A comparative study on the horizontal coefficient of consolidation (Cr) obtained from lab and field tests

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VIETNAM NATIONAL UNIVESITY, HANOI

VIETNAM JAPAN UNIVERSITY

Hanoi, 2020

TRAN QUYNH GIAO

A COMPARATIVE STUDY ON

THE HORIZONTAL

COEFFICIENT OF

CONSOLIDATION (C

r

) OBTAINED

FROM LAB TESTS

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VIETNAM NATIONAL UNIVESITY, HANOI

VIETNAM JAPAN UNIVERSITY

Hanoi, 2020

TRAN QUYNH GIAO

A COMPARATIVE STUDY ON

THE HORIZONTAL

COEFFICIENT OF

CONSOLIDATION (C

r

) OBTAINED

FROM LAB TESTS

MASTER’S THESIS

MAJOR: INFRASTRUCTURE ENGINEERING

CODE: 8900201.04 QTD

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ABSTRACT

When a soft ground is improved by PVDs, consolidation takes place under the
condition of drainage in both horizontal and vertical directions. Naturally,
horizontal coefficient of consolidation (cr) is larger than the vertical coefficient of

consolidation (cv) by a factor of 3 to 5. The cv value is commonly interpreted from

consolidation test using incremental loading method [1]. However, up to date, there
have not been any similar standards for the consolidation test with horizontal
drainage (using incremental loading method).

The key goals of the research are: (1) determine the most reliable methods among
the proposed methods for determining the horizontal coefficient of consolidation
(cr) in the literature; (2) determine correlations between cr values obtained from

central drain (CD) test and peripheral drain (PD) test; (3) determine correlations
between vertical coefficients of consolidation (cv) and radial cr for a number of test

sites in Vietnam.

A desk study is carried out to secure the following: (1) a literature review on
equipment used for the test and existing methods used to evaluate the cr value; (2)

the thesis using data collected from the following sources literature review and test
site in Vietnam.

Overall, The most reliable methods for determining the horizontal coefficient of
consolidation (cr) is non-graphical method and the root t can be used to determine 
the radial (horizontal) coefficient of consolidation (cr).

cr,PD is less than the cr,CD by a factor of 0.32 to 0.64 from intact samples and 0.33 to

0.58 from remolded samples.

cr PD is larger than the cv by a factor of 0.90 to 2.33, cr CD is larger than the cv by a

factor of 2.14 to 5.12 from intact samples. cr PD is less than the cv by a factor of 0.35

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ACKNOWLEDGEMENTS

I would like to express my sincere appreciation for the lecturers of Master of
Infrastructure Engineering Program for their help during my undergraduate at
Vietnam Japan University (VJU).

My thesis supervisor Dr. Nguyen Tine Dung for his enthusiasm, patience, advice
and continuous source of ideas for me. Dr. Dung is always ready to answer my
questions. His support in professional matters is invaluable.

I would like to acknowledge the sincere inspiration from Prof. Nguyen Dinh Duc
and Prof. Hironori Kato. Their lectures covered not only specialist knowledge but
also the responsibility and mission of a new generation of Vietnam. I am grateful to

Dr. Phan Le Binh for his support in the last two years since I have studied at
Vietnam Japan University. Thanks to him, I have learned the professional courtesy
of Japanese people as well as Japanese culture.

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iii

TABLE OF CONTENTS

Page

ABSTRACT ... i

ACKNOWLEDGEMENTS ... ii

TABLE OF CONTENTS ... iii

LIST OF TABLES ... vi

LIST OF FIGURES ... vi

LIST OF ABBREVIATIONS ... viii

CHAPTER 1. INTRODUCTION ... 1

1.1 Problem statement ... 1

1.2 Necessity of study ... 3

1.3 Objectives ... 4

1.4 Scope of study ... 4

1.5 Structure of thesis ... 4

CHAPTER 2. LITERATURE REVIEW ... 6

2.1 Introduction ... 6

2.1.1 Consolidation Theory with Horizontal Drainage ... 8

2.1.2 Solution of the governing equation (2.2) for a central drain (CD) under
equal strain loading (ESL) condition ... 8

2.1.3 Solution of the governing equation (2.2) for a peripheral drain (PD)
under free strain loading (FSL) condition ... 9

2.1.4 Solution of the governing equation (2.2) for a peripheral drain (PD)
under equal strain loading (ESL) condition ... 9

2.2 Existing methods for determining cr from consolidation test with a peripheral
drain using incremental loading ... 10

2.2.1 Root t method [6] ... 10

2.2.2 Inflection point method [9] ... 11

2.2.3 Full – match method [10] ... 13

2.3 Existing methods for determining cr from consolidation test with a central
drain using incremental loading method ... 15

2.3.1 Root t method [11] ... 15

2.3.2 Matching log (de2/t) and Ur method [12] ... 16

2.3.3 Inflection point method [13] ... 17

2.3.4 Non-graphical method [14] ... 18

2.3.5 Log - log method [15] ... 19

2.3.6 Steepest tangent fitting method [16] ... 20

2.3.7 Log t method [17]... 22

2.3.8 Full – match method [10] ... 24

2.4 Summary of methods for determining cr ... 25

2.5 Linear regression analysis ... 25

2.6 Log normal distribution method ... 26

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3.1 Introduction ... 27

3.2 Data collection ... 28

3.3 Improvement for inflection point methods ... 28

3.3.1 Theoretical development ... 28

3.3.2 The procedure for this method ... 29

3.4 Analysis of Time – Compression curve ... 29

3.5 Procedure to select the best methods ... 30

3.6 Procedure to determine ratios of cr PD /cr CD or cr /cv ... 31

CHAPTER 4. TEST RESULTS & DISCUSSIONS ... 33

4.1 Introduction ... 33

4.2 Summary of database ... 33

4.2.1 Data collected from the literature ... 33

4.2.2 Data collected from test sites in Vietnam ... 34

4.2.3 Summary of test data ... 37

4.3 Evaluation and selection the best methods on intact samples ... 38

4.3.1 Graph results on intact samples ... 38

4.3.2 Summary of results on intact samples... 40

4.3.3 Summary of rank method on intact samples ... 47

4.4 Evaluation and selection the best methods on literature data ... 49

4.4.1 Graph results on literature data ... 49

4.4.2 Summary of results on literature data ... 51

4.4.3 Summary of rank method on literature data... 52

4.5 Evaluation and selection the best methods on remolded samples ... 54

4.5.1 Graph results on remolded samples ... 54

4.5.2 Summary of results on remolded samples ... 56

4.5.3 Summary of rank method on remolded samples ... 62

4.6 Comparison of cr CD and cr PD on intact samples ... 64

4.6.1 Graph results on intact samples ... 64

4.6.2 Summary of results on intact samples... 64

4.7 Comparison of cr CD and cr PD on remolded samples ... 66

4.7.1 Graph results on remolded samples ... 66

4.7.2 Summary of results from remolded samples... 66

4.8 Comparison of cv and cr PD on intact samples... 68

4.8.1 Graph results on intact samples ... 68

4.8.2 Summary of results on intact samples... 68

4.9 Comparison of cv and cr CD on intact samples ... 70

4.9.1 Graph results on intact samples ... 70

4.9.2 Summary of results on intact samples... 70

4.10 Comparison of cv and cr PD on remolded samples ... 72

4.10.1 Graph of results on remolded samples ... 72

4.10.2 Summary of results on remolded samples ... 72

4.11 Comparison of cv and cr CD on remolded samples ... 74

4.11.1 Graph results on remolded samples ... 74

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LIST OF TABLES

Page

Table 2.1. Boundary condition ... 9

Table 2.2. Existing methods for determining cr from radial consolidation ... 25

Table 4.1. Summary of data from literature for the PD – ESL condition ... 33

Table 4.2. Summary of data from literature for the CD – ESL condition ... 34

Table 4.3. Summary of tests done on intact samples ... 37

Table 4.4. Summary of tests done on remolded samples ... 37

Table 4.5. Summary of results from PD tests on intact samples ... 40

Table 4.6. Summary of results from CD tests on intact samples ... 42

Table 4.7. Rank of each criterion with each pressure from PD tests on intact
samples... 44

Table 4.8. Rank of each criterion with each pressure for CD case on intact samples
... 45

Table 4.9. Summary of rank for each method from PD tests on intact samples ... 47

Table 4.10. Summary of rank on each meth1od from CD tests on intact samples ... 48

Table 4.11. Summary of results from PD tests on literature for 8 methods. ... 51

Table 4.12. Summary of results from CD tests on literature for 8 methods. ... 52

Table 4.13. Summary of rank on each method from PD tests on literature ... 52

Table 4.14. Summary of rank on each method from CD tests on literature ... 53

Table 4.15. Summary results from PD tests on remolded samples for 8 methods ... 56

Table 4.16. Summary of results from CD tests on remolded samples for 8 methods
... 58

Table 4.17. Rank of each criterion with each pressure from PD tests on remolded
samples for 8 methods ... 59

Table 4.18. Rank of each criterion with each pressure from CD tests on remolded
samples for 8 methods ... 61

Table 4.19. Summary of rank each method from PD tests on remolded samples .... 62

Table 4.20. Summary of rank each method from CD tests on remolded samples .... 63

Table 4.21. Summary of results from PD and CD tests on intact samples ... 65

Table 4.22. Summary of boundary for PD and CD case on intact samples ... 65

Table 4.23. Summary of correlations for CD and PD case on remolded samples .... 67

Table 4.24. Summary of boundary for CD and PD case on remolded samples ... 67

Table 4.25. Summary of correlations for PD case on intact samples ... 69

Table 4.26. Summary of boundary for PD case on intact samples ... 69

Table 4.27. Summary of correlation for CD case on intact samples ... 71

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vii

Table 4.29. Summary of correlations for PD case on remolded samples ... 73

Table 4.30. Summary of boundary for PD case on remolded samples ... 73

Table 4.31. Summary of correlations for CD method on remolded samples ... 75

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viii

LIST OF FIGURES

Page

Figure 1.1. Map of distribution of major soil types in Indochinese ... 1

Figure 1.2. Soil phase diagram [3] ... 2

Figure 1.3. An Illustration of soft ground improved by PVDs ... 2

Figure 2.1. Research direction of the thesis [5] ... 7

Figure 2.2. Illustration of flow conditions for equal-strain case [6] ... 7

Figure 2.3. Time - deformation plot during consolidation for a given load increment
[3] ... 8

Figure 2.4. Consolidation curve relating square - Root time factor to for drainage

radially outwards to periphery with equal strain loading [6]. ... 11

Figure 2.5. Log (Ur/Tr) - log Ur relationship [10] ... 13

Figure 2.6. Determine the value of intersection point in full – match method ... 14

Figure 2.7. Theoretical log(de2/t) versus Ur curves [12] ... 16

Figure 2.8. (a) Theretical Ur - log Tr curve and (b) d(Ur)/dlog Tr plot [13] ... 17

Figure 2.9. Log( - 0) versus log t plot [15] ... 20

Figure 2.10. Steepest tangent fitting method for determination of cr ... 21

Figure 3.1. Flow chart of the study ...
Figure 3.2. Experimental data [9] ... 28

Figure 3.3. Flowchart of identifying the best methods ... 30

Figure 3.4. Flowchart of identifying the best methods ... 31

Figure 4.1. Locations of test sites in Viet Nam (VSIP site, DVIZ site, Kim Chung
site) ... 34

Figure 4.2. Test location at Kim Chung site ... 35

Figure 4.3. Test location at VSIP site ... 35

Figure 4.4. Test location at DVIZ site ... 35

Figure 4.5. Soil profile at DVIZ ... 36

Figure 4.6. Soil profile at VSIP ... 36

Figure 4.7. Soil profile at KC ... 36

Figure 4.8. Results from PD tests on intact samples (at 800 kPa) for 8 methods ... 38

Figure 4.9. Results from CD tests on intact samples (at 800 kPa) for 8 methods .... 39

Figure 4.10. Results from PD tests on intact samples (at 800 kPa) for 8 methods ... 49

Figure 4.11. Results from CD tests on literature for 8 methods ... 50

Figure 4.12. Results from PD tests on remolded samples (at 800 kPa) for 8 methods
... 54

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Figure 4.15. Comparison of cr CD and cr PD obtained from non-graphical method at all

data ... 64
Figure 4.16. Comparison of c r,CD and cr,PD obtained from root t method at all data 66

Figure 4.17. Comparison of cr CD and cr PD obtained from non-graphical method at

all data ... 66
Figure 4.18. Comparison of cv and cr,PD obtained from root t method at all data ... 68

Figure 4.19. Comparison of cv and cr,PD obtained from non-graphical method at all

data ... 68
Figure 4.20. Comparison of cv and cr CD, obtained from root t method at all data .... 70

Figure 4.21. Comparison of cv and cr CD obtained from non-graphical method at all

data ... 70
Figure 4.22. Comparison of cv and cr,PD obtained from root t method at all data .... 72

Figure 4.23. Comparison of cv and cr,PD obtained from non-graphical method at all

data ... 72
Figure 4.24. Comparison of cv and cr,CD obtained from root t method at all data .... 74

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LIST OF ABBREVIATIONS

cr Horizontal coefficient of consolidation

cr,CD Horizontal coefficient of consolidation under for a central

drain (CD) condition

cr,PD

Horizontal coefficient of consolidation under for a
peripheral drain (PD) condition

cr,Root CD Horizontal coefficient of consolidation form root t method

under for a central drain (CD) condition

cr,NG PD

Horizontal coefficient of consolidation form non-graphical

method under for a peripheral drain (PD) condition

cv Vertical coefficient of consolidation

de Diameter of the soil sample

dw Drain diameter

f Source/sink term; function; cyclic load natural frequency

n Ratio of influence radius to drain radius

r Radial coordinate

t Time

t50 Time required to reach 50% consolidation

t90 Time required to reach 90% consolidation

t66 Time required to reach 66% consolidation

tinf Time at d(Ur) /dlog Tr the maximum.

Tr Time factor for horizontal consolidation

T90 Time factor for horizontal consolidation to reach 90% consolidation

T66 Time factor for horizontal consolidation to reach 66% consolidation

Tv Time factor for vertical consolidation

U Degree of consolidation

u Pore-water pressure

Δu Change in pore pressure

0 Initial settlement

100 Finally settlement at Primary consolidation

t Settlement at time t

p Predicted settlement

m Measured settlement

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kv Permeability coefficient from vertical consolidation
mr Soil stiffness from radial consolidation

mv Soil stiffness from vertical consolidation

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CHAPTER 1. INTRODUCTION

1.1 Problem statement

Fig. 1.1 shows a typical map of distribution of major soil types in Viet Nam.
Among the soil types, the soft and young deposits distributed in major deltas in
Vietnam (Red River Delta, Mekong Delta and Saigon – Dongnai River delta) and
along the coast are very much concerned in construction of the infrastructure
system.

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In this area, civil constructions and seaports must take measures to treat the ground
before construction.

The objectives of ground treatment are:

- To increase bearing capacity of the ground
- To decrease the permeability of soil

Therefore, there are many methods used to reinforce or to increase the stiffness of
the soft soil, in which consolidating the soft soil is one of the methods. According to
soil mechanics theory, soil is formed from two or three phases (see Figure 1.2). The
voids surrounding the soil particles are filled by water, air or a combination of both.
Consolidation is the process of contraction of voids under the applied load in
association with the process of water drainage.

Figure 1.2. Soil phase diagram [3]

Among several common ground improvement methods in practice, ground
improvement by Prefabricated Vertical Drain (PVD) is one of the methods most
commonly applied in practice. Fig. 1.3 shows a typical configuration of ground
improved by PVDs.

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Under the surcharge loading, drainage in the ground improved by PVDs takes place
in two directions (as show in Figure 1.3): vertical direction and horizontal (radial)
direction. The consolidation settlement of the ground therefore happens due to both
vertical and horizontal drains.

1.2 Necessity of study

consolidation (cv) by a factor of 3 to 5. In addition, in many cases, when the soft

clay layer is thick, the consolidation would happen mainly due to the horizontal
drainage. The cr value is therefore very important for the design, sometimes much

more important than the cv value.

Currently, the cv value is commonly interpreted from consolidation test using

incremental loading method [1]. This is because the method is simple and
applicable in routine laboratories around the world. However, up to date, there have
not been any similar standards for the consolidation test with horizontal drainage
(using incremental loading method). Although cr value might be determined from

some Constant Rate of Strain (CRS) tests (e.g., Chung 2019, Sridharan 1996…), the
equipment and test procedures are too complicated to apply in routine tests. Thus, cr

value is mostly obtained from empirical correlations, for example from cv value.

In the literature, there are about 10 methods suggested to determine cr value

obtained from result of the consolidation test with horizontal drainage using
incremental loading. However, it is unclear as which methods are the best. In
addition, there have been no systematic studies on cr value of soft clay in the North

of Vietnam. It is therefore very necessary to make a comparative study on the
methods to determine the cr value and the value for soft clay in the North of

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4
1.3 Objectives

The main objectives of the study are:

1. To determine the most reliable methods among the proposed methods for
determining the horizontal coefficient of consolidation (cr) in the literature;

2. To determine correlations between cr values obtained from central drain (CD)

test and peripheral drain (PD) test;

3. To determine correlations between vertical coefficients of consolidation (cv) and

radial cr for a number of test sites in Vietnam.

1.4 Scope of study

The scope of the study is limited to the following:

- Collect existing data in the literature and data from experiments of the
supervisor‟s research program.

- Perform analytical analyses to obtain the three objectives described above.
Test data on consolidation test with radial drainage (using incremental loading
method) are collected from the following sources:

- Existing data from the literature (remolded samples);

- Test site in Kim Chung – Di Trach (Hanoi) (both remolded and intact
samples).

- Test site in Dinh Vu Industrial Zone (DVIZ) (Hai Phong) test data (intact
samples).

- Test site in Vietnam Singarpore Industrial Park (VSIP) (Hai Phong) (both
remolded and intact samples).

1.5 Structure of thesis

The rest of the thesis is organized as follows.

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- Chapter 3: Describes the methodologies used to evaluate the coefficients and
correlations

- Chapter 4: Methodology provides methods for determining cr values for PD
& CD cases and provides evaluation methods to select the best methods.
- Chapter 5: Outlines, discusses the results obtained and describes the

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CHAPTER 2. LITERATURE REVIEW

2.1 Introduction

When a soil layer is subjected to a compressive stress, such as during the
construction of a structure, it will exhibit a certain amount of compression. This
compression is achieved through a number of ways, including rearrangement of the
soil solids or extrusion of the pore air and/or water. Terzaghi (1943) recommends,
“A decrease of water content of a saturated soil without replacement of the water by
air is called a process of consolidation”.

Terzaghi (1943) first suggested the one-dimensional consolidation testing
procedure. This test performed in a consolidometer (sometimes referred to as an
Odometer).

Baron [4] (1948) presented the basic theory of sand drains. In key study of sand
drains, the author has two fundamental cases.

- Free-strain case: When the surcharge applied at the ground surface is of a
flexible nature, there will be equal distribution of surface load. This will
result in an uneven settlement at the surface.

- Equal-strain case: When the surcharge applied at the ground surface is rigid,
the surface settlement will be the same all over. However, this will result in
an unequal distribution of stress.

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Figure 2.1. Research direction of the thesis [5]

A peripheral drain (PD) case A central drain (CD) case
Figure 2.2. Illustration of flow conditions for equal-strain case [6]

To obtain a coefficient of consolidaiton, a curve of time vesus deformation (Figure
2.3) obtained from consolidation test is taken into analysis. The curve has three
distinct stages described as follows [3]:

- Stage I: Initial compression, which is caused mostly by preloading.

- Stage II: Primary consolidation, during which excess pore water pressure
gradually is transferred into effective stress because of the expulsion of pore
water.

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Figure 2.3. Time - deformation plot during consolidation for a given load increment [3]

2.1.1 Consolidation Theory with Horizontal Drainage

Barron [4] (1948) developed the basic theory of consolidation. The governing
differential equation for the dissipation of excess pore water pressure in both
horizontal and vertical drainage directions under the equal strain loading (ESL)
condition is:

2 2

w w

v v

r k a

k u u u u

r r r z e t

 

       
        
 

    (2.1)

In case of only horizontal drainage direction (kv = 0), Eq. (2.1) becomes:

1
r

u u u

c

r r r t

    

 

    

  (2.2)

2.1.2 Solution of the governing equation (2.2) for a central drain (CD) under 
equal strain loading (ESL) condition

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 





 




n
F
T
u
u
U r
r
8
exp
1
1
0
(2.3)
where the Time factor (Tr) is defined as follows:

r r e

T c t d (2.4)

where de is the diameter of the soil sample, and the function F(n) is defined as 
follows:

 



2 2



 



2 2



3 1
ln
4
1
n
n

F n n

n
n

 

 
(2.5)
/
e w

n d d (2.6)

where n = spacing ratio, dw = diameter of the drain

2.1.3 Solution of the governing equation (2.2) for a peripheral drain (PD) under 
free strain loading (FSL) condition

For a PD under free strain loading (FSL) condition, Silverira [7] (1951) solved the
governing equation (Eq. 2.2) using the following boundary conditions.

Table 2.1. Boundary condition

No. Condition Result

1 t = 0, de ≥ r ≥ 0. u = uo

3 t  0, r = de/2 u = 0

4 t  0, r = 0. u(r,t)/r = 0

The solution is expressed as follows:



n r



n

n n

r B T

B
u
u
U 2
1 2
0

4
exp
1
4
1

1   







 (2.7)

2.1.4 Solution of the governing equation (2.2) for a peripheral drain (PD) under 
equal strain loading (ESL) condition

For a PD under the equal strain loading (ESL) condition, the solution of the
governing equation is expressed as follows [8].



r



r T

u
u

U 1 1 exp 32

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2.2 Existing methods for determining cr from consolidation test with a

peripheral drain using incremental loading

2.2.1 Root t method [6]

Introduction 
2.2.1.1

The method proposed based on the equation for the equal vertical strain condition
[4]. Settlement and volume – change measurements govern by the deformation of
the sample, as a whole analysis is dependent on an overall “average” behavior.
Some method of “curve fitting” is necessary for graph base on these measurements
relate to the conditions at a particular point [6].

In PD case, slope factor is 1.17 and the value of T90 is 0.288 [6].

The radial (horizontal) coefficient of consolidation is determined in this case:

0.288 e

r

d
c

t



(2.9)

The procedure for determine cr

2.2.1.2

- Step 1: Graph with  - t0.5 then finding a straight line within Ur = 20% to
Ur = 60% on the curve

- Step 2: Drawing a second line with the ratio of the length of vertical axis is
(second line / the straight line in step 1) = 1.17.

- Step 3: Find the intersection of a second line (Step 2) and consolidation
curve. This point is t90.

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Figure 2.4. Consolidation curve relating square - Root time factor to for drainage
radially outwards to periphery with equal strain loading [6].

Evaluation of the method 
2.2.1.3

Advantages

- This method is easy to practice for all engineers.

- Determination of cr in this method does not require the determination of 0

and 100.

- The definition is a straight line within Ur = 20% to Ur = 60% on the curve

Disadvantages

- cr,90 is influenced by secondary consolidation.

2.2.2 Inflection point method [9]

Introduction 
2.2.2.1

Ganesalingam [9] (2013) solved the governing equation for the relationship

Ur = f[log (Tr)]. The value of Ur maximum is the position of the derivative

d(Ur)/dlog Tr the maximum. Chung (2019) redefines the value of Tr with dU/d(lnt).

The value of Tr is 1/32 = 0.03125.

In thesis, the author recommends that the value of Tr calculated with dU/logTr.

Time factor can determine with value of y.

log r

y T

(2.10)
In which

10 ln10y

r

dy dT

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Substituting of Eq. (2.4) from Eq. (2.10). The settlement () collateral t is expressed



100 0



1 exp( 32.10 ) 0

y

       

(2.12)
Derivative of v = -32.10y

32.10 ln10y

dv  dy

(2.13)
The derivative for Eq. (2.13) with the variable Tr



100 0



exp 32.10





32.10 .ln 10

 

log( )

y y

r

d d d dv

d T dy dv dy

            

 



100 0



exp 32.





32. .ln 10

 

log( )r r r

d d d dv

T T

d T dy dv dy

           

   

(2.14)
Substituting of u, v



100 0



exp 32.10





y

u   



100 0



32.10 ln 10 exp 32.10

 





y y

du    

     

 

32.10 ln 10y

v  dv32.10 ln 10y

 

2dy

  (2.15)

The derivative for Eq. (2.15) with the variable Tr





 

2 2

log( )r

d uv

d d du dv

v u

dy dy dy dy

d T

     











 







2 2

2 exp 32.10 32.10 . ln 10 1 32.10

log( )

y y y

r
d d
dy
d T
        
 
 











 







2 2
2

2 exp 32 32. . ln 10 1 32.

log( )r r r r

d d

T T T

dy
d T
        
   
 
(2.16)

The last term (1 – 32Tr) should be zero to obtain d2/d(log Tr)2 = 0. Therefore

r,inf

0.03125
32

T  

(2.17)

The radial (horizontal) coefficient of consolidation is determined in this case:

2
inf
0.03125 e
r
d
c
t

 
(2.18)

The procedure for determine cr

2.2.2.2

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- Step 2: Plot (Ur - log Tr) to t then find time max value (Ur - log Tr). This is

the value tinf.

- Step 3: cr is calculated using Eq.(2.18).
 Evaluation of the method

2.2.2.3

Advantages

- Determination of cr in this method does not require the determination of 0

and 100.

- The infection point method can find tinf.

Disadvantages

- There is no method to find tinf from experimental data.

- The accuracy of results depends on the time distance between measurement
results

2.2.3 Full – match method [10]

Introduction 
2.2.3.1

This method combines two methods: graphical method and non – graphical

matching method. The relationship between [log(Ur/Tr) & logUr] studied to

characterize for between the two straight lines in primary consolidation and
secondary compression.

Figure 2.5. Log (Ur/Tr) - log Ur relationship [10]

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The theoretical solutions (PD case and CD case) are rearranged in terms of time:

100

1 exp( )

m o

r

ult o

U    t

  



    

 (2.19)

The radial (horizontal) coefficient of consolidation is determined in this case:

32
e
r

d

C 

(2.20)

The procedure for determine cr from Full – match method

2.2.3.2

- Step 1: A log (δ/t) – log δ graph is plotted using the monitored data, and an 
intersection (δint) between two straight lines is determined.

- Step 2: A selected δ – t data range (0 – δint) is substituted into Eq. (2.19) and

the unknowns (δ0 & η) are appropriately determined using the Microsoft

Excel Solver.

- Step 3: With η, de ,Fn and cr is calculated using Eq. (2.20)

Figure 2.6. Determine the value of intersection point in full – match method

Evaluation of the Full – match method 
2.2.3.3

Advantages

- It inherits the advantages of method a graphical method.
- Value an ultimate settlement δult is determined exactly.

Log  (mm)

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15
Disadvantages

- The way to choose two straight lines is relative.

- Determining the value of δult on the logarithmic coordinate system is often

difficult

2.3 Existing methods for determining cr from consolidation test with a central 
drain using incremental loading method

2.3.1 Root t method [11]

Introduction 
2.3.1.1

The method proposed based on the equation for the equal vertical strain condition
[4]. In Eq. (2.3) have Ur = f[Tr, F(n)] then the author can find Tr = f[Ur, F(n)].

(n) ln(1 U )
8

r
r

F

T   

(2.21)

T90 is the time factor at 90% average degree of consolidation so the value of T90 can

calculated by F(n), Ur.

Berry (1969) commented that all the curve show linear portions between about 20%
- 60% average degree of consolidation. Thus a straight line is drawn through the
experimental volume change –t0.5 results between about 20% to 60% consolidation,
and a second line is then constructed having an abscissa 1.17 time that of the first
[11].

The radial (horizontal) coefficient of consolidation is determined in this case:

90
90
e
r
T d
c
t

 
(2.22)

The procedure for determine cr

2.3.1.2

The steps for determining the radial (horizontal) coefficient are the same as
described in section.2.2.1.2

Evaluation of the method 
2.3.1.3

Advantages

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- Identify a straight line within Ur = 20% to Ur = 60% on the curve.

- This method does not need to find value 0 and 100.

Disadvantages

- Straight line depends on the subjective evaluation of data processing
engineers

2.3.2 Matching log (de2/t) and Ur method [12]

Introduction 
2.3.2.1

The method proposed based on the equation for the equal vertical strain condition
[4]. This approach solves the equation of Eq. (2.3) to find the dependence of Tr on
Ur & F(n) then replaces Tr = f[Ur, F(n)] into Eq.(2.4).

Thus, the radial (horizontal) coefficient of consolidation (cr) is determined

2 8

( ) ln(1 U )

e r

r

d c

t  F n  (2.23)
 The procedure for determine cr

2.3.2.2

- Step 1: Plot log (de2/t) versus Ur curve considering the δ - t data

on Figure 2.7.

- Step 2: Identify a zone where the experimental curve is parallel to
the theoretical curves

- Step 3: Using graphical or Eq. (2.23) can be determined cr.

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Evaluation of the method 
2.3.2.3

Advantages

- cr can determine easily by the graph.

Disadvantages

- Matching between theoretical and experimental curve does not always occur
- The variable Ur needs to determine exact values for 0 &100.

2.3.3 Inflection point method [13]

Introduction 
2.3.3.1

The method was developed based on [13] and [4]. Eq. (2.3) can show the
relationship Ur = f[log (Tr)].

According to the mathematical definition, the value of Ur maximum when the

derivative d(Ur)/dlog Tr the maximum.

Figure 2.8. (a) Theretical Ur - log Tr curve and (b) d(Ur)/dlog Tr plot [13]

In this case, The degree of consolidation at the inflection point also the same for all
the curves at Ur = Ur,inf = 63,21% with maximum derivative .

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r,inf

(n)ln(1 0.631) (n)

8 8

F F

T    

(2.24)
The radial (horizontal) coefficient of consolidation is determined in this case:

2
inf
( )
8
e

r
d
F n
c
t


(2.25)

The procedure for determine cr

2.3.3.2

- Step 1: Plot (Ur - log t) to t then finding time at max value (Ur - log t). This is

the value tinf.

- Step 2: cr can be determined cr by Eq.(2.25)
 Evaluation of the method

2.3.3.3

Advantages

- 0, 100 does not need to be identified.

- In this method, the author finds tinf value.

Disadvantages

- There is no method yet to find tinf from Experimental data.

- The accuracy of results depends on the time distance between measurement
results.

2.3.4 Non-graphical method [14]

Introduction 
2.3.4.1

The method proposed based on the equation for the equal vertical strain condition
[4].

The laboratory time (t) – compression r is described by the equation.

100 0

r Ur

   

(2.26)

Ur is change in Eq. (2.26) from [4].



100 ,0



2 0

8
1 exp
( )

r
r r
e
C t

F n d

         

 

  (2.27)
Combine Eq of (2.27) and constant values of de and 100, 0. F(n) can be found by

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The procedure for determine cr

2.3.4.2

Finding cr with100, 0, F(n), de and r – t curve by A source code or program on Eq.

(2.27).

Evaluation of the method 
2.3.4.3

Advantages

- Use a coding program to resolve results independent of the implementer.

Therefore, the value has high accuracy.

- Results processing time is fast.
Disadvantages

- Matching between theoretical and experimental curve does not always occur
- The value depends on the data range.

- Eq of (2.27) variable Ur needs to determine the exact values for 0 and 100.

2.3.5 Log - log method [15]

Introduction 
2.3.5.1

The value of o can be calculated by selecting two time – settlement in the range

Ur < 20% at experimental data(1, t1) & (2, t2).

2 2
1 1
o
o
t
t
 
 
    
    
 

  (2.28)
Two straight lines depicted in Figure 2.9. The radial (horizontal) coefficient of
consolidation is determined in this case:

2
,66

(T )r e
r
d
c
t

(2.29)

The procedure for determine cr

2.3.5.2

- Step 1: Calculate the initial compression (0) using Eq. (2.28) from the time

– compression data by choosing two points in the early stages of
consolidation. The value of 0 can be calculated by selecting two time –

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- Step 2: Plot the time t – corrected settlement ( – 0) in a log – log plot.

- Step 3: Identify the initial linear portion and draw line.

- Step 4: Identify the linear secondary compression portion by drawing a line
and extending it to intersect the initial straight line. The time at the point of
intersection (t66) corresponds to a degree of consolidation of 66%.

- Step 5: cr can be determined by Eq. (2.29)

Figure 2.9. Log( - 0) versus log t plot [15] 
 Evaluation of the method

2.3.5.3

Advantages

- This method can determine 0 & 66.

- Methods Inheriting advantages of graphical method.
Disadvantages

- From Experimental data the value of 0 within Ur < 20% is not constant

2.3.6 Steepest tangent fitting method [16]

Introduction 
2.3.6.1

The method Inflection point in Section 2.3.3 has disadvantages, Inflection point is
difficult to determine exactly with experimental data. Vinod (2010) found a straight

line through an Inflection point [16].

The equation of tangent through Inflection point on the semi-log graph (Figure
2.10) is determined:

 = b - alog(t)

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where a, b = constant and (t, ) value of experimental data.

One log cycle, the author chooses value (1, t1), (2, t2) on the condition (t1 = 10

time), (t2 = 100 time) & (1 - 2 = h). Substituting (1, t1), (2, t2) into Eq. (2.30)

1 = b – a & 2 = b – 2a Thus 1 - 2 = a = h

(2.31)
Put a from Eq. (2.31).

 = b - hlog(t)

(2.32)
P(o, to) is the corrected initial experimental data (Figure 2.10). Put b with P(o, to)

from Eq. (2.32).

 = [0 + hlog(t0)]- alog(t) = 0 + hlog(t0 / t)

(2.33)

Figure 2.10. Steepest tangent fitting method for determination of cr

Similarly, a straight line through Inflection point on Ur-log Tr and d(Ur) /dlog Tr as

shown Figure 2.8. Function for tangent on Ur - log Tr.
Ur = c - Slog(Tr)

(2.34)
where c is constant and (Tr, Ur) value of predicted curve.

The value of S is defined by Section 2.3.3.

r,inf

0.847
63.2%

(log )
r

r

dU
S

U

d T

 

 (2.35)
Similarly, The corrected initial P(0, t0, Tr,0, Ur,0) is given by Ur,0 = c - Slog(T0)

Substituting b with P(0, t0, Tr,0, Ur,0)

Ur = [Ur,0 + Slog(Tr,0)] - Slog(Tr) = Ur,0 + Slog(Tr,0 / Tr)

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22
(Ur - Ur,0) / S = x / S = log(Tr,0 / Tr) = log(t0 / t)

(2.37)
Eq. (2.37) and put log(to / t) from Eq. (2.33). Thus, function for steepest tangent is

described as follows:

x = 0 + h x / S

(2.38)
Author (Vinod, 2010) has determined the value of o as follows:

1 1

0 1 2

2 2

/ 1

t t

        

    (2.39)

The procedure for determine cr

2.3.6.2

- Step 1: Plot the dial reading against time on semi log graph as show in Figure
2.10.

- Step 2: Determine o in Eq. (2.39)

- Step 3: Draw a tangent PQ to the steepest part of the consolidation curve.
- Step 4: Find h, which is the slope of the tangent PQ.

- Step 5: Find x use Eq.(2.38)

- Step 6: cr is calculated using Eq. (2.35).
 Evaluation of the method

2.3.6.3

Advantages

- This method finds the 0 values.

- Only conduct experiments to Ur = 60%.

- Overcoming method disadvantages Inflection point.
Disadvantages

- Experimental data the value of 0 is not constant.

2.3.7 Log t method [17]

Introduction 
2.3.7.1

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 

0
100 0

1 exp Tr

F n
 
 
 
   
 

    

    (2.40)
Replace t time in t1, t2 and 2t1 = t2

 

1 0

1
100 0

1 exp Tr 1 exp A

F n
 
 
 
     
 
    

    (2.41)

 

2 0

2
100 0

1 exp Tr 1 exp A

F n
 
 
 
     
 
    
   

Substituting A1, A2 with Eq.(2.42)

 

1 0 100 1

100 0 100 0

exp A 1    

   

   

  

 

  (2.42)

 

2 0 100 2

100 0 100 0

exp A 1    

   
   
  
 
 
Then
100 1
1
100 0
ln

A  

 

  

   

  (2.43)

100 2
2

100 0

A  

 

  

   

 

Substituting A1,/A2 with Eq.(2.43)

100 1
100 0
2

1 100 2

100 0
ln
2
ln
A
A
 
 
 
 
  
  
 
 
  
  

  (2.44)
In Eq. (2.44)

100 1 100 2 100 2

100 0 100 0 100 0

ln   2ln   ln  

     

        

 

        

      (2.45)

2
100 1 100 2

100 0 100 0

   
   
 
 
  
   
Then





100 1 2 1

100 2
(2 )
o
   


 
   
   

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Tr relationship fits approximately as a straight line within 0 < Ur < 20%.

The initial compression may be also determined graphically.

If the data points are selected such that t2 = 2t1, then Eq. (2.28) can show that

2 – 1 = 1 – 0

(2.47)
The radial (horizontal) coefficient of consolidation is determined in this case:

2
50
50

(T )r e
r

d
c

t



(2.48)

The procedure for determine cr

2.3.7.2

- Step 1: Plot the time (t) – settlement () in a log t –  plot. 
- Step 2: Draw a tangent through the inflection point.

- Step 3: identify the asymptotic secondary compression portion, draw a line,
and extend it to intersect the tangent line. The point of intersection
corresponds to a degree of consolidation of 100 % (100).

- Step 4: The value of 0 can be obtained using Eq. (2.28) or graphically using

Eq.(2.46).

- Step 5: cr is calculated using Eq. (2.48).
 Evaluation of the method

2.3.7.3

Advantages

- The value 0 can determine in this method.

- Only conduct experiments to Ur = 60%.

- Overcoming method disadvantages Inflection point.

Disadvantages

- Experimental data the value of 0 is not constant.

2.3.8 Full – match method [10]

This method is identical for both CD & PD. The method is mentioned in the section
(2.2.3)

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25
2
8
n e
r
F d

c 

(2.49)
2.4 Summary of methods for determining cr

The author summarizes the methods for determining cr as follows.

Table 2.2. Existing methods for determining cr from radial consolidation

Group No. Peripheral drain Central drain

Section-based

1 Root t method [6] Root t method [11]

2 Matching log (de

/t) and Ur method

[12]

One-
point

3 Log - log method [15]

4 Log t method [17]

5 Inflection point method [9] Inflection point method [13]

6 Steepest tangent fitting method [16]

Full-match

7 Full – match method [10] Full – match method [10]

8 Non graphical matching method [14]

2.5 Linear regression analysis

Suppose that from some experiment of n observations, i.e. values of a dependent 
variable y measured at specified values of an independent variable x, have been 
collected. In other words, we have set data points (x1, y1), (x2, y2), (x3, y3),… , (xn, yn)

for i = 1, 2, .. n. The function for linear y = bx with in intercept = 0 through n point 
can be determined.

Slope of linear

1
2
1
n
i i
i
n
i
i
y x
b
x






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26
Coefficient of determination

2
2 1

2
2 1
1
1
n
i
i
n
i
n
i
i
i
e
R
y
y
n



 
 
 
 




(2.51)

where

t i i

e  y bx

(2.52)
2.6 Log normal distribution method

The bell shaped curve appearing in figure 3.6 is generated using the probability
density function [18].

2 2

( ) /2

1
( )

2
x

f x e  

 

 



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CHAPTER 3. METHODOLOGY

3.1 Introduction

The studies for this thesis belong to experimental research focusing on the
evaluation of radial (horizontal) coefficient of consolidation of soil. The general
methodology of the research shows in Figure 3.1. Literature review provides
methods for determining cr values for PD & CD cases and provides evaluation

methods to select the best methods.

The focus of the research is to evaluate and select the Best methods for determining
the radial (horizontal) coefficient of consolidation and find correlations of cr,CD &
cr,PD as well as correlations between cr,CD (and cr,PD) and cv.

Literature review Problem identification

Data collection and analyses

Coefficient of consolidation (cr, cv)

Correlations of

cr CD & cr PD

Conclusion
Find best methods

for determining cr

Figure 3.1. Flow chart of the study

Correlations of cr CD

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28
3.2 Data collection

In this study, the author does not directly perform field and laboratory tests. In fact,
the author collected data of consolidation test with radial drainage, which have been
published in the literature. More remarkably, most of the data used for the thesis
were obtained from the laboratory test program of the supervisor. From this source,
consolidation test results from DVIZ, VSIP, and Kim Chung (KC) were used for the
analyses. Fig. 3.2 shows an example of raw data, settlement & time curve, obtained
from consolidation test with a peripheral drain (PD) [9].

Figure 3.2. Experimental data [9]
3.3 Improvement for inflection point methods

3.3.1 Theoretical development

The author has commented in Inflection point method as follows and substituting of
Eq. (2.14) from Tr in Eq. (2.4).

In PD case



100 0



exp 32. 2 32. 2.ln 10

 

log( )

r r

r e e

c t c t

d

d T d d

       

     

   

  (3.1) 
In CD case



100 0



 

8 8

exp . . .ln 10

log( )r ( ) r ( ) r

d

T T

d T F n F n

        

     

   

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3.3.2 The procedure for this method

A. Determine the value of  /logTr from Experimental data

Constant values of o, ult, the author can calculate the value of Ur corresponding to

log (t) with Experimental data.

100

o
r

o

U  

 




 (3.3)

Find the average rate of change (Slope) of Ur and log t.









, 1 , , 1 , , 1 ,

1 1 , 1 ,

ope=

log log log log / log / T log

r n r n r n r n r n r n

r r

n n n n r n r n r

Sl

t t t t t T T

     

    

  

  

 

   

   (3.4)

B. Determine the predict curve from theory

In PD, case uses Eq. (3.3) and CD case using Eq. (3.4).
C. Finding the predict curve from Experimental data

Using curve-fitting method: least squares method both the slope of test data and the
slope of curve prediction. The author finds the most optimal curve for the data
series.

From the prediction cure equation, cr can be determined.

3.4 Analysis of Time – Compression curve

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30
3.5 Procedure to select the best methods

Figure 3.3. Flowchart of identifying the best methods

As in section 3.4, the author has determined the coefficient cr values from which the

author can calculate the value of predicted settlement for each method as well as for 
each experiment.

Input from each test

- Predicted Settlement - Measured settlement

Step 1: Each site 
Combine data in each site

- Predicted Settlement - Measured settlement

Step 2: All data 
Combine data in all data

- Predicted Settlement - Measured settlement

Step 3: Find correlation: 
- p = a  m

- R2 square

Step 4: Find the best method 
The conditions to find the optimal method:

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The purpose of the methods the author is studying is to determine the coefficient cr

values. In practice, it is to find the forecast curve predicted settlement of measured

settlement. Therefore, the choice of the Best methods is to choose which method

yields the predicted settlement results closest to reality.

Based on the data in the table, the author proposed using method ranking based on
optimal point‟s multi criteria decision-making method for the evaluation.

The author chooses the criteria:

1. The method for finding the coefficient a nearest 1. 
2. The method for finding the coefficient R2 nearest 1.

The author ranked the criteria in the same pressure with the rankings from 1 to 8. 1
point corresponds to the method with the best results in the selection criteria and the
score drops to 8 according to the results of the selection criteria.

The author summarizes all evaluation points for each method. The best method is
the method that gives the lowest total score.

3.6 Procedure to determine ratios of cr PD /cr CD or cr /cv

Figure 3.4. Flowchart of identifying the best methods
Input from each test

- cr PD & cr CD or cv

Step 1: Each site

Combine data in each site

- cr PD & cr CD or cv

-

Step 2: All data 
Combine data in all data

- cr PD & cr CD or cv

-

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As in section 3.4, Author has determined the coefficient cr values. Procedure to

determine ratio of cr PD/cr CD or cr /cv as shown in Figure 3.4.

The author uses Log normal distribution method for ratio of cr PD/cr CD or cr /cv to

eliminate values that cause interference to data and then find relationships in a
straight line:

- For cr PD and cr CD. The correlations is cr PD =   cr CD

- For cr PD and cv. The correlations is cr PD =   cv

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CHAPTER 4. TEST RESULTS & DISCUSSIONS

4.1 Introduction

This chapter illustrates the results derived from laboratory tests. Section 4.2 briefly
describes the data used in the project. This chapter presents the results estimated
from the Experimental data by using different analytical methods and correlations
of cr CD and cr PD as well as correlations between cr CD (and cr PD)/cv.

4.2 Summary of database

4.2.1 Data collected from the literature

In the thesis, author has collected data from papers in the literature. Table 4.1 and
Table 4.2 summarize test data collected from the literature.

Table 4.1. Summary of data from literature for the PD – ESL condition

No Soil type Pressure

(kPa) Reference

PD-ESL 1 Brisbane dredged mud 230 Ganesalingam et al. (2013) (Fig. 4a)

PD-ESL 2 Brisbane dredged mud 60 Ganesalingam et al. (2013) (Fig. 6a)

PD-ESL 3 Brisbane dredged mud 120 Ganesalingam et al. (2013) (Fig. 6b)

PD-ESL 4 Brisbane dredged mud 235 Ganesalingam et al. (2013) (Fig. 6c)

PD-ESL 5 Brisbane dredged mud 470 Ganesalingam et al. (2013) (Fig. 6d)

PD-ESL 6 Townsville dredged mud 60 Ganesalingam et al. (2013) (Fig. 6a)

PD-ESL 7 Townsville dredged mud 120 Ganesalingam et al. (2013) (Fig. 6b)

PD-ESL 8 Townsville dredged mud 235 Ganesalingam et al. (2013) (Fig. 6c)

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Table 4.2. Summary of data from literature for the CD – ESL condition

No Soil type Pressure

(kPa) Reference

CD-ESL 1 Black cotton soil 400 Sridharan et al. (1996) (Fig. 5)

CD-ESL 2 Black cotton soil 25 Robinson (1997) (Fig. 3)

CD-ESL 3 Black cotton soil 50 Robinson and Allam (1998) (Fig. 3)

CD-ESL 4 Kaolinite 50 Robinson (2009) (Fig. 9)

CD-ESL 5 Singapore marine clay 100 Robinson (2009) (Fig. 9)

CD-ESL 6 IIT Madras lake clay 50 Sridhar and Robinson (2011) (Fig. 7)

4.2.2 Data collected from test sites in Vietnam

Location of the test sites

In the thesis, author has collected data from test sites in Vietnam. Figure 4.1 and
Figure 4.2, Figure 4.3 presents the location of test sites..

Figure 4.1. Locations of test sites in Viet Nam (VSIP site, DVIZ site, Kim Chung site)

Kim Chung site

VSIP site

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Figure 4.2. Test location at Kim Chung site

Figure 4.3. Test location at VSIP site

Figure 4.4. Test location at DVIZ site

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36
Geological profiles at the test site

Figure 4.5 presents the geological conditions at DVIZ site. The site has 7 soil layers
and the ground water level is at 0.9 m below ground surface.

Figure 4.5. Soil profile at DVIZ

Figure 4.6. Soil profile at VSIP Figure 4.7. Soil profile at KC

0.0

5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
55.0
60.0

Elastic silt, mixed with oganic
Sandy silt, clayed sand

Lean clay with sand

Poorly graded sand

Sandy lean clay
Lean clay, fat clay

 = 16.6 KN/m3
e0 = 1.53,

Ip = 32.9%
Soil profile Description

Sand with silt

45.0

50.0

55.0

60.0

Back fill

Silty clay stone
Sandy Lean clay
Elastic silt with sand, very soft
 = 16.40 KN/m3

e0 = 1.50, Ip = 14.1%

Fat clay, somewhere elastic silt,
mixed, fine gravee0 = 0.93,
 = 18.60 KN/m3, I

p = 20%
Soil profile Description

0.0
5.0
10.0
15.0
20.0

25.0
30.0
35.0
40.0
Silty sandstone
Clay loam

 = 18.1 KN/m3
e0 = 0.97

Ip = 21.4%
Description
Soil profile
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
55.0
60.0

Gravel,  = 2.65 g/cm3

Back fill

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Figure 4.6 presents the geological conditions at DVIZ site. The site has 5 soil layers
and the groundwater level is at 1.5 m below ground surface.

Figure 4.7 presents the geological conditions at KC site. The site has 5 soil layers
and the ground water level is at 15.80 m below ground surface.

4.2.3 Summary of test data

Besides data collected from the literature, test data from the supervisor were also
collected for analyses. Table 4.3 and Table 4.4 summarize test data obtained from
the supervisor.

Table 4.3. Summary of tests done on intact samples

Source

VD CD PD

Samples Data curves Samples Data curves Samples Data curves

Literature 0 0 0 0 0 0

DVIZ 19(17) 92(82) 10 47 17 82

VSIP 32 156 32 154 31 149

KC 5 25 5 25 5 25

Table 4.4. Summary of tests done on remolded samples

Source

VD CD PD

Samples Data curves Samples Data curves Samples Data curves

Literature 0 0 6 6 9 9

DVIZ 0 0 0 0 0 0

VSIP 0 0 3 15 3 15

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4.3 Evaluation and selection the best methods on intact samples

4.3.1 Graph results on intact samples

Figure 4.8 presents typical correlations between measured settlement and predicted
settlement obtained from PD tests on intact samples (at 800 kPa) for 8 methods.

(a) Root t method (b) Log de 2/t method

(g) Log - log method (h) Steepest tangent - method

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(i) Log t method (k) Full-match method

Figure 4.8 (Cont.). Results from PD tests on intact samples (at 800 kPa) for 8 methods

Figure 4.9 presents typical correlations between measured settlement and predicted
settlement obtained from CD tests on intact samples (at 800 kPa) for 8 methods.

(a) Root t method (b) Log de 2/t method

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(g) Log - log method (h) Steepest tangent - method

(i) Log t method (k) Full-match method

Figure 4.9 (Cont.). Results from CD tests on intact samples (at 800 kPa) for 8 methods

4.3.2 Summary of results on intact samples

Table 4.5 presents correlations of measured settlement and predicted settlement
obtained from PD tests on intact samples.

Table 4.5. Summary of results from PD tests on intact samples

Pressure

(kPa) Method a (y = ax) R - square No. of data point (n)

PD 50

Root t 0.99 0.984 6493

Log de2/t 0.93 0.753 6594

Inflection Point 1.13 0.552 6594

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41
Pressure

(kPa) Method a (y = ax) R - square

No. of data 
point (n)

Log-Log 0.90 0.879 4359

Steepest tangent 1.08 0.908 6393

Log t 1.03 0.985 3653

Full-match 0.98 0.983 3552

PD 100

Root t 0.99 0.990 7436

Log de2/t 1.00 0.988 7593

Inflection Point 0.84 0.798 7593

Non-graphical 1.00 0.995 7593

Log-Log 0.92 0.901 5605

Steepest tangent 1.10 0.855 7593

Log t 1.01 0.990 4957

Full-match 0.98 0.987 5435

PD 200

Root t 0.98 0.991 10722

Log de2/t 1.01 0.994 10722

Inflection Point 0.85 0.900 10722

Non-graphical 1.00 0.996 10722

Log-Log 0.88 0.926 8372

Steepest tangent 1.16 0.902 10722

Log t 1.03 0.992 6733

Full-match 0.95 0.975 6978

PD 400

Root t 0.95 0.994 12280

Log de2/t 1.02 0.997 12699

Inflection Point 0.82 0.990 12699

Non-graphical 1.00 0.998 12699

Log-Log 0.87 0.986 8284

Steepest tangent 1.14 0.975 12699

Log t 1.04 0.997 8284

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42
Pressure

(kPa) Method a (y = ax) R - square

No. of data 
point (n)

PD 800

Root t 0.98 0.989 10124

Log de2/t 1.01 0.985 10124

Inflection Point 0.87 0.795 10124

Non-graphical 1.00 0.988 10124

Log-Log 0.87 0.889 7906

Steepest tangent 1.08 0.629 10124

Log t 1.03 0.995 7906

Full-match 0.98 0.992 7906

Table 4.6 presents correlations of measured settlement and predicted settlement
obtained from CD tests on intact samples.

Table 4.6. Summary of results from CD tests on intact samples
Pressure

(kPa) Method a (y = ax) R - square

No. of data 
point (n)

CD 50

Root t 0.97 0.968 4756

Log de2/t 1.01 0.984 4890

Inflection Point 1.00 0.198 4890

Non-graphical 1.00 0.989 4890

Log-Log 0.92 0.897 3516

Steepest tangent 1.11 0.794 4653

Log t 1.03 0.984 3465

Full-match 0.97 0.985 3668

CD 100

Root t 0.98 0.987 4938

Log de2/t 1.00 0.990 4938

Inflection Point 1.07 0.152 4938

Non-graphical 1.00 0.994 4938

Log-Log 0.90 0.881 3806

Steepest tangent 1.09 0.875 4861

Log t 1.02 0.989 3648

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Pressure

(kPa) Method a (y = ax) R - square

No. of data 
point (n)

CD 200

Root t 0.97 0.983 7479

Log de2/t 1.01 0.992 7479

Inflection Point 0.90 0.637 7479

Non-graphical 1.00 0.995 7479

Log-Log 0.90 0.931 5702

Steepest tangent 1.14 0.899 7348

Log t 1.03 0.991 4905

Full-match 0.96 0.984 5696

CD 400

Root t 1.00 0.989 8578

Log de2/t 1.01 0.992 8359

Inflection Point 0.88 0.788 8578

Non-graphical 1.00 0.996 8578

Log-Log 0.89 0.926 6591

Steepest tangent 1.13 0.873 8145

Log t 1.01 0.991 6591

Full-match 0.95 0.979 6591

CD 800

Root t 0.98 0.991 8321

Log de2/t 1.01 0.992 8278

Inflection Point 0.90 0.959 8321

Non-graphical 1.00 0.997 8321

Log-Log 0.84 0.858 8278

Steepest tangent 1.07 0.842 8278

Log t 0.98 0.966 7994

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Table 4.7 presents the rank of each criterion with each pressure obtained from PD
tests on intact samples.

Table 4.7. Rank of each criterion with each pressure from PD tests on intact
samples

Pressure (kPa) Method Rank of a (y = ax) Rank of R - square

PD 50

Root t 2 3

Log de2/t 5 7

Inflection Point 8 8

Non-graphical 1 1

Log-Log 7 6

Steepest tangent 6 5

Log t 4 2

Full-match 3 4

PD 100

Root t 3 3

Log de2/t 2 4

Inflection Point 8 8

Non-graphical 1 1

Log-Log 6 6

Steepest tangent 7 7

Log t 4 2

Full-match 5 5

PD 200

Root t 3 4

Log de2/t 2 2

Inflection Point 7 8

Non-graphical 1 1

Log-Log 6 6

Steepest tangent 8 7

Log t 4 3

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Pressure (kPa) Method Rank of a (y = ax) Rank of R - square

PD 400

Root t 5 5

Log de2/t 2 2

Inflection Point 8 6

Non-graphical 1 1

Log-Log 6 7

Steepest tangent 7 8

Log t 4 3

Full-match 3 4

PD 800

Root t 4 3

Log de2/t 2 5

Inflection Point 7 7

Non-graphical 1 4

Log-Log 8 6

Steepest tangent 6 8

Log t 5 1

Full-match 3 2

Table 4.8 presents the rank of each criterion with each pressure from CD tests on
intact samples.

Table 4.8. Rank of each criterion with each pressure for CD case on intact samples

Pressure

(kPa) Method Rank of a (y = ax) Rank of R - square

CD 50

Root t 6 5

Log de2/t 3 3

Inflection Point 1 8

Non-graphical 2 1

Log-Log 7 6

Steepest tangent 8 7

Log t 5 4

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46
Pressure

(kPa) Method Rank of a (y = ax) Rank of R - square

CD 100

Root t 4 4

Log de2/t 2 2

Inflection Point 6 8

Non-graphical 1 1

Log-Log 8 6

Steepest tangent 7 7

Log t 3 3

Full-match 5 5

CD 200

Root t 3 5

Log de2/t 2 2

Inflection Point 7 8

Non-graphical 1 1

Log-Log 6 6

Steepest tangent 8 7

Log t 4 3

Full-match 5 4

CD 400

Root t 1 4

Log de2/t 4 2

Inflection Point 7 8

Non-graphical 2 1

Log-Log 6 6

Steepest tangent 8 7

Log t 3 3

Full-match 5 5

CD 800

Root t 3 3

Log de2/t 2 2

Inflection Point 7 5

Non-graphical 1 1

Log-Log 8 7

Steepest tangent 5 8

Log t 4 4

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4.3.3 Summary of rank method on intact samples

Table 4.9 presents the rank of each criterion with each method obtained from PD
tests on intact samples and shows the best methods.

Table 4.9. Summary of rank for each method from PD tests on intact samples

Method Rank of a (y = ax) Rank of R - square Sum of index Rank

Root t 17 18 35 4

Log de2/t 13 20 33 3

Inflection Point 38 37 75 8

Non-graphical 5 8 13 1

Log-Log 33 31 64 6

Steepest tangent 34 35 69 7

Log t 21 11 32 2

Full-match 19 20 39 5

The authors obtain the summary of result from PD test on intact samples:
- Best method is Non – graphical method and the function of linear

p = m & R2 = 0.994 (4.1)

- Rank as 2 is Log t method and the function of linear

p = 1.03m & R2 = 0.992 (4.2)

- Rank as 3 is log de2/t method and the function of linear

p = 1.00m & R2 = 0.938 (4.3)

- Root t is ranked as 4 and the function of linear

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Table 4.10 presents the rank of each criterion with each method obtained from CD
tests on intact samples and shows the best methods.

Table 4.10. Summary of rank on each meth1od from CD tests on intact samples

Method a (y = ax) Rank of R - square Rank of Sum of index Rank

Root t 17 21 38 4

Log de2/t 13 11 24 2

Inflection Point 28 37 65 6

Non-graphical 7 5 12 1

Log-Log 35 31 66 7

Steepest tangent 36 36 72 8

Log t 19 17 36 3

Full-match 25 22 47 5

The authors obtain the summary of result from CD test on intact samples:
- Best method is Non – graphical method and the function of linear

p = m & R2 = 0.994 (4.5)

- Rank as 2 is log de2/t method and the function of linear

p = 1.01m & R2 = 0.990 (4.6)

- Rank as 3 is log t method and the function of linear

p = 1.01m & R2 = 0.984 (4.7)

- Root t is ranked as 4 and the function of linear

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4.4 Evaluation and selection the best methods on literature data

4.4.1 Graph results on literature data

Figure 4.10 presents typical correlations between measured settlement and predicted
settlement obtained from PD tests on literature for 8 methods.

(a) Root t method (b) Log de 2/t method

(g) Log - log method (h) Steepest tangent - method

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(i) Log t method (k) Full-match method

Figure 4.10 (Cont.). Results from PD tests on literature for 8 methods

Figure 4.11 presents typical correlations between measured settlement and predicted
settlement obtained from CD tests on literature for 8 methods.

(a) Root t method (b) Log de 2/t method

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(g) Log - log method (h) Steepest tangent - method

(i) Log t method (k) Full-match method

Figure 4.11 (Cont.). Results from CD tests on literature for 8 methods

4.4.2 Summary of results on literature data

Table 4.11 presents correlations of measured settlement and predicted settlement
obtained from PD tests on literature for 8 methods.

Table 4.11. Summary of results from PD tests on literature for 8 methods.
Method a (y = ax) R - square No. of data point (n)

Root t 1.01 0.951 254

Log de2/t 1.02 0.990 254

Inflection Point 0.83 0.977 254

Non-graphical 1.01 0.992 254

Log-Log 0.82 0.887 254

Steepest tangent 1.14 0.947 254

Log t 1.00 0.983 254

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Table 4.12 presents correlations of measured settlement and predicted settlement
obtained from CD tests on literature for 8 methods.

Table 4.12. Summary of results from CD tests on literature for 8 methods.
Method a (y = ax) R - square No. of data point (n)

Root t 0.99 0.993 242

Log de2/t 1.00 0.997 242

Inflection Point 0.96 0.995 242

Non-graphical 1.00 0.998 242

Log-Log 0.87 0.958 242

Steepest tangent 1.04 0.947 242

Log t 0.99 0.997 242

Full-match 0.99 0.998 242

4.4.3 Summary of rank method on literature data

Table 4.13 presents the rank of each criterion with each method obtained from PD
tests on literature and shows the best methods.

Table 4.13. Summary of rank on each method from PD tests on literature
Method a (y = ax) R - square Sum of index Rank

Root t 3 6 9 4

Log de2/t 5 2 7 3

Inflection Point 7 4 11 6

Non-graphical 2 1 3 1

Log-Log 8 8 16 8

Steepest tangent 6 7 13 7

Log t 1 3 4 2

Full-match 4 5 9 4

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p = 1.01m & R2 = 0.992 (4.9)

- Rank as 2 is log t method and the function of linear

p = 1.00m & R2 = 0.983 (4.10)

- Rank as 3 is log de2/t method and the function of linear

p = 1.02m & R2 = 0.990 (4.11)

- Root t is ranked as 4 and the function of linear

p = 1.01m & R2 = 0.951 (4.12)

Table 4.14 presents the rank of each criterion with each method obtained from CD
tests on literature and shows the best methods.

Table 4.14. Summary of rank on each method from CD tests on literature

Method a (y = ax) R - square Sum of index Rank

Root t 3 6 9 5

Log de2/t 1 4 5 2

Inflection Point 6 5 11 6

Non-graphical 2 1 3 1

Log-Log 8 7 15 7

Steepest tangent 7 8 15 7

Log t 5 3 8 4

Full-match 4 2 6 3

The authors obtain the summary of result from CD test on literature:
- Best method is Non – graphical method and the function of linear

p = 1.00m & R2 = 0.998 (4.13)

- Rank as 2 is log de2/t method and the function of linear

p = 1.00m & R2 = 0.997 (4.14)

- Rank as 3 is full-match method and the function of linear

p = 0.99m & R2 = 0.998 (4.15)

- Root t is ranked as 5 and the function of linear

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4.5 Evaluation and selection the best methods on remolded samples

4.5.1 Graph results on remolded samples

Figure 4.12 presents typical correlations between measured settlement and predicted

settlement obtained from PD tests on remolded samples for 8 methods.

(a) Root t method (b) Log de 2/t method

(g) Log - log method (h) Steepest tangent - method

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(i) Log t method (k) Full-match method

Figure 4.12. (Cont.). Results from PD tests on remolded samples for 8 methods

Figure 4.13 presents typical correlations between measured settlement and predicted
settlement obtained from CD tests on remolded samples for 8 methods.

(a) Root t method (b) Log de 2/t method

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(g) Log - log method (h) Steepest tangent - method

(i) Log t method (k) Full-match method

Figure 4.13 (Cont.). Results from CD tests on remolded samples for 8 methods

4.5.2 Summary of results on remolded samples

Table 4.15 presents correlations between measured settlement and predicted
settlement obtained from PD tests on remolded samples for 8 methods.

Table 4.15. Summary results from PD tests on remolded samples for 8 methods
Pressure

(kPa) Method a (y = ax) R - square No. of data point (n)

PD 50

Root t 1.00 0.987 498

Log de2/t 1.00 0.982 498

Inflection Point 0.82 0.966 498

Non-graphical 1.00 0.994 497

Log-Log 0.92 0.953 75

Steepest tangent 1.07 0.964 469

Log t 0.99 0.991 75

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57
Pressure

(kPa) Method a (y = ax) R - square No. of data point (n)

PD 100

Root t 1.00 0.982 454

Log de2/t 1.02 0.992 454

Inflection Point 0.84 0.972 454

Non-graphical 1.00 0.993 454

Log-Log 0.87 0.936 113

Steepest tangent 1.02 0.982 375

Log t 1.01 0.983 113

Full-match 0.99 0.987 113

PD 200

Root t 1.00 0.991 524

Log de2/t 1.03 0.988 524

Inflection Point 0.83 0.981 524

Non-graphical 1.00 0.996 524

Log-Log 0.78 0.871 385

Steepest tangent 1.10 0.957 524

Log t 1.01 0.996 385

Full-match 0.97 0.992 339

PD 400

Root t 1.00 0.989 394

Log de2/t 1.03 0.990 394

Inflection Point 0.84 0.983 394

Non-graphical 1.00 0.996 394

Log-Log 0.87 0.920 296

Steepest tangent 1.11 0.933 394

Log t 1.00 0.994 296

Full-match 0.99 0.992 296

PD 800

Root t 0.97 0.975 206

Log de2/t 1.04 0.984 206

Inflection Point 0.81 0.976 206

Non-graphical 1.02 0.989 206

Log-Log 0.77 0.894 206

Steepest tangent 1.07 0.973 206

Log t 1.02 0.993 206

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Table 4.16 presents correlations between measured settlement and predicted
settlement obtained from CD tests on remolded sample for 8 methods.

Table 4.16. Summary of results from CD tests on remolded samples for 8 methods
Pressure

(kPa) Method a (y = ax) R - square No. of data point (n)

CD 50

Root t 1.00 0.983 321

Log de2/t 1.08 0.984 321

Inflection Point 0.91 0.745 321

Non-graphical 1.01 0.992 321

Log-Log 0.95 0.976 245

Steepest tangent 1.04 0.946 321

Log t 1.01 0.994 245

Full-match 0.95 0.981 245

CD 100

Root t 1.00 0.985 277

Log de2/t 1.04 0.990 277

Inflection Point 0.83 0.960 277

Non-graphical 1.01 0.994 277

Log-Log 0.88 0.884 260

Steepest tangent 1.02 0.980 260

Log t 1.01 0.992 260

Full-match 0.97 0.989 260

CD 200

Root t 0.97 0.989 397

Log de2/t 0.95 0.977 397

Inflection Point 0.95 0.949 397

Non-graphical 1.00 0.996 397

Log-Log 0.82 0.914 397

Steepest tangent 1.10 0.972 253

Log t 0.90 0.959 397

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59
Pressure

(kPa) Method a (y = ax) R - square No. of data point (n)

CD 400

Root t 1.00 0.992 270

Log de2/t 1.04 0.984 270

Inflection Point 0.85 0.974 307

Non-graphical 1.00 0.996 307

Log-Log 0.81 0.931 114

Steepest tangent 1.09 0.956 270

Log t 0.99 0.995 195

Full-match 0.98 0.995 195

CD 800

Root t 0.98 0.975 148

Log de2/t 1.05 0.992 148

Inflection Point 0.90 0.917 148

Non-graphical 1.02 0.993 148

Log-Log 0.78 0.878 148

Steepest tangent 1.08 0.959 148

Log t 1.01 0.993 148

Full-match 0.99 0.995 148

Table 4.17 presents the rank of each criterion with each method obtained from PD
tests on remolded sample and shows the best methods.

Table 4.17. Rank of each criterion with each pressure from PD tests on remolded
samples for 8 methods

Pressure (kPa) Method Rank of a (y = ax) Rank of R - square

PD 50

Root t 3 4

Log de2/t 2 5

Inflection Point 8 6

Non-graphical 1 1

Log-Log 7 8

Steepest tangent 6 7

Log t 4 3

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Pressure (kPa) Method Rank of a (y = ax) Rank of R - square

PD 100

Root t 2 6

Log de2/t 5 2

Inflection Point 8 7

Non-graphical 1 1

Log-Log 7 8

Steepest tangent 6 5

Log t 3 4

Full-match 4 3

PD 200

Root t 2 4

Log de2/t 5 5

Inflection Point 7 6

Non-graphical 1 2

Log-Log 8 8

Steepest tangent 6 7

Log t 3 1

Full-match 4 3

PD 400

Root t 1 5

Log de2/t 5 4

Inflection Point 8 6

Non-graphical 3 1

Log-Log 7 8

Steepest tangent 6 7

Log t 2 2

Full-match 4 3

PD 800

Root t 4 6

Log de2/t 5 4

Inflection Point 7 5

Non-graphical 3 3

Log-Log 8 8

Steepest tangent 6 7

Log t 2 2

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Table 4.18 presents the rank of each criterion with each method obtained from CD
tests on remolded samples and shows the best methods.

Table 4.18. Rank of each criterion with each pressure from CD tests on remolded
samples for 8 methods

Pressure (kPa) Method Rank of a (y = ax) Rank of R - square

CD 50

Root t 1 4

Log de2/t 7 3

Inflection Point 8 8

Non-graphical 2 2

Log-Log 6 6

Steepest tangent 4 7

Log t 3 1

Full-match 5 5

CD 100

Root t 1 5

Log de2/t 6 3

Inflection Point 8 7

Non-graphical 3 1

Log-Log 7 8

Steepest tangent 4 6

Log t 2 2

Full-match 5 4

CD 200

Root t 2 2

Log de2/t 4 4

Inflection Point 3 7

Non-graphical 1 1

Log-Log 8 8

Steepest tangent 7 5

Log t 6 6

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Pressure (kPa) Method Rank of a (y = ax) Rank of R - square

CD 400

Root t 1 4

Log de2/t 5 5

Inflection Point 7 6

Non-graphical 2 1

Log-Log 8 8

Steepest tangent 6 7

Log t 3 3

Full-match 4 2

CD 800

Root t 4 5

Log de2/t 5 4

Inflection Point 7 7

Non-graphical 3 3

Log-Log 8 8

Steepest tangent 6 6

Log t 2 2

Full-match 1 1

4.5.3 Summary of rank method on remolded samples

Table 4.19 presents the rank of each criterion with each method obtained from the
PD case on remolded samples and shows the best methods in this case.

Table 4.19. Summary of rank each method from PD tests on remolded samples

Method Rank of a (y = ax) Rank of R - square Sum of index Rank

Root t 12 25 37 4

Log de2/t 22 20 42 5

Inflection Point 38 30 68 7

Non-graphical 9 8 17 1

Log-Log 37 40 77 8

Steepest tangent 30 33 63 6

Log t 14 12 26 2

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The authors obtain the summary of result from PD test on remolded samples:
- Best method is Non – graphical method and the function of linear

p = 1.00m & R2 = 0.994 (4.17)

- Rank as 2 is log t method and the function of linear

p = 1.01m & R2 = 0.991 (4.18)

- Rank as 3 is full match method and the function of linear

p = 0.99m & R2 = 0.991 (4.19)

- Root t is ranked as 4 and the function of linear

p = 1.00m & R2 = 0.985 (4.20)

Table 4.20 presents the rank of each criterion with each method obtained from the
CD case on remolded samples and shows the best methods in this case.

Table 4.20. Summary of rank each method from CD tests on remolded samples

Method Rank of a (y = ax) Rank of R - square Sum of index Rank

Root t 9 20 29 2

Log de2/t 27 19 46 5

Inflection Point 33 35 68 7

Non-graphical 11 8 19 1

Log-Log 37 38 75 8

Steepest tangent 27 31 58 6

Log t 16 14 30 3

Full-match 20 15 35 4

The authors obtain the summary of result from CD test on remolded samples:
- Best method is Non – graphical method and the function of linear

p = 1.01m & R2 = 0.994 (4.21)

- Rank as 2 is Root t method and the function of linear

p = 0.99m & R2 = 0.985 (4.22)

- Rank as 3 is log t method and the function of linear

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4.6 Comparison of cr CD and cr PD on intact samples

4.6.1 Graph results on intact samples

Figure 4.14 and Figure 4.15 presents typical correlations of cr CD and cr PD obtained

from non-graphical method and root t method at all data on intact samples.

Figure 4.14. Comparison of cr CD and cr PD obtained from root t method at all data

Figure 4.15. Comparison of cr CD and cr PD obtained from non-graphical method at all data

4.6.2 Summary of results on intact samples

Table 4.21 presents correlations of cr CD and cr PD obtained from intact samples for

root t method and non-graphical method.

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Table 4.21. Summary of results from PD and CD tests on intact samples

Pressure
(kPa)

cr,Root PD /cr,Root CD cr,NG PD /cr,NG CD

a (y = ax) square R - No. of data point (n) a (y = ax) square R - No. of data point (n)

50 0.52 0.74 20 0.50 0.63 30

100 0.52 0.68 29 0.56 0.79 33

200 0.46 0.77 28 0.40 0.65 33

400 0.41 0.40 28 0.44 0.51 31

800 0.39 0.83 24 0.37 0.60 21

All data 0.47 0.80 110 0.47 0.81 125

Table 4.22. Summary of boundary for PD and CD case on intact samples

Pressure 
(kPa)

cr,Root PD /cr,Root CD cr,NG PD /cr,NG CD

Lower Upper Distribution area Lower Upper Distribution area

50 0.24 0.74 80.00% 0.30 0.78 80.00%

100 0.28 0.70 80.00% 0.37 0.71 80.00%

200 0.18 0.63 80.00% 0.23 0.69 80.00%

400 0.17 0.67 80.00% 0.27 0.67 80.00%

800 0.26 0.53 80.00% 0.28 0.53 80.00%

All data 0.26 0.62 80.00% 0.32 0.64 80.00%
The authors obtain the result in Table 4.21 and Table 4.22 for correlations of cr PD

and cr PD from intact samples for Root t method and Non-graphical method.

Average correlations of cr CD/cr PD and boundary of cr CD/cr PD with 80% distribution

area ratio of cr CD/cr PD can be determined:

a. For Root method

- cr PD = 0.47cr CD & R2 is 0.80, cr PD = (0.26 – 0.62)cr CD (4.24)

b. For Non-graphical method

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4.7 Comparison of cr CD and cr PD on remolded samples

4.7.1 Graph results on remolded samples

Figure 4.16 and figure 4.17 presents the comparison of cr CD and cr PD obtained from

non-graphical method and root t at all data on remolded samples.

Figure 4.16. Comparison of c r,CD and cr,PD obtained from root t method at all data

Figure 4.17. Comparison of cr CD and cr PD obtained from non-graphical method at all data

4.7.2 Summary of results from remolded samples

Table 4.23 presents correlations of cr,CD and cr,PD obtained from intact samples for

root t method and non-graphical method.

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Table 4.23. Summary of correlations for CD and PD case on remolded samples

Pressure 
(kPa)

cr,Root PD /cr,Root CD cr,NG PD /cr,NG CD

a

(y = ax) square R - No. of data point (n) (y = ax) a square R - No. of data point (n)

50 0.33 0.70 7 0.39 0.79 8

100 0.32 0.87 6 0.34 0.90 6

200 0.48 0.94 6 0.43 0.85 9

400 0.43 1.00 5 0.49 0.96 7

800 0.29 0.89 8 0.38 0.98 7

All data 0.33 0.87 36 0.41 0.87 38

Table 4.24. Summary of boundary for CD and PD case on remolded samples

Pressure 
(kPa)

cr,Root PD / cr,Root CD cr,NG PD / cr,NG CD

Lower Upper Distribution area Lower Upper Distribution area

50 0.25 0.47 80.00% 0.33 0.57 80.00%

100 0.24 0.53 80.00% 0.34 0.51 80.00%

200 0.43 0.58 80.00% 0.19 1.15 80.00%

400 0.42 0.47 80.00% 0.42 0.60 80.00%

800 0.28 0.49 80.00% 0.33 0.48 80.00%

All data 0.30 0.56 80.00% 0.33 0.58 80.00%
The authors obtain the result in Table 4.23 and Table 4.24 for correlations of cr PD

and cr PD from intact samples for Root t method and Non-graphical method.

Average correlations of cr CD/cr PD and boundary of cr CD/cr PD with 80% distribution

area ratio of cr CD/cr PD can be determined:

a. For Root method

- cr PD = 0.33cr CD & R2 is 0.87, cr PD = (0.30 – 0.56)cr CD (4.26)

b. For Non-graphical method

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4.8 Comparison of cv and cr PD on intact samples

4.8.1 Graph results on intact samples

Figure 4.18 and Figure 4.19 presents the comparison of cr PD and cv obtained from

non-graphical method and root t at all data on intact samples.

Figure 4.18. Comparison of cv and cr,PD obtained from root t method at all data

Figure 4.19. Comparison of cv and cr,PD obtained from non-graphical method at all data

4.8.2 Summary of results on intact samples

Table 4.25 presents correlations of cv and cr PD obtained from intact samples for root
t method and non-graphical method.

Table 4.26 presents boundary of cv and cr PD obtained from intact samples for root t

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Table 4.25. Summary of correlations for PD case on intact samples

Pressure 
(kPa)

cr,Root PD /cv cr,NG PD /cv

a

(y = ax) square R - No. of data point (n) (y = ax) a square R -

No. of 
data 
point (n)

50 1.47 0.37 30 1.77 0.47 29

100 1.60 0.69 36 1.29 0.68 41

200 1.57 0.67 45 1.05 0.56 47

400 2.05 0.73 42 1.52 0.76 51

800 1.68 0.76 45 1.04 0.68 44

All data 1.59 0.78 173 1.31 0.71 188

Table 4.26. Summary of boundary for PD case on intact samples

Pressure 
(kPa)

cr,Root PD /cv cr,NG PD /cv

Lower Upper Distribution area Lower Upper Distribution area

50 0.59 2.46 80.00% 1.04 2.65 80.00%

100 0.71 2.60 80.00% 0.77 2.25 80.00%

200 0.60 2.66 80.00% 0.54 2.02 80.00%

400 1.04 2.85 80.00% 0.77 3.05 80.00%

800 0.62 3.38 80.00% 0.74 2.23 80.00%

All data 0.90 2.33 80.00% 0.86 2.26 80.00%
The authors obtain the result in Table 4.25 and Table 4.26 for correlations of cv and
cr PD from intact samples for Root t method and Non-graphical method.

Average correlations of cr PD/cv and boundary of cr PD/cv with 80% distribution area

ratio of cr PD/cv can be determined:

a. For Root method

- cr PD = 1.59cv & R2 is 0.78, cr PD = (0.90 – 2.33) cv (4.28)

b. For Non-graphical method

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4.9 Comparison of cv and cr CD on intact samples

4.9.1 Graph results on intact samples

Figure 4.20 and Figure 4.21 presents the comparison of cv and cr CD obtained from

non-graphical method and root t method at all data on intact.

Figure 4.20. Comparison of cv and cr CD, obtained from root t method at all data

Figure 4.21. Comparison of cv and cr CD obtained from non-graphical method at all data

4.9.2 Summary of results on intact samples

Table 4.27 and Table 4.28 presents the comparison of cv and cr CD obtained from

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Table 4.27. Summary of correlation for CD case on intact samples

Pressure 
(kPa)

cr,Root CD /cv cr,NG CD /cv

a 
(y = ax)

R - 
square

No. of 
data 
point (n) 
a 
(y = ax)

R - 
square 
No. of 
data 
point 
(n)

50 3.53 0.70 20 2.78 0.81 24

100 3.44 0.81 20 2.43 0.62 18

200 3.26 0.92 20 2.52 0.82 32

400 3.82 0.82 20 3.47 0.82 21

800 3.44 0.56 17 2.24 0.10 18

All data 3.38 0.76 115 2.41 0.63 140

Table 4.28. Summary of boundary for CD method on intact samples

Pressure 
(kPa)

cr,Root CD /cv cr,NG CD /cv

Lower Upper Distribution area Lower Upper Distribution area

50 2.34 4.88 80.00% 2.02 3.71 80.00%

100 2.47 4.16 80.00% 1.99 3.17 80.00%

200 2.20 4.29 80.00% 1.33 3.58 80.00%

400 1.89 7.97 80.00% 2.95 5.15 80.00%

800 2.24 5.73 80.00% 2.15 5.10 80.00%

All data 2.14 5.12 80.00% 1.52 4.29 80.00%
The authors obtain the result in Table 4.27 and Table 4.28 for correlations of cv and
cr CD from intact samples for Root t method and Non-graphical method.

Average correlations of cr CD/cv and boundary of cr CD/cv with 80% distribution area

ratio of cr CD/cv can be determined:

a. For Root method

- cr CD = 3.38cv & R2 is 0.76, cr CD = (2.14 – 5.12) cv (4.30)

b. For Non-graphical method

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4.10 Comparison of cv and cr PD on remolded samples

4.10.1 Graph of results on remolded samples

Figure 4.22 and Figure 4.23 presents the comparison of cv and cr,PD obtained from

non-graphical method and root t method at all data.

Figure 4.22. Comparison of cv and cr,PD obtained from root t method at all data

Figure 4.23. Comparison of cv and cr,PD obtained from non-graphical method at all data

4.10.2 Summary of results on remolded samples

Table 4.29 and Table 4.30 presents the comparison of cv and cr,PD obtained from

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Table 4.29. Summary of correlations for PD case on remolded samples

Pressure 
(kPa)

cr,Root PD /cv cr,NG PD /cv

a

(y = ax) square R - No. of data point (n) (y = ax) a square R -

No. of

data 
point (n)

50 0.50 -0.43 3 0.56 0.12 3

100 0.67 0.97 4 0.64 0.69 5

200 0.47 0.56 5 0.45 0.44 5

400 0.77 0.83 6 0.70 0.85 5

800 0.41 0.80 4 0.31 0.80 4

All data 0.46 0.71 24 0.58 0.79 20

Table 4.30. Summary of boundary for PD case on remolded samples

Pressure 
(kPa)

cr,Root PD /cv cr,NG PD /cv

Lower Upper Distribution area Lower Upper Distribution area

50 0.36 0.89 80.00% 0.44 0.87 80.00%

100 0.60 0.94 80.00% 0.40 1.27 80.00%

200 0.27 1.08 80.00% 0.21 1.21 80.00%

400 0.45 1.30 80.00% 0.56 1.00 80.00%

800 0.36 0.66 80.00% 0.26 0.48 80.00%

All data 0.35 1.01 80.00% 0.41 1.09 80.00%
The authors obtain the result in Table 4.29 and Table 4.30 for correlations of cv and
cr PD from remolded samples for Root t method and Non-graphical method.

Average correlations of cr PD/cv and boundary of cr PD/cv with 80% distribution area

ratio of cr PD/cv can be determined:

a. For Root method

- cr PD = 0.46cv & R2 is 0.71, cr PD = (0.35 – 1.01) cv (4.32)

b. For Non-graphical method

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4.11 Comparison of cv and cr CD on remolded samples

4.11.1 Graph results on remolded samples

Figure 4.24 and 4.25 presents the comparison of cv and cr CD obtained from

non-graphical method and root t method at all data.

Figure 4.24. Comparison of cv and cr,CD obtained from root t method at all data

Figure 4.25. Comparison of cv and cr,CD obtained from Root t method at all data

4.11.2 Summary of results on remolded samples

Table 4.31 and table 4.32 presents the comparison of cv and cr,PD obtained from

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Table 4.31. Summary of correlations for CD method on remolded samples

Pressure (kPa)

cr,Root CD / cv cr,NG CD / cv

a (y = ax) R - 
square

No. of 
data point

(n)

a 
(y = ax)

R - 
square

No. of 
data

point 
(n)

50 0.50 0.72 3 0.78 0.49 5

100 0.88 0.67 5 0.94 0.67 5

200 0.44 0.63 4 0.36 0.67 4

400 0.66 0.65 3 0.54 0.46 4

800 0.58 0.60 4 0.55 0.77 4

All data 0.53 0.61 15 0.55 0.79 16

Table 4.32. Summary of boundary for CD method on remolded samples

Pressure 
(kPa)

cr,Root CD / cv cr,NG CD / cv

Lower Upper Distribution area Lower Upper Distribution area

50 0.42 1.12 80.00% 0.35 2.96 80.00%

100 0.72 1.84 80.00% 0.57 1.82 80.00%

200 0.34 0.61 80.00% 0.27 0.47 80.00%

400 0.39 1.23 80.00% 0.36 1.14 80.00%

800 0.39 0.95 80.00% 0.39 0.78 80.00%

All data 0.36 0.82 80.00% 0.41 0.82 80.00%
The authors obtain the result in Table 4.31 and Table 4.32 for correlations of cv and
cr CD from remolded samples for Root t method and Non-graphical method.

Average correlations of cr CD/cv and boundary of cr CD/cv with 80% distribution area

ratio of cr CD/cv can be determined:

a. For Root method

- cr CD = 0.53cv & R2 is 0.61, cr CD = (0.36 – 0.82)cv (4.34)

b. For Non-graphical method

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CHAPTER 5. CONCLUSIONS & RECOMMENDATIONS

The following are key conclusions drawn from this study.

1. The most reliable methods for determining the horizontal coefficient of 
consolidation (cr):

- Best method is Non-graphical method for determining cr for all case and the

function of linear

p = 1.0m & R2 = 0.99 (5.1)

This is the best method because this method determines cr is by matching to find

the best curve for the data series

- Rank as 2 or 3 is usually log de2/t or log t.

- These two methods are matching methods, so it gives good results.
- Root method is usually rank as 4 and the function of linear

p = (0.98 - 1.00)m & R2 = (0.95 – 0.99) (5.2)

- Result of p from root t method is almost equal to m in the both test (CD and

PD) tests on the both samples (intact and remolded). Therefore, Root t method
may become the standard for determining cr values as it is the standard method

for determining cv values.

- The root method is matching data within Ur = 20% to Ur = 60% but it is usually

ranked 4 because the most appropriate method with measured curves is similar
to predicted curve. Especially actual samples with sand or mixed impurities such
as seashells, small rocks ... make measured settlement curve different from the
theory.

- Full-match method also uses the principle of matching but does not rank well
because determining two straight lines on the logarithmic coordinate system is

often difficult.

- The remaining methods also do not have high rankings because the value of 0

varies greatly in the range Ur = 20%. Range Ur = 20% is the initial compression.

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pockets in pore spaces and partly due to the rearrangement of particles in the
soil, and a small percentage may be due to elastic compression due to the value
of 0 varies greatly in this range

- Determining 0 from steepest tangent method is incorrect. It is only true in the

vertical consolidation.

2. Correlations between cr values obtained from central drain (CD) test and 
peripheral drain (PD) test.

Due to differences in drainage boundary, so

, ,

, , , ,

w w

r PD r CD

r PD r CD r PD r CD

r r

k k

k k c c

m m

 

    

  (5.3)
Where: kr PD (kr CD) is the permeability coefficient from PD case (CD case),



w is

water unit weight and mr is soil stiffness from radial consolidation.

Correlations of cr PD/ cr CD changes difference by level of pressure loading:

a. On intact samples
For Root method

cr PD = 0.47cr CD & R2 is 0.80, cr PD = (0.26 – 0.62)cr CD (5.4)

For Non-graphical method

cr PD = 0.47cr CD & R2 is 0.81, cr PD = (0.32 – 0.64)cr CD (5.5)

b. On remolded samples

For Root method

cr PD = 0.33cr CD & R2 is 0.87, cr PD = (0.30 – 0.56)cr CD (5.6)

For Non-graphical method

cr PD = 0.41cr CD & R2 is 0.87, cr PD = (0.33 – 0.58)cr CD (5.7)

3. Correlations between cr and vertical coefficients of consolidation (cv)

Due to differences in drainage boundary, so

w w

v
r

r v r v

r v

k
k

k k c c

m m

 

    

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Where: kr (kv) is the permeability coefficient from radial consolidation (vertical

consolidation), w is water unit weight and mr (mv) is soil stiffness from radial

consolidation (vertical consolidation)

Correlations of cr PD/cv and cr CD/cv changes difference by level of pressure loading:

a. On intact samples
For Root method

- cr PD = 1.59cv & R2 is 0.78, cr PD = (0.90 – 2.33) cv (5.9)

- cr CD = 3.38cv & R2 is 0.76, cr CD = (2.14 – 5.12) cv (5.10)

For Non-graphical method

- cr PD = 1.31cv & R2 is 0.71, cr PD = (0.86 – 2.26) cv (5.11)

- cr CD = 2.41cv & R2 is 0.63, cr CD = (1.52 – 4.29) cv (5.12)

b. On remolded samples
For Root method

- cr PD = 0.46cv & R2 is 0.71, cr PD = (0.35 – 1.01) cv (5.13)

- cr CD = 0.53cv & R2 is 0.61, cr CD = (0.36 – 0.82)cv (5.14)

For Non-graphical method

- cr PD = 0.58cv & R2 is 0.79, cr PD = (0.41 – 1.09) cv (5.15)

- cr CD = 0.55cv & R2 is 0.79, cr CD = (0.41 – 0.82)cv (5.16)

The limitation of the study is that the amount of data is still limited due to the
urgent time, so it has not been able to perform many samples a and there is no
permeability test to verify the ratio in theory.

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REFERENCES

[1]. ASTM D2435 / D2435M – 11. ASTM International, West Conshohocken.
(2011). Standard Test Methods for One-Dimensional Consolidation Properties
of Soils Using Incremental Loading.

[2]. Terzaghi. K (1943). Theoretical soil mechanic. NewYork, Wiley.
1943

[3]. Das B. M., & Sobhan, K Principle of Geotechnical Engineering. Global
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