Consolidation analysis of PVD installed soft deposits considering soil disturbance and discharge capacity reduction

120 CHAPTER 5: CONSOLIDATION BEHAVIOR OF PVD-INSTALLED DEPOSIT CONSIDERING DISCHARGE CAPACITY REDUCTION WITH DEPTH .... vii LIST OF SYMBOLS AND UNITS a factor used to describe the hydra

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(Chairman) Kim, Jin Man

(Member) Kim, Tae-Hyung

(Member) Shin, Hosung

i

TABLE OF CONTENTS

TABLE OF CONTENTS i

LIST OF SYMBOLS AND UNITS vii

ABSTRACT xiii

SUMMARY IN KOREAN xv

LIST OF FIGURES xvii

LIST OF TABLES xxii

CHAPTER 1: INTRODUCTION 1

1.1 General 1

1.2 Purpose and application of vertical drains 3

1.3 Overview of PVD-improved construction works 5

1.4 Objectives and the scope of study 8

1.5 Organization of the thesis 10

CHAPTER 2: LITERATURE REVIEW 12

2.1 History and Development of Vertical Drains 12

2.2 Parameters related to PVDs performance 14

2.2.1 Equivalent drain diameter 14

2.2.2 Mandrel Size and Shape 15

2.2.3 Installation Procedure 16

2.2.4 Drain spacing and influence zone 17

2.2.5 Soil disturbance caused by PVD installation and discharge capacity 18

2.3 Soil disturbance effect 19

2.3.1 Soil disturbance generation 19

ii

2.3.2 Analytical models of soil disturbance 19

2.3.3 Estimation of the smear zone properties 23

2.3.4 Difference between experimental and field permeability in smear zone 24

2.4 Discharge capacity 25

2.4.1 Definition of discharge capacity of drain 26

2.4.2 Discharge capacity requirement of prefabricated vertical drains 26

2.4.2.1 Discharge capacity from drain resistance approach 27

2.4.2.2 Discharge capacity based on the discharge in the PVD 28

2.4.3 Discharge capacity reduction with depth and time 29

2.5 Theory of vertical consolidation 35

2.5.1 General 35

2.5.2 One-dimensional consolidation test 38

2.5.3 Calculation of the ultimate consolidation settlement 41

2.5.4 Secondary consolidation settlement 43

2.6 Theory of radial consolidation with vertical drain 44

2.6.1 General 44

2.6.2 Analytical solution considering smear zone effects 47

2.6.3 Analytical solution considering discharge capacity reduction effects 50

2.7 Large (finite) strain theory for radial consolidation 52

2.7.1 Large strain governing equation with radial flow 52

2.7.2 Relationship between large-strain effect and vertical strain 54

2.8 Plane strain consolidation model of PVD-installed deposit 55

2.8.1 One-Dimensional drainage elements (1-D drainage element) 56

2.8.2 Macro-element formulation (Sekiguchi et al 1986) 57

2.8.3 kve method (Chai et al 2001) 57

2.8.4 Modelling PVD in plane strain by solid element 58

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2.8.4.1 Method of Shinsha et al (1982) 58

2.8.4.2 Method of Indraratna and Redana (1997) 58

2.8.4.3 Method of Kim and Lee (1997) 60

2.9 Finite element method in consolidation 61

2.9.1 General 61

2.9.2 Plaxis 2D software 62

2.10 Material models 63

2.10.1Morh-Coulomb model 63

2.10.2Soft soil model 65

2.10.2.1 Isotropic states of stress and strain  ' ' ' 1 2 3    65

2.10.2.2 Yield function for triaxial stress state  ' ' 2 3   66

2.11 Summary 67

CHAPTER 3: AN ANALYTICAL MODEL FOR CONSOLIDATION OF PVD-INSTALLED DEPOSIT CONSIDERING SOIL DISTURANCE 70

3.1 General 70

3.2 A simple analytical solution for an axisymmetric unit cell with soil disturbance71 3.2.1 A nonlinear distribution of hydraulic conductivity and compressibility 71

3.2.2 Analytical solution 76

3.2.3 Analysis results and comparisons 80

3.3 Application to field behavior 86

3.3.1 Field conditions 86

3.3.2 Consolidation analysis 90

3.4 Summary and conclusion 95

CHAPTER 4: RADIAL CONSOLIDATION OF PVD-INSTALLED DEPOSIT

iv

WITH DISCHARGE CAPACITY REDUCTION USING LARGE STRAIN

THEORY 97

4.1 General 97

4.2 A large-strain radial consolidation equation for PVD-installed deposits 100

4.2.1 Governing Equations 100

4.2.2 Overconsolidated soils 105

4.3 Effects of various parameters on consolidation behavior 106

4.3.1 The discharge capacity reduction factor  107

4.3.2 Disturbance degree of hydraulic conductivity 108

4.3.3 The C c /C k ratio 109

4.3.4 Initial effective stress of a soft deposit 110

4.4 Application to a test embankment 113

4.4.1 A test embankment at Saga Airport 113

4.4.2 A consolidation test of large block sample 118

4.5 Summary and conclusions 120

CHAPTER 5: CONSOLIDATION BEHAVIOR OF PVD-INSTALLED DEPOSIT CONSIDERING DISCHARGE CAPACITY REDUCTION WITH DEPTH 122

5.1 General 122

5.2 Analytical models of axisymmetric unit cell with a varied discharge capacity123 5.2.1 Varied discharge capacity with a nonlinear distribution 123

5.2.2 Comparison of solutions 125

5.3 A proposed k've method considering a varied discharge capacity 129

5.4 Verification of analytical models with varied discharge capacity with numerical analysis 130

5.5 Summary and Conclusion 136

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CHAPTER 6: AN EQUIVALENT PLANE STRAIN MODEL OF PVD-IMPROVED SOFT DEPOSIT CONSIDERING SOIL DISTURBANCE AND

WELL RESISTANCE 138

6.1 General 138

6.2 Formulation of an equivalent 2-D model of PVD-installed deposit 139

6.2.1 Equivalent width of vertical drain in 2-D model 140

6.2.2 Equivalent horizontal permeability in 2-D model 142

6.3 Application to a test embankment 144

6.3.1 Test embankment on soft clay deposit in eastern China 145

6.3.2 Test embankment on soft clay in Malaysia 155

6.3.3 Comparison three-dimension (3-D) numerical simulation 161

6.4 Summary and conclusion 165

CHAPTER 7: CONCLUSION AND RECOMMENDATIONS 167

7.1 General Summary 167

7.2 Specific observations 168

7.2.1 An analytical model for consolidation of PVD-installed deposit considering soil disturbances 169

7.2.2 Radial consolidation of PVD-installed normally consolidated soil with discharge capacity reduction using large strain theory 169

7.2.3 Analysis of consolidation behavior of PVD-installed deposits considering a varied discharge capacity with depth 170

7.2.4 An equivalent plane strain model of PVD-installed Deposit 171

7.3 Recommendations for application in practice 171

7.4 Recommendations for future work 173

REFERENCES 175

APPENDIX 194

vi

Appendix I 194

Appendix II 197

Appendix III 198

ACKNOWLEDGMENTS 201

CURRICULUM VITAE 203

vii

LIST OF SYMBOLS AND UNITS

a factor used to describe the hydraulic conductivity change (a = khw/kh)

a w width of the prefabricated vertical drain (m)

a wx ratio of area in the axisymmetric model

a wpl ratio of the area in the equivalent 2-D plane strain model

A dimensionless factor use to describe discharge capacity reduction degree

with depth

A 1 dimensionless factor use to describe discharge capacity reduction degree

with depth following Deng et al (2013)

A 2 dimensionless factor use to describe discharge capacity reduction degree

with depth following Deng et al (2013)

A wpl areas of the drain in the equivalent plane strain model

A soilpl areas of the surrounding soil in the equivalent plane strain model

b factor describe the ratio representing compressibility change (b = mvw/mv)

b w equivalent plane-strain radius of the drain (m)

B half width of plane strain unit cell (m)

c cohesion of soil (kN/m2)

C k permeability index

C c compression index

C s swelling index

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C d constant factor (= 3.54) in Chai et al (2001)’s model

C f the hydraulic conductivity ratio between the field and laboratory values

C α secondary compression index

c h coefficient of consolidation for horizontal drainage (m2/s)

c v coefficient of consolidation for vertical drainage (m2/s)

D e diameter of influence zone (m)

d w diameter of drain (well) (m)

d s diameter of smear zone (m)

e 0 initial void ratio

e current void ratio

e f final void ratio

e p void ratio at the end of primary consolidation

f yield function of the Soft-Soil model

F n influence factors of PVD spacing

F s influence factors of smear zone

F r influence factors of well resistance

G s specific gravity

H thickness of soil layer (m)

H dr drainage length (m)

h head of water (m)

ix

i dimensionless hydraulic gradient

k permeability coefficient of soil (m/s)

k ve equivalent vertical hydraulic conductivity in Chai et al (2001)

k' ve equivalent vertical hydraulic conductivity in author’s method

k y vertical permeability coefficient in undisturbed zone (m/s)

k h horizontal permeability coefficient in undisturbed zone (m/s)

k hp equivalent horizontal permeability coefficient in plane strain (m/s)

k hw horizontal permeability coefficient in disturbed zone at drain (m/s)

k h(r) horizontal permeability coefficient in unit cell at radius r (m/s)

k s horizontal permeability coefficient in smear zone (m/s)

k w vertical permeability coefficient in drain (m/s)

k w(t) vertical permeability coefficient in drain at time t (m/s)

L PVD-improved length (m)

m v volume compressibility coefficient of soil (kPa-1)

m v(r) volume compressibility coefficient of soil at radius r (m2/kN)

m vw volume compressibility coefficient of soil at drain (kPa-1)

n ratio r e /r w in axisymmetric condition

OCR over consolidated ratio

P (t) applied load at time t (kN/m2)

PVDs prefabricated vertical drains

x

q the radial flow of water in the soil mass

q w drain discharge capacity (m3/s)

q wo initial discharge capacity of drain (m3/s)

q re required drain discharge capacity (m3/s)

Q average quantity of water discharge per unit time (m3/s)

Q in(t) total flow that enters the drain at time t from the surrounding soil (m3/s)

R radial of influence zone (m); R = r e

r radius in unit cell (m)

r w radial of drain (m)

r s radial of smear zone (m)

r e radial of influence zone (m)

r m Radius of mandrel (m)

r tr radius of transition zone (m)

S vertical drain spacing/ settlement (m)

S f final primary consolidation settlement (m)

S 0(t) consolidation settlement at time t in convective coordinates (m)

t time (s, day)

T h dimensionless time factor for horizontal drainage

T v dimensionless time factor for vertical drainage

u excess pore water pressure (kN/m2)

xi

u r excess pore water pressure at radius r in the unit cell (kN/m2)

u 0 initial excess pore water pressure (kN/m2)

r

u average excess pore water pressure for the unit cell (kN/m2)

w

u average excess pore water pressure at drain (kN/m2)

U h radial (horizontal) consolidation degree (%)

U v vertical consolidation degree (%)

V volume of the soil mass (m3)

v r velocity of flow (at radius r) (m/s)

v x velocity of flow (at distance x) (m/s)

 factor reflecting the well resistance effects in Deng et al (2013)

 factor used in Indraratna et al (1997)’s model

 modified compression index

 factor in Hansbo’s solution

 poison ratio

 height in convective coordinate (m)

o(t) height in convective coordinate at time t (m)

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Consolidation Analysis of PVD-Installed Soft Deposits Considering Soil

Disturbance and Discharge Capacity Reduction

Author: Ba-Phu Nguyen

Department of Ocean Engineering, the Graduate School, Pukyong National University

ABSTRACT

Prefabricated vertical drains (PVDs) combined with preloading are frequently used to accelerate rate of consolidation and gain shear strength in soft soils PVD discharge capacity reduction and soil disturbance caused by PVD installation are important factors in ground improvement design, these factors significantly affect the consolidation behavior of PVD-improved ground In this thesis, a numerical solution

for radial consolidation of PVD-installed deposits, formulates a general expression for discharge capacity reduction with consolidation process, is proposed based on large-

strain theory The effects of soil disturbance, such as a nonlinear distribution for radial hydraulic conductivity, are captured The proposed solution was applied to a test embankment at Saga Airport and an experimental test The predicted results of consolidation behaviors were in good agreement with observed data in all cases of the verification

In order to perform a multi-drain analysis in numerical model, equivalent plane strain models were proposed An equivalent vertical hydraulic conductivity ( '

ve

k method) is proposed to consider the effects of PVD discharge capacity reduction

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with increased confining pressure The proposed method was validated via a test embankment on a thick soft ground for construction site in Busan New Port The results indicated that it is necessary to consider the PVD discharge capacity reduction with depth on consolidation analysis A nonlinear distribution of discharge capacity with depth is recommended to use in practice

To realistically simulate existence of PVD in soft ground, an equivalent plane strain model using solid element was further proposed In the proposed method, an equivalent horizontal permeability was obtained from the matching of the total volume of water to be discharged in an axisymmetric model and the total changes in flow in a plane strain, while the geometry of the drains was deduced from the balancing of the area ratio The effects of the soil disturbance and well resistance were also considered The verification was implemented; and the predicted results by the proposed method were in good agreement with observed data for two case histories, including the test embankment on the soft clay of eastern China and the Malaysian soft muar clay It is recommended that the proposed models could be used for

consolidation analysis of the PVD-installed soft deposits

한 요소로서, 이러한 요인은 PVD로의 지반개량 압밀거동에 큰 영향을 미친

다 본 논문에서는 PVD가 설치된 연약지반의 방사형 압밀을 위한 수치적 해법이 통수 능력 감소를 고려한 식으로 제시되며, 대변형 이론(large-strain theory)에 기초한다 또한 방사형 수리전도도에 대한 비선형 분포와 같은

토양 교란의 영향을 고려하며, 제안된 모델은 사가(Saga) 공항의 현장 및

시험 결과를 이용하여 검증하였다 본 모델을 이용하여 예측한 압밀거동의

해석 결과는 현장에서 관측된 데이터와 일치하였다

수치 모델에서 다중 배수 분석을 수행하기 위해 등가 평면 변형 모델(equivalent plane strain models)이 제안되었다 PVD 통수 능력 감소와 결합

압력 증가를 고려한 등가 수직 수리전도도( '

ve

k method)가 제안되었다 제안

된 방법은 부산신항 건설현장 부지의 두꺼운 연약지반 시험 제방을 통해 검증되었다 그 결과, 압밀 분석에서 깊이에 따라 PVD 통수능력 감소를 고

려할 필요가 있음을 나타냈다 깊이에 통수능력의 비선형 분포는 실제 현장에서 사용할 것을 권장한다

연약지반에서 PVD를 현실적으로 시뮬레이션하기 위해, 솔리드 요소(solid element)를 사용한 등가 평면 변형 모델(equivalent plane strain model)을 추가로 제안했다 제안된 방법에서는, 축대칭 모델(axisymmetric model)에서 배출될 총 물의 부피와 평면 변형률(plane strain)과의 일치를 얻었으며, 배

xvi

수재의 기하학적 구조는 면적 비의 균형에서 추론되었다 또한, 지반의 교

란 영향과 웰 저항도 고려되었다 제안된 방법에 의한 예측 결과는 중국 동부의 연약 점토에 대한 시험 제방과 말레이시아의 Muar 연약 점토를 포

함한 두 가지 사례 이력에 대해 관측된 데이터와 일치했다 이를 통해 PVD

를 설치한 연약지반의 압밀 분석에 대해 본 연구에서 제안한 모델 적용을 검증할 수 있다

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LIST OF FIGURES

Figure 1.1 Efficiency of PVD on drainage path in ground 2

Figure 1.2 The shape and structures of PVDs 4

Figure 1.3 PVD installation process (https://www.geoengineer.org with modification)5 Figure 1.4 Overview of PVD-improved deposit with preloading 6

Figure 1.5 Deformed drain in a laboratory model test (after Sun et al 2011) 8

Figure 2.1 Equivalent drain diameter of PVDs 14

Figure 2.2 Examples of mandrel shapes, (a) rectangular, (b) rhombic and (c) circular (After Ali 2014) 16

Figure 2.3 PVD installation equipment, (a) crane and drain delivery arrangement, and (b) vertical drain surrounded by hollow mandrel and attached to the anchor plate at bottom (after Ali 2014) 17

Figure 2.4 Influence zone of PVD: (a) square patter and (b) triangular pattern 18

Figure 2.5 Horizontal hydraulic conductivity variation in axisymmetric unit cell 21

Figure 2.6 Proposed values for smear zone characteristics (after Ali 2014) 24

Figure 2.7 Variation of vertical discharge capacity with confining stress (after Hansbo 1983 and Rixner et al 1986) 30

Figure 2.8 Deformation patterns of PVDs in ground tested at the termination of the tests 32

Figure 2.9 Discharge capacity reduction with consolidation time 34

Figure 2.10 One-dimensional consolidation of a clay layer 35

Figure 2.11 Determination of drainage path length Hdr 37

Figure 2.12 One-dimensional consolidation test apparatus (After Helwany 2007) 38

Figure 2.13 Deformation versus time curve (semilog) (Das and Sobhan 2013) 39

Figure 2.16 Variation of e with log t under a given load increment and definition of

secondary consolidation index (After Das and Sobhan 2013) 44

Figure 2.17 Schematic of soil cylinder with vertical drain 46 Figure 2.18 Conceptual compression behaviour of soil with different disturbance

levels (Indraratna 2017) 49

Figure 2.19 (a) Model geometry and coordinate system for consolidation with

vertical drains; (b) pore water flow in the influential area (After Indraratna et al 2017) 53

Figure 2.20 Relationship between vertical strain and error for the small strain

solution (After Indraratna et al 2017) 55

Figure 2.21 Conversion of an axisymmetric unit cell into plane strain condition 60 Figure 2.22 Position of nodes and stress points in triangular soil elements (after

Brinkgreve and Vermeer 1998) 62

Figure 2.23 The Mohr-Coulomb yield surface in principal stress space (c = 0) (after

Brinkgreve and Vermeer 1998) 64

Figure 2.24 Logarithmic relation between volumetric strain and mean stress 65

Figure 2.25 Yield surfaces of the SS-model in p’-q plane (Neher et al 2001) 67

Figure 3.1 Nonlinear variation of horizontal hydraulic conductivity and

compressibility of soil around drain due to mandrel installation 73

Figure 3.2 Axisymmetric unit cell with nonlinear distributions of horizontal hydraulic

conductivity and compressibility 74

compressibility 85

Figure 3.8 Degree of horizontal consolidation with variation of both the horizontal

hydraulic conductivity and compressibility 86

Figure 3.9 Cross-section and loading schedule of trial embankment in Pacific

Figure 4.2 Distribution of the excess pore water pressure with radius and depth

during consolidation of soil deposits 102

Figure 4.4 Average degree of radial consolidation with variation of disturbance

degree of hydraulic conductivity 109

Figure 4.5 Average degree of radial consolidation with variation of Cc/Ck 110

Figure 4.6 Average degree of radial consolidation with variation of initial effective

xx

Figure 4.9 Nonlinear distribution of horizontal hydraulic conductivity around the

PVD of the Saga Airport embankment 116

Figure 4.10 Measured and predicted settlement with time in the Saga Airport

embankment 118

Figure 4.11 Comparison of settlement results among observed data and solutions 119 Figure 5.1 Nonlinear distribution of discharge capacity of PVD with depth 124 Figure 5.2 Comparison of the normalized excess pore water pressure with initial

excess pore water pressure with depth obtained from different solutions 127

Figure 5.3 Comparison of horizontal degree of consolidations for different

distributions of discharge capacity 128

Figure 5.4 Layout of construction plan of Busan new port, West Terminal Phase 2-5

(Busan Port Authority 2016) 131

Figure 5.5 Cross-section at CY2-4 (No.6) in Phase 2-5 in construction site 132 Figure 5.6 Finite element mesh and boundary conditions 135 Figure 5.7 The predicted settlements in numerical method and measured data at West

Terminal Phase 2-5 in Busan New Port 136

Figure 6.1 Axisymmetric model and equivalent 2-D plane strain model 141 Figure 6.2 Cross-section of test embankment and arrangement of PVD 146 Figure 6.3 Geometry and boundary condition in plane strain FEM of test

xxi

Figure 6.8 Geometry and boundary condition in plane strain FEM of test

embankment on soft muar clay in Malaysia 157

Figure 6.9 Loading schedule and comparison of the settlement results of test

embankment on soft muar clay in Malaysia 158

Figure 6.10 Comparison of the excess pore water results of test embankments on the

soft muar clay in Malaysia 160

Figure 6.11 3D finite element discretization of test embankment in soft mucky clay

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LIST OF TABLES

Table 2.1 PVD assisted preloading projects 13 Table 2.2 Suggested equations for equivalent diameter of PVD 15

Table 2.3 Proposed values for Cf (after Chai and Miura 1999) 25

Table 2.4 The radial consolidation solution of PVD with varied discharge capacity 51 Table 3.1 Soil parameters used in a case study analysis (after Rujikiatkamjorn and

Indraratna 2015) 90

Table 4.1 Existing models for radial consolidation 99 Table 4.2 Properties of PVD-installed soft soil under the Saga embankment test 117 Table 4.3 Summary information of PVD-improved soil deposit 119 Table 5.1 Geotechnical properties of subsoil in numerical analysis 133 Table 6.1 Properties of PVD used for test embankment in soft mucky clay deposit 146 Table 6.2 In-situ and equivalent permeability of soil deposits 147 Table 6.3 Geotechnical properties of soft mucky clay deposit in numerical analysis 149 Table 6.4 Geotechnical properties of soft muar clay deposit in numerical analysis 157

1

CHAPTER 1 INTRODUCTION

roads, rail tracks, and other forms of major infrastructure (Johnson 1970; Indraratna 2017) Therefore, it is imperative to improve these soils before beginning construction

to prevent unacceptable differential settlement However, attempts to improve deep bearing deposit may not be commensurate with the overall cost of the infrastructure (Bo et al 2003) In the past, various types of vertical drains such as sand drains, sand compaction piles, prefabricated vertical drains (PVDs), stone columns, and gravel piles have been used to accelerate consolidation and increase strengthen the soil deposits PVDs are often preferred due to relative low cost and ease of installation (Rujikiatkamjorn 2005; Ali 2014; Indraratna 2017) Moreover, PVDs installation can significantly reduce soil disturbance degree, environmental effects, comparing with other improved methods PVDs can be installed in moderate to highly compressible

2

soils (up to 40 m deep) that are normally consolidated or lightly overconsolidated When PVDs combined with surcharge preloading were applied, vertical drains provide a much shorter drainage path in a horizontal direction, as shown in Figure 1.1 This allows the height of the surcharge embankment to be reduced to prevent any instability and lateral movement in the soil Noted here that PVDs can combine with vacuum preloading in practical ground improvement to reduce the surcharge embankment However, the efficiency of vacuum method may be limited because vacuum pressure can be significantly decreased along length of deposits (Indraratna et

al 2012a)

Long drainage paths

(a) Ground without PVD (b) Ground with PVD

Figure 1.1 Efficiency of PVD on drainage path in ground

Application of vertical drains for soft ground improvement in Korea has been

recently reported as Busan New Port (East Terminal) (Chung et al 2014); Busan New Port (West Terminal) (Busan Port Authority 2016); Hwajeon site at West Nakdong River (Chung et al 2007); The Noksan reclamation site (Jang and Chung 2014) Because the PVD-improved method is a cost-effective method in terms of time and economics, it is widely used in the ground improvement Although the consolidation theory related to aspects of PVD have received significant attention,

3

there is still uncertainty and remains discrepant among researchers for problems related

to discharge capacity of PVDs and soil disturbance due to PVD installation process (Sengul et al 2016) To provide an up-to-date reference for engineers and researchers

in PVD-ground improvement engineering, consolidation solutions with numerical analysis for PVD-installed soft deposit includes both axisymmetric unit cell and equivalent plane strain condition, is further developed in this study

1.2 Purpose and application of vertical drains

The consolidation settlement of soft deposit creates a lot of problems on geotechnical engineering In the soft deposit, the hydraulic conductivity is usually very low, thus the consolidation process takes a long time to complete consolidation process To reduce the consolidation time, vertical drains are typically installed together with preloading

by surcharge embankment or vacuum pressure During consolidation of clay deposits, pore water flows horizontally toward the drain and the collected flow then moves vertically in the drain toward permeable drainage layers Moreover, vertical drains can

gain shear strength of soft soil, thereby improving the stability of structures on weak clay (Bergado et al 1996) Vertical drains were typically used as sand drains, sand compaction piles, gravel piles and PVD (geosynthetic) Among these various type of vertical drains, PVDs were often used with fast installation (Rujikiatkamjorn 2005) Figure 1.2 shows shape of a PVD and structures of PVDs PVDs have a channeled or studded plastic core wrapped with a geotextile The plastic core functions as support for the filter fabric, and provides longitudinal flow paths along the drain length It also causes resistance to longitudinal stretching as well as buckling of the drain The drain jacket acts as a filter to limit the passage of fine grained soil into the core area It also functions to prevent closure of the internal water flow paths under lateral soil pressure

4

(a) Shape of PVD (https://www.geoengineer.org)

(b) Cross-section of various of PVDs (after Chai et al 2004)

Figure 1.2 The shape and structures of PVDs

5

1.3 Overview of PVD-improved construction works

In practice, PVDs can be installed with a static or dynamic method In the static method, the mandrel is installed into the soil via a static force In the dynamic method, the mandrel is pushed into the ground using a vibrating hammer Static procedure is preferable for driving the mandrel into the ground, whereas the dynamic methods seem

to create a greater disturbance of the surrounding soil during installation Figure 1.3 shows PVD installation process, where a vertical drain is driven into soft ground using

a mandrel hoisted by a crane This process generates a significant disturbance of the soil around the PVD, especially when the mandrel is installed with a vibration method (Indraratna and Chu 2005) The disturbance degree during installation depends on several factors such as the soil types, mandrel size, mandrel shape and soil macrofabric

Drain Stitcher

Excavator Mandrel

Anchored drain

Soft deposit to

be consolidated

Figure 1.3 PVD installation process (https://www.geoengineer.org with modification)

Experimental researches and field studies have indicated that soil disturbance

due to mandrel installation reduces horizontal hydraulic conductivity and increases the compressibility of the soil surrounding the drain (Rujikiatkamjorn et al 2013) These

6

effects cause consolidation delays in PVD-installed soil deposits (Chai and Miura 1999; Sharma and Xiao 2000; Saye 2001; Zhu and Yin 2005; Basu et al 2006; Walker and Indraratna 2006, 2007; Rujikiatkamjorn and Indraratna 2015) Based on the results

of experimental tests, Yune et al (2013) stated that narrowing the drain spacing reduced efficiency of vertical drain function due to soil disturbance Therefore, the effects of soil disturbance around the drain must be considered in predictions of consolidation of PVD-installed soil deposits

Figure 1.4 shows a typical cross-section of PVD-installed ground with preloading and essential instruments required to monitor the performance of soil foundation beneath an embankment Before installing the PVDs, general site preparations including the removal of vegetation and surficial soil, establishing site grading and placing a compact drainage blanket are required (Rujikiatkamjorn 2005) The drainage blanket is employed to expel water away from the PVDs and to provide a sound-working mat for PVDs system

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Field instrumentation for monitoring and evaluating the performance of embankments is essential to examine and to control the geotechnical problems Evaluation of performance of embankment is also important to improve settlement predictions and to provide sound guidelines for future projects (Rujikiatkamjorn 2005) Based on the construction stages, field instrumentation can be divided into two groups (Bo et al 2003) The first group is used to prevent sudden failures during construction (e.g settlement plates, inclinometers and piezometers), whereas the second group is used to record changes in the rate of settlement and excess pore pressure during loading stages (e.g multilevel settlement gauges and piezometers)

During consolidation of clay deposits, pore water flows horizontally toward the drain and the collected flow then moves vertically in the drain toward permeable drainage layers Therefore, the effectiveness of PVD improvement method is closely

related to PVD discharge capacity (qw) (Chai and Miura 1999; Tran-Nguyen et al 2010) Theoretical and experimental researches combined with field practices indicated that the discharge capacity of PVD is influenced by a number of factors, including type

and shape of the core, cross-sectional area of drain, confining pressure, permeability and durability of filter (Deng et al 2013) The confining pressure from the surrounding soil increases with depth (Figure 1.4), which results in decreasing discharge capacity of PVD Moreover, the discharge capacity usually decreases with consolidation process which results in delay of the consolidation rate (Hansbo 1983; Rixner et al 1986; Miura and Chai 2000; Aboshi et al 2001; Chai et al 2001; Bo 2004; Chai et al 2004; Chu et al 2006; Deng et al 2013, 2014; Indraratna et al 2016) This is attributable to squeezing of the filter sleeve into core channels, thus reducing channel cross-sectional areas Moreover, discharge capacity also reduces due to the folding of the PVD when subjected to large strains, which is important factor in design of PVD ground improvement Figure 1.5 shows a typical PVD deformation in a laboratory model test

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Figure 1.5 Deformed drain in a laboratory model test (after Sun et al 2011)

Generally, the main factors influencing the PVD efficiency are soil disturbance and discharge capacity which related to well resistance factor The installation process

of a vertical drain usually causes some disturbance to the surrounding soil This region of disturbance is described as the ‘smear zone’ In this zone, the lateral permeability of the soil is decreased and compressibility is increased, thereby reducing the rate of consolidation and increase vertical strains in ground The resistance to water flowing along the vertical drain is known as the ‘well resistance’ Discharge capacity of PVD directly is closed to well resistance factor The deep installation of vertical drains or a limited discharge capacity of the drain will increase the well resistance In addition to smear and well resistance, drain unsaturation

occurring from the gap between dry vertical drain and mandrel during installation is also an important factor since it affects the drain efficiency (Indraratna 2017)

1.4 Objectives and the scope of study

The main objective of this study is to examine the consolidation behavior of installed soft deposit considering discharge capacity reduction and soil disturbance due

PVD-9

to PVD installation

First, an analytical solution for radial consolidation of PVD-installed deposit is developed to consider effects of soil disturbance A parabolic functions were used to describe the nonlinear properties of the hydraulic conductivity and compressibility in the disturbed zone

Second, a numerical solution for radial consolidation in axisymmetric model of PVD-installed deposits was developed to represent the effect of discharge capacity reduction with time using large-strain theory Nonlinear variations of permeability and compressibility during consolidation were incorporated The effects of soil disturbance

on consolidation behavior were also captured in the proposed solution To validate the proposed solution, the proposed solution was applied to a case study of a test embankment at Saga airport and a case of experimental test

Thirdly, an equivalent vertical hydraulic conductivity considering discharge

capacity with depth (k've) was proposed, in which nonlinear distribution of discharge capacity with depth was assumed Then, the proposed solution was validated through

finite element method (FEM) A thick deposit in West Terminal (Phase 2-5) in Busan New Port was analyzed to verify the proposed model

Finally, an equivalent plane strain (2-D) model of the PVD-improved ground, where the PVD is modeled by the solid elements, was proposed An equivalent width

of the PVD and an equivalent horizontal permeability of the subsoil in the plane strain model were proposed, in which effects of the smear zone and the well resistance were taken into account Verification of the proposed method was performed by comparing the settlement and the excess pore water pressure distribution with regard to the observed results of two case histories including the embankment tests on the soft mucky clay of eastern China and the Malaysian soft muar clay The approaches of Indraratna and Redana (1997) and Kim and Lee (1997) were also applied and

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compared with regard to the proposed method

1.5 Organization of the thesis

Following this introduction, Chapter 2 presents a comprehensive survey of the literature associated with PVD-installed deposits The history and development of PVDs, present theories related to radial drainage, basic behavior of embankments improved with vertical drains and related numerical and analytical solutions are briefly reviewed

Chapter 3 develops a simple analytical solution for radial consolidation of PVD-installed deposit, in which the effects of horizontal hydraulic conductivity and compressibility variations within the surrounding soils were considered simultaneously The horizontal hydraulic conductivity and compressibility of surrounding soils in an axisymmetric unit cell were assumed to have nonlinear variations The proposed analytical solution was validated using the case history of a test embankment along the Pacific Highway between Sydney and Brisbane, Australia

(Indraratna et al 2012b, 2014; Rujikiatkamjorn and Indraratna 2015) The approaches

of Walker and Indraratna (2006), Basu et al (2006) and Rujikiatkamjorn and Indraratna (2015) were also applied and compared with the proposed method The effects of parameters in the analytical solution, which affect predicted results, was also investigated in Chapter 3

Chapter 4 develops a numerical solution for the radial consolidation of installed soft deposits considering discharge capacity reduction with time using large-strain theory The effects of soil disturbance with nonlinear distribution in hydraulic conductivity as Chapter 3 were also captured in the proposed solution To validate the proposed solution, the proposed solution was applied to a case study of a test embankment at Saga Airport and a case of experimental test The classical solutions

PVD-11

in small-strain theory were also applied and compared to the results of the proposed solution The parameters, which affect the consolidation behavior, were discussed Chapter 5 develops an analytical solution in axisymmetric model to analyze consolidation behavior of PVD-installed deposit, in which the nonlinear reduction with depth of PVD discharge capacity was considered The nonlinear distribution of discharge capacity was assumed in proposed solution based on previous experimental test (Hansbo 1983 and Rixner et al 1986) as evidences The analysis results of consolidation behaviors in proposed solution are compared with Deng et al (2013) and Hansbo (1981) The parameters, which affect the consolidation behavior, were also discussed Then, an equivalent vertical hydraulic conductivity method considering discharge capacity variation (k method) was proposed to mutil-drain ve'

analysis A thick deposit in West Terminal (Phase 2-5) in Busan New Port was analyzed to verify the proposed model

Chapter 6 proposes an equivalent plane strain (2-D) model of the improved ground where the PVD is modeled using the solid elements An equivalent

PVD-width of the PVD and an equivalent horizontal permeability of the subsoil in the plane strain model were proposed, in which effects of the smear zone and the well resistance were taken into account Verification of the proposed method was performed in multi-drain finite element analysis by two case histories including the embankment tests on the soft mucky clay of eastern China and the Malaysian soft muar clay The approaches of Indraratna and Redana (1997) and Kim and Lee (1997) were also applied and compared with regard to the proposed method

Chapters 7 presents the main conclusions of the current research, thereby deducing recommendations for further research, followed by Appendices

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CHAPTER 2 LITERATURE REVIEW

2.1 History and Development of Vertical Drains

To improve soft ground, different types of vertical drainage systems such as sand compaction piles, stone piles, gravel piles and prefabricated vertical drains (PVDs) have been used extensively over the past few decades After Johnson (1970), a vertical drainage system was first applied around the 1920’s The vertical sand drain was first proposed to use in 1925, and patented in 1926, by Daniel D Moran (Moseley and Kirsch 1993) He also suggested the first practical application of sand drains to improve the mud soil beneath the roadway approach to the San Francisco Oakland Bay Bridge

Walter Kjellman installed the first prefabricated vertical drains system in a field test in 1937 Field tests on a large scale were made using tubes, which were made from

a fibred material, but after realizing this material was inappropriate and too expensive,

Kjellman invented and patented a band shaped cardboard drain as well as a method for driving it into the ground in 1939 Since than a great number of laboratory and field investigations on deep-drainage with this drain have been performed This cardboard drain consisted of two cardboard sheets glued together with an external cross section that was 100 mm wide and 3 mm thick, with 3-mm wide and 1 mm thick longitudinal internal channels The efficiency of cardboard wicks was firstly investigated at Lilla Mellosa in Sweden, in a full-scale test, after which several types of prefabricated band drains such as Geodrain (Sweden), Alidrain (England), and Mebradrain (Netherlands), were developed Basically, prefabricated vertical drains (PVDs) have a rectangular cross section consisting of a filter fabric sleeve or jacket surrounding a plastic core The sleeve acts as a physical barrier separating the core and the surrounding soil but

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permits pore water to enter the drain It is made from non-woven polyester geotextiles, polypropylene geotextiles, or synthetic papers The plastic core has grooved channels, which act as flow paths and supports for the filter sleeve (Bergado et al 1996)

In the last 20 years, the PVDs assisted preloading have been widely used as an efficient ground improvement technique A selected number of successful PVD assisted projects are summarized in Table 2.1

Table 2.1 PVD assisted preloading projects

Projects Locations References

Ningbo international airport China Zhu et al (1993)

Coal & iron ore stack yard India Bhosle and Vaishampayan (2009) Changi east reclamation project Singapore Bo et al (2007)

Sunshine motorway Australia Sathananthan et al (2008)

Chittagong airport Bangladesh Dhar et al (2011)

Sarapui trial embankmnet Brazil Almeida et al (2005)

Barra da Tijuca embankmnet Brazil Almeida et al (2005)

Cumbulum trial embankment Australia Kelly (2008)

Pacific Highway between Sydney

and Brisbane

Australia Rujikiatkamjorn and Indraratna

(2015) Ballina Bypass project Australia Chai et al (2018)

Muar test embankments Malaysia Balasubramaniam et al (2007)

Haarajoki trial embankment Finland Yildiz and Karstunen (2009)

Busan New Port (East Terminal) Korea Chung et al (2014)

Noksan reclamation Korea Jang and Chung (2014)

Hwajeonsite(West Nakdong River) Korea Jang and Chung (2014)

Busan New Port/West terminal Korea Busan Port Authority (2016)

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2.2 Parameters related to PVDs performance

The design of PVDs varies according to the specific application The key parameters and factors influencing the PVD assisted preloading design are the equivalent diameter, the filter and apparent opening size, the tensile strength, the discharge capacity and well resistance, smear zone, soil macro fibre, mandrel size and shape, installation procedure, and the drain spacing and influence zone, all of which are explained in detail in the following section In this study, the parameters related to effects of soil disturbance due to PVD installation and discharge capacity of drains will be reviewed

as main points

2.2.1 Equivalent drain diameter

To conveniently design of PVD-improvement, it is necessary to convert the actual shape of PVDs into an equivalent circular diameter called the “equivalent diameter,” as shown in Figure 2.1

Figure 2.1 Equivalent drain diameter of PVDs

Different equations for the equivalent drain diameter (d w) of band shaped PVD have been proposed and are presented in Table 2.2