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

A radial consolidation test RCT might be conducted using incremental loading IL method with either a central drain CD or a peripheral drain PD.. 17 Figure 2.9: Shapes of consolidation cu

i

ABSTRACT

The radial (horizontal) coefficient of consolidation (cr) is a key parameter which impacts the total consolidation of the PVD-improved grounds In practice, the cr value can be interpreted from field tests and laboratory tests A radial consolidation test (RCT) might be conducted using incremental loading (IL) method with either a central drain (CD) or a peripheral drain (PD) The key goals of the research are: (1)

to design and manufacture a multi-directional flow consolidometer (VCT, RCT-PD, RCT-CD) using incremental loading method; (2) to make a comparative study on the

cr values obtained from the RCTIL using a PD and a CD; (3) to make a comparative study on the cr values derived from RCT-based method and CPTu-based method

A desk study is carried out to secure the following: (1) a literature review on equipment used for the test and existing methods used to evaluate the cr value; (2) graphical design of a multi-directional flow consolidation cell Sampling and CPTu dissipation tests are carried out at sites Besides the basic physical lab tests, the RCTIL

with a CD and a PD will be performed using the designed consolidation cell under same condition test

Overall, the ratio of kr/kv is approximately equal the ratio of cr/cv The cr, PD & cr,

CD are double to triple higher than cv The cr, CD values are about 1.5 times larger than figures of cr, PD Finally, the cr values determined from CPTu-based method are doubled higher than cr values obtained from RCT-based method

The reliability of the new device is confirmed Moreover, the results of cr values

in the case of both PD and CD obtained by interpreting with traditional method like square root time method is more reliable than non-graphical method

The limitation of the study is that the amount of data is still limited so it is still not enough to fully confirm the reliability of the multi-directional flow consolidation cell

In the future, the author intends to perform more consolidation and permeability tests

to ensure that the new designated consolidation can be applied in routine performance

ii

ACKNOWLEDGEMENTS

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

My thesis supervisor Dr Nguyen Tien Dung for his enthusiasm, patience, advice and constant source of ideas Dr Dung has always been available to reply to my questions His support in professional matters has been priceless

Special gratitude is given to LAS- XD 442 lab and the staff at Institute of Foundation and Underground, Golden Earth Inc for their kindly support for performing the laboratory work

And finally, I want to spent my thank to my parents and friends for their unflinching support in the tough time Their support, spoken or unspoken, has helped

me complete my master thesis

iii

TABLE OF CONTENTS

ABSTRACT i

ACKNOWLEDGEMENTS ii

TABLE OF CONTENTS iii

LIST OF FIGURES vii

LIST OF TABLES ix

LIST OF ABBREVIATIONS xi

CHAPTER 1: INTRODUCTION 1

1.1 Background 1

1.2 Consolidation 1

1.2.1 Settlement with Prefabricated Vertical Drains (PVD) 3

1.3 Problem statement 5

1.4 Objectives and scope of present study 6

CHAPTER 2: LITERATURE REVIEW 9

2.1 Fundamentals of One Dimensional Consolidation 9

2.1.1 Consolidation Theory with Vertical Drainage 10

2.1.2 Consolidation Theory with Horizontal Drainage 11

2.2 Consolidation Tests in Laboratory 15

2.2.1 Vertical oedometer consolidation test 15

iv

2.2.2 Horizontal Consolidation Test 16

2.3 Determination of Coefficient of Consolidation 17

2.3.1 Analysis of Time-Compression Curve 17

2.3.2 Graphical Method 18

2.3.2 Non-graphical Method 21

2.4 Falling Head Permeability Test 24

2.5 The piezocone penetration test (CPTu) 26

2.5.1 Introduction 26

2.5.2 Pore-water Dissipation Tests 27

2.5.3 Coefficient of Consolidation 28

CHAPTER 3: METHODOLOGY 32

3.1 Introduction 32

3.2 Radial Consolidation Test 33

3.2.1 Design of the equipment 33

3.2.2 Manufacture of the equipment 35

3.2.3 Testing procedure 37

3.2.4 Analysis procedure 38

3.3 Vertical consolidation test 38

3.3.1 Testing procedure 38

3.3.2 Analysis of Time-Compression Curve 38

3.4 Permeability test 39

3.4.1 Equipment of permeability test 39

3.4.2 Testing procedure 39

v

3.4.3 Analysis procedure 40

3.5 CPTu dissipation test 41

3.5.1 Equipment 41

3.5.2 Testing procedure 42

3.5.3 Analysis procedure 42

3.6 Results verification and comparison 42

CHAPTER 4: TEST RESULTS & DISCUSSIONS 43

4.1 Introduction 43

4.2 Summary of test performed 43

4.3 Comparison of cr,PD and cv 46

4.3.1 Square root time method 46

4.3.2 Non-graphical method 47

4.3.3 Inflection point method 48

4.4 Comparison cr,CD and cv 49

4.4.1 Square root time method 49

4.4.2 Non-graphical method 50

4.4.3 Inflection point method 51

4.5 Comparison cr,PD and cr, CD 52

4.5.1 Square root time method 52

4.5.2 Non-graphical method 53

4.5.3 Inflection point method 54

4.6 Horizontal coefficient of consolidation (cr) from CPTu 55

4.6.1 Estimate cr value from monotonic dissipation curves 55

vi

4.6.2 Estimate cr value from non-standard dissipation curves 59

4.7 Test verification 61

4.8 Comparison cr,PD, cr,CD vs cr, CPTu 62

CHAPTER 5: CONCLUSIONS & RECOMMENDATIONS 65

REFERENCES 68

vii

LIST OF FIGURES

Figure 1.1: Soil phase diagram (Das, 2008) 1

Figure 1.2: Primary consolidation (Das, 2008) 2

Figure 1.3: Typical oedometer settlement (Das, 2008) 3

Figure 1.4: Settlement damage 4

Figure 1.5: Drainage with and without drains 5

Figure 2.1: Mechanism of consolidation 9

Figure 2.2: Uv versus Tv relationship (Head, 1986) 11

Figure 2.3: Schematic diagram of an RCT with central drain and peripheral drain 11

Figure 2.4: (a) Scheme of arrangement of the consolidation test in the triaxial apparatus, with drainage towards the cylindrical surface; (b) Cylindrical element of the sample 12

Figure 2.5: Distribution of pore pressures within the soil sample related to r and t 13

Figure 2.6: Schematic of oedometer test (Head, 1986) 15

Figure 2.7: Schematic of the apparatus used for conducting radial consolidation test 16

Figure 2.8: Rowe cell test under equal strain loading, horizontal outward drainage 17

Figure 2.9: Shapes of consolidation curve gained from oedometer test 18

Figure 2.10: Theoretical curve linkage square-root time factor to degree of consolidation for vertical drainage (Taylor, 1942) 20

Figure 2.11: Consolidation curve relating square-root time factor to for drainage radially outwards to periphery with equal strain loading (Head, 1986) 21

Figure 2.12: (a) Theoretical Ur-log Tr curve for n = 5; (b) (dUr/d log Tr)-log Tr plot showing the inflection point (Sridhar and Robinson, 2011) 23

Figure 2.13: Falling-head permeability test (Das, 2017) 24

Figure 2.14: Principal sketch of horizontal and vertical trimming of samples from determining vertical and horizontal coefficient of permeability 25

Figure 2.15: Overview of the cone penetration test per ASTM D 5778 procedures 27

Figure 2.16: Strain path solution for CPTu1 dissipation tests (The and Houlsby, 1991) 30

Figure 2.17: Strain path solution for CPTu2 dissipation tests (The and Houlsby, 1991) 30

Figure 2.18: "Non-standard" dissipation curve ( Chai et al., 2012) 30

Figure 3.1: Equipment for radial consolidation test with peripheral drainage 33

viii

Figure 3.2: Flow chart of the study 34

Figure 3.3: Equipment for radial consolidation test with central drainage 35

Figure 3.4: Manufacture of the equipment for radial consolidation with PD 36

Figure 3.5: Manufacture of equipment for radial consolidation test with CD 36

Figure 3.6: Radial consolidation with peripheral drain and central drain setup 37

Figure 3.7: Equipment of falling head permeability test 39

Figure 3.8: Falling head permeability test setup 40

Figure 3.9: The typical and complete electrical CPT system 42

Figure 4.1: Comparison of cv and cr,PD obtained from square root time method at 400 kPa & 800 kPa 46

Figure 4.2: Comparison of cv and cr,PD obtained from non-graphical method at 400

kPa & 800 kPa 47

Figure 4.3: Comparison of cv and cr,PD obtained from inflection point method at 400 kPa & 800 kPa 48

Figure 4.4: Comparison of cv and cr,CD obtained from square root time method at 400 kPa & 800 kPa 49

Figure 4.5: Comparison of cv and cr,CD obtained from non-graphical method at 400

kPa & 800 kPa 50

Figure 4.6: Comparison of cv and cr,CD obtained from inflection point method at 400 kPa & 800 kPa 51

Figure 4.7: Comparison of cr,PD and cr,CD obtained from square root time method at 400 kPa & 800 kPa 52

Figure 4.8: Comparison of cr,PD and cr,CD obtained from non-graphical method at 400 kPa & 800 kPa 53

Figure 4.9: Comparison of cr,PD and cr,CD obtained from inflection point method at 400 kPa & 800 kPa 54

Figure 4.10: Strain path solution for monotonic dissipation tests at 11 & 17m 57

Figure 4.11: Strain path solution for monotonic dissipation tests at 18.5 & 20.5m 58

Figure 4.12: Dilatory dissipation curve at 8.5m 59

Figure 4.13: Dilatory dissipation curve at 9.5 & 11.3 m 60

Figure 4.14: Results of test verification which compares the ratios between kr/kv with cr/cv 61

Figure 4.15: Comparison between cr,CPTu with cr,PD obtained from square root time method at 400 kPa 64

ix

Figure 5.1 Comparison between results obtained from square root time, non-graphical and inflection point method at 400 kPa 67Figure 5.2: Comparison between results obtained from square root time, non-graphical and inflection point method at 800 kPa 67

x

LIST OF TABLES

Table 4.1: Laboratory and in-situ tests done 44

Table 4.2: Soil profile of borehole BH08 55

Table 4.3: Estimate cr value from modified time factor, T* 56

Table 4.4: Estimate cr values from “non-standard” dissipation curves 59

Table 4.5: Coefficient of permeability obtained from permeability tests 62

Table 4.6: Comparison cr,PD and cr,CD obtained by square root time method with cr,CPTu 63

xi

LIST OF ABBREVIATIONS

xii

1

CHAPTER 1: INTRODUCTION 1.1 Background

Throughout the world, due to rapid urbanization and development, construction projects are rapidly built on fine-grained soils Natural soils in their original condition may be inappropriate for short or long term structure activities and so must be enhanced before use In particular, many coastal areas contain deep multi-layers of compressible clay initially deposited by sedimentation from lakes, rivers, and seas These fine-grained soils have poor bearing capacity and indicate excessive settlements under the load One

of the most broadly and successfully used techniques to boost soft soils is preloading with vertical drains to consolidate the soil and expedite strength growth My thesis mainly builds on the understanding of consolidation by both vertical and horizontal drains developed in the last decades

This chapter illustrates the perception of consolidation and how surcharge with vertical drains can accelerate the water expulsion process The progress of vertical and horizontal drain concepts is discussed

1.2 Consolidation

Figure 1.1: Soil phase diagram (Das, 2008)

2

Soil formed from two or three phase composition (see Figure 1.1) The space inside the soil particles are replaced by water, air or a combination of both Consolidation associates the contraction of voids under load It develops in three stages (see Figure 1.3) Immediate settlement happens instantly after loading with zero volume change, i.e shape change only In saturated soil (i.e no air) the expansion in pressure emerging from the load is immediately carried out by the liquid which is incompressible Such excess pore-water pressure regularly disappears as water seeps out of the soil and the stress is transferred to the soil skeleton This is defined as primary consolidation (see Figure 1.2) Primary consolidation may last year’s depending on soil permeability When additional pore-water pressure has expelled, the soil remains to consolidate continually as the soil particles rearranges to fill into voids

Figure 1.2: Primary consolidation (Das, 2008)

3

Figure 1.3: Typical oedometer settlement (Das, 2008) Consolidation of soils can lead to serious problems for constructions like embankments founded on them If structures settle uniformly little damage is experienced except perhaps to services feeding it However, settlement is rarely uniform Varied loading and the nonhomogeneous characteristic of soil lead to differential settlement This produces added loads that often create cracking in the structure If soils have insufficient strength to withstand the applied loads it may be difficult to build such structures in the first place Soil density largely affects shear strength in soil The densification of soil due to consolidation thus results in considerable strength gain, allowing increased loads to be subjected to the soil

1.2.1 Settlement with Prefabricated Vertical Drains (PVD)

Pre-consolidation is a method adopted to reduce the consequence of consolidation on structures and enhance the strength of the ground Basically, a surcharge is applied to the ground, usually in the form of an embankment, where a structure located on This embankment induces the foundation soil to consolidate Once the required primary consolidation is attained the pre-consolidation load is discharged and the structure built Thus after construction, the soil foundation experiences the slow gradual process of

of soil enhances and is able to prevent increased loads without failure To hasten the consolidation process so surcharges can be set up more quickly (or not built up as high

in the first place), one must speed the egress of water from the soil frame The establishment of vertical drains reduce the leakage path for water to seep out under the additional pore-water pressure (see Figure 1.5) In particular, they equip both a radial outflow path in addition to vertical outflow path Clays have greater horizontal permeability than in the vertical permeability Usually, water only seeps out in the vertical direction due to the large extent of the clay body Vertical drains allow the increased horizontal permeability to be exploited

6

existing methods for determining the consolidation parameters were proposed for the IL method This research focuses on the CRSIL

The RCTIL can be conducted using either a central drain (CD) (i.e., inward drainage)

or a peripheral drain (PD) (i.e., outward drainage) Existing methods for determining cr

value are mainly focused on the test with a CD rather than a PD This is because the test results can conveniently be interpreted using the well-known theoretical solutions of Barron (Barron, Lane, Keene, & Kjellman, 2002) However, the test with a CD is often associated with three typical problems: (1) the interpreted cr value is a function of n

=de/dw, where de is radius of soil specimen and dw is the radius of the central drain; (2) soil disturbance resulted from preparation of the central drain affects the test results significantly; and (3) the attainment of the test depends greatly on the central placement

of the central drain (if it is a porous stone), which is quite difficult in routine test For a given soil under the same magnitude of applied pressure, the RCTIL of both drainage types should result in the same value of cr, but the problems associated with the test using

a CD can be avoided by using a PD Since not much attention has been paid to explore the advantages of the test with a PD, an in-depth study on this drainage condition is therefore very necessary to take its advantages in routine performances

1.4 Objectives and scope of present study

The key goals of the research are to investigate the effectiveness of the RCTIL using

a PD compared with the test using a CD and to propose a comprehensive method to evaluate cr value of clays from the test so that the method can conveniently be applied

in routine performances The particular objectives of the research are:

- To design and manufacture a multi-directional flow consolidation cell that should

be able to perform the RCTIL using either a CD or a PD

- At research site, boring and sampling was conducted for one borehole up to 23.0 m

A total of 06 sampling tubes (at 06 sampling depths) as obtained The sampling tubes were brought to the laboratory and preserved for laboratory test

- One CPTu sounding in association with CPTu dissipation test was conducted nearby the sampling borehole location The CPTu test results are used characterize the soil at the site and the CPTU dissipation test results are used to determine the coefficient of radial consolidation (cr) which will be compared with that with that obtained from radial consolidation test in the lab In total, 06 dissipation points at the centers of 06 sampling depths, respectively, were conducted at the site At each test depth the penetration was halted to conduct the dissipation test until at least 50% of excess pore water pressure has been dissipated

8

- Designed and manufactured a consolidation cell that could be able to perform the RCTIL using either a CD or a PD, and more importantly the cell could be able to function using the standard loading frame and monitoring system of the conventional oedometer test (ASTM D2435 / D2435M - 11, 2011)

- Perform all basic laboratory tests (e.g., Atterberg limits, water content, unit weight, specific gravity, and conventional consolidation test) to characterize the soil, and RCTIL

using a CD and a PD

- Analyze test data and compare the cr values obtained from laboratory and field tests

9

CHAPTER 2: LITERATURE REVIEW 2.1 Fundamentals of One Dimensional Consolidation

A soil may be known to be a skeleton of solid particles enclosing voids which may

be filled with combination of gas and liquid If a sample of soil subjected to sustained pressure so that its volume is reduced in a drained manner

As the compression happens, the pore water is seeped out based on Darcy’s law, (Taylor 1948) At the same time, a slow expulsion of water accompanied by the reduction

in the volume of the soil mass, which results in settlement

(a) Initial loading, water

takes load, soil (i.e

spring) has no load

(b) Dissipation of excess water pressure, water seeping out and soil starts

10

The consolidation of clay under a surcharge does not occur instantaneously; clays are impermeable that the water is relatively trapped into the pores When an increment of load is subjected the pore water cannot seep out promptly Since clay particles have a tendency to approach one another and pressure increases in the pore water which is known the excess pore pressure The hydraulic gradients appear due to this excess pressure lead the fluid to escape from the soil As drainage continuous, the excess pressures dissipate and later the externally constant applied stress is gradually transferred

to the soil frame The part of pressure carried by soil frame is defined as effective stress Soil skeleton then changes under the rise in effective stresses This is called consolidation

2.1.1 Consolidation Theory with Vertical Drainage

The soil property designated by cv is called the coefficient of consolidation:

2 2 v

A dimensionless time factor is illustrated as:

2

v v d

c tTH

and average degree of consolidation

2

4 2

11

The relation between Uavg and Tv can be observed from Figure 2.2

Figure 2.2: Uv versus Tv relationship (Head, 1994) 2.1.2 Consolidation Theory with Horizontal Drainage

Case for Equal Vertical Strain – For the case where loading and compression are as

in the standard test, but where pore water flow is restricted to the radial direction only,

it has been shown in Eq (2.4) that the differential equation of consolidation is:

2 2

12

2.1.2.1 For the case of a peripheral drain (PD)

By isolating an element of the sample to a distance r from the axis (Figure 2.4, if we call u=u(r,t) the pore pressure at a time t, then the difference between the volume of water flowing into and out of the element will be:

2 2 w

P

STEEL PLATE (IMPERVIOUS)

De LOADING PLATE (IMPERVIOUS)

13

2 2

Since the value of the vertica

l strain ε is independent of r and only a function of time (equal strain), we have

2 2

At any given time, t after loading, diagram of u (hypothesis) changes as following:

Figure 2.5: Distribution of pore pressures within the soil sample related to r and t Solving this equation is achieved by applying the following boundary conditions: 1) u = 0 at r = De/2 and t ≥ 0

Where u0 = initial excess pore pressure at t = 0, Tr c t dr / e2 is time factor

2.1.2.2 For the case of a center drain (CD)

The answer of Eq (2.4) for the equal vertical strain condition (Barron, 1948) is described by

 

8 /

1 T F n r r

2/

2 2

ln

41

nn

nn

15

where dw is the length of the drain The following equation is obtained:

  2

ln(1 )8

e r

r

dU

r r

U

(2.18)

2.2 Consolidation Tests in Laboratory

2.2.1 Vertical oedometer consolidation test

In this test, the undisturbed specimen is undergoing axially in increment of subjected stress Each stress increment is loaded constantly until finishing primary consolidation During this transform, water is expelled, leading to a reduced in size which is assessed

at reasonable intervals

Figure 2.6: Schematic of oedometer test (Head, 1994)

Dial gage

Porous stone

Water bath Soil

sample

16

2.2.2 Horizontal Consolidation Test

2.2.2.1 Horizontal consolidation test with center drain

Radial drainage inwards to a sand column drain was achieved in a conventional oedometer by Rowe (1959) Apparatus with radial drainage were performed on remolded soil samples was amended to perform conventional consolidation test (Sridhar & Robinson, 2011) A description of the consolidation cell, after modification, is shown in Fig 2.7

Figure 2.7: Schematic of the apparatus used for conducting radial consolidation test

(Sridhar & Robinson, 2011)2.2.2.2 Horizontal consolidation test with peripheral drain

Horizontal (radial) drainage to a pervious boundary at the perimeter with the top and bottom faces sealed; equal strain loading is described in Figure 2.8

17

Figure 2.8: Rowe cell test under equal strain loading, horizontal outward drainage 2.3 Determination of Coefficient of Consolidation

2.3.1 Analysis of Time-Compression Curve

Figure 2.9 illustrates three differently shapes of consolidation curve obtained from conventional consolidation experiment on different types of soil (Leonards and Girault, 1961) Type I curve is the most typical one and described by Terzaghi’s theory with S-shaped curve

sample

18

Figure 2.9: Shapes of consolidation curve gained from oedometer test

(Leonards and Girault, 1961) 2.3.2 Graphical Method

In the graphical methods, the coefficient of consolidation in conventional oedometer experiment can be derived by curve fitting methods The characteristics feature of Tr

versus Ur association is analyzed The same association is then implemented to the time (t) versus settlement (S) linkage to determine cr Sridharan (Sridharan, Prakash, & Asha, 1996) proposed a √t method, where t is the time, for the determination of cr These empirical approaches were created to fit approximately the observed laboratory test data

to the Terzaghi’s theory of consolidation The following procedure was approved by Taylor:

peripheral drain (Figure 2.8)

Step 3: DQ and the curve intersect at point G

Step 4: Horizontal line stretches from G to the ordinate (D90) The point illustrates the value of √t90 The value of T corresponds to U = 90% is 0.848 in the case of vertical drain; 0.288 in the case of radial drainage to periphery, equal strain loading

Step 5:

Thus

2 90

0.848 dv

Hc

t

 

2 90 90

r CD

T dc

t

2 ( )

90

0.288 e

r PD

dc

t

20

Figure 2.10: Theoretical curve linkage square-root time factor to degree of

consolidation for vertical drainage (Taylor, 1942)

Robinson and Allam (Robinson & Allam, 1998) suggested a non-graphical matching method for interpreting the time corresponding compression data The settlement (S) collateral t is expressed as

23

Figure 2.12: (a) Theoretical Ur-log Tr curve for n = 5; (b) (dUr/d log Tr)-log Tr plot

showing the inflection point (Sridhar & Robinson, 2011)

24

2.4 Falling Head Permeability Test

Figure 2.14 shows a schematic drawing of a falling head test setup For practical engineering purposes, the coefficient of permeability of clay is often depicted from one dimensional incremental loading oedometer compression tests (IL tests) The vertical coefficient of consolidation cv is obtained from the vertical compression modulus Mv and the vertical hydraulic conductivity kv (Larsson and Sa¨llfors, 1986):

25

However, in projects using prefabricated vertical drains (PVDs), consolidation is mainly carried out by the horizontal flow through the soil towards the drains, so it is preferable to conduct tests allowing for evaluation of horizontal coefficient of permeability kr and the horizontal coefficient of consolidation cr Figure 2.15 described method for trimming horizontal soil specimen to conduct permeability test In other expression, cr is defined as a function of Mr and kr:

Vertical trimming for determining

vertical coefficient of permeability

Horizontal trimming for determining horizontal coefficient of permeability Figure 2.14: Principal sketch of horizontal and vertical trimming of samples from

determining vertical and horizontal coefficient of permeability

Natural soils are usually anisotropic in which the hydraulic conductivity in horizontal direction (kh) is often larger than that in vertical direction (kv) This characteristic is due

to the fact that soils are deposited in layers Table 2.4 shows typical ratios of kh/kv from some natural soil types The hydraulic conductivity (k) of any given soil is function of void ratio, grain size distribution, viscosity of water, and in-situ temperature In cases of

27

Figure 2.15: Overview of the cone penetration test per ASTM D 5778 procedures

(P.W Mayne, 2007) 2.5.2 Pore-water Dissipation Tests

Dissipation testing monitors pore water pressures as they dissipate with time A displacement device such as a cone penetrometer evaluates the appearance of additional pore water pressures (Δu) locally around the head of probe In clean sands, the Δu will decay rapidly because of the high hydraulic conductivity of sands, whereas in clays and silts of low hydraulic conductivity the measured Δu will take a noticeable time to equilibrate The static pore-water will eventually record to u0 Thus, the obtained porewater pressures (um) are a combination of transient and hydrostatic pressures, such that:

full-0 m

28

During the permanent stop, the rate at which Δu declines with time It can be monitored and used to depict the coefficient of consolidation and permeability of the soil media Dissipation readings are regularly plotted on log scales; therefore, in clays with low hydraulic conductivity it becomes impractical to wait for full equilibrium that corresponds to Δu = 0 and um = u0 A standard of practice is to record the time to achieve 50% dissipation, designated t50

R h

T a Ic

t

where t = corresponding measured time during dissipation (usually taken at 50% equalization), T* = modified time factor, IR = G/su = rigidity index soil and a = probe radius

The strain path solutions (Teh, 1991) are described in Figure 2.18(a) and (b) for both midface and shoulder type elements in the case of monotonic dissipation response, respectively

For clays, the rigidity index (IR) is the ratio of shear modulus (G) and shear strength (su) and may be calculated from different means including: (a) measured triaxial stress-strain curve, (b) measured pressuremeter tests, and (c) empirical correlation One correlation based on the index: