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

[UCI]I804:21031-200000181361 Thes s for the e ree of o tor of h oso h o so to s s of oft e os ts o s er s h r e o t h e rt e t of e te to e r r st r e e The r o st eer hoo ers t to e e o so to s s of st e oft e os ts o s er o st r e s h r e t e to 연직배수재가 설치된 연약지반의 지반 수 sor rof Te h thes s s tte rt e f f e t of the re re e t for the e ree of o tor of h oso h e rt e t of e o eer to e r r the r ers t te hoo h e 의 공학박사 학위 주 심 공학박사 김 진 만 위 원 공학박사 김 태 형 위 원 공학박사 신 호 성 위 원 공학박사 안 재 훈 위 원 공학박사 김 윤 태 o so o s er to s s of o st r e st e s h r e oft e os ts t e to ssert t o h e ro e (Chairman) Kim, Jin Man (Member) Kim, Tae-Hyung (Member) Shin, Hosung (Member) Ahn, Jaehun (Member) Kim, Yun-Tae e r r 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 General 1.2 Purpose and application of vertical drains 1.3 Overview of PVD-improved construction works 1.4 Objectives and the scope of study 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 i 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 ii 2.9 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 Finite element method in consolidation 61 2.9.1 General 61 2.9.2 Plaxis 2D software 62 2.10 Material models 63 2.10.1 Morh-Coulomb model 63 2.10.2 Soft 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 PVDINSTALLED 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 iii 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 Cc/Ck 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 iv CHAPTER 6: AN EQUIVALENT PLANE STRAIN MODEL OF PVDIMPROVED 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 v Appendix I 194 Appendix II 197 Appendix III 198 ACKNOWLEDGMENTS 201 CURRICULUM VITAE 203 vi multidrain embankments have commonly been conducted under “plane strain” conditions for optimizing computational efficiency Therefore, to employ a realistic 2D plane strain analysis for vertical drains, the appropriate equivalence between the plane strain and axisymmetric analysis needs to be established in terms of consolidation settlement Various methods for modeling the PVD-improved subsoil in plane strain analysis were presented, which can be classified into four categories 2.8.1 One-Dimensional drainage elements (1-D drainage element) Based on Hansbo’s (1981) theory, Hird et al (1992) formulated the degree of horizontal consolidation in the plane strain unit cell and matched it with the degree of radial consolidation in the axisymmetric model The following relationship was obtained: khp kh  2B2  r k r 3 3re2 ln e  ax ln s    rs ks rw  (2.53) For incorporating well resistance, the following dimensionless expression can be used: qwp qw  2B  re2 (2.53) Chai et al (1995) successfully extended the analysis by Hird et al (1992) to include the effect of well resistance and clogging In this approach, the discharge capacity of the drain in plane strain (qwp) for matching the average degree of horizontal consolidation is given by qwp  4kh L2  17 L2 kh  n k  B ln    h ln  s     12 3qwa   s  ks  (2.55) A 1-D drainage element was used to model the effect of PVD in the plane strain 56 analysis In this way, the 1-D drainage element can express that the excess pore water pressure at PVD is equal to zero (u = 0) Although, Hird et al (1992) and Chai et al (1995) incorporated the smear zone and well resistance in their formulation, the effects of PVD including stiffness, geometry were neglected 2.8.2 Macro-element formulation (Sekiguchi et al 1986) Sekiguchi et al (1986) formulated a quadrilateral macro-element to simulate the effect of PVD in the ground, in which the smear zone effect was neglected and the discharge capacity of PVD was assumed to be infinite This method is exceptionally time-consuming (Chai et al 2001) and exceedingly inconvenient in engineering practice 2.8.3 kve method (Chai et al 2001) A simple approximate method for modelling the effect of PVD is proposed by Chai et al (2001) Because PVD increases the mass permeability of subsoil in the vertical direction, it is logical to establish a value for vertical permeability which approximately represents the effect of vertical drainage of natural subsoil and radial permeability toward the PVD This equivalent vertical permeability (kve) was derived from an equal average degree of consolidation under the 1-D condition To obtain a simple expression for kve, an approximation equation for consolidation in the vertical direction was proposed: U v   exp  Cd Tv  (2.56) where Tv is the time factor for vertical consolidation, and Cd is constant and equal to 3.54 The equivalent vertical permeability, kve, can be expressed as: 57  2.5L2 kh  kve  1  k  De2 kv  v  (2.57) where L is drain length, De the equivalent diameter of unit cell, and  followed Hansbo’s solution (Eq 2.34) This is an easy and a convenient method to simulate the PVD-improved soil deposit; however, the concept is unrealistic with regard to the existence of PVD in the subsoil 2.8.4 2.8.4.1 Modelling PVD in plane strain by solid element Method of Shinsha et al (1982) Shinsha et al (1982) first proposed an acceptable matching criterion for converting the permeability coefficients The equivalent coefficient of permeability was calculated on the assumption that the required time for a 50% degree of consolidation in both schemes was the same, giving  B  Thp   kh  re  Th khp (2.58) where Thp is the time factor for the plane strain condition calculated by Terzaghi’s 1-D consolation theory; and Th the time factor for the consolidation of an axisymmetric unit cell due to effect of PVD 2.8.4.2 Method of Indraratna and Redana (1997) Indraratna and Redana (1997) converted the vertical drain system shown in Figure 2.21 into an equivalent parallel drain wall by adjusting the coefficient of soil permeability They assumed that the half-widths of unit cell B, of drains bw, and of smear zone bs are the same as their axisymmetric radius re, rw and rs, respectively The equivalent permeability of the model is then determined by 58   k kh    hp    Lz  z   ksp   khp   n kh kh  ln  ln s     Lz  z   qwp   s ks (2.59) The associated geometric parameters  ,  and the flow term  are given by    and 2bs  bs bs2  1    B  B 3B  (2.60) b b  bw   s  3bw2  bs   s B 3B (2.61) 2khp2  bw   1  ksp Bqwp  B (2.62) where qwp  2qw / B is the equivalent plane strain discharge capacity In Eq (2.52), as khp appears on both sides of the equation The solution is obtained by ' iteration with an initially assumed khp /khp ratio 59 kwp ksp kw H kh ks rw rs H khp bw bs re 2B (a) Axisymmetric (b) Plane strain Figure 2.21 Conversion of an axisymmetric unit cell into plane strain condition Indraratna and Redana (1997) proposed the following approximation on khp/kh by ignoring both the smear effect and the well resistance khp kh  0.67 ln  n   0.67 (2.63) To use the solution of the plane strain unit cell with the smear effect in 2D FEM analysis, a plane strain unit cell has to be modelled by at least five columns of finite elements, namely for PVD, for the smear zone and for the remaining zone In actual engineering practice, this may not be convenient to use 2.8.4.3 Method of Kim and Lee (1997) 60 They assume that the time durations for the two systems (plane strain and axisymmetric) to achieve a 50% and 90% degree of consolidation are the same Then, the following simple expression is obtained: B T T S    h 50 h90 kh  re  Thp 50 Thp 90  d w khp (2.64) where Th50  0.197 and Th90  0.848 ; i.e., time factors in the plane strain model, and Thp 50 and Thp 90 are those for the corresponding radial flow The time factors of radial flow can be calculated by Th   ln 1  U h  /8 from Hansbo’s analytical solution 2.9 Finite element method in consolidation 2.9.1 General Finite element analysis is a method of solving continuous problems governed by differential equation by dividing the continuum into a finite number of parts (elements), which are specified by a finite number of parameters (Zienkiewicz et al 2005) Different methods of numerical analysis have been widely used by geotechnical engineers to rectify the limitations of analytical approaches in simulating complex PVD assisted preloading projects to predict the ground behaviour, as well as conduct parametric studies and back calculate the properties of the smear zone Different numerical programs such as CRISP, PLAXIS, ABAQUS, and FLAC have been used by researchers to conduct numerical analyses A problem is solved by dividing the larger geometry into small elements, which are interconnected with nodes Each element is assigned an element property In solid mechanics, the properties include stiffness characteristics for each element This force displacement relationship is expressed as 61 k e  e  Fe (2.65) where  k e is the element stiffness matrix,  e is the nodal displacement vector of the element and F e is the nodal force vector (Bhavikati 2005) 2.9.2 Plaxis 2D software Plaxis 2D is an advanced finite element method software intended for analysing twodimensional problems of deformation and stability in geotechnical engineering The development of the software began in 1987 at Delft University of Technology The Plaxis 2D software comprises three sub programs namely the input program, the calculation program and the output program It performs analysis with either an assumption of plane strain or axi-symmetry with 6-noded or 15-noded triangular elements (Figure 2.22) Figure 2.22 Position of nodes and stress points in triangular soil elements (after Brinkgreve and Vermeer 1998) 62 2.10 Material models 2.10.1 Morh-Coulomb model The Mohr-Coulomb yield condition is an extension of Coulomb's friction law to general states of stress In fact, this condition ensures that Coulomb's friction law is obeyed in any plane within a material element The full Mohr-Coulomb yield condition consists of six yield functions when formulated in terms of principal stresses: f1a  '    3'    2'   3'  sin   c cos   2 (2.66a) f1b  '    2'    3'   2'  sin   c cos   2 (2.66b) f2a  '    1'    3'   1'  sin   c cos   2 (2.66c) f 2b  ' 1   3'   1'   3'  sin   c cos   2 (2.66d) f 3a  '    2'    1'   2'  sin   c cos   2 (2.66e) f3b  '    1'    2'   1'  sin   c cos   2 (2.66d) The two plastic model parameters appearing in the yield functions are the wellknown friction angle  and the cohesion c These yield functions together represent a hexagonal cone in principal stress space as shown in Figure 2.23 63 Figure 2.23 The Mohr-Coulomb yield surface in principal stress space (c = 0) (after Brinkgreve and Vermeer 1998) In addition to the yield functions, six plastic potential functions are defined for the Mohr-Coulomb model: g1a  '    3'    2'   3'  sin  2 (2.67a) g1b  '    2'    3'   2'  sin  2 (2.67b) g2a  '    1'    3'   1'  sin  2 (2.67c) g 2b  '    3'    1'   3'  sin  2 (2.67d) g3a  '    2'    1'   2'  sin  2 (2.67e) g3b  '    1'    2'   1'  sin  2 (2.67f) The plastic potential functions contain a third plasticity parameter, the dilatancy 64 angle  This parameter is required to model positive plastic volumetric strain increments (dilatancy) as actually observed for dense soils For stress states within the yield surface, the behaviour is elastic and obeys Hooke's law for isotropic linear elasticity Hence, besides the plasticity parameters c,  , and  , input is required on the elastic Young's modulus E and Poisson's ratio  2.10.2 Soft soil model 2.10.2.1 Isotropic states of stress and strain 1'   2'   3'  In the Soft-Soil model, it is assumed that there is a logarithmic relation between the volumetric strain,  v , and the mean effective stress, p', which can be formulated as:  p'  '   po   v   v   * ln  (2.68) where  * is the modified compression index, which determines the compressibility of the material in primary loading, as shown in Figure 2.24 The relationship between  * and compressibility index of soil is be expressed as: *  Cc 2.3 1  e0  Figure 2.24 Logarithmic relation between volumetric strain and mean stress 65 (2.69) During isotropic unloading and reloading a different path (line) is followed, which can be formulated as:  p'   p   ve   ve0   * ln  (2.70) where  * is the modified swell index, as shown in Figure 2.24 The relationship between  * and swell index of soil is be expressed as: *  2Cr 2.3 1  e0  (2.71) 2.10.2.2 Yield function for triaxial stress state  2'   3'  The Soft Soil model is capable to simulate soil behaviour under general states of stress However, for clarity, in this section, restriction is made to triaxial loading conditions under which  2'   3' For such a state of stress the yield function of the Soft-Soil model is defined as: f  peq  peq p (2.72) where p eq is related to the actual stress state and, p eq the pre consolidation stress, p is the equivalent pre-consolidation stress, see Figure 2.25 p eq  q2   p ' c cot   M  p ' c cot   (2.73) This stress p eq is a function of the plastic strain p   vp  eq p eq p  p po exp  * *      (2.74) The yield function f can be described as ellipses in the p’-q plane The tops of the 66 ellipses are located on a line with the inclination M In the modified Cam-Clay model (Burland 1965, 1967), the M line represents the critical state line, which describes the stress states at post peak failure It should be noted that in the SS-model, the MCcriterion with the strength parameters  and c is used to describe the failure Both the MC line and the M line are given the same shift of c cot  away from the origin This is illustrated in Figure 2.25 and is taken into account in (Eq 2.73) The total yield contour shown in Figure 2.25 by the bold lines is the boundary of the elastic area The MC failure line is fixed, but the cap (ellipse with p eq p ) may increase due to primary compression Figure 2.25 Yield surfaces of the SS-model in p’-q plane (Neher et al 2001) 2.11 Summary General, PVDs have been widely used to accelerate consolidation of clay deposits However, it is often difficult to predict the displacements and pore pressures accurately due to uncertain factors such as: the equivalent diameter, the filter and apparent opening size, the tensile strength, the discharge capacity and well resistance, smear 67 zone, soil macro fibre, mandrel size and shape, installation procedure, and the drain spacing and influence zone Among these factors, soil disturbance caused by PVD installation and discharge capacity of drains remarkably affect efficiency of the PVD assisted preloading method In this Chapter, the consolidation theory related to PVD-installed deposit was mainly summarized The significant point in literature of PVD-installed deposit can be drawn: - During the placement of the PVD in the ground using a steel mandrel, soil disturbance was created, which is a significant factors that influences the performance of PVDs The determination of the width and hydraulic conductivity of soil disturbance is an important consideration in PVD improvement design Therefore, effect of soil disturbance due to PVD installation is still uncertainty and this topic remains discrepant among researchers - The discharge capacity is a critical parameter controlling the performance of PVDs The discharge capacity usually reduced with increasing effective stress (or with depth) and with consolidation time A reduction in PVD thickness, the clogging of the filter, the deformation of the PVDs cause a reduction in the discharge capacity It causes significant delay in consolidation behaviors of PVD-installed deposits Therefore, discharge capacity of PVDs and its behaviors must be considered in PVD-improvement design - The available theories for the consolidation of soft clayey soil improved by a PVD have been developed using a unit cell model (i.e a cylinder of soil around a single vertical drain) The solutions were well captured effects of soil disturbance and PVD discharge capacity However, these analytical solutions often developed based on small strain theory, although large strain typically 68 occurred in very soft clay deposits - For most projects, the field characteristics is very complex The subsoil is not uniform; the deformation of ground is not always in 1-D condition; construction time and schedule in sites may be dragged or interrupted due to ground stability or construction condition Therefore numerical method, a plane strain numerical analysis was especially used The methods for modelling the effect of prefabricated vertical drain (PVD) in a plane strain finite-element analysis have been reviewed and classified into four groups of using: (a) solid elements; (b) macro-elements, (c) one-dimensional (1D) drainage elements and (d) equivalent vertical hydraulic conductivity (kve) The development of new solutions and the consolidation behavior of PVD- installed deposits considering effects of soil disturbance and discharge capacity reduction are explained in the subsequent chapters 69 CHAPTER AN ANALYTICAL MODEL FOR CONSOLIDATION OF PVD-INSTALLED DEPOSIT CONSIDERING SOIL DISTURBANCE 3.1 General General, the installation of PVDs generates a significant disturbance of the soil around the PVD, which reduces horizontal hydraulic conductivity and increases the compressibility of the soil surrounding the drain (Rujikiatkamjorn et al 2013) These effects cause consolidation delays in PVD-installed soil deposits This disturbed zone significantly affects the rate of settlement and excess pore pressure dissipation In previous analytical solutions (Hansbo 1981; Basu et al 2006; Walker and Indraratna 2006), soil compressibility has been kept constant for both the disturbed and undisturbed zones In numerical analysis, Rujikiatkamjorn et al (2013) considered the compressibility variation of soil in the smear and transition zones using constant void ratio and compression index values Rujikiatkamjorn and Indraratna (2015) developed an analytical solution for radial consolidation incorporating the effects of soil disturbance on soil structure characteristics and horizontal hydraulic conductivity, in which the compressibility variation of soil toward the drain was represented by an average void ratio value This solution did not investigate the effect of increased compressibility on consolidation delay as well as vertical strain variation due to mandrel-induce disturbance Moreover, the transition zone was ignored in solution of Rujikiatkamjorn and Indraratna (2015) Deb and Behera (2017) analyzed the rate of consolidation for stone column ground improvement considering variable hydraulic conductivity and compressibility in the smear zone only They stated that degree of consolidation was significantly influenced due to strength reduction in the smear zone for higher extent of disturbed zone, which causes an increase in the compressibility of 70 ... reduction (1/time) xii Consolidation Analysis of PVD- Installed Soft Deposits Considering Soil Disturbance and Discharge Capacity Reduction Author: Ba-Phu Nguyen Department of Ocean Engineering,... 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. .. (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