(Luận văn thạc sĩ) analytical and numerical analyses on stiffness enhancement of ground improved by head enlarged CDM columns

VIETNAM NATIONAL UNIVESITY HANOI VIETNAM JAPAN UNIVERSITY HOANG DUY PHUONG ANALYTICAL AND NUMERICAL ANALYSES ON STIFFNESS ENHANCEMENT OF GROUND IMPROVED BY HEAD-ENLARGED CDM COLUMNS MAJOR: INFRASTRUCTURE ENGINEERING CODE: 8900201.04QTD RESEARCH SUPERVISOR Dr NGUYEN TIEN DUNG MASTER’S THESIS Hanoi, 2020 TABLE OF CONTENTS ABSTRACT ACKNOWLEDGEMENTS LIST OF TABLES LIST OF FIGURES LIST OF ABBREVIATIONS CHAPTER I: INTRODUCTION 1.1 General introduction of deep mixing method 1.2 Necessity of research 1.3 Objective and Scope of research 1.3.1 Objective of the study 1.3.2 Scope of the study CHAPTER 2: LITERATURE REVIEW 2.1 Overview of deep mixing method 2.1.1 Brief view of deep mixing method 2.1.2 Application of CDM 2.1.3 Classification 2.1.4 Equipment and machine 10 2.1.5 Construction procedure 11 2.1.6 Fixed type and floating type improvement 12 2.2 Improvement of conventional CDM method 12 2.2.1 T-shaped soil- cement column 12 2.2.2 The PF method 15 2.3 Theory of settlement evaluation 16 2.3.1 The equivalent elastic modulus and 3D settlement of composite grounds 16 2.4 Theory of numerical method 18 2.4.1 Preliminaries on material modelling 18 2.4.2 Linear elastic model 18 2.4.3 Mohr-Coulomb model 21 2.4.4 Hardening soil model 24 2.4.5 Soft soil model 33 CHAPTER 3: METHODOLOGY 35 3.1 Analysis approaches 35 3.2 Analyses using analytical method 36 3.3 Analyses using numerical method 38 CHAPTER 4: LABORATORY AND FIELD TEST 40 4.1 Introduction of Samse project 40 4.1.1 General information of project 40 4.1.2 The PF groups 40 4.1.3 Soil profile and footing parameters 41 4.2 Laboratory tests for Samse project 43 4.3 Static load test on PF groups 47 4.3.1 The geometry and installation PF groups 47 4.3.2 Installing strain gauges 48 4.4 Static load test on single PF column 49 4.4.1 Soil profile 49 4.4.2 Footing parameters 49 CHAPTER 5: SETTLEMENT ANALYSIS AND RESULTS 51 5.1 Settlement analyses using elastic theories 51 5.1.1 Verification analysis 51 5.1.2 Analyses for Ideal case and JEF case 52 5.1.3 Results and discussions 56 5.2 Settlement analyses using nonlinear models 61 5.2.1 Analyses for ideal case 61 5.2.2 Analyses for the experimental single PF column 62 5.2.3 Analyses for PF groups at SAMSE project 63 CHAPTER 6: CONCLUSIONS AND RECOMMENDATIONS 71 6.1 Conclusions 71 6.2 Limitations and suggestions 72 REFERENCES 73 APPENDIX 76 ABSTRACT Point Foundation (PF) method is an advanced technology introduced by EXT Co Ltd company from Korea, which has more advantages than CDM method The shape of PF columns makes a big difference in settlement compared to conventional CDM This study presents a comparative study on stiffness enhancement of grounds improved by Point Foundation method and by the conventional CDM method using analytical and numerical analyses In addition, the analysis results are compared with experimental program The stiffness enhancement is evaluated through induced settlement values under four shallow footing cases, of which one is ideally assumed and the other is an actual footing constructed Results from both analytical analysis and numerical analysis, in which elastic models are used, indicate that in general the PF method produces a more proper stiffness distribution with depth, which in turn results in smaller settlement values Numerical analysis results also indicate that when only soil area under the footing is improved settlement of the footing is significantly larger than that on ground improved entirely, the case of theoretical elastic soil model This is attributed to the influence of larger horizontal displacement around the footing Results from numerical analysis, in which inelastic model used, settlement of shallow footing on PF columns is smaller settlement of conventional CDM columns for the same ground model under certain conditions By true 3D model of column and soil, when the load-settlement is still in relatively linear range, the settlement values from the equivalent soil model and true 3D column and soil model are relatively equal This may suggest the equivalent soil model can be used in practice as it has been used in the elastic analyses PF columns has been analyzed the true behavior between columns and soil (shape of PF column, interaction between column and soil), the results analysis show that when analyzing settlement of shallow footings on PF columns in soft clay, special attention should be paid to the stiffness ratio between PF column and soil 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) First of all, I am very grateful Dr Nguyen Tien Dung, who guided me to conduct this thesis for the part one year He spent a lot of time telling me complicated issues in geotechnical engineering Not about knowledge, he also taught me valuable lesson about the seriousness and carefulness in scientific research These valuable lessons will follow me throughout the future study 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 I would also like to acknowledge the staff of Vietnam Japan University, Mr Bui Hoang Tan for their help and support I would also like to thank Prof Junichi Koseki, Assoc Prof Kenji Watanabe, Assist Prof Hiroyuki Kyokawa as well as other members of Koseki lab, where I had 80 meaningful days internship at The University of Tokyo It was very helpful to me Special thanks to Associate professor Nguyen Chau Lan, lecturer at University of Transport and Communication His explanations in geotechnical engineering helped me a lot in this study His successful way in research encouraged me more than anything else Thanks to Dr Nguyen Cong Oanh (Vietnam Academic for Water Resources), he explained in detail the complex problems in finite element method for geotechnical engineering Finally, Thanks are due to my family, who are always and support me in studies and research LIST OF TABLES Table 2.1 Typical properties of Stabilized soil (wet method) (Modified from Elias et al 2006) Table 2.2 Typical Properties of Lime–Cement Stabilized Soils (Dry Method) (Modified from Elias et al 2006) Table 4.1 Unconfined compression test results 44 Table 4.2 Strength parameters of samples collected from the PF column 50 Table 5.1 Input parameters for calibration analysis 52 Table 5.2 Input parameters for settlement analysis 55 Table 5.3 Input parameters for the single PF column 63 Table 5.4 Material model and parameter used for Samse factory project 64 LIST OF FIGURES Figure 1.1 Configuration of improved CDM columns: (a) Point foundation (PF) (Nguyen et al 2019a): (b) T-shape column (Liu et al 2012) Figure 2.1 Available ground improvement methods for different soil types (modified from Schaefer et al., 2012) Figure 2.2 Classification of deep mixing method (Kitazume & Terashi, 2013) Figure 2.3 Equipment of deep mixing method (DJM machine) 10 Figure 2.4 Drilling machine (left) and Mixing shaft and blades of DJM machine (right) 11 Figure 2.5 Machine has two mixing shafts and Binder Plant for DJM method (by the courtesy of Dry Jet Mixing Association) 11 Figure 2.6 Type of ground improvement (Kitazume & Terashi, 2013) 12 Figure 2.7 The T-shaped soil cement column overlain by embankment (Song-Yu at el, 2012) 14 Figure 2.8 Displacement of soil under TDM and SCC (Yaolin et al., 2012) 14 Figure 2.9 Load- settlement curves of conventional DCM and TDM pile from physical model test (Chana Phutthananon et al, 2012) 15 Figure 2.10 Site construction of PF method 16 Figure 2.11 Flexible rectangular loaded area 16 Figure 2.12 General three demensional coordinate systems and sign convention for stress 19 Figure 2.13 Basic ideal of an elastic perfectly plastic model (Plaxis manual) 22 Figure 2.14 The Mohr-Coulomb yield surface in the principal stress space (c=0) 23 Figure 2.15 Hyperbolic stress- strain curve (Ducan & Chang, 1970) 25 Figure 2.16 Stress circles at yield (Plaxis manual) 26 Figure 2.17 Relationship between initial tangent modulus and confining pressure 27 Figure 2.18 Unloading and reloading of silica sand under drain triaxial test consolidation (Ducan and Chang 1970) 28 Figure 2.19 Hyperbolic stress–strain relationship in primary loading for a standard drained triaxial test (Schanz, 1999) 30 Figure 2.20 Representation total yield of the HS model in principle space stress for cohesionless soil 31 Figure 2.21 Yield surface of hardening model (Schanz et al., 1999) 32 Figure Configuration of CDM and PF columns 35 Figure Plan view of SAMSE factory project 40 Figure Plan view of three PF groups 41 Figure 4.3 Shape of PF columns: (Left) Group (LPF=8.5m), (Middle) Group (LPF=6 m); 42 Figure 4.4 Soil profile of SAMSE factory project 42 Figure 4.5 Collection of mixed cement- soil samples 45 Figure 4.6 Secant Modulus E50 46 Figure 4.7 Relationship between secant modulus of elasticity and unconfined compressive strength (SAMSE project) 46 Figure 4.8 Static load test on instrumented PF groups 47 Figure 4.9 Test installation: (a) the geometry of PF columns, (b) increment load applies on steel plate, (c) displacement sensors on steel plate and groundb 47 Figure 4.10 Strain gauge installation: (a) installation of sensors along the depth of PF, (b) setting up sensors into PF, (c) strain gauge instruments, (d) sensor in PF 48 Figure 4.11 Soil profile at Songdo site (Kim et al 2016) 49 Figure 4.12 Configuration of the instrumented column (Kim et al 2016) 50 Figure 4.13 Instrumentations implemented on variable cross-section soft ground reinforced foundation (Kim et al 2016) 50 Figure 5.1 Foundation and soil domain in the numerical analysis 51 Figure 5.2 Comparison of vertical stress profiles obtained from analytical and numerical analyses 52 Figure 5.3 Soil profile under the examined footings (Ideal case) 53 Figure 5.4 Soil profile under the examined footings (JEF project) 54 Figure 5.5 Cross-sectional and plan views of the examined footing at JFE project 55 Figure 5.6 Settlement value from analytical method for Ideal case 57 Figure 5.7 Settlement value from analytical method for JEF case 58 Figure 5.8 Variation of Scorr,PF,min/Scorr,CMD ratio 58 Figure 5.9 Settlement values from analytical and numerical analyses for Ideal case 59 Figure 5.10 Settlement values from analytical and numerical analyses for JEF project 60 Figure 5.11 Settlement analysis from numerical method for ideal case 61 Figure 5.12 Settlement analysis from numerical method for JEF case 61 Figure 5.13 Load- settlement curves from MC model 62 Figure 5.14 Load settlement curves from Numerical method for PF column and conventional CDM 63 Figure 5.15 Load settlement curves from Numerical method for PF columns and CDM columns using equivalent material (E50=150qu) 65 Figure 5.16 Load settlement curves from Numerical method for PF groups and CDM groups using true 3D model of PF columns and soil 66 Figure 5.17 Settlement profiles with depth of footings on PF and CDM columns from numerical method using equivalent material model (q = 800 kPa) 68 Figure 5.18 Load settlement curves from Numerical method for PF columns and conventional CDM columns (Optimal shape design for PF columns) 68 Figure 5.19 Variation of settlement () and effective vertical stress (v) at the toe of CDM and PF columns obtained from numerical analysis using true 3D model 69 Figure 5.20 Mohr- Coulomb failure criterion 76 LIST OF ABBREVIATIONS as ascc CDM c (c’) Cc Cs D Dh Df Dt eo Ei Eoed E50 Eu Eur Ec Ecomp Es E’s HCC HS L Lc Lh Lt M MC Ms NC OCR PF PI qu Improvement area ratio Improvement area ratio of conventional CDM column Cement deep mixing method Cohesion strength Compression index Swelling index Diameter of conventional soil cement column (m) Diameter of cap of HCC (m) Embedded depth (m) Diameter of tail of HCC (m) Initial void ratio Initial tangent modulus Oedometric modulus Scant elastic modulus of soil at 50 percent (kPa) Undrained elastic modulus of soil (kPa) Unloading and reloading Young’s modulus Elastic modulus of soil cement column (kPa) Elastic modulus of improved ground (kPa) Elastic modulus of soil (kPa) Young’s modulus in term of effective stress Head-enlarged soil cement column Hardening soil model Length of conventional soil cement column (m) Length of cone of PF column (m) Length of head of PF column (m) Length of tail of PF column (m) Shape factor for Cam clay ellipse/slope of critical state line Mohr Coulomb model Constrained modulus of soil (kPa) Normal consolidation Over consolidation ratio Point foundation Plasticity index (%) Unconfined compressive strength (kPa) (MC) failure criterion For this, footing and soil profile for the ideal case were adopted for the analysis, in which one typical value of  = 1.6 was used and analyzed For each  value, a maximum applied pressure pmax = 100 kPa was targeted Figure 5.13 shows applied press - settlement curves obtained from the analysis for different  values As shown, the settlement curves obtained from  = 0.3 and 0.4 exhibit largest resistance (or bearing capacity) or smallest settlement a given applied pressure level This result agrees well with that obtained from linear analysis as shown in Figure 5.11 It is clear that, these results are preliminary and more analyses on actual cases/projects are needed to make more comprehensive conclusions 0.000 Settlement, Scorr (m) 0.020 0.0 10.0 0.040  value 0.080 0.30 0.060 0.100 0.120 0.140 0.160 0.180 0.200 Applied pressure, p (kPa) 20.0 30.0 40.0 50.0 60.0 70.0 80.0 0.20 0.40 0.50 0.60 0.70 0.80 Ideal case, MC model 1.00 ( = 2.0,  = 1.6, DCDM = 1.0 m) 0.90 Figure 5.13 Load- settlement curves from MC model 5.2.2 Analyses for the experimental single PF column Input parameters In this case, the subsoil was modelled using hardening soil model and the PF column was modelled using Mohr-Coulomb (MC) model For this case of single column, the axial symmetry method is the most reasonable Input parameters are given in Table 5.3 Settlement analysis Figure 5.14 show load- settlement curves for static load test, PF column and CDM column in the same ground From load- settlement curves of PF column and load settlement curve of static load test, there are no significant difference between two curves, numerical method 62 to predict settlement of PF column is accepted Under the same volume, soil profile, settlement of PF column is smaller than settlement of CDM Reduce settlement between PF column and CDM column follow as equation: S  S CDM  S PF 100  80 100%  %  20% with Q=500 kN S CDM 100 Table Input parameters for the single PF column Layer Material model Silty clay HS Silty sand Es (kPa) Su (kPa) (1200-1500)N1(60) 6N1(60) MC 1000N1(60) Silty sand MC (1200-1500)N1(60) Rigid steel plate Linear elastic 10^12 CDM MC Es,avg v’ 6N1(60) 0.2 6N1(60) 0.2 - 0.2 qu 0.2 Note: MC= Mohr- Coulomb; HS= Hardening soil Settlement (mm) 0 100 200 Axial load (kPa) 300 400 500 600 PF group (Equivalent model) CDM group (Equivalent model) 10 15 Static load test Single PF column Figure 5.14 Load settlement curves from Numerical method for PF column and conventional CDM 5.2.3 Analyses for PF groups at SAMSE project Input parameters 63 Table 5.4 Material model and parameter used for SAMSE factory project Parameter Model Material behavior Elastic modulus, Es’ Unit weigh,  v’ Cc Cs einit POP E cohesion, c’ E friction angle, ’ Unit Fill layer MC kPa kN/m3 kPa kPa degree Drained 30000 18.0 0.25 30 Note: MC= Mohr-Coulomb; SS= soft soil Soft soil Medium clay clay SS SS PF/CDM Steel plate MC 17.82 0.15 0.03 0.86 30 10 27 390,000 23.0 0.25 1300 - Elastic d=0.15 m 1012 78.5 0.2 - Undrained Undrained Undrained 17.82 0.15 0.03 0.86 10 27 Within the improved zone, PF column have three parts: Head of PF, cone of PF and tail of PF Similarly, the improved zone have three parts: Head of the improve zone, cone of the improved zone and tail of the improved zone Using equation (3.5), the parameters of stiffness (Es), effective cohesion (c’), effective friction angle (’) change by depth (m) In this case, each footing has three columns, thus it is quite complicated for equivalent method In the model, the size of of the plate B  L = 2.4  2.4 m was used to fully cover the columns Table 5.4 shows material models and input parameters for Samse project It is important to note that settlement of PF group (PF length = 8.5 m) is not presented in this section This is because the measured settlement values of the group are too small to match with any constitutive model used More time is needed to investigate the settlement of this group Thus, in the following sections, comparisons are made for the group and group at the site Settlement analysis In this cases, the PF columns and soil under the footing are modelled using two approaches: (i) An equivalent material; (ii) A true 3D model of PF columns and soil (i) An equivalent model: 64 The effectiveness when the treated zone under the footing is modelled as an equivalent material (with secant modulus for PF/CDM columns: E50=150qu) Figure 5.15 (a) and (b) show load-settlement curves of the simulated footings on PF columns, CDM columns and from the static load test Two distinct points from the comparison are:  Settlement of the footing on PF columns and CDM columns is almost equal  Generally, the difference in settlement of footings on PF columns and static load test is not much (less than 10%), this value is accepted for numerical analysis 0 100 200 Axial load (kPa) 300 400 500 600 700 800 Settlement (mm) 20 40 PF group (Equivalent model) 60 CDM group (Equivalent model) Static load test 80 100 Samse project group 02 120 (a) Group 02 (LPF=6 m) 0 100 200 Axial load (kPa) 300 400 500 600 Settlement (mm) 20 40 60 80 100 120 PF group (Equivalent model) CDM group (Equivalent model) Static load test Samse project group 03 (b) Group 03 (LPF=4 m) Figure 5.15 Load settlement curves from Numerical method for PF columns and CDM columns using equivalent material (E50=150qu) 65 0 100 Axial load (kPa) 200 300 400 500 600 700 800 Settlement (mm) 20 40 PF group (Equivalent model) 60 PF group (3D model) CDM group (Equivalent model) 80 CDM group (3D model) Static load test 100 Samse project group 02 120 (a) Group 02 (LPF=6 m) 0 100 200 Axial load (kPa) 300 400 500 600 Settlement (mm) 20 40 60 80 100 120 PF group (Equivalent model) PF group (3D model) CDM group (Equivalent model) CDM group (3D model) Static load test Samse project group 03 (b) Group 03 (LPF=4 m) Figure 5.16 Load settlement curves from Numerical method for PF groups and CDM groups using true 3D model of PF columns and soil (ii) A true 3D model of PF columns and soil Figure 5.16 (a) and (b) show a comparison of load- settlement curves otbained from simulated footings on PF and CDM columns using both equivalent material and true 3D approaches (with secant modulus for PF/CDM columns: E50 =150qu kPa) and from the Some key points from the results are as follows: 66  Generally, settlement of simulated footing on PF columns is also close to settlement of the footing from static load test This result can be acceptable  Settlement of footings on PF (or CDM) columns using equivalent model is slightly smaller than settlement of footings on PF (or CDM) columns using the true 3D model The difference might be attributed to some reasons such as shape of the columns, foundation size (steel plate), soil characteristics, etc However, the settlement discrepancy is unnoticeable when the load-settlement curves in the relatively linear range This means that under service loading conditions, in which settlement curve is almost linear, both models result in rather similar settlement values  Settlement of the footings on CDM columns is smaller than settlement of footings on PF columns for both equivalent material and true 3D models For these two experimental PF groups, why is the settlement of footings on CDM columns smaller than settlement of footings on PF columns? This result is against previous finds that the settlement of footings on PF columns is generally smaller settlement of footings on CDM columns Possible reasons and proof As discussed above, there are possible reasons that make settlement of the footings on PF columns smaller than settlement of the footings on CDM columns: Reason 1: The PF columns shape is not the optimal shape In the ideal case and JEF case, there exist a minimum settlement value at certain  value in the range of 0.4 to 0.5, but in SAMSE project: (i) =Lh/L=1/6=0.16 < 0.4 for PF columns of group 02 (LPF=6 m); (ii)  = Lh/L = 1/4 =0.25 < 0.4 for PF columns of group 03 (LPF = m) These values not make a difference in settlement of shallow footings on PF columns and CDM columns Reason 2: The settlement consists parts: Settlement of improved zone and settlement of layers under improved zone The main difference in stiffness between columns and the soil is so high, therefore, the settlement of improved zone is very small compared with the total settlement 67 Figs 5.17(a) and 5.17(b) show the settlement profiles with depth of the footings on PF groups and As shown, for each group, settlement profiles from footings on PF and CDM columns are almost identical Settlement (mm) Settlement (mm) 20 40 60 80 100 Samse project (Group 02) 12 Depth (m) Depth (m) 13 14 15 Samse project (Group 03) 10 11 13 CDM columns PF columns 14 15 (a) Group 02 10 11 Samse project (Optimal shape) 12 12 CDM columns PF columns 50 100 150 200 5 4 3 11 50 100 150 200 2 1 10 Depth (m) Settlement (mm) 13 CDM columns PF columns 14 15 (b) Group 03 (c) Optimal shape Figure 5.17 Settlement profiles with depth of footings on PF and CDM columns from numerical method using equivalent material model (q = 800 kPa) 0 100 200 Axial load (kPa) 300 400 500 600 700 800 Settlement (mm) 50 100 150 200 PF group CDM group Samse project Optimal shape design for PF group Figure 5.18 Load settlement curves from Numerical method for PF columns and conventional CDM columns (Optimal shape design for PF columns) 68 q (kPa) 'v,CDM (v,CDM) 'v,PF (v,PF) 800 800 700 700 600 600 500 Axial load (kPa) Axial load (kPa) (a) PF group and CDM group in Samse project PF group CDM group 400 300 200 PF group CDM group 400 300 200 100 500 100 Shallow footing Group 02 20 40 60 Settlement (mm) 80 Shallow footing Group 02 100 200 300 400 Effective vertical stress at toe (kPa) 600 600 500 500 400 Axial load (kPa) Axial load (kPa) (b) Group 02 PF group CDM group 300 200 100 20 40 60 Settlement (mm) PF group CDM group 300 200 100 Shallow footing Group 03 400 80 100 Shallow footing Group 03 100 200 300 400 Effective vertical stress at toe (kPa) 500 600 (c) Group 03 Figure 5.19 Variation of settlement () and effective vertical stress (v) at the toe of CDM and PF columns obtained from numerical analysis using true 3D model 69 Fig 5.17(c) shows the settlement profiles of footings on PF group with two parameters changed: (1) the PF columns were extended from Lh = 1.0 m, Lc = 1.0 m, and Lt = 2.0 m (i.e.,  = 1/4 = 0.25) to have Lh = 4.0 m, Lc = 1.0 m, and Lt = 1.0 m (i.e.,  = 4.0/6.0 = 0.66); (2) the stiffness ratio of the columns to soil was changed from E c/Es = 150 to Ec/Es = 65 (an average value taking into account the variation of soil stiffness with depth) As shown, the settlement of the footing on PF columns is smaller than that on CDM columns The results indicate two important points: (i) the head length should be long enough to cover the upper soft soil layer: (ii) If the stiffness ratio is too high, the settlement of the footings come mainly from the settlement of the soft layers underneath the treated zone Note that common stiffness ratio of 10 to 20 are found from many case studies (Kitazume and Terashi 2013) Fig 5.18 shows load-settlement curves of footings on PF group extended discussed in the previous graph It is very clear that the settlement of the footing on PF columns is smaller than that of CDM columns The results support findings from previous cases Settlement () and effective vertical stress (v) at the toe of CDM and PF columns obtained from numerical analysis using true 3D model (Discussed in Fig 5.16; E50 = 150qu for the PF/CDM columns; using soft soil model) are shown in Fig 5.19 As shown, for group 02 (Fig 5.19(b)) the applied pressure-toe settlement curves as well as applied pressure- toe pressures from PF columns and CDM columns are almost identical However, the group 3, the curve show different trend: both settlement and effective vertical stress at toe PF columns’ toe are larger than the values at CDM columns’ toe This indicates a very important point that soft soil layers under the floating columns play very important in the total settlement of the footing 70 CHAPTER 6: CONCLUSIONS AND RECOMMENDATIONS 6.1 Conclusions This study presents a comparative study on the effectiveness of PF columns and conventional CDM columns in reducing settlement of shallow foundations using analytical method and numerical methods The following are key conclusions drawn from the study On settlement analysis using elastic theory: 1) Under the same ground models, settlement of the footings on PF columns is smaller than that on conventional CDM columns 2) Settlement curves (S versus ) from both analytical method and numerical method show similar trends 3) For each  value, an optimal shape of PF column is obtained (i.e., giving minimum settlement) for a certain value of  (,  are defined in chapter 4) When  varies from 1.4 to 1.6, the optimal PF columns are obtained with  varies from 0.4 to 0.6 The optimal settlement from ground improved by PF columns may be as small as 0.9 times that from ground improved by CDM columns On settlement analyses using nonlinear materials: 1) For single columns, settlement of PF column is smaller than settlement of conventional CDM column The larger head of PF column reduces the pressure transfer to the lower portion of the column 2) Under the following conditions: (i) the ratio of stiffness of PF column (or CDM column) over that of the surrounding soil varies from 10 to 20 times; (ii) the head of the PF columns installed sufficiently deep in the soft soil layers, the settlement of footing on PF columns is generally smaller than that on CDM columns The first condition is to make sure that the equivalent material model is applicable When the stiffness of the PF columns (or CDM columns) is much larger than the stiffness of surrounding soil layer (typically larger than 20 times), the columns would act as piles In this case, the effectiveness of PF columns is insignificant 71 On the behavior of true 3D column model over the equivalent material model: Analyses using the true 3D model of columns and soil show that if the PF columns not satisfy the two conditions above then the use of PF columns is not effective By true 3D model of columns and soil, when the load-settlement is still in relatively linear range, the settlement values from the equivalent soil model and true 3D column and soil model are relatively equal This may suggest the equivalent soil model can be used in practice as it has been used in the elastic analyses For 3D column of columns and soil, the settlement of shallow footing on PF columns is affected by soft soil layers under the floating columns In many cases, when using PF columns, pay attention to the position of columns’ toe and stiffness of PF columns 6.2 Limitations and suggestions Limitation: In my thesis, the research is still limited It is: 1) Not fully analyzed the behavior of soil and PF columns (true 3D model of PF column and soil) 2) In four cases, the footing is rigid foundation In case, the footing is flexible foundation, we need analyze settlement of footing on PF columns This is a problem need consider Suggestion: 1) Analysis ultimate bearing capacity of footing on PF columns both numerical method and analytical method by equivalent materials 2) Analysis ultimate bearing capacity of footing on PF columns both numerical method and analytical method by true 3D model of PF columns and soil 72 REFERENCES [1] Bergado, D T (1996) Soft Ground Improvement: In Lowland and Other Environment [2] Bergado, D T., T Ruenkrairergsa, Ã., Taesiri, Y., & Balasubramaniam, A (1999) Deep soil mixing to reduce embankment settlement Ground Improvement [3] Brinkgreve, R B J., E Engin, and W M Swolfs "PLAXIS 3D 2013 user manual." 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Acta Geotechnica 12.5 (2017): 1077-1088 [48] Zwillinger, D (2018) CRC Standard Mathematical Tables and Formulas 75 APPENDIX Appendix A: The relationship between compressive strength and confining pressure may be expressed conveniently in terms of Mohr- Coulomb failure criterion as: (  )f  2c cos   2 sin   sin  Figure 5.20 Mohr- Coulomb failure criterion Prove:  1   1   ) f  IH'  3 ( ) f  H'Q'+Q'N'+N'I'  3 ( ) f  HQ+MN+N'I' ( (1) And: HQ = ccos MN = 3 sin   N’I’= ( ) f sin  (2) From (1), (2) So:  3 2c cos   2 sin   3  3 )f  ( ) f  c cos    sin   ( ) f sin   ( 2  sin  76 ... focused on introduction of concept of the method as well as of a simple analytical method to evaluate settlement of soft ground improved by the PF columns Much of understandings on the PF columns. .. structural conditions, (2) geotechnical conditions, (3) environmental constraints, (4) construction conditions, and (5) reliability and durability Structural conditions: The structural conditions may... allowed construction time, (3) availability of construction material, (4) availability of construction equipment and qualified contractor, and (5) construction cost The selection of a ground improvement