Determination of the horizontal (radial) coefficient of consolidation by from oedometer test with horizontal drainage using incremental loading method

ABSTRACT The radial (horizontal) coefficient of consolidation (cr) is a key parameter which impacts the total consolidation of the PVD-improved grounds In practice, the cr value can be interpreted from field tests and laboratory tests A radial consolidation test (RCT) might be conducted using incremental loading (IL) method with either a central drain (CD) or a peripheral drain (PD) The key goals of the research are: (1) to design and manufacture a multi-directional flow consolidometer (VCT, RCT-PD, RCT-CD) using incremental loading method; (2) to make a comparative study on the cr values obtained from the RCTIL using a PD and a CD; (3) to make a comparative study on the cr values derived from RCT-based method and CPTu-based method 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) graphical design of a multi-directional flow consolidation cell Sampling and CPTu dissipation tests are carried out at sites Besides the basic physical lab tests, the RCT IL with a CD and a PD will be performed using the designed consolidation cell under same condition test Overall, the ratio of kr/kv is approximately equal the ratio of cr/cv The cr, PD & cr, CD are double to triple higher than cv The cr, CD values are about 1.5 times larger than figures of cr, PD Finally, the cr values determined from CPTu-based method are doubled higher than cr values obtained from RCT-based method The reliability of the new device is confirmed Moreover, the results of cr values in the case of both PD and CD obtained by interpreting with traditional method like square root time method is more reliable than non-graphical method The limitation of the study is that the amount of data is still limited so it is still not enough to fully confirm the reliability of the multi-directional flow consolidation cell In the future, the author intends to perform more consolidation and permeability tests to ensure that the new designated consolidation can be applied in routine performance 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 Tien Dung for his enthusiasm, patience, advice and constant source of ideas Dr Dung has always been available to reply to my questions His support in professional matters has been priceless Special gratitude is given to LAS- XD 442 lab and the staff at Institute of Foundation and Underground, Golden Earth Inc for their kindly support for performing the laboratory work And finally, I want to spent my 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 i ACKNOWLEDGEMENTS ii TABLE OF CONTENTS iii LIST OF FIGURES vii LIST OF TABLES ix LIST OF ABBREVIATIONS xi CHAPTER 1: INTRODUCTION 1.1 Background 1.2 Consolidation 1.2.1 Settlement with Prefabricated Vertical Drains (PVD) 1.3 Problem statement 1.4 Objectives and scope of present study CHAPTER 2: LITERATURE REVIEW 2.1 Fundamentals of One Dimensional Consolidation 2.1.1 Consolidation Theory with Vertical Drainage 10 2.1.2 Consolidation Theory with Horizontal Drainage 11 2.2 Consolidation Tests in Laboratory 15 2.2.1 Vertical oedometer consolidation test 15 iii 2.2.2 Horizontal Consolidation Test 16 2.3 Determination of Coefficient of Consolidation 17 2.3.1 Analysis of Time-Compression Curve 17 2.3.2 Graphical Method 18 2.3.2 Non-graphical Method 21 2.4 Falling Head Permeability Test 24 2.5 The piezocone penetration test (CPTu) 26 2.5.1 Introduction 26 2.5.2 Pore-water Dissipation Tests 27 2.5.3 Coefficient of Consolidation 28 CHAPTER 3: METHODOLOGY 32 3.1 Introduction 32 3.2 Radial Consolidation Test 33 3.2.1 Design of the equipment 33 3.2.2 Manufacture of the equipment 35 3.2.3 Testing procedure 37 3.2.4 Analysis procedure 38 3.3 Vertical consolidation test 38 3.3.1 Testing procedure 38 3.3.2 Analysis of Time-Compression Curve 38 3.4 Permeability test 39 3.4.1 Equipment of permeability test 39 3.4.2 Testing procedure 39 iv 3.4.3 Analysis procedure 40 3.5 CPTu dissipation test 41 3.5.1 Equipment 41 3.5.2 Testing procedure 42 3.5.3 Analysis procedure 42 3.6 Results verification and comparison 42 CHAPTER 4: TEST RESULTS & DISCUSSIONS 43 4.1 Introduction 43 4.2 Summary of test performed 43 4.3 Comparison of cr,PD and cv 46 4.3.1 Square root time method 46 4.3.2 Non-graphical method 47 4.3.3 Inflection point method 48 4.4 Comparison cr,CD and cv 49 4.4.1 Square root time method 49 4.4.2 Non-graphical method 50 4.4.3 Inflection point method 51 4.5 Comparison cr,PD and cr, CD 52 4.5.1 Square root time method 52 4.5.2 Non-graphical method 53 4.5.3 Inflection point method 54 4.6 Horizontal coefficient of consolidation (cr) from CPTu 55 4.6.1 Estimate cr value from monotonic dissipation curves 55 v 4.6.2 Estimate cr value from non-standard dissipation curves 59 4.7 Test verification 61 4.8 Comparison cr,PD, cr,CD vs cr, CPTu 62 CHAPTER 5: CONCLUSIONS & RECOMMENDATIONS 65 REFERENCES 68 vi LIST OF FIGURES Figure 1.1: Soil phase diagram (Das, 2008) Figure 1.2: Primary consolidation (Das, 2008) Figure 1.3: Typical oedometer settlement (Das, 2008) Figure 1.4: Settlement damage Figure 1.5: Drainage with and without drains Figure 2.1: Mechanism of consolidation Figure 2.2: Uv versus Tv relationship (Head, 1986) 11 Figure 2.3: Schematic diagram of an RCT with central drain and peripheral drain 11 Figure 2.4: (a) Scheme of arrangement of the consolidation test in the triaxial apparatus, with drainage towards the cylindrical surface; (b) Cylindrical element of the sample 12 Figure 2.5: Distribution of pore pressures within the soil sample related to r and t 13 Figure 2.6: Schematic of oedometer test (Head, 1986) 15 Figure 2.7: Schematic of the apparatus used for conducting radial consolidation test 16 Figure 2.8: Rowe cell test under equal strain loading, horizontal outward drainage 17 Figure 2.9: Shapes of consolidation curve gained from oedometer test 18 Figure 2.10: Theoretical curve linkage square-root time factor to degree of consolidation for vertical drainage (Taylor, 1942) 20 Figure 2.11: Consolidation curve relating square-root time factor to for drainage radially outwards to periphery with equal strain loading (Head, 1986) 21 Figure 2.12: (a) Theoretical Ur-log Tr curve for n = 5; (b) (dUr/d log Tr)-log Tr plot showing the inflection point (Sridhar and Robinson, 2011) 23 Figure 2.13: Falling-head permeability test (Das, 2017) 24 Figure 2.14: Principal sketch of horizontal and vertical trimming of samples from determining vertical and horizontal coefficient of permeability 25 Figure 2.15: Overview of the cone penetration test per ASTM D 5778 procedures 27 Figure 2.16: Strain path solution for CPTu1 dissipation tests (The and Houlsby, 1991) 30 Figure 2.17: Strain path solution for CPTu2 dissipation tests (The and Houlsby, 1991) 30 Figure 2.18: "Non-standard" dissipation curve ( Chai et al., 2012) 30 Figure 3.1: Equipment for radial consolidation test with peripheral drainage 33 vii Figure 3.2: Flow chart of the study 34 Figure 3.3: Equipment for radial consolidation test with central drainage 35 Figure 3.4: Manufacture of the equipment for radial consolidation with PD 36 Figure 3.5: Manufacture of equipment for radial consolidation test with CD 36 Figure 3.6: Radial consolidation with peripheral drain and central drain setup 37 Figure 3.7: Equipment of falling head permeability test 39 Figure 3.8: Falling head permeability test setup 40 Figure 3.9: The typical and complete electrical CPT system 42 Figure 4.1: Comparison of cv and cr,PD obtained from square root time method at 400 kPa & 800 kPa 46 Figure 4.2: Comparison of cv and cr,PD obtained from non-graphical method at 400 kPa & 800 kPa 47 Figure 4.3: Comparison of cv and cr,PD obtained from inflection point method at 400 kPa & 800 kPa 48 Figure 4.4: Comparison of cv and cr,CD obtained from square root time method at 400 kPa & 800 kPa 49 Figure 4.5: Comparison of cv and cr,CD obtained from non-graphical method at 400 kPa & 800 kPa 50 Figure 4.6: Comparison of cv and cr,CD obtained from inflection point method at 400 kPa & 800 kPa 51 Figure 4.7: Comparison of cr,PD and cr,CD obtained from square root time method at 400 kPa & 800 kPa 52 Figure 4.8: Comparison of cr,PD and cr,CD obtained from non-graphical method at 400 kPa & 800 kPa 53 Figure 4.9: Comparison of cr,PD and cr,CD obtained from inflection point method at 400 kPa & 800 kPa 54 Figure 4.10: Strain path solution for monotonic dissipation tests at 11 & 17m 57 Figure 4.11: Strain path solution for monotonic dissipation tests at 18.5 & 20.5m 58 Figure 4.12: Dilatory dissipation curve at 8.5m 59 Figure 4.13: Dilatory dissipation curve at 9.5 & 11.3 m 60 Figure 4.14: Results of test verification which compares the ratios between kr/kv with cr/cv 61 Figure 4.15: Comparison between cr,CPTu with cr,PD obtained from square root time method at 400 kPa 64 viii Figure 5.1 Comparison between results obtained from square root time, non-graphical and inflection point method at 400 kPa 67 Figure 5.2: Comparison between results obtained from square root time, non-graphical and inflection point method at 800 kPa 67 ix LIST OF TABLES Table 4.1: Laboratory and in-situ tests done 44 Table 4.2: Soil profile of borehole BH08 55 Table 4.3: Estimate cr value from modified time factor, T* 56 Table 4.4: Estimate cr values from “non-standard” dissipation curves 59 Table 4.5: Coefficient of permeability obtained from permeability tests 62 Table 4.6: Comparison cr,PD and cr,CD obtained by square root time method with cr,CPTu 63 x 4.6 Horizontal coefficient of consolidation (cr) from CPTu 4.6.1 Estimate cr value from monotonic dissipation curves For monotonic dissipation response, the strain path solutions are performed in Figure 4.10 to determine horizontal coefficient of consolidation (cr) Soil profile of borehole BH08, where dissipation tests were conducted, is shown in table 4.1 The estimated values of cr derived from the strain path solution for dissipation test are summarized in table 4.2 Table 4.2: Soil profile of borehole BH08 Depth Average (m) OCR Fill 0-2 NA 2-3 e0 ɣ cv Cc Cr NA NA 0.06 1.65 740 0.52 0.06 1.65 56 0.52 0.06 1.5 1.2 1.65 56 0.52 0.06 8-10 1.5 1.2 1.65 56 0.52 0.06 10-15 1.5 1.76 1.65 56 0.52 0.06 15-25 1.5 1.2 1.7 56 0.52 0.06 (g/cm3) (cm /d) NA 1.89 3-6 1.5 6-8 55 Table 4.3: Estimate cr value from modified time factor, T* Test Depth σ'vo Vs Su G0 G cr No (m) (kPa) (m/s) (kPa) (kPa) (kPa) 03 11 135.3 141 29.8 33473.1 8703.1 292.4 0.00591 05 17 175.3 157 38.6 41500.9 10790.2 279.8 0.00542 06 18.5 185.8 158 40.9 42031.2 10928.1 267.3 0.00847 07 20.5 199.8 198 44.0 66006.7 17161.8 390.4 0.01484 IR 56 (cm/s) Strain Path Solution for Dissipation test 03- 11.01m Noralized Excess Pore Pressures U2* 0.9 0.8 0.7 0.6 0.5 0.4 0.3 Measured Data 0.2 Approximately curve 0.1 0.0001 0.001 0.01 0.1 Modified Time Factor T* Strain Path Solution for dissipation test 05- 17.01m Noralized Excess Pore Pressures U2* 0.9 0.8 0.7 0.6 0.5 0.4 0.3 Measured Data 0.2 Approximately Curve 0.1 0.0001 0.001 0.01 0.1 Modified Time Factor T* Figure 4.10: Strain path solution for monotonic dissipation tests at 11 & 17m 57 Strain Path Solution for dissipation test 06 - 18.51m Noralized Excess Pore Pressures U2* 0.8 0.6 0.4 Measured Data Approximately Curve 0.2 0.0001 0.001 0.01 0.1 Modified Time Factor T* Noralized Excess Pore Pressures U2* Strain Path Solution for dissipation test 07 - 20.51m 0.0001 0.8 0.6 0.4 Measured Data 0.2 Approximately Curve 0.001 0.01 0.1 Modified Time Factor T* Figure 4.11: Strain path solution for monotonic dissipation tests at 18.5 & 20.5m 58 4.6.2 Estimate cr value from non-standard dissipation curves The estimated values of cr derived from the empirical equation for correcting t50, which was proposed by Chai et al (2012) are summarized in table 4.3 Figure 4.11 described measured data obtained from dissipation tests and time for 50% excess pore pressure dissipation Table 4.4: Estimate cr values from “non-standard” dissipation curves Test No Depth (m) Ir t50 (s) tumax (s) t50c (s) cr (s) 01 8.5 318.3 946 14 417.8 0.03333 02 9.51 308.4 3560 47 1648.2 0.00832 04 11.3 288.2 4290 15 2925 0.00453 Excess pore water pressure u (kPa) Dissipation test 01 - 8.5m 210 200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 t50 10 100 1000 10000 Time t (s) Figure 4.12: Dilatory dissipation curve at 8.5m 59 100000 Excess pore water pressure u (kPa0 Dissipation test 02 - 9.51 m 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 t50 10 100 1000 10000 100000 Time t (s) Dissipation test 04 - 11.3 m 300 250 200 t50 150 100 50 10 100 1000 10000 Figure 4.13: Dilatory dissipation curve at 9.5 & 11.3 m 60 100000 4.7 Test verification Figure 4.12 illustrates the results of test verification which compares the ratios between kr/kv with cr/cv 3.8 3.7 3.6 3.5 cr,PD / cv 3.4 3.3 3.2 3.1 3.0 2.9 400 kPa 2.8 8.0 - 9.0 m 9.0 - 10.0 m 16.5 - 17.3 m 2.7 2.6 2.5 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 kr / k v 3.5 3.4 3.3 cr,PD / cv 3.2 3.1 3.0 2.9 2.8 800 kPa 2.7 8.0 - 9.0 m 9.0 - 10 m 10.5 - 11.5 m 2.6 2.5 2.4 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 kr / kv Figure 4.14: Results of test verification which compares the ratios between k r/kv with cr/cv 61 Coefficient of hydraulic conductivity can be measured base on the permeability test through equation 3.1 The coefficient of permeability is shown in Table 4.4 Table 4.5: Coefficient of permeability obtained from permeability tests Depth kr (*10-6 cm/s) kv (10-6 cm/s) kr/kv 8.0 – 9.0 m 0.29540 0.09932 2.974 9.0 - 10.0 m 0.62120 0.21093 2.945 16.5 - 17.3 m 0.26315 0.08614 3.055 4.8 Comparison cr,PD, cr,CD vs cr, CPTu The value of cr,PD , cr,CD obtained by using square root time method at 400 kPa and 800 kPa and cr derived from monotonic and dilatory dissipation curves are listed in table 4.4 Figure 4.12 presents the comparison between cr,PD obtained from square root time method at 400 kPa and cr estimated from dissipation curves 62 Table 4.6: Comparison cr,PD and cr,CD obtained by square root time method with cr,CPTu 400 kPa 800 kPa Depth (m) cr,CPTu cr,PD (cm2/s) cr,CD (cm2/s) cr,PD (cm2/s) cr,CD (cm2/s) (cm2/s) 8.0 – 9.0 0.01599 0.01705 0.01596 0.01593 0.03333 9.0 – 10.0 0.00774 10.5 – 11.5 0.00388 0.00349 0.00377 0.00345 0.00591 16.5 – 17.3 0.00530 0.00539 0.00399 0.00404 0.00542 18.0 – 18.7 0.00388 0.00404 0.00383 0.00404 0.00847 19.5 – 20.5 0.00386 0.00438 0.00377 0.00426 0.01484 0.00840 63 0.00832 0.035 0.030 cr, PD (cm /s) 0.025 0.020 0.015 8.0 - 9.0 m 9.0 - 10.0 m 10.5 - 11.5 m 16.5 - 17.3 m 18.0 - 18.7 m 19.5 - 20.5 m 0.010 0.005 0.000 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 cr, CPTu (cm2/s) Figure 4.15: Comparison between cr,CPTu with cr,PD obtained from square root time method at 400 kPa 64 CHAPTER 5: CONCLUSIONS & RECOMMENDATIONS For the accuracy of multi- directional flow consolidation cell is designed to conduct oedometer test with both peripheral drain and central drain is verified with the test results from permeability test The ratio of kr/kv is around which is satisfy the ranged of fine-grained soil In contrast, the fraction of cr/cv is also ranged from to with difference depth of soil samples These ratios is somewhat connect with each other and plot around 1:1 axis Hence the multi-directional consolidation cell could be response to the oedometer test in both case of peripheral drain and central drain The data obtained from multi-directional consolidation cell to estimate three important consolidation parameters of soil including vertical coefficient of consolidation and radial coefficient of consolidation with PD and CD at n = 2.21 Based on the results derived from consolidation curves, when applying the square root time method, the cr,PD value estimated is nearly double to the cv value at same loading condition of 400 kPa and 800 kPa Meanwhile, the cr,CD value is around three times to the cv value This indicates that the horizontal coefficient of consolidations obtained from multi-directional consolidation cell with both outward drainage and inward drainage are not identical as theory and it ranged from to 1.5 when conducted tests with new devices In other hand, when applying non-graphical method and inflection point method to analyze the time- settlement curves monitored from conventional oedometer test the results also fluctuate The horizontal coefficient of consolidation calculated from consolidation test with PD larger than approximately three times with vertical coefficient of consolidation In the same case, the cr,CD values is much larger and when compares with vertical coefficient of consolidation the ratios is also vicinity with Moreover, the results of radial coefficient of consolidation in the case of both 65 peripheral drain and central drain obtained by interpreting with these methods is somewhat the largely difference The ratios of cr,PD and cr,CD is ranged from 1.5 to which is far from the 1:1 ratio as the theory has approved Hence the interpreting of horizontal coefficient of consolidation with both inward and outward drainage by applying traditional method like square root time method is more reliable than nongraphical method Figure 5.1 and 5.2 illustrates the difference between the results obtained when depicting with three difference analytical methods The results of radial coefficient of consolidation estimated from CPTu dissipation tests is much higher than these value calculated when subjected by both 400 kPa and 800 kPa The ratios of these values are changed around 1:2 line In the future, the multi-directional flow consolidation cell should be conducted more tests at another place to verify its reliable before employing in routine performance The limitation of the study is that the amount of data is still limited due to the rush time so it is still not enough to fully confirm the reliability of the multi-directional flow consolidation cell In the future, the author intends to perform more consolidation and permeability tests to ensure that the new designated consolidation can be applied in routine performance 66 0.022 0.020 0.018 cr, CD (cm /s) 0.016 0.014 0.012 0.010 0.008 400 kPa 0.006 Square root time method Non- graphical method Inflection point method 0.004 0.002 0.000 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 cr, PD (cm /s) Figure 5.1 Comparison between results obtained from square root time, nongraphical and inflection point method at 400 kPa 0.020 0.018 0.016 cr, CD (cm /s) 0.014 0.012 0.010 0.008 0.006 800 kPa 0.004 Square root time method Non- graphical method Inflection point method 0.002 0.000 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 cr, PD (cm /s) Figure 5.2: Comparison between results obtained from square root time, nongraphical and inflection point method at 800 kPa 67 REFERENCES ASTM D2435 / D2435M - 11 (2011) Standard Test Methods for One-Dimensional Consolidation Properties of Soils Using Incremental Loading ASTM International, West Conshohocken https://doi.org/10.1520/D2435_D2435M-11 Barron, R A., Lane, K S., Keene, P., & Kjellman, W (2002) Consolidation of finegrained soils by drain wells In Geotechnical Special Publication (Vol 113) Chai, J., Sheng, D., Carter, J P., & Zhu, H (2013) Corrigendum to “Coefficient of consolidation from non-standard piezocone dissipation curves” [Comput Geotech 41 (2012) 13–22] Computers and Geotechnics https://doi.org/10.1016/j.compgeo.2013.03.002 Chung, S., Lee, N., & Kim, S.-R (2009) Hyperbolic Method for Prediction of Prefabricated Vertical Drains Performance In Journal of Geotechnical and Geoenvironmental Engineering (Vol 135) https://doi.org/10.1061/(ASCE)GT.1943-5606.0000042 Das, B M., & Sobhan, K (2008) Principle of Geotechnical Engineering In Global Engineering Fahey, M., & Carter, J P (2008) A finite element study of the pressuremeter test in sand using a nonlinear elastic plastic model: Reply Canadian Geotechnical Journal https://doi.org/10.1139/t94-096 Head, K H (1994) Manual of soil laboratory testing Vol Permeability, shear strength and compressibility tests In Geoderma https://doi.org/10.1016/00167061(95)90001-2 Jamiolkowski, M., Ladd, C C., Germaine, J T., & Lancellotta, R (1985) New developments in field and laboratory testing of soils , SAN FRANCISCO, 12-16 AUGUST 1985 11th Int Conf on Soil Mechanics and Foundation Engineering 68 Krage, C P., DeJong, J T., & Schnaid, F (2014) Estimation of the Coefficient of Consolidation from Incomplete Cone Penetration Test Dissipation Tests Journal of Geotechnical and Geoenvironmental Engineering https://doi.org/10.1061/(asce)gt.1943-5606.0001218 Mayne, P.W (2007) NEHRP-Cone Penetration Testing a Synthesis of Highway Practice In Nchrp Mayne, Paul W (2001) Stress-strain-strength-flow parameters from enhanced in-situ tests Proceedings of the International Conference on In-Situ Measurement, Bali, Indonesia, May 21-24, 2001 Robinson, R G., & Allam, M M (1998) Analysis of consolidation data by a nongraphical matching method Geotechnical Testing Journal https://doi.org/10.1520/GTJ10752J Sridhar, G., & Robinson, R (2011) Determination of radial coefficient of consolidation using log t method International Journal of Geotechnical Engineering https://doi.org/10.3328/ijge.2011.05.04.373-381 Sridharan, A., Prakash, K., & Asha, S R (1996) Consolidation behavior of clayey soils under radial drainage Geotechnical Testing Journal Teh, C I (1991) An analytical study of the cone penetration test in clay G&technique Vesic, A S (1973) On penetration resistance and bearing capacity of piles in sand 8th International Conference on Soil Mechanics and Foundation Engineering 69