An evaluation of the effectiveness of head enlarged soil cement columns hcc in ground improvement

The principle of deep mixing method is mixing admixture with in-situ soil to create constant diameter mixed soil columns and therefore the soft ground is improved consequently.. To overc

VIETNAM NATIONAL UNIVESITY HANOI

VIETNAM JAPAN UNIVERSITY

NGUYEN DUC TRUNG

AN EVALUATION OF THE EFFECTIVENESS OF HEAD-ENLARGED SOIL CEMENT COLUMN (HCC) IN

GROUND IMPROVEMENT

MASTER’S THESIS

Hanoi, 2019

VIETNAM NATIONAL UNIVESITY HANOI

VIETNAM JAPAN UNIVERSITY

NGUYEN DUC TRUNG

AN EVALUATION OF THE EFFECTIVENESS OF HEAD-ENLARGED SOIL CEMENT COLUMN (HCC) IN

TABLE OF CONTENTS

ABSTRACT iii

ACKNOWLEDGEMENTS iv

LIST OF ABBREVIATIONS v

LIST OF TABLES vi

LIST OF FIGURES vii

CHAPTER 1 - INTRODUCTION 1

1.1 General introduction of deep mixing method 1

1.2 Necessity of research 2

1.3 Objective and scope 3

1.3.1 Objectives: 3

1.3.2 Scope of research: 4

CHAPTER 2 - LITERATURE REVIEW 5

2.1 Overview of cement deep mixing method 5

2.1.1 Brief view of deep mixing method 5

2.1.2 Application of CDM 6

2.1.3 Classification 7

2.1.4 Equipment and machine 9

2.1.5 Construction procedure 10

2.1.6 Fixed type and floating type improvement 11

2.2 Innovation of conventional CDM method 11

2.2.1 T-shaped soil-cement column 11

2.2.2 The PF method 13

2.3 Theory of settlement evaluation 14

2.3.1 Brief overview of settlement 14

2.3.2 The use of 1D, 2D and 3D model in evaluating settlement 17

2.4 The equivalent elastic modulus and 1D settlement of composite ground 31

2.4.1 Equivalent elastic modulus 31

2.4.2 One-dimensional settlement 32

2.5 A suggested method for evaluating the settlement of spread footing on improved

ground 33

2.6 Verification from comparison of predict and measured load-settlement curves 33 CHAPTER 3 - METHODOLOGY 35

3.1 The performance of research 35

3.2 The analyze of research proposal 37

3.2.1 The percentage of settlement reduction 37

3.2.1 The percentage of material reduction 38

3.3 Verification by load-settlement curve 38

3.3.1 Initial elastic modulus of composite ground 38

3.3.2 Bearing capacity of composite ground (q u,comp ) 39

CHAPTER 4 - SETTLEMENT ANALYSIS 40

4.1 Theoretical analysis 40

4.1.1 Ideal case and assumed parameters 40

4.1.2 Results and discussion 42

4.2 A case study 44

4.2.1 General information of project 44

4.2.2 Soil profile and footing parameters 44

4.2.3 Settlement analysis 46

4.2.4 Economic analysis 49

4.2.5 Load-settlement curve from calculation and measurement 50

CHAPTER 5 - CONCLUSIONS 61

5.1 Conclusion 61

5.2 Limitation and suggestion 61

REFERENCES 63

ABSTRACT

Cement deep mixing methods (CDM) are seen to be used widely for improving ground, especially for infrastructure project such as embankment, dam, quay, etc The principle of deep mixing method is mixing admixture with in-situ soil to create constant diameter mixed soil columns and therefore the soft ground is improved consequently It can be seen that, the load of these construction mentioned above is considered as large load area which mentioned in most CDM books and design manuals Whereby, the used of one-dimensional settlement (1D) is applied

In recent years, the application of CDM for civil construction such as buildings, parking lots which use pad foundations has increased quickly It requires a research

on estimating settlement of improved ground overlain by limited load area which cannot be seen widely

Indeed, for limited applied load area such as spread footing, under 3D condition, load distributed significantly at upper layers and reduces along the depth of ground

so that the conventional CDM showed its limitations when the constant diameter mixed soil columns improve soil equally In other words, both soft and stiff layers are improved equally instead of focusing on soft layers (which normally are upper layers) Consequently, the settlement could be increased by applying conventional CDM or soil cement column (SCC) for spread footing

To overcome this circumscription, an optimal shaped of mixed soil column called head enlarged soil cement column (HCC) is studied for answering two questions:

- What is the optimal shape of mixed soil columns that performs the minimum

settlement of spread footing resting on improved ground? How to determine it?

- What percentage of material can be saved by applying that optimal shape of mixed soil columns?

Both theoretical and case studies were considered The results showed that, by applying HCC, settlement of spread footing could be reduced 10%, and material can

be saved up to 12%

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 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

I would also like to acknowledge the staff of Vietnam Japan University, especially

Mr Nguyen Ngoc Dung and Mr Bui Hoang Tan for their help and support

Special thanks to my best undergraduate friend, Nguyen Trung Thanh, a geotechnical researcher at University of Wollongong His explanations in geotechnical engineering helped me a lot in this study His successful way in research encouraged me more than anything else

Thanks are due to my family, especially to my beloved wife, Thuy Le for her deep understanding and encouraging me to take part in this master’s course from the beginning to the end

LIST OF ABBREVIATIONS

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

Eu undrained elastic modulus of soil (kPa)

Ecomp elastic modulus of improved ground (kPa)

su undrained shear strength of soil (kPa)

 ratio of length of cap and the total length of HCC

 ratio of diameter of cap of HCC and diameter of tail of HCC

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

z vertical stress increment (kPa)

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

 poisson ratio of soil in drained condition

u poisson ratio of soil in undrained condition

LIST OF TABLES

Table 2.1 Relative importance of immediate, consolidation, and secondary

compression for different soil types (Holtz, 1991) 15

Table 2.2 Method for estimating equivalent elastic modulus 24

Table 2.3 Theoretical values of Binc at fully saturation 29

Table 4.1 Info of footing categories and parameters 45

Table 4.2 Unconfined compression test results 56

LIST OF FIGURES

Figure 2.1 The effectiveness of using CDM for clayey soil 6

Figure 2.2 The effectiveness of using CDM for sandy soil 6

Figure 2.3 The application of CDM for on land construction 6

Figure 2.4 The application of CDM for on land construction 7

Figure 2.5 Type of column installation 7

Figure 2.6 Classification of deep mixing method 8

Figure 2.7 Mixing shaft 8

Figure 2.8 Typical equipment of on-land CDM construction 9

Figure 2.9 Equipment of CDM method 9

Figure 2.10 Procedure construction of CDM 10

Figure 2.11 Type of ground improvement 11

Figure 2.12 The T-shaped soil cement column overlain by embankment 12

Figure 2.13 Displacement of soil under TDM and SCC 13

Figure 2.14 PF method 13

Figure 2.15 Plain strain condition 16

Figure 2.16 Intensity of pressure based on Boussinesq approach 19

Figure 2.17 Pressure at point of Depth z bellow the center of the circular area acted on by pressure qo 20

Figure 2.18 Flexible rectangular loaded area 21

Figure 2.19 Shallow foundation under unit load 22

Figure 2.20 Variation of IG and  23

Figure 2.21 Variation of strain influence factor with depth and L/B 26

Figure 2.22 The field e-log’ curves 28

Figure 2.23 Settlement calculation from e- curve 28

Figure 2.24 Stress increment of a soil element at the center below circular load 29

Figure 2.25 Settlement ratio for circular and continuous foundation 30

Figure 2.26 Stress distribution of soil and columns under rigid foundation 31

Figure 2.27 Comparison of predict and measured settlement values 34

Figure 3.1 Shape of SCC and HCC 36

Figure 3.2 Initial and secant elastic modulus 39

Figure 4.1 Square footing and HCC parameters 40

Figure 4.2 Idealized soil profile 41

Figure 4.3 Settlement of HCC column 42

Figure 4.4 Volume reduction of HCC 43

Figure 4.5 Plan view of the JINCHEON factory and views of a typical footing 44

Figure 4.6 Soil profile of JINCHEON project 46

Figure 4.7 Comparison of settlement induced by HCC and SCC 48

Figure 4.8 Settlement by 3D elastic method (up to z = 10.4 m) 48

Figure 4.9 Variation of Scorr,HCC,min/Scorr,SCC 48

Figure 4.10 Variation of volume reduction 49

Figure 4.11 Plan view of SAMSE factory project 50

Figure 4.12 Soil profile of SAMSE factory project 51

Figure 4.13 Settlement and volume reduction analysis of SAMSE project 52

Figure 4.14 Static loading test on instrumented PF group 52

Figure 4.15 Test installation 53

Figure 4.16 Strain gauge installation 54

Figure 4.17 PVC sampling 55

Figure 4.18 Attached sampler 55

Figure 4.19 A typical unconfined compression test result 56

Figure 4.20 The estimation of secant elastic modulus at 50 percent (E50) 58

Figure 4.21 Strain influence from elastic theory and empirical study 59

Figure 4.22 Load-settlement curves estimated from measurement, linear and nonlinear analytical calculation 60

CHAPTER 1

INTRODUCTION

1.1 General introduction of deep mixing method

Thousands of years ago, ancient people started to implement marine constructions such as levee, dam etc In order to construct them, our ancestors have invented simple methods of ground improvement For constructed a levee, riding elephants for ground compaction was a very creative method

Nowadays, there are many methods for improving ground such as compaction method, drainage method, pre-compression and vertical drains, vibration method, deep mixing method, and other miscellaneous method One of effective methods are used widely is deep mixing method

Deep mixing method (DMM) or cement deep mixing (CDM) is the method of treating soft soil by mixing in-situ soil with an admixture Soil cement columns (SCC) are created for increasing the stiffness and control the stability of soft ground

as well as reduce the settlement of upper structure

Deep mixing method has developed since the 1970s (Kitazume & Terashi, 2013) and became one of the widely used ground improvement In general, sub-soils at different places have unique behavior under same loading condition so that finding

a solution which satisfies both technical and financial requirements is always an interesting question for geotechnical engineers

The application of deep mixing method is wide and various which can be seen for both on-land and marine construction Compared to other ground improvement techniques, deep mixing has advantages such as the large strength increase within short time, little adverse impact on environment and high applicability to soils if binder type and amount are properly selected The application covers on-land and in-water constructions ranging from strengthening the foundation ground of

buildings, embankment supports, earth retaining structures, retrofit and renovation

of urban infrastructures, liquefaction hazards mitigation, man-made island constructions and seepage control Due to the versatility, the total volume of stabilized soil by the mechanical deep mixing method from 1975 to 2010 reached 72.3 million m3 for the wet method and 32.1 million m3 for the dry method of deep mixing in the Japanese market (Kitazume & Terashi, 2013)

Besides the advantages, the conventional deep mixing method has limitations The constant diameter of soil cement column showed the ineffectiveness when improving soft soil equally along the depth of ground instead of focusing on weaker layers

1.2 Necessity of research

As mentioned above, the conventional deep mixing method has advantages but also exist limitations Due to the increase of stiffness of soil from upper layers to the deeper layers, the conventional method for improving ground seems to be not effective as the constant diameter of SCC improves the ground equally from the top

to the bottom It could be said in a different way that the shape of SCC must be accessed to utilize the material

A new shape of mixed soil column proposed by Yaolin, et al (2012) has improved the limitations of conventional deep mixing method Some researches on T-shaped soil cement column (Yi, Liu, & Puppala, 2018) showed remarkable results in settlement and lateral movement reduction compared with conventional method

Although a series researches on T-shaped soil cement column have been proposed,

it has not proposed the optimal shape of this kind of soil column

This research focused on answering the question: “what is the optimal shape of mixed soil column and how to determine it?”

Base on knowledge about conventional deep mixing method as well as T-shaped soil cement column, this research aimed to minimize the settlement of pad foundation resting on treated ground by figuring out the optimal shape of soil

column (the minimum volume of material) With the same ideological thinking, this research also interpreted the following question: “With a given requirement of settlement, what is the shape of column that cost the less of material?”

Most of case studies of deep mixing method using soil cement column are seen to

be applied for improving ground overlain by infinity loaded area such as embankment Hence, the settlement can be evaluated under one-dimensional condition However, in practice, SCC is also applied to civil constructions for improving ground under shallow footing The behavior of treated ground under spread footing (i.e limited loaded area) is totally different with that of subsoil under infinity loaded area This research aims to determine the settlement of improved ground using HCC under shallow footing as well as the behavior of treated soil

Hence, depending on sub-soil characteristics, the depth of treatment, type of ground improvement (i.e fixed type or floating type) the settlement of improved ground will be evaluated as elastic settlement or/and consolidation settlement

1.3 Objective and scope

1.3.1 Objectives:

This research has two main objectives, which are as follows,

- To determine the optimal shape of head soil cement columns and the minimum settlement induced by them as well as the settlement reduction by using HCC compared to that of SCC (with the condition that the ground improved by HCC and SCC has the same characteristics, treated by same number of soil columns and volume of material for each column)

- To determine the percentage of amount of material can be saved by applying HCC compared to SCC

To tackle these two objectives, first, theoretical study was carried out for figuring out the settlement of both HCC and SCC By comparing the settlement results, the effectiveness of HCC was displayed by its settlement reduction The results showed

HCC is suitable for reducing settlement by applying 3D settlement calculation while 1D settlement is seen to be applied widely for estimating the settlement of embankment In other words, HCC exhibits its effectiveness in improving soft ground under limited loading area (i.e spread footing)

Then, a case study will be used to demonstrate the effectiveness and advantages of HCC method comprehensively

Figure 1.1 Plan view and cross section of mixed soil columns

1.3.2 Scope of research:

Most of design manual, guide books or standards and codes have instructed ground improvement as well as its theory of calculations for the ground under embankment Hence, one-dimensional (1D) settlement is considered and used for settlement estimation

This research focuses on improving ground under spread footing which implies that three-dimensional (3D) settlement must be considered for estimating settlement The principle, the distinguish between 1D and 3D settlement as well as the reason for applying 3D settlement for estimating settlement of shallow foundation will be discussed

d d d

CHAPTER 2

LITERATURE REVIEW

2.1 Overview of cement deep mixing method

As mentioned in the objective section of this report, this study focuses strongly on reducing the settlement of soft ground Hence, a critical overview of soil cement column, as well as the behavior of composite ground, will be considered first then the theory of settlement evaluation will be assessed for choosing the appropriated methods for the calculation of this study

It has a lot of research on deep mixing method (or cement deep mixed soil column)

It could be named some famous scholars in this field such as Kitazume and Terashi (2013); Bergado (1996); Rujikiatkamjorn, Indraratna, and Chu (2005); Chai and Carter (2011); Han (2015); Bruce, M.E.C., Berg, R.R., Collin, J.G., Filz, G.M., Terashi, M., and Yang (2013); Bredenberg, Broms, and Holm (1999); Kirsch and Bell (2012); etc

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 Depends on the characteristics of soil, the purposes and effectiveness of using CDM are quite different as shown in Figure 2.1 and Figure 2.2

Mixed soil columns created by deep mixing method has the elastic modulus at 50

percent (E50) increase with the strength of column (qu) and is 75 to 1,000 × qu

(Kitazume & Terashi, 2013) depends on the characteristic of clay soil (500,000 to 2,000,000 kPa), but smaller than that of concrete pile (30,000,000 kPa), and hence,

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

Figure 2.1 The effectiveness of using CDM for clayey soil

Figure 2.2 The effectiveness of using CDM for sandy soil

Figure 2.3 The application of CDM for on-land construction

Figure 2.4 The application of CDM for in-water construction

The improved ground or composite ground includes soil and mixed soil column so that the arrangement of mixed soil columns affects significantly to the strength, the stiffness or the equivalent elastic modulus of composite ground Depend on the purpose and properties of constructions, characteristics of improved types are chosen Several types of column installation patterns and their applications classified by Kitazume & Terashi (2013) are shown in Figure 2.5

Figure 2.5 Type of column installation

2.1.3 Classification

The cement deep mixing method can be classified in to three types (Kitazume & Terashi, 2013) as follows

Figure 2.6 Classification of deep mixing method 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 bottom end

of each mixing shaft Wet method or dry method are used depend on the characteristic of soil (i.e moisture content) Slurry admixture is used for wet method while powdery material is chosen for dry method

- High pressure injection mixing (wet method) which material is injected from the outlet of mixing shaft to the soil under high pressure in both penetration and withdraw-process The admixture could be only binder, binder and air or the mixing

of binder, air and water

- The combination of mechanical mixing and high pressure injection mixing

Figure 2.7 Mixing shaft

Deep mixing method

Mechanical mixing

High pressure injection (wet method)

Combination of mechanical and high pressure injection

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 2.8 Typical equipment of on-land CDM construction

a) Drilling machine

b) Binder plant

c) Machine has two mixing shafts Figure 2.9 Equipment of CDM method

Then all equipment are 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 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 2.11 Type of ground improvement (Kitazume & Terashi, 2013)

2.2 Innovation 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

Figure 2.12 The T-shaped soil cement column overlain by embankment (Song-Yu

at el, 2012)

A previous research of 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 geosynthestic 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

Laboratory tests and in-situ test was carried out for verifying the application of TDM column Figure 2.13 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 high-way construction The diameter of most column

caps is 0.9~1.2 m, which is approximately 1.3~2.4 that of deep-depth column The column length (L) is 11~25 m (Yaolin et al, 2012)

Figure 2.13 Displacement of soil under TDM and SCC (Yaolin et al., 2012)

2.2.2 The PF method

The PF method has introduced by EXT company since 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

Figure 2.14 PF method

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 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

2.3 Theory of settlement evaluation

2.3.1 Brief overview of settlement

2.3.1.1 The compressibility of soil

The settlement evaluation is a process of complicated calculation, depended on types and characteristics of soil as well as loading condition This research cannot cover all the theory of the soil settlement, but the author try to understand and present the very basic principle of compressibility of soil

Basically, the compressibility of soil caused by (1) the deformation of soil elements, (2) the rearrangement of soil elements, and (3) the reduction volume of water in the ground The total settlement of foundation is determined as follows:

Ss is secondary compression settlement

For differential types of soil, the values of the three board categories of settlement

above (i.e Se, Sc, Ss) are different Indeed, for the compressive clays, the consolidation can be several times greater than elastic settlement Especially, for saturated clay soil, elastic settlement is approximately to be nil In contrast, for the

permeable material such as sandy soil, because water can escape immediately (within a time period of about 7 days) (Bowles, 1977a) as the load is applied, consolidation settlement can be omitted and the settlement is mostly caused by elastic settlement This phenomenon can be explained as follow,

As we knew, the consolidation settlement is the process of volume reduction in ground caused by escaping of water in void and the rearrangement of soil elements simultaneously For the fine material such as clays, the soil particle size of clay is too small (i.e smaller than 0.002 mm) (Das & Sobhan, 2013) which implies that the void size is small, too Hence, when the load is applied, water cannot flow easily through voids It needs time for the mitigation of water in void, or in other words, the volume can only be reduced gradually Normally, the time of consolidation settlement for most construction takes 3 to 10 years (Bowles, 1977b) Especially, this process could be taken place for a very long time such as the Leaning Tower of Pisa in Italy has spent over 700 years settling For the saturated clay which has full

of water filling all void volume, load distributes significantly on water Because water is uncompressible material, the volume of clay soil cannot deform immediately which cause the elastic settlement is insignificant But for sandy soil which has particle size larger than 0.06 mm (Das & Sobhan, 2013), water can be expelled from the voids immediately right after loading which lead soil particles bear the surcharge significantly Consequently, the consolidation settlement is omitted and the elastic settlement is the result of deformation of soil particles

Table 2.1 Relative importance of immediate, consolidation, and secondary

compression for different soil types (Holtz, 1991)

settlement

Consolidation settlement

Secondary settlement Sands

Clays

Organic soils

Yes Possibly Possibly (Yes)

No Yes Possibly (No)

No Possibly Yes

2.3.1.2 Corrected settlement

When using Eq (2.1) for estimating the settlement of shallow foundation, corrected factors are needed to integrate These factors cover the embedment depth effect as well as the rigidity of foundation Hence, the corrected total final settlement of shallow foundation is given as follows:

TF corr E F e c

where

S TF,corr is corrected total final settlement

IE is settlement correction factor for embedment depth (Df) effect

IF is settlement correction factor for foundation rigidity

The factor of IF IE are estimated as the Eq (2.15) and Eq (2.16), respectively

2.3.1 Brief overview of 1D, 2D and 3D settlement evaluation

In order to determine the settlement of foundation, the application of exact calculation model is very important Different structures with different loaded area impose different stresses in soil That understanding the distribution of applied surface stressed is so necessary for preventing failure of structures Naturally, for one-dimensional settlement, the cubic of soil (ground) deform as a foregone direction which normally is vertical This model is often seen in most of settlement evaluation instructed in CDM-books and manuals for determining the settlement of embankment The embankment is the strip structure (continuous foundation) that is very long in one dimension and has a uniform cross section In this case, the strain along the long dimension could be assumed negligible (plain strain condition) The use of 2D settlement could be applied to determine the settlement

Figure 2.15 Plain strain condition (Helwany, 2007)

C

For the elements near the axisymmetric plane (i.e ABC plane or elements on the

edge BC in plain strain xy), the deformation can be assumed as vertical direction (which can be implied that there is only vertical displacement as axis y) which

implies the use of 1D settlement can be applied as seen in most book manual

For limited surcharge load area case, the behavior of elements affected by the Poisson effect, the phenomenon in which material tends to expand in directions perpendicular

to the direction of compression Thus, in order to evaluating the settlement of spread footing or limited surcharge load area, the 3D model is needed to apply

2.3.2 The use of 1D, 2D and 3D condition for evaluating settlement

As mentioned above, depends on categories of soil, the appropriate model (i.e either elastic or consolidation model) is chosen for evaluating settlement The use of 2D is omitted because it is a specific case of 3D

2.3.2.1 Elastic settlement

Theory of elasticity is used to estimate the settlement of foundation Although the Elasticity assumes soil as an isotropic and homogenous material, its application is reliable at the area of influence depth (from 0 to 4B or 5B) In general, the settlement of foundation can be estimated as following equation (Bowles, 1977a):

v

E M

The equation (2.3) could be expressed as

b) 3D elastic settlement – elastic settlement of footing:

i) Stress increase in soil due to point load

Base on the Theory of Elasticity, Boussinesq (1885) proposed an equation for estimating the stress increment of a soil element at depth z, induced by a point load

on the surface of a semi-infinite, homogenous, isotropic, weightless, elastic space shown in Figure 2.16, which is given as follows:

where Q is the point load (the total load applied), z is stress at Depth z, z is depth

where z is considered, r is radial distance to the point of application

Figure 2.16 Intensity of pressure based on Boussinesq approach

The deformation of a soil element at depth z in the stratum bearing the “Point” load

Q is estimated as given equations:

where xx , yy , zz are the strain of soil element at depth z

ii) The uniformly loaded flexible circular area:

In general, the function of foundation is to spread point load to “uniform” load so that the very high stresses at the contact point (z=0) are avoided One, considering

the contact pressure qo to be applied to a loaded, the load Q could be presented as follows

x

z



Figure 2.17 Pressure at point of Depth z bellow the center of the circular area acted

on by pressure qo

But dA=2rdr, by substituting to the Eq (2.7) and Eq (2.8), we have

0 0

3 1

qo is uniform pressure at ground surface as shown in Figure 2.17

B is diameter of circular loaded area as shown in Figure 2.17

Ic = f (, H/B) is corrected factor

z

r

dq Z

Q

R dr

dQ=q dA

0

dA=2  dr

B

iii) The uniformly loaded rectangular area:

Figure 2.18 Flexible rectangular loaded area The settlement of corner point of a rectangular loaded area on surface area shown in Figure 2.18 can be estimated as follows:

iv) Settlement of shallow foundation

Figure 2.19 Shallow foundation under unit load (Das, 2015)

Mayne & Poulos (1999) proposed a method for estimating the elastic settlement of circular shallow foundation (Figure 2.19) as following equation:

qnet is net applied pressure

Be is equivalent diameter of foundation

Eo is equivalent elastic modulus of soil beneath foundation

IG is the influence factor for the variation of Es with depth IG could be determined through the variation of it with  = Eo/kBe as shown in Figure 2.20

Figure 2.20 Variation of IG and (Mayne & Poulos, 1999)

IF is foundation rigidity correction factor, which can be estimated as

E

e f

I

B D

Eq (2.14) can be used for the rectangular foundation by determining the equivalent

diameter Be of a rectangular foundation (i.e Be = (4BL/)0.5) where B and L are the width and length of the foundation, respectively)

The elastic modulus Eo in Eq (2.14) is the equivalent deformation modulus of considered thick ground for evaluating the settlement Naturally, the ground

including several layers which have different values of Elastic modulus causes challenges for evaluating its deformation Therefore, a widely common method is converting the Elastic moduli values of layers to an equivalent value

Generally, there are three methods for estimating this equivalent value They are (1) the Arithmetric average, (2) Weighted average based on thickness and (3) Weighted average based settlement influence factor The first is the worst and the third is the best method The detail of these three method are expressed in Table 2.2

Table 2.2 Method for estimating equivalent elastic modulus

A Fraser, 1976)

avg

1/

1

n

si i i

i i

I E

where Es,avg is average (or equivalent) modulus, n is the total number sub-layers in

influence zone (normally at the depth of 4B), Es,i is the elastic modulus of layer i,

hi is the thickness of layer i, Izi is the change of Iz value from the top to the

bottom of layer i (Iz can be estimated in Eq (2.13))

The use of equivalent modulus (Eo) which implies that the load-settlement curve is linear In reality, because the considered ground including soil layers with different values of elastic modulus, the load-settlement is definitely nonlinear Fahey and Carter (1993) proposed a reliable method called The Modified Hyperbola which fit the real behavior of equivalent elastic modulus of soil due to the adjustment of stress increment at the considered depth The expression is of the form (Mayne & Poulos, 1999):

max

max 1

Emax = 2Gmax (1+) (2.18)

Gmax = TVs2,T is total mass density, Vs is shear wave velocity, Gmax is shear

modulus, and E is elastic modulus

q is current net applied pressure (is also the stress increment at considered depth for

evaluating the elastic modulus of a thickness of ground at identified depth)

qmax is ultimate applied unit load of ground (or ultimate stress of a thickness ground

C   q q q  is correction factor for the depth of foundation embedment

C2 = 1+0.2 log (time in years/0.1) is correction factor to account for creep in soil

qis stress at the level of the foundation

q = Df is effective stress at the base of foundation

Is is strain influence factor which can be estimated as in Figure 2.21 The values of

Is at special values of Depth z are given as:

Figure 2.21 Variation of strain influence factor with depth and L/B proposed by

Schmertmann (1978), instructed by Das (2015)

2.3.2.2 Consolidation settlement

As mentioned above, the settlement of fine-grained, clay soils depend on time of the dissipation of water pore pressure The consolidation settlement of clay and fine to medium sand can be estimated as the equation (Das, 2015):

where

z = e/(1+eo) is vertical strain

e = f (o, c, ’) is change of void ratio

a) One dimensional (1D) consolidation settlement

The 1D consolidation settlement occurs when load is applied to confined clay soils For the normally consolidated clay, the consolidation settlement can be estimated as follows

where e = Cc [log ('0+') – log'0]

Equating this to Eq (2.21), we obtain

where Cc is compression index, Cs is swelling index, H is thickness of the clay layer,

eo is initial void ratio, ’o is average effective pressure on the clay layer before the construction of foundation, ’ is average increase in effective pressure on the clay layer overlain by foundation, c’ is pre-consolidation pressure

The consolidation settlement can also be estimated by pick e off the given plot of

the field e-’ curves from the laboratory test data as well as the field e-log’ curves

as shown in Figure 2.22

The applied load causes the increase of stress of soil stratum (clay stratum) and

hence, the void ratio decrease from eo to e as shown in Figure 2.23 The relationship

of them can be expressed as (Murthy, 2001):