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 to 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 INTRODUCTION .1 1.1 Problem statement .1 1.2 Necessity of study .3 1.3 Objectives 1.4 Scope of study 1.5 Structure of thesis CHAPTER LITERATURE REVIEW 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 2.1.3 Solution of the governing equation (2.2) for a peripheral drain (PD) under free strain loading (FSL) condition 2.1.4 Solution of the governing equation (2.2) for a peripheral drain (PD) under equal strain loading (ESL) condition 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 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 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 CONCLUSIONS & RECOMMENDATIONS 76 REFERENCES 79 v LIST OF TABLES Page Table 2.1 Boundary condition 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 methods 51 Table 4.12 Summary of results from CD tests on literature for 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 methods 56 Table 4.16 Summary of results from CD tests on remolded samples for methods 58 Table 4.17 Rank of each criterion with each pressure from PD tests on remolded samples for methods .59 Table 4.18 Rank of each criterion with each pressure from CD tests on remolded samples for 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 Figure 1.2 Soil phase diagram [3] Figure 1.3 An Illustration of soft ground improved by PVDs Figure 2.1 Research direction of the thesis [5] Figure 2.2 Illustration of flow conditions for equal-strain case [6] Figure 2.3 Time - deformation plot during consolidation for a given load increment [3] 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 methods .38 Figure 4.9 Results from CD tests on intact samples (at 800 kPa) for methods 39 Figure 4.10 Results from PD tests on intact samples (at 800 kPa) for methods 49 Figure 4.11 Results from CD tests on literature for methods .50 Figure 4.12 Results from PD tests on remolded samples (at 800 kPa) for methods 54 Figure 4.13 Results from CD tests on remolded samples for methods 55 Figure 4.14 Comparison of cr CD and cr PD obtained from root t method at all data 64 viii 4.7 Comparison of cr CD and cr PD on remolded samples 4.7.1 Graph results on remolded samples Figure 4.16 and figure 4.17 presents the comparison of cr CD and cr PD obtained from non-graphical method and root t at all data on remolded samples Figure 4.16 Comparison of c r,CD and cr,PD obtained from root t method at all data Figure 4.17 Comparison of cr CD and cr PD obtained from non-graphical method at all data 4.7.2 Summary of results from remolded samples Table 4.23 presents correlations of cr,CD and cr,PD obtained from intact samples for root t method and non-graphical method Table 4.24 presents boundary of cr CD and crPD obtained from intact samples for root t method and non-graphical method 66 Table 4.23 Summary of correlations for CD and PD case on remolded samples Pressure (kPa) 50 cr,Root PD /cr,Root CD cr,NG PD /cr,NG CD a RNo of data a RNo of data (y = ax) square point (n) (y = ax) square point (n) 0.33 0.70 0.39 0.79 100 0.32 0.87 0.34 0.90 200 0.48 0.94 0.43 0.85 400 0.43 1.00 0.49 0.96 800 0.29 0.89 0.38 0.98 All data 0.33 0.87 36 0.41 0.87 38 Table 4.24 Summary of boundary for CD and PD case on remolded samples Pressure (kPa) cr,Root PD / cr,Root CD cr,NG PD / cr,NG CD Lower Upper 50 0.25 0.47 Distribution area 80.00% Lower Upper 0.33 0.57 Distribution area 80.00% 100 0.24 0.53 80.00% 0.34 0.51 80.00% 200 0.43 0.58 80.00% 0.19 1.15 80.00% 400 0.42 0.47 80.00% 0.42 0.60 80.00% 800 0.28 0.49 80.00% 0.33 0.48 80.00% All data 0.30 0.56 80.00% 0.33 0.58 80.00% The authors obtain the result in Table 4.23 and Table 4.24 for correlations of cr PD and cr PD from intact samples for Root t method and Non-graphical method Average correlations of cr CD/cr PD and boundary of cr CD/cr PD with 80% distribution area ratio of cr CD/cr PD can be determined: a For Root method - cr PD = 0.33cr CD & R2 is 0.87, cr PD = (0.30 – 0.56)cr CD (4.26) b For Non-graphical method - cr PD = 0.41cr CD & R2 is 0.87, cr PD = (0.33 – 0.58)cr CD (4.27) 67 4.8 Comparison of cv and cr PD on intact samples 4.8.1 Graph results on intact samples Figure 4.18 and Figure 4.19 presents the comparison of cr PD and cv obtained from non-graphical method and root t at all data on intact samples Figure 4.18 Comparison of cv and cr,PD obtained from root t method at all data Figure 4.19 Comparison of cv and cr,PD obtained from non-graphical method at all data 4.8.2 Summary of results on intact samples Table 4.25 presents correlations of cv and cr PD obtained from intact samples for root t method and non-graphical method Table 4.26 presents boundary of cv and cr PD obtained from intact samples for root t method & non-graphical method 68 Table 4.25 Summary of correlations for PD case on intact samples Pressure (kPa) cr,Root PD /cv cr,NG PD /cv a (y = ax) Rsquare No of data point (n) a (y = ax) Rsquare 50 1.47 0.37 30 1.77 0.47 No of data point (n) 29 100 1.60 0.69 36 1.29 0.68 41 200 1.57 0.67 45 1.05 0.56 47 400 2.05 0.73 42 1.52 0.76 51 800 1.68 0.76 45 1.04 0.68 44 All data 1.59 0.78 173 1.31 0.71 188 Table 4.26 Summary of boundary for PD case on intact samples Pressure (kPa) cr,Root PD /cv cr,NG PD /cv Lower Upper 50 0.59 2.46 Distribution area 80.00% Lower Upper 1.04 2.65 Distribution area 80.00% 100 0.71 2.60 80.00% 0.77 2.25 80.00% 200 0.60 2.66 80.00% 0.54 2.02 80.00% 400 1.04 2.85 80.00% 0.77 3.05 80.00% 800 0.62 3.38 80.00% 0.74 2.23 80.00% All data 0.90 2.33 80.00% 0.86 2.26 80.00% The authors obtain the result in Table 4.25 and Table 4.26 for correlations of cv and cr PD from intact samples for Root t method and Non-graphical method Average correlations of cr PD/cv and boundary of cr PD/cv with 80% distribution area ratio of cr PD/cv can be determined: a For Root method - cr PD = 1.59cv & R2 is 0.78, cr PD = (0.90 – 2.33) cv (4.28) b For Non-graphical method - cr PD = 1.31cv & R2 is 0.71, cr PD = (0.86 – 2.26) cv (4.29) 69 4.9 Comparison of cv and cr CD on intact samples 4.9.1 Graph results on intact samples Figure 4.20 and Figure 4.21 presents the comparison of cv and cr CD obtained from non-graphical method and root t method at all data on intact Figure 4.20 Comparison of cv and cr CD, obtained from root t method at all data Figure 4.21 Comparison of cv and cr CD obtained from non-graphical method at all data 4.9.2 Summary of results on intact samples Table 4.27 and Table 4.28 presents the comparison of cv and cr CD obtained from intact samples for root t method and non-graphical method 70 Table 4.27 Summary of correlation for CD case on intact samples cr,Root CD /cv cr,NG CD /cv a (y = ax) Rsquare No of data point (n) 50 3.53 0.70 20 2.78 0.81 No of data point (n) 24 100 3.44 0.81 20 2.43 0.62 18 200 3.26 0.92 20 2.52 0.82 32 400 3.82 0.82 20 3.47 0.82 21 800 3.44 0.56 17 2.24 0.10 18 All data 3.38 0.76 115 2.41 0.63 140 Pressure (kPa) a (y = ax) Rsquare Table 4.28 Summary of boundary for CD method on intact samples Pressure (kPa) cr,Root CD /cv cr,NG CD /cv Lower Upper 50 2.34 4.88 Distribution area 80.00% Lower Upper 2.02 3.71 Distribution area 80.00% 100 2.47 4.16 80.00% 1.99 3.17 80.00% 200 2.20 4.29 80.00% 1.33 3.58 80.00% 400 1.89 7.97 80.00% 2.95 5.15 80.00% 800 2.24 5.73 80.00% 2.15 5.10 80.00% All data 2.14 5.12 80.00% 1.52 4.29 80.00% The authors obtain the result in Table 4.27 and Table 4.28 for correlations of cv and cr CD from intact samples for Root t method and Non-graphical method Average correlations of cr CD/cv and boundary of cr CD/cv with 80% distribution area ratio of cr CD/cv can be determined: a For Root method - cr CD = 3.38cv & R2 is 0.76, cr CD = (2.14 – 5.12) cv (4.30) b For Non-graphical method - cr CD = 2.41cv & R2 is 0.63, cr CD = (1.52 – 4.29) cv (4.31) 71 4.10 Comparison of cv and cr PD on remolded samples 4.10.1 Graph of results on remolded samples Figure 4.22 and Figure 4.23 presents the comparison of cv and cr,PD obtained from non-graphical method and root t method at all data Figure 4.22 Comparison of cv and cr,PD obtained from root t method at all data Figure 4.23 Comparison of cv and cr,PD obtained from non-graphical method at all data 4.10.2 Summary of results on remolded samples Table 4.29 and Table 4.30 presents the comparison of cv and cr,PD obtained from remolded samples for root t method and non-graphical method 72 Table 4.29 Summary of correlations for PD case on remolded samples Pressure (kPa) cr,Root PD /cv cr,NG PD /cv a (y = ax) Rsquare No of data point (n) a (y = ax) Rsquare 50 0.50 -0.43 0.56 0.12 No of data point (n) 100 0.67 0.97 0.64 0.69 200 0.47 0.56 0.45 0.44 400 0.77 0.83 0.70 0.85 800 0.41 0.80 0.31 0.80 All data 0.46 0.71 24 0.58 0.79 20 Table 4.30 Summary of boundary for PD case on remolded samples Pressure (kPa) cr,Root PD /cv cr,NG PD /cv Lower Upper 50 0.36 0.89 Distribution area 80.00% Lower Upper 0.44 0.87 Distribution area 80.00% 100 0.60 0.94 80.00% 0.40 1.27 80.00% 200 0.27 1.08 80.00% 0.21 1.21 80.00% 400 0.45 1.30 80.00% 0.56 1.00 80.00% 800 0.36 0.66 80.00% 0.26 0.48 80.00% All data 0.35 1.01 80.00% 0.41 1.09 80.00% The authors obtain the result in Table 4.29 and Table 4.30 for correlations of cv and cr PD from remolded samples for Root t method and Non-graphical method Average correlations of cr PD/cv and boundary of cr PD/cv with 80% distribution area ratio of cr PD/cv can be determined: a For Root method - cr PD = 0.46cv & R2 is 0.71, cr PD = (0.35 – 1.01) cv (4.32) b For Non-graphical method - cr PD = 0.58cv & R2 is 0.79, cr PD = (0.41 – 1.09) cv (4.33) 73 4.11 Comparison of cv and cr CD on remolded samples 4.11.1 Graph results on remolded samples Figure 4.24 and 4.25 presents the comparison of cv and cr CD obtained from nongraphical method and root t method at all data Figure 4.24 Comparison of cv and cr,CD obtained from root t method at all data Figure 4.25 Comparison of cv and cr,CD obtained from Root t method at all data 4.11.2 Summary of results on remolded samples Table 4.31 and table 4.32 presents the comparison of cv and cr,PD obtained from remolded samples for root t method and non-graphical method 74 Table 4.31 Summary of correlations for CD method on remolded samples cr,Root CD / cv cr,NG CD / cv a (y = ax) Rsquare No of data point (n) 50 0.50 0.72 0.78 0.49 No of data point (n) 100 0.88 0.67 0.94 0.67 200 0.44 0.63 0.36 0.67 400 0.66 0.65 0.54 0.46 800 0.58 0.60 0.55 0.77 All data 0.53 0.61 15 0.55 0.79 16 Pressure (kPa) a (y = ax) Rsquare Table 4.32 Summary of boundary for CD method on remolded samples Pressure (kPa) cr,Root CD / cv cr,NG CD / cv Lower Upper 50 0.42 1.12 Distribution area 80.00% Lower Upper 0.35 2.96 Distribution area 80.00% 100 0.72 1.84 80.00% 0.57 1.82 80.00% 200 0.34 0.61 80.00% 0.27 0.47 80.00% 400 0.39 1.23 80.00% 0.36 1.14 80.00% 800 0.39 0.95 80.00% 0.39 0.78 80.00% All data 0.36 0.82 80.00% 0.41 0.82 80.00% The authors obtain the result in Table 4.31 and Table 4.32 for correlations of cv and cr CD from remolded samples for Root t method and Non-graphical method Average correlations of cr CD/cv and boundary of cr CD/cv with 80% distribution area ratio of cr CD/cv can be determined: a For Root method - cr CD = 0.53cv & R2 is 0.61, cr CD = (0.36 – 0.82)cv (4.34) b For Non-graphical method - cr CD = 0.55cv & R2 is 0.79, cr CD = (0.41 – 0.82)cv (4.35) 75 CHAPTER CONCLUSIONS & RECOMMENDATIONS The following are key conclusions drawn from this study The most reliable methods for determining the horizontal coefficient of consolidation (cr): - Best method is Non-graphical method for determining cr for all case and the function of linear p = 1.0m & R2 = 0.99 (5.1) This is the best method because this method determines cr is by matching to find the best curve for the data series - Rank as or is usually log de2/t or log t - These two methods are matching methods, so it gives good results - Root method is usually rank as and the function of linear p = (0.98 - 1.00)m & R2 = (0.95 – 0.99) - (5.2) Result of p from root t method is almost equal to m in the both test (CD and PD) tests on the both samples (intact and remolded) Therefore, Root t method may become the standard for determining cr values as it is the standard method for determining cv values - The root method is matching data within Ur = 20% to Ur = 60% but it is usually ranked because the most appropriate method with measured curves is similar to predicted curve Especially actual samples with sand or mixed impurities such as seashells, small rocks make measured settlement curve different from the theory - Full-match method also uses the principle of matching but does not rank well because determining two straight lines on the logarithmic coordinate system is often difficult - The remaining methods also not have high rankings because the value of 0 varies greatly in the range Ur = 20% Range Ur = 20% is the initial compression The initial compression phase takes place due to the compression of small air 76 pockets in pore spaces and partly due to the rearrangement of particles in the soil, and a small percentage may be due to elastic compression due to the value of 0 varies greatly in this range - Determining 0 from steepest tangent method is incorrect It is only true in the vertical consolidation Correlations between cr values obtained from central drain (CD) test and peripheral drain (PD) test Due to differences in drainage boundary, so kr , PD  kr ,CD  cr , PD  kr , PD k  cr ,CD  r ,CD  w  mr  w  mr (5.3) Where: kr PD (kr CD) is the permeability coefficient from PD case (CD case), w is water unit weight and mr is soil stiffness from radial consolidation Correlations of cr PD/ cr CD changes difference by level of pressure loading: a On intact samples For Root method cr PD = 0.47cr CD & R2 is 0.80, cr PD = (0.26 – 0.62)cr CD (5.4) For Non-graphical method cr PD = 0.47cr CD & R2 is 0.81, cr PD = (0.32 – 0.64)cr CD (5.5) b On remolded samples For Root method cr PD = 0.33cr CD & R2 is 0.87, cr PD = (0.30 – 0.56)cr CD (5.6) For Non-graphical method cr PD = 0.41cr CD & R2 is 0.87, cr PD = (0.33 – 0.58)cr CD (5.7) Correlations between cr and vertical coefficients of consolidation (cv) Due to differences in drainage boundary, so kr  kv  cr  kv kr  cv   w  mr  w  mv (5.8) 77 Where: kr (kv) is the permeability coefficient from radial consolidation (vertical consolidation), w is water unit weight and mr (mv) is soil stiffness from radial consolidation (vertical consolidation) Correlations of cr PD/cv and cr CD/cv changes difference by level of pressure loading: a On intact samples For Root method - cr PD = 1.59cv & R2 is 0.78, cr PD = (0.90 – 2.33) cv (5.9) cr CD = 3.38cv & R2 is 0.76, cr CD = (2.14 – 5.12) cv (5.10) For Non-graphical method - cr PD = 1.31cv & R2 is 0.71, cr PD = (0.86 – 2.26) cv (5.11) cr CD = 2.41cv & R2 is 0.63, cr CD = (1.52 – 4.29) cv (5.12) - - b On remolded samples For Root method - cr PD = 0.46cv & R2 is 0.71, cr PD = (0.35 – 1.01) cv (5.13) cr CD = 0.53cv & R2 is 0.61, cr CD = (0.36 – 0.82)cv (5.14) For Non-graphical method - cr PD = 0.58cv & R2 is 0.79, cr PD = (0.41 – 1.09) cv (5.15) cr CD = 0.55cv & R2 is 0.79, cr CD = (0.41 – 0.82)cv (5.16) - - The limitation of the study is that the amount of data is still limited due to the urgent time, so it has not been able to perform many samples a and there is no permeability test to verify the ratio in theory In the future, the author intends to carry out consolidation and permeability tests for different sites to test the theory In thesis has not been evaluated and selected the best value 0 & 100, developed the equation of correlations cr with CPTu 78 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consolidation (cr) is larger than the vertical coefficient of consolidation (cv) by a factor of. .. 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