also extended to Mr. Alan Grant, senior technical officer at
the University of Wollongong for his valued help during the experimental phase
of this project. His advice, support and availability, even after hours, made the
complex laboratory work possible.
A special note of appreciation is offered to Dr. Hadi Khabbaz,
Professor Timothy McCarthy, Dr. Neaz Sheikh, and Dr. Jayan Sylaja Vinod for
their continuing support, friendly advice and useful comments throughout this
research.
The writer takes this opportunity to thank all past and present members of the
Department of Civil Engineering at the University of Wollongong for their
discussion and support. The writer would also like to thank the
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ACKNOWLEDGMENTS
vii
Cooperative Research Centre (CRC) for Railway Innovation for providing the
scholarship for this project.
The writer wholeheartedly and respectfully dedicates this piece of work as a
tribute to his beloved parents, Mr. Mohammad Ghandeharioon and
Mrs. Soodabeh Ataei, and his darling wife, Mrs. Mahgol Shekalzahi, for their
continuing love, prayers, encouragement and many sacrifices throughout this
research period, without which the writer could never have reached where he is
today. The writer is also grateful to his brother, Mr. Amir Ghandeharioon, for his
humour and support in times of stress.
Finally, and most importantly, the writer offers his heartfelt gratitude as a
compliment to his adored wife for her unfailing support during the highs and lows
of an academic career that started with a M.Sc. thesis at the Ferdowsi University
of Mashhad in Iran. Mahgols affections have been the source of the writers
strength and inspiration the whole time.
Ali Ghandeharioon
University of Wollongong, Australia
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PUBLICATIONS
viii
PUBLICATIONS
The following publications are related to this PhD thesis:
Ghandeharioon A., Indraratna B. and Rujikiatkamjorn C. (2010). Laboratory
and Finite Element Investigation of Soil Disturbance Associated with the
Installation of Mandrel-driven Prefabricated Vertical Drains. submitted to the
Journal of Geotechnical and Geoenvironmental Engineering.
Ghandeharioon A., Indraratna B. and Rujikiatkamjorn C. (2010). Analysis of
Soil Disturbance Associated with Mandrel-driven Prefabricated Vertical
Drains Using an Elliptical Cavity Expansion Theory.International Journal of
Geomechanics, 10(2), 53-64.
Indraratna B., Rujikiatkamjorn C. and Ghandeharioon A.(2008). Modelling of
Soft Ground Consolidation via Combined Surcharge and Vacuum
Preloading. Proceedings of the 2nd International Workshop on Geotechnics
of Soft Soils: Focus on Ground Improvement, CRC Press, Taylor and Francis
Group, London, UK, 43-53.
Rujikiatkamjorn C., Indraratna B. and Ghandeharioon A. (2008). Finite
Element Simulation of Mandrel Penetration in a Normally Consolidated Soil.
Proceedings of the 2nd International Workshop on Geotechnics of Soft Soils:
Focus on Ground Improvement, CRC Press, Taylor and Francis Group,
London, UK, 287-292.
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TABLE OF CONTENTS
ix
TABLE OF CONTENTS
CERTIFICATION...ii
ABSTRACT....iii
ACKNOWLEDGMENTS..vi
PUBLICATIONS......viii
TABLE OF CONTENTS....ix
LIST OF FIGURES..xiv
LIST OF TABLES......xxxi
LIST OF SYMBOLS.xxxii
1 INTRODUCTION.........................................................................................1
1.1 General...1
1.2 Application of Vertical Drains ..6
1.3 Application of Cavity Expansion Theory....10
1.4 Objectives and Scope of the Study...15
1.5 Organisation of the Dissertation...17
2 LITERATURE REVIEW...20
2.1 Installation and Monitoring of Prefabricated Vertical Drains..20
2.2 Characteristics of Prefabricated Vertical Drains..24
2.2.1 Equivalent Drain Radius..24
2.2.2 Influence Zone of Drains.26
2.2.3 Smear Zone of Drains..27
2.2.4 Discharge Capacity of Drains..35
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TABLE OF CONTENTS
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2.2.5 Well Resistance of Drains38
2.2.6 Filtration Mechanism of PVDs and Apparent Opening Size of
Filters..39
2.3 Consolidation Theories43
2.3.1 Theory of Vertical Consolidation.43
2.3.1.1 Terzaghis Theory of 1-D Consolidation..45
2.3.1.2 Other Theories of 1-D Consolidation47
2.3.1.3 Evaluation of the Coefficients of Consolidation and
Permeability..48
2.3.2 Theory of Radial Consolidation...50
2.3.2.1 Barrons Theory of Radial Consolidation.50
2.3.2.2 Hansbos Theory of Radial Consolidation55
2.3.2.3
Method (Hansbo 1979, 1997, 2001).56
2.3.2.4 Evaluation of the Coefficient of Consolidation with
Radial Drainage.58
2.3.2.4.1 ( )rU1ln vs. t Approach...58
2.3.2.4.2 Plotting Settlement Data.59
2.3.3 Theory of Simultaneous Vertical and Radial Consolidation....60
2.4 Modelling Consolidation via Vertical drains Under Field
Conditions62
2.4.1 Permeability and Geometry Matching.63
2.4.2 Concept of Equal Discharge Rate64
2.4.3 Matching the Well Resistance .64
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TABLE OF CONTENTS
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2.4.4 The Concept of an Equivalent Parallel Drain Wall..65
2.5 Analysis of Soil Disturbance due to Installation of the PVDs.68
2.5.1 Bearing Capacity Theory.68
2.5.1.1 Limit Equilibrium Method69
2.5.1.2 Slip-line Method70
2.5.2 Strain Path Method...72
2.5.3 Cavity Expansion Theory.77
2.5.4 Incremental Displacement Finite Element Method..81
2.6 Summary..88
3 THEORITICAL CONSIDERATIONS.90
3.1 General.90
3.2 Assumptions and Definition of the Problem91
3.3 Development of the Elliptical Cavity Expansion Theory93
3.3.1 Elastic Analysis...93
3.3.2 Plastic Analysis.102
3.4 Analysis of Soil Behaviour Around Mandrels Using the Elliptical
CET ...107
3.5 Validating the Elliptical CET with the Data Available in the
Literature....110
3.6 Summary118
4 LABORATORY STUDIES.120
4.1 General...120
4.2 Large-scale Laboratory Tests.121
4.2.1 Test Apparatus...121
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TABLE OF CONTENTS
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4.2.2 Test Materials.126
4.2.3 Test Procedure132
4.3 Results of the Large-scale Laboratory Tests..137
4.4 Summary150
5 FINITE ELEMENT MODELLING152
5.1 General...152
5.2 Development of the Finite Element Model154
5.3 Simulating Installation of the Mandrel.163
5.4 Results of the Finite Element Simulation.......166
5.5 Summary183
6 CASE STUDIES185
6.1 General...185
6.2 Muar Clay Region, Malaysia.187
6.2.1 Soil Conditions...189
6.2.2 Analytical Investigation of Smear Zone and Validating the
Prediction...191
6.3 Sunshine Motorway, Australia ..194
6.3.1 Soil Conditions...196
6.3.2 Analysis of the Variation of Smear Zone with Depth and its
Verification............................................................................197
6.4 Second Bangkok International Airport, Thailand..201
6.4.1 Soil Conditions...203
6.4.2 Finite Element Studying of the Installation of PVDs.205
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TABLE OF CONTENTS
xiii
6.4.3 Numerical Prediction of Disturbance in Soil and its
Verification208
6.5 Summary211
7 CONCLUSIONS AND RECOMMENDATIONS..213
7.1 General Summary...213
7.2 Specific Observations.214
7.2.1 Developing a New Elliptical Cavity Expansion Theory to
Analyse Soil Disturbance...215
7.2.2 Large-scale Laboratory Program to Study the Installation of
PVDs .217
7.2.3 Using Finite Element Modelling to Evaluate the Installation of
PVDs..218
7.2.4 Case Histories Validating the Developed Models.220
7.3 Recommendations for Future Research.....221
REFERENCES...224
APPENDIX A: CONSTITUTIVE MODELLING OF SOILS...247
A.1 Cam Clay Model..252
A.2 Modified Cam Clay Model..255
APPENDIX B: CODE FOR NUMERICAL MODELLING......257
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LIST OF FIGURES
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LIST OF FIGURES
Figure 1.1 Structure built on an unstable soft soil deposit (a) just after the
construction; and (b) after differential settlement......1
Figure 1.2 Effect of vertical drains on providing short drainage paths2
Figure 1.3 Potential benefit of vertical drains combined with pre-loading (after
Lau and Cowland (2000)....3
Figure 1.4 Prefabricated vertical drains (a) typical front view (after Global
Synthetics 2010); and (b) a cross section of different types (unit: mm, after
Chai et al. 2004)7
Figure 1.5 Typical geometries of mandrel and shoe (after Saye 2001)...8
Figure 1.6 Common installation rigs on site (after Menard 2010)...8
Figure 1.7 General scheme of a system of prefabricated vertical drains combined
with pre-loading (after Geo-Technics America Inc 2010).....9
Figure 2.1 Common instrumentation of an embankment (after Rixner et
al. 1986)....22
Figure 2.2 Conversion of a typical PVD to a circular drain (a) PVD with cross-
section of mn; and (b) an equivalent circular vertical drain with radius
wr .....24
Figure 2.3 Equivalent radius of a PVD based on various studies..........................25
Figure 2.4 Radii of influence zones as a function of common installation patterns
(a) square pattern; and (b) triangular pattern....................................................27
Figure 2.5 Variations of horizontal permeability in relation to the radial distance
from the centre of the drain (after Onoue et al. 1991)......................................29
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LIST OF FIGURES
xvi
Figure 2.6 A schematic illustration of the consolidation apparatus (after Indraratna
and Redana 1998).............................................................................................30
Figure 2.7 Variations of the normalised horizontal coefficient of permeability in
relation to the radial distance from the centre of the drain (after Indraratna and
Redana 1998)...................................................................................................31
Figure 2.8 Variations of the normalised differential pore pressure in relation to the
radial distance from the centre of the drain (after Hird and Moseley
2000)................................................................................................................32
Figure 2.9 A radial profile of the moisture content (after Sharma and Xiao
2000)..32
Figure 2.10 Variations of normalised horizontal coefficient of permeability in
relation to the radial distance from the centre of the drain (after Sathananthan
and Indraratna 2006)........................................................................................33
Figure 2.11 Variations of moisture content in relation to the radial distance (after
Sathananthan and Indraratna 2006)..................................................................34
Figure 2.12 Common discharge capacities of different types of PVD under unit
hydraulic gradient (after Rixner et al. 1986)....................................................36
Figure 2.13 Deformation modes of a PVD associated with ground compression
(a) uniform bending; (b) sinusoidal bending; (c) local bending; (d) local
kinking; and (e) multiple kinking (after Holtz et al.
1991)................................................................................................................36
Figure 2.14 One-dimensional consolidation (a) void ratio vs. effective stress; and
(b) void ratio vs. Permeability..........................................................................44
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LIST OF FIGURES
xvii
Figure 2.15 Variations of the vertical average degree of consolidation in relation
to the modified time factor (after Lekha et al.
2003)....48
Figure 2.16 A schematic view of the soil with a vertical drain modelled as a unit
cell51
Figure 2.17 Evaluating the horizontal coefficient of consolidation (after Aboshi
and Monden 1963)...58
Figure 2.18 Estimating the horizontal coefficient of consolidation (after Asaoka
1978)................................................................................................................59
Figure 2.19 Converting an axi-symmetric unit cell into a plane strain
condition...........................................................................................................62
Figure 2.20 Variation of excess pore pressure at the periphery of the drain in
relation to the depth (after Chai et al. 1995)....................................................65
Figure 2.21 Assumed failure mechanism for the deep penetration problem
(a) Terzaghi (1943); (b) De Beer (1948), Meyerhof (1951); (c) Berezantzev et
al. (1961), Vesic (1963); and (d) Biarez et al. (1961), Hu (1965) (after
Durgunoglu and Mitchell 1975)...70
Figure 2.22 Slip-line network for the wedge and cone penetration analysis
(after Yu and Mitchell 1996)71
Figure 2.23 Strain path method for deep penetration viewed as a problem
involving steady flow (after Baligh 1985)...73
Figure 2.24 Strain paths due to cone penetration for the soil elements located
initially at a radial distance of one cone radius from the axis of penetration
(a) 1E vs. 2E ; and (b) 3E vs. 2E (after Teh and Houlsby 1991)74
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LIST OF FIGURES
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Figure 2.25 Location of the elastic-plastic boundary in the cone penetration
problem (after Teh and Houlsby 1991)....75
Figure 2.26 Expansion of a cylindrical cavity in clay (after Cao et al. 2001)........80
Figure 2.27 Variation of normalised elastic-plastic boundary with the isotropic
overconsolidation ratio (after Cao et al. 2001).................................................81
Figure 2.28 Eulerian method for cone penetration (after van den Berg et al.
1996)................................................................................................................83
Figure 2.29 Numerical simulation of piezocone penetration (after Abu-Farsakh et
al. 2003)............................................................................................................85
Figure 2.30 Contours of excess pore pressure in kPa at the end of (a) Stage 1; and
(b) Stage 2 (after Abu-Farsakh et al. 2003)......................................................86
Figure 3.1 Expansion of an elliptical cavity in an infinite soft saturated cohesive
soil, shown in polar coordinates...92
Figure 3.2 The strain components due to (a) radial displacements; and
(b) tangential displacements.....96
Figure 3.3 The Effective Stress Path (ESP) for constant volume deformation of
(a) normally consolidated soil; and (b) lightly overconsolidated soil
(after Wood 1990)..103
Figure 3.4 An undrained triaxial compression test on normally consolidated soil
(a) effective stress path; and (b) deviator stress/excess pore pressure versus
shear strain.108
Figure 3.5 The distribution patterns for stresses near a mandrel in the horizontal
plane, 0.5m below the surface just after the mandrel installation
(preconsolidation pressure = 20 kPa).110
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LIST OF FIGURES
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Figure 3.6 The distribution patterns predicted for excess pore pressure with the
radial distance using elliptical CET and cylindrical CET along the major axis
of the mandrel 0.5m below the soil surface, and measured when tip of the
drain shoe passed the horizontal plane under consideration, with a (a)
preconsolidation pressure = 30 kPa; and (b) preconsolidation pressure =
50 kPa.....111
Figure 3.7 The distribution pattern of excess pore pressure 0.5m below the surface
predicted using the developed elliptical CET and conventional cylindrical
CET (preconsolidation pressure= 30 kPa) along the (a) o45 polar axis; (b) o90
polar axis113
Figure 3.8 The distribution pattern of excess pore pressure 0.5m below the surface
predicted using the current elliptical CET and conventional cylindrical CET
(preconsolidation pressure = 30 kPa) along the mandrel quadrant114
Figure 3.9 Variations in the ratio of the horizontal coefficient of permeability to
the vertical coefficient of permeability and the plastic shear strain in relation
to the radial distance normalised by the equivalent elliptical radius of the
mandrel...114
Figure 3.10 Variations in (a) effective stress in the qp : plane; and (b) strain in
the pqp
V : plane associated with the mandrel installation highlighting the
locations described in Figure 3.9...115
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LIST OF FIGURES
xx
Figure 3.11 The distribution pattern for the ratio of the plastic shear strain to the
rigidity index in relation to the radial distance normalised by the equivalent
elliptical radius of the mandrel characterising the disturbed soil surrounding a
PVD...117
Figure 4.1 The schematic design of the assembled consolidometer cell
(unit: mm)...122
Figure 4.2 Doughnut pressure chamber mounted on top of the consolidometer
cell..123
Figure 4.3 Fast response pore pressure transducer used in the tests....123
Figure 4.4 The dead weight testing machine used for calibrating the
transducers......124
Figure 4.5 Radial positions (planar view) of the fast response pore pressure
transducers (Ts) in relation to the centre of the cell, at levels identified in the
Figure 4.1 (unit: mm).....125
Figure 4.6 The digital data logger used for monitoring and recording the signals
from the transducers...126
Figure 4.7 The mechanical mixing bowl used for mixing clay and water...127
Figure 4.8 The clay deposit held under water level to ensure full saturation..128
Figure 4.9 The prefabricated vertical drain used in the tests (a) roll sourcing the
vertical drain; and (b) section of vertical drain..129
Figure 4.10 The mandrel used for installing the prefabricated vertical drains
(a) the front view; and (b) the section view.......130
Figure 4.11 The conical shoe attached to the PVD for anchoring purposes (a) the
front view; and (b) the side view...131
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LIST OF FIGURES
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Figure 4.12 Schematic illustration of the mandrel attached to the driving module
(a) the front view; and (b) the side view (unit: mm)..133
Figure 4.13 Positioning the mandrel-driving machine on top of the consolidometer
(a) transferring process; and (b) alignment process...134
Figure 4.14 Final setup of the specially designed machine for driving mandrels
mounted on the large-scale consolidometer...135
Figure 4.15 Planar view of the locations of samples cored in order to evaluate the
extent of smear zone (each mark represents three adjacent samples)....136
Figure 4.16 Variations of excess pore pressure measured in the laboratory during
installation of a PVD and withdrawal of the mandrel at (a) T3 and T6; (b) T2
and T5; and (c) T1 and T4, as identified in Figure 4.5 (surcharge
loading=20 kPa).139
Figure 4.17 Variations of excess pore pressure measured in the laboratory during
installation of a PVD and withdrawal of the mandrel at (a) T9 and T12; (b) T8
and T11; and (c) T7 and T10, as identified in Figure 4.5 (surcharge
loading=20 kPa).....140
Figure 4.18 Variations of excess pore pressure measured in the laboratory during
installation of a PVD and withdrawal of the mandrel at (a) T3 and T6; (b) T2
and T5; and (c) T1 and T4, as identified in Figure 4.5 (surcharge
loading=32.5 kPa)..141
Figure 4.19 Variations of excess pore pressure measured in the laboratory during
installation of a PVD and withdrawal of the mandrel at (a) T9 and T12; (b) T8
and T11; and (c) T7 and T10, as identified in Figure 4.5 (surcharge
loading=32.5 kPa)..142
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LIST OF FIGURES
xxii
Figure 4.20 Variations of excess pore pressure measured in the laboratory during
installation of a PVD and withdrawal of the mandrel at (a) T3 and T6; (b) T2
and T5; and (c) T1 and T4, as identified in Figure 4.5 (surcharge
loading=50 kPa).143
Figure 4.21 Variations of excess pore pressure measured in the laboratory during
installation of a PVD and withdrawal of the mandrel at (a) T9 and T12; (b) T8
and T11; and (c) T7 and T10, as identified in Figure 4.5 (surcharge
loading=50 kPa).144
Figure 4.22 The distribution patterns predicted for excess pore pressure with the
radial distance using elliptical CET and cylindrical CET along the major axis
of the mandrel 0.26 m below the soil surface, and measured when base of the
drain shoe passed the horizontal plane under consideration, with a surcharge
loading=20 kPa...145
Figure 4.23 The distribution patterns predicted for excess pore pressure with the
radial distance using elliptical CET and cylindrical CET along the major axis
of the mandrel 0.24 m below the soil surface, and measured when base of the
drain shoe passed the horizontal plane under consideration, with a surcharge
loading=32.5 kPa....146
Figure 4.24 The distribution patterns predicted for excess pore pressure with the
radial distance using elliptical CET and cylindrical CET along the major axis
of the mandrel 0.21 m below the soil surface, and measured when base of the
drain shoe passed the horizontal plane under consideration, with a surcharge
loading=50 kPa...146
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LIST OF FIGURES
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Figure 4.25 Variations of the moisture content of soil measured in the laboratory
along the o0 , o45 and o90 axes in relation to the installed PVD
(surcharge loading = 20 kPa, consolidation pressure = 40 kPa)....147
Figure 4.26 Variations of the moisture content of soil measured in the laboratory
along the o0 , o45 and o90 axes in relation to the installed PVD
(surcharge loading = 32.5 kPa, consolidation pressure = 50 kPa).....148
Figure 4.27 Variations of the moisture content of soil measured in the laboratory
along theo
0 ,o
45 ando
90 axes in relation to the installed PVD
(surcharge loading = 50 kPa, consolidation pressure = 80 kPa)148
Figure 4.28 Variations of the normalised equivalent radius of the smear zone in
relation to the in-situ vertical effective stress in laboratory...149
Figure 5.1 A schematic view of the contact kinematics at the mandrel-soil
interface using the master-slave concept155
Figure 5.2 Characteristics of a lightly overconsolidated soil where (a) the original
contact kinematics incorporate the concept of shear strength; (b) the shear
stress versus shear strain; (c) the contact constraints are in the context of the
penalty method in a normal direction; and (d) the contact constraints are in the
context of the penalty method in a tangential direction.....158
Figure 5.3 The axi-symmetric finite element model (a) geometry, mesh and the
boundary conditions; and (b) characteristics of the CAX8P element
incorporated into the analysis (after ABAQUS Analysis Users Manual
2007)..162
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LIST OF FIGURES
xxiv
Figure 5.4 The deformed mesh and state of excess pore pressure due to a (a) drain
shoe with a rapid edge transition; (b) drain shoe with a semi gradual edge
transition; and (c) drain shoe with a gradual edge
transition.....164
Figure 5.5 Constraints of physical contact and the deformed mesh associated with
the penalty parameters of (a)3
4105.1m
kN ; (b)
3
4105.2m
kN ; and
(c) 34
1075.3 m
kN ....165
Figure 5.6 Variations of (a) excess pore water pressure measured in the laboratory
and predicted numerically, and (b) the shear stress estimated in the finite
element model during installation of a PVD and withdrawal of the mandrel at
T3 and T6, as identified in Figure 4.5 (surcharge loading=20 kPa)..168
Figure 5.7 Variations of (a) excess pore water pressure measured in the laboratory
and predicted numerically, and (b) the shear stress estimated in the finite
element model during installation of a PVD and withdrawal of the mandrel at
T2 and T5, as identified in Figure 4.5 (surcharge loading=20 kPa)..169
Figure 5.8 Variations of (a) excess pore water pressure measured in the laboratory
and predicted numerically, and (b) the shear stress estimated in the finite
element model during installation of a PVD and withdrawal of the mandrel at
T1 and T4, as identified in Figure 4.5 (surcharge loading=20 kPa)..170
Figure 5.9 Variations of (a) excess pore water pressure measured in the laboratory
and predicted numerically, and (b) the shear stress estimated in the finite
element model during installation of a PVD and withdrawal of the mandrel at
T3 and T6, as identified in Figure 4.5 (surcharge loading=32.5 kPa)...171
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LIST OF FIGURES
xxv
Figure 5.10 Variations of (a) excess pore water pressure measured in the
laboratory and predicted numerically, and (b) the shear stress estimated in the
finite element model during installation of a PVD and withdrawal of the
mandrel at T2 and T5, as identified in Figure 4.5 (surcharge loading=32.5
kPa)172
Figure 5.11 Variations of (a) excess pore water pressure measured in the
laboratory and predicted numerically, and (b) the shear stress estimated in the
finite element model during installation of a PVD and withdrawal of the
mandrel at T1 and T4, as identified in Figure 4.5 (surcharge loading=32.5
kPa)....173
Figure 5.12 Variations of (a) excess pore water pressure measured in the
laboratory and predicted numerically, and (b) the shear stress estimated in the
finite element model during installation of a PVD and withdrawal of the
mandrel at T3 and T6, as identified in Figure 4.5 (surcharge loading=50
kPa)....174
Figure 5.13 Variations of (a) excess pore water pressure measured in the
laboratory and predicted numerically, and (b) the shear stress estimated in the
finite element model during installation of a PVD and withdrawal of the
mandrel at T2 and T5, as identified in Figure 4.5 (surcharge loading=50
kPa)....175
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LIST OF FIGURES
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Figure 5.14 Variations of (a) excess pore water pressure measured in the
laboratory and predicted numerically, and (b) the shear stress estimated in the
finite element model during installation of a PVD and withdrawal of the
mandrel at T1 and T4, as identified in Figure 4.5 (surcharge loading=50
kPa)....176
Figure 5.15 Contours of excess pore pressure predicted numerically during
different stages of installing a mandrel when the (a) depth of installation=230
mm; (b) depth of installation=461 mm; and (c) depth of installation=690 mm
(surcharge loading=32.5 kPa)....177
Figure 5.16 Displacement of soil nodes 0.39 m below the surface and four times
the radius of the mandrel away, during mandrel penetration (based on the
finite element model) transposed into (a) radial movements; and (b) vertical
movements (surcharge loading=32.5 kPa).179
Figure 5.17 Development of the plastic zone and failed zone in the consolidometer
during installation of a mandrel-driven PVD according to the numerical model
when the (a) depth of installation= 230 mm; (b) depth of installation= 461
mm; and (c) depth of installation= 690 mm (surcharge loading=32.5
kPa)....180
Figure 5.18 Variations of numerically predicted normalised plastic shear strain
together with the moisture content of soil measured in the laboratory along the
o
0 ,o
45 ando
90 axes in relation to the installed PVD (surcharge loading = 20
kPa, consolidation pressure = 40 kPa)...181
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LIST OF FIGURES
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Figure 5.19 Variations of numerically predicted normalised plastic shear strain
together with the moisture content of soil measured in the laboratory along the
o0 , o45 and o90 axes in relation to the installed PVD (surcharge loading=32.5
kPa, consolidation pressure=50 kPa).181
Figure 5.20 Variations of numerically predicted normalised plastic shear strain
together with the moisture content of soil measured in the laboratory along the
o0 , o45 and o90 axes in relation to the installed PVD (surcharge loading=50
kPa, consolidation pressure=80 kPa).182
Figure 6.1 Location of the trial embankments in Muar clay region, Malaysia (after
Google Maps Malaysia 2010a)......................................................................187
Figure 6.2 The cross section of a test embankment and subsoil profile at Muar
clay region in Malaysia (after Indraratna and Redana 2000).........................188
Figure 6.3 Geotechnical properties of Muar clay (after Indraratna et al.
1994)..............................................................................................................190
Figure 6.4 Variations of field vane strength and cone resistance of Muar clay in
relation to depth (after Indraratna et al. 1992)...............................................190
Figure 6.5 The variations of plastic shear strain normalised by the rigidity index in
relation to the radial distance used for determining the extent of smear zone in
the case history of the Muar clay embankment in Malaysia..........................192
Figure 6.6 The cross section of the mandrel, the assumed elliptical cavity, the
elliptical smear zone, and the circular-equivalent smear zone for the case
history of the Muar clay embankment in Malaysia........................................193
Figure 6.7 Location of the development route proposed for the Sunshine
Motorway in Australia (after Google Maps Australia 2010b)...194
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LIST OF FIGURES
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Figure 6.8 Trial embankment built at the Sunshine Motorway site in Australia (a)
Planar view; and (b) Typical cross section (after Queensland Department of
Main Roads 1992)..195
Figure 6.9 Geotechnical properties of the layer of silty clay in the development
route proposed for the Sunshine Motorway (after Queensland Department of
Main Roads 1992)..197
Figure 6.10 The variations of plastic shear strain normalised by the rigidity index
in relation to the radial distance used for assessing the boundary of the smear
zone in the case history of the Sunshine Motorway in Australia in (a) soft silty
clay located 2.5-5 m below ground level; and (b) silty clay located 5-11 m
below ground level.199
Figure 6.11 The variation of the extent of the smear zone with depth in the case
history of the Sunshine Motorway in Australia.200
Figure 6.12 Location of the Second Bangkok International Airport site in Thailand
(after Google Maps Thailand 2010c).............................................................201
Figure 6.13 The cross section of a test embankment and subsoil profile at the
Second Bangkok International Airport site in Thailand (after Indraratna and
Redana 2000)...............................................................................................202
Figure 6.14 Geotechnical properties of the Second Bangkok International Airport
site (after Sangmala 1997).204
Figure 6.15 Initial void ratio, compression index, and overconsolidation ratio of
the Second Bangkok International Airport site (after Sangmala 1997).204
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LIST OF FIGURES
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Figure 6.16 The geometry, boundary conditions and initial configuration of the
axi-symmetric numerical model analysing a case study of the Second Bangkok
International Airport...207
Figure 6.17 The finite element prediction of total pore water pressure at selected
locations, at the site of the Second Bangkok International Airport during
installation of a 12 metre long PVD and withdrawal of the mandrel at a
(a) depth = 1 m; (b) depth = 5 m; and (c) depth = 10 m...209
Figure 6.18 Variations of the normalised radius of the smear zone and the
isotropic overconsolidation ratio in relation to depth, at the site of the Second
Bangkok International Airport...210
Figure A.1 Normal compression line and swelling line (after Schofield and Wroth
1968)......248
Figure A.2 Critical state line in the qp : plane (after Schofield and Wroth
1968)......249
Figure A.3 The critical state line in the :lnp plane (after Schofield and Wroth
1968)......250
Figure A.4 The position of the initial state of a soil sample in the :lnp
plane...251
Figure A.5 Plastic potential and plastic strains for Cam clay model (after Roscoe
et al. 1963)..252
Figure A.6 Cam clay model (a) yield locus in the qp : plane; and (b) state
boundary surface (after Roscoe et al. 1963)...254
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LIST OF FIGURES
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Figure A.7 Yield locus in qp : plane for the modified Cam clay model (after
Roscoe and Burland 1968).256
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LIST OF TABLES
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LIST OF TABLES
Table 2.1 Reduction in the discharge capacity of a PVD due to different
deformation modes (after Bergado et al. 1996a)......37
Table 2.2 Well resistance indices proposed by various investigators39
Table 3.1 The magnitudes of plastic shear strain and the associated ratio of the
cavity radius at the failure threshold of the elements of cavity wall for three
different experiments 109
Table 4.1 Specifications of the fast response pore pressure transducers utilised in
the laboratory studies (after DGSI Materials Testing Catalog 2009)....124
Table 4.2 Radial distance between the tip of each installed transducer and the
centre of the cell.125
Table 4.3 Properties of the reconstituted soft clay deposit..127
Table 5.1 Properties of the soft saturated clay used in the finite element
simulation...163
Table 6.1 The Cam clay properties for the soft silty clay located 8-18 m below
ground level at the Muar clay embankment in Malaysia (after Indraratna and
Redana 2000).191
Table 6.2 The Cam clay properties for the silty clay located 2.5-11 m below
ground level in the development route proposed for the Sunshine Motorway in
Australia (after Sathananthan 2008)...198
Table 6.3 The profile and parameters of the soil at the site of the Second Bangkok
International Airport in Thailand (after Indraratna and Redana 2000)..205
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LIST OF SYMBOLS
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LIST OF SYMBOLS
a Final radius of the piezocone (m)
0a Semimajor axis of the initial elliptical cavity (m)
1a Semimajor axis of the instantaneous elliptical cavity (m)
va Coefficient of compressibility ( kNm /
2)
wA Cross-sectional area of a drain (2
m )
0b Semiminor axis of the initial elliptical cavity (m)
1b Semiminor axis of the instantaneous elliptical cavity (m)
smearb Half-width of the smear zone in the plane strain condition (m)
wb Half-width of the drain in the plane strain condition (m)
B Half-width of the influence zone in the plane strain condition (m)
Skemptons pore pressure parameter
hc Horizontal coefficient of consolidation ( sm /
2)
uc Undrained cohesion (kPa)
v
c Vertical coefficient of consolidation ( sm /2
)
cC Compression index of soil
kC Slope of the line in ek:log plane, Index of permeability change
sC Swell index of soil
15D Diameter of soil particles corresponding to 15% passing (m)
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LIST OF SYMBOLS
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50D Diameter of soil particles corresponding to 50% passing (m)
85D Diameter of soil particles corresponding to 85% passing (m)
0e Initial void ratio of soil
cse Void ratio of soil at critical state
Le Void ratio of soil at liquid limit
E Youngs modulus (kPa)
ng Minimum distance in the normal direction between an arbitrary point onthe slave surface and its projection on the master surface (m)
tg Relative displacement in the tangential direction between the two
partnered points (m)
G Shear modulus (kPa)
drH Thickness of the drainage path (m)
0i Threshold gradient below which no flow occurs
li Gradient required overcoming the maximum binding energy of mobile
pore water
rI Rigidity index of soil
0J Bessel function of the first kind of zero order
1
J Bessel function of the first kind of first order
k Coefficient of permeability (m/s)
0k Initial coefficient of permeability (m/s)
filterk Coefficient of permeability of the filter (m/s)
hk Horizontal coefficient of permeability (m/s)
hpk Horizontal coefficient of permeability in the plane strain condition (m/s)
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LIST OF SYMBOLS
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Horizontal coefficient of permeability of undisturbed soil (m/s)
sk Horizontal coefficient of permeability in smear zone (m/s)
spk Horizontal coefficient of permeability in smear zone in the plane strain
condition (m/s)
soilk Coefficient of permeability of the soil (m/s)
vk Vertical coefficient of permeability (m/s)
eqvk . Equivalent vertical coefficient of permeability (m/s)
wk Coefficient of permeability of drain (m/s)
0K Coefficient of lateral earth pressure at rest
l Length of vertical drain (m)
vm Coefficient of volume compressibility ( kNm /
2)
M Slope of critical state line in the qp : plane
pn Isotropic overconsolidation ratio
N Specific volume of soil at 1=p kPa
OCR Overconsolidation ratio
50O Size larger that 50% of the fabric pores in a filter (m)
95O Apparent opening size of a filter (m)
p Total mean stress (kPa)
0p Initial total mean stress (kPa)
p Effective mean stress (kPa)
0p Initial effective mean stress (kPa)
cp Preconsolidation stress (kPa)
dundisturbehk
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LIST OF SYMBOLS
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yp Yielding stress under isotropic conditions (kPa)
0y
p Maximum isotropic preconsolidation stress (kPa)
iP Internal pressure of the cavity (kPa)
maxiP Maximum internal pressure of the cavity (kPa)
miniP Minimum internal pressure of the cavity to yield the soil elements adjacent
to the wall of cavity (kPa)
q Deviator stress (kPa)
wq Specific discharge capacity of a drain ( sm /
3)
wpq Discharge capacity of a drain in the plane strain condition ( sm /
3)
Theoretical discharge capacity of a drain ( sm /3
)
yq Deviator stress of the soil elements just after the initial yielding of the wall
of cavity (kPa)
r Instantaneous position of a soil element measured from the centre of cavity
(m)
Radial position measured from the centre of the cell (m)
0r Initial radius of an elliptical cavity (m)
Initial horizontal position of a soil node measured from the centre of
mandrel (m)
1r Instantaneous radius of an elliptical cavity (m)
ir Radius of the equivalent circular influence zone (m)
mr Equivalent radius of the mandrel (m)
( )mr Distance from the centre of cavity to the wall of cavity (m)
Equivalent radius of the mandrel (m)
)(requiredwq
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LIST OF SYMBOLS
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pr Radial extent of the plastic zone (m)
Radius of plastic zone measured from the centre of the cavity (m)
smearr Radius of the smear zone (m)
wr Radius of the equivalent vertical drain (m)
0R Initial position of a soil element measured from the center of the cavity
(m)
us Undrained shear strength of the soil (kPa)
S Drains spacing (m)
Component of body force in a radial direction ( )3m
t Time (s)
Time increment (s)
ct Time required to establish contact between the mandrel shoe and the soil
elements at the initial wall of the cavity (s)
T Component of body force in a tangential direction ( )3m
hT Time factor related to the horizontal consolidation
hpT Time factor related to the horizontal consolidation in the plane strain
condition
vT Time factor related to the vertical consolidation
vT Modified time factor related to the vertical consolidation
u Pore water pressure (kPa)
U Component of displacement in a radial direction (m)
10U 10% of the degree of consolidation
U Overall average degree of consolidation
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LIST OF SYMBOLS
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rU Average degree of consolidation due to radial flow
zr
U,
Average degree of consolidation at a depthzdue to radial flow
zrpU , Average degree of consolidation at a depthzdue to radial flow in the plane
strain condition
vU Average degree of consolidation due to vertical flow
V Component of displacement in a tangential direction (m)
rV Displacement rate of the soil elements in a radial direction (m/s)
tV Relative tangential velocity between the two partnered points (m/s)
vV Installation rate of the mandrel (m/s)
0Y Bessel function of the second kind of zero order
1Y Bessel function of the second kind of first order
pz Vertical distance between the tip of cone and the boundary of plastic zone(m)
Greek letters
Apex angle of the mandrel shoe (degree)
Friction angle between the contacting bodies
ij Kronecker delta
p Increment of the plastic strain
r Variations in total radial stress (kPa)
Variations in total tangential stress (kPa)
r Variations in total shear stress (kPa)
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LIST OF SYMBOLS
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u Excess pore water pressure (kPa)
0u Initial excess pore water pressure (kPa)
ru Excess pore water pressure due to radial flow (kPa)
zu Excess pore water pressure due to vertical flow (kPa)
zru , Excess pore water pressure at any point (kPa)
ru Excess pore water pressure along the radial direction between wr and ir
(kPa)
i Strain
n Penalty parameter in the normal direction ( )3/mkN
rr Radial strain
Circumferential strain
zz Axial strain
t Penalty parameter in the tangential direction ( )3/mkN
p
V Plastic volumetric strain
Angle of internal friction of the soil (degrees)
ps Critical state angle of friction in a plane strain condition (degrees)
tc Critical state angle of friction in a triaxial compression condition (degrees)
te Critical state angle of friction in a triaxial extension condition (degrees)
Specific volume of the soil in the critical state at 1=p kPa
Shear strain
ij Shear strain
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LIST OF SYMBOLS
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rz Shear strain
e
q Elastic shear strain
p
q Plastic shear strain
w Unit weight of water (3
/mkN )
Stress ratio
Slope of elastic swelling line in the :lnp plane
Slope of normal compression line in the :lnp plane
Coefficient of friction between the master and slave surfaces
Plastic volumetric strain ratio
Pore water flow (m/s)
Poisons ratio
Polar angle (degrees)
Settlement (m)
final Final Settlement (m)
1 Total major stress (kPa)
2 Total intermediate stress (kPa)
3 Total minor stress (kPa)
ij Total stress (kPa)
n Normal stress at the contacting surfaces (kPa)
pr Total radial stress at the elastic-plastic boundary (kPa)
0 Initial internal pressure of the cavity, also the uniform pressure acting on
the soil boundaries at infinity (kPa)
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LIST OF SYMBOLS
xl
1 Effective major stress (kPa)
2 Effective intermediate stress (kPa)
3 Effective minor stress (kPa)
ij Effective stress (kPa)
0v Initial overburden stress (kPa)
fv Final overburden stress (kPa)
Shear stress across the interface (kPa)
ij Shear stress (kPa)
max Maximum shear stress that can be transferred at the interface between the
contacting surfaces (kPa)
failure Shear stress at failure (kPa)
Soil specific volume
Electrical resistance (ohms)
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CHAPTER 1 INTRODUCTION
1
1 INTRODUCTION
1.1 General
The population boom and associated development in metropolitan areas have
necessitated the use of soft clay land for construction purposes. These deposits are
normally characterised by low shear strength, high compressibility, and a low
coefficient of permeability, characteristics which make them a difficult
engineering exercise. This thesis presents the research conducted by the Author at
the University of Wollongong as a part of a continuous study program to
investigate the different aspects of ground improvement using vertical drains. As
shown in Figure 1.1, unacceptable differential settlements and severe damage may
occur due to the heterogeneity and high compressibility of the underlying soil if a
structure has been constructed before the ground was stabilised.
Unstable Soft Soil Layer Unstable Soft Soil Layer
Settlement
Damaged Structure
New Structure
Bearing Stratum Bearing Stratum
Unstable Soft Soil Layer Unstable Soft Soil Layer
Settlement
Damaged Structure
New Structure
Bearing Stratum Bearing Stratum
(a) (b)
Figure 1.1 Structure built on an unstable soft soil deposit (a) just after the
construction; and (b) after differential settlement
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CHAPTER 1 INTRODUCTION
2
Vibro-replacement, electro-osmotic, explosion based, and deep mixing, are some
stabilisation techniques used to mitigate unacceptable differential settlements of
underlying soft soil (Indraratna and Chu 2005) but the associated cost may
become excessive when the soft layer is very thick (15 m - 20 m). Pre-loading is
one of the classical techniques used to mitigate the effects of differential
settlement on structures and increase the shear strength of the soft soil deposits. In
this method, a surcharge load, usually in the form of an embankment that is equal
to or greater than the expected foundation loading, is applied to the layer of soft
soil until most of the primary consolidation has been achieved. Because the
magnitude of the surcharge load is limited by the failure criteria of the soil, the
loads are increased in stages as the shear strength of the soil amplifies. With thick
deposits of soft clay where the permeability is low, the time required to
consolidate the soil only with a surcharge is very long. Indraratna et al. (2005a)
stated that vertical drains combined with pre-loading are amongst the most
effective techniques known for accelerating consolidation and stabilising ground.
As illustrated in Figure 1.2, vertical drains reduce the drainage path and accelerate
the dissipation of excess pore water pressure generated from the application of
surcharge loads.
Drainage without PVDs Drainage with PVDs
Surcharge Surcharge
Vertical
DrainsSoft Soil
ImperviousLayer
Sand
blanket
Figure 1.2 Effect of vertical drains on providing short drainage paths
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CHAPTER 1 INTRODUCTION
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According to Indraratna et al. (2005b) and Indraratna (2008), vertical drains in
particular:
(i) increase the shear strength of soft soils by decreasing the moisturecontent, which in turn reduces the void ratio
(ii) decrease the time required for the application of surcharge loads(iii) reduce differential settlement in the course of primary consolidation(iv) shorten the height of surcharge fill necessary to achieve the desired
compression when combined with vacuum
Figure 1.3 reveals the potential benefit of vertical drains to reduce the time
required for a specific degree of consolidation.
Pre-loading without vertical drains
Pre-loading with vertical drains @ 1.5m spacing
Pre-loading with vertical drains @ 1m spacing
Pre-loading with vertical drains @ 2m spacing
Pre-loading without vertical drains
Pre-loading with vertical drains @ 1.5m spacing
Pre-loading with vertical drains @ 1m spacing
Pre-loading with vertical drains @ 2m spacing
Figure 1.3 Potential benefit of vertical drains combined with pre-loading (after
Lau and Cowland 2000)
The installation of vertical drains creates a disturbed region known as the smear
zone where the structure of the clay layer is altered such that the horizontal
permeability is reduced and compressibility is increased (Indraratna and Redana
1998). The parameters required to characterise the smear effect are the extent of
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CHAPTER 1 INTRODUCTION
4
the smear zone and the ratio between the horizontal coefficient of permeability in
the undisturbed zone and that in the smear zone (Chai and Miura 1999).
Previously at the University of Wollongong, Redana (1999) analysed the effect of
smear in soft soils by converting the axi-symmetric (radial) permeability into an
equivalent plane strain model. The experimental studies of smear zone
propagation around vertical drains were conducted using a large-scale radial
drainage consolidometer. Then the simulation of smear effects in a 2-D plane
strain finite element model was performed using the modified Cam clay theory.
Subsequently, a multi-drain, plane strain analysis was carried out to study the
performance of the entire embankment stabilised by vertical drains, for a number
of case histories. Sathananthan (2005) developed a modified consolidation theory
incorporating vacuum pressure distributed linearly (trapezoidal) for axi-symmetric
and plane strain conditions. In addition, a new plane strain consolidation theory
was presented for non-Darcian flow. Based on the tests in a large-scale
equipment, the settlement of the soil stabilised by vertical drains was compared
with the proposed plane strain model. Several 2-D plane strain numerical analyses
were also performed to predict the failure height of the embankments under a
number of conditions such as, preloading, different geometry of embankments,
and various spacing of drains. Rujikiatkamjorn (2005) investigated the effect of
various factors such as, change of soil permeability and compressibility, variation
of vacuum pressure, well resistance and smear on consolidation of the soil around
vertical drains under vacuum preloading. Based on the results of the multi-drain,
plane strain analyses it was shown that the efficiency of the prefabricated vertical
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CHAPTER 1 INTRODUCTION
5
drains depends on the magnitude and distribution of vacuum pressure, and the
extent to which air is prevented from leaking. Subsequently, Rujikiatkamjorn
(2005) studied the length of vertical drains, anisotropic permeability of the soil
and vacuum pressure, and compared the reduction in consolidation time through
vacuum preloading with other available methods. Walker (2006) examined the
spatially varied properties of the soil in the smear zone, and developed linear and
parabolic variations in permeability to discuss the possibility of overlapping smear
zones. A nonlinear radial consolidation model was presented incorporating void
ratio dependant soil properties and non-Darcian flow. Thereafter, an analytical
solution was developed for multi-layered consolidation problems with vertical and
horizontal drainage using the spectral method. Models were verified against
analytical solutions available, laboratory experiments, and case histories.
As discussed by Bo et al. (2003), rectangular or rhomboidal mandrels are used
typically in the field. However, existing models consider a circular disturbed
region surrounding the mandrels. In this thesis the installation of mandrel-driven
prefabricated vertical drains (PVDs) and associated disturbance in cohesive soils
were investigated by developing a new elliptical cavity expansion theory (CET)
that predicts an elliptical smear zone around the PVDs. Large-scale laboratory
experiments and numerical modelling were conducted at realistic rates to study
the pattern of disturbed regions and factors affecting them. Furthermore, a number
of case histories taken from Malaysia and Thailand were analysed to examine the
associated soil disturbance during installation of prefabricated vertical drains.
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CHAPTER 1 INTRODUCTION
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1.2 Application of Vertical Drains
Vertical drains come in two categories, displacement and non-displacement. Non-
displacement vertical drains involve the removal of soft soil and backfilling with a
more permeable material. Cylindrical cavities may be created by driving, jetting
or auguring with typical diameters of 200-450 mm (Hausmann, 1990), and are
usually filled with sand. Sand drains are susceptible to damage from lateral
movement of the ground. Improvements in installation and competitive
production costs over the past two decades have increased the popularity of
prefabricated vertical drains (displacement type vertical drains) over conventional
sand drains (Bo et al. 2003). Although there are several types of prefabricated
vertical drains (PVDs) on the market they basically consist of a plastic core
surrounded by a filter sleeve with a typical cross section of 100 mm x 4 mm
(Holtz 1987). Figure 1.4 demonstrates typical PVDs and cross sections of the
different types available on the market. Prefabricated vertical drains are normally
spooled out and threaded through a hollow mandrel that is generally rectangular
or rhomboidal (Bo et al. 2003). The free end of a PVD is attached to a shoe which
anchors it in stiffer clay and prevents soil entering the mandrel. The shoe may
vary from a simple reinforced steel bar of 10-20 mm in diameter to a thin mild
steel plate with a strip welded on as a handle (Karunaratne et al. 2003). Figure 1.5
illustrates the typical geometries of both mandrel and shoe. PVDs are usually
installed in a square or triangular pattern. Drains in a square pattern may be easier
to install in the field but a triangular layout reduces the zones of influence and
results in a more uniform consolidation between them (Indraratna et al. 2003).
Vertical drains may also be installed dynamically with a vibrating or drop
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hammer, or statically. According to Indraratna et al. (2003), a dynamic installation
disturbs the surrounding soil more than the static method. Common installation
rigs at a site are shown in Figure 1.6.
Filter sleeve
Plastic core
Filter sleeve
Plastic core
Plastic coreFilter sleeve
Plastic coreFilter sleeve
Figure 1.4 Prefabricated vertical drains (a) typical front view (after Global
Synthetics 2010); and (b) a cross section of different types (unit: mm, after
Chai et al. 2004)
(b)
(a)
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Mandrel
Shoe
Shoe Plate
Shoe
Mandrel
Mandrel
Mandrel
Shoe
Shoe Plate
Shoe
Mandrel
Mandrel
Figure 1.5 Typical geometries of mandrel and shoe (after Saye 2001)
Installation rigs
Rows of PVDs
Sand blanket
Installation rigs
Rows of PVDs
Sand blanket
Figure 1.6 Common installation rigs on site (after Menard 2010)
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A typical scheme of prefabricated vertical drains system is presented in Figure
1.7. It is necessary to remove vegetation and surface debris, and then grade the
ground before installing PVDs. A sand blanket is commonly laid onto the soil to
expel water from the vertical drains and act as a working platform for installing
rigs. To further facilitate drainage, horizontal drains may be implemented on the
surface. Monitoring and evaluating the performance of embankments by field
instrumentation is vital in order to control any geotechnical issues that occur
during the course of construction, to record the rate of settlement, and to verify the
design parameters. According to Bo et al. (2003), field instrumentation may be
divided into two groups by considering the construction phases. The first group
are used to prevent sudden failure during construction stages; inclinometers,
settlement plates, and piezometers fit into this category. The second group are
used to monitor/record changes in settlement and excess pore water pressures over
time, during the loading stages. Multi-level settlement gauges and piezometers
belong to this category.
Installation rig
PVDsPeripheral trench
Installation rig
PVDsPeripheral trench
Figure 1.7 General scheme of a system of prefabricated vertical drains combined
with pre-loading (after Geo-Technics America Inc 2010)
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In addition to the smear effect, the well resistance, and drains not being saturated
are also the factors that adversely influence the efficiency of PVDs and retard the
consolidation process. The resistance to water flowing along the PVD is known as
the well resistance. Although the deep installation of drains and their limited
discharge capacity contribute to the well resistance factor, this issue can be
ignored in the case of modern PVDs where the discharge capacity is usually high
enough and the drains will not kink during installation. The gap between dry PVD
and the mandrel during installation contributes to the non-saturated-drain
phenomenon. This issue adversely affects the compression of soft soil but need
only be considered in the early stages of consolidation because it diminishes as the
soil consolidates and the PVD becomes saturated.
1.3 Application of Cavity Expansion Theory
Cavity expansion theory studies the changes in stresses, displacements and pore
pressures attributable to the expansion and contraction of cavities. In
geomechanis, cavity expansion in soil and rock is a fundamental problem. The
theory has been extensively applied in the areas of in-situ soil testing, deep
foundations, tunnels and underground excavations, and wellbore instability.
In-situ soil testing is broadly used in geotechnical engineering. The pressuremeter
and cone penetrometer are among the most commonly used in-situ soil testing
devices. The mechanical action created by these devices is similar to the
expansion of a cavity, and hence the cavity expansion theory has been used in the
interpretation of the measured data to obtain the soil properties (e.g. Wroth 1984,
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Clarke 1995, Lunne et al. 1997, Yu and Mitchell 1998). It is generally assumed
that the pressuremeter tests can be simulated as the expansion or contraction of an
infinitely long cylindrical cavity in soils. This assumption then makes it possible
to develop analytical correlation between the cavity expansion curves and the soil
properties, such as the shear modulus, in-situ total horizontal stress, and for clays
undrained shear strength and the coefficient of horizontal consolidation. The
similarity between the cone penetration and cavity expansion was first discussed
by Bishop et al. (1945). Predicting the cone resistance using the cavity expansion
theory can be achieved by developing the theoretical solutions of the limit
pressure for the cavity expansion in soil, and then correlating these limit pressures
to cone resistance. According to Yu and Mitchell (1998), because the cavity
expansion theory considers the effect of soil stiffness, compressibility and
dilatancy, and horizontal stress due to penetration it provides a more accurate
prediction of cone resistance than that obtained using the bearing capacity theory.
While small-strain cavity expansion solutions are only required for the
interpretation of the self-boring pressuremeters, large-strain solutions have been
developed to derive soil properties from the results obtained by cone
pressuremeters (e.g. Yu et al. 1996, Houlsby and Withers 1988).
The shaft friction and end bearing capacity of driven piles in soils can be studied
by cavity expansion theory. This analysis is a large-strain problem which involves
high nonlinear nature of the material and geometry. During the deep installation of
a pile in soil, much of the soil is displaced predominantly outwards in the radial
direction. Measurements of the radial displacements of soil near the pile
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mid-depth taken from field data presented by Cooke and Price (1978) the model
tests of Randolph et al. (1979) show that the radial movement of the soil can be
predicted by cylindrical cavity expansion theory. Nystrom (1984) highlighted that
the simple one dimensional cavity expansion model can predict the behaviour of
piles similar to more complicated two dimensional finite element methods. The
installation of a pile can reasonably be modelled as an undrained loading case
when the pile is driven rapidly into the ground. Cavity expansion theory can be
used to study (Yu 2000):
(i) The installation of a pile as the expansion of a cylindrical cavity fromzero radius to the radius of the pile. The shaft friction may then be
estimated by the changes of stress in soil surrounding the pile obtained
from this analysis.
(ii) End bearing capacity of a pile from the limit pressure of a sphericalcavity in a semi empirical way.
Bishop et al. (1945) and Hill (1950) discussed that the pressure required to create
a deep hole in an elastic-plastic material is relative to that essential to expand a
cavity of the same volume and under the same conditions with no friction. Gibson
(1950) was the first to express the end bearing pressure of a deep foundation as a
function of the limit pressure of a cavity. It is worth noting that while the end
bearing capacity of piles in clays in the long term drained condition is much larger
than its value in the short term undrained condition, the short term capacity of the
pile is necessary to be large enough to prevent a failure immediately after
installation, and the settlements essential to mobilise the long term capacity of the
pile may be beyond the tolerance defined by the serviceability criteria. Therefore,
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it is a standard practice to consider an undrained condition for clays when
evaluating the end bearing capacity of the piles (Fleming et al. 1985).
Tunnelling and underground excavations involve reducing the in-situ stresses
along the excavated circumference through removal of geomaterials from their
primary locations, and therefore can be simulated by unloading cavities from a
state of in-situ stress. Evaluation of tunnelling-induced settlements has
conventionally been based on an empirical relationship suggested by Peck (1969)
with the assumption that the profile of transverse surface settlement follows a
normal probability curve. The theoretical approach to this problem includes
simple cavity unloading solutions (e.g. Pender 1980, Lo et al. 1984, Ogawa and
Lo 1987, Mair and Taylor 1993) and nonlinear elastic-plastic finite element
methods (e.g. Ghabousssi et al. 1978, Rowe and Kack 1983, Clough et al. 1985,
Lee and Rowe 1990, Rowe and Lee 1992), both of which involve simulating
construction of the tunnel by inferring the tractions that are acting around the
surface of the tunnel before excavation and then removing these tractions.
Lo et al. (1980) and Ogawa and Lo (1987) showed that the plane strain cylindrical
cavity unloading solution after applying a correction factor, can be used to
estimate the soil displacements measured around tunnels. Mair and Taylor (1993)
pointed out that the spherical cavity unloading solutions can be applied to study
the soil behaviour around an advancing tunnel heading. According to Yu (2000),
while the cavity unloading solution in an infinite medium can be used to assess
the displacement of the tunnel wall, it tends to underestimate the surface
movement significantly for shallow tunnels. This inconsistency is mainly because
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the cavity unloading in an infinite soil mass does not consider the effect of the free
ground surface. Sagaseta (1987) and Verruijt and Booker (1996) investigated the
unloading of a cavity in a half space considering the effect of the free ground
surface and derived analytical solutions for displacements. Stability of the tunnels,
on the other hand, is to ensure that the geomaterials surrounding the tunnels do
not collapse as a result of insufficient internal pressure of support. Cavity
unloading solutions dealing with stability mainly follow Caquot and Kerisel
(1966) by assuming that collapse of a tunnel will occur when the plastic zone
reaches the ground surface. Mair (1979) showed that the stability of tunnels
predicted by the cavity expansion solution agree with the results of centrifuge
tests. Sloan and Assadi (1993) found that the cavity expansion solutions are
usually very similar to the rigorous upper and lower bound stability solutions.
Wellbore instability during drilling in petroleum engineering is a key problem that
can be analysed by the cavity expansion theory. According to Bradley (1979) and
Santarelli et al. (1986), wellbore instabilities as a result of stress can be divided
into:
(i) Reduction of hole size as a consequence of ductile yield of the rock,(ii) Enlargement of hole size due to fracture or rupture of the brittle rock,
and
(iii) Unintentional hydraulic fracturing caused by excessive pressure ofmud
Kulhawy (1974) discussed that the pre-yield and pre-peak stress-strain properties
of some rocks are nonlinear and the elastic properties are a function of the
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pressure. Santarelli et al. (1986) carried out a numerical study on the stresses
acting on a borehole using a nonlinear elastic model with pressure dependent
Youngs modulus. Lekhnitskii (1963) and Wu et al. (1991) presented the elastic
solutions for the expansion of a thick walled cylinder with a cross-anisotropic
model. Wu and Hudson (1991) investigated the effect of stress-induced anisotropy
on wellbore stability, and showed that it has a very significant effect on the
distribution of elastic stress around a borehole. While Carter and Booker (1982)
assumed incompressibility for the pore fluid and particles in developing a semi
analytical poroelastic solution for the time dependent displacements and stress
around a long circular opening in a saturated elastic medium, Detournay and
Cheng (1988) included the compressibility of the pore fluid and particles in their
analysis. Charlez (1997) developed plastic analysis of the wellbore instability
problem by using the critical state models. Yu and Rowe (1999) presented an
analytical solution for cavity contraction in critical state materials to study the
borehole stability.
1.4 Objectives and Scope of the StudyThe main objective of this research is to better understand the disturbance and
pore water pressure in soft soils due to the installation of mandrel-driven PVDs.
The disturbed regions surrounding the mandrels and the stresses distributed in
soils predicted from the analytical and numerical models were compared with the
results of the laboratory tests. A number of case histories were also studied to
evaluate the significance the models developed in practical situations. In
particular, this research is aimed at:
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1. Developing a new elliptical CET and characterising the soil around a PVD
Mandrel penetration into soft saturated clays and the resulting disturbance were
studied analytically with a new elliptical cavity expansion theory (CET). The
elliptical CET developed uses modified Cam clay parameters to address the
analysis of PVDs being installed in soft clay deposits in undrained conditions. The
pattern of distribution for excess pore pressure, calculated analytically, was
verified using the data available in the literature.
2. Installing PVDs at a realistic rate and assessing the factors affecting the smear
A number of large-scale laboratory tests incorporating field conditions and the
effects of confining pressures were performed. In particular, the installation of
PVDs under different surcharge loads was accomplished using a mandrel-driving
machine at a penetration rate within the range of usual practices. The variations of
pore water pressure during installation of a PVD and withdrawal of the mandrel
were monitored. The extent of the smear zone in the large-scale consolidometer
was determined using the results of moisture content tests.
3. Simulating the installation of PVDs using the finite element method
A numerical simulation of the mandrel installation process was achieved using the
ABAQUS finite element software package. A series of coupled analyses, which
took into account the large-strain formulation, were performed. The deformation
and movement of soil were predicted as the mandrel was pushed into the soft soil.
The variations of pore water pressure are illustrated at different locations during
installation of a PVD and withdrawal of the mandrel.
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4. Applying the models developed to case histories
The analytical formulation and finite element model established were applied to
case histories from the Muar clay region in Malaysia, the Sunshine Motorway in
Australia and the Second Bangkok International Airport in Thailand. The results
demonstrate that the models developed are applicable to field conditions.
1.5 Organisation of the DissertationThe significance of stabilising layers of soft soil, the privilege of a system of
vertical drains, and the goals of the present research are covered in this
introductory chapter. Chapter 2 presents a detailed literature review associated
with vertical drains where the characteristics of prefabricated vertical drains and
the factors influencing their efficiency are discussed in depth. It also describes
consolidation theories coupled with vertical drains, and the plane strain modelling
that is essential for analysis in field conditions. It focuses on the analysis of soil
disturbance associated with the installation of mandrel-driven PVDs.
Chapter 3 identifies the analytical theory developed in this research to investigate
mandrel penetration and its resulting disturbance in soft saturated clays. It also
introduces a new elliptical cavity expansion theory (CET) that incorporates the
modified Cam clay parameters to study the installation of PVDs into soft clay
deposits. This formulation accounts for the rate of mandrel penetration and the
time factor for predicting the internal pressure in the cavity, and the corresponding
stresses and excess pore pressure in the soil while driving the mandrel. A more
realistic elliptical smear zone based on the elliptical CET is also expressed.
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Chapter 4 presents the large-scale laboratory tests conducted in this research. The
installation of prefabricated vertical drains, incorporating the field conditions, was
performed using a mandrel-driving machine capable of working at rates within the
range of usual practices. By using pore pressure transducers capable of a fast
response, the variations in pore water pressure during installation of a PVD and
withdrawal of the mandrel were examined. Finally, a criterion based on the extent
of smear zone measured in the large-scale consolidometer was developed to
interpret the results of this study.
Chapter 5 discusses the finite element modelling of mandrel installation using the
ABAQUS software package. By incorporating the large-strain formulation and the
penalty method, a number of coupled analyses were completed. The changes in
pore water pressure at different locations during various stages of the simulation
were compared with the quantities measured in the laboratory. The extent of
smear zone was studied according to the numerical simulation of the mandrel
installation.
Chapter 6 provides case histories from the Muar clay region in Malaysia, the
Sunshine Motorway in Australia and the Second Bangkok International Airport in
Thailand. The layers of soft soil were examined to characterise the smear zone
associated with the installation of prefabricated vertical drains. The results of
these analyses which incorporated the models developed in this research were
then compared with the data published previously.
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Chapter 7 draws conclusions from the present research and offers
recommendations for future investigations. A list of references followed by
Appendices appears at the end.
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2 LITERATURE REVIEW
2.1 Installation and Monitoring of Prefabricated Vertical Drains
On major projects it is imperative to have a prediction of the required length of
prefabricated vertical drains as