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Settlement of structures on soft clay deposits results from flow and consolidation of soil. In the latter case, water squeezes out from under the structure, whereas in the former case soil squeezes out. Settlement resulting from flow of soil depends on the factor of safety against undrained instability. In construction situations where the factor of safety is small, an accurate prediction of settlement reSUlting from flow of soil is required. Field measurements of horizontal deformation of soft clays during and after construction of embankments and storage facilities have been collected from throughout the world, covering 180 case histories, to relate lateral deformation to the factor of safety and to develop a practical procedure for computing settlements resulting from flow of soil.

- 1. GEOTECHNICAL ENGINEERING Dr. Malek Smadi Ph.D. Thesis LATERAL DEFORMATION AND ASSOCIATED SETTLEMENT RESUL TING FROM EMBANKMENT LOADING OF SOFT CLAY AND SILT DEPOSITS THESIS Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Civil Engineering in the Graduate College of the University of Illinois at Urbana-Champaign, 2001 Urbana, Illinois 14074 Trade Center Drive, Suite 102 Fishers, IN 46038 Ph. 317-449-0033 Fax 317- 285-0609 (info@geotill.com) Geotechnical, Environmental and Construction Materials Testing Professionals www.geotill.com GEOTILL Inc. Geotechnical Engineering Subsurface Exploration Environmental Services Construction Testing and Material Engineering
- 2. LATERAL DEFORMATION AND ASSOCIATED SETTLEMENT RESULTING FROM EMBANKMENT LOADING OF SOFT CLAY AND SILT DEPOSITS Volume I ofII BY MALEK M. SMADI B.s., Jordan University of Science and Technology, 1988 M.S., Jordan University of Science and Technology, 1991 THESIS Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Civil Engineering in the Graduate College of the University of Illinois at Urbana-Champaign, 2001 Urbana, Illinois
- 3. © Copyright by Malek M. Smadi, 2001
- 4. UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN GRADUATE COLLEGE JANUARY 2001 date WE HEREBY RECOMMEND THAT THE THESIS BY MALEK M. SMADI ENTITLED LATERAL DEFORMATION AND ASSOCIATED SETTLEMENT RESULTING FROM EMBANKMENT LOADING OF SOFT CLAY AND SILT DEPOSITS BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY ~~ Director of Thesis Research Head of Department tRequired for doctor's degree but not for master's. 0-517
- 5. LATERAL DEFORMATION AND ASSOCIATED SETTLEMENT RESULTING FROM EMBANKMENT LOADING OF SOFT CLAY AND SILT DEPOSITS Malek M. Smadi, Ph.D. Department of Civil Engineering University oflllinois at Urbana Champaign, 2001 Gholamreza Mesri, Advisor Settlement of structures on soft clay deposits results from flow and consolidation of soil. In the latter case, water squeezes out from under the structure, whereas in the former case soil squeezes out. Settlement resulting from flow of soil depends on the factor of safety against undrained instability. In construction situations where the factor of safety is small, an accurate prediction of settlement reSUlting from flow of soil is required. Field measurements of horizontal deformation of soft clays during and after construction of embankments and storage facilities have been collected from throughout the world, covering 180 case histories, to relate lateral deformation to the factor of safety and to develop a practical procedure for computing settlements resulting from flow of soil. The available methods for predicting the undrained settlement and lateral deformation, including solutions based on elasticity, empirical procedures, and numerical techniques, were reviewed. The behavior of clay foundations subjected to embankment loading and empirical methods using lateral deformation as a measure of undrained stability, were reviewed and discussed. The 180 case histories of embankments on soft clay and silt deposits with lateral deformation measurements cover a wide range of subsurface conditions, including plasticity index Ip from 5 to 340, undrained shear strength Su from 5 to 80 kPa, Eu/su from 200 to 1000, cr/plcr/vo from 1 to 5, embankment width B from 8.5 m to 630 m, embankment height h from 1 to ill
- 6. 35m, embankment slope width L from 1.35 to 195 m, and depth of foundation Lo from 7 to 63 m. An empirical correlation, based on 58 cases was developed between maximum lateral deformation Dm or area of lateral deformation profile AD and factor of safety against undrained failure. Parameters such as Eu, L, B/2 were also included in the correlation. A procedure, based on 16 cases with three or more inclinometers at several distances from the centerline, was developed for determining distribution of maximum lateral deformation and flow settlement across the embankment as a function of LoIB and UO.5B. The procedure could be used either with one inclinometer measurement e.g. near the toe of the embankment, or together with the empirical correlation between Dm and factor of safety. A procedure was developed for determining settlement trough resulting from lateral deformation of soil out from under the embankment. The procedure could be used together with inclinometer measurements at one location, e.g. near the toe of the embankment or with Dm or AD determined from the empirical correlation between lateral deformation and factor of safety. Using the empirical database and the developed procedures, it was possible to make successful prediction of lateral deformation and associated settlement for embankments on soft clay and silt deposits. IV
- 7. ACKNOWLEDGMENTS This thesis is based on theoretical and empirical studies of field observations conducted at the University of lllinois. It has been prepared under the direct supervision of Dr. G. Mesri, Ralph B. Peck Professor of Civil Engineering, to whom the writer is indebted for his constructive criticism, guidance, and encouragement in the preparation of the manuscript. During graduate study, the writer was employed part time in the office of Minority Student Affairs. Special acknowledgement is due Mr. Otis Williams, Associate Director of Minority Student Affairs at University of lllinois for his valuable help. Special thanks are extended to Professors E. J. Cording, J. H. Long, T. D. Stark, and Dr. G. Fernandez for their encouragement during writer's graduate study at the University of lllinois. The writer wishes to thank his office mates Dr. H. Eid and Mr. B Vardhanabhuti, and Dr. M. Shahain, M. Al-zoubi, M. Ajlouni, V. Schifano, and M. Maniaci, graduate students at the University of lllinois, for discussions and constructive criticism during the preparation of this thesis. The author wishes to express his gratitude to the Department of Civil Engineering and the National Science Foundation (NSF) for their continued support during writer's graduate study at the University of lllinois at Urbana Champaign. Finally the writer gratefully appreciates the continued encouragement, support and patience of his parents, brothers, and sisters throughout his education. v
- 8. TABLE OF CONTENTS Page CHAPTER 1 INTRODUCTION.................................................................. 1 1.1 Statement of the Problem.................................................... 1 1.2 Objectives of the Study ....................................................... 3 1.3 Scope ..............................................................................".... 4 CHAPTER 2 PREDICTION OF SETTLEMENT AND LATERAL DEFORMATIONS.......................................... 6 2.1 Introduction ...................................................................... 6 2.2 Prediction of Undrained Settlement and Lateral Deformation Using Theory of Elasticity.............. 6 2.2.1 Flow Settlement........................................................... 6 2.2.2 Lateral Defolmation .................................................... 9 2.3 Prediction of Settlement and Lateral Deformation Using Constitutive Models.............................................. 11 2.3.1 Constitutive Models .................................................. 11 2.3.2 Implementing Finite Element Analysis on Case Histories............................................................ 12 2.3.3 Prediction of Deformations by The Finite Element Method ............................................. 16 2.4 Predictions of Deformations Using Empirical procedures....................................................... 17 2.4.1 Undrained Settlement................................................ 17 vi
- 9. 2.4.2 Lateral Deformation during Construction ................ 20 2.4.3 Long Term Lateral Deformation............................... 22 2.4.4 Lateral Deformation during Stage-construction....... 23 2.4.5 Effect of Vertical Drains on Lateral Deformation.... 24 2.4.6 Field Deformation Analysis (FDA) ......................... 25 2.4.6.1 Loading Stage...................................................... 25 2.4.6.2 Post-Loading Stage ............................................. 30 CHAPTER 3 BILHAVIOR OF CLAY FOUNDATIONS SUBJECTED TO E:MBANKMENT LOADING ........................................ 67 3.1 Yielding of Clay Foundations Subjected to Embankment Loading......"................................................. 67 3.1.1 Yielding of Clay Structure............................................ 67 3.1.2 Yielding of Clay Foundation under Embankments ..... 68 3.1.3 Foundation Behavior Described Using Effective Stress Path ..................................................................... 69 3.2 Parewater Pressures in Clay Foundations under Embankments ........................................................... 72 3.2.1 Porewater Pressure Predictions during Single Stage Embankment Construction................................. 72 3.2.2 Porewater Pressure Changes During Construction.................................................................. 75 3.3 Lateral Deformation with Depth......................................... 81 3.3.1 Effect of Soil Type on the Distribution of Lateral Deformation ................................................. 81 3.3.2 Effect ofLc/B on the Distribution of V11
- 10. Lateral Deformation ..................................................... 81 3.3.3 Effect of Preconsolidation Pressure on the Distribution of Lateral Deformation ............................ 81 3.3.4 Effect of Time on the Distribution of Lateral Deformation ..................................................... 84 3.3.5 Prediction of the Normalized Lateral Deformation Profile...................................................... 84 3.4 Stability Analysis of Embankments on Soft Clay Foundations ................................................................ 85 3.4.1 Choosing Values for the Undrained Strength .............. 86 3.4.1.1 Vane Tests............................................................... 86 3.4.1.2 The Mobilized Undrained Shear Strength ............. 87 3.4.2 The Value of Factor of Safety that Triggers an Abrupt Increase in Rate of Lateral Deformation .... 88 3.5 Shear Stress Level and Undrained Shear Deformations .... 89 3.6 Undrained Modulus of Soft Clay and Silt Deposits........... 92 3.7 Lateral Deformation under Reinforced Embankments ...... 94 CHAPTER 4 CONTROL OF ElfBANKMENTS CONSTRUCTION BY OBSERVING LATERAL DEFORMATION .......... 131 4.1 Measurement of Dm and St.............................................. 131 4.2 Evaluation of AD and As ................................................. 132 4.3 UsingHorizontal Displacement, Fill height, and Time....................................................... 133 4.4 Horizontal Displacement at the Surface and the Factor of Safety .................................................. 133 4.5 Dm/St and St ..................................................................... 134 viii
- 11. 4.6 Lateral Deformability Factor and Total Load (~q/M)m and q) ) ......................................... 136 4.7 Other Methods.............................................................·.... 137 4.8 Maximum Lateral Deformation and Factor of Safety Against Undrained Failure .............................. 139 4.9 Non-dimensional Lateral Deformation Analysis .......... 140 CHAPTER 5 CASE mSTORIES .............................................................. 193 CHAPTER 6 PREDICTING SETTLEMENT RESULTING FROM LAT~RAL DEFORMATION ...,....................................... 330 6.1 Introduction ..................................................................... 330 6.2 Lateral Deformation Profile............................................ 332 6.3 Lateral Displacement Volume of Soil and Associate Settlements ...................................................................... 333 6.3.1 Methodology ............................................................. 333 6.3.2 Deformability factor ................................................. 335 6.3.3 Effect of Embankment Width and Foundation Thickness on Consolidation..................................... 336 6.4 Deformation of Lateral Across Embankment Width ..... 338 6.4.1 Lateral Deformation Distribution Across Embankment Width.................................................. 338 6.4.2 Prediction of Lateral Deformation Across Embankment Width .................................................. 339 6.5 Settlement Trough........................................................... 343 6.5.1 Total Settlement Trough ........................................... 343 6.5.2 Undrained Settlement trough.................................... 343 1X
- 12. 6.6 Prediction of Undrained Settlement ............................... 346 6.7 Undrained Settlement Prediction for Embankment 1-95 Sec 246 Using the Proposed Method...................... 351 6.7.1 The Influence of the Inclinometer Location on the Predicted Undrained Settlement for Embankment 1-95 Sec 246 Using the Proposed Method................. 352 6.7.2 Undrained Settlement Prediction for Embankment 1-95 Sec 246 Using the Proposed Method and the Giroud (1973) Method................................. 352 6.7.3 Undrained Settlement Prediction for Embankment . 1-95 Sec 246 Using the Proposed Method and Poulos (1972b) Method ..................................... 353 6.7.4 Maximum Lateral Deformation Profile Across the Embankment Width for 1-95 Sec 246 using the proposed method and MIT-E3 .......................... 353 6.7.5 Maximum Lateral Deformation Profile Across the Embankment Width for Rio de Janeiro Trial Embankment Using the Proposed Method and CRISP........................................................................ 354 6.8 Total Settlement Prediction forEmbankment 1-95 Sec 246 using ILL1CON for Consolidation Settlement and the Proposed Method for the Undrained Settlement........................................................................... 355 6.8.1 Introduction ............................................................... 355 6.8.2 One Dimensional Settlement Analysis for Embankment 1-95 Sec 246 Using ILLICON............. 356 x
- 13. CHAPTER 7 SUMMARY AND CONCLUSIONS................................. 546 7.1 Summary ......................................................................... 546 7.2 Conclusions ..................................................................... 551 REFERENCES ............................................................................................. 557 APPENDIX A ................................................................................................ 593 APPENDIX B ............................................................................................. 595 VITA ............................................................................................................... 602 Xl
- 14. A AD Af As Asu B B cy D e LIST OF SYMBOLS Porewater-pressure coefficient Volume of soil per unit length of embankment that displaces laterally, measured at the toe. Pore pressure parameter A at (crl - cr3)max Total volume of soil per unit length of embankment and B/2 that displaces vertically. Volume of soil per unit length of embankment and B/2 that displaces vertically due to lateral flow of soil = AD Coefficient of compressibility Width of the loaded area The ratio of incremental excess porewater pressure to the incremental mean effective stress Compression index Permeability change index, ile/log k Swelling index Secondary compression index Coefficient of consolidation Lateral deformation at any depth Maximum lateral deformation Largest maximum lateral deformation across the embankment width Lateral deformation at ground surface Undrained Young's modulus Drained modulus Void ratio xii
- 15. EOC EOP FS G IDC K Ko KoUC KoUE k Initial void ratio End of construction End of primary consolidation Factor of safety Undrained shear modulus Specific gravity of solids Height of the embankment Threshold height or critical height Influence value, depending on the shape of the loaded area and the depth of the elastic layer Isotropic (equal all-round pressure) consolidated drained compression test Influence value, depending on the geometry of the problem Liquidity index Plasticity index Isotropic (equal all-round pressure) consolidated undrained compression test Lateral stress ratio (dh/ d v) Coefficient of Earth Pressure at rest Laterally constrained consolidated undrained compression test Laterally constrained consolidated undrained extension test Permeability Permeability in the vertical direction Permeability in the horizontal direction Width of the embankment slope Thickness of the compressible layer Non-dimensional Deformation Method Lateral deformation at certain depth z / Maximum lateral X111
- 16. Nz NZsum pi Su Su (ruC) Su (ruE) Su (KoUC) Su (KoUE) Su (mob) Su (vane) USSA UU deformation (= DlDm) Depth of certain point at depth z 1Whole depth of the lateral deformation profile (= z/ZD Depth of Maximum lateral deformation 1Whole depth of the lateral deformation profile (= Zrr/ZI = 0.26 ± 0.14) Depth of minimum undrained shear strength 1Total depth of the lateral deformation profile (dl +d3)12, (dy + d h)12 (d1 - d 3)12, (dy - d h)12 Net foundation pressure. Consolidation settlement The end-of-primary settlement resulting from compression of the voids Shear stress level Maximum settlement at the center The undrained shear settlement resulting from lateral deformation of the foundation soil Maximum undrained settlement across the embankment width Undrained shear strength Undrained strength from ruc test Undrained strength from ruE test Undrained strength from KoUC test Undrained strength from KoUE test Mobilized undrained shear strength Undrained vane shear strength Undrained Strength Stability Analysis Unconsolidated undrained test XlV
- 17. Wf Water content at failure defined at, (0"1 - 0"3)ma:x/2 w o Natural water content WI Liquid limit wp Plastic limit z Depth of any point in the foundation soil ZI Depth of influence of lateral deformation Zm Depth of maximum lateral deformation a Deformability factor ~ Side slope of the embankment mm Increment of maximum lateral deformation near the toe per increment of time Llu /'),V y Loading Pressure Increment of maximum settlement at the center per increment of time Excess porewater pressure Shear induced excess porewater pressure Volume change Strain Axial strain Axial strain at failure, (d1 - d3)ma:x/2 Radial strain Volumetric strain Unit weight In situ effective vertical stress, effective overburden pressure Final effective vertical stress xv
- 18. d ho d ve d p qY <j>'m <j>'d V In situ effective horizontal stress Vertical consolidation stress Preconsolidation pressure Friction angle Mobilized friction angle at (d1 - d 3)max/2 Drained friction angle Poisson's ratio XV1
- 19. CHAPTER 1 INTRODUCTION 1.1 Statement of the Problem When an embankment load is rapidly applied to a deposit of saturated clay, the clay deforms at constant volume to accommodate the imposed shear stresses. The settlement associated with these deformations, which occurs without significant dissipation of excess porewater pressures, is called undrained settlement. Evaluation of the undrained settlement of structures on clay is important for a number of reasons. First, Undrained settlement may constitute a large portion of the total final settlement, depending on the nature of the soil, the loading geometry, and the thickness of the compressible layer. Second, analysis of undrained settlement is an integral part of the analysis of the overall settlement-time behavior of foundations. Third, undrained settlement is closely related to the undrained stability of a foundation. Excessive undrained settlement may be a warning of impending failure. The two basic components in the theoretical analysis of undrained settlement are: an analysis to relate settlement to the loading geometry and the soil properties; and the determination of the appropriate stress-strain and strength properties of the soil to input to the theoretical solutions. The finite element method of analysis facilitates the solution of a broad range of boundary loading problems involving inhomogeneous, anisotropic and nonlinear soil properties. However, even though improved analytical capabilities have been developed, accurate determination of stress-strain properties in undrained shear for in situ clay deposits remains a major obstacle to the successful analytical prediction of undrained 1
- 20. settlement. Therefore, the principal aim herein is to present an empirical method for estimating undrained settlement using the in situ measurements of lateral deformations. When an embankment, storage facility, or a footing is constructed, that is of limited size in comparison with the thickness of the compressible ground, there are two components of deformation; one is the volumetric compression due to consolidation and the other is the shear distortion. An example of the latter is the immediate lateral deformation and associated settlement under undrained conditions. Shear deformation or flow causes horizontal displacement of soil. The undrained shear deformation depends on soil profile, nature of the soil deposits, type of structure, and rate and method of construction. Shear deformation can cause large initial and post construction settlements. Experience with the construction of embankments on soft ground has shown that there have been many instances of base failure of embankments. However, evaluating and comparing entire ground deformations may allow a prediction of ground failure during embankment construction. The lateral deformation of soft clay due to embankment loading is becoming more of interest because lateral deformation has detrimental effect on the behavior of adjacent structures such as pile foundations, movement of bridge abutments, and movement of water and gas pipelines. In this study current empirical, numerical, and elastic-theory methods for the prediction of undrained lateral deformation, and settlement of clay foundations subjected to embankment loading are reviewed. Field measurements of lateral deformation for 180 embankments on soft clay and silt deposits were used in the present investigation. The distribution of lateral displacement with depth is used to calculate the settlement resulting from lateral deformation. In general, finite element methods have not been very successful in predicting lateral deformation. Accuracy of predictions however has increased for the finite element methods which properly model constitutive equations of soil, the loading procedure, and time dependent creep. Empirical methods for estimating lateral deformation are 2
- 21. presented predicting settlement resulting from lateral flow for undrained and drained conditions. 1.2 Objectives of the Study The objectives of this research are to develop, using field observation of lateral deformation, empirical procedures for: (a) determining distribution of lateral deformation across an embankment, based on a limited number of inclinometers measurements, (b) predicting settlement resulting from lateral deformation, (c) relating lateral deformation to factor of safety against undrained failure, (d) using lateral deformation as a measure of undrained stability, (e) examining time-dependant deformation of soil subjected to embankment loading and different drainage boundary conditions, (f) superimposing undrained deformation and drained one-dimensional consolidation settlement. Field measurements of horizontal deformation of soft clay and silt deposits during and after construction of embankments and storage facilities have been collected from throughout the world, covering 180 case histories. These probably represent 95% of cases with lateral deformation measurements reported in the literature. The undrained settlement resulting from the lateral deformation of the foundation soil is computed from an integration of the lateral deformation profile obtained at various locations across the embankment width. Lateral deformation of the ground resulting from embankment loading has been the subject of numerous studies for years. There has been an interest in predicting lateral deformation because of the observed detrimental effect of lateral deformation on adjacent structures and also because plastic flow that produces lateral deformation may lead to ground failure. However, even in the absence of a ground failure and adjacent structures, lateral deformation is important because it contributes to settlement of the embankments, storage facilities, and structures on soft ground. In some situations, part of lateral deformation results from multidimensional consolidation. A procedure has been 3
- 22. developed for estimating lateral deformation using an empirical correlation between lateral deformation and factor of safety against undrained failure. The correlation includes influence of ground condition as well as the geometry of the embankment. 1.3 Scope In Chapter 2, the available methods for predicting the undrained settlement and lateral deformation are reviewed. They are divided into three categories: solutions based on elasticity, numerical techniques, and empirical procedures. In Chapter 3, behavior of clay foundations subjected to embankment loading is reviewed and discussed. The behavior includes, yielding of clay structure, porewater pressures produced by embankment loading, lateral deformation with depth, stability analysis and choosing the mobilized undrained shear strength, the value of factor of safety that triggers an abrupt increase in rate of lateral deformation, shear stress level and undrained shear deformations, and the undrained modulus of soft clay and silt deposits. In Chapter 4, methods using lateral deformation as a measure of undrained stabiltty are reviewed and discussed. In addition, a method to control embankment construction by observing lateral deformation is developed through relating lateral deformation to factor of safety against undrained failure. The same empirical correlation could be used to estimate the maximum lateral deformation at the toe or the area of lateral deformation profile with depth, given the factor of safety against undrained failure. In Chapter 5, the collected database covering 180 case histories is presented. These probably represent 95% of cases with lateral deformation measurements reported in the literature. All the parameters that are believed to affect the undrained deformations are identified for the cases and are included in Table 5.1. The references for the cases are tabulated in Table 5.2. These cases are sorted by case name in Table 5.3 and they are sorted by case ID in Table 5.4. In addition, the general parameters whenever available for the case that were used in the present empirical analyses are tabulated in Table 5.5. The 4
- 23. behavior of the lateral deformation with depth is strongly dependant on the soil type. Therefore, normalized lateral deformation measurements are presented together with the soil profile and soil properties. In Chapter 6, displacement volume of soil and associate settlements is discussed. Two types of correlations have been examined for each case history. In the first correlation, the lateral deformation near the toe has been compared with the total settlement at the embankment center during and after construction. In the second correlation, the area of lateral deformation has been compared with the area of total settlement during and after construction. From these correlations the values of the deformability factor RDS for different cases have been computed and the averages are tabulated in Table 6.1 for different periods during and after construction. Two empirical procedures are presented and discussed: (1) predicting distribution of lateral deformation across embankment, (2) predicting settlement resulting from lateral deformation. Then the two proposed methods are verified by implementing them on several case histories. Finally, in Chapter 7, the summary and conclusions are presented. 5
- 24. CHAPTER 2 PREDICTION OF SETTLEMENT AND LATERAL DEFORMATIONS 2.1 Introduction Loading the soft clay and silt deposits by embankments or storage facilities creates vertical settlement and lateral deformation. In some cases, the undrained shear distortion, which is included in the undrained settlement and lateral deformation, causes stability problems for the embankment or storage facilities and adjacent structures. Therefore, a prediction of lateral deformations prior to construction would allow (a) an estimate of settlements resulting from flow of soil for stable situations and (b) soil improvement measures and construction procedures to prevent excessive deformations or unstable conditions. The available methods for predicting the undrained settlement and lateral deformation can be divided into three categories: solutions based on elasticity, numerical techniques (e.g. using FEM), and empirical procedures. 2.2 Prediction of Undrained Settlement and Lateral Deformation Using Theory of Elasticity The theory of elasticity has been previously used to predict undrained settlement and lateral deformation. 2.2.1 Flow Settlement The settlement resulting from lateral deformation or flow of saturated soils has 6
- 25. been previously termed, initial settlement, immediate settlement, elastic settlement, shear settlement, and undrained settlement. In this thesis settlement resulting from lateral deformation of soil is termed flow settlement to distinguish it from consolidation settlement. Flow settlement results from time-independent as well as time-dependent flow of soil from under the structure, whereas consolidation settlement in saturated soils results from time-dependent flow of water from under the structure. Terzaghi (1943), using the solution by Steinbrenner (1934), expressed elastic settlement for a flexible load on a circular area in terms of values of surface load q, thickness of elastic layer La, modulus of elasticity of the layer, E, and Poisson's ratio v, Fig. 2.1. In Figs. 2.1 band 2.1c the base of the elastic layer is rigid and elastic layer adheres perfectly to the rigid base. Figure 2.1 shows that the ground surface under and outside the loaded area settle and the magnitude of settlement at the edge of loaded area is about 50 to 70% of the settlement at the center. In Fig. 2.1 c where the depth ratio LaIR is smaller than 2/3 and Poisson's ratio is close to 0.5, the settlement is maximum at a distance of two third of the radius from the center of the loaded area, it is near zero at the edge of the loaded area, and ground surface heaves outside the loaded area. The settlement of an elastic layer subjected to uniform flexible strip load has been expressed in different forms. They are summarized in Table 2.1 and Figs. 2.2 to 2.5. However. It has the general form: (2. 1) Where: q = Net foundation pressure. B = Width of the loaded area. v =Poisson's ratio. (v =0.5 for saturated clays). 7
- 26. I =Influence value, depending on the shape of the loaded area and the depth of the elastic layer. Eu = Undrained young's modulus. The use of elastic theory to predict undrained deformations ignores the effect of local yielding that is likely to occur even at very high factors of safety. D'Appolonia et aI. (1970, 1971) proposed a modified elastic method taking into account the effects of local yielding. They suggested a correction factor SR based on theoretical considerations to correct the computed elastic settlement. D'Appolonia and Lambe (1970) proposed a finite element method taking into consideration variation of modulus with depth and local yielding. The undrained elastic settlement of a finite elastic layer subjected to embankment loading was studied by Giroud (1973). Balasubramaniam and Brenner (1981) presented the work of Giroud where the influence factors are expressed in term of the geometry of the embankment and thickness of elastic layer, Fig. 2.6. The value of the undrained settlement of the ground surface was expressed by Giroud (1973) as: (2.2) Where: q = Net foundation pressure. Eu = undrained Young's modulus. bI = half of embankment width at the bottom. 8
- 27. b2 =half of embankment width at the top. rl and r2 = Influence factors. Analysis has been made using Giroud's method to predict the undrained settlement trough for an embankment located on a thin and thick deposit. It has been found as it is shown in Fig. 2.7 that the method can't predict a reasonable trough for a thick deposit. Figure 2.7 shows that the undrained settlement trough for an embankment located on a thick deposit becomes zero at an unrealistic distance from the center, that is 10 times the width of the embankment. However, for a thin layer Giroud's method predicts a realistic near zero settlement at the toe of the embankment. 2.2.2 Lateral Deformation Theoretical analysis of undrained shear deformation of soils is quite complicated and there is no widely accepted method for predicting lateral deformation. Prediction of lateral deformation is difficult partly because consolidation produces inward movement, whereas undrained and drained deformation including creep produce outward movement. The most significant part of lateral deformation beneath an embankment generally occurs during construction when the undrained condition exists. The settlement under the embankment is produced by time dependent lateral flow of soil. Poulos (l972b) attempted to predict lateral deformation using the theory of elasticity. The computation of the lateral deformation based on theory of elasticity mainly used Poisson's ratio v = 0.5 and an undrained modulus of elasticity Eu. Poulos (1972b) expressed lateral deformation for v = 0.5 as: 9
- 28. (2.3) Where: q = Net foundation pressure. Lo = Thickness of the compressible layer. Ih = Influence value, depending on the geometry of the problem. Eu = Undrained Young's modulus. The influence factor Ih is shown in Fig. 2.8c for the horizontal deformation at the surface at any distance from centerline and Fig. 2.8d for the horizontal deformation at any depth beneath the edge. Poulos (1972b) concluded that there is a discrepancy between measured and predicted lateral deformation beneath an embankment for the following reasons: 1) The difficulty of estimating the soil Poisson's ratio 2) Anisotropy 3) Non-linear stress-strain behavior 4) In-homogeneity 5) Neglect of embankment stiffness and roughness at the bottom of elastic layer. Poulos (1972b) examined the influence of the five factors on elastic settlement and horizontal deformation. The results are shown in Table 2.2, and the effects of inhomogeneity and anisotropy are illustrated Figs. 2.8 and 2.9, respectively. Based on the comparison of calculated and observed behavior shown in Fig. 2.10 Poulos concluded 10
- 29. that the linear elastic models give poor prediction of foundation deformations and there is a need for detailed evaluation of field observations. Tavenas et al. (1974) and stille et al. (1976) attempted to resolve the discrepancy between calculations and observed behavior of natural clays by including nonlinear and anisotropic response. Tavenas et. al. (1974) used finite element elastic analysis to predict the deformations for Saint-Alban B, C, and D. The analysis gave lateral deformations much larger than those observed and distributed differently over the depth of the foundation, even though a value of 0.3 was assigned for Poisson's ratio which is less than 0.5. Stille et. al. (1976) considered the anisotropy of the soil in a finite element elastic analysis for Kalix embankment. A close agreement between calculated and measured values was obtained when a Poisson's ratio of 0.4 was used in the analysis. 2.3 Prediction of Settlement and Lateral Deformation Using Constitutive Models The most significant development in lateral deformation calculation started with the introduction of the finite element method, which permitted calculation of lateral deformations under the slopes of embankments (Clough and Woodward 1967). The plane strain state of deformation that exists under some embankments could be modeled with non-linear constitutive models. 2.3.1 Constitutive Models Stress-strain relationships, or more generally the constitutive equations used to describe the soil behavior are the essential elements in the finite element analysis. There has been a substantial literature describing constitutive models for soils, and they have been summarized in comprehensive State of the Art reports (e.g. Hashiguchi, 1985; Sekiguchi, 1985). Duncan (1994) listed most of the models that have been used to analyze embankments and dams. The wide variety of soils leads one to conclude that no 11
- 30. material model will be able to encompass the behavior of all soils under all conditions. The parameters for any useful constitutive model should be measured directly by simple laboratory or insitu tests and should have a clear physical meaning. 2.3.2 Implementing Finite Element Analysis on Case Histories The finite element method has found one of its major uses in geotechnical engineering in the analysis of embankment deformations. The earliest reported application was by Clough and Woodward (1967), who also simulated the process of construction of the embankment by adding elements, representing layers of fill, at successive stages of construction. Other researchers also adopted the finite element method for embankment deformation analysis (Hollingshead and Raymond 1971, Shibata et al 1976, Davis and Poulos 1975, Tavenas et al. 1974, Stille et al. 1976, Wroth and Simpson 1972, Ladd 1972, Simon et al. 1974, Smith and Hobbs 1974, Smith and Hobbs 1976). Some investigators considered creep deformations (Christian and Watt 1972, Thoms et al. 1976, Akagi et al. 1976). Ladd et al. (1994) implemented MIT-E3 model in a finite element analysis for the 1-95 Sec 246 embankment using the ABAQUAS program (HKS 1989) together with subroutines (user materials) for the effective stress models being used at MIT (Hashash and Whittle 1993). For comparison purposes the same analysis was carried out using the Modified cam clay (MCC) model. Figures. 2.11 and 2.12 compare predictions of horizontal displacements by MIT-E3 and MCC, respectively, with the measurements from inclinometers 13, 14, 15, and 16 at the end of construction (CD 620 day) and at CD 2000 day corresponding to the end of the field monitoring. The largest lateral movements are measured in the upper clay by inclinometer 14 located close to the toe of the embankment. All the inclinometers measured progressive outward displacements at all elevations in the clay throughout the entire monitoring period (up to CD 2000). There are large differences in predictions of lateral deflections by the two soil models. There is 12
- 31. also a significant difference between measured and computed lateral deformations in the upper 15 m of clay. The patterns of the measured lateral deformations as they change with time are different from those of the calculated movements; especially near to the toe of the embankment. While the measured values show large increase with time near the fill base, the predictions show significant increases at deeper depths. This is true for both the Modified Cam clay and the MIT-F3 method. The MIT-E3 model gives much more realistic predictions of lateral deformation at the end of construction at all four inclinometer locations. Analyses were made using upper and lower bound estimates of the preconsolidation pressure, profiles 1 and 2. The results for profiles 1 and 2 in Fig. 2.11 show the importance of the stress history on the magnitude of the lateral deformation, but have little effect on the distribution of deformation. ill general, the model overestimates the lateral deformation in layer F, with maximum outward displacements occurring in layer D under the embankment. In contrast, the MIT-E3 shape of the measured data shows maximum movements in layer B. Ladd et al. (1994), suggested that the results from MIT-E3 are encouraging and show that lateral deformation during consolidation or post construction can be described by a model which includes anisotropic yielding and does not include creep effect. The Modified Cam Clay greatly overestimates the measured lateral deformation at the end of construction (Fig. 2.12), especially in the bottom half of the deposit. Ladd et al. (1994) offered several reasons for lack of agreement between the MIT- E3 model and the measurements. In the MIT-E3 method there is a smooth transition to normally consolidated behavior. The simplification of this transition during the formulation of the MIT-E3 model may decrease the overall accuracy of the method. The MIT-E3 model incorporates fifteen (15) parameters; these parameters must be selected carefully. It is known that these parameters are somewhat difficult to measure, and that a small error in several parameters may lead to a large error in the final calculations. The MIT-E3 also assumes throughout that the soil is a rate independent material (i.e., creep effects are not considered). However, if tp (time to reach end of primary consolidation) is 13
- 32. relatively short and effective vertical stress is near the preconsolidation pressure, significant secondary settlements may occur. In addition, one of the input parameters, 2GIK is the ratio of the tangential elastic shear modulus to the bulk modulus, which is related to Poisson's ratio, v, of the soil. Since Poisson's ratio changes with loading and consolidation, Ladd et al. (1994) used an approximation to estimate 2GIK. There is no way to verify the validity of the approximation. Almeida and Ramalho-Ortigao (1982) presented results of finite element analysis of Rio De Janeiro trial embankment using two programs CRISP and FEECON. Analyses carried out were: elasto plastic undrained and coupled consolidation using the CRISP program and the elastic non-linear undrained using FEECON program. The results of lateral deformations from numerical analyses were compared with observed values during embankment construction as shown in Fig. 2.13. Computed results and measured values of lateral deformations at the base of the embankment are presented in Fig. 2.13(a). The main observations by Almeida and Ramalho-Ortigao (1982) from Fig 2.13(a) were that computed deformations are within the range of measured values under the embankment platform, however, are larger under the slope and outside. In addition, computed values showed the maximum lateral deformation in front of the embankment slope whereas the observed maximum values occurred under the slope. Lateral deformation with depth that would be measured by inclinometers was also predicted. The computed lateral deformations, shown in Fig. 2.13b, were higher than the measured. Chai and Bergado (1993) used the modified Cam clay model (Roscoe and Burland 1967) and a hyperbolic nonlinear constitutive model, for the soft foundation soil in analyzing the deformations for the Malaysian trial embankment (scheme 6/8). The analysis was based on applying the embankment load by two methods: 1) increasing the self weight of all of the embankment elements, and 2) increasing the load by placing a new layer of elements, while correcting the coordinates of the nodes above of topmost embankment surface. Method 1 involves modeling the entire embankment as completed, at the beginning of the analysis. Giving the entire embankment a percentage of its entire 14
- 33. completed weight, which simulates the construction procedure. The percentage of weight corresponds to the actual weight of the fill on the foundation at that time. This method is referred to as loading by percentage method, which implies that, the stiffness of the whole embankment elements existed at the beginning of the analysis. Method 2 adds new nodes to the finite element analysis as the fill is constructed. As a new fill layer is constructed, placing a new layer of nodes simulates the effect. The location of the nodes was corrected for the settlement of the fill and foundation prior to placement of the new layer of fill. This method is referred to as the loading by layer method. The results suggested that the finite element analysis by loading layer by layer, and correcting the node location predicted results that were in better agreement with measurements for both settlements and lateral deformation. The conclusion of Chai and Bergado (1993) was that the deformation pattern of the soft ground predicted by a finite element analysis not only depends on the magnitude of the load, but also on the sequence of applying the load. Russell (1996) calculated the rate of lateral deformation for whitewall creek embankment using finite element analysis to assist the assessment of failure during embankment construction. The finite element analyses were carried out using a version of CRISP program with the modified Cam-clay constitutive model, which allowed a gain in the undrained shear strength during consolidation. The drains were included in the analysis using the method developed by Hird et al. (1992). The finite element predictions and observed behavior are compared for the maximum lateral deformation below the toe in Fig. 2.14. Russell stated that the comparison of the lateral deformation with the measurements is encouraging considering the difference between actual construction schedule and that assumed in the prediction in the duration of the loading and post loading stages. Tavenas et al. (1979) summarized from literature comparisons between measured and computed, by finite element techniques, total settlements at the center and maximum lateral displacements near the toe for a number of case histories. This comparison is presented in Fig. 2.15. Tavenas et al. (1979) concluded that the quality of the settlement 15
- 34. prediction is apparently remarkable not withstanding the C-l type of predictions (Lambe 1973) with an opportunity to adjust the large number of assumptions and parameters. On the other hand, the lateral displacement predictions by the same analyses are all much larger than the observed displacements, which indicate that experience up to 1979 was not successful in lateral deformation prediction by means of finite element analysis. The most recent effort on the use of constitutive models together with finite element techniques has been by Whittle and co-workers (Kavvadas 1982, 1983, Whittle 1987, 1993, Whittle et al. 1994). The latest version of their model has 15 parameters. 2.3.3 Prediction of Deformations by The Finite Element Method Sekiguchi et al. (1988) developed a chart to assess the effect of partial drainage on lateral soil movements. The chart was developed from coupled stress- flow analysis using the finite element method. A plane strain elasto-viscoplastic constitutive model for clays was implemented for the analysis. Figure 2.16 shows the effect of partial drainage on the soil movements. The VDand Vs are defined in Fig. 2.17. (Uy)ec is the degree of elasto- viscoplastic consolidation at the end of construction and can be assessed from Fig. 2.18. Note that for a 10 m thick clay layer with Cy = 3 m2 /year and draining from top and bottom, subjected to an embankment loading completed in 1112 of a year, Tc = 0.01 which leads to U =6 %. This means that at the end of construction VDNs =0.66 and 0.28 for BIH of 2 and 6, respectively. Loganathan et al. (1993) studied the deformation of clay under embankment using the finite element program CRISP, developed at the University of Cambridge. Constitutive soil models included in this program are the Cam-Clay (both the original and the modified version), elastic perfectly plastic (options for the Von Mises, Tresca, Drucker-Prager, and Mohr-Coulomb models) and elastic isotropic and anisotropic models. They found that the maximum lateral deformation beneath the toe of the embankment is approximately 0.28 times the maximum settlement observed below the 16
- 35. center of the embankment at the end of loading. 2.4 Predictions of Deformations Using Empirical procedures There are only a limited number of empirical procedures in the literature for computing settlement resulting from lateral flow of soil during construction as well as in the long term. 2.4.1 Undrained Settlement Assuming that significant undrained shear settlement begins when the yield stress is exceeded and the soil becomes normally consolidated, Leroueil et al. (1990) pointed out that this settlement resulting from plastic flow of soil can not be analyzed in terms of theory of elasticity. On the other hand, the more satisfactory procedure using elastoplastic constitutive equations together with finite element procedure is too complex for general use in practice. Tavenas and Leroueil (1980) assumed that the undrained shear settlement begins to occur when the embankment height reaches what they termed the threshold height Rne which is the height of the embankment at the moment when the effective vertical stresses in the foundation exceed the preconsolidation pressure. They suggested an empirical expression for predicting the undrained shear settlement at the center of embankment at the end of construction: (2.4) Where R is the height of embankment after the Rne has been reached and exceeded. Tavenas and Leroueil (1980) concluded that the construction settlement during the stage where the effective vertical stress in the foundation is less than the 17
- 36. preconsolidation pressure is due to recompression. However, field measurements show that the lateral deformation starts at very early stages of construction when H is less than Hnc (Tavenas et al. 1979). In addition, Eq. 2.4 provides Su up to the end of construction. However, the undrained shear settlements continue even after the end of construction as has been demonstrated by significant lateral deformations observed by inclinometers especially when the embankment has steep slopes or has been built with a low safety factor. The undrained settlement resulting from the lateral deformation of the foundation soil can be computed from an integration of the lateral deformation profile obtained at the toe of the embankment slope. Mesri et al. (1994) integrated the lateral deformation profile and concluded the following relationship: S =Dm u 2 Where: (2.5) Su =The undrained shear settlement resulting from lateral deformation of the foundation soil. Dm = The maximum lateral deformation within the foundation depth. Mesri et al. (1994) combined an empirical relationship, which relates Dm to consolidation settlement (Tavenas et al. 1979), and Eq. 2.5 to obtain the following relationship between Su and the end of primary settlement, Sp, for embankments with a factor safety is near 1.4 against undrained failure: 18
- 37. (2.6) Where: Sp = The end-of-primary settlement resulting from compression of the voids. Equation 2.6 indicates that for a properly engineered embankment, i.e., with a factor of safety against undrained bearing capacity failure greater than 1.4, the settlement resulting from lateral deformation is expected to be small as compared to the total settlement. Terzaghi et al. (1996) stated that the settlement caused by flow of soil from under the structure is then likely to be less than 10% of the end-primary-settlement resulting from compression of the voids. It is clear that there is a need for a simple empirical procedure for predicting the undrained shear settlement when the factor of safety is different from 1.4. For factor of safety less than 1.4 the embankment foundation may experience large undrained plastic flow resulting in large undrained settlement or failure. Bjerrum (1972), in describing Ska Edeby test embankment VI, mentioned that "The factor of safety of the embankment is low, probably of the order of 1.2 when the rate effect on undrained shear strength is taken into account. The component of the settlements resulting from the lateral yield is unusually large, as it amounts to more than a quarter of the total settlements". Ska Edeby VI is considered to be an important example of large shear deformation (Kallstenius and Bergau 1961, Osterman and Lindskog 1963, Burland 1971, Holtz and Lindskog 1972, Marche and Chapuis 1974, Holm and Hotz 1977, Hansbo et al. 1981, Larsson 1986). Larsson (1986) calculated undrained settlement due lateral deformation for Ska Edeby Test Embankment VI directly after full load application in amount of 5 cm based 19
- 38. on empirical relations between undrained shear strength, plasticity index and calculated factor of safety. Foott et a1. (1987) estimated the undrained settlement for the Chek Lap Kok main test embankment by examining the measured settlement and lateral deformation profiles. It was concluded that the total undrained settlement resulting from undrained lateral deformation was about 13 to 22 cm. However, it is not clear how they came up with these numbers. Foot et a1. (1987) stated "Undrained settlement was estimated by an examination of the load/settlement plots and by consideration of the lateral mud deformations recorded by inclinometers on the periphery of the main test area. Total undrained settlements of 0.08-0.13 m were estimated for the first 250 contract days, with an additional 0.050-0.09 m occurring between approximately CD 400 and 4350." (CD = Contract day). 2.4.2 Lateral Deformation during Construction Lateral deformation of the ground reSUlting from embankment loading has been the subject of numerous studies for years. There has been an interest in predicting lateral deformation because of the observed detrimental effect of lateral deformation on adjacent structure~ (O~terman 1952, Heyman 1965, Stermac et a1. 1968, Leussink and Wenz 1969, Broms 1972. Stewart et a1. 1994, and Goh et a1. 1997) and also because plastic flow that produces Literal deformation may lead to ground failure. However, even in the absence of a ground failure and adjacent structures, lateral deformation is important because it contribute" to differential settlement of the embankments, storage facilities, and structures on soft ground. In some situations part of lateral deformation results from multidimensional consolidation. Ta'enas et a1. (1979) stated that lack of success in predicting the lateral deformation in clay foundation under embankments is not only due to the reasons 20
- 39. presented by Poulos (1972b), but also due to the basic assumption of a truly undrained response of the clay foundation during embankment construction. Tavenas et al. (1979) indicated that when the preconsolidation pressure is only slightly in excess of the effective overburden pressure, the foundation clay becomes normally consolidated at an early stage of construction and the development of lateral deformations is governed by undrained shear distortion of the clay. In this case, the maximum lateral deformation at the toe, Dm , is equal to the construction settlement at the center. The Lanester test embankment (Pilot et al. 1973) exhibited this behavior under the O.4-m-high initial working platform where the final effective vertical stress exceeded the preconsolidation pressure, as shown in Fig. 2.19. To understand the influence of preconsolidation pressure, cr'p on clay behavior, Tavenas et al. (1979) studied the variation of the maximum lateral displacement, Dm, with the height of fill. The results are shown in Fig. 2.20(a). They noticed that for all cases Dm remains small initially, increasing at a rate of about 1 cm per meter of fill. However, at a later stage of construction the displacement increments are very large, typically reaching 8 cm per meter of fill. They observed that the change in the rate of increase of Dm was relatively abrupt and occurred at a height of fill that was 25-75% of the height at failure. Tavenas et al. (1979) stated that when the clay foundation is in an overconsolidated condition, the stiffness and the coefficient of consolidation are relatively high. Excess pore water pressures induced by an embankment load can dissipate partially or fully, allowing the clay to consolidate. During consolidation of the clay shear stresses induced by the embankment load are not large enough in comparison to the strength of soil to cause significant lateral movement. Hence, the lateral deformation increments are small in comparison to the vertical settlement increments which are shown in Fig. 2.20(b). Tavenas et al. (1979) found from observations on 21 embankments that Dm/St vary between 0.06 and 0.36 with mean value of 0.18, during the partially drained loading in the recompression range. In summary, Tavenas et al. (1979) 21
- 40. obtained from their empirical study the following: For overconsolidated states at the beginning of banking: Dm = (0.18 ± 0.09) St (2.7) For normally consolidated states during embankment construction: (2.8) Suzuki (1988) observed settlement and lateral deformation of 11 embankments. He found that the relationship between the lateral deformation and embankment settle- ment for partially drained loading of the preconsolidated clay in recompression could be expressed as; Dm = (0.208 ±0.052)St (2.9) Leroueil et al. (1990) reviewed these empirical rules for prediction of lateral deformation and concluded that there is insufficient data to establish a relationship for variable depths of soft clay. 2.4.3 Long Term Lateral Deformation Tavenas et al. (1979) collected data on lateral deformation with time during consolidation for 14 embankments. As shown in Fig. 2.21 they found that during primary consolidation the increment of maximum vertical settlement and increment of maximum lateral deformation are related linearly with an average ratio according to: (2. 10) For Ska Edeby VI embankment settlement and lateral deformation measurements have been carried out for 17 years. Using these measurements Tavenas et al. (1979) computed Wm / D"St up to 17 years according to Eq. 2.11. 22
- 41. (2. 11) They explained the drop m LlDmlLlSt in terms of increased significance of "secondary deformations at this site", (apparently implying secondary compression contributes to settlement but not to lateral deformation). Suzuki (1988) found that the relationship between the increment of the maximum lateral deformation and the increment of the maximum vertical settlement during each stage of the stage-construction of 8 embankments to be: Wm = (O.24±O.03)LlSr (2. 12) Equation 2.12 was obtained from observations for consolidation periods immediately after construction. Therefore, it is not possible to consider Eq. 2.12 for long term lateral deformation after the completion of construction. 2.4.4 Lateral Deformation during Stage-construction Construction in stages has been used to assure stability of embankments during construction. Biemond (1936) took advantage of the increase in shear strength during consolidation by construction of an embankment in stages which otherwise would have failed. In addition, Middlebrooks (1936) described a case where the increase in the undrained shear strength that took place during construction stabilized the embankment. Development of maximum lateral deformation Dm with the settlements St, observed under the Palavas test fill (Bourges et al. 1973) is shown in Figure 2.22, during two stages of construction and consolidation. The 25.7 m thick foundation deposit consists of an upper normally consolidated plastic clay layer, 14 m thick, overlying slightly overconsolidated clay. During the first loading, the upper clay layer immediately became normally consolidated, but the lower layer remained over-consolidated. As a result, the deformations were essentially governed by the behavior of the upper layer. 23
- 42. During the first consolidation period, lasting for 9 months, Dm was observed to increase with St at a rate corresponding to mm = 0.15 ~St. During this period, the thickness of the zone in a normally consolidated state apparently increased somewhat (Fig. 2.23) due to the increase in cr'v. As shown in Fig. 2.22, the application of the second loading stage produced increment of Dm almost equal to the increment of settlement. The increased embankment load at the end of this second loading was sufficient to bring the foundation to a normally consolidated state, and the distribution of lateral deformations with depth was modified accordingly (Fig. 2.23). In the final 11 month period of consolidation, lateral deformations increased at a rate mm = 0.34 ~St (Fig. 2.22), probably because of the reduced factor of safety (FS) of the embankment (at the end of the second loading, FS =1.25, as compared to FS =1.6 at the end of the first loading). Teparaksa (1992) presented the lateral deformation with time for the stage construction in Bang Na-Bang Pakong highway. Figure 2.24 shows that the rate of lateral deformation mm/~t, was 0.029 cm/day during the first stage, decreased after halting the construction in the first stage, and then it increased to 0.061 cm/day during the second stage of loading. The relationship between maximum lateral deformation and maximum vertical settlement at the first stage and second stage of construction is shown in Fig. 2.25. It can be seen that the ratio of maximum lateral deformation to the maximum vertical settlement (mm/~St) increased from 0.33 during the first stage to 0.46 during the second stage. The increase in the rate of lateral deformation and the increase in the ratio (mml~St) in Figs. 2.24 & 2.25 are consistent with the increase in rate of loading. 2.4.5 Effect of Vertical Drains on Lateral Deformation When a soft clay layer is very thick or the permeability is low, the preloading technique is likely to be inefficient when used alone because an inordinately long period of time will be needed to bring about significant compression. In these circumstances, 24
- 43. radical improvements in the preloading time can be affected by the installation of vertical drains to shorten the drainage path during consolidation of the clay. The advantage of vertical drains is assessed in terms of the acceleration achieved in primary consolidation over the consolidation rate that would have occurred without the drains. Using vertical drains allows rapid increases in the undrained modulus and the undrained shear strength, and thus less settlement resulting from undrained deformation should develop with time. Ladd (1991) studied the effect of vertical drains on Dm versus St using the measurements of Palavas test fill. Case A in Fig. 2.26 represents construction without drains and it showed the essential features described by Tavenas et al. (1979); i.e., partially drained and then undrained behavior during filling, followed by consolidation having mm/LlSt = 0.15. Case B has an identical loading history, but the vertical drains now cause significant drainage throughout filling; much larger EOC St and slightly smaller EOC Dm. Rapid consolidation also reduces mm/LlSt after construction from 0.15 to 0.10 due to smaller effects of undrained creep. Case C places more fill in less time, resulting in a much larger mm/LlSt = 0.4 during filling, which also produces larger mm/LlSt during consolidation due to higher rates of creep. 2.4.6 Field Deformation Analysis (FDA) Loganathan et al. (1993) presented a methodology called Field Deformation analysis (FDA) to separate and quantify settlement components for both loading and post loading stages of embankments. FDA is a formulation based on volume of deformation concept and developing linear relationships between measured quantities and settlement components. 2.4.6.1 Loading Stage The basic components of settlement observed beneath embankments were classified as undrained settlement, consolidation settlement, and secondary compression. In the case of stage constructed embankments on soft soils the settlements and lateral 25
- 44. deformations observed by field instrumentation are considered separately for loading and post loading stages. Figure 2.27 shows the subsoil deformation pattern, which is likely to occur during a loading stage. Undrained settlement volume, which is designated as AOC in the figure, should be equal to the lateral deformation volume APM if undrained conditions prevail during loading stage. However, some dissipation of excess pore water pressures during loading stage may simultaneously cause consolidation. The resulting volume changes due to consolidation during loading stage are designated as ABC vertically and APMQA laterally in Fig. 2.27. It should be noted that the volumes referred to here are for the unit length of the embankment. The volume changes at any time interval are obtained by integrating field measurements as given in Eqs. 2.13 & 2.14 BI2 VVL = JSx' dx o Where: (2. 13) VVL = the observed settlement volume in the field from settlement gauge readings, for half the embankments. Sx =settlement at a distance x from the centerline of the embankment. B = the width of the embankment. (2. 14) Where: VDL = the observed lateral displacement volume in the field from 26
- 45. inclinometer measurements. Dz = the lateral displacement measured at the depth z. Lo =the thickness of the soil stratum. Loganathan et al. (1993) defined the volume changes at any time interval during construction as in Eqs. 2.15 & 2.16. (2. 15) (2. 16) Lateral consolidation volume ex =-------------- Consolidation settlement volume (VdL) (2. 17) Where: The subscript L stands for loading and, VVL = observed vertical settlement volume in the field, from settlement gauge readings, for half the embankments. VDL = observed lateral deformation volume in the field, from inclinometer measurements near the toe. "dL =volume of consolidation settlement. VuL =volume of undrained settlement. aVdL =lateral volume reduction during consolidation. a = ratio of lateral consolidation volume to consolidation 27
- 46. settlement volume (Vd). From Eqs. 2.15 & 2.16, the lateral deformation volume components of an embankment foundation (undrained and drained) during construction stage can be separated as given in Eqs. 2.18 & 2.19. v - VVL - V DL dL - l+a (2. 18) (2. 19) Loganathan et al. (1993) found a value by assuming that for plane strain conditions the undrained settlement is linearly related to embankment height (i.e., VuL = A . h, where A is a constant). They based this assumption on the expression for elastic immediate settlement expressed by Eq. 2.20, assuming B(1-v2 )I/E to be a constant. However, assuming B(1-v2 )I/E as a constant for different loading stages including the modulus of elasticity, underestimates the values of E for the consecutive loading stages, especially if there is a consolidation period between them. (2.20) Where: q =Net foundation pressure. 28
- 47. B = Width of the loaded area. v =Poisson's ratio. (v = 0.5 for saturated clays). I =Influence value, depending on the shape of the loaded area and the depth of the elastic layer. E =Young's modulus. Because B(1-v2 )I/E is assumed to be constant, the load applied on embankment foundation is proportional to the height of the embankment. Loganathan et al. (1993) evaluated the constant A at the end of each loading stage using Eqs. 2.21 & 2.22. Stage j (2.21) Stage j+1 (VVL )j+! (VDL )j+! () a. + A = V uL j+! = h j +! hj+l hj +! 1+a (2.22) Because A is assumed to be a constant by (Eqs. 2.21 & 2.22) the value a can be obtained as follows: 29
- 48. (2.23) 2.4.6.2 Post-Loading Stage It is considered that the total settlement observed in the field during the post loading stage is the resultant of consolidation settlement Sd and undrained settlement SUo The lateral consolidation volume ratio a and the lateral shear deformations volume ratio ~ compared to their respective settlement volumes are assumed as: Lateral consolidation volume ex =--------------- Consolidation settlement volume (VdC) (2. 24) f3 = Lateral deformation volume Undrained settlement volume (Vue) (2.25) f3 = 1, if its assumed that only undrained shear deformation takes place in the field, and drained shear deformation is ignored The volume change pattern during post loading stage of an embankment is shown in Fig. 2.28. As derived for the loading stage, the volumes Vvc and VDC can be written as Eqs. 2.26 & 2.27. 30
- 49. (2.26) (2.27) Where C stands for post-construction From Eqs. 2.26 & 2.27, the volumetric deformation of the embankment foundation due to consolidation and undrained shear deformation can be written as in Eqs. 2.28 & 2.29. v - f3 Vvc - VDC dC - ex + f3 (2.28) (2.29) In both normally consolidated and overconsolidated clays, time dependent deformation due to shear deformations can be quite large (Christian and Watt 1972). Because shear deformation is a time-dependent parameter, Loganathan et al. (1993) assumed that: 31
- 50. (2.30) where Band 'Yare constants. For different post loading stages the constant B can be obtained as for loading stage. Stage j, t =tj B= at;r)jH(V;;)j] a+f3 (2. 31) Stage j+1 a .[(VV~)j+!1 + [(VD~ )j+!] t j+! t j+! B =-=-----=--=-----= a+f3 (2.32) By equating Eqs. 2.31 & 2.32 the ratio ex can be evaluated as shown in Eq. 2.33. (2. 33) 32
- 51. Loganathan et al. (1993) stated that coupling of drained shear deformations in the analysis with the undrained shear deformations is more oppressive. Consideration of drained shear deformations increases the number of unknowns and, thus, results in indeterminacy in the formulation of FDA. Therefore, it was assumed that only undrained shear deformations takes place in the field (i.e., ~ =1). The field deformation analysis (FDA) methodology was implemented on the Malaysian Trial Embankments (scheme 3/2) and (scheme 6/6). Both embankments were constructed as control embankment without any foundation ground improvement, 3m and 6m high respectively. The lateral deformation volume characteristics during loading were established by computing ex, values using Eq. 2.23. Figure 2.29 shows that values of ex, obtained for both embankments at different stages of loading, are in the range of 0.10- 0.32. These suggest an average ex, value of 0.24. The approximate deformation volume characteristics of the control embankments during loading stage due to undrained deformation and consolidation were evaluated by substituting the average ex, value in Eqs. 2.18 & 2.19 as follows: v - VVL - VDL dL - 1.24 aVVL - V DL V =--'-=-_":::='" uL 1.24 (2.34) (2.35) The values of VVL and VDL were calculated from the field settlement gauge and inclinometer measurements using Eqs. 2.13 & 2.14. It was observed from the surface settlement profile, during different stages of loading, that the surface settlements (St) 33
- 52. were uniformly related with the settlement volumes (Vv). These relationships for both 3 m and 6 m control embankments are given as: V 3 m control embankment - St = _V_ 12.5 (2.36) V 6 m control embankment - St = _V_ 23.0 (2.37) Where: St =the settlement at the centerline of the embankment. Vv =the settlement volume. Using these linear relationships, for the loading stage, the undrained and the consolidation settlement components were obtained. The relationship between undrained settlement and consolidation settlement during construction are shown in Fig. 2.30. To obtain consolidation and undrained settlement components, a similar analysis was performed for the post-construction stage. The relationship of these two settlement component;, with time is shown in Fig. 2.31. As can be seen in Figs. 2.30 & 2.31, the field deformation analysis (FDA) was successful in correlating the settlement component". However, the total settlement obtained by adding the settlement component... from FDA, does not represent the total settlement observed in the field for long dur..Ilion of construction period. Clnlcloglu and Togrol (1995) described the FDA with its formulation based on volumetric deformation concept as an important contribution to the present design practice. However, they stated that there is still a requirement for a method which is based on fundamental soil behavior and which can be used in conjunction with stress path behavior, so that links can be established from field measurements to the design 34
- 53. considerations. Therefore, they proposed a methodology using the Cam clay model of the critical state theory. 35
- 54. Table 2.1 Elastic settlement of a layer of infinite thickness subjected to uniform strip load. Reference, assumption Steinbrenner (1934) Eu constant with depth, v =0.5 Janbu, Bjerrum and Kjaemsli (1956) Eu constant with depth, v = 0.5 Davis and Poulos (1968) Eu not constant with depth, v =0.5 Equation for maximum settlement Su = (qB)0.75F1 Eu B =width of foundation. Fl =Steinbrenner factor. (2.9) qB Su =E 110111 (2.6) u !J,o and !J,1 from Fig. 2.2; modified by Christian and Carrier (1978), Fig. 2.3 Ll<ix, Ll<iy and Ll<iz are computed at mid depth of Llz from elastic distribution. D'Appolonia et al. (1970), (1971) S = _1 qB I v = 0.5, take into account local U SR Eu (2.2) yielding. Elastic settlement under an embankment Giroud (1973) v =0.5, elastic layer, finite thickness. SR = Se/Su where Se is settlement without taking into account local yielding, Figs. 2.4 and 2.5. (2.3) q ='Y HE where 'Y =unit weight of embankment and HE height of embankment. b1, b2, rl and r2 are defined on Fig. 2.6. 36
- 55. Table 2.2 Results of parametric studies of seven factors on surface settlement for elastic layer constructed on elastic foundation (after Poulos 1972). SUMMARY OF EFFECT OF VARIOUS FACTORS Factor Effect on settlemetn, Effect on lateral Remarks (1) Su deformation, D (4)(2) (3) Poisson's ratio v Su increases as D Increases as v Effect on D much of Soil v decreases decreases greater than on Su Anisotropy of soil. Su increases as EhlEv D Increases as Effects most (cross anisotropy) decreases EhlEv decreases pronounced for D EhlEv when EhlEv < 1 VVH Very significant Effect on D greater Very significant than on Su increase in Su as VVH increase in D as VVH decreases, decreases (forEhlEv = 2) Little effect for D increases as VH Effect on D greater VH decreases than on Su E~v=2 Nonlinear stress Local yield Local yielding Effect on D greater strain soil behavior increases, Su increases D and than on Su changes distribution of D versus depth Embankment Very little effect Little effect Effect on D greater stiffness than on Su, but is probably negligible Roughness at base Small reduction in Very significant Effect on D greater of elastic layer Su for full adhesion, reduction in D for than on Su, not as compared to no full adhesion as adhesion compared to no relevant to case adhesion studies Eh, Ev = Young's modulus in horizontal and vertical directions, respectively. VVH = Poisson's ratio for effect of horizontal strain on vertical strain. VH =Poisson's ratio for effect of horizontal strain on complementary horizontal strain. 37
- 56. R 111111~q '777f?? j"»' L =00 i 1 i I (a) q I I Lo =5 Rj I I I / ~I~ r/.l II ......""" 4-< 0 IZl Q) ::l -cd > ~I~ r/.l II ......""" 4-< 0 IZl Q) ::l C;; > (b) 0 1 2 0 1 2 R Radial distance R 1 ~~I 1 1 ---'--1-- 1 1 I I I -------~--------~-- R I I ~=5 I R I --------1-- ~=O.3 I v=O.2 I v=O.O 1 I I -------~--------~-- O~--------~~~~~~~--- //1/////////////////////' (c) ~I~ r/.l II ......""" 4-< o IZl Q) ::l ~ 1 R v=O.5 b------ 1 I 1 R 3 1 1 I I--1---------1-- 1 1 Figure 2.1 Settlement of flexible load on circular area on surface of elastic layer for three different depth ratios (After Terzaghi 1943). 38
- 57. 3-0 L LIB / 100/ L =length ~ / 50 n q / oIIII!!II""" 2-5 'f'JII'//-1t--Y /,)...'- I///-",</A D l - a:. ........ " ~ U'- t---, 20 T , H If"" ~ I-"""'"" / ../ ) =0-5 /"' 10 2-0 ////////////////// V ----I"""" ~ ~ 5/ ~ fJ-, 1-5 POo s = q Bi (-LO(-Ll- E - 1-0 ~ ./ /~ 0-5 ~ ~ ~ ~ ioo""" 0-0 ........ 0-' 0-2 0-5 1·0 O-g 0·8 0·7 0·6 0·5 0,' 0·2 0·5 1// ~ ~~.JIIII' h D' , ~ L/" ---- 2 2 --- 5 10 20 H/B 5 10 20 D/B 2 ~ Square I "H Circle I 50 100 1000 50 100 1000 Figure 2_2 Coefficients for vertical displacement (After Janbu, Bjerrum, and Kjaemsli 1956)_ 39
- 58. 1.5~--------~--------~~~----~---5----~ I-ll 1.0 t-------+-----:l~__+-----;_----___1 Square Circle 0.5~--------~~~--~--------~--------~ O~~~~~~~~~~~--~~~~--~~~~ 0.1 1 10 HIB 100 1000 1.O.-----.------~~----._----_, I-lo 0.9 t--~~__t__-__+_-__+_-_____I~-------r---~~--~ 0.8 ______...1..-_______--'-_ _ _ _-.1._ _ _ _-----1 o -" 15 Figure 2.3 Values of I-lo and I-ll for elastic settlement calculation (After Christian and Carrier 1978) 40 20
- 59. 1.0 r---r----r---.,-----,--~-___r-~-_r__r_,___, 0.6~~~~------~------------_+------~----~--_4 CLAY 0.4 .:......___-BOSTON BLUE CLAY I0.2 r-t-----~~s.s;:::::==::::, CLAY '. -0.2 t--t----------___r----- (i] UNDISTURBED OSLO CLAY -0." o UNDISTURBED KAWASAKI CLAY X REMOLDED VICKSBURG BUCKSHOT -0.6L-~______~____~______~____~__~__~--~~~~ 4 6 e 10 Overconsolidation Ratio Figure 2.4 Relationship between initial shear stress ratio and overconsolidation ratio (After D'Appolonia et al. 1971) 41
- 60. ::l IZl -<I.) IZl II e>:: IZl 0.8 ~---+-~..:--~-----J:Ioo...,...---.:::!I.....t--o .........--1 0.6~---~---~~~--~--- 0.4 ~---~---~-----+---"'-,,~-+---...--; 0L---~---L--~----~--~--~__-4__~____~__~ o 0.2 0.4 0.6 0.8 1.0 Applied Stress Ratio, q / qu 1.0 r----,.........,.'T'""--,-'"'I::""-r-....~.....,-~r__-T"""-"T'""-..., 0.6~---+---~~---4-~~-~~-~-~ 0.4~----4----~~~---~~----+-~.-~ 0.2 LIB =1.0 o 0.2 0.4 0.6 o.e 1.0 Applied Stress Ratio, q / qu 1.0 0.8 0.6 0.4 0.2 t----L IB =1.5 --+-----+-----+--"'"'.......:----1 o °0 Figure 2.5 O~ 0.6 0.8 1.0 Applied Stress Ratio, q / qu Relationship between settlement ratio and applied stress ratio for strip foundation on homogeneous isotropic elastic layer (After D'Appolonia et al. 1971). 42
- 61. .j:>.. VJ ~ f) ,...... I-t x / bl or x / b2 -o·~to:;bj>~i g Iii ~o La 15 1 1('1• i I ) v=O.5 2.0~IL----+----4----~----+---~--- Incompressible layer Immediate settlement at point M: 2 [ ( )2]S - rh bl r; _ b2 r: /I - E b -b I b 2 /I I 2 I 2.5' t. • Figure 2.6 Graph for calculating immediate settlement under embankment load(after Giroud 1973).
- 62. S<.) ";> -+::>. (/) -+::>. x,m 0 / 5 - -- 10 15 20 25 30 35 - - LolB= 10 - - - LolB = 0.5 40 Figure 2.7 Undrained settlement trough across the embankment width using Giroud's method (1973) for thick and thin deposit at embankment height of 11m.
- 63. xlb _0.2 0 1 2 - 0.' > 0...., 0.1 0.2 0.3 0.4 (a) qb Sll =-·lv Etl 00 01 Q2 0.3 0.40.5 0.2 >-4 0 0.4 N O.6 0.8 1.0 '---~""'--"---'---.J (b) S = qLo. 1It E v It Uniformly loaded strip X 0 0.0 ..c:...., -0.1 0 0 0.2 004 t::3 NO.6 0.8 1.0 Ca;e v = 0.49 Lo = 1.7b xlb 1 2 (c) qb Ds =-'[h Etl Ih - 0.1 - 0.2 - 0.3 D = qLo. 1 E h u 2 E o5 2, (d) 0 ~ 3 ,. GZ Figure 2.8 Influence of soil inhomgeneity on displacements (After Poulos 1972). 45
- 64. a =Radius r =Radial distance q =Applied pressure Eit G Case Vh Vvh Vhv - Ev Ev e 2.0 0.2 0.2 0.4 1.0 f 1.0 0.2 0.2 0.2 0.83 g 0.5 0.2 0.2 0.1 0.5 ria ria 0 1 2 0 1 2 0 0 0.5 0.5 1.0 1.0 ;> ......, 1.5 ..c; ......, 1.5 2.0 2.5 2.0 qa qa (a) Su =-·Iv (b) Ds =-·IIt Ev Ev Displacement on surface Ds = horizontal displacement at the edge of the loaded area, at the ground surface Figure 2.9 Effect of modular ratio EhlEv on settlement and surface lateral displacement by a circular loading of semi-infinite cross anisotropic soil (After Poulos 1972). 46
- 65. oj::>. S --.l ..d..... 0.. Q) Q Lateral Deformation, cm 012345678012345678910 0 1 2345678910 012345678 Ol'TTT"nTrTTT1TrTTT1TT1TTTTT"lTTTTTTTT"1rTTTT1 5 10 15 20 25 30 35 40 45 50 55 60 65 / SI-l SI-3 (49 m L of c.L.) (16 m R of C.L.) / } / / SI-4 (33 m R of c.L.) - - Measured values for embnakment elevation 12.5 m at Nov. - Dec. 1968 - - Predicted values (initial movement only) / / /SI-5 I J j (56 m R of c.L.) Figure 2.10 Comparison between measured and predicted lateral deformation at various locations of 1-95 sec. 246 embankment (After Poulos 1972).
- 66. 10 lc .2 :;,. ·20 .!/ UJ .]0 ...0 620 (EOC) 2lXX> •~!!-- --~~~~-'~--+---~ F o 4 • 12 16 0 4 • Laleral Deneclion (em) ../.... t 'r'".j..... .j..... i Figure 2.11 Comparison of MIT-E3 predictions and measured horizontal displacements (After Ladd et al. 1994). ·10 ! g .~ •• ·20 ~ .]0 "'0 B ..;-........ u C..:0 ·;·0····· .g........ 8 E~ F o 4 • 12 0 4 • 12 16 0 4 • Lateral Defleclion (em) o 4 • Figure 2.12 Comparison of MCC predictions and measured horizontal displacements (After Ladd et al. 1994). 48
- 67. 8 8 t:: 0 .-...... ro 8;... t.8<l) Q c;j ;... <l) ...... ro .....4 (a) (b) Lateral Deformation h = 1.3 m 0 8 4 ..c.... h = 1.3 m 0.. <l) Q -20 -10 8 100 11 II 0 8 ..d' 4 ...... 0.. <l) 0 Q D 8 -+ h=2.0m -aJ -10 0 10 11 D -+ h = 2.8 m -10 o -20 10 8 13 4r--+~~--~--~-H~~~~+-~ fr Q Distance (m) from Embankment Toe Distance (m) from Embankment Toe Run F = FEECON Undrained Run U = CRISP Undrained Run C = CRISP Coupled Consolidation Figure 2.13 Finite element analyses with measurements of Rio De Janeiro trial embankment at three stages of construction, (a) lateral deformation at embankment base, (b) lateral deformation at inclinometers (After Almeida and Ramalho-Ortigao 1982). 49
- 68. E E 600 500 d' 400 o .-....... c<:S E ~ 300 0) "d 100 Range of finite element results "'" Observed O~~----L-------~'-------L------~------~------~----~ o 20 40 Nov. 1992 60 80 Time, weeks Nov. 1993 100 Nov. 1994 120 Figure 2.14 Observed and predicted lateral deformation at Whitewall Creek embankment (After Russell 1996). 50 140
- 69. a() a() ~ 50 / / • / • •• 5 10 15 20 25 30 Computed maximum Lateral Deformation, Dm(calc)' em .1 , /. ./ / • 35 o~~~LL~-L~~-L~~-L~~~~~LL~~LL~-L~ o 10 20 30 40 50 60 70 80 Computed Settlement at center, S calc' em Fig 2.15 Comparison of predictions using finite element technique and observations of construction settlements St and lateral deformation D (After Tavenas et al. 1979). 51
- 70. 1.0 - BIH=2 0.8 • - •. BIH =3 _.- BIH=4 - .- BIH=6 0.6CI:l > -0 > 0.4 0.2 o 20 40 60 80 100 Degree of Consolidation, (Uv)ec (%) Figure 2.16 The ratio of lateral displacement volumes to settlement volume plotted against the degree of consolidation (After Sekiguchi et al. (1988). B/2 B12 VrJ2 Soft Clay Soft Clay Firm Stratum (a) (b) Figure 2.17 Cross-section of an embankment foundation system together with principal symbols indicated. 52
- 71. ,-.... ~ '-' ~ §o ..... .- ........ (.) .a 2......... - C/l o ~ C/l 0 ~ (.) o,-+-< U 0 '-+-<-0 o ~ I!) I!) I!) I!) I-<..c ~ .... O~ time Factor 0.001 0.01 0.1 1 10 0 10 20 30 40 50 60 70 80 90 100 Figure 2.18 Calculated relationship between the degree of consolidation and construction time factor (After Sekiguchi et al. 1988). 53
- 72. 28 E 24u ci 0 '.g E 20i-< t8OJ Q 'Cd 16i-< ~ ...J E:::I E 12 'R ro ~ "E 8Q 4 o~~~~~~-L~-L~~~~~~~~-L~-L~-L~~~~ o 4 8 12 16 20 24 28 32 St' Total Construction Settlement at center, cm Figure 2.19 Variation of the maximum lateral deformation at the toe with the construction settlement for Lanester embankment (After Tavenas et al. 1979). 54
- 73. 8(J =.S::01-' ro 8;... <2ClJ Q c;a;... ClJ01-' ro .....:l 8 ::l 8 ><ro ~ Q- ........ u -.., .... -;... -,.;:; u ""' .. u - .-... .,... £ - "" 20 Development of a normally Hconsolidated state as indicated by pore-pressure observations 15 10 5 (a) o~~art~~~~~~~~~~~~~~ 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 H, Height of fill, m --.- Cubzac les Ponts - A - Kalix 15 -0- King's Lynn -0- Tickton 10 (b) o~~~~~wu~~~~~~~~~~~~~~~ o 5 10 15 20 25 30 35 40 45 50 St' Settlement dring consturction, cm Figure 2.20 Variations of the maximum lateral deformation with (a) the height of fill and (b) the construction settlement in slightly overconsolidated clay foundations (After Tavenas et al. 1979). 55
- 74. 25 := Cubzac B0 7 .-~ 20 0 ProvinsS..... 0 Palavas, with drains.8Q) • Palavas, without drain0 ~ 15 !:::,. St. Alban B..... 0Q) Drammen II~ ... .....:l • SkaEdeby VI S;:j 10 S.>< ro ;;S 5~E 0<] o ~~~~~~~~~~~~~~~~~~~~~~~~~~ o 10 20 30 40 50 60 70 80 90 100 ~St' Maximum Verical Settlement, cm Figure 2.21 Relationship between the maximum lateral deformation and the total settlement after the end of construction under seven embankments (After Tavenas et al. 1979). 56
- 75. 8 a -r.;:: 6 4-< 0 4...... ...c: b.O.,..., C) 2::r: ...c: 0 0 100 200 300 400 Time, day 1st loading Consolidation 2nd loading stage during 268 days stage 500 600 Consolidation during 335 days 700 100 ~~~--------~~----~~------------------~ 80 40 B=60m IE ~I 20 /3:1 ~ tLO= 26 m 0 0 20 40 60 80 100 120 140 160 180 St' Total Settlement at the center during consturction , em 800 200 Figure 2.22 Development of maximum lateral deformation with the settlement during stage constructin - Palavas test fill (After Tavenas et al. 1979). 57
- 76. ~- N II N Z 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 rrlrTI-,--r.."..,--r-,....,,....,-T'"'T",,.,rTI-r-T.,--r-........-r-r,....,-T'"'T",..........,,.....,.....,o:::r-r-r-l<,,...,....,.....,.....,....,....,...., 0.1 ----- 1st Loading stage - - 2nd Loading stage 0.2 0.3 0.4 0.5 / 0.6 0.7 0.8 0.9 1.0 Figure 2.23 Lateral deformation profiles at variours stages of construction under the Palavas test fill (After Tavenas et al. 1979). 58
- 77. 22 Feb 02Jun 10 Sep 19 Dec 1991 1991 1991 1991 10 S 9u d .s 8.....~ S 7I-< <211) 6Q '"@ 5I-< 11) Cil .....:l S 4 S 3 ·R ~ 2 2nd loading stage :;s Fill height = 2.02 m ~E 1 Rate of lateral Q deformation = 0.061 em/day 0 0 50 100 150 200 250 300 350 400 Time (days since 22 Feb'91) Figure 2.24 Variations of the maximum lateral deformation with the time during stage constructin - Bang Na-Bang Pakong (After Teparaksa 1992). 59
- 78. 12 S(.) ci 100 .-~ SI-< 8t80) 0 C; 6I-< 0) ...... ~ .-:l E 4 E.;< ~ ~ 2 ~E 0 0 0 2 4 6 8 10 12 St' Total Settlement, em 2nd loading stage Fill height = 2.02 ill .:iDm/.:iS, =0.46 14 16 18 20 Figure 2.25 Variations of the maximum lateral deformation with total settlement during stage eonstruetin - Bang Na-Bang Pakong (After Teparaksa 1992). 60
- 79. ~ o ..g 50 8I-< <2Q.) 40 q ~ I-< ~ 30 8 S 20.~ C'Q ~ "6 10 q Note: (0.15) = Value of I:!.Dm/I:!.St ____--Case A & B Time [F;~~.31-- ~)~ C: Vertical Drain EOC [FS =1.3] ,/'" -..- A: No Drains ~--,.. ,/'" J - (O.~ ~ EOC ,/'" - - - [FS > 1.3] ___ --:;.- B: Vertical Drain (0.10) o ~~~~~~~~~~~~~~~~~~~~~~~~WL~ o 10 20 30 40 50 60 70 80 90 100 St' Consturetion Settlement, ern Figure 2.26 Variations of the maximum lateral deformation with the settlement for first stage eonstruetin - Palavas test fill (After Ladd 1991). 61
- 80. r___B/2 x . _~(U~D~)_~-t--- C.... B~--- UD - u d n b I H1V' ----._co - consolidation deformation boundary / / I M Flfure 2.27 Deformation pattern of embankment foundation at end of loading stage (After Loganathan et al. 1993). 62
- 81. tI Embankment LoodinQ End of Loading (EL) BL----- EL......-~ I F---- H I I / / / • • (CO) cr - creep deformation boundary M Figure 2.28 Defonnation pattern of embankment foundation at end of consolidation (After Loganathan et al. 1993). 63
- 82. 1.00.-------------------------1 Define Stage 1 Stage 2 Stage 3 0.80 Scheme 312 0.27 0.33 0.14 Scheme 6/6 0.27 0.10 0.33 0.60 ()-O-{) Scheme 3/2 <1) ....... Scheme 6/6 ;:l c;3 > c::5 0.40 ,. .... 0.20 .... ""- , / .. ".... ..... /.... " , 'fl 0.00 0 100 200 300 Time, days Figure 2.29 a-values for different stages of construction (After Loganathan et al. 1993). 64
- 83. § 100 iQ) a~ :::::Q) C/) c o0.g :-9 '0rJl § 200 u 50 Undrained Settlement, mm 100 150 200 250 Loading Stage htL- Time, days • 300------------------------------------------------~ Figure 2.30 Relationship between undrained settlement and consolidation settlement during construction (After Loganathan et al. 1993). 65
- 84. Undrained Settlement, mm o 100 150 200 • Consolidation Stage 100 8 8 h t/-- • ......s Time, daysc(!) 8 ~............(!) CI) c .S...... ro ~ -0 rn C 0 U 200 • 300 Su =0.0012 Sd·2 Sd =in mm • 400+-------------------------------------------------1 Figure 2.31 Relationship between undrained settlement and consolidation settlement during post-construction (After Loganathan et al. 1993). 66
- 85. CHAPTER 3 BEHAVIOR OF CLAY FOUNDATIONS SUBJECTED TO EMBANKMENT LOADING 3.1 Yielding of Clay Foundations Subjected to Embankment Loading 3.1.1 Yielding of Clay Structure The concept of yielding is very important for understanding the behavior of clay foundation beneath embankments. After yielding, the deformation of soil includes plastic flow causing irrecoverable deformation. Also the soil compressibility and associated pore water pressure increase. Yield stress separates 'elastic' and 'plastic' deformation states of the soil, however, for any mode of loading, it depends on the rate of loading. Evidence that natural clays possess a yield locus comes from the work of Mitchell (1970) and others (Loudon 1967, Crooks and Graham 1976, Tavenas and Leroueil 1979, Baracos et al. 1980). The most common observation of yielding for clays is the preconsolidation pressure measured in one-dimensional consolidation tests (Casagrande, 1936). Terzaghi et al. (1996) stated that the one dimensional consolidation in odometer test represents one of an infinite number of stress paths that could be generated to cause yielding under a drained condition. The effective stress path and the corresponding compression curve for an oedometer test are shown in Fig. 3.1. Yield envelope can be defined by obtaining sufficient number of yield points. The preconsolidation pressure (Jp' corresponds to the effective major principal stress at yield for the oedometer mode of loading. At effective vertical stresses less than the yield stress compression of the specimen is small and mostly recoverable. At stresses exceeding the yield stress. The compression is relatively large and mostly irrecoverable. In drained tests the specimens suffer large volume 67
- 86. compression and associated distortion as the stress path crosses the yield envelope. In the undrained condition yield occurs when the structure of the soil breaks down and relatively high pore water pressures develop. The most complete experimental work has been carried out on highly sensitive or structured natural clays (Mitchell 1970, Pender et al. 1975, Wood 1980, Tavenas and Leroueil 1977 & 1979, Leroueil et aI. 1979 and Tavenas et aI., 1979). For these materials, yielding is very pronounced and causes a drastic change in observed behavior which is assumed to be caused by destructuring of the material (Leroueil et al. 1979) beyond the yield condition (Mitchell 1970, Tavenas et aI. 1979). From a modeling perspective, these clays do not exhibit normalized behavior. Secondary compression leads to an increase in the yield loci for clays (Bjerrum 1967, 1972, Mesri and Choi 1979, 1984, Mesri 1993). 3.1.2 Yielding of Clay Foundation under Embankments Most natural soft clay deposits, as they occur in situ, have developed some degree of preconsolidation in a sense that they display a preconsolidation pressure greater than the present effective overburden pressure. This overconsolidation can be a result of secondary compression, thixotropic hardening, chemical changes, or geologic process, such as erosion, water table fluctuations, and temporary snow loads, or any combination of these processes (Mesri 1993). A recompression range and preconsolidation pressure, as exhibited on a plot of end of primary void ratio-logarithm of effective stress (EOP e- log cr'v), result from the preconsolidation. A typical EOP e-log cr'v for structured soft clay with a preconsolidation pressure, cr'p, is presented in Fig. 3.2. This overconsolidation results in large coefficients of consolidation, Cy , typically of the order of 5 to 50 m2/year in the recompression range(Mesri and Rokhsar 1974, Tavenas et aI. 1979, Terzaghi et al. 1996). 68
- 87. When an embankment is constructed on a clay foundation that exhibits a preconsolidation pressure, significant pore water pressure dissipation can occur during the initial stages of construction (Mesri and Rokhsar 1974). Leroueil et al. (1978) observed this behavior under 29 embankments on slightly preconsolidated clay foundations. During recompression consolidation, drainage occurs, and lateral deformation is expected to be small. If the final effective vertical stress, cr'vf, due to the embankment load is less than cr'p, lateral deformations may be negligible. However, if cr'vf due to the embankment load exceeds cr'p, the preconsolidation pressure is surpassed during embankment construction. In this case, the soil yields while total stress is still increasing. When the effective stress reaches the preconsolidation pressure, the soil yields, and additional increases in total stress occur under a practically undrained condition. An undrained condition is expected because of the increase in compressibility associated with the yielding of soil. In an undrained state. increments of lateral deformation near the toe should be approximately equal to Increments of vertical deformation at the center. This condition will apply until the end of construction. At the end of construction, total stress increase is complete, and drainage occurs. This drainage allows consolidation, and further lateral deformation (creep) 1sexpected to develop at a decreasing rate. 3.1.3 Foundation Behavior Described Using Effective Stress Path Til ena" et al. (1979) qualitatively described the above behavior and the de'elopment of lateral deformation in terms of effective stress path based on data collected b:- Leroueil et al. (1978b), as shown in Fig. 3.3. Figure 3.3 presents a typical effectie stress path for a preconsolidated clay foundation subjected to an embankment load. Points 0 and 0' represent the total and effective stress states of the foundation before embankment loading, respectively. Segments OPFR represent the total stress path of the clay throughout loading. 69
- 88. Upon initial loading, the effective stress path follows O/p/. This path corresponds to the behavior of a preconsolidated soil, and represents a soil in the recompression range on the field BOP e-Iog d y curve. In terms of elastic analysis, this path corresponds to a drained loading, and a Poisson's ratio less than 0.5. (A Poisson's ratio of 0.5 represents undrained elastic behavior, and is typically employed in elastic analyses throughout the construction period.) From point 0 1 to pi on the effective stress path, lateral deformations are expected to be small. The effective stress path reaches the yield envelope (or limit surface) at an effective vertical stress approximately equal to the preconsolidation pressure. At this point, the soil yields and becomes normally consolidated. From point pi, continued increase in total stress, i.e. continued embankment construction would cause the stress path to follow the yield envelope from P' to F'. Along this path, loading causes an undrained plastic flow of the clay, and lateral strain increments should be equal to vertical strain increments. At point FI, progressive failure begins, and continued embankment loading will cause strain softening until the soil reaches the critical state at point R/. Folkes and Crooks (1985) also analyzed the effective stress paths measured under several embankments. They concluded that soft clay behavior under embankment loading cannot be characterized by a single effective stress path. In a discussion of the work conducted by Folkes and Crooks (1985), Leroueil and Tavenas (1986) concede that more than one effective stress path is needed to properly describe soft clay foundation behavior. However, Leroueil and Tavenas (1986) point out that a majority of the 45 embankments analyzed at that time had behaved according to the model described in Fig. 3.3. They described three effective stress paths and pore pressure generation to characterize the behavior of soft clay under embankment loading. Pore pressure generation is described by the pore pressure coefficient BI = flu/flcry • During undrained loading, BI assumes a value of 1.0, and under drained conditions, i.e., during consolidation, BI assumes a value less than unity dependent upon the value of Cy , length of the drainage path, and rate of construction. Leroueil and Tavenas (1986) anticipated 70
- 89. that at least one additional effective stress path and pore pressure generation is necessary to describe possible foundation behavior under embankment loading. Figure 3.4 illustrates the five cases of effective stress path and pore pressure generation. Effective stress path (A) is observed in a foundation soil when yielding and failure are reached at the same time (point Y in Fig. 3.4a). This behavior has been observed in clay foundations where the value of cr'p - cr'yO was small and apparently either very rapid construction or rather low Cy and thick layer. In other words, this represents a soil with a small preconsolidation pressure and corresponding low undrained shear strength. In this case, the excess porewater pressure increase, Llu, is slightly less than the increase in total vertical stress, Llcry , i.e., B' is slightly less than one corresponding to a normally consolidated condition. Upon reaching point Y, strain softening occurs and the value of B' becomes larger than one. Effective stress path (B1) (see Fig. 3.4b) is observed in a foundation soil that exhibits a significant preconsolidation pressure. At the beginning of construction, drainage and consolidation occur, resulting in a value of B' less than one. Upon reaching the preconsolidation pressure, continued loading until the end of construction occurs under an undrained condition. While undrained, B' is equal to unity. Effective stress path (B2) (see Fig. 3.4c) is a special case of effective stress path (Bl) where the end of construction occurs after local failure of the soil. This is the case described by Tavenas et al. (1979). The B' coefficient initially behaves in the same manner as in case (B 1), however, after failure of the foundation clay, large shear-induced excess pore water pressures resulting from local failure cause B' to assume a value larger than one until the end of construction. Effective stress path (C) (see Fig. 3.4d) corresponds to a clay foundation with a preconsolidation pressure, and a value of (cr'yf that is greater than cr'p). In this case, the end of construction occurs before sufficient consolidation has taken place to reach the yielding of the clay (apparently fast loading or thick layer with low cy ). During 71