Tài liệu A comparative study on the horizontal coefficient of consolidation (cr) obtained from lab and field tests

VIETNAM NATIONAL UNIVESITY, HANOI VIETNAM JAPAN UNIVERSITY TRAN QUYNH GIAO A COMPARATIVE STUDY ON THE HORIZONTAL COEFFICIENT OF CONSOLIDATION (Cr) OBTAINED FROM LAB TESTS MASTER’S THESIS Hanoi, 2020 VIETNAM NATIONAL UNIVESITY, HANOI VIETNAM JAPAN UNIVERSITY TRAN QUYNH GIAO A COMPARATIVE STUDY ON THE HORIZONTAL COEFFICIENT OF CONSOLIDATION (Cr) OBTAINED FROM LAB TESTS MASTER’S THESIS MAJOR: INFRASTRUCTURE ENGINEERING CODE: 8900201.04 QTD RESEARCH SUPERVISOR: Dr. NGUYEN TIEN DUNG Hanoi, 2020 ABSTRACT When a soft ground is improved by PVDs, consolidation takes place under the condition of drainage in both horizontal and vertical directions. Naturally, horizontal coefficient of consolidation (cr) is larger than the vertical coefficient of consolidation (cv) by a factor of 3 to 5. The cv value is commonly interpreted from consolidation test using incremental loading method [1]. However, up to date, there have not been any similar standards for the consolidation test with horizontal drainage (using incremental loading method). The key goals of the research are: (1) determine the most reliable methods among the proposed methods for determining the horizontal coefficient of consolidation (cr) in the literature; (2) determine correlations between cr values obtained from central drain (CD) test and peripheral drain (PD) test; (3) determine correlations between vertical coefficients of consolidation (cv) and radial cr for a number of test sites in Vietnam. A desk study is carried out to secure the following: (1) a literature review on equipment used for the test and existing methods used to evaluate the cr value; (2) the thesis using data collected from the following sources literature review and test site in Vietnam. Overall, The most reliable methods for determining the horizontal coefficient of consolidation (cr) is non-graphical method and the root t can be used to determine the radial (horizontal) coefficient of consolidation (cr). cr,PD is less than the cr,CD by a factor of 0.32 to 0.64 from intact samples and 0.33 to 0.58 from remolded samples. cr PD is larger than the cv by a factor of 0.90 to 2.33, cr CD is larger than the cv by a factor of 2.14 to 5.12 from intact samples. cr PD is less than the cv by a factor of 0.35 to 1.01, cr CD is less than the cv by a factor of 0.41 to 0.82 from intact samples. i ACKNOWLEDGEMENTS I would like to express my sincere appreciation for the lecturers of Master of Infrastructure Engineering Program for their help during my undergraduate at Vietnam Japan University (VJU). My thesis supervisor Dr. Nguyen Tine Dung for his enthusiasm, patience, advice and continuous source of ideas for me. Dr. Dung is always ready to answer my questions. His support in professional matters is invaluable. I would like to acknowledge the sincere inspiration from Prof. Nguyen Dinh Duc and Prof. Hironori Kato. Their lectures covered not only specialist knowledge but also the responsibility and mission of a new generation of Vietnam. I am grateful to Dr. Phan Le Binh for his support in the last two years since I have studied at Vietnam Japan University. Thanks to him, I have learned the professional courtesy of Japanese people as well as Japanese culture. Finally, I want to spend thank to my parents and friends for their unflinching support in the tough time. Their support, spoken or unspoken, has helped me complete my master thesis. ii TABLE OF CONTENTS Page ABSTRACT ................................................................................................................ i ACKNOWLEDGEMENTS ....................................................................................... ii TABLE OF CONTENTS .......................................................................................... iii LIST OF TABLES .................................................................................................... vi LIST OF FIGURES................................................................................................... vi LIST OF ABBREVIATIONS ................................................................................. viii CHAPTER 1. INTRODUCTION ...............................................................................1 1.1 Problem statement .............................................................................................1 1.2 Necessity of study .............................................................................................3 1.3 Objectives ..........................................................................................................4 1.4 Scope of study ...................................................................................................4 1.5 Structure of thesis ..............................................................................................4 CHAPTER 2. LITERATURE REVIEW ....................................................................6 2.1 Introduction .......................................................................................................6 2.1.1 Consolidation Theory with Horizontal Drainage .......................................8 2.1.2 Solution of the governing equation (2.2) for a central drain (CD) under equal strain loading (ESL) condition ..................................................................8 2.1.3 Solution of the governing equation (2.2) for a peripheral drain (PD) under free strain loading (FSL) condition ...........................................................9 2.1.4 Solution of the governing equation (2.2) for a peripheral drain (PD) under equal strain loading (ESL) condition ........................................................9 2.2 Existing methods for determining cr from consolidation test with a peripheral drain using incremental loading ............................................................................10 2.2.1 Root t method [6] .....................................................................................10 2.2.2 Inflection point method [9] ......................................................................11 2.2.3 Full – match method [10] .........................................................................13 2.3 Existing methods for determining cr from consolidation test with a central drain using incremental loading method ...............................................................15 2.3.1 Root t method [11] ...................................................................................15 2.3.2 Matching log (de2/t) and Ur method [12] ..................................................16 2.3.3 Inflection point method [13] ....................................................................17 2.3.4 Non-graphical method [14] ......................................................................18 2.3.5 Log - log method [15] ..............................................................................19 2.3.6 Steepest tangent fitting method [16] ........................................................20 2.3.7 Log t method [17].....................................................................................22 2.3.8 Full – match method [10] .........................................................................24 2.4 Summary of methods for determining cr.........................................................25 2.5 Linear regression analysis ...............................................................................25 2.6 Log normal distribution method .....................................................................26 CHAPTER 3. METHODOLOGY ............................................................................27 iii 3.1 Introduction .....................................................................................................27 3.2 Data collection ................................................................................................28 3.3 Improvement for inflection point methods .....................................................28 3.3.1 Theoretical development ..........................................................................28 3.3.2 The procedure for this method .................................................................29 3.4 Analysis of Time – Compression curve ..........................................................29 3.5 Procedure to select the best methods ..............................................................30 3.6 Procedure to determine ratios of cr PD /cr CD or cr /cv .......................................31 CHAPTER 4. TEST RESULTS & DISCUSSIONS .................................................33 4.1 Introduction .....................................................................................................33 4.2 Summary of database ......................................................................................33 4.2.1 Data collected from the literature.............................................................33 4.2.2 Data collected from test sites in Vietnam ................................................34 4.2.3 Summary of test data ................................................................................37 4.3 Evaluation and selection the best methods on intact samples .........................38 4.3.1 Graph results on intact samples ...............................................................38 4.3.2 Summary of results on intact samples......................................................40 4.3.3 Summary of rank method on intact samples ............................................47 4.4 Evaluation and selection the best methods on literature data .........................49 4.4.1 Graph results on literature data ................................................................49 4.4.2 Summary of results on literature data ......................................................51 4.4.3 Summary of rank method on literature data.............................................52 4.5 Evaluation and selection the best methods on remolded samples ..................54 4.5.1 Graph results on remolded samples .........................................................54 4.5.2 Summary of results on remolded samples ...............................................56 4.5.3 Summary of rank method on remolded samples ......................................62 4.6 Comparison of cr CD and cr PD on intact samples ..............................................64 4.6.1 Graph results on intact samples ...............................................................64 4.6.2 Summary of results on intact samples......................................................64 4.7 Comparison of cr CD and cr PD on remolded samples ........................................66 4.7.1 Graph results on remolded samples .........................................................66 4.7.2 Summary of results from remolded samples............................................66 4.8 Comparison of cv and cr PD on intact samples..................................................68 4.8.1 Graph results on intact samples ...............................................................68 4.8.2 Summary of results on intact samples......................................................68 4.9 Comparison of cv and cr CD on intact samples .................................................70 4.9.1 Graph results on intact samples ...............................................................70 4.9.2 Summary of results on intact samples......................................................70 4.10 Comparison of cv and cr PD on remolded samples .........................................72 4.10.1 Graph of results on remolded samples ...................................................72 4.10.2 Summary of results on remolded samples .............................................72 4.11 Comparison of cv and cr CD on remolded samples .........................................74 4.11.1 Graph results on remolded samples .......................................................74 4.11.2 Summary of results on remolded samples .............................................74 iv CHAPTER 5. CONCLUSIONS & RECOMMENDATIONS ..................................76 REFERENCES ..........................................................................................................79 v LIST OF TABLES Page Table 2.1. Boundary condition ....................................................................................9 Table 2.2. Existing methods for determining cr from radial consolidation ..............25 Table 4.1. Summary of data from literature for the PD – ESL condition .................33 Table 4.2. Summary of data from literature for the CD – ESL condition ................34 Table 4.3. Summary of tests done on intact samples ................................................37 Table 4.4. Summary of tests done on remolded samples ..........................................37 Table 4.5. Summary of results from PD tests on intact samples ..............................40 Table 4.6. Summary of results from CD tests on intact samples ..............................42 Table 4.7. Rank of each criterion with each pressure from PD tests on intact samples...............................................................................................................44 Table 4.8. Rank of each criterion with each pressure for CD case on intact samples ...........................................................................................................................45 Table 4.9. Summary of rank for each method from PD tests on intact samples .......47 Table 4.10. Summary of rank on each meth1od from CD tests on intact samples ...48 Table 4.11. Summary of results from PD tests on literature for 8 methods. ............51 Table 4.12. Summary of results from CD tests on literature for 8 methods. ............52 Table 4.13. Summary of rank on each method from PD tests on literature ..............52 Table 4.14. Summary of rank on each method from CD tests on literature .............53 Table 4.15. Summary results from PD tests on remolded samples for 8 methods ...56 Table 4.16. Summary of results from CD tests on remolded samples for 8 methods ...........................................................................................................................58 Table 4.17. Rank of each criterion with each pressure from PD tests on remolded samples for 8 methods .......................................................................................59 Table 4.18. Rank of each criterion with each pressure from CD tests on remolded samples for 8 methods .......................................................................................61 Table 4.19. Summary of rank each method from PD tests on remolded samples ....62 Table 4.20. Summary of rank each method from CD tests on remolded samples ....63 Table 4.21. Summary of results from PD and CD tests on intact samples ...............65 Table 4.22. Summary of boundary for PD and CD case on intact samples ..............65 Table 4.23. Summary of correlations for CD and PD case on remolded samples ....67 Table 4.24. Summary of boundary for CD and PD case on remolded samples .......67 Table 4.25. Summary of correlations for PD case on intact samples .......................69 Table 4.26. Summary of boundary for PD case on intact samples ...........................69 Table 4.27. Summary of correlation for CD case on intact samples ........................71 Table 4.28. Summary of boundary for CD method on intact samples .....................71 vi Table 4.29. Summary of correlations for PD case on remolded samples .................73 Table 4.30. Summary of boundary for PD case on remolded samples .....................73 Table 4.31. Summary of correlations for CD method on remolded samples ...........75 Table 4.32. Summary of boundary for CD method on remolded samples ...............75 vii LIST OF FIGURES Page Figure 1.1. Map of distribution of major soil types in Indochinese ............................1 Figure 1.2. Soil phase diagram [3] ..............................................................................2 Figure 1.3. An Illustration of soft ground improved by PVDs ...................................2 Figure 2.1. Research direction of the thesis [5] ..........................................................7 Figure 2.2. Illustration of flow conditions for equal-strain case [6] ...........................7 Figure 2.3. Time - deformation plot during consolidation for a given load increment [3] ................................................................................................................................8 Figure 2.4. Consolidation curve relating square - Root time factor to for drainage radially outwards to periphery with equal strain loading [6]. ...................................11 Figure 2.5. Log (Ur/Tr) - log Ur relationship [10] .....................................................13 Figure 2.6. Determine the value of intersection point in full – match method .........14 Figure 2.7. Theoretical log(de2/t) versus Ur curves [12] ...........................................16 Figure 2.8. (a) Theretical Ur - log Tr curve and (b) d(Ur)/dlog Tr plot [13] ..............17 Figure 2.9. Log( - 0) versus log t plot [15] ............................................................20 Figure 2.10. Steepest tangent fitting method for determination of cr .......................21 Figure 3.1. Flow chart of the study ............................................................................... Figure 3.2. Experimental data [9] .............................................................................28 Figure 3.3. Flowchart of identifying the best methods ............................................30 Figure 3.4. Flowchart of identifying the best methods .............................................31 Figure 4.1. Locations of test sites in Viet Nam (VSIP site, DVIZ site, Kim Chung site) ............................................................................................................................34 Figure 4.2. Test location at Kim Chung site .............................................................35 Figure 4.3. Test location at VSIP site .......................................................................35 Figure 4.4. Test location at DVIZ site ......................................................................35 Figure 4.5. Soil profile at DVIZ ................................................................................36 Figure 4.6. Soil profile at VSIP .................................................................................36 Figure 4.7. Soil profile at KC ....................................................................................36 Figure 4.8. Results from PD tests on intact samples (at 800 kPa) for 8 methods .....38 Figure 4.9. Results from CD tests on intact samples (at 800 kPa) for 8 methods ....39 Figure 4.10. Results from PD tests on intact samples (at 800 kPa) for 8 methods ...49 Figure 4.11. Results from CD tests on literature for 8 methods ...............................50 Figure 4.12. Results from PD tests on remolded samples (at 800 kPa) for 8 methods ...................................................................................................................................54 Figure 4.13. Results from CD tests on remolded samples for 8 methods .................55 Figure 4.14. Comparison of cr CD and cr PD obtained from root t method at all data .64 viii Figure 4.15. Comparison of cr CD and cr PD obtained from non-graphical method at all data ............................................................................................................................64 Figure 4.16. Comparison of c r,CD and cr,PD obtained from root t method at all data 66 Figure 4.17. Comparison of cr CD and cr PD obtained from non-graphical method at all data .......................................................................................................................66 Figure 4.18. Comparison of cv and cr,PD obtained from root t method at all data .....68 Figure 4.19. Comparison of cv and cr,PD obtained from non-graphical method at all data ............................................................................................................................68 Figure 4.20. Comparison of cv and cr CD, obtained from root t method at all data ....70 Figure 4.21. Comparison of cv and cr CD obtained from non-graphical method at all data ............................................................................................................................70 Figure 4.22. Comparison of cv and cr,PD obtained from root t method at all data ....72 Figure 4.23. Comparison of cv and cr,PD obtained from non-graphical method at all data ............................................................................................................................72 Figure 4.24. Comparison of cv and cr,CD obtained from root t method at all data ....74 Figure 4.25. Comparison of cv and cr,CD obtained from Root t method at all data ..74 ix LIST OF ABBREVIATIONS cr cr,CD cr,PD cr,Root CD cr,NG PD cv de dw f n r t t50 t90 t66 tinf Tr T90 T66 Tv U u Δu 0 100 t p m kr PD kr CD Horizontal coefficient of consolidation Horizontal coefficient of consolidation under for a central drain (CD) condition Horizontal coefficient of consolidation under for a peripheral drain (PD) condition Horizontal coefficient of consolidation form root t method under for a central drain (CD) condition Horizontal coefficient of consolidation form non-graphical method under for a peripheral drain (PD) condition Vertical coefficient of consolidation Diameter of the soil sample Drain diameter Source/sink term; function; cyclic load natural frequency Ratio of influence radius to drain radius Radial coordinate Time Time required to reach 50% consolidation Time required to reach 90% consolidation Time required to reach 66% consolidation Time at d(Ur) /dlog Tr the maximum. Time factor for horizontal consolidation Time factor for horizontal consolidation to reach 90% consolidation Time factor for horizontal consolidation to reach 66% consolidation Time factor for vertical consolidation Degree of consolidation Pore-water pressure Change in pore pressure Initial settlement Finally settlement at Primary consolidation Settlement at time t Predicted settlement Measured settlement Permeability coefficient from PD case Permeability coefficient from CD case x kv mr mv w Permeability coefficient from vertical consolidation Soil stiffness from radial consolidation Soil stiffness from vertical consolidation Water unit weight xi CHAPTER 1. INTRODUCTION 1.1 Problem statement Fig. 1.1 shows a typical map of distribution of major soil types in Viet Nam. Among the soil types, the soft and young deposits distributed in major deltas in Vietnam (Red River Delta, Mekong Delta and Saigon – Dongnai River delta) and along the coast are very much concerned in construction of the infrastructure system. Figure 1.1. Map of distribution of major soil types in Indochinese 1 In this area, civil constructions and seaports must take measures to treat the ground before construction. The objectives of ground treatment are: - To increase bearing capacity of the ground - To decrease the permeability of soil Therefore, there are many methods used to reinforce or to increase the stiffness of the soft soil, in which consolidating the soft soil is one of the methods. According to soil mechanics theory, soil is formed from two or three phases (see Figure 1.2). The voids surrounding the soil particles are filled by water, air or a combination of both. Consolidation is the process of contraction of voids under the applied load in association with the process of water drainage. Figure 1.2. Soil phase diagram [3] Among several common ground improvement methods in practice, ground improvement by Prefabricated Vertical Drain (PVD) is one of the methods most commonly applied in practice. Fig. 1.3 shows a typical configuration of ground improved by PVDs. Figure 1.3. An Illustration of soft ground improved by PVDs 2 Under the surcharge loading, drainage in the ground improved by PVDs takes place in two directions (as show in Figure 1.3): vertical direction and horizontal (radial) direction. The consolidation settlement of the ground therefore happens due to both vertical and horizontal drains. 1.2 Necessity of study When a soft ground is improved by PVDs, consolidation takes place under the condition of drainage in both horizontal and vertical directions. Naturally, horizontal coefficient of consolidation (cr) is larger than the vertical coefficient of consolidation (cv) by a factor of 3 to 5. In addition, in many cases, when the soft clay layer is thick, the consolidation would happen mainly due to the horizontal drainage. The cr value is therefore very important for the design, sometimes much more important than the cv value. Currently, the cv value is commonly interpreted from consolidation test using incremental loading method [1]. This is because the method is simple and applicable in routine laboratories around the world. However, up to date, there have not been any similar standards for the consolidation test with horizontal drainage (using incremental loading method). Although cr value might be determined from some Constant Rate of Strain (CRS) tests (e.g., Chung 2019, Sridharan 1996…), the equipment and test procedures are too complicated to apply in routine tests. Thus, cr value is mostly obtained from empirical correlations, for example from cv value. In the literature, there are about 10 methods suggested to determine cr value obtained from result of the consolidation test with horizontal drainage using incremental loading. However, it is unclear as which methods are the best. In addition, there have been no systematic studies on cr value of soft clay in the North of Vietnam. It is therefore very necessary to make a comparative study on the methods to determine the cr value and the value for soft clay in the North of Vietnam. 3 1.3 Objectives The main objectives of the study are: 1. To determine the most reliable methods among the proposed methods for determining the horizontal coefficient of consolidation (cr) in the literature; 2. To determine correlations between cr values obtained from central drain (CD) test and peripheral drain (PD) test; 3. To determine correlations between vertical coefficients of consolidation (cv) and radial cr for a number of test sites in Vietnam. 1.4 Scope of study The scope of the study is limited to the following: - Collect existing data in the literature and data from experiments of the supervisor‟s research program. - Perform analytical analyses to obtain the three objectives described above. Test data on consolidation test with radial drainage (using incremental loading method) are collected from the following sources: - Existing data from the literature (remolded samples); - Test site in Kim Chung – Di Trach (Hanoi) (both remolded and intact samples). - Test site in Dinh Vu Industrial Zone (DVIZ) (Hai Phong) test data (intact samples). - Test site in Vietnam Singarpore Industrial Park (VSIP) (Hai Phong) (both remolded and intact samples). 1.5 Structure of thesis The rest of the thesis is organized as follows. - Chapter 2: Find out the principles that have been determined for consolidation theory with Horizontal drainage, existing method for determining from radial consolidation test and theory of comparison method selects the best methods. 4 - Chapter 3: Describes the methodologies used to evaluate the coefficients and correlations - Chapter 4: Methodology provides methods for determining cr values for PD & CD cases and provides evaluation methods to select the best methods. - Chapter 5: Outlines, discusses the results obtained and describes the conclusion. 5 CHAPTER 2. LITERATURE REVIEW 2.1 Introduction When a soil layer is subjected to a compressive stress, such as during the construction of a structure, it will exhibit a certain amount of compression. This compression is achieved through a number of ways, including rearrangement of the soil solids or extrusion of the pore air and/or water. Terzaghi (1943) recommends, “A decrease of water content of a saturated soil without replacement of the water by air is called a process of consolidation”. Terzaghi (1943) first suggested the one-dimensional consolidation testing procedure. This test performed in a consolidometer (sometimes referred to as an Odometer). Baron [4] (1948) presented the basic theory of sand drains. In key study of sand drains, the author has two fundamental cases. - Free-strain case: When the surcharge applied at the ground surface is of a flexible nature, there will be equal distribution of surface load. This will result in an uneven settlement at the surface. - Equal-strain case: When the surcharge applied at the ground surface is rigid, the surface settlement will be the same all over. However, this will result in an unequal distribution of stress. The study in this thesis focuses on equal-strain case. During consolidation process, pore water may drain through a Peripheral drain (PD) or a Central drain (CD). 6 Figure 2.1. Research direction of the thesis [5] A peripheral drain (PD) case A central drain (CD) case Figure 2.2. Illustration of flow conditions for equal-strain case [6] To obtain a coefficient of consolidaiton, a curve of time vesus deformation (Figure 2.3) obtained from consolidation test is taken into analysis. The curve has three distinct stages described as follows [3]: - Stage I: Initial compression, which is caused mostly by preloading. - Stage II: Primary consolidation, during which excess pore water pressure gradually is transferred into effective stress because of the expulsion of pore water. - Stage III: Secondary consolidation, which occurs after complete dissipation of the excess pore water pressure, when some deformation of the specimen takes place because of the plastic readjustment of soil fabric 7