Numerical modelling of extraction of spudcans

NUMERICAL MODELLING OF EXTRACTION OF SPUDCANS ZHOU XIAOXIAN NATIONAL UNIVERSITY OF SINGAPORE 2006 NUMERICAL MODELLING OF EXTRACTION OF SPUDCANS ZHOU XIAOXIAN (B.Eng.,M.Eng., Hohai) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CIVIL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2006 i ACKNOWLEDGEMENTS I would like to express my sincere appreciation to my supervisors, Professor Chow Yean Khow and Professor Leung Chun Fai for their guidance and advice given to me at all times. Without their help, the accomplishment of the thesis could not be possible. I am also grateful to Associate Professor Tan Thiam Soon and Associate Professor Lin Pengzhi for their helpful suggestions. I would like to thank the other research students in the dynamic offshore geotechnical research group: Purwana Okky Ahmad, Teh Kar Lu, Xie Yi, Gan Cheng Ti, etc, for valuable discussions in regular group meetings. Especially Okky, who carried out centrifuge tests of the spudcan extraction, deserves my acknowledgement for many useful discussions, suggestions, and providing me with experimental data for comparison with my numerical results. My sincere thanks also go to all other former and current research students in the geotechnical group for their friendship and assistance during my study. Special thanks are given to Dr Gu Qian, Dr Zhang Yaodong, Dr Zhang Xiying, Dr Chen Xi, Dr Phoon Hung Leong, Dr Cheng Yonggang, Mr Zou Jian and Mr Li Liangbo. ii TABLE OF CONTENTS ACKNOWLEDGEMENTS TABLE OF CONTENTS DEDICATION SUMMARY i ii vii viii LIST OF TABLES LIST OF FIGURES LIST OF SYMBOLS Introduction x xi xix 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Modeling of Breakout Phenomenon . . . . . . . . . . . . . . . . . . . . . . . . 1.3 The Need for More Research . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Objectives and Scope of Present Work . . . . . . . . . . . . . . . . . . . . . . 1.5 Overview of Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Literature Review 10 10 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 General Aspects of Finite Element Methods for Problems of Soil Consolidation 11 2.3 2.2.1 Consolidation problems in geotechnical engineering . . . . . . . . . . . 11 2.2.2 Development of finite element methods for consolidation problems . . 11 2.2.3 Discretization of spatial and temporal domains for consolidation problems 12 Low-order Finite Elements in Solid Mechanics . . . . . . . . . . . . . . . . . . 13 2.3.1 Hybrid stress (HS) elements . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.2 Enhanced assumed strain (EAS) elements . . . . . . . . . . . . . . . . 18 2.3.3 Equivalence of HS elements and EAS elements . . . . . . . . . . . . . 19 iii 2.4 2.5 2.6 2.7 2.8 2.9 Low-order Finite Elements for Consolidation Problems . . . . . . . . . . . . . 20 2.4.1 Studies by Pastor et al. (1999) . . . . . . . . . . . . . . . . . . . . . . 22 2.4.2 Studies by Papastavrou et al. (1997) . . . . . . . . . . . . . . . . . . . 22 2.4.3 Studies by Mira et al. (2003) . . . . . . . . . . . . . . . . . . . . . . . 22 2.4.4 Studies by Li et al. (2003) . . . . . . . . . . . . . . . . . . . . . . . . . 23 Finite Element Methods for Prediction of Collapse Loads . . . . . . . . . . . 23 2.5.1 Displacement-based finite element methods with exact integration . . 24 2.5.2 Finite element methods with reduced/selective integration . . . . . . . 25 2.5.3 Finite element methods based on mixed variational principles . . . . . 26 Breakout of Objects Without Soil Failure . . . . . . . . . . . . . . . . . . . . 27 2.6.1 Studies by Sawicki and Mierczy´ nski (2003) . . . . . . . . . . . . . . . 27 2.6.2 Studies by Foda (1982) . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.6.3 Studies by Mei et al. (1985) . . . . . . . . . . . . . . . . . . . . . . . . 30 Breakout of Objects With Soil Failure . . . . . . . . . . . . . . . . . . . . . . 32 2.7.1 Studies by U.S. NCEL in 1960s . . . . . . . . . . . . . . . . . . . . . . 32 2.7.2 Studies by Byrne and Finn (1978) . . . . . . . . . . . . . . . . . . . . 33 2.7.3 Studies by Rapoport and Young (1985) . . . . . . . . . . . . . . . . . 34 2.7.4 Studies by Vesi´c (1971) . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.7.5 Studies by Rowe and Davis (1982) . . . . . . . . . . . . . . . . . . . . 36 2.7.6 Studies by Thorne et al. (2004) . . . . . . . . . . . . . . . . . . . . . . 37 Breakout of Spudcans Completely Embedded in Soft Soil . . . . . . . . . . . 38 2.8.1 Studies by Craig and Chua (1990b) . . . . . . . . . . . . . . . . . . . . 39 2.8.2 Studies by Purwana et al. (2005) . . . . . . . . . . . . . . . . . . . . . 39 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Hybrid and Enhanced Finite Element Methods for Linear Elastic Consolidation Problems 49 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.3 Enhanced Finite Element for Consolidation Problems . . . . . . . . . . . . . 54 3.4 3.3.1 Derivation of enhanced finite element . . . . . . . . . . . . . . . . . . 54 3.3.2 Choice of interpolative functions . . . . . . . . . . . . . . . . . . . . . 58 3.3.3 Recovery of effective stresses and pore fluid fluxes . . . . . . . . . . . 60 3.3.4 Effects of enhanced strains and enhanced pore pressure gradients . . . 62 Hybrid Finite Element for Consolidation Problems . . . . . . . . . . . . . . . 63 iv 3.5 3.6 3.4.1 Derivation of hybrid finite element . . . . . . . . . . . . . . . . . . . . 63 3.4.2 Choice of interpolative functions . . . . . . . . . . . . . . . . . . . . . 65 3.4.3 Faster solution method for hybrid finite element method . . . . . . . . 67 Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.5.1 Stability of pore fluid pressures when approaching undrained limit state 70 3.5.2 Consolidation problems involving variable soil permeability within elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.5.3 Consolidation problems involving materials with high Poisson’s ratio . 71 3.5.4 Related poroelastic problems where bending effect is dominant . . . . 72 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Enhanced Finite Element Method for Prediction of Collapse Loads of Undrained and Consolidation Problems 83 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.2 EAS Element for Elasto-Plastic Undrained Problems . . . . . . . . . . . . . . 85 4.2.1 Finite element formulation . . . . . . . . . . . . . . . . . . . . . . . . 85 4.2.2 Two-dimensional 4-noded elements . . . . . . . . . . . . . . . . . . . . 86 4.2.3 Algorithm for solving non-linear system of equations . . . . . . . . . . 88 4.2.4 Numerical examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Enhanced Element for Elasto-Plastic Consolidation Problems . . . . . . . . . 93 4.3.1 “Initial stress” algorithm for consolidation problems . . . . . . . . . . 94 4.3.2 Numerical examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.3 4.4 Numerical Modelling of the Breakout Process of a Disk at Seabed Surface107 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.2 Numerical Model for No-gap Stage of the Breakout Process . . . . . . . . . . 109 5.2.1 Governing equation for elastic porous seabed . . . . . . . . . . . . . . 110 5.2.2 Derivation of Sawicki and Mierczy´ nski (2003) theory from Biot’s theory 111 5.2.3 Finite element model for no-gap stage . . . . . . . . . . . . . . . . . . 112 5.2.4 Comparisons between the present numerical model and Sawicki and Mierczy´ nski (2003) theory . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.3 5.2.5 Non-dimensional analysis for no-gap stage . . . . . . . . . . . . . . . . 115 5.2.6 Parametric study for no-gap stage . . . . . . . . . . . . . . . . . . . . 116 5.2.7 Criterion for separation of disk from seabed surface . . . . . . . . . . . 116 Numerical Model for With-gap Stage of the Breakout Process . . . . . . . . . 117 v 5.3.1 Governing equation for fluid motion in tiny gap . . . . . . . . . . . . . 118 5.3.2 Derivation of the numerical model for the with-gap stage . . . . . . . 119 5.3.3 Implementation of the present numerical model . . . . . . . . . . . . . 122 5.3.4 Extension theory of Mei et al. (1985) . . . . . . . . . . . . . . . . . . . 125 5.3.5 Non-dimensional analysis for with-gap stage . . . . . . . . . . . . . . . 127 5.3.6 Comparisons between the present numerical model and the extension theory of Mei et al. (1985) . . . . . . . . . . . . . . . . . . . . . . . . . 130 5.3.7 Parametric study for with-gap stage . . . . . . . . . . . . . . . . . . . 131 5.4 Transition Stage to Link No-gap Stage and With-gap Stage . . . . . . . . . . 132 5.5 Numerical Model for Whole Breakout Process . . . . . . . . . . . . . . . . . . 132 5.6 5.5.1 Numerical model for whole breakout process . . . . . . . . . . . . . . 133 5.5.2 Verification of numerical model for whole breakout process . . . . . . 134 5.5.3 Parametric studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 Numerical Modelling of the Breakout Process of Spudcan Partially Embedded in Seabed 167 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 6.2 Modification of the Previous Numerical Model 6.3 Effect of Angle α on the Breakout Time . . . . . . . . . . . . . . . . . . . . . 171 6.4 Parametric Studies for the Breakout Process of Spudcan . . . . . . . . . . . . 172 6.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 . . . . . . . . . . . . . . . . . 168 Numerical Modelling of the Breakout Process of Spudcan Completely Embedded in Seabed 183 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 7.2 Finite Element Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 7.3 7.2.1 Finite element mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 7.2.2 Choice of constitutive model . . . . . . . . . . . . . . . . . . . . . . . 187 7.2.3 Sequence of analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 7.2.4 Stress field after installation of spudcan . . . . . . . . . . . . . . . . . 191 7.2.5 Validation of assumed stress field . . . . . . . . . . . . . . . . . . . . . 195 Comparison of Numerical Results and Centrifuge Results . . . . . . . . . . . 198 7.3.1 Effect of waiting time . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 7.3.2 Effect of ratio of maintained vertical load over maximum installation load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 vi 7.4 7.5 Failure Mechanism in Extraction Process . . . . . . . . . . . . . . . . . . . . 205 7.4.1 Separation of spudcan base from soil beneath . . . . . . . . . . . . . . 205 7.4.2 Displacement vector field . . . . . . . . . . . . . . . . . . . . . . . . . 206 7.4.3 Excess pore pressure field . . . . . . . . . . . . . . . . . . . . . . . . . 207 7.4.4 Plastic strain magnitude field . . . . . . . . . . . . . . . . . . . . . . . 208 7.4.5 Effective stress path . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 Parametric Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 7.5.1 Effect of waiting time . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 7.5.2 Effect of ratio of maintained vertical load over maximum installation load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 7.6 7.5.3 Effect of pullout rate of spudcan . . . . . . . . . . . . . . . . . . . . . 212 7.5.4 Effect of soil permeability . . . . . . . . . . . . . . . . . . . . . . . . . 213 7.5.5 Effect of penetration depth of spudcan . . . . . . . . . . . . . . . . . . 214 7.5.6 Effect of geometric size of spudcan . . . . . . . . . . . . . . . . . . . . 216 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 Conclusions 273 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 8.2 Main Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 8.3 Areas for Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 8.3.1 Extending numerical model for partially embedded spudcans to objects with any geometric shape . . . . . . . . . . . . . . . . . . . . . . . . . 278 8.3.2 Modeling installation process of spudcans . . . . . . . . . . . . . . . . 279 8.3.3 Using large strain finite element method for completely embedded spudcans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 REFERENCES 280 vii To my family viii SUMMARY Spudcans are used extensively as foundations of mobile jack-up rigs in the offshore industry. As jack-up rigs are usually not permanent structures, they would be moved from one location to another. Therefore, spudcans need to be extracted from the sea bottom after each operation. The objectives of this research were to develop numerical models to simulate the breakout process of spudcans from the sea bottom and to get a better understanding of the problem using the numerical models developed. The hybrid and enhanced finite element methods with bi-linear interpolations for both the solid displacements and the pore fluid pressures were derived based on mixed variational principles for problems of elastic soil consolidation. Both of these two low-order elements could eliminate the oscillations of nodal pore pressures even in the undrained conditions, would not cause volumetric locking and shear locking, and are insensitive to mesh distortions. Thereafter, the plane strain and axisymmetric enhanced elements developed for elastic consolidation problems were extended to elasto-plastic problems and such elements were demonstrated to be capable of predicting the collapse loads accurately. The enhanced consolidation elements were used later in the numerical models for simulation of the breakout process of spudcans. Spudcans may be either partially or completely penetrated into the seabed depending on the loading, seabed condition and geometric size of the spudcans. In this thesis, firstly, a numerical model was developed to simulate the breakout process of a circular disk initially lying on the seabed surface, thereafter, it was extended to simulate the breakout process of a partially penetrated spudcan. In the numerical model, the soil was assumed to be linear elastic and the breakout process was assumed to comprise three stages in sequence: no-gap stage, transition stage and with-gap stage. The whole breakout process could be simulated consistently by solving a consolidation problem of the seabed subjected to different boundary conditions in the three stages at the seabed surface. The numerical results were compared to some available theoretical and experimental published results. Thereafter, some parametric studies were performed using the numerical model for the breakout process of the spudcan. Another finite element model was developed to simulate the breakout process of spudcans 8.2: Main Findings 274 ter, 1970, 1971; Sandhu et al., 1977). Both plane strain and axisymmetric problems were studied. It was found that by choosing appropriate interpolation of enhanced strains in the enhanced method, and by choosing appropriate interpolations of strains, effective stresses and enhanced strains in the hybrid method, the oscillations of nodal pore pressures could be eliminated. Several numerical examples demonstrating the capability and performance of the enhanced and hybrid finite element methods were presented. It was also shown that for some situations, such as problems involving high Poisson’s ratio and in other related problems where bending effects are evident, the performance of the enhanced and hybrid methods were superior to that of the conventional displacement-based method. The results from the hybrid method were better than those from the enhanced method for some situations, such as problems in which soil permeability is variable or discontinuous within elements. Since all the element parameters except the nodal displacements and nodal pore pressures were assumed at the element level and could be eliminated by static condensation, the implementations of the enhanced method and the hybrid method were basically the same as the conventional displacement-based finite element method. The present enhanced method and hybrid method could be extended to non-linear consolidation problems. Since the extension of the hybrid method is more difficult, only the enhanced method was extended to non-linear consolidation problems in this research. Many low-order displacement-based finite elements with exact integration are not suitable for estimating collapse loads of undrained geotechnical problems, especially for axisymmetric cases (Sloan and Randolph, 1982). As a result, higher-order elements have to be used for these situations. In this research, the enhanced assumed strain (EAS) finite element method proposed by Simo and Rifai (1990) for elasticity problems were extended to plasticity problems to determine collapse loads. The numerical results for the problem of a smooth rigid surface footing on a deep purely cohesive undrained soil layer were given. It was demonstrated that the 4-noded quadrilateral EAS finite element is capable of estimating the collapse loads accurately for both undrained plane strain and axisymmetric problems. Based on the above work, the plane strain and axisymmetric enhanced elements developed for elastic consolidation problems were extended to plasticity soil consolidation prob- 8.2: Main Findings 275 lems. The low-order consolidation element could predict not only collapse loads accurately, but could also suppress the oscillation of the nodal pore pressures even when the undrained condition is approached. The enhanced consolidation elements were used in the numerical models developed to simulate the breakout process of spudcans. Spudcans may either be partially or completely penetrated into the seabed depending on the loading, seabed condition and geometric size of spudcans, etc. Since different physical mechanisms are involved in these two situations, different numerical models were developed in this research. Firstly, the breakout process of a circular disk initially resting at the seabed surface was studied. Thereafter, the numerical model developed for the disk at the seabed surface was extended to the partially penetrated spudcan problem. In the numerical model, the seabed was assumed to be elastic and porous, and the objects (disk or spudcan) were assumed to be rough and rigid. The breakout process was assumed to comprise three stages in sequence: no-gap stage, transition stage and with-gap stage. The no-gap stage was defined from the time when the uplift force is applied on the disk to the time when the disk begins to be separated from the seabed surface. The transition stage was defined from the time when the disk begins to be separated from the seabed surface to the time when the disk is separated from the seabed surface by a tiny gap. And the with-gap stage was defined from the time when the disk is separated from the seabed surface by a tiny gap to the time when the disk is lifted up. In the numerical model, Biot’s consolidation theory was employed as the governing equations for the seabed in all the above three stages. The numerical model developed in this research could simulate the whole breakout process consistently, in which we only need to solve a consolidation problem of the seabed subjected to different boundary conditions in the no-gap stage, transition stage and with-gap stage at the seabed surface. Some numerical predictions for the whole breakout process of the disk initially lying on the soil surface were compared with the experimental results provided in Sawicki and Mierczy´ nski (2003) and was found that they were in fair agreement. The numerical model was used to perform some parametric studies for the breakout process of a disk resting on the seabed surface and a spudcan partially penetrated into the 8.2: Main Findings 276 seabed. It was found that the Young’s modulus and the Poisson’s ratio of the seabed affect the no-gap stage and the transition stage significantly, whereas their influence on the withgap stage may be neglected when strong seabed (> 10MPa) and not very large net unit force (< 10kPa) were involved. The time durations of both the no-gap stage and the transition stage were approximately inversely proportional to the Young’s modulus and the permeability of the soil, and were related to the ratio of the total uplift force over the submerged weight of the disk. It was also found that the time duration of the with-gap stage was approximately inversely proportional to the net uplift force and proportional to k −2/3 , where k is the soil permeability. The time durations required by the three stages were also compared and it was shown that the relative magnitudes of these time durations depend on the parameters involved and it would be difficult to decide a priori which stage is dominant during the breakout process. In the final part of this research, a finite element model based on the enhanced method was developed to simulate the breakout process of spudcans completely embedded in soft soil. In this model, a form of the modified Cam clay constitutive model originally proposed by Roscoe and Burland (1968) was used, in which the yield and plastic potential surfaces are given by a Mohr-Coulomb hexagon and a circle respectively in the deviatoric plane. The finite element model was verified through back-analyzing the centrifuge tests by Purwana et al. (2005). In the finite element model, the stress field immediately after the installation of the spudcan should be known in order to simulate the extraction of the spudcan. From the stress field immediately after the installation of the spudcan we can obtain the stress field at the initial stage of the extraction process after simulating the preloading stage by reducing the maximum installation load to the maintained vertical load and allowing consolidation of the soil to take place to simulate the operation period of the spudcan. However, because of the complexity of the spudcan installation process which would involve large displacements and large strains, certain assumptions were made to approximate the state of stresses in the soil after the installation of the spudcan. In the finite element model, initially, the spudcan was assumed to be “wished-in-place” at a predetermined depth of the soil. The analysis procedure involved four steps: (1) using assumptions to approximate the effective 8.2: Main Findings 277 stress field and the excess pore pressure field in the soil above the spudcan top after the installation of the spudcan. The effective stress field and the excess pore pressure field in the soil below the spudcan base after the installation of the spudcan were obtained by applying load on the spudcan until bearing failure of the soil beneath is achieved. The maximum installation load on the spudcan is the load on the spudcan at the end of this stage, (2) reducing the maximum installation load on the spudcan to the maintained vertical load, (3) letting the soil consolidate for a predetermined time, i.e. the operation (waiting) time, and (4) applying uplift force to extract the spudcan. The numerical results were compared to the comprehensive experimental results of Purwana et al. (2005) and it was found that they were in good agreement. After the development and verification of the finite element model, some parametric studies were also performed using the finite element model, in which the properties of the Singapore lower marine clay was used for the soil instead of the Malaysia kaolin clay used in Purwana et al. (2005). In addition to the effects of waiting time and ratio of the maintained vertical load over the maximum installation load on the breakout process of the spudcan examined in Purwana et al. (2005), the effects of the pullout rate of the spudcan, permeability of the soil, penetration depth of the spudcan, and geometric size of the spudcan were studied. It was found that for the marine clays, the breakout force increases considerably with the elapse of the waiting time, and the increase of the breakout force is attributable mainly to the increase in the suction force at the base of the spudcan. With an increase in the ratio of the maintained vertical load over the maximum installation load, the breakout force will also increase. These conclusions are similar to those obtained using the Malaysia kaolin clay in Purwana et al. (2005). It was also found that for marine clays, the breakout force does not change significantly when usual pullout rate of the spudcan (10−5 m/s ∼ 10−2 m/s) is used. The soil permeability (10−5 m/s ∼ 10−10 m/s) will affect the breakout force significantly since the consolidation of the soil during the waiting time is closely related to the soil permeability and the excess pore pressures in the soil before the extraction of the spudcan will influence the breakout force significantly. Utilizing the finite element results, there was an attempt to relate the breakout force to the maximum installation load. The ratio of the difference 8.3: Areas for Future Research 278 between the breakout force and the top resistance at breakout over the maximum installation load is related to the soil properties, the waiting time and the geometric size of the spudcan. For the Singapore marine clay and the spudcan with 12.5m diameter used in Purwana et al. (2005), it was found that the ratio is 10% when the waiting time is zero and is 30% when the waiting time is 2000 days (5.4 years) for all the cases with various spudcan penetrations. To eliminate the effect of the geometric size of the spudcan on the soil consolidation during the waiting time, different waiting times are used for spudcans with different geometric sizes by letting them have the same adjusted time factor c¯t/R2 , where c¯ is the adjusted coefficient of consolidation, t is the waiting time and R is the radius of the widest part of the spudcan. After the above adjustment of the waiting time, it was found that the ratio of the difference between the breakout force and the top resistance at breakout over the maximum installation load is approximately constant for all the cases involving spudcans with different geometric sizes. The top resistance at breakout does not vary significantly with the variation of the waiting time and may be approximated as the buoyant weight of the soil above the spudcan. As a result, the breakout force could be estimated from the maximum installation load if the ratio of the difference between the breakout force and the top resistance at breakout over the maximum installation load is known. 8.3 Areas for Future Research Because few numerical/analytical models for the breakout phenomenon could be found in the public domain, there is much scope for future research. 8.3.1 Extending numerical model for partially embedded spudcans to objects with any geometric shape In this research, only axisymmetric objects, i.e. disk and spudcan, were considered in the numerical model when simulating the breakout process of objects lying on the seabed surface or partially embedded in the seabed. For an object with plane strain or axisymmetric geometric shape, the governing equations for the fluid motion in the tiny gap between the object and the seabed surface can be solved analytically in the with-gap stage. Consequently, the with-gap stage in the breakout process could be handled by converting the coupled disk- 8.3: Areas for Future Research 279 fluid-seabed interaction into appropriate boundary conditions at the seabed surface below the object. However, for an object with any geometric shape, numerical methods may have to be used to solve the governing equations for the fluid motion in the tiny gap. 8.3.2 Modeling installation process of spudcans In this research, the spudcan was “wished-in-place” at the predetermined depth, and thereafter some approximations were used to obtain the effective stress field and excess pore pressure field in the soil immediately after the installation of the spudcan so that the simulation of the complex installation process of the spudcan was avoided. However, this is an approximate method and soil remoulding is not simulated. Therefore, the simulation of the installation process of the spudcan would be necessary to study how it cause changes in the soil properties. 8.3.3 Using large strain finite element method for completely embedded spudcans For the breakout process of the spudcan completely embedded in soft soil, the breakout force will not be achieved until the displacement of the spudcan is quite large (about 15% of the diameter of the spudcan). In this research, small strain finite element method was used to simulate the breakout process. Though the results from the small stain finite element model were satisfactory compared to the experimental results presented in Purwana et al. (2005), large strain finite element method is recommended for future research in order to capture more details of the breakout process of the spudcan. 280 REFERENCES Abu-Farsakh, M., M. Tumay and G. Voyiadjis. 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Comparison of time durations of with-gap stage from present numerical model µk and extension theory of Mei et al (1985), where = 10−12 γw R 2 Comparison of time durations of the with-gap stage from present numerical µk model and extension theory of Mei et al (1985), where = 10−14 γw R2 Comparison of time durations of with-gap stage from present numerical model µk and extension theory of Mei... size of spudcans, where d is penetration depth of spudcan and D is diameter of spudcan 270 7.58 Maximum installation load, breakout force and force components at breakout divided by area of widest section of spudcan corresponding to various geometric size of spudcans, where d is penetration depth of spudcan and D is diameter of spudcan 271 7.59 Ratios of. .. seems that no numerical/ analytical model is available in the public domain to simulate the breakout process of spudcans 1.3 The Need for More Research Extraction of spudcans from the sea bottom is one of the critical phases in jack-up operations (Young et al., 1984) Usually the extraction is carried out by the machinery on the platform In the offshore industry, the typical extraction rate of spudcans is... in the field, usually the extraction of spudcans from the sea bottom is difficult, especially when spudcans are deeply penetrated into soft clay An approach commonly used in the field operations to ease the extraction is by moving spudcans upward and downward continuously in a cyclic manner The aim of this approach is to weaken the soil around spudcans However, the effectiveness of this approach in the field... vector of local element parameters of enhanced strains ∗ Convolution integral Chapters 5 & 6: d Vertical displacement of object E Young’s modulus F Uplift force F1 Vertical working load plus buoyant weight of spudcan F2 Uplift force minus buoyant weight of spudcan F Uplift force excess of submerged weight of object G Shear modulus G Submerged weight of object h Vertical displacement of object H Depth of. .. National University of Singapore to investigate the breakout phenomenon of spudcans and for which some useful conclusions have been obtained (Purwana et al., 2005; Purwana, 2007), the development of numerical models is still helpful to give a better understanding of the breakout of spudcans Further, it is expected to predict the extraction force and time required for the breakout of spudcan with reasonable... present numerical model The present numerical results were compared with published theoretical and experimental results 3 Developing numerical model for uplift problem of completely embedded spudcan When the subsurface soil is soft, spudcans may be completely embedded into the seabed A numerical model was developed to simulate the breakout of completely embedded spudcan in soft soil In the numerical. .. used in numerical analyses (axisymmetric 4-noded elements), where disk is not included in the mesh 151 5.13 Effect of Young’s modulus of soil on time duration of with-gap stage 153 5.14 Comparison of relationships between normalized time and normalized displacement of disk from present numerical model and extension theory of Mei et al (1985), where d is uplift displacement of disk... extraction rate of spudcans is about 7mm/s with a total jacking capacity of around 15, 000tons (Keppel, 2006) The penetration of spudcans depends mainly on the geometric shapes of spudcans, the subsurface soil condition and the preload applied The extraction is more difficult when the seabed is soft resulting in the deep penetration of spudcans (which can be about 2∼3 spudcan diameters) The delay or inability... problem in Chapter 5 to simulate the breakout process of spudcans partially embedded in the seabed Chapter 7 describes the numerical model developed to simulate the breakout process of spudcans completely embedded in soft seabed Verification of the numerical model and some parametric studies are also presented Chapter 8 summarizes the results and conclusions of the research and presents some recommendations . NUMERICAL MODELLING OF EXTRACTION OF SPUDCANS ZHOU XIAOXIAN NATIONAL UNIVERSITY OF SINGAPORE 2006 NUMERICAL MODELLING OF EXTRACTION OF SPUDCANS ZHOU XIAOXIAN (B.Eng.,M.Eng.,. capable of predicting the collapse loads accurately. The enhanced con- solidation elements were used later in the numerical models for simulation of the breakout process of spudcans. Spudcans. Comparison of time durations of with-gap stage from present numerical model and extension theory of Mei et al. (1985), where µk γ w R 2 = 10 −12 . . . . . . . . . 140 5.6 Comparison of time durations of