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 ABSTRACT ACKNOWLEDGEMENTS TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF ABBREVIATIONS CHAPTER INTRODUCTION 1.1Problem statement 1.2Necessity of study 1.3Objectives 1.4Scope of study 1.5Structure of thesis CHAPTER LITERATURE REVIEW 2.1Introduction 2.1.1Consolidation Theo 2.1.2Solution of the gov equal strain loading (ESL) condition 2.1.3Solution of the gov under free strain loading (FSL) condition 2.1.4Solution of the gov under equal strain loading (ESL) condition 2.2Existing methods for determining cr from consolida drain using incremental loading 2.2.1Root t method [6] 2.2.2Inflection point me 2.2.3Full – match metho 2.3Existing methods for determining cr from consolida drain using incremental loading method 2.3.1Root t method [11] 2.3.2Matching log (de /t 2.3.3Inflection point me 2.3.4Non-graphical meth 2.3.5Log - log method [1 2.3.6Steepest tangent fit 2.3.7Log t method [17] 2.3.8Full – match metho 2.4Summary of methods for determining cr 2.5Linear regression analysis 2.6Log normal distribution method CHAPTER METHODOLOGY iii 3.1Introduction 3.2Data collection 3.3Improvement for inflection point methods 3.3.1Theoretical develo 3.3.2The procedure for 3.4Analysis of Time – Compression curve 3.5Procedure to select the best methods 3.6Procedure to determine ratios of cr PD /cr CD or cr /cv CHAPTER TEST RESULTS & DISCUSSIONS 4.1Introduction 4.2Summary of database 4.2.1Data collected from 4.2.2Data collected from 4.2.3Summary of test d 4.3Evaluation and selection the best methods on intact 4.3.1Graph results on in 4.3.2Summary of resul 4.3.3Summary of rank 4.4Evaluation and selection the best methods on literat 4.4.1Graph results on li 4.4.2Summary of result 4.4.3Summary of rank 4.5Evaluation and selection the best methods on remol 4.5.1Graph results on re 4.5.2Summary of result 4.5.3Summary of rank 4.6Comparison of cr CD and cr PD on intact samples 4.6.1Graph results on in 4.6.2Summary of resul 4.7Comparison of cr CD and cr PD on remolded samples 4.7.1Graph results on re 4.7.2Summary of resul 4.8Comparison of cv and cr PD on intact samples 4.8.1Graph results on in 4.8.2Summary of resul 4.9Comparison of cv and cr CD on intact samples 4.9.1Graph results on in 4.9.2Summary of resul 4.10 Comparison of cv and cr PD on remolded samples 4.10.1 Graph of results on remolded samples 4.10.2 Summary of results on remolded samples 4.11 Comparison of cv and cr CD on remolded samples 4.11.1 Graph results on remolded samples 4.11.2 Summary of results on remolded samples 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 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] Figure 2.5 Log (Ur/Tr) - log Ur relationship [10] Figure 2.6 Determine the value of intersection point in full – match method Figure 2.7 Theoretical log(de /t) versus Ur curves [12] Figure 2.8 (a) Theretical Ur - log Tr curve and (b) d(Ur)/dlog Tr plot [13] Figure 2.9 Log(δ - δ0) versus log t plot [15] Figure 2.10 Steepest tangent fitting method for determination of c r Figure 3.1 Flow chart of the study Figure 3.2 Experimental data [9] Figure 3.3 Flowchart of identifying the best methods Figure 3.4 Flowchart of identifying the best methods Figure 4.1 Locations of test sites in Viet Nam (VSIP site, DVIZ site, Kim Chung site) Figure 4.2 Test location at Kim Chung site Figure 4.3 Test location at VSIP site Figure 4.4 Test location at DVIZ site Figure 4.5 Soil profile at DVIZ Figure 4.6 Soil profile at VSIP Figure 4.7 Soil profile at KC Figure 4.8 Results from PD tests on intact samples (at 800 kPa) for methods Figure 4.9 Results from CD tests on intact samples (at 800 kPa) for methods Figure 4.10 Results from PD tests on intact samples (at 800 kPa) for methods Figure 4.11 Results from CD tests on literature for methods Figure 4.12 Results from PD tests on remolded samples (at 800 kPa) for methods Figure 4.13 Results from CD tests on remolded samples for methods Figure 4.14 Comparison of cr CD and cr PD obtained from root t method at all data 64 viii = (0.90 – 2.33) cv = (0.86 – 2.26) cv 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 Pressure (kPa) 50 100 200 400 800 All data Table 4.28 Summary of boundary for CD method on intact samples Pressure (kPa) 50 100 200 400 800 All data 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 b For Non-graphical method - cr CD = 2.41cv & R2 is 0.63, cr CD = (2.14 – 5.12) cv = (1.52 – 4.29) cv 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) 50 100 200 400 800 All data Table 4.30 Summary of boundary for PD case on remolded samples Pressure (kPa) 50 100 200 400 800 All data 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: b For Non-graphical method a For Root method - cr PD = 0.46cv & R is 0.71, cr PD - cr PD = 0.58cv & R2 is 0.79, cr PD = (0.35 – 1.01) cv = (0.41 – 1.09) cv 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 Pressure (kPa) 50 100 200 400 800 All data Table 4.32 Summary of boundary for CD method on remolded samples Pressure (kPa) 50 100 200 400 800 All data 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 b For Non-graphical method - cr CD = 0.55cv & R2 is 0.79, cr CD = (0.36 – 0.82)cv = (0.41 – 0.82)cv 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 δp = 1.0δm & R2 = 0.99 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 de /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 δp = (0.98 - 1.00)δm & R2 = (0.95 – 0.99) - Result of δp from root t method is almost equal to δm 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 δ0 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 δ0 varies greatly in this range - Determining δ0 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