Analytical and numerical analyses on stiffness enhancement of ground improved by head enlarged CDM columns

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

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

1.1 General introduction of deep mixing method 1

1.2 Necessity of research 2

1.3 Objective and Scope of research 3

1.3.1 Objective of the study 3

1.3.2 Scope of the study 3

CHAPTER 2: LITERATURE REVIEW 4

2.1 Overview of deep mixing method 4

2.1.1 Brief view of deep mixing method 4

2.1.2 Application of CDM 6

2.1.3 Classification 8

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) 5

Table 2.2 Typical Properties of Lime–Cement Stabilized Soils (Dry Method) (Modified from Elias et al 2006) 5

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) 2

Figure 2.1 Available ground improvement methods for different soil types (modified from Schaefer et al., 2012) 8

Figure 2.2 Classification of deep mixing method (Kitazume & Terashi, 2013) 9

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 3 1 Configuration of CDM and PF columns 35

Figure 4 1 Plan view of SAMSE factory project 40

Figure 4 2 Plan view of three PF groups 41

Figure 4.3 Shape of PF columns: (Left) Group 1 (LPF=8.5m), (Middle) Group 2 (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

ascc Improvement area ratio of conventional CDM column

E50 Scant elastic modulus of soil at 50 percent (kPa)

E’ s Young’s modulus in term of effective stress

M Shape factor for Cam clay ellipse/slope of critical state line

q Deviator stress

 Ratio of length of cap and the total length of PF column

 Ratio of diameter of cap of HCC and diameter of tail of PF column

xy Horizontal stress increment (kPa)

z Vertical stress increment (kPa)

 Ratio of distance between two columns and the diameter of column

u Poisson ratio of soil in undrained condition

ur Poisson ratio for unloading and reloading

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CHAPTER I: INTRODUCTION 1.1 General introduction of deep mixing method

The sustainability of the building depends largely on the foundation of the building (about from 40 to 60% value of project) Therefore, the design of the foundation is an important element in the design work Under the development of science and technology, there are many foundation design options that are widely used

Nowadays, there are many methods for improving soft grounds such as compaction methods, vertical drains under surcharge and vacuum preloading, vibration methods, deep mixing method, and other miscellaneous methods Among the methods, deep mixing method (DMM) is widely used as an effective method for ground reinforcement

in the world The method creates cement deep mixing (CDM) columns to increase the stiffness (i.e., to reduce settlement) and to control the stability of embankment or excavations In general, sub-soils at different places have unique behavior under same loading condition so that finding an optimal solution that satisfies both technical and financial requirements is always an interesting question for geotechnical engineers The DMM has been extensively used for many types of construction project, for example embankment supports, buildings, earth retaining structures, retrofit and renovation of urban infrastructures, liquefaction hazards mitigation, manmade island construction and seepage control Deep mixing has been mostly used to improve soft cohesive soils, but it is sometimes used to reduce permeability and mitigate liquefaction

of cohesionless soils

Besides the advantages, the conventional CDM column also has some limitations when

it is applied to reinforce grounds under shallow foundations Soil layers in the upper part

is often weaker than that in the lower part (deeper layers), however, under shallow footings, introduced stresses are mainly distributed in the depths right below the footing This combination of natural ground and CDM columns in cases of shallow footings is therefore ineffective There should be a better shape of CDM columns to reinforce the ground more optimal

of the PF column and its construction method were introduced in Trung (2019), Nguyen

et al (2019a and 2019 b)

Liu et al (2012) developed special equipment that has foldable augers to install deep mixing (DM) columns at different diameters Due to the shape of the columns like the letter T, they are named this DM columns T-shaped columns (Fig 1.1b) Some researches on T-shaped soil cement column (e.g., Yi et al 2018) showed remarkable results in settlement and lateral movement reduction compared with conventional method

(a) (b) Figure 1.1 Configuration of improved CDM columns: (a) Point foundation (PF) (Nguyen et al 2019a): (b) T-shape column (Liu et al 2012)

Although there were some initial researches on PF columns (i.e., Trung 2019, Nguyen

et al 2019), these studies 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 under shallow foundations, such as the influence or nonlinearity of soil and the influence of stiffness of PF columns to the settlement of the foundations are unfolded It is therefore necessary to have a study to

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further understand the behavior of PF groups under actual foundation conditions (e.g., actual soil layers, nonlinear characteristics of soil materials)

1.3 Objective and Scope of research

1.3.1 Objective of the study

General objective:

To evaluate the effectiveness of PF columns over that of CDM columns in reducing settlement of shallow footings on reinforced grounds using both analytical and numerical methods for the same foundation models

1.3.2 Scope of the study

To obtain the objectives above, this study focuses on the following:

1 Evaluate settlement of shallow footings using classical theory of foundation on elastic materials For this, settlement of shallow footings on an ideal soil profile and

on an actual project soil profile is evaluated using both analytical and numerical methods

2 Compare predicted and measured settlement values of shallow footings using linear behavior of soil material For this, settlement of shallow footings on an experimental single PF column and on experimental PF groups is evaluated using numerical method

non-3 Compare predicted and measured settlement values of shallow footings on experimental PF groups, in which the treated zone is modelled as an equivalent elastic material and as a true 3D model of PF columns and soil

et al (2013), Bredenberg et al (1999), Kirsch and Bell (2012)

2.1.1 Brief view of deep mixing method

As mentioned in the introduction, deep mixing method increases the stiffness of ground by mixing in-situ soil with admixture (cement and necessary additives) Mixed soil columns created by deep mixing method has the elastic modulus at 50 percent (E50) of 75 to 1,000 times qu, where qu is the unconfined compressive strength of the column material (Kitazume & Terashi, 2013), but the value is still smaller than that of concrete pile (30,000,000 kPa) Thus, It can be considered that the work of mixed soil columns and surrounding soft soil as composited ground (not pile) Base on this assumption, most previous scholars proposed an equivalent elastic modulus of composited ground for determining the stiffness as well as deformation

The typical properties of stabilized soils are provided in Table 1.1 based on the wet method

of deep mixing and Table 1.2 based on the dry method of deep mixing The effects of different factors on the unconfined compressive strengths of stabilized soils have been discussed above

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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)

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2.1.2 Application of CDM

Selection of ground improvement method should consider the following conditions: (1) structural conditions, (2) geotechnical conditions, (3) environmental constraints, (4) construction conditions, and (5) reliability and durability

Structural conditions: The structural conditions may include type, shape, and dimension

of structure and footing, flexibility and ductility of structural and footing elements, type, magnitude, and distribution of loads, and performance requirements (e.g., total and differential settlements, lateral movement, and factor of safety) Geotechnical conditions: The geotechnical conditions may include geographic landscape, geologic formations, type, location, and thickness of problematic geo-material possible end-bearing stratum, age, composition, distribution of fill, and groundwater table Soil type and particle size distribution are essential for preliminary selection of ground improvement methods as shown in Figure 2.1 This guideline is suitable for ground improvement methods for foundation support The thickness and location of problematic geo-material are also important for the selection of ground improvement methods For example, when a thin problematic geo-material layer exists at a shallow depth, the over excavation and replacement method is one of the most suitable and economic method When a relatively thick loose cohesionless geo-material layer exists near ground surface, dynamic compaction and vibro-compaction methods are suitable ground improvement methods When a relatively thick soft cohesive geo-material layer exists near ground surface, preloading and deep mixing methods may be used When a site needs to be excavated, tieback anchors, soil nails, deep mixed columns, and jet grouted columns may be used When a site needs to be elevated, geo-synthetic-reinforced slopes and walls can be good choices The level of groundwater table often affects the selection of ground improvement methods For example, when deep excavation happens in ground with a high groundwater table, deep mixed column walls may be better than soil nailed walls because they not only can retain the geo-material but also can cut off water flow

Environmental constraint: The environmental constraints may include limited vibration, noise, traffic, water pollution, deformation to existing structures, spoil, and headspace For example, dynamic compaction induces vibration and noise, which may not be suitable in a

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residential area The wet method to construct stone columns by water jetting produces spoil

on site, which may be troublesome for a site with limited space Under such a condition, the dry method may be used instead Preloading induces settlements at nearby areas, which may be detrimental to existing structures

The selection of a ground improvement method should consider the following construction conditions: (1) site condition, (2) 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 method must consider whether the site is accessible to its associated construction equipment, such as access road and headspace Construction time is one of the most important factors for the selection of a ground improvement method For example, preloading is a cost-effective ground improvement method to improve soft soil; however, it takes time for the soil to consolidate The use of prefabricated vertical drains can accelerate the rate of consolidation, but sometimes it still may not meet time requirement As a result, other accelerated ground improvement methods may be used, such as deep mixing and vibro concrete column methods Most ground improvement methods use specific materials during construction For example, stone columns and rammed aggregate columns use aggregate Cement is used for deep mixing and grouting When natural material is used, such as aggregate or sand, the cost of the material depends on the source of the material and its associated transportation distance For example, in a mountain area, aggregate is often less expensive; therefore, stone columns or aggregate columns are often a cost-effective solution In general, the use of locally available material results in more cost-effective ground improvement To select a ground improvement method, engineers should gather information about possible qualified contractors and their available construction equipment It is preferable to use a locally available qualified contractor because this will reduce the mobilization cost and the contractor is more familiar with local conditions Construction cost is always one of the key factors that dominate the selection of a ground improvement method The construction cost should include mobilization, installation, material, and possible disposal costs

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Reliability and DurabilityReliability of a ground improvement method depends on several factors, such as the level of establishment, variability of geotechnical and structural conditions, variability of construction material, quality of the contractor, quality of installation, and quality control and assurance Several researchers have exported that samples from deep mixed columns have a high variability in terms of their unconfined compressive strengths Automatic or computer-controlled installation processes can reduce the variability of improved geo-materials The number of well documented successful or failure case histories is also the evidence of the reliability of a specific ground improvement method Ground improvement methods are used for temporary and permanent structures For permanent structures, the durability of the construction material should be evaluated

or considered in the design For example, geosynthetics have creep behavior The corrosion

of steel reinforcement with time reduces its thickness The strength of cement-stabilized soil in seawater degrades with time (Ikegami et al., 2002)

Figure 2.1 Available ground improvement methods for different soil types (modified

from Schaefer et al., 2012) 2.1.3 Classification

The techniques most commonly employed for in-situ deep mixing in Japan can be divided into three groups: mechanical mixing by vertical rotary shafts with mixing blades at the

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bottom end of each mixing shaft, high pressure injection mixing, and combination of the mechanical mixing and high pressure injection mixing The various methods in these groups are classified in Figure 5.1 In the mechanical mixing techniques, binder is injected into a ground with relatively low pressure and forcibly mixed with the soil by mixing blades equipped to vertical mixing shaft(s) The binder is used either with powder form (dry method) or slurry form (wet method) The Dry Jet Mixing (DJM) method is the most common dry method of deep mixing and has usually been applied for on-land works (Dry Jet Mixing Association, 2010)

Figure 2.2 Classification of deep mixing method (Kitazume & Terashi, 2013) The Cement Deep Mixing (CDM) method, the most common wet method of deep mixing, has frequently been applied for both in-water and on-land works (Cement Deep Mixing Method Association, 1999) In the high pressure injection technique, on the other hand, ground is disturbed by a high pressure jet of water and/or air, while at the same

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time binder slurry is injected and mixed with the soil The combination of mechanical mixing and high pressure injection mixing exploits the features of both basic techniques 2.1.4 Equipment and machine

Basically, the equipment for deep mixing construction includes binder plant and drilling machine The binder plant is a system of equipment where admixture is produced by mixing material with water, air, etc Then binder is supplied to the shafts of drilling machine through independent pumps for mixing with in-situ soil

Figure 2.3 Equipment of deep mixing method (DJM machine)

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Figure 2.4 Drilling machine (left) and Mixing shaft and blades of DJM machine (right)

Figure 2.5 Machine has two mixing shafts and Binder Plant for DJM method (by the

courtesy of Dry Jet Mixing Association) 2.1.5 Construction procedure

The construction procedure of deep mixing method has 4 steps First, the preparation of site is carried out to guarantee all condition needed for the construction such as leveling of working platform, inspection of obstacles below ground Then all equipment is calibrated during the field trial test, especially for the less experience in similar soil conditions When all conditions are already tested, the next step is construction work which is the main step

of the CDM method, including the penetration and withdraw process Binder is injected during both penetration and withdraw for gaining the effectiveness of mixing Finally, the quality control is executed in both during and after the construction work for controlling

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the quality and geometry of treated column The rotating speed of mixing blades and the penetrated speed of shafts are monitored for creating the mixed soil column as designed 2.1.6 Fixed type and floating type improvement

Generally, there are two types of ground improvement which are fixed type and floating type The distinguishable idea bases on the stiffness of layer that mixed soil columns penetrate The fixed type is a type of ground improvement which mixed soil columns reach the stiff layer On the other hand, for the floating type, mixed soil columns do not fully penetrate bearing layer Both fixed type and floating type

is normally used for reducing the excessive settlement of soft ground under construction However, for the bridge structure, if the stabilized soil reaches the so stiff layer, the large differential settlement may occur between the structure of bridge and the adjacent embankment or road The objective of floating type is controlling the equilibrium deformation of different structures placed on soft ground

Figure 2.6 Type of ground improvement (Kitazume & Terashi, 2013)

2.2 Improvement of conventional CDM method

2.2.1 T-shaped soil- cement column

The T-shaped soil-cement column has the shape of letter “T” as its name implies, proposed

by Yaolin Yi at el Basically, the T-shaped deep mixing (TDM) column has two parts which are the cap with larger diameter in the shallow depth and the tail has smaller diameter

in the deep depth just for fulfilling the stiffness requirement A previous research of

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settlement under embankment load (Bergado et al, 1999) had showed the settlement of surrounding soft soil is always higher than that of mixed soil column This differential settlement between soil and mixed column cause the instability of embankment as well as the destruction of the pavement above The use of compacted granular material or geosynthetic reinforce could overcome this problem, increase the stability of structure However, its cost could be increased By reducing the stress concentration ratio, the TDM mitigate the differential settlement of soil and column Hence, the TDM column was proposed for solving this problem

The research of TDM column covered: the bearing capacity of composite ground consists

of T-shaped soil-cement column and soft clay, vertical bearing capacity of single TDM column, the vertical and lateral displacement of improved ground using TDM column comparing with that of conventional mixed soil column, the performance of TDM column supports soft ground overlain by embankment, the application of TDM column in China, etc Figure 2.9 shows the advantage of TDM by comparing the difference between vertical and lateral displacement of TDM and that of SCC At present, TDM has been applied widely in China, especially for improving soft ground under embankment of highway construction The diameter of most column caps is 0.9~1.2 m, which is approximately 1.3~2.4 m that of deep-depth column The column length (L) is 11~25 m (Yaolin et al, 2012) Dependence of ultimate bearing capacity and failure behavior of T-shape deep mixing piles on enlarged cap shape and pile strength (Chana Phutthananon et al, 2012) In this study, the author points out that the T column has a smaller bearing capacity than the CDM column under the same volume condition when using a physical experiment The author also found the optimal shape for T column (Figure 2.9)

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Figure 2.9 Load- settlement curves of conventional DCM and TDM pile from physical

model test (Chana Phutthananon et al, 2012) 2.2.2 The PF method

The PF method was recently introduced by EXT company (2012) in Korea and has been applied extensively in the country since 2014 (Nguyen at el, 2019) Two advantaged points of this method: (1) The shape of mixed soil column is analogous to the funnel which has three parts: the head, cone and tail as shown in Figure 2.14(b); (2) the binder of PF method is not only more environment-friendly but also has compressive strength value 1.5

to 2 times higher than common cement to mix with in-situ soils

The method was patented in Korea (No 10-1441929), in the US (No US 9,546,465 B2) and in China (No CN 104411891 B), received many certificates of excellent technology and environment-friendly method from professional organizations and ministries in Korea Similar to SCC, the PF method can be applied to reinforce grounds under roads, industrial buildings, storage yards, and especially can be used as pile foundation for transportation lightweight structures and for low-rise buildings with a maximum applied pressure up to

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300 kPa Most PF columns have the length of head is equal to that of cone, and is 1 m, the diameter of head is ranged from 1.2 to 1.4 m while that of tail is from 0.6 to 0.8 m

(a) Site construction of PF method (b) A PF column

Figure 2.10 Site construction of PF method 2.3 Theory of settlement evaluation

2.3.1 The equivalent elastic modulus and 3D settlement of composite grounds

The uniformly loaded rectangular area:

Figure 2.11 Flexible rectangular loaded area The settlement of corner point of a rectangular loaded area on surface area shown in Figure 2.12 can be estimated as follows:

Ecomp,i is the (drained) composite modulus of sub-layer i;

x,i, y,i, andz,i = (effective) stress increments in x, y, z directions at the center

of sub-layer i under the estimated settlement point The stress increments under uniformly loaded rectangle can analytically be calculated by equations described in Poulos and Davis (1974) or in CFEM (2006)

i = Poisson’s ratio of composite material of sub-layer i;

hi = thickness of sub-layer i The composite modulus can be determined as follows:

E  a E  a E (2.6)

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where EPF,i and Es,i = equivalent (drained) elastic modulus of mixed soil-cement column

(PF column) and of untreated soil of sub-layer i respectively; aPF,i = improved area ratio by

PF columns in sub-layer i

The corrected settlement of the at the center of the foundation is evaluated as:

S S I I (2.7) where IE and IF are settlement correction factors for foundation embedment and foundation

rigidity, respectively (CFEM 2006)

2.4 Theory of numerical method

2.4.1 Preliminaries on material modelling

A material model is described by a set of mathematical equations that give a relationship

between stress and strain Material models are offer expressed in a form in which

infinitesimal increments of stress are related to infinitesimal increments of strain All

material models in implemented in Plaxis are based on a relationship the effective stress

rates and the strain rates

2.4.2 Linear elastic model

General definitions of stress

Stress is a tensor which can be represented by a matrix in Cartesian coordinates:

In the standard deformation theory, the stress tensor is symmetric such as xy=yx,

yz=zy and zy=yz In this situation, stress is often written in vector notation, which

involve only six different components:

det ' I ' 0 (2.13) Where I = identity matrix

General definitions of strain

Strain is a tensor which can be represented by a matrix Cartesian coordinates as:

       where i and j are x, y or z

Strain are often written in vector notation, which involve only six different components:

is the increment of stiffness per unit of depth, together with the input of Einc the input of

yref become relevant Above yref the stiffness is equal to Eref Below the stiffness is given by:

( ) ref ( ref ) inc

E y  E  y  y E y<yref (2.22) 2.4.3 Mohr-Coulomb model

The linear elastic perfectly-plastic model is a first order model that includes only a limited number of features that soil behavior shows is reality Although the increase of stiffness

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with depth can be taken into account, the Mohr-Coulomb model does neither stress dependency nor strain-path dependency of stiffness or anisotropic stiffness In general, effective stress at failure are quite well described using Mohr-Coulomb failure criterion with effective strength parameter c’, ’ For undrain materials, the Mohr-Coulomb model may be used to with the friction angle set to zero and the cohesion c set to Su, to enable a direct control of undrain shear strength In that case note that the model does not automatically include the increase of shear strength with consolidation

The basic principle of elastoplastic is that strains and strain rates are decomposed into elastic part and a plastic part:

     (2.23) Hook’s law is used to relate the stress rates to the elastic strain rates Hook’s law lead to:

Figure 2.13 Basic ideal of an elastic perfectly plastic model (Plaxis manual)

Formulation of the Mohr- Coulomb model:

The Mohr- Coulomb yield condition is an extension of Mohr Coulomb’s friction law to general states of stress In fact, this condition ensures that Coulomb’s law is obeyed in any plane within a material element

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The full Mohr Coulomb yield condition consists of six yield functions when formulated in

terms of principle stresses (see for instance Smith and Griffith, 1982):

Figure 2.14 The Mohr-Coulomb yield surface in the principal stress space (c=0)

The two plastic model parameters appearing in the yield functions are the well-known

friction angle  and the cohesion c The condition fi=0 for all yield functions together

(where fi=0 is used denote each individual yield function) represents a fixed hexagonal

cone in principle stress space as show in Figure 2.15

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Basis parameters of the Mohr- Coulomb model:

The linear elastic perfectly plastic Mohr Coulomb model requires a total of five parameters, which are generally familiar to most geotechnical engineers and which can be obtained from basic tests on samples These parameters with their standard units are listed below: E: Young’s modulus, v: Poison’s ratio, c: Cohesion, : Friction angle, : Dilatancy angle Instead of using the Young’s modulus as a stiffness parameter, alternative stiffness parameters can be entered These parameters with their standard units are listen bellow: G: Shear modulus, Eoed: Oedometer modulus

Parameters can either be effective parameters or undrain parameters, depending on the selected drain type

2.4.4 Hardening soil model

Non-linearity and stress dependency

Kondner and his coworkers have shown tha the nonlinear stress and strain curve of both clay and sand may be approximate by hyperbolae with a high degree of accuracy The hyperbolic equation proposed by Kondner was:

Rf the failure ratio,

(1-3)f’: The compressive strength or stress difference at failure The relationship between compressive strength and confining pressure may be expressed conveniently in terms of Mohr- Coulomb failure criterions as:

Ei: the initial tangent modulus

Janbu have shown that the relationship between initial tangent modulus and confining pressure may be expressed as:

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Figure 2.17 Relationship between initial tangent modulus and confining pressure

(Ducan and Chang 1970) Tangent modulus values:

The incremental strains for each load increment are related to the incremental stress

changers for that increment by the generalized Hook’s law:

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Figure 2.18 Unloading and reloading of silica sand under drain triaxial test consolidation

(Ducan and Chang 1970) Davis and Poulos (1970) have shown that soil is an elasto- plastic material in the sense that strains included upon primary loading are only partially recoverable upon loading, and reloading behaves nearly elastically This linear behavior is independent only upon the confining pressure 3

The results of the number of test involving unloading and reloading on the silica sand have shown that the variation of the modulus value with confining pressure may be represent by:

Kur: The corresponding modulus number

Eur: The reloading- unloading modulus value

n: is for practical purposes the same for unloading- reloading as for primary loading Hardening soil model in the PLAXIS:

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Initially, the Hardening Soil Model (HSM) was introduced in the PLAXIS programme as

an extension of the Mohr–Coulomb Model (Nordal, 1999) Then, in PLAXIS Version 7,

an additional cap was added to the model to allow for the pre-consolidation pressure to be

taken into account Indeed, the HSM has been developed under the framework of the theory

of plasticity In the model, the total strains are calculated using a stress-dependent stiffness,

which is different for both loading and unloading/reloading The hardening is assumed to

be isotropic, depending on the plastic shear and volumetric strains A non-associated flow

rule is adopted when related to frictional hardening and an associated flow rule is assumed

for the cap hardening

Schanz et al (1999) and Brinkgreve (2002) explained in detail, the formulation and

verification of the Hardening Soil Model The essential backgrounds of the model are

summarised in this section Unlike the Mohr–Coulomb Model, the stress–strain

relationship, due to the primary loading, is assumed to be a hyperbolic curve in the HSM

(Figure 2 20) The hyperbolic function, as given by Kondner (1963), for the drained

triaxial test can be formulated as:

The stress–strain behavior for primary loading is highly non-linear The parameter E50 is a

confining stress dependent stiffness modulus for primary loading E50 is used instead of the

initial modulus E0 for small strain which, as a tangent modulus, is more difficult to

determine experimentally, and is given as: