evaluation of consolidation parameters of cohesive soils

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LSU Master's Theses Graduate School

2007

Evaluation of consolidation parameters of cohesivesoils using PCPT methodRohit Raj PantLouisiana State University and Agricultural and Mechanical College, [email protected]

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EVALUATION OF CONSOLIDATION PARAMETERS OF COHESIVE SOILS USING PCPT METHOD

A Thesis

Submitted to the Graduate Faculty of the Louisiana State University and

Agricultural and Mechanical College in partial fulfillment of the

requirements for the degree of Master of Science in Civil Engineering

in

The Department of Civil and Environmental Engineering

by Rohit Raj Pant

B.E., Regional Engineering College-Rourkela, 2002 August 2007

ii

DEDICATION

To

My grandparents

My parents

My family

LTRC

and

My Alma Mater

iii

ACKNOWLEDGEMENTS

I would like to acknowledge the support and guidance I received from my advisors Dr.

Murad Abu-Farsakh and Dr. Khalid A. Alshibli throughout this study. I would especially like

to thank Dr. Abu-Farsakh for the financial support during my graduate studies. He has been a

great teacher, guide and a mentor for me and I appreciate all his helps. I would like to express

my gratitude to my family for all their blessings, love and support.

I am also grateful to Dr. Radhey Sharma and Dr. Gouping Zhang for being in my

advisory committee; their cooperation and guidance has been invaluable. I would like to

thank fellow students and staffs working at Louisiana Transportation Research Centre,

especially Gavin Gautreau, Melba Bounds, Paul Brady, Bill Tierny, Auron Austin and Dr.

Xion Zhang for their help during innumerable field trips. Sincere thanks to Pallavi Bhandari

who helped to code and design the settlement program.

Finally, I would like to thank all my friends and faculty at Louisiana State University

who have made my stay pleasant and successful.

iv

TABLE OF CONTENTS

DEDICATION.……………….………………………………..……………….………….…ii ACKNOWLEDGEMENTS……………………...…………………………….……………iii LIST OF TABLES..…………………………….….……………………….………………vii LIST OF FIGURES.…………………………….……....………………….…………...…viii ABSTRACT ….………….……….........................……………….………………………..xiv CHAPTER 1 INTRODUCTION............................................................................................ 1

1.1 Introduction to Problem .................................................................................. 1 1.2 Scope and Objectives of the Thesis................................................................. 3

1.2.1 Analytical Study of Existing Correlations ................................................. 4 1.2.2 Exploring New Correlation Models ........................................................... 5 1.2.3 Verification of Existing and Proposed models .......................................... 5 1.2.4 Back Calculation of in situ Consolidation Parameters Using

Observational Method ................................................................................. 5 1.3 Thesis Outline ................................................................................................... 6

CHAPTER 2 LITERATURE REVIEW ............................................................................... 7 2.1 Analysis of Settlement: Basic Principle .......................................................... 7

2.1.1 Magnitude of Total Settlement ................................................................... 7 2.1.2 Time Rate of Consolidation ....................................................................... 10

2.2 Soil Profiling and Estimation of Soil Properties ......................................... 11 2.3 Cone Penetrometer and Piezocones ............................................................. 12 2.4 Interpretation of cone penetration measurement ....................................... 13

2.4.1 Cone tip resistance ..................................................................................... 13 2.4.2 Sleeve Friction ............................................................................................ 15 2.4.3 Pore pressure .............................................................................................. 15

2.5 Pore Water Pressure Correction for cq and sf .......................................... 16 2.6 Interpretation of PCPT Measurements ....................................................... 17 2.7 Consolidation Parameters of Cohesive Soil from PCPT measurement .... 18

2.7.1 Constrained Modulus, M........................................................................... 18 2.8 Preconsolidation Pressure and OCR ............................................................ 22

2.8.1 Models Based on Cone Tip Resistance ..................................................... 22 2.8.2 Models Based on pore pressure measurement ........................................ 25 2.8.3 Models Based on Cone Tip Resistance and Pore Pressure

Measurements ............................................................................................ 27 2.9 Coefficient of Consolidation .......................................................................... 31 2.10 Other Related Parameters ............................................................................ 37

2.10.1 Undrained Shear strength (Su) ................................................................. 37 2.10.2 Soil Rigidity Index...................................................................................... 38

CHAPTER 3 SOIL TESTING AND PIEZOCONE DATABASE .................................... 41 3.1 Methodology ................................................................................................... 41

3.1.1 Laboratory Tests ........................................................................................ 41 3.1.2 In situ Tests ................................................................................................. 42 3.1.3 Field Settlement Monitoring ..................................................................... 42

3.2 Description of the Sites .................................................................................. 46 3.2.1 Manwell Bridge, Evangeline Site .............................................................. 47

v

3.2.2 US 90 - La 88 Interchange Site - New-Iberia ........................................... 49 3.2.3 LA Peans Canal Bridge Site - Lafourche ................................................. 49 3.2.4 Pearl River Bridge Site .............................................................................. 49 3.2.5 East Airport Site ........................................................................................ 54 3.2.6 Flat River-Bossier Site ............................................................................... 54 3.2.7 Pavement Research Facility Site ............................................................... 57

3.3 Soil Classification Based on PCPT Data. ..................................................... 60 3.4 Verification Sites ............................................................................................ 63

3.4.1 Juban North Embankment ....................................................................... 63 3.4.2 Juban South Embankment ....................................................................... 69 3.4.3 LTRC test wall at PRF site ....................................................................... 75 3.4.4 John Darnell site ........................................................................................ 75 3.4.5 Louisiana Avenue site ................................................................................ 76

CHAPTER 4 STATISTICAL ANALYSIS ......................................................................... 79 4.1 Statistical Techniques .................................................................................... 79

4.1.1 Regression Analysis ................................................................................... 79 4.1.2 Indices for Model Assessment ................................................................... 80 4.1.3 Assumptions, Limitations, Practical Considerations .............................. 82

4.2 Statistical analysis for Constrained Modulus (M) ...................................... 82 4.2.1 Variables in the statistical analysis ........................................................... 82 4.2.2 Regression Modeling for Constrained Modulus (M) .............................. 85 4.2.3 Models in Terms of Cone Tip Resistance ................................................ 87 4.2.4 Models in Terms of Sleeve Friction .......................................................... 90 4.2.5 Relationship between Cone Tip Resistance (qt) and Compression Index

(Cc, Cr) ......................................................................................................... 90 4.3 Statistical Analysis for Overconsolidation Ratio (OCR) ............................ 92

4.3.1 Regression Modeling for OCR .................................................................. 95 4.3.2 OCR Models in Terms of Cone Tip Resistance and Sleeve Friction ..... 96 4.3.3 OCR Models in Terms of Pore Water Pressure Measurements ............ 98 4.3.4 OCR Models with Cone Tip, Sleeve Friction and Pore Pressure

Measurements ............................................................................................ 98 4.4 Regression Models for Coefficient of Consolidation ................................. 101 4.5 Regression Modeling for Undrained Shear Strength ............................... 107

CHAPTER 5 SETTLEMENT ANALYSIS AND VERIFICATION OF STATISTICAL MODLES ...................................................................................................... 109

5.1 Verification of Statistical Models ............................................................... 109 5.1.1 Constrained Modulus (M) ....................................................................... 109 5.1.2 Overconsolidation ratio (OCR) .............................................................. 112 5.1.3 Coefficient of consolidation (Cv) ............................................................. 115

5.2 Field Settlement Analysis and Back Calculation of Consolidation Parameters .................................................................................................... 116

5.2.1 Magnitude of Total Settlement ............................................................... 116 5.2.2 Time Rate of Consolidation Settlement ................................................. 118

5.3 Settlement Curves and Back Calculation of Consolidation Parameters for Juban Road I-12 Intersection sites ............................................................. 120

5.3.1 Comparison with Horizontal Inclinometer Measurements ................. 120 5.3.2 Comparison with Vertical Extensometer Measurements .................... 120

CHAPTER 6 SOFTWARE DEVELOPMENT ................................................................ 127 6.1 Introduction .................................................................................................. 127

vi

6.2 Startup Windows and Input Files .............................................................. 127 6.3 Project Information ..................................................................................... 128 6.4 Plot of PCPT Profile and Soil Classification ............................................. 129

6.4.1 Classify Soil .............................................................................................. 129 6.4.2 Soil Unit Weight ....................................................................................... 129 6.4.3 Soil Properties .......................................................................................... 129 6.4.4 Dissipation ................................................................................................ 130 6.4.5 Units .......................................................................................................... 130 6.4.6 Settlement ................................................................................................. 131 6.4.7 Summary of Input Parameters ............................................................... 131 6.4.8 Provision for Design of Surcharge Height and PVD Installation ........ 131

CHAPTER 7 CONCLUSION AND RECCOMENDATIONS ........................................ 134 7.1 Conclusions ................................................................................................... 134 7.2 Recommendations ........................................................................................ 135

REFERENCES ..................................................................................................................... 136 APPENDIX A ....................................................................................................................... 143 APPENDIX B ....................................................................................................................... 145 APPENDIX C ....................................................................................................................... 150 VITA ........................................................................................................................ 152

vii

LIST OF TABLES

Table 1.1: List of Soil Properties estimated using piezocone parameters ................................. 4

Table 2.1: Sanglerat’s αm coefficient ....................................................................................... 19

Table 2.2: Modified time factor T* for Houlsby and Teh (1986) ............................................ 34

Table 2.3: Evaluation summary of different PCPT methods for predicting cv. ....................... 37

Table 2.4:Typical values of friction angle .............................................................................. 39

Table 3.1: Summary of soil properties for the investigated sites…………………………….60

Table 3.2 :Summary of soil properties for Juban North Site ................................................... 69

Table 3.3 :Summary of soil properties for Juban South Embankment .................................... 75

Table 4.1: Regression Models for M ....................................................................................... 86

Table 4.2: Regression Models for OCR……………………………………………………...95

Table 4.3: Regression Models for cv ...................................................................................... 105

Table 4.4: Regression Models for Undrained Shear Strength ............................................... 107

Table 5.1: Summary of back calculated constrained Modulus (M). ...................................... 126

viii

LIST OF FIGURES

Figure 2.1: e versus σ curve for one dimensional oedometer consolidation test ..................... 9

Figure 2.2. Fugro Electric Peizocone Penetrometer (Abu-Farsakh, 2003). ............................. 13

Figure 2.3: Types of Piezocone ............................................................................................... 13

Figure 2.4: Component of the forces acting on sleeve ............................................................. 15

Figure 2.5: Effect of pore water pressure on cone tip resistance (qc) and sleeve friction (fs). . 17

Figure 2.6: Cc Versus qc .. ....................................................................................................... 20

Figure 2.7. Comparison of modulus (Mn) for Glava clay ....................................................... 21

Figure 2.8 Relationship between net cone resistance and Constrained Modulus, M .............. 21

Figure 2.9: Relationship between su/σ’vo, Ip and OCR ........................................................... 22

Figure 2.10: Normalized resistance versus OCR from compilation of world data ................. 24

Figure 2.11: ( )vocq σ− versus p'σ . ....................................................................................... 25

Figure 2.12 : Yield stress versus Δu1. ...................................................................................... 27

Figure 2.13: Pore Pressure ratio versus OCR for Louisiana Clays .......................................... 29

Figure 2.14: Bq versus OCR .................................................................................................... 29

Figure 2.15: Yield stress versus Effective cone resistance for world data ............................. 30

Figure 2.16: Graphical representation of type 1 and type II curves ....................................... 31

Figure 2.17: Time factor for Torstensson’s (1975, 1977) model. ............................................ 33

Figure 2.18. Dissipation curves at different location of a 60o cone penetrometer .................. 34

Figure 2.19. Interpretation of time factor (T) .......................................................................... 35

Figure 2.20. Calculating the gradient of initial linear section (m) ........................................... 35

Figure 2.21: Interpretation of dissipation test and rate factor according to method. ............... 36

Figure 3.1 RST digital horizontal inclinometer system. .......................................................... 43

Figure 3.2 : RST digital horizontal inclinometer probe ........................................................... 44

Figure 3.3: Magnetic Extensometer system ............................................................................. 45

Figure 3.4: Installation of settlement plates at ALF site .......................................................... 47

Figure 3.5. Soil boring profile for Manwell Bridge, Evangeline site. ..................................... 48

Figure 3.6: PCPT profile for Manwell Bridge, Evangeline site. ............................................. 48

Figure 3.7: Dissipation tests at Evangeline site ....................................................................... 49

Figure 3.8: Soil profile for New Iberia site at US 90 and La 88. ............................................. 50 Figure 3.9: PCPT profiles and soil classification at US 90–La 88 interchange ....................... 50

Figure 3.10: Dissipation tests at US 90 – La 88 interchange, New Iberia site ....................... 51

Figure 3.11: Soil profile for LA PEANS canal, Lafourche ..................................................... 51

Figure 3.12: PCPT profiles and soil classification for LA Peans canal Bridge, Lafourche . . 52

ix

Figure 3.13: Dissipation tests at LA Peans canal Bridge, Lafourche site ............................... 52

Figure 3.14: Soil profile for Pearl River site. ........................................................................... 53

Figure 3.15: PCPT profile for Pearl River site. ....................................................................... 53

Figure 3.16: Dissipation tests at Pearl River site. .................................................................... 54

Figure 3.17: Soil boring profile for East Airport site. .............................................................. 55

Figure 3.18: PCPT profiles and soil classification for East Airport site. ................................. 55

Figure 3.19: Dissipation tests at East Airport site. .................................................................. 56

Figure 3.20: Soil boring profile for Flat River site. ................................................................. 56

Figure 3.21: PCPT profiles and soil classification for Flat River site. .................................... 57

Figure 3.22: Soil boring profile for PRF site. .......................................................................... 58

Figure 3.23: PCPT profiles and soil classification for PRF site. ............................................. 58

Figure 3.24 : Dissipation tests at PRF site. .............................................................................. 59

Figure 3.25 Plasticity chart for USCS Classification at investigated sites. ............................. 59

Figure 3.26: Soil Classification chart per Shmertmann (1978) ............................................... 61

Figure 3.27 Soil Profile Chart as per Douglas and Olsen (1981) ............................................ 61

Figure 3.28 Classification Chart as per Robertson (1990) ....................................................... 62

Figure 3.29 Soil behavior type classification chart based on normalized PCPT data ............ 62

Figure 3.30 Soil behavior type classification chart based on normalized PCPT data ............. 63

Figure 3.31 Soil boring profile for Juban North Embankment site. ........................................ 64

Figure 3.32: PCPT profiles and soil classification for North Embankment site. ..................... 65

Figure 3.33: Dissipation tests at Juban North Embankment site. ............................................ 65

Figure 3.34: Oedometer test result for depth 0-1.5m ............................................................... 66

Figure 3.35: Oedometer test result for depth 1.5-3.0 ............................................................... 66

Figure 3.36: Oedometer test result for depth 3.0-4.6 m. .......................................................... 67



Figure 3.39: Oedometer test result for depth 11.28-12.2 m. .................................................... 68

Figure 3.40: Soil boring profile for Juban South Embankment site. ....................................... 70

Figure 3.41: PCPT profiles and soil classification for South Embankment site. ..................... 70

Figure 3.42: Dissipation tests at South Embankment site........................................................ 71

Figure 3.43: Oedometer test result for depth 0-1.5m ............................................................... 71





Figure 3.48: Oedometer test result for depth 9.1-10.67 m. ...................................................... 74

x

Figure 3.49: Oedometer test result for depth 10.67 -12.2 m. ................................................... 74

Figure 3.50: Plan and the elevation of LTRC wall at ALF site .............................................. 76

Figure 3.51 PCPT profile and soil classification at John Darnell site ..................................... 77

Figure 3.52 Dissipation curves at John Darnell site ................................................................ 77

Figure 3.53 :PCPT profile and soil classification profile at LA avenue site .......................... 78

Figure 3.54 Dissipation curves LA avenue site ....................................................................... 78

Figure 4.1: Simple linear relation between X and Y. .............................................................. 79

Figure 4.2: M versus qt. ............................................................................................................ 83

Figure 4.3: M versus fs. ........................................................................................................... 83

Figure 4.4: M versus u1 ............................................................................................................ 84

Figure 4.5: M versus u2 ............................................................................................................ 84

Figure 4.6: M versus σvo .......................................................................................................... 84

Figure 4.7:M versus Field Moisture Content ........................................................................... 84

Figure 4.8: M versus PI ............................................................................................................ 85

Figure 4.9: M versus Probability of CL-CH (Zhang and Tumay,2000) .................................. 85

Figure 4.10 Regression model for M versus qt ........................................................................ 88

Figure 4.11: Regression model for M versus (qt-σvo) ............................................................. 88

Figure 4.12: Measured versus Predicted M using relation ..................................................... 88

Figure 4.14: Measured versus Predicted M. ............................................................................ 89

Figure 4.18: Regression model for M versus √fs .................................................................... 90

Figure 4.19: Measured versus Predicted M. ............................................................................ 90

Figure 4.20: cc versus qt .......................................................................................................... 91

Figure 4.21: cr versus qt .......................................................................................................... 91

Figure 4.22: cr versus qt ( loading-unloading) ........................................................................ 91

Figure 4.23: CR versus qt ........................................................................................................ 91

Figure 4.24: CR versus qt ........................................................................................................ 92

Figure 4.25: qt/CR versus qt .................................................................................................... 92 Figure 4.26: OCR versus qt ...................................................................................................... 93

Figure 4.27: OCR versus fs ...................................................................................................... 93

Figure 4.28: OCR versus u1 ..................................................................................................... 93

Figure 4.29:OCR versus u2 ...................................................................................................... 93

Figure 4.30: OCR versus σvo .................................................................................................... 94

Figure 4.31: M versus Field Moisture Content ........................................................................ 94

Figure 4.32: OCR versus PI ..................................................................................................... 94

Figure 4.33: OCR versus Probability of CL-CH (Zhang and Tumay, 2000) ........................ 94

Figure 4.34: OCR versus (qt-σvo)/σ’vo ..................................................................................... 97

xi

Figure 4.35: OCR versus normalized total cone resistance [(qt+fs)/σνο]. ................................ 97

Figure 4.36: OCR versus normalized sleeve friction ............................................................... 97

Figure 4.37: Measured versus predicted OCR ......................................................................... 97

Figure 4.40: OCR versus (u1-u0) ............................................................................................. 99

Figure 4.41: OCR versus PPD. ................................................................................................ 99

Figure 4.42: Measured versus predicted OCR ......................................................................... 99

Figure 4.44: OCR versus (qt-u1)/σ’vo ..................................................................................... 100

Figure 4.45: OCR versus (qt+fs)/u0 ........................................................................................ 100

Figure 4.46 OCR versus Bq1 .................................................................................................. 100

Figure 4.47: OCR versus u1/qt ............................................................................................... 100

Figure 4.48: OCR versus u1/fs ............................................................................................... 101

Figure 4.49: OCR versus (u1-u0)/(qt-u0) ................................................................................. 101

Figure 4.50: Measured versus predicted OCR ...................................................................... 101

Figure 4.51: Measured versus predicted OCR ................................................................... 101

Figure 4.52: cv versus t50 ........................................................................................................ 102

Figure 4.53: cv versus u50 ....................................................................................................... 102

Figure 4.54: cv versus ui ......................................................................................................... 103

Figure 4.55: cv versus (u1- u0) ................................................................................................ 103

Figure 4.56: cv versus (u2- u0) ................................................................................................ 103

Figure 4.57: : cv versus √qt .................................................................................................... 103

Figure 4.58: cv versus FR ...................................................................................................... 104

Figure 4.59: cv versus t50/ ui ................................................................................................... 104

Figure 4.60: cv versus (√qt/ t50) .............................................................................................. 104

Figure 4.61: cv versus 1/( t50√FR) .......................................................................................... 104

Figure 4.62: cv versus ui/( t50√FR) ......................................................................................... 106

Figure 4.63: Measured versus predicted cv for Teh and Houlsby (1988) method. ................ 106

Figure 4.64: Measured versus predicted cv for Robertson et al. (1992) method. .................. 106

Figure 4.65: Comparision of cv predicted using proposed correlation with cv predicted using Teh and Houlsby (1988) method. .......................................................................................... 106

Figure 4.66: Su versus (qt-σvo) ............................................................................................... 108

Figure 4.67: Su versus (qt-u2) ................................................................................................. 108

Figure 4.68: Su versus (qt+ fs-σvo) .......................................................................................... 108

Figure 4.69: Su versus fs ......................................................................................................... 108

Figure 5.1: Measured versus Predicted M for Juban Road .................................................... 109

Figure 5.3: Measured versus Predicted M for Juban Road ................................................... 110


xii

Figure 5.5: Measured versus Predicted M for Juban Road ................................................... 110


Figure 5.7: PCPT predicted versus laboratory measured profile of M (Juban North) ........... 111

Figure 5.8: : PCPT predicted versus laboratory measured profile of M (Juban North) ......... 111

Figure 5.9: PCPT predicted versus laboratory measured profile of M (Juban South) ........... 111

Figure 5.10: PCPT predicted versus laboratory measured profile of M (Juban South) ......... 111

Figure 5.11 : Measured versus predicted OCR for Juban Road site ...................................... 112

Figure 5.12: Measured versus predicted OCR for Juban Road site ...................................... 112

Figure 5.13: Measured versus predicted OCR for Juban Road site ....................................... 113

Figure 5.14: Measured versus predicted OCR for Juban Road site .................................. 113

Figure 5.15: Measured versus predicted OCR for Juban Road site ....................................... 113

Figure 5.16: Measured versus predicted OCR for Juban Road site ................................. 113

Figure 5.17: OCR profile with depth (Juban North) .............................................................. 114

Figure 5.18: : OCR profile with depth (Juban North) ............................................................ 114

Figure 5.19: OCR profile with depth (Juban South) .............................................................. 114

Figure 5.20: OCR profile with depth (Juban South) .............................................................. 114

Figure 5.21: Measured versus predicted cv for Juban Road Site .......................................... 115

Figure 5.22: : Measured versus predicted cv for Juban Road Site ........................................ 115

Figure 5.23:Measured versus predicted cv for Juban Road Site ......................................... 115

Figure 5.24: Measured versus predicted cv using Teh and Houlsby (1986) for JubanRoad Site ......................................................................................................................................... 115

Figure 5.25 Elastic solution for the incremental stress under embankment loading (Poulos and Davis, 1973) ........................................................................................................................... 117

Figure 5.26: Layered soil with different permeability and consolidation characteristics ...... 119

Figure 5.27: Comparison of predicted settlement profile with field measurement (North Embankment). ........................................................................................................................ 121 Figure 5.28: Comparison of predicted settlement profile with field measurement ............... 122

Figure 5.29: a) Lift schedule b) Rate of settlement for Juban Road North Embankment. .... 123

Figure 5.30: a) Lift schedule b) Rate of settlement for Juban South Embankment. .............. 124

Figure 5.31: Comparison of PCPT correlations with laboratory and back calculated constrained Modulus (M) (Juban South Embankment) ......................................................... 125

Figure 5.32: Comparison of PCPT correlations with laboratory and back calculated constrained Cv (Juban South Embankment) .......................................................................... 125

Figure 6.1: Embankment settlement program. ....................................................................... 127

Figure 6.2 : Opening window with navigation links and input parameters. .......................... 128

Figure 6.3 Project information window ................................................................................. 128

Figure 6.4 : Plot of PCPT profile and soil classification at the test site. ............................... 129

xiii

Figure 6.5: Soil unit weight input window. ........................................................................... 130

Figure 6.6: Normalized dissipation curves for different depths. ........................................... 130

Figure 6.7: Input window for embankment dimension, fill characteristics and PVD design. .................................................................................................................................... 132

Figure 6.8: Progress of settlement profile along the width of embankment with time. ......... 132

Figure 6.9: Comparison of time rate of settlement curve at the centre for with and with out surcharge condition. ............................................................................................................... 133

Figure 6.10: Summary table for design parameters used in calculation. ............................... 133

xiv

ABSTRACT

The piezocone penetration test (PCPT) has emerged as most widely used in situ method for

obtaining soil profile as well as physical properties. The PCPT method provides three

independent and nearby continuous measurements with the depth; they are: tip stress (qc),

sleeve friction (fs) and pore pressure (u1, u2, or u3). These measurements have been

successfully used to correlate various soil properties such as undrained shear strength, unit

weight and consolidation parameters. This study presents the evaluation of the PCPT

interpretation methods for their capability to reasonably estimate the consolidation

parameters namely constrained modulus, overconsolidation ratio and vertical coefficient of

consolidation (cv) of cohesive soils in Louisiana. Statistical analyses were conducted to

evaluate current interpretation methods and to explore new correlations. Test data collected

previously from seven sites in Louisiana were used for this. Settlement analysis and

monitoring results from five different project sites were used for field verification of PCPT

correlations. User friendly Visual Basic program was developed to facilitate the analyses of

PCPT data and estimate of magnitude and time rate of settlement under the embankment

loading.

1

CHAPTER 1

1 INTRODUCTION

1.1 Introduction to Problem

Compressibility of clay has always been the subject of intense research among the

researchers and engineers. In fact the settlement of the foundation and embankment under the

load is one of the challenges of the structural design; as such immense effort has been put to

predict the settlement, its prevention or at least its restriction to tolerable value.

Terzaghi in his paper “settlement analysis- the backbone of Foundation Research”,

that was presented in World Engineering Conference held in Tokyo in 1929, outlined the

settlement analysis as five specific and successive steps:

• Condense the results of the test borings to a geological profile,

• Determine the physical properties for a few typical samples,

• Reduce the physical conditions of the problem to terms simple enough to permit

mathematical treatment,

• Estimate the settlement on the theoretical conceptions of the case and the results of the

soil tests,

• Compare the results with what actually happened and make a careful investigation of the

causes and the difference between theory and practice.

The First two steps are the initial but the significant steps for settlement analysis and

equally difficult to perfect. First major obstacle is that soil deposits are hardly “homogenous”

in nature; heterogeneity is more common trait of the soil layer in sites. As such accurate

profiling of the soil and determination of representative properties is practically impossible.

No matter how rigorous settlement analysis is, accuracy will always be corrupted by the

“missed” information such as pocket of the compressible clay between the silt or sand lenses

untracked during boring or samplings. Peck (1994) thus emphasized on more use of sounding

techniques such as cone penetrometer to identify the compressible layers. He stated “it is

abuse of settlement analysis to idealize the subsurface conditions on the basis of too little

information.”

Another setback in the accurate estimation of field settlement is conventional practice

of evaluation of mechanical/ chemical properties of soil using laboratory method. Soil

samples obtained from the boreholes along different depths and different sections of the site

under consideration are tested in laboratory in order to predict its behavior under similar field

2

condition. This method is thus very often extrapolation or interpolation based on parameters

obtained in controlled environment which may or may not be exact simulation of field state.

In addition, conventional laboratory tests such as one dimensional Oedometer test or triaxial

are quite time consuming and expensive to run, thus, putting the limitations on the number of

tests to be performed. This, in turn, has significant impact on the reliability and accuracy of

the predicted settlement.

In situ testing method such as cone penetration tests (CPT), standard penetration test

(SPT), dilatometer tests, pressure meter tests etc., on the other hand, uses the techniques and

instruments deployed directly in the field. This allows investigation of soils in their natural

intact state and stress condition thus giving more accurate quantification of soil properties

such as shear strength, deformability and drainage characteristics. Mitchell et al. (1978)

identified the following reasons for increased use of field testing:

• To determine properties of the soil that cannot be easily sampled in the undisturbed state

such as sea bed sediments, organic soil deposits, sands, etc.

• To avoid some of the difficulties and uncertainties in laboratory testing such as sample

disturbance, proper simulation of in situ stresses, temperature, chemical and biological

environments.

• To test a volume of soil larger than conveniently tested in laboratory.

• To increase the cost effectiveness of an exploration and testing program.

Another approach is the observational method in which actual stress and the

deformation are monitored in the field and consolidation parameters are back-calculated

using appropriate theoretical model. Often large scale experimental models are constructed in

the field and back calculated parameters are used to evaluate the performance of prototypes.

Construction of such model is quite expensive and monitoring, analysis and interpretation of

the field data is rigorous and time consuming. As such this approach is used for projects of

high importance and demanding high accuracy. Moreover this approach requires laboratory

or in situ measurement of the soil properties at certain stages in order to assess/ verify

boundary conditions establish theoretical framework. However, observational methods

provide excellent tool for comparison of existing laboratory or in situ techniques for

assessment of soil properties.

It is evident from above discussion that in situ testing can provide both reliable and

accurate soil properties and expedites the exploration process in the field. Various

experimental and commercial devices are available for in situ testing. Choice of particular

3

device depends on the scope of analysis procedure and nature of soil properties under

consideration. In the last two decades, Piezocone Penetration test (PCPT) has emerged as

most widely used in situ method for obtaining soil profile as well as physical properties. The

PCPT method provides three independent and nearby continuous measurements with the

depth; they are: tip stress (qc), sleeve friction (fs) and pore pressure (u1, u2, or u3). These

measurements have been successfully used to correlate various soil properties such as

undrained shear strength, unit weight and stress histories (Table 1.1). Significant

developments have been made both in theory and practice for correlating PCPT

measurements to that of consolidation characteristics of soil deposit in different part of the

globe. This is a major breakthrough as this method enables the repeatable and reliable

assessment of in situ soil profile and consolidation parameters such as constrained Modulus,

OCR and cv from single testing. As the PCPT results are repeatable, reliable, economical and

fast, large number of test can be carried out with convenience for each site enabling better

understanding of soil profile and closer estimate of in situ soil properties, which would, in

turn render more confidence in the settlement analysis and predicted behavior.

1.2 Scope and Objectives of the Thesis

The main focus of this thesis is on estimating consolidation parameters of cohesive soil

deposits in Louisiana from PCPT method predict the total and the time rate of embankment

settlement. A Preliminary study by Abu-Farsakh (2003) found good correlation between the

laboratory estimated and PCPT predicted soil parameters. In this study, several commonly

used correlation models were evaluated with that of laboratory assessed deformation

parameters. Simple correlations were also proposed using cone tip resistance (qt) for the

prediction of constrained modulus (M) as well as overconsolidation ratio (OCR) in Louisiana

soil. However, this study is mainly focused at the evaluating existing models given by

different researcher and comparing them with laboratory parameters. The study also proposed

direct linear correlation for estimating M and OCR. The initial study established the

capability of PCPT methods in assessing deformation parameters of cohesive soils in

Louisiana.

It is a well established fact that no unique relationship exist and only regional

correlations are valid when estimating soil parameters from PCPT (Demers and Leroueil,

2002). As such local relations have to be explored in order to obtain more confidence in the

prediction. The Scope of Abu-Farsakh (2003) study did not cover the exploration of all

possible correlations e.g. non linear and indirect correlation (using PCPT parameters and soil

4

properties) and assessment of regional constants for various empirical relations. This study is

thus a continuation of the work carried out by Abu-Farsakh (2003) and covers the exploration

of new relations for interpretation of PCPT results. My thesis will focus on following areas:

Table 1.1: List of Soil Properties estimated using piezocone parameters

SN Parameter Reference

1 Soil Classification

Begemann (1965), Sanglerat et al. (1974), Schmertmann

(1978), Douglas and Olsen(1981) Robertson (1990),

Senneset & Janbu (1985) and others.

2 In situ Stress State (Ko) Masood and Mitchell (1993); Brown and Mayne (1993) Mayne and Kulhawy (2002)

3 Effective Friction angle )'(φ

Senneset and Janbu (1985); Sandven (1990)

4 Constrained Modulus (M) Buisman (1940); Sanglerat (1972); Khulway and Mayne

(1990), Abu-Farsakh (2003, 2007) and others.

5 Shear Modulus (Gmax) Mayne and Rix (1993)

6 Stress History ),'( OCRpσ Baligh et al. (1980), Senneset et al. (1982), Konrad and

Law (1987), Sully et al. (1988), Chen and Mayne (1994),

Abu-Farsakh (2003) and others.

7 Sensitivity (St ) Robertson and Campenella (1988)

8 Undrained Strength (Su ) Aas et al. (1986); Konrad and Law (1987)

9 Hydraulic Conductivity )(k Robertson et al. (1992a)

10 Coefficient of

Consolidation (cv )

Houlsby and Teh (1988), Robertson et al. (1992a)

Senneset et al. (1982), Baligh et al. (1981), Torstensson

et al. (1975) , Abu- Farsakh (2003, 2007) and others

11 Unit weight )( tγ Larson and Mulabdic (1993), Robertson et al. (1986)

12 Effective cohesion

intercept (c’)

Senneset et al. ( 1989)

1.2.1 Analytical Study of Existing Correlations

Different correlation models proposed in literature are found to give varied results for

different soil deposits. The effectiveness of the correlation equation needs to be locally

identified and constants involved have to be calibrated based on local experience. As such

this study will include the following

5

• Compare the results from existing proposed relations to that of laboratory and field

measurements.

• Conduct simple and multiple regression analysis to determine the best correlations

between PCPT and consolidation parameters (direct approach).

• Refine existing models by introducing other influencing mechanical characteristics of soil

such as Plasticity index, natural water content, or clay content (indirect approach).

1.2.2 Exploring New Correlation Models • Previously collected PCPT and dissipation data will be used to conduct linear and non

linear regression analysis and new relations (direct and indirect) will be explored to

evaluate different consolidation parameters (M, OCR, and cv).

• Formulation of relation involving parameters that can be assessed directly from PCPT,

such as qt , fs, and um (u1 or u2) or combination of three (Direct Models).

• Explore correlation models using sleeve friction, fs. Commonly used correlation models

are based on cone tip stress, qc and/ or um (u1 or u2) measurements. However, preliminary

analysis in this study has identified other models formulated using fs giving good

prediction.

• Exploring effect of other soil properties such as moisture content, Atterberg limits,

rigidity index, overburden stress etc, and formulate refined relationships including

parameters supplemented from laboratory or borehole testing (Indirect Models).

• Explore possibilities of evaluation cc or cs using PCPT results.

• Explore possibilities of evaluation of Ir directly from PCPT results.

1.2.3 Verification of Existing and Proposed models

Consolidation parameters predicted from PCPT based correlation will be compared with

laboratory estimated values as well as field measurements. Total settlement as well as time

rate of settlement predicted from both laboratory and PCPT method will be compared to

measurements of actual field settlement for different sites including Juban Road I-12

intersection site.

1.2.4 Back Calculation of in situ Consolidation Parameters Using Observational Method

Back-calculated consolidation parameters from settlement monitoring instruments that

includes horizontal inclinometer and vertical extensometer in Juban Road I-12 intersection

site will be compared to that of laboratory and PCPT prediction methods.

6

1.3 Thesis Outline

This thesis is divided into seven chapters. First chapter gives the basic introduction to the

research background, outlines the scope and objectives of the research and structure of this

thesis. Brief introduction of the basic principle of analysis of settlement and Piezocone

penetration test are given in the Second Chapter. Chapter Two also presents the detail review

of the previous research that was done to determine consolidation parameters using PCPT.

Description of all the test sites and the soil properties are presented in Chapter Three. Chapter

Four gives the background for the statistical analysis of data. Results of the regression

analysis to refine existing correlation and to explore new models are discussed in details.

Chapter Five compares the consolidation parameters obtained using oedometer test and PCPT

predictions. Analysis of the settlement monitoring at the Juban Road I-12 intersection site and

back calculation of the consolidation parameters are also discussed. Development of the

software application to evaluate consolidation parameters using PCPT and determining field

settlement underneath an embankment loading is discussed in Chapter Six. Chapter Seven

summarizes the conclusions of the thesis with remarks and recommendations on practice of

PCPT methods for evaluation of consolidation parameters.

7

CHAPTER 2

2 LITERATURE REVIEW

A brief review of classical method of settlement prediction is presented in this chapter. Also a

brief introduction of the electric piezocone device, parameters obtained from piezocone and

various factors affecting piezocone measurements are given. Detail review of estimation of

consolidation parameters of cohesive soil using PCPT methods and the existing correlations

obtained from past experience in this field are also presented in this chapter.

2.1 Analysis of Settlement: Basic Principle

2.1.1 Magnitude of Total Settlement

If the soil skeleton and the pore fluids in the soil pore space assumed incompressible, the total

volume change in the soil due to load will occur due to squeezing of pore fluid out of soil

skeleton known as consolidation. As squeezing proceeds, soil grains rearrange themselves

into a more stable and denser configuration and decrease in volume and surface settlements

results (Holtz and Kovac, 1981). Since the change of the state of stress produces settlement,

the first step in the analysis is to obtain the vertical stress profile along the soil layers. The net

addition/ change in load on the soil element due external cause such as surface loading can be

estimated using elastic approach (Poulos and Davis, 1974) or by using plastic approach

(Janbu 1967). Determination of stresses in the underlying layers beneath foundation or

embankment is discussed in Appendix A.

Infinitesimal small strain,ε for a layer dz at any arbitrary depth z below foundation

level, with effective overburden pressure σvo’ and subjected to additional stress Δσv gives the

following incremental settlement, ds

dzds ε= [1]

The total compression of the entire soil layer of thickness H is thus the summation of

the compression of each individual layer and expressed as

∫=H

dz0

s ε [2]

This strain is generally dependent on both σvo and Δσv and the relation between

vertical strain and stress has to be determined for above equation. Conventionally, such

stress-strain relation is obtained from one dimensional consolidation test in Oedometer or

triaxial test, for which Terzaghi’s classical consolidation equation holds good, that is,

dzm u vds Δ= or u vΔ= mvε [3]

8

where 'u vσΔ=Δ

Coefficient of volume change mv is thus the slope of compression curve for 1-D

compression test and defined as

v

v

dd

m'v σ

ε= [4]

ov e

eHH

+Δ

=Δ

=1

ε [5]

in which εv is vertical compression or strain, H is height of the soil specimen and eo is

the initial void ratio. Reciprocal of the mv is termed as constrained modulus, M, or oedometric

modulus, D. As strain of the soil layer is function of both soil deposit as well as stress, shape

of the compression curve and thus interpretation of stress-strain relationship also depends on

the presentation of the data.

For normally consolidated soils, Terzaghi proposed that e is related to 'voσ by

empirical formula

vo

voco Cee

''

logσ

σσ Δ+−= [6]

where Cc is compression index and is defined as slope of the straight portion of

consolidation curve e versus log v'σ (Figure 2.1), e0 is initial void ratio and 'voσ is average

effective overburden pressure on the middle of that layer. This leads to

vo

voc

oov C

eee

HAHA

''

log1

11.

.σ

σσε

Δ++

=+Δ

=Δ

= [7]

where A is the cross sectional area of the soil specimen.

Total settlement of normally consolidated soils can also be evaluated as

vo

voc

o

Ce

H'

'log

1 σσσ

δδΔ+

+Σ=ΣΔ= [8]

The above relation is also known as Terzaghi- Buisman relation.Other indices such as

coefficient of compressibility, av, constant of compressibility C or compression ratio Cce are

also frequently used and discussed elsewhere (Holtz and Kovacs, 1981). Janbu (1967)

advocated for the global use of tangent constrained modulus or deformation modulus such

that

εσ

ddM = [9]

9

a

aa P

mPM−

⎥⎦

⎤⎢⎣

⎡=

1'σ [10]

0.1 1.0 10.0 100.0

Vertical effective stress (TSF)

0.6

0.7

0.8

0.9

Void

Rat

io

(Pc= 1.05 TSF)

Cc= 0.158

Cs= 0.054

Cr= 0.05

Figure 2.1: e versus σ curve for one dimensional oedometer consolidation test

where m is modulus number, a is stress exponent, σ’ vertical stress and Pa is reference

pressure which equals to 1 atmosphere, introduced solely for obtaining dimensionally correct

expression. The compression of the soil layer is then be calculated as

MHvσ

δδΔ

== ∑ [11]

where M is the constrained modulus for the soil specimen for the stress range of

vo'σ to vvo σσ Δ+' , determined as the reciprocal of mv estimated from one dimensional

consolidation tests , as discussed earlier. Several correlations have been proposed to relate the

laboratory measured M to the cone tip resistance (qc) and will be discussed in the subsequent

sections.

From the above discussion it is evident that constrained Modulus, M, defines the soil

resistance against deformation (volumetric). However, value of M depends both on states of

relative stress as well as on the magnitude of stress in primary direction where stress-strain

measurements are made. Therefore, careful considerations have to be made while simulating

stress condition in the field.

Another significant aspect in the soil deformation analysis is the “memory’ of the soil

for the stress- strain history encountered in the past (Casagrande, 1936). It is evident from

consolidation test on undisturbed soil samples that slope of the compression curve is

10

characteristically different for two portion, one for the stress state of the soil which is simply

undergoing reconsolidation and the other which portion where soil is under going virgin

compression that is deformation due to stress beyond “maximum stress” level ever

encountered by soil. This maximum past pressure, known as preconsolidation pressure, σ’p, is

usually determined from the consolidation curve using Casagrande method (Casagrande,

1936) or work energy method (Becker et al. 1987). The Stress history of the soil deposit in

the field can be expressed by overconsolidation ratio, OCR, as

vo

pOCR''

σσ

= [12]

In which σ’p is preconsolidation pressure and σvo’ is the current effective overburden

pressure in the field.

2.1.2 Time Rate of Consolidation

As discussed in the previous section, consolidation of the clay results from the squeezing of

the pore fluid and gradual increase in effective stress, which readily leads to the fact that

settlement, depends both on stress as well as time. Thus

)',( vtf σε =

From the solution of Terzaghi’s classical differential equation

2

2

z

uvC

tu

∂

∂=

∂∂ [13]

u= f(t, σ) is determined using suitable boundary condition which in turn leads to

degree of consolidation Uz as

'''

σσσ

Δ−

=−

= t

i

tiz u

uuU [14]

and zult Us .s t = [15]

where ts is the settlement at any time t and ults is total settlement. From above

discussion, it is found that the coefficient of consolidation vwv mkC γ= is another

characteristic consolidation parameter governing the rate of settlement in the field at

particular time period. Similar differential equation can be formulated to simulate the rate of

consolidation due to radial flow

⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+∂∂

=∂∂

tu

rzuC

tu

r1

2

2

[16]

11

where Cr is coefficient of consolidation in radial direction, r is the length of radial

drainage. The contribution of any vertical flow can be incorporated by inclusion of equation

[13] and expressed as:

2

212

2

z

uvC

tu

rzuC

tu

r∂

∂+⎟⎟

⎠

⎞⎜⎜⎝

⎛∂∂

+∂∂

=∂∂ [17]

If Ur is the average degree of consolidation of a layer due to plane radial drainage at a

given time t and Uz is the average degree of consolidation of a layer due to vertical drainage

at same time then degree of consolidation U due to combine linear and radial drainage can be

determined by following equation,

( )( )vr UUU −−= 11 [18]

The discussion above presents a brief outline for the consolidation process and

identifies the parameters essential for estimating consolidation settlement. Next step in the

settlement analysis is the assessment of correct theoretical model that would represent the

stress-strain relation in the field and governing boundary conditions. The quantitative

estimate of the consolidation parameter has to be done in order to simulate field condition

and the following sections discuss the common practices and principle of such measurements

related to PCPT.

2.2 Soil Profiling and Estimation of Soil Properties

Any analysis work is preceded by the physical characterization of soil as well estimation of

mechanical/ chemical properties. In practice, the compressible layer is divided into sub layers

of heights h1, h2, h3…hn. For each layer, the average representative value of effective

overburden stress, the induced stress increment due to external effect and compressibility

constants are determined. If the underlain layer is a homogenous soil deposit, acquiring the

desired sample from the field and conducting suitable tests in the laboratory can fairly predict

its settlement behavior. However, for non- homogenous soil deposits such as containing

erratic or lenticular deposits of sand, silt or soft clay, the conventional method of soil

profiling with limited number of boreholes may often miss the vital information for weak

pockets of compressible layers. In such cases, piezocone penetration tests (PCPT) can

provide robust and reliable information not only about the soil profile, but can also be used to

extrapolate or interpolate laboratory estimated soil parameters. Further, if suitably calibrated,

the information from the penetrometer measurements itself can be adequate to estimate soil

properties such as physical state, strength parameters as well as deformation characteristic.

12

The cone penetrometer has been used to identify soil type, stratigraphy, and

variability for more than 60 years. It has evolved from an original mechanical cone to an

electric cone and a piezocone that are currently used for in situ testing (see Figure 2.3.1).

Electric cones are capable of continuously measuring tip resistance and skin resistance. When

equipped with piezometric elements, they can measure pore pressure at different locations

depending on location of filter element. The Following sections of this chapter briefly discuss

the piezocone penetration device and procedure in general.

2.3 Cone Penetrometer and Piezocones

The testing equipment consists of a cone attached to end of pushing rods, a thrust mechanism,

a reaction system and data acquisition system. Standard electronic cones widely used today

refers to cones with an apex angle of 60o, cone diameter of 35.7 mm ( 10 cm2 cross sectional

area) and 150 cm2 friction sleeve located above the cone (Figure 2.2) . ASTM also allows for

the cone with 15 cm2 cross sectional area. The total force acting on the cone, Qc, divided by

the projected area gives the cone tip resistance, qc. The total force acting on the friction sleeve

Fs, divided by the surface area of the friction sleeve As produces sleeve friction, fs. The

measurement of cone resistance, qc, and sleeve friction fs, are usually derived from

measurements on the electrical strain gauge load cells. Although the design of the load cells

and data acquisition system differs from one manufacturer to another, the three main design

types are common (Lune et. al 1997)

• Two independent compressive load cells measuring qc and fs

• Compressive load cell for measuring qc and sleeve friction, fs, is usually measured by a

load cell in tension.

• Subtraction type cone in which sleeve friction load cell, in compression, measures

summation of both cone resistance and sleeve friction, the sleeve friction being obtained

from the difference of this sum total load and measurement from another compressive

load cell recording cone tip resistance only.

In piezocone penetrometer, pore pressure transducers are introduced which allows the

measurement of pore water pressure during penetration. The position of the filter for

measurement of pore pressure is not standardized but filter position just behind the cone is

preferred. This allows for correction of cone resistance for pore water pressure effects

(section 2.6). Also filter at this position are less prone to damage and measurements are less

affected by factors such as element compressibility, test procedures (Lune et al. 1997). Other

locations are on the cone tip (u1) or behind the friction sleeve (u3) as shown in Figure 2.3.

13

2.4 Interpretation of cone penetration measurement

2.4.1 Cone tip resistance

In order to correlate cone tip resistance to soil properties, analogy of penetrometer to

that of pile loaded to ultimate bearing pressure is made. Using Terzaghi’s formula for

ultimate bearing pressure,

DNqBNcNq cul γγ γ ++=21 [19]

where B= depth of footing, D= depth of embedment of footing γ= density of soil, Nγ,

Nq, Nc are dimensionless bearing capacity factor.

Figure 2.2. Fugro Electric Peizocone Penetrometer (Abu-Farsakh, 2003).

Figure 2.3: (bottom to top): Miniature 4 cm2 Electric Cone; 10 cm2 Type 2 Piezocone (shoulder element); Type 1 (mid-face) piezocone; Type 2 Seismic, Hogentogler Dual Type1

& 2 Seismic; 15 cm2 Fugro Triple-Element Cone. (Mayne et al., 1995)

14

In case of penetrometer, the surface term γγBN21 is negligible and thus cone tip

resistance is a function of angle of internal friction and cohesion, that is,

),( cfqc φ= Therefore the following relationships exist:

DNqqc γ= for cohesionless soil [20]

cc cNDq += γ for cohesive soil. [21]

Alternatively, the cone tip resistance in cohesive soil is expressed in terms of

undrained shear strength Cu such that

ukTc CNDq += γ [22]

where NkT is the cone bearing capacity factor . The bearing factor depends on specific

theory employed and Konrad and Law (1987b) summarized 13 different expressions. For

Vesic’s (1977) spherical cavity expansion theory, NkT , it is expressed as:

12

)1(ln34

+++=π

rkT IN [23]

where Ir is the rigidity index.

Another interpretation was suggested by De Beer (1948, 1950, and 1964) using an

expression derived by Buisman in Delft laboratory, which in turn were derived from Prandtl-

Caquot Equations. For a strip footing, the maximum soil bearing pressure imposed at the

bottom and the overburden pressure voσ can be related by Prandtl’s equation for

cohensionless materials

φπφπσ tan2

24tan eq voul ⎟

⎠⎞

⎜⎝⎛ += [24]

This relationship can be extended to cohesive soils using Caquot’s theorem as

⎭⎬⎫

⎩⎨⎧

−⎟⎠⎞

⎜⎝⎛ ++⎟

⎠⎞

⎜⎝⎛ += 1

24tan

tan24tan tan2tan2 φπφπ φπ

φφπσ eceq voul [25]

For conical shape of penetrometer point with 10 cm2 cross-section and apex angle of

60o, empirical multiplication coefficient of 1.3 was introduced by Buisman based on his

experimental data from tests at Delft. Thus tip resistance can be expressed as

⎥⎦

⎤⎢⎣

⎡

⎭⎬⎫

⎩⎨⎧

−⎟⎠⎞

⎜⎝⎛ ++⎟

⎠⎞

⎜⎝⎛ += 1

24tan

tan24tan3.1 tan2tan2 φπφπ φπ

φφπσ eceq voc [26]

i.e. ),,( voc cfq σφ=

15

2.4.2 Sleeve Friction

Accurate interpretation of sleeve friction and soil properties is still a matter of scrutiny and no

exact relation has been proposed. But with analogy to deep foundation, it can be suggested

that

),( cff s φ= [27]

Kerisel (1964) expressed average skin friction of pile and undrained shear strength,

based on his test data on relatively homogenous, green saturated clay of Bagnolet as

us Sf α= [28]

where α is the coefficient decreases as Su increases.

Vesic (1969) on the other hand argues that there is no direct correlation between shaft

adhesion and undrained shear strength of soil especially for stiff and hard clays. In fact, he

suggest that skin resistance (fs) of the deep foundation in stiff and hard clays should be

compared to the frictional component of their drained shear strength and analyzed as

(Sanglerat, 1972)

δσ tanvoss Kf = [29]

The following relationship was proposed for sand

δtanps qKf = [30]

where Ks and Kp are the coefficient of lateral earth pressure created by displacement

of soil by the pile and the values vary from 1 to 3, δ is the angle of friction between soil and

the shaft and depends both on soil type and material of the shaft, q is the total penetration

resistance as shown in Figure 2.4.

Figure 2.4: Component of the forces acting on sleeve

2.4.3 Pore pressure

The penetration process causes a change in the stress regime of the soil and the pore fluid in

the local vicinity of the probe. In the case of clayey soils, an undrained loading condition

q

qKp

dδ

16

develops thereby generating large excess pore pressures relative to hydrostatic condition.

This excess pressure is a combination of the physical displacement of soil and the driving of

the probe (normal induced) as well as from the shear stress generated at the soil penetrometer

(shear induced). In Piezocone penetrometer, the excess pore pressure is typically measured at

one, two or three locations known as, on the cone tip (u1), behind the cone (u2) and behind

the friction sleeve (u3).The excess pore water pressure, om uuu −=Δ , generated during

penetration can be explained on the theoretical basis of cavity expansion and critical state

concept as:

shearoctm uuu Δ+Δ=Δ [31]

For the pore pressure measured at tip (u1), Baligh (1986) proposed that excess pore

pressure is dominated by octahedral stress with shear stresses ( shearuΔ ) less than 20%. For

most of the analytical model, shearuΔ is thus neglected for all practical purpose. On the other

hand, pore pressure measured for filter position behind the cone or behind the friction sleeve

is significantly influenced by shear component and has to be incorporated in analytical

models. Theoretical de-coupling of the excess pore pressure measured at the various

reference position and evaluation of octahedral and shear stress component using analytical

analysis was discussed in the literature (Vesic, 1972; Wroth, 1984; Chen & Mayne, 1994).

Also see section 2.7.

2.5 Pore Water Pressure Correction for cq and sf

Due to geometric design of the cone, ambient pore water pressure will act on the shoulder

area behind the cone and on the ends of the friction sleeve which is known as unequal area

effect (Figure 2.5). Thus the total stress measured from cone and sleeve friction has to be

corrected for this unequal area effect. The corrected cone tip resistance (qt) is given as:

2u a)-(1ctq += q [32]

a= an/ac is the effective area ratio of the cone where an= cross sectional area of the

load cell and ac is the projected area of the cone. Similarly, corrected sleeve friction ft is

expressed as :

sA

)3ustA-2u sb(A-sftf = [33]

where,

Asb = bottom cross sectional area of friction sleeve

17

Ast= top cross sectional area of friction sleeve

As = surface are of the friction sleeve

But generally u3 measurement is seldom taken and in that case correction should not

be applied (Lune et al 1997). Apart from unequal area correction, other factors that may

effect the penetration measurements such as inclination, temperature, effect of axial loading,

wear and tear of the cone and friction sleeve, calibration of load cells etc were discussed by

various researcher and was summarized by Lune et al (1997).

2.6 Interpretation of PCPT Measurements

Based on theoretical, semi-empirical or/and empirical approaches, several correlation are

developed in the literature to estimate deformation as well as strength parameters using PCPT

Figure 2.5: Effect of pore water pressure on cone tip resistance (qc) and sleeve friction (fs) (Lune et al 1997).

results. Empirical approaches have been found to give good evaluation of soil parameters.

Their acceptance in the engineering practice is well established and justified owing to the

simplicity and lack of simple rational theoretical alternative (Zhang et al. 2004). In addition,

good progress has been made in the understanding of the fundamental mechanics of the

penetration test. Yu and Mitchell (1996, 1998) discussed various difficulties of carrying out a

rigorous analysis of cone penetration problems and gave brief review and evaluation of the

theoretical methods that may be used for such analysis. The most commonly used approaches

(Yu, 2004) are:

18

• Bearing capacity methods (BCM)

• Cavity expansion methods (CEM)

• Strain path method (SPM)

• Finite element methods (FEM)

While these theories have conventionally been used alone for the interpretation,

successful models have also been achieved by combine approach such as CEM-FEM (Abu-

Farsakh et al. 2003) SPM-FEM (Teh and Houlsby, 1991), CEM-SPM (Yu and Whittle, 1999)

and CEM-BCM (Salgado et al. 1997). Brief discussion of the commonly used interpretation

relationships available in the literature is presented in the following section.

2.7 Consolidation Parameters of Cohesive Soil from PCPT measurement

2.7.1 Constrained Modulus, M

Early research was done by Dutch to investigate the relationship between compressibility and

cone tip resistance qc of the cone. Buisman (1940, 1941) theoretically derived the following

formula for soft cohesionless soil based on following hypothesis:

(i) The point of penetrometer is similar to the cone that is pushed through a semi infinite

compressible mass. Also, for highly a compressible soil, the soil is first consolidated

before being displaced laterally.

(ii) Modulus of compressibility is constant and equal to consolidation modulus. He

assumed that the shape of the surface transmitting the load is half a sphere with a

radius of ro , where ro is the radius of cone.

(iii) Boussinesq‘s theory of stress is applicable.

(iv) The stress increment is small compared to overburden pressure at the point under

consideration.

The compressibility of the sand was expressed as:

cv

qm

M 5.11== [34]

For cohesive soils, Kerisel (1969), Sanglerat et al. (1972), Kantey (1965), Meigh and

Corbett (1969), Thomas (1968) and others proposed the linear equation replacing coefficient

1.5 by α, a variable depending on the nature of soil. The general linear relationship can be

expressed as

cm qM α= [35]

19

Sanglerat et al. (1972) summarized comprehensive array of αm for different soil types

with different cone tip resistances. These values are based on the 600 set of data from the test

sites in and arround France and Spain. 200 data sets used in their study were obtained from

alluvium of the Rhone-Alps region. Most of the soils in this data were classified as CL and

CH, but the set also included the organic soil, peat and chalk as well as sand. The summary of

α values from Sanglerat’s study are presented in Table 2.1.

It is note worthy to mention that values presented in the Table (2.1) are recommended

to calculate settlement beneath the shallow foundation where pressure increment in the layer

underneath is in the order of 100 kilopascals (1 bar). Also for the values of qc> 2 MPa, the α

were found to be independent of the nature of soil.

Table 2.1: Sanglerat’s αm coefficient (adopted from Sanglerat, 1972)

Criteria αm Soil Type

qc<0.7 MPa 3<αm<8 Clay of low plasticity (CL)

0.7<qc<2 MPa 2<αm<5

qc>2 MPa 1<αm<2.5

qc<2 MPa

qc>2 MPa

3<αm<6

1<αm<2

Silts of low plasticity (ML)

qc<2 MPa

qc>2 MPa

2<αm<6

1<αm<2

Highly plastic silts and clay (MH CH)

qc<1.2 MPa 2<αm<8 Organic Loam (OL)

qc<0.7 MPa Peat and Organic clay (Pt, OH)

50<w<100 1.5<αm<4

100<w<200 1<αm<1.5

w>200 0.4<αm<1

2<qc<3 MPa 2<αm<4 Chalks

qc>3 MPa 1.5<αm<3

qc<5 MPa

qc>10 MPa

αm=2

αm=1.5

Sands

w:water content

Value of coefficient of compressibility, Cc were also plotted with respect to qc (Figure

2.6) and for majority of points were located in the region bound by hyperbolic curve defined

by 4062.4

−−

=c

cc q

qC and [36]

20

205.0

−=

c

cc q

qC [37]

The work of Bachelier and Parez (1965), gave similar results as that of Sanglerat

(1972). For the clay of Flanders, the range was found to be 2.3<αm<7.7. Similarly, Jones and

Rust (1995) found αm =2.75±0.55 for South African alluvial clay.

Senneset et al. (1989) expressed the relation in term of the net cone resistance also

taking into account for overburden pressure and proposed the following relation

( )votini qqM σαα −== [38]

for use in preconsolidation range where αm ranges from 5 to 15. For normally

consolidated clays αi was found close to 8 (Figure 2.7).

Figure 2.6: Cc Versus qc (modified from Sanglerat 1972). Vertical scale changes at 0.5.

Kulhawy and Mayne (1990) conducted the extensive analysis of various world data

(figure 2.8) and proposed the general relation as:

( )votqM σ−= 25.8 [39]

Similarly Abu-Farsakh (2003) proposed the use of αi =3.58 for Louisiana soil

deposits. His study also found good correlation between corrected cone tip resistances (qt)

and M and proposed relation

tqM 15.3= [40]

21

Experimental study in the various regions has thus confirmed that preliminary

assessment of the compressibility of clay can be made thorough qc measurement. As a

practical rule, Sanglerat (1972) suggested that soil with qc >1.2 MPa, undergoes negligible

settlement. On the other hand for the soil with qc <1.2 MPa, further analysis such as

oedometer test should be done especially when w >40%.

Figure 2.7. Comparison of modulus (Mn) for Glava clay (Senneset et al.,1989)

Figure 2.8 Relationship between net cone resistance and Constrained Modulus, M (Kulhawy and Mayne , 1990)

22

2.8 Preconsolidation Pressure and OCR

The Determination of yield stress ( y'σ ) or preconsolidation pressure ( p'σ ) and OCR in

cohesive soil by PCPT is one of the consuming topics of the research in this field. In last two

decades, there have been theoretical developments (Senneset et al. 1982; Konrad et al. 1987;

Chen and Mayne, 1994) as well as empirical relations (Abu-Farsakh, 2003; Robertson et al.

1986; Sully et al., 1988 and others) to correlate PCPT parameters to that of stress history of

soil.

For simplicity of comparison, these methods can be grouped under three main

headings; based on (i) cone tip resistance alone, (ii) pore pressure measurement alone and

(iii) combining the both measurements (Demers and Leroueil, 2002).

2.8.1 Models Based on Cone Tip Resistance

Estimation of OCR from PCPT data was presented by Schmertmann (1978) utilizing

SHANSEP concept to correlate 'vouS σ with OCR. In this method, undrained shear

strength, uS , is first estimated from cone tip measurement, cq . The overburden stress 'voσ is

estimated either from laboratory density data or using approximate value using CPT

classification charts. The corresponding normally consolidated value of 'vouS σ is then

estimated using measured or estimated plasticity index (Ip) (Ladd et al. 1977). OCR can then

be calculated using charts such as Figure 2.9 or other correlations (Ladd et al. 1977).

Figure 2.9: Relationship between su/σ’vo, Ip and OCR (Anderson et al., 1979)

23

For the cases where overconsolidation is caused solely by mechanical removal of

overburden, Schmertmann (1978) also proposed the method based on the shape of cq profile.

In this approach, increase in the cq with respect to the depth is assumed linear, extrapolation

of which approximates original ground profile. This in turn approximates p'σ profile with

depth. Similar approach was given by Sandven et al. (1988) to distinguish normally

consolidated and over consolidated soil. By assuming typical range of bearing capacity

factor, CN , undrained shear strength factor, 'vouS σ and unit weight ratio, they proposed the

plot of reference line given by zqt γ2= in tq versus depth plot. If the tq profile in the clay

deposit is close to this theoretical line, soil is most likely to be NC, otherwise it is more likely

to be in OC state.

Direct relationship between tip resistance and pre-consolidation pressure was first

proposed by Tavenas and Leroueil (1979). They proposed the empirical

correlation 3' cp q≈σ for the soil deposits in Eastern Europe. This approach was further

rectified by Wroth (1984), by including overburden pressure at the site. Several theoretical

models have also evolved (Mayne, 1986, Konrad and Law, 1987 Wroth 1984) that explains

prediction of OCR from tip resistance. By expressing cone tip resistance in clay in terms of

undrained shear strength, as

ukTo CNPqc

+= [41]

where NkT is cone bearing capacity factor and Po is total normal stress .

For Vesic’s (1977) spherical cavity expansion theory

12

)1(ln34

+++=π

rkT IN [42]

Combining above two expression leads to

+=− ruo ICPqc

ln33.1 12

+π [43]

Mayne (1991) proposed the use of Modified Clam Clay model for determination of Cu

as recommended by Wroth and Houlsby (1985) such that

( ) ou POCRMC '2/2 Λ= [44]

where )'sin3/('sin6 φφ −=M

='φ Effective friction angle

=Λ Plastic volumetric strain ratio= cs CC /1 −

24

cC = isotropic compression index

=sC Isotropic swelling index

Thus by combining the last two equations presented atop, Mayne (1991) proposed the

relation for in situ determination of OCR as Λ

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

++

−=

/1

12

)ln1(3/4

'/))(/2(2

πr

oo

I

PPqMOCR c [45]

Since the value of oP and oP' is not usually known for the sites, it is approximated

with total and effective overburden stress, voσ and vo'σ . Thus the practical version of the

normalized piezocone tip parameter is

( )vo

votqKOCR

'.

σσ−

= [46]

For the 83 piezocone sites studied by Mayne (1991) indicate that clear trend exist

between OCR and normalized piezocone tip resistance and above equation bounded the data

for typical range of oo 40'20 << φ and 50050 << rI . Similarly, Chen and Mayne (1994)

found K=0.317 for world data as shown in Figure 2.10 Abu-Farsakh found the good

correlation for the Louisiana soils (R2 = 0.90) and proposed K=0.152.

Figure 2.10: Normalized resistance versus OCR from compilation of world data (Chen & Mayne, 1994).

25

Tavenas and Leroueil (1987) obtained good relationship between p'σ and ( )votq σ−

for the 11 sites in Canadian Clays (Figure 2.11) and proposed the following relationship

( )t

vocp N

q

σ

σσ

−=' . [47]

Value of Nσt, however is found to be differing from site to site and highly dependent

on soil properties. Mayne and Holtz (1988), based on their study of world data found the

average value of Nσt =2.5 for the relation of (qc-σvo) and σ’p. Chen and Mayne (1996) used qt

instead of qc and gave the value of 3.28. Similarly, Leroueil (1984) found 3.6 for Canadian

soils and Larsson and Mulabdic (1991) proposed mean value of 3.43 for Scandinavian soils.

It is noteworthy to mention that, normalizing above relation with vo'σ gives the similar

parameter as proposed in the study of Mayne (1991), Wroth (1988) and Robertson (1990) as

given in equation [45].

2.8.2 Models Based on pore pressure measurement

The basic principle behind evaluation of OCR from PCPT method is to relate octahedral

stress to net cone resistance and in turn to undrained shear strength. By assuming normalized

behavior of clay, uS is related to OCR. The excess pore pressure, typically measured at tip,

can also be indicator of OCR in clay especially in high OCR range where muΔ is dominated

by octahedral stress.

Figure 2.11: ( )vocq σ− versus p'σ (Tavenas & Leroueil, 1987).

26

For advancing probes, excess pore pressure generate at any reference position is given

as;

shearoctm uuu Δ+Δ=Δ [48]

For the filter position at tip, neglecting shearuΔ ,

octuu Δ=Δ 1 [49]

This octahedral pore pressure can be related to OCR using spherical cavity expansion

concept proposed by Vesic (1972) as

( )1ln34

+=Δ ruoct ISu [50]

For the more general case, Chen and Mayne (1994) proposed the following relation to

incorporate shearuΔ

oshear pu '2=Δ for type 1 cone

Λ

⎟⎠⎞

⎜⎝⎛ −=Δ

21' OCRpu oshear for type 2 cone

and mean effective stress voop '' σ≈

By using the average representative value of 75.0=Λ , Chen and Mayne (1994)

theoretically derived the following relation, 33.1

1'

2⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛ −=

vo

ouuOCR

σ [51]

Similar expression were given empirically by Sully and Campanella (1991) and

Larson and Mulabdic (1991). Chen and Mayne (1994), examined this parameter for the

compilation of world data and found relatively weak correlation (R2=0.69) even when

fissured clay data were ignored.

Sully et al (1998) introduced parameters obtained from pore pressure measurement as

a predictor of OCR in clay as and proposed a relationship between OCR and PPD as

)(43.166.0 PPDOCR ±= [52]

where ( ) 021 uuuPPD −= and is derived solely from pore pressure measurements.

Azzouz et al. (1983), Mayne (1986), Kabir and Lutenegger (1988) proposed the

following relationship between excess pore pressure and stress state of the soil deposits in the

site:

( )oEPPp uuK −='σ [53]

27

where u = u1 or u2

Mayne (1986, 1987), Mayne and Holtz (1988) and Mayne and Bachus (1988, 1989)

suggested normalizing KEPP with vo'σ for evaluating OCR. For type 1 and type 2 piezocone,

empirical trends are shown in Figure 2.12 .Direct trend between yield stress, p'σ , and excess

pore pressure 1uΔ or 2uΔ were also observed. Because u2 values can be negative in case of

penetration through stiff over consolidated soils, u1 is widely used. But Chen and Mayne

(1994) showed from the compilation of the world data that results obtained from u2 are more

consistent.

Figure 2.12 : OCR versus 1uΔ (Chen and Mayne ,1994).

2.8.3 Models Based on Cone Tip Resistance and Pore Pressure Measurements

Combine methods were proposed for interpretation of OCR and preconsolidation pressure

using both pore pressure parameters and tip resistance. Baligh et al. (1980) and Tumay et al.

(1981) suggested using the ratio between excess pore pressure and measured tip

resistance, cqu1 . For low OCR range ( )21 ≤≤ OCR , test result showed that the parameter

cqu1 decreased as OCR increases (Figure 2.13).

Wroth (1984), recommended the use of parameter Bq, making correction over

Sennesset et al. (1982) and Jefferies and Funegard (1983), as

28

( ))(

0

votq q

uuB

σ−

−= [54]

)17.3(3.2

−=

q

q

BB

OCR [55]

Because of its analogy to Skempton’s pore pressure parameter

( ) ( )21 σσ Δ−ΔΔ−Δ= uuA and Henkel’s parameter ( ) octoctua τσΔ−Δ=' this parameter

was investigated by number of researchers (Jamiolkowski et al. 1985; Keaveny & Mitchell,

1986; Robertson et al., 1986, Demers et al. 2000). However this parameter is highly

dependent on both the drainage condition and stress history of the soil, which resulted in

highly scattered range as shown in Figure 2.14.

Based on CE/MCC approach as discussed earlier, Mayne (1991) developed the

equation based on effective tip resistance and pore pressure measurement u1 and u2 as

^1

1'

1195.1

12

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟

⎠

⎞

⎜⎜

⎝

⎛+

−

+=

vo

utq

MOCR

σ [56]

^1

'2

195.112

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −

+=

vo

utq

MOCR

σ [57]

where M is the slope of the critical state line defined by ( ) )'sin3('sin6 φφ − and ^ is

plastic volumetric strain ratio given as cs cc−1 , where Cs and Cc are swelling index and

compression index respectively. For the natural intact clays, ^ is found to be constant with

average value of 0.75. Also, the effective stress angle ranges between 00 43'17 ≤≤ φ (Diaz-

Rodriquez et al., 1992). For this range Chen and Mayne (1996) suggested the following

approximate relation to estimate OCR

( )vo

iti uqkOCR'σ−

= [58]

where ui = u1 or u2, and value of k1 and k2 are thus given to be 0.81 and 0.46

respectively. Based on the statistical analysis of 205 clay sites, the value were found close to

0.75 and 0.50 (Chen and Mayne, 1994). Similarly, Abu-Farsakh (2003) investigated this

parameter for the soils of Louisiana soils and proposed the value of k1 =0.161 with R2 = 0.91.

Similarly, direct correlation was also established between preconsolidation pressures

and ( )mt uq − , as shown in (Figure 2.15).

29

Figure 2.13: Pore Pressure ratio versus OCR for Louisiana Clays (Tumay et al. 1982)

Figure 2.14: Bq versus OCR (Robertson et al., 1986)

30

(a)

(b)

Figure 2.15: Yield stress versus Effective cone resistance for world data (Chen and Mayne, 1994). a) Type 1 cone b) type 2 cone

31

2.9 Coefficient of Consolidation

The time rate of consolidation settlement in the field depends on the rate of dissipation of

excess pore pressure induced by the imposed loading (Equations [12], [13], [14]), which in

turn, is defined by the soil permeability (k) and coefficient of consolidation (cv). These

parameters are conventionally estimated by laboratory tests such as falling head permeability

test or oedometer test and by in situ test such as borehole permeameter, self boring

permeameter or piezo probes (Abu-Farsakh, 2005). The rate of consolidation parameters can

also be assessed from the PCPT by conducting the dissipation tests. In dissipation test,

advancing probe is stopped at required depth and then the decay of pore pressure with time is

recorded. The response of dissipation curve depends on several factors such as location of

pore pressure filter (u1 or u2), stress history, drainage condition and permeability (Lavadox

and Baligh, 1980, 1986).In general, for normally consolidated clays, the excess pore pressure

decays in monotonic manner (type I curve). But in case of stiff clays and soils with high

OCR, redistribution of excess pore pressure around the probe occurs , resulting in sudden

drop in excess pore pressure ( Type II curve) or dilatory response of decay curve ( type III

curve) , before monotonic decay occurs (Burns and Mayne, 1998, Baligh et al. 1986). Figure

2.16 shows typical type II and type III curves with depiction of correction for excess initial

pore pressure (ui).

Figure 2.16: Graphical representation of type 1 and type II curves ( Abu- Farsakh and Nazzal, 2005)

Also for interpretation, it is convenient to normalize the pore pressure relative to

initial pore pressure at the beginning of dissipation (ui) and equilibrium in situ pore pressure

(u0) expressed as;

32

)()(

0

0

uuuu

Ui

t

−−

= [59]

where u t is excess pore pressure at time t.

Several empirical and theoretical relations have been proposed for the interpretation

of dissipation curves. It is noteworthy to mention that consolidation (pore pressure

dissipation) in the piezocone penetration are largely horizontal in direction and thus the PCPT

data models for ch or horizontal coefficient of consolidation. The vertical coefficient of

consolidation has to be determined assuming an isotropic behavior of the soil as:

⎟⎟⎠

⎞⎜⎜⎝

⎛=

h

v

k

k

hcvc [60]

where cv and ch represents vertical and horizontal coefficient of consolidation

respectively and kv and kh represents the permeability in the horizontal and vertical direction

respectively. Torstensson (1975, 1977) developed an interpretation relation based on elasto-

plastic soil model and cavity expansion theories. He suggested that horizontal coefficient of

consolidation should be interpretated at 50% dissipation as given by

2

50

50hc r

t

T= [61]

where ch is coefficient of consolidation in direction perpendicular to cone axis, T50 is

theoretical time factor parameter, t50 is time corresponding to 50% dissipation and r is

penetrometer radius for cylindrical model and equivalent radius for spherical model. The

selection of the appropriated model and thus value of r is guided by the location of filter

element. For example if the filter is located in the cone (u1) spherical model is adopted for

analysis. Graphical solution for T factor proposed by Torstensson (1975, 1977) is presented

Figure 2.17.Another approach was based on the strain path analysis that was developed by

Baligh (1985, 1986), Baligh and Lavadoaux (1986), Houlsby and Teh (1988), Teh and

Houlsby (1991). Using the approach similar to Levadoux and Baligh for Boston Blue Clay

(BBC), Houlsby and Teh (1988) gave a general expression that also takes inot account

varying rigidity index of the soil.

tc

rIh

.2r*T= [62]

where rigidity index, ur SGI = and T* is a modified dimensionless time factor

33

obtained theoretically. Several tables and charts have been developed to give T* value for

different degree of consolidation and for different location of filter. Table 2.2 gives the

tabulated summary of time factor, T*, from consolidation analysis (Houlsby and Teh, 1988).

Figure 2.18 presents normalized dissipation curve for Ir=100 and for different locations of

filter positions. However, comparison between the much simplified model of the Torstensson

(1977) and sophisticated Houslby and Teh (1988) for the T* for element locations at u1 and

u2 yielded similar plot (Lune et al.1997). Robertson et al. (1992) also produced a simplified

graphical chart for evaluation of ch from his analysis of the dissipation data from piezocone

tests using Houlsby and Teh method (1988).

(a) Cylinder

(b) Spherical

Figure 2.17: Time factor for Torstensson’s (1975, 1977) model.

34

Table 2.2: Modified time factor T* for Houlsby and Teh (1986)

Location

Degree of

consolidation

Cone

(u1)

Cylindrical extension behind cone base (u2)

20% 0.014 0.038

30% 0.032 0.078

40% 0.063 0.142

50% 0.118 0.245

60% 0.226 0.439

70% 0.463 0.804

80% 1.04 1.60

Figure 2.18. Dissipation curves at different location of a 60o cone penetrometer (Teh and Houlsby, 1991)

Teh (1987) represented the dissipation curve in the square root of time scale and

proposed the following correlation model

2*.2

rrIMmch ⎟

⎟⎠

⎞⎜⎜⎝

⎛= [63]

where M= theoretical curve for a given probe geometry and filter location (MG =1.63

for u1 and 1.15 for u2, represented in Figure 2.19 ) and m= measured gradient of the initial

linear dissipation (Figure 2.20)

35

Figure 2.19. Interpretation of time factor (T) (Teh, 1987)

Time (sec)

Nor

mal

ized

exc

ess

pore

pre

ssur

e (Δ

u/ Δ

u i)

1/m

Figure 2.20. Calculating the gradient of initial linear section (m) (after Teh, 1987, adopted from Abu-Farsakh and Nazzal, 2005)

Senneset et al. (1982) suggested an equation to predict ch(piezo) from the dissipation

rate diagram as follows:

itoch uurpiezoc / )( 2 ΔΔ= &λ [64]

36

μ T

∂∂

=cλ [65]

where λc is the rate factor, tu& Δ is the rate of dissipation at a given dissipation level

( tutu / ∂∂=Δ & ), Δui is the initial excess pore pressure at t = 0, T is the time factor, and μ is

the normalized pore water pressure. Figure 2.21 depicts the terminology for interpretation of

dissipation tests. The rate factor is a function of soil rigidity index (Ir) and degree of pore

pressure dissipation (Δut /Δui).

Figure 2.21: Interpretation of dissipation test and rate factor according to Senneset et al. (1982) method.

Jones and Rust (1995) suggested a direct estimation of cv for the standard piezocone,

based on their experience in South African alluvium clay

50

150t

cv = [66]

where cv is in m2/year, and t50 in minutes. However, the field measured cv is about six

times the laboratory measured cv. This is due to the fact that undisturbed sampling of recent

alluvial deposits is difficult, leading to unrepresentative laboratory tested samples (Jones and

Rust, 1995).

Abu-Farsakh and Nazzal (2005) conducted a comparative study of different

interpretation method for estimation of coefficient of consolidation (cv) in Louisiana soil

deposits. They compared the laboratory estimated (cvm) coefficient of consolidation with that

37

predicted by interpretation of dissipation curves (cvfit). Summary of evaluation of different

methods is given in Table 2.3.

Table 2.3: Evaluation summary of different PCPT methods for predicting cv. (Abu-Farsakh and Nazzal, 2005)

Method

Best fit calculations

Arithmetic calculations of

Log(cv-p)/ Log(cv-m)

Log(cv-Fit)/

Log(cv-m)

R2*

Mean (cm2/sec)

SD# COV** (%)

Teh and Houlsby (1988) 1.05 0.88 1.07 0.19 17.8

Levadoux and Baligh (1986) 0.74 0.85 0.75 0.20 26.7

Robertson and Campanella (1988)

0.72 0.84 0.73 0.19 26.0

Teh (1988) 0.98 0.89 0.99 0.22 22.2

Senneset et al. (1982) -a 0.81 0.85 0.82 0.20 24.4

Senneset et al. (1982) -b 0.84 0.86 0.85 0.19 22.4

Jones and Rust (1995) 0.71 0.84 0.71 0.20 28.2 * No. of data points = 29 ** COV = coefficient of variation #Standard Deviation

2.10 Other Related Parameters

Several analytical as well as empirical relations discussed above require additional soil

parameters as input such as undrained shear strength, rigidity index, effective friction angle

and others. In most cases, such parameters are either approximated within reliable range for

practical consideration or are replaced by equivalent relation from cone measurement.

Summary of soil parameters that can be determined from PCPT measurements are

summarized in Table 2.1.1. A brief review of methods to evaluate undrained shear strength

and rigidity index is discussed in the sub sections.

2.10.1 Undrained Shear strength (Su)

Use of cone penetration method to determine undrained shear strength (Su) dates back as

early as to the development of mechanical Dutch cone. Based on the analogy of static cone

penetration to driven pile, undrained shear strength was related to cone tip resistance and

overburden stress, as discussed in previous sections. Preliminary assessment of undrained

shear strength can be summarized as follows:

38

(i) Based on total cone resistance )( vocq σ−

k

vocu N

qS

)( σ−= [67]

where Nk is empirical cone factor and its value depends not only in the geology and

stress state of the soil but also on the reference shear strength to calibrate Su . By replacing

cq by tq , modified cone factor was introduced that takes into account for pore pressure

correction in to cone measurement. Several studies performed over the years suggested that

empirical cone factors for most of the clays falls in the range of 15-20

(ii) Based on effective cone resistance )( 2uqt −

Senneset et al. (1982) recommended the use of effective cone tip resistance to

evaluate the undrained shear strength. They introduced the cone factor Nke such that

ek

cu N

uqS

)( 2−= [68]

Senneset et al. (1982) found the range of Nke = 9±1.

(iii) Based on excess pore pressure )( 02 uuu −=Δ

Using theoretical and semi-empirical based on cavity expansion theory (Vesic, 1972;

Battaglio et. al 1981; Randolph and Wroth, 1979; Campanella et al., 1985), several relations

has been proposed to correlate excess pore pressure and undrained shear strength which has

the form:

uu N

uuS

Δ

−=

)( 02 [69]

where uNΔ varies between 2 to 20.

2.10.2 Soil Rigidity Index

Rigidity index in soil mechanics is defined as

ur S

GI = [70]

Where G is the shear modulus and Su is undrained shear strength. Also

GEs 3= and GEsu 3= [71]

where sE and suE are modulus of Elasticity in drained and undrained conditions.

Since the shear stresses in the soil are resisted solely by the soil particles and their magnitude

39

are independent of pore pressure (drainage condition), it can be reasonably assumed for

isotropic elastic soil that above two moduli are alike (Aysen, 2002).

Thus,

u

sr S

EI

3= [72]

The range of undrained rigidity index varies between 20 and 1000 in natural clays.

Approximate evaluation of rigidity index can be indirectly made by back calculating several

parameters using PCPT. Also several analytical models incorporate rigidity index which can

give direct evaluation by substitution. By using hybrid CE- MCC model by Chen and Mayne

(1994) as discussed in previous sections, rigidity index can be evaluated as

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛= −⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛

−

−+ 925.2

21

5.1exputqvotq

MrIσ

[73]

where M is the slope of the critical state line defined by ( ) )'sin3('sin6 φφ − . This

relation requires additional information on effective stress angle. The effective stress angle

ranges between 00 43'17 ≤≤ φ (Diaz- Rodriquez et al., 1992) for most of the intact clays and

for varies by small difference for given soil type. As such good approximation can be made

based on previous experience or available charts. Table 2.4 gives approximate range of the

friction angle in cohesive soils

Table 2.4: Typical values of friction angle (after Senneset et al., 1989)

SN Soil Type 'tanφ 'φ (degrees)

1 Clay, soft 0.35-0.45 19-24

2 Clay, medium 0.40-0.55l 19-29

3 Clay, stiff 0.50-0.60 27-31

4 Silt, soft 0.50-0.60 27-31

5 Silt, medium 0.55-0.65 29-33

6 Silt, stiff 0.60-0.70 31-35

Similarly Teh (1987) gave the theoretical solution for modified cone factor Nkt ¸ as

ασ

2)1('

)ln(64.219.0 +−−+= ou

vorkt K

SIN [74]

where =α Roughness coefficient and is equal to 0 for smooth surface and 1 for rough

surface. Ko for the in situ soil can be determined from PCPT data using charts given by

40

Khulhawy and Mayne (1990) or Sully and Campanella (1991). Alternatively following

relation (Khulhawy and Mayne, 1990) can be used

⎟⎟⎠

⎞⎜⎜⎝

⎛ −=

vo

voto

qK

'1.0

σσ

[75]

In the relation for Nkt , undrained shear strength can also be eliminated in terms of

effective cone measurement and Nkt , Thus for given valaue of Nkt , which again can be

calibrated for given soil deposits, closed form solution can be given for rigidity index.

Similarly Baldi et al. (1981, 1988) suggested following equations for rI from CPT

rr f

I 300= Dutch cone tip [76]

rr f

I 170= Electric cone tip [77]

41

CHAPTER 3

3 SOIL TESTING AND PIEZOCONE DATABASE

This Chapter gives a brief introduction of the piezocone test sites and summary of the in situ

and laboratory test results. Seven sites were selected in Louisiana to conduct in situ and

laboratory tests. In addition 3 sites were used by Abu-Farsakh (2003) for verification by

comparing the predicted settlements with the field measurements.

Additional two sites were available in 2004 as ramp construction project commenced

for Juban road interchange between I-12 and LA 1026, located north-east of Baton Rouge in

Livingston Parish. In addition to the borehole sampling and PCPT tests, settlement

monitoring instrument were installed and thus this site provides a unique opportunity for filed

verification of both in situ and laboratory settlement prediction methods.

3.1 Methodology

3.1.1 Laboratory Tests

In each of the investigated sites, boreholes were drilled and high quality 76 mm (3 inch)

Shelby tube samples were recovered at different depths. Basic soil characterization tests such

as water content, unit weight, Atterberg limits, grain size distribution and specific gravity

were carried out.

One-dimensional consolidation test (ASTM D2435-04) was performed on high

quality undisturbed sample oriented in both horizontal and vertical directions. Three

incremental load oedometer devices were used in this study. The applied load increment ratio

was one (LIR=1) and each increment applied at the interval of 24 hours. Specimens were

loaded in increments up to maximum applied vertical stress of 16 TSF (1.53 MPa), and then

unloaded stepwise to 0.5 TSF. Displacement readings were recorded and stored automatically

using digital dial gauge system interfaced with laboratory computer unit and using data

acquisition software. Data obtained from this software was exported to MS EXCEL for

further calculation and analysis. Casagrande’s method (1936b) was employed to determine

d100, the corresponding void ratio (e) for each load increment, preconsolidation stress, time

for 50% consolidation (t50) and subsequently the coefficients of consolidation (ch or cv).

Reference parameters include horizontal and vertical coefficient of consolidation (ch

and cv), constrained modulus (M), OCR and compression indices cc and cr. In addition,

unconfined compression tests and ko-consolidated undrained triaxial tests (Ck0U) were

performed to estimate undrained shear strength (Su) and shear modulus (G) of the soil and to

42

estimate rigidity index (Ir).Laboratory test results for the previous seven sites were performed

by Abu-Farsakh (2003).

3.1.2 In situ Tests

The in situ test program includes performing both Piezocone penetration and Piezocone

dissipation tests. Two state of art cone penetration system are available at the Louisiana

Transportation Research Centre (LTRC). These systems are the 20- ton Research Vehicle for

Geotechnical In situ testing and Support (REVEGITS) and the Continuous Intrusion

Miniature cone Penetration test (CIMCPT) system. REVEGITS is an in situ test and support

system consisting of hydraulic pushing and leveling system, 1 m segmented rods, cone

penetrometer, and data acquisition system. Piezocone used in this study are subtraction type

Fugro cone penetrometer.

At each site, several PCPT test were performed around the drilled boreholes as well

sections of interest using 10 cm2 and 15 cm2 piezocone penetrometers. The 10 cm2 piezocone

has sleeve area of 150 cm2 and a pore pressure transducer located 5 mm behind the base (u2

measurement). The 15 cm2 piezocone has a sleeve area of 200 cm2 with pore pressure

transducers located on the cone face and behind the sleeve (u1 and u3 measurements). During

the penetration phase, cone was pushed at the rate of about 2 cm/sec. Other standards and

calibration procedure as recommended by International Society of Soil Mechanics and

Foundation Engineering (ISSMFE) were followed in all of the PCPT tests.

3.1.3 Field Settlement Monitoring

In order to monitor the field settlement, one or more of the following types of devices were

installed in the verification sites.

3.1.3.1 Horizontal Inclinometer Horizontal inclinometers are one of the widely used monitoring devices that give high

resolution settlement or heave profiles. In this study, digital horizontal inclinometer

manufactured by RST instruments Ltd. was used. The Digital horizontal inclinometer system

consists of inclinometer casing, a horizontal probe, control cable, pull cable, and a readout

unit (Figure 3.1.1). The inclinometer casing is 85 mm (3.34”) in diameter and has two sets of

perpendicular grooves. The casing is installed in a horizontal trench or borehole with one set

of grooves oriented vertically. Inclinometer probe employs high resolution fluid damped uni-

axial servo-accelerometer that measures inclination from horizontal in the plane of the probe

wheels. A change in inclination indicates that movement has occurred. The amount of

movement is calculated by finding the difference between the current inclination reading and

43

the initial reading and converting the result to a vertical distance. Data is retrieved directly on

iPAQTM pocket PCTM via a wireless link to the digital cable reel.

A survey is conducted by drawing the probe from one end of the casing to the other,

halted in its travel at four foot intervals for inclination measurements. Probe is inserted with

cable connected to short end (serial number inscribed, refer to Figure 3.2) and hard wheels

located on the bottom. After the probe has reached to opposite end, it is withdrawn, turned

180o and cable is connected to long end. The probe is reinserted into the casing with hard

wheel down and readings taken same as before. The reading represents vertical displacement,

defined by [(1/2m)* Sin (a)] where “a” is the angle between the horizontal and longitudinal

axis of the probe as shown in Figure 3.2. The positive reading from the short side indicates

settlement and negative reading indicates heave. The opposite sign convention applies when

cable is connected to long end. The first survey establishes the initial profile of the casing

known as baseline survey. Subsequent surveys reveal changes in the profile if ground

movement has occurred.

Figure 3.1 RST digital horizontal inclinometer system (casing not shown).

3.1.3.2 Magnetic Extensometer The Magnet Extensometer consists of a series of ring magnets that slides on a central access

pipe. These magnets are installed in a borehole or placed subsequently during earthwork at

specified depths. Measurements are taken by lowering a probe through the access pipe to

44

detect the depth of the magnets. When probe enters the magnetic field of the target magnet,

audible sound is emitted at the ground level. Data from the magnetic extensometer can

indicate settlement of each layer as well as total settlement.

Figure 3.2 : RST digital horizontal inclinometer probe

Figure 3.1.3 (a) shows the schematic diagram of the magnetic extensometer

arrangement in the field. Different components of the extensometers and their installation

procedure is discussed as under

(i) Access pipe: Access pipes are usually hollow PVC pipes with size ranging from 1 to

3.34 inches in diameter. Each pipe section is about 10 feet long and subsequent pipes

are joined together using telescoping joints

(ii) Datum Magnet: Datum magnet is fixed directly to the bottom section of the pipe and

installed at least 2 feet above the pipe end. It is used in the case where bottom end of

the pipe is anchored to the stable ground and is used as reference.

(iii) Spider Magnets: Spider magnets have steel spring legs attached to ring magnet that

slides down the access pipe. These spring legs couple with the soil and moves as soil

settles or heave. Spider magnets are generally used in boreholes i.e. in the natural soil

layers. In order to install spider magnets, desired locations are marked in the access

pipe and spider magnets are slide to the marks. Spider legs are then compressed and

tied using string and release pin assembly as shown in the Figure 3.1.4 (b). Spider

magnets are temporarily attached to the access pipe using slider arrangement or weak

duct tape. A long string is then attached to release pin sufficient enough to reach to

the surface. Once all the magnets are installed and pipe is assembled, it is gently

45

lowered into the borehole. String attached to release pin are then pulled starting from

the top magnet. The bore hole is then grouted using cement slurry or other grouting

chemicals.

(iv) Plate Magnets: Plate magnets are used in fills and have large area to couple with soil

layer (Figure 3.3 c).

(v) Read out unit: It consists of a probe, reel tape and built in light and sound buzzer

(Figure 3.3 d). A probe attached to tape is lowered and each time it passes through the

magnets, triggers light and/ or sound buzzer signal. Once the installation of

extensometer is complete, fist set of reading is taken to locate position of spiders and

plate magnets. As the settlement progresses, periodic readings are taken to locate the

magnets. Data from the extensometer can then be used to calculate settlement of each

layer and total settlement under the foundation or embankment.

(a) Schematic diagram of the extensometer in the field.

(b) Spider magnets assembly before installation

Figure 3.3: Magnetic Extensometer system

46

(c) Plate Magnet assembly

(d) Read Out unit

Figure 3.3 (continued)

3.1.3.3 Settlement Plates Settlement plates are simple circular or rectangular plates made of steel or wood. A reference

rod and protective pipe is attached to platform. Plates are placed on an existing ground

surface before construction and additional rods are attached as fill height increases.

Settlement is determined by measuring periodic elevation of the settlement plate with

reference to stable bench mark that is well beyond the influence of settlement zone. Figure

3.4 shows the installation of settlement plates in the Pavement Research Facility (PRF) site.

3.2 Description of the Sites

The stiff clay deposits in and around the region of Baton Rouge area are Pleistocene Age

terrace deposits that were originally deposited in a deltaic environment and latter subjected to

high desiccation ( Mayne et al. 1995). Early works (Arman and McManis, 1977, LADOTD

boring records, Abu-Farsakh, 2003) suggest that these soil deposits are commonly oxidized

(reddish brown or yellow in color) and contains calcareous concretions or iron oxide bands.

However, total calcium and dolomite contents test results from previous studies (Mayne et al.

1995) indicate no signs of cementation. Also, these clays are generally weakened by network

of fissures and slickenside and occasional pockets of sands.

A brief record of seven investigated sites and soil tests result is given in the following

sub sections. Detailed in situ and laboratory test results are discussed by Abu-Farsakh (2003).

47

Figure 3.4: Installation of settlement plates at ALF site (Farrag et. al, 2004)

3.2.1 Manwell Bridge, Evangeline Site

The Manwell Bridge is located at about 20 miles northwest of Opelousas, Louisiana. The

results of a soil boring test at this site are given in Figure 3.5. The rigidity index (Ir) for this

site was estimated to be 40.

Three PCPT tests were conducted at the Manwell Bridge site, two PCPT using u1

measurements and one PCPT using u2 measurement. The profiles of two PCPT test results

are presented in Figure 3.6. First column presents the corrected cone tip resistance, qt, profile.

Column 2 presents the sleeve friction (fs) profile. Friction ratio (Rf) profile, which is the ratio

between the sleeve friction and tip resistance in percent, is given in third column. Fourth

Column plots the pore pressure profiles of u1 and u2. Fifth column gives the soil classification

using the CPT probabilistic region estimation method developed by Zhang and Tumay

(1999). The results of eight dissipation tests conducted at different depths (3.7 m, 5.26 m,

6.46 m, 12.6 m, 19.3 m, 20.78 m, and 22.13 m) are presented in Figure 3.7. The water table at

this site was at about 2 m.

48

0123456789

1011121314151617181920212223242526

Dep

th (m

)

Soil Type0 20 40 60 80 100

m.c, L.L. and P.L.

0 2 4 6 8 10

Modulus, M (MPa)

1E-5 1E-4 1E-3 1E-2

cv (cm2/sec)

0 2 4 6 8

OCR

Brown silty sand

Medium brown and gray clay

Brown and grayclay with lenses of silt

0 50 100 150 200

Su (kPa)

Brown lean clay

Brown silt and sand

Gray sand

Gray and Brown clay

Gray lean claywith lenses of silt

Gray silt

Gray silty sand

P.L.

m.c.

L.L.

Figure 3.5. Soil boring profile for Manwell Bridge, Evangeline site ( Abu-Farsakh, 2003).

0123456789

1011121314151617181920212223242526

Dep

th (m

)

0 5 10 15 20 25 30 35

Tip Resistance (MPa)

0123456789

1011121314151617181920212223242526

0123456789

1011121314151617181920212223242526

0 2 4 6 8 10

Rf (%)

0123456789

1011121314151617181920212223242526

0.0 0.5 1.0 1.5 2.0

Pore Pressure (MPa)

0123456789

1011121314151617181920212223242526

0 20 40 60 80 100

Probability of soil type (%)

Silty

Clayey

Sandy

u1- test 1

u2- test 2 Test 1

Test 2

0.0 0.1 0.2 0.3 0.4

Sleeve Friction (MPa)

Test 1

Test 2

Figure 3.6: PCPT profile for Manwell Bridge, Evangeline site (Abu-Farsakh, 2003).

49

1 10 100 1000 10000

Time (sec)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

Nor

mal

ized

exc

ess

pore

pre

ssur

e (Δ

u/ Δ

u i)

Depth

15.72 m

3.7 m

5.26 m

6.46 m

12.6 m

19.3 m

20.78

22.12 m

Figure 3.7: Dissipation tests at Evangeline site (Abu-Farsakh, 2003)

3.2.2 US 90 - La 88 Interchange Site - New-Iberia

This site is about 10 miles south of New Iberia at US 90 interchange at La highway 88. The

soil profile and in situ soil parameters based on boring logs are given in Figure 3.8. The

rigidity index was estimated to be Ir = 50.Figure 3.9 presents the profile of PCPT data at New

Iberia and plots of five dissipation tests conducted at this site at depths of 1.8 m, 2.8 m, 4.28

m, 5.8 m, and 7.24 m is given in Figure 3.10. The water table was located at about 1.5 m

below ground surface.

3.2.3 LA Peans Canal Bridge Site - Lafourche

The LA Peans canal bridge site is located at about 5 miles southeast of Thibodaux, Lafourche

Parish. Summary of the bore log, laboratory soil test results, PCPT profile and dissipation

tests are presented in the Figures 3.11 through 3.13. The rigidity index was estimated to be Ir

= 35. The water table at this site was located at about 1.75 m below ground surface.

3.2.4 Pearl River Bridge Site

The Pearl River Bridge is located at I-10 near the State border between Louisiana and

Mississippi. Bore log, laboratory test and PCPT profile at the test site are given in Figure 3.14

through 3.15. Pore pressure dissipation tests were performed at different depths (1.68, 2.60,

and 4.42 6.25, 7.15, and 9.0 m). The water table was at about 1.0 m depth. The results of the

dissipation tests are presented in Figure 3.16. The dissipation test curve obtained at 2.6 m

showed initial increase in pore pressure before it the start to decay in monotonic manner.

50

0

1

2

3

4

5

6

7

8

9

10

Dep

th (m

)

Soil Type0 10 20 30 40 50 60

m.c, L.L. and P.L.

0 2 4 6 8 10

Modulus, M (MPa)

1E-4 1E-3 1E-2 1E-1

cv (cm2/sec)

0 2 4 6 8 10

OCR

Stiff to medium dark gray silty clay

medium brown silty clay

P.L.

m.c.

L.L.

Stiff tan and gray silty clay

Silty sand and sandy soils interbedded with thin thin layers ofsilty clay and silt

0 40 80 120 160

Su (kPa)

Figure 3.8: Soil profile for New Iberia site at US 90 and La 88 (Abu-Farsakh, 2003).

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Dep

th (m

)

0 5 10 15 20

Tip Resistance, qt, (MPa)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

0.0 0.1 0.2 0.3

Sleeve Friction, fs, (MPa)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

0 2 4 6 8

Rf (%)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

0 1 2 3

Pore Pressure (MPa)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

0 20 40 60 80 100


Clayey

Silty

u1- test 1

u2- test 2

Sandy

Test 1

Test 2

Test 1

Test 2Test 1

Test 2

Figure 3.9: PCPT profiles and soil classification at US 90–La 88 interchange, New Iberia site (Abu-Farsakh, 2003).

51

1 10 100 1000 10000

Time (sec)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

Nor

mal

ized

exc

ess

pore

pre

ssur

e (Δ

u/ Δ

u i)

Depth

1.8 m

2.8 m4.28 m

5.8 m

7.24 m

Figure 3.10: Dissipation tests at US 90 – La 88 interchange, New Iberia site ( Abu-Farsakh, 2003)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Dep

th (m

)

Soil Type0 20 40 60 80 100

m.c, L.L. and P.L.

0 2 4 6

Modulus, M (MPa)

1E-5 1E-4 1E-3 1E-2

cv (cm2/sec)

0 1 2 3 4 5

OCR

Medium brown to gray silty clay

P.L.

m.c.

L.L.

Gray silty sand

Medium silty sand interbedded with silty clay lenses

0 20 40 60 80

Su (kPa)

Soft to medium brown silt clay and clay soil

Figure 3.11: Soil profile for LA PEANS canal, Lafourche (Abu-Farsakh, 2003).

52

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Dep

th (m

)

0 2 4 6 8 10


0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

0.00 0.05 0.10 0.15


0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

0 2 4 6 8 10

Rf (%)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

0.0 0.2 0.4 0.6

Pore Pressure (MPa)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

0 20 40 60 80 100


Clayey

Silty

Sandy

u1- test 1

u2- test 2Test 1

Test 2

Test 1

Test 2

Figure 3.12: PCPT profiles and soil classification for LA Peans canal Bridge, Lafourche site (Abu-Farsakh, 2003).

1 10 100 1000 10000

Time (sec)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

Nor

mal

ized

exc

ess

pore

pre

ssur

e (Δ

u/ u

i)

Depth

2.5 m

7.0 m8.5 m

11.0 m

Figure 3.13: Dissipation tests at LA Peans canal Bridge, Lafourche site (Abu-Farsakh, 2003).

53

0

1

2

3

4

5

6

7

8

9

10

Dep

th (m

)

Soil Type0 20 40 60 80 100

m.c, L.L. and P.L.

0 2 4 6 8 10

Modulus, M (MPa)

1E-5 1E-4 1E-3

cv (cm2/sec)

0 2 4 6 8 10 12

OCR

Loose tan fine sand

Medium stiff tan & gray sandy clay

0 50 100

Su (kPa)

Soft gray siltyclay with clay layers and wood

Very soft gray silty clay with wood

Stiff gray silty clay with wood

Loose tan fine sand

P.L.

m.c.

L.L.

Figure 3.14: Soil profile for Pearl River site (Abu-Farsakh, 2003).

0

1

2

3

4

5

6

7

8

9

10

Dep

th (m

)

0 5 10 15 20


0

1

2

3

4

5

6

7

8

9

10

0.0 0.1 0.2


0

1

2

3

4

5

6

7

8

9

10

0 2 4 6 8

Rf (%)

0

1

2

3

4

5

6

7

8

9

10

0 1 1 2

Pore Pressure (MPa)

0

1

2

3

4

5

6

7

8

9

10

0 20 40 60 80 100


Sandy

Silty

Clayey

u1- test 1

u2- test 2 Test 1

Test 2

Test 1

Test 2

Figure 3.15: PCPT profile for Pearl River site (Abu-Farsakh, 2003).

54

1 10 100 1000 10000

Time (sec)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

Nor

mal

ized

exc

ess

pore

pre

ssur

e (Δ

u/ Δ

u i)

1.68 m

Depth

2.60 m

4.42 m

6.25 m

7.15 m

9.0 m

Figure 3.16: Dissipation tests at Pearl River site (Abu-Farsakh, 2003).

3.2.5 East Airport Site

This site is located at 300 East Airport Road in Baton Rouge. Five boreholes were drilled in

the site with depths up to 10 m. Summary of the bore log and laboratory test result is given in

Figure 3.17. PCPT profile and dissipation test result are presented in Figure 3.18 and 3.19.

The rigidity index was estimated to be Ir = 30. The water table in this site was at about 1.0 m.

The dissipation tests were conducted at depths of 1.5 m, 3.2 m, 4.7 m, 6.1 m and 6.74 m as

shown in Figure 3.19. The dissipation curves for the soil layer at the depth of 4.7 m and 6.7 m

shows the initial increase in excess pore pressure, before actual monotonic decay starts (type3

curves).

3.2.6 Flat River-Bossier Site

The site is located on the east bank of the Flat River in Bossier Parish. The soil profile at this

site consists of soft to medium silty clay soils down to 4.6 m, medium to stiff heavy clay from

4.6 to 8 m, followed by sand underneath it. Bore log, laboratory test and PCPT profile at the

investigated site are given in Figure 3.20 and 3.21. The water table at this site was deeper

than the clay layer, as can be seen from the pore pressure profile. Therefore, dissipation tests

were not conducted in this site, and only the relations that are not dependent on pore pressure

measurements are used in the analysis (Abu-Farsakh, 2003).

55

0

1

2

3

4

5

6

7

8

9

10

Dep

th (m

)

Soil Type0 10 20 30 40 50 60

m.c, L.L. and P.L.

0 2 4 6 8 10

Modulus, M (MPa)

1E-4 1E-3 1E-2 1E-1

cv (cm2/sec)

0 5 10 15 20 25

OCR

Gray clay with organic trace

Clayey sand with layers of sand

P.L.

m.c.

L.L.

Medium clay with clayey sand

Sand

0 40 80 120 160

Su (kPa)

Stiff clay

Stiff clayey sand

Figure 3.17: Soil boring profile for East Airport site (Abu-Farsakh, 2003).

0

1

2

3

4

5

6

7

8

9

10

Dep

th (m

)

0 5 10 15 20 25 30 35


0

1

2

3

4

5

6

7

8

9

10

0

1

2

3

4

5

6

7

8

9

10

0 2 4 6 8 10

Rf (%)

0

1

2

3

4

5

6

7

8

9

10

0.0 0.5 1.0 1.5 2.0

Pore Pressure (MPa)

0

1

2

3

4

5

6

7

8

9

10

0 20 40 60 80 100


Silty

Clayey

Sandy

u1- test 1

u2- test 2

Test 1

Test 2

0.0 0.1 0.2 0.3 0.4


Test 1

Test 2

Figure 3.18: PCPT profiles and soil classification for East Airport site (Abu-Farsakh, 2003).

56

1 10 100 1000 10000

Time (sec)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

Nor

mal

ized

exc

ess

pore

pre

ssur

e (Δ

u/ Δ

u i)

Depth

4.7 m

1.5 m

6.1 m

6.74 m

3.2 m

Figure 3.19: Dissipation tests at East Airport site (Abu-Farsakh, 2003).

0

1

2

3

4

5

6

7

8

9

10

Dep

th (m

)

Soil Type0 20 40 60 80 100

m.c, L.L. and P.L.

0 2 4 6 8 10

Modulus, M (MPa)

0 2 4 6 8 10

OCR

Soft to mediumbrown silty clay

Medium brown silty clay

P.L.

m.c.

L.L.Sand

0 20 40 60 80 100

Su (kPa)

Medium to stiff brown heavy clay

Figure 3.20: Soil boring profile for Flat River site (Abu-Farsakh, 2003).

57

0

1

2

3

4

5

6

7

8

9

10

11

12

13

Dep

th (m

)0 5 10 15 20


0

1

2

3

4

5

6

7

8

9

10

11

12

13

0.0 0.1 0.2


0

1

2

3

4

5

6

7

8

9

10

11

12

13

0 2 4 6 8

Rf (%)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

0.0 0.2 0.4 0.6 0.8 1.0

Pore Pressure (MPa)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

0 20 40 60 80 100


Clayey

Sandy

Silty

Figure 3.21: PCPT profiles and soil classification for Flat River site (Abu-Farsakh, 2003).

3.2.7 Pavement Research Facility Site

The Pavement Research Facility, PRF, site is a research site located at about 2 miles

west of Baton Rouge. This site was used in this study for the evaluation of the PCPT

interpretation methods, and for the verification of settlement prediction. The boring profile

and soil properties of the PRF site are presented in Figure 3.22.The rigidity index for the PRF

site is Ir = 30. The profiles of PCPT test results (qt, fs, Rf, u1 and u2) and the corresponding

CPT soil classification using Zhang and Tumay (1999) method are presented in Figure 3.23.

Six dissipation tests were conducted at PRF site at 1.66 m, 2.64 m, 3.32 m, 3.8 m, 4.36 m and

5.08 m depths. The water table at the PRF site was about 1.0 m below the surface. Figure

3.24 depicts the results of these dissipation tests. Some of the dissipation curve follows the

initial increase in pore pressure before real dissipation starts (type III curve), trend observed

also at Pearl River site.

Tabulated summary of the soil properties at all the seven investigated sites is

presented in the Table 3.1. The results of the PI versus LL plotted on the plasticity chart from

the Unified Soil Classification System in Figure 3.25, indicates that the soils primarily

consists of CL and CH materials.

58

0

1

2

3

4

5

6

7

8

9

10

Dep

th (m

)

Soil Type0 30 60 90 120150

m.c, L.L. and P.L.

0 2 4 6 8 10

Modulus, M (MPa)

1E-5 1E-4 1E-3 1E-2

cv (cm2/sec)

0 5 10 15 20

OCR

Medium gray silty clay

Medium brown silty clay

P.L.

m.c.

L.L.

Stiff gray clay

Loose gray fine silty sand with lenses of clayey sand and silt

0 20 40 60 80

Su (kPa)

Soft to medium gray clayey silt

Figure 3.22: Soil boring profile for PRF site.

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

Dep

th (m

)

0 5 10 15 20


0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

0.0 0.1 0.2


0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

0 2 4 6 8 10

Rf

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

0.0 0.5 1.0

Pore Pressure (MPa)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

0 20 40 60 80 100


Clayey

Silty

u1- test 1

u2- test 2

Sandy

Test 1

Test 2

Test 1

Test 2

Test 1

Test 2

Figure 3.23: PCPT profiles and soil classification for PRF site(Abu-Farsakh, 2003).

59

1 10 100 1000 10000

Time (sec)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

Nor

mal

ized

exc

ess

pore

pre

ssur

e (Δ

u/ Δ

u i)

Depth

5.08 m

3.80 m

4.36 m

3.32 m

2.64 m

1.66 m

Figure 3.24 : Dissipation tests at PRF site (Abu-Farsakh, 2003).

0 10 20 30 40 50 60 70 80 90 100

Liquid Limit (LL)

0

10

20

30

40

50

60

PI

U-line

Test Sites:AlfLafourcheNew Iberia

EvangelenePearl RiverEast AirportBossier A-line

MH or OHCL ML

or OL

CH

CL-ML

Figure 3.25 Plasticity chart for USCS Classification at investigated sites (Developed from Casagrande, 1948, and Howard , 1977).

60

Table 3.1: Summary of soil properties for the investigated sites.

Site

Unit weight (kN/m3)

Water content (%)

Liquid Limit (%)

Plasticity Index

Clay content (%)

Su (kN/m2)

OCR

Manwell Bridge Evangeline

16 – 20 (18.5)

17 – 48 (32)

23 – 77 (48.9)

6 – 44 (25)

17 – 66 (42.3)

29 – 142 (71)

1 – 5.2

US 90 – La 88 New Iberia

18.2–18.8 (18.3)

23 – 33 (25.5)

30 – 35 (33.2)

9 – 17 (12)

22 – 26 (24.3)

38 – 118 (87)

1.2 – 4.3

LA Peans canal bridge Lafourche

15 – 19 (16.8)

29 – 61 (38.8)

34 – 66 (46.8)

13 – 39 (21.4)

42 – 57 (52.2)

12.5 – 48 (28.4)

1 – 3.4

Pearl River 15 – 18.5 (16.2)

21 – 45 (32.2)

42 – 64 (53.6)

22 – 39 (30.3)

26 – 68 (43.6)

14.5–43.9 (25.7)

1.5 – 9.8

East Airport Baton Rouge

16.5 – 19 (17.6)

12.4-28 (20)

30 – 41 (33.7)

12 – 23 (16.8)

26.2-69.6 (51)

38.3–118 (80.8)

3.5 - 21

Flat River Bossier

15.8–19.2 (17.4)

29.5–46 (36.1)

44 – 81 (63.6)

25 – 49 (36)

41.2–83 (66.6)

43.2–76 (54.8)

1 – 5.84

PRF 16–16.9 (16.6)

31–63 (49)

64 – 115 (91.7)

25 – 41 (31.8)

25 – 45 (41.4)

18.3– 43.9 (25.7)

2 – 16.5

3.3 Soil Classification Based on PCPT Data.

Various charts have been developed by different researchers such as Shmertmann (1978),

Douglas and Olsen (1981), Robertson et al. (1986), Robertson (1990) and others, which can

be used for prediction of soil types. Although the PCPT classification charts may not

necessarily provide the accurate prediction of soil type based on grain size distribution, they

offer a good guide to soil behavior type (Douglas and Olsen, 1981). Figures 3.26 to Figure

3.30 presents the soil classification for test sites determined based on common CPT charts.

Shmertmann (1978) chart is based results from the mechanical cone data from North Central

Florida soils. Also the original chart used the uncorrected cone tip resistance (qc). However,

in this study corrected cone tip (qt) is used for plotting.

Douglas and Olsen (1981) chart, on the other hand, was developed based on the test

results from electric cone penetrometer. The chart also incorporates the unified soil

classification and indicates the trend for liquidity index, sensitivity and lateral earth pressure

as shown in Figure 3.27. Robertson et al. (1986) and Robertson (1990) chart were based on

electric piezocone tests data and used corrected cone tip resistance. These charts divide the

area into twelve zones that identify different soil types. A novel feature in these profiling

charts is the delineation of Zones 1, 11, and 12, representing somewhat extreme soil

responses thus enabling the PCPT to uncover more than just soil grain size. Zones 3 through

10 indicate a gradual transition from fine-grained to coarse-grained soil.

61

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

FR=fs/qt %

1

10

2.00

4.00

6.00

8.00

20.00

40.00

0.80

0.60

0.40

0.20

Con

e tip

resi

stan

ce,q

t (M

Pa)

Organic ClaysMixed Soils

Very Soft

Sandy andSilty Clay

Loose

Clayey-Sands and Silts

Silt and Sand Mixtures

Insensitivenon fissuredorganic Clays

Very Stiff

Stiff

Medium

Soft

Shel

ls, S

ands

Lim

eroc

ks

Dense orCemented

Sand

Figure 3.26: Soil Classification chart per Shmertmann (1978)

0.0 1.0 2.0 3.0 4.0 5.0 6.0

FR=fs/qt %

1

10

100

1000

2

4

68

20

40

6080

200

400

600800

Cone

tip

resi

stanc

e,q t

(TSF

)

1

10

2

4

6

8

20

40

60

80M

PaIncreasing Fine Content

SM & SP

Non CohesiveCoarse Grained

CL CH

ML

Increasing Grain Size

Increasing Void Ratio

SensitiveClays

fs=0.025 TSF

f s=0.125 TSF

fs=0.5 TSF

fs=2.0 TSFNon CohesiveCoarse and FineGrained Cohesive Non

Cohesive Fine Grained

Cohesive Fine Grained

Incr

easin

g K o

Incr

easin

g LI

Sensitive MixedSoils

Metastable Sands

Figure 3.27 Soil Profile Chart as per Douglas and Olsen (1981)

62

0.1 1.0 10.0

Normalised Friction Ratio, fs/(qt−σνο)

1

10

100

1000

Nor

mal

ised

Con

e tip

resi

stan

ce, (

q t-σ

νο)/σ

' νο Test Sites :AlfLafourcheNew Iberia

EvangelenePearl RiverEast Airport

1

Normally Consolidated

2

34

5

6

7 8

9

Increasing

Sensitivity

Increasing

OCR & age

Increasing

OCR, age,

cementationφ'

Zone Soil Behavior Type 1 Sensitive, Fine grained 2 Organic soils-peats 3 Clays-clay to silty clay 4 Silt Mixtures clayey silt to silty clay 5 Sand Mixtures, silty sand to sandy silts 6 Sands, clean sands to silty sands 7 Gravelly sand to sand8 Very stiff sand to clayey sand 9 Very stiff fine grained

Figure 3.28 Classification Chart as per Robertson (1990)

0.0 0.4 0.8 1.2

Bq2=(u2-u0)/(qt-σ'νο)

1

10

100

1000

Nor

mal

ised

Con

e tip

resi

stan

ce, (

q t-σ

νο)/σ

' νο

12

3

4

5

6

7Zone Soil Behavior Type 1 Sensitive, Fine grained 2 Organic soils-peats 3 Clays-clay to silty clay 4 Silt Mixtures clayey silt to silty clay 5 Sand Mixtures, silty sand to sandy silts 6 Sands, clean sands to silty sands 7 Gravelly sand to sand8 Very stiff sand to clayey sand 9 Very stiff fine grained

Test Si tes:AlfLafourcheNew Iberia


Figure 3.29 Soil behavior type classification chart based on normalized PCPT data (modified after Robertson , 1990)

63

0.0 0.4 0.8 1.2

Bq1=(u1-u0)/(qt-σ'νο)

1

10

100

1000

Nor

mal

ised

Con

e tip

resi

stan

ce, (

q t-σ

νο)/σ

' νο

12

3

4

5

6

7Zone Soil Behavior Type 1 Sensitive, Fine grained 2 Organic soils-peats 3 Clays-clay to silty clay 4 Silt Mixtures clayey silt to silty clay 5 Sand Mixtures, silty sand to sandy silts 6 Sands, clean sands to silty sands 7 Gravelly sand to sand8 Very stiff sand to clayey sand 9 Very stiff fine grained



Figure 3.30 Soil behavior type classification chart based on normalized PCPT data (modified after Robertson, 1990)

3.4 Verification Sites

In total five sites will be used for the verification of statistical correlations obtained from data

collected from seven investigated sites. In addition to laboratory and in situ tests, settlement

under the embankment loading was also monitored in these sites which will be used to back

calculate the consolidation parameters and to compare the settlement profile with those

predicted from laboratory and PCPT method. Brief description of test results and soil profiles

at the verification site is presented in the following subsections:

3.4.1 Juban North Embankment

Test site is related to the embankment of ramp construction project for Juban road

interchange between I-12 and LA 1026, located north-east of Baton Rouge in Livingston

Parish.

Two boreholes drilled on north side of the embankment. Basic soil stratigraphy as

revealed from drilling results can be described as top soil layers consisting of Brown gray

lean clay with occasional traces of organics and/or concretion. Soil below the depth of 10 m

is silty-clay with lenses of sand and is underlain by dense sand at the depth of about 25 m.

Groundwater level is about 2 m below ground surface.

64

Sample taken from the soil boring showed that the natural water content is close to

plastic limit with a mean value of w = 25%. The unit weight lies in the range of γ= 15 kN/m3

to 21 kN/m3. Undrained shear strength, su varies from 17 kPa to 177.5 kPa. Coefficient of

consolidation (cv) as obtained from oedometer test is in the range of 1.36 x 10-4 cm2/ sec to

9.6 x 10-3 cm2/sec.

High overconsolidation because of various effects occurs in the top layer down to the

depth of 2 m. On the north side, OCR was fairly constant at 4 and decreased to almost 3 at the

depth of about 11 m.

Description of soil profile to the depth of 20 m showing the soil log, Atterberg limits,

undrained shear strength, constrained modulus, coefficient of consolidation and OCR is

shown in Figures 3.31. A summary of the laboratory tests is presented in the Table 3.2.

Figure 3.32 presents the PCPT profile and results of the dissipation tests conducted at

different depths are plotted in Figure 3.33. The results of the one-dimensional consolidation

tests conducted on the sample taken from the site different depths are plotted in Figures 3.34

through Figure 3.39.

PLLLmc

0 20 40 60 80 100mc, LL and PL

0 50 100 150 200Su (kPa)

0 2 4 6 8Modulus M (MPa)

1E-004 1E-003 1E-002Cv (cm2/sec)

Silty

Soil Type

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Stiff Brown +Gray Lean Clay w/ SI SA

Gray Clay w/ IROXORG = 9%

Stiff Brown Sandy Clay

Stiff Brown+Gray Clay w/ lens of sand

Brown +Gray Clay

w/ TR ORG

Stiff Brown + Gray Clay w/ sand

w/ Conc

w/TR ORG

0 5 10 15 20 25OCR

Medium dense Gray Siltysand

w/ TR Clay

Stiff Gray Clay

Very stiff Gray Sandy Clay

Stiff Gray + Brown Lean Clay w/ conc.

w/ TR. ORG 11 %

Figure 3.31 Soil boring profile for Juban North Embankment site.

65

Figure 3.32: PCPT profiles and soil classification for North Embankment site.

4.017 m

2.125 m

9.829 m6.04 m 10.809 m

1 10 100 1000 10000 100000

Time (sec)

0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.7

Nor

mal

ized

exc

ess

pore

pre

ssur

e (Δ

u/ u

i)

7.905 m

6.04 m

7.798 m

11.01 m

Figure 3.33: Dissipation tests at Juban North Embankment site.

66

0.1 1.0 10.0 100.0


0.6

0.7

0.8

0.9

Void

Rat

io

(Pc= 1.05 TSF)

Cc= 0.158Cr= 0.054

3.0E-004 4.0E-004 5.0E-004 6.0E-004

Coefficient of consolidation (cm2/sec)

0.6

0.7

0.8

0.9

Figure 3.34: Oedometer test result for depth 0-1.5m

(Pc= 0.81 TSF)

Cc= 0.164 Cr= 0.048

0.1 1.0 10.0 100.0


0.6

0.7

0.8

0.9

Void

Rat

io

0.0E+000 1.0E-004 2.0E-004 3.0E-004


0.6

0.7

0.8

0.9

Figure 3.35: Oedometer test result for depth 1.5-3.0

67

(Pc= 1.05 TSF)

Cc= 0.22 Cr= 0.092

0.1 1.0 10.0 100.0


0.6

0.7

0.8

0.9

1.0

Void

Rat

io

0.0E+000 4.0E-004 8.0E-004 1.2E-003


0.6

0.7

0.8

0.9

1.0

Figure 3.36: Oedometer test result for depth 3.0-4.6 m.

(Pc= 1.6 TSF)

Cc= 0.215 Cr= 0.081

0.1 1.0 10.0 100.0


0.6

0.7

0.8

0.9

1.0

Void

Rat

io

6.0E-005 8.0E-005 1.0E-004 1.2E-004


0.6

0.7

0.8

0.9

1.0


68

(Pc= 4 TSF)

Cc= 0.166 Cr= 0.038

0.1 1.0 10.0 100.0


0.3

0.4

0.5

0.6Vo

id R

atio

0.0E+000 1.0E-003 2.0E-003 3.0E-003 4.0E-003 5.0E-003


0.3

0.4

0.5

0.6


(Pc= 3 TSF)

Cc= 0.174 Cr= 0.085

0.1 1.0 10.0 100.0


0.3

0.4

0.5

0.6

Void

Rat

io

0.0E+000 1.0E-003 2.0E-003 3.0E-003 4.0E-003


0.3

0.4

0.5

0.6


69

Table 3.2 : Summary of soil properties for Juban North Site

Depth (m)

γ (kN/ m3)

Water Cont ent (%)

Liquid Limit (%)

Plastic Limit (%)

Su (kN/ m2)

OCR Cv

(cm2

/sec) Cc Cr e0

0- 1.5

17.9-18.8 13-26 45-50 20-25 67-150 20.8 6.6E-04 0.158 0.054 0.882

1.5-3.0

18.8-20.3 20-26 45-51 20-24 67-112 6.47 - 0.164 0.048 0.915

3.0-4.6

19.5-20.3 20-66 47-50 15-24 90-123 4.01 2.1E-03 0.220 0.092 0.954

4.6-6.1

18.7-19.5 24-66 30-72 20-23 63-90 4.37 1.4E-04 0.215 0.081 0.987

6.1-7.6

18.4-19.0 24-28 30-74 20-23 63-69 7.94 2.4E-03 0.166 0.038 0.586

7.6-9.1

18.4-18.7 25-28 64-74 23-26 69-116 4.42 3.0E-04 0.255 0.110 0.579

9.1- 11.3

18.5-19.0 25-26 67-70 21-23 48-116 2.95 9.6E-03 0.200 0.085 0.609

11.3-12.2

19.0-20.3 15-25 67-70 15-21 23-48 2.94 3.7E-03 0.174 0.085 0.530

3.4.2 Juban South Embankment

The test site is at the south embankment of the ramp constructed for Juban road

interchange between I-12 and LA 1026, located north-east of Baton Rouge in Livingston

Parish.

Two boreholes drilled on south side revealed the basic soil stratigraphy as top soil

layers consisting of Stiff Grey to lean brown gray lean clay with occasional traces of

organics and/or irox. Soil between the depths of 12 m to 17 m consist of dense silty sand

followed by stiff brown clay to grey silty clay down to the depth of 20 m. This was followed

by stiff clay to dense sand underlain by very dense sand. Groundwater level is at about 2 m

below ground surface.

Laboratory tests on the soil samples extracted from the site showed that natural water

content is close to plastic limit with a mean value of w = 25 %. Unit weight lies in the range

of γ= 15 kN/m3 to 19 kN/m3. Undrained shear strength, su varies from 40 kPa to 137 kPa.

Coefficient of consolidation as obtained from oedometer test is in the range of 4.8 x 10-4 cm2/

sec to 3.2 x 10-3 cm2/sec. Figure 3.40 depicts the soil profile to the depth of 20 m. Figure 3.41

70

and Figure 3.42 shows the PCPT profile and results of dissipation tests at the test site.

Summary of the laboratory test results is presented in the Table 3.3. Results from one-

dimensional consolidation test are plotted in Figure 3.43 to Figure 3.49.

PLLLmc

0 20 40 60 80 100mc, LL and PL

0 50 100 150 200Su (kPa)

0 2 4 6 8Modulus M (MPa)

1E-004 1E-003 1E-002Cv (cm2/sec)

Silty

Soil Type

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Stiff Gray Lean Clay w/ TR IROXORG=6%

Gray Clay w/ IROX

ORG = 11%

Stiff Gray Clay

w/ TR ORG

w/ TR Irox

Stiff Brown + Gray Clay

w/TR ORG

w/ SI

0 5 10 15 20 25OCR

Dense Gray Siltysand

Stiff Gray + Brown Lean Clay w/ conc.

w/ TR. IROXw/ ORG 9 %

Brown Lean Clay w/ Conc.

w/ LENS SI

Figure 3.40: Soil boring profile for Juban South Embankment site.

Figure 3.41: PCPT profiles and soil classification for South Embankment site.

71

2.125 m

6.03m 8.09 m

1 10 100 1000 10000 100000

Time (sec)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

Nor

mal

ized

exc

ess

pore

pre

ssur

e (Δ

u/ u

i)

4.05 m10.013

Figure 3.42: Dissipation tests at South Embankment site.

0.1 1.0 10.0 100.0


0.3

0.4

0.5

0.6

0.7

0.8

Void

Rat

io

(Pc= 1.8 TSF)

Cc= 0.22Cr= 0.1

0.0E+000 1.0E-004 2.0E-004 3.0E-004 4.0E-004 5.0E-004


0.3

0.4

0.5

0.6

0.7

0.8

Figure 3.43: Oedometer test result for depth 0-1.5m

72

0.1 1.0 10.0 100.0


0.2

0.3

0.4

Void

Rat

io

(Pc= 1.6 TSF)

Cc= 0.084Cr= 0.018


0.1 1.0 10.0 100.0


0.5

0.6

0.7

0.8

0.9

1.0

Void

Rat

io

(Pc= 1.2 TSF)

Cc= 0.280Cr= 0.08

1.0E-004 2.0E-004 3.0E-004 4.0E-004 5.0E-004


0.5

0.6

0.7

0.8

0.9

1.0


73

0.1 1.0 10.0 100.0


0.3

0.4

0.5

0.6

0.7

0.8

Void

Rat

io

(Pc= 1.6 TSF)

Cc= 0.21Cr= 0.085

0.0E+000 1.0E-004 2.0E-004 3.0E-004


0.3

0.4

0.5

0.6

0.7

0.8


0.1 1.0 10.0 100.0


0.6

0.7

0.8

0.9

1.0

1.1

Void

Rat

io

(Pc= 1.2 TSF)

Cc= 0.251Cr= 0.12

0.0E+000 1.0E-004 2.0E-004 3.0E-004 4.0E-004 5.0E-004


0.6

0.7

0.8

0.9

1.0

1.1


74

(Pc= 1.6TSF)

Cc= 0.235Cr= 0.102

0.1 1.0 10.0 100.0


0.4

0.5

0.6

0.7

0.8

0.9Vo

id R

atio

0.0E+000 4.0E-004 8.0E-004 1.2E-003 1.6E-003 2.0E-003


0.4

0.5

0.6

0.7

0.8

0.9


(Pc= 1.1TSF)

Cc= 0.27Cr= 0.100

0.1 1.0 10.0 100.0


0.4

0.5

0.6

0.7

0.8

0.9

Void

Rat

io

0.0E+000 4.0E-004 8.0E-004 1.2E-003 1.6E-003 2.0E-003


0.4

0.5

0.6

0.7

0.8

0.9

Figure 3.49: Oedometer test result for depth 10.67 -12.2 m.

75

Table 3.3: Summary of soil properties for Juban South Embankment

Depth (m)

γ (kN /m3)

Water Cont ent %)

Liquid Limit (%)

Plastic Limit (%)

Su (kN /m3)

OCR Cv

(cm2

/sec) Cc Cr e0

0- 1.5

15.2-18.4 14-28 35-47 22-23 56 14.8 4.8E-04 0.22 0.100 0.705

1.5- 3.0

18.2-19.9 21-28 35-47 14-23 56-79 6.0 - 0.084 0.018 0.410

3.0- 4.6

19.9-18.2 21-34 47-66 14-16 45-79 2.5 7.6E-04 0.285 0.08 0.964

4.6- 6.1

18.2-18.5 28-34 66-90 16-30 45-90 3.8 - 0.203 0.068 0.761

6.1- 7.6

18.2-19.3 24-28 37-60 19-20 40-65 1.7 3.9E-04 0.251 0.120 1.101

7.6- 9.1

19.2-19.3 24-33 37-48 15-19 40-104 2.9 - 0.250 0.090 0.665

9.1-10.7

19.2-19.3 25-33 48-56 15-12 46-104 1.1 1.9E-03 0.235 0.102 0.837

10.7-12.2

18.8-19.3 25-29 48-70 12-24 46-137 1.0 3.2E-03 0.270 0.100 0.843

3.4.3 LTRC test wall at PRF site

A 6 m high and 48 m long instrumented reinforced-soil wall was constructed at PRF for

another study of soil- geosythetic interaction mechanism to evaluate the effect of

reinforcement properties on the deformation and stress distribution of reinforced wall (Farrag

et al., 2003). Detail soil properties and instrumentation at the PRF test site is discussed in the

report (FHWA/ LA03/379). Soil profile and PCPT profile at the test wall were discussed in

the section 3.2. This site was instrumented with the horizontal inclinometer and settlement

plates as shown in Figure 3.50.

3.4.4 John Darnell site

This verification site is located at the intersection of John Darnell Road with LA 88. A 2.56

m high embankment was constructed on the west side that is underlain by natural soil mainly

consisting of silty clay down to the depth of 13.5m. The PCPT profile and the dissipation

tests curves at the test site are given in Figure 3.51 to Figure 3.52. In order to accelerate the

time rate of settlement under the embankment, 3 feet surcharge and PVD with a 5 feet

triangular spacing was used. Settlement under the embankment was monitored using

settlement plates.

76

Figure 3.50: Plan and the elevation of LTRC wall at ALF site (Farrag et al., 2003)

3.4.5 Louisiana Avenue site

The settlement under an embankment constructed at the east approach of the intersection of

LA Avenue with I-10, near Lafayette was monitored using settlement plates. The

embankment has the height of 22 feet and surcharge of 3 feet along with PVD at the

triangular spacing of 5 feet was used to accelerate the rate of consolidation settlement. PCPT

profile and the plot of dissipation test results at the investigated site are given in Figure 3.53

and Figure 3.54 respectively. The last three sites were analyzed by Abu-Farsakh and they

were only used to test the embankment settlement program developed here in this study.

77

0123456789

1011121314151617181920

Dep

th (m

)

0 10 20


0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

0.0 0.1 0.2 0.3 0.4 0.5


0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

0 2 4 6 8 10

Rf (%)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

0.0 0.5 1.0 1.5

Pore Pressure (MPa)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

0 20 40 60 80 100


Clayey

Sandy

U1

Figure 3.51 PCPT profile and soil classification at John Darnell site (Abu-Farsakh, 2003)

1 10 100 1000 10000Time (sec)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Nor

mal

ized

exc

ess

pore

pre

ssur

e (Δ

u/ u

i) Depth

6.76 m

3.04 m5.2 m

9.54 m

11.46 m

12.88 m

1 10 100 1000 10000

Time (sec)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Nor

mal

ized

exc

ess

pore

pre

ssur

e (Δ

u/ u

i) Depth

6.7 m

13.5m

3.38 m

4.64 m 8.8 m

Figure 3.52 Dissipation curves at John Darnell site (Abu-Farsakh, 2003)

78

0123456789

1011121314151617181920

Dep

th (m

)

0 10 20 30 40 50


0123456789

1011121314151617181920

0.0 0.1 0.2 0.3 0.4 0.5


0123456789

1011121314151617181920

0 2 4 6 8 10

Rf (%)

0123456789

1011121314151617181920

0.0 0.5 1.0 1.5

Pore Pressure (MPa)

0123456789

1011121314151617181920

0 20 40 60 80 100


Clayey

Sandy

U1

Figure 3.53 :PCPT profile and soil classification profile at LA avenue site (Abu-Farsakh,2003).

Figure 3.54 Dissipation curves LA avenue site (Abu-Farsakh, 2003)

1 10 100 1000 10000Time (sec)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Nor

mal

ized

exc

ess

pore

pre

ssur

e (Δ

u/ u

i)

Depth

7.98 m

3.98 m

6.0 m

10.86 m

11.8 m

1 10 100 1000 10000Time (sec)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

Nor

mal

ized

exc

ess

pore

pre

ssur

e (Δ

u/ u

i)

Depth

1.98 m

7.86 m

9.94 m

10.38 m

5.98 m4.14 m

79

CHAPTER 4

4 STATISTICAL ANALYSIS

A brief review of statistical models, regression analyses, assumptions, limitations and

practical considerations is given in this chapter. Results from statistical analyses to calibrate

existing models and/ or to explore new models for evaluation of consolidation parameter are

presented in details.

4.1 Statistical Techniques

A mathematical model is a simple description of physical, chemical or biological processes.

Simple example of the mathematical model is a relation between two variables with a straight

line. Y equals a slope times X plus an intercept (Figure 4.1). In some cases relation between

the variable may be determined from the theoretical relation, however, relation can also be

obtained from the statistical analysis of measured set of X and Y using standard techniques

such as regression or curve fitting methods.

Figure 4.1: Simple linear relation between X and Y.

4.1.1 Regression Analysis

Simple linear regression (SLR) analysis is a relation between two variables X and Y such that

best fit straight line pass through the set of data. The goal of linear regression is to adjust the

values of slope and intercept to find the line that best predicts Y from X. More precisely, the

goal of regression is to minimize the sum of the squares of the vertical distances (errors) of

the points from the line.

The regression line can then be expressed as:

εββ ++= XY *10 [78]

80

where 0β is intercept term and 1β is slope of the. ε is random error term that arises

from the fact that in nature we hardly have perfect fit and there is always a substantial

variation of the observed points around the fitted regression line.

Multiple linear regression (MLR) can be conceived as an extension of simple linear

regression (SLR) where the dependent variable is influenced by more than one variable. In

that case, the regression equation can be visualized as plane rather than straight line.

εββββ ++++= nn XXXY *........** 22110 [79]

In terms of matrix notation, above equation is presented as

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

⎪⎪⎪

⎭

⎪⎪⎪

⎬

⎫

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

⎪⎪⎪

⎭

⎪⎪⎪

⎬

⎫

=

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

⎪⎪⎪

⎭

⎪⎪⎪

⎬

⎫

nnpnnn

p

p

p

n xxxx

xxxxxxxxxxxx

y

yyy

β

βββ

M

L

MLMMM

L

L

L

2

1

0

321

3333231

2212121

1121211

3

2

1

: [80]

or

[ ] [ ] [ ]βxy =

where y is 1×n vector of observation, x is a matrix of pn× where p is the number

of independent variable and β is 1×p vector of unknown parameters.

4.1.2 Indices for Model Assessment

There are various techniques that are used to assess the “goodness” of regression model in

explaining the relation between the dependent and independent variables. Most common

indices are summarized below:

4.1.2.1 Scatter Plot First step in regression modeling starts with exploring relationship between dependent

variable and different predictors. In addition to existing theoretical or empirical models that

correlate different variables, simple graphical displays are used to explore correlation. One of

the common tools used in statistics is Scatter plot which is the graphical representation of two

quantitative variables out of multidimensional data set. It shows the direction, strength, and

shape of the relationship between the two variables. If the direction of the points is from the

lower left of the plot to the upper right, high values of one variable occur with high values of

the other variable (a positive relationship). When points go from the upper left to the lower

right, high values of one variable occur with low values of the other (a negative relationship).

A scatter plot can also be used to spot outliers and nonlinear association.

81

4.1.2.2 Predicted and Residual Scores The deviation of a particular point from the regression line (its predicted value) is called the

residual value. For the perfect fit a straight line or plane passes through all the point and thus

residual value is zero. However, such ideal cases rarely exist and thus objective regression is

to fit a straight line or plane through the observation point such that sum of squares of

residual is minimized. Hence the model giving the minimum sum of square is rendered as the

one with better correlation.

4.1.2.3 Residual variance and R-square The smaller the variability of the residual values around the regression line relative to the

overall variability, the better is our prediction. For example, if there is no relationship

between the X and Y variables, then the ratio of the residual variability of the Y variable to the

original variance is equal to 1.0. If X and Y are perfectly related then there is no residual

variance and the ratio of variance would be 0.0. In most cases, the ratio would fall

somewhere between these extremes, that is, between 0.0 and 1.0. 1.0 minus this ratio is

referred to as R-square or the coefficient of determination.

SSTSSER −=12 [81]

where SSE =∑ − 2)( ii yy is the residual sum of square and SST is total sum of

squares, ∑ 2iy .

The R-square value is an indicator of how well the model fits the data (e.g., an R-

square close to 1.0 indicates that we have accounted for almost all of the variability with the

variables specified in the model). However, R-square increases with increase in number of

predictor in the model, even when the role of individual predictor is not significant. In case of

multiple regression analysis, thus alternative statistics is defined known as adjusted R2

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

−=pn

nSSTSSERadj

112 [82]

where n is the total number of observations and p is the number of predictors in the

model (independent variables)

4.1.2.4 Estimate of Standard Error (Es) The efficiency of regression line can also be evaluated through the estimation of standard

error given as

)(2

pnSSEEs −

= [83]

82

)( pnSSEEs −

= [84]

where Es2 is the unbiased estimator of variance and the smaller the variance the better

is the model.

4.1.3 Assumptions, Limitations, Practical Considerations

4.1.3.1 Assumption of Linearity Simple or multiple linear regressions assume that the relationship between variables is linear.

In practice this assumption can virtually never be confirmed; fortunately, multiple regression

procedures are not greatly affected by minor deviations from this assumption. However, as a

rule it is prudent to always look at bivariate scatterplot of the variables of interest. If

curvature in the relationships is evident, one may consider either transforming the variables,

or explicitly allowing for nonlinear components.

4.1.3.2 Check for Outlier An outlier is an observation which appears too large or too small in comparison to the other

values. An outlier may be an observation resulting from incorrect experimental process,

calculation and/ or sampling or the observed value is due to different mechanism other than

that guides rest of the data set. Sometimes, even if the observation is correct, but statistically

way out of the line relative to other values, it is necessary to omit point.

Outliers in the sample can be judged using scatter plot of residual against predictor.

Other parameters such as STUDENT, RSTUDENT test for residuals are also used as an

indicator. As a rule of thumb, RSTUDENT value greater than 3.0 indicates an outlier. SAS

also provides more sophisticated tools such as ROBUST REG procedure for outlier

diagnostic as well estimate of parameters that are less influenced by outlier observations.

4.2 Statistical analysis for Constrained Modulus (M)

4.2.1 Variables in the statistical analysis

One dimensional consolidation tests (ASTM D2435-04) were performed on high quality

Shelby tube samples obtained from the field. Piezocone data compiled included corrected

cone tip resistance (qt), sleeve friction (fs) and the pore pressure measured at various locations

(u1 and u2). Also, the soil information was collected on the index properties: moisture content

(mc), liquid limit (LL), plastic limit (PL), Plasticity index (PI). Undrained shear strength (Su),

average overburden pressure (σvo), average effective overburden pressure (σ’vo) and

hydrostatic pressure (u0) were estimated for corresponding layers based on bore hole log

83

information. In addition, parameters indicating the probabilities of soil types using PCPT

measurement (Zhang and Tumay, 1999) were also included in the study.

Scatter plot of Oedometric constrained modulus and various PCPT parameters are

presented in Figures 4.2 through 4.10. Direct linear increasing trend is evident from the

scatter plot between M versus qt (Figure 4.2). However data shows slight scattering at higher

value of qt and suggest bi-linear or non linear relationship. Figure 4.3 reveals increase in M

with increasing sleeve friction, though data are relatively scattered than in the plot against M

versus qt.

0 2 4

Cone Tip Resistance, qt (MPa)

0

2

4

6

8

Con

stra

ined

Mod

ulus

, M (M

Pa)

0 10 20 30 40TSF

0

10

20

30

40

50

60

70

80

TSF


EvangelenePearl RiverEast AirportBossier

Figure 4.2: M versus qt.

0.00 0.05 0.10 0.15 0.20

Sleeve friction, fs (MPa)

0

2

4

6

8

Con

stra

ined

Mod

ulus

, M (M

Pa)

0.0 0.4 0.8 1.2 1.6 2.0TSF

0

10

20

30

40

50

60

70

80

TSF



Figure 4.3: M versus fs.

Very weak trend was observed between M and the pore pressure measurement at cone

face (u1), as shown in Figure 4.4. On the other hand, data are highly scattered in the plot

between M versus u2 (Figure 4.5). Similarly, plot of M versus average overburden pressure

(σvo) shows the increasing trend but data are again, scattered as shown in Figure 4.6.

Similarly, Figures 4.7 and 4.8 shows the decreasing trend of M with increasing moisture

constant or plasticity index. Relations between compressibility and Atterberg’s limit were

also observed in other studies and reported in literature (Skemptom, 1944; Terzaghi and

Peck, 1967; Al-Khafaji and Andersland, 1992 and others). However, plot of M versus CL-

CH Figure 4.9) shows no clear trend where CL-CH represents the probability of finding clay

using Zhang and Tumay (2000) method.

84

0.00 0.50 1.00 1.50 2.00

Type 1 porepressure, u1( MPa)

0

2

4

6

8

Cons

train

ed M

odul

us, M

(MPa

)

0 4 8 12 16 20TSF

0

10

20

30

40

50

60

70

80

TSF



Figure 4.4: M versus U1

-0.20 0.00 0.20 0.40 0.60

Type 2 Pore Pressure, U2 (MPa)

0

2

4

6

8

Con

stra

ined

Mod

ulus

, M (M

Pa)

0 2 4 6TSF

0

10

20

30

40

50

60

70

80

TSF



Figure 4.5: M versus U2

0.00 0.10 0.20 0.30 0.40

σνο (MPa)

0

2

4

6

8

Cons

train

ed M

odul

us, M

(MPa

)

TSF

0

10

20

30

40

50

60

70

80

TSF



Figure 4.6: M versus σvo

10 20 30 40 50 60 70

Moisture Content , mc (%)

0

2

4

6

8

Con

stra

ined

Mod

ulus

, M (M

Pa)

0

10

20

30

40

50

60

70

80

TSF



Figure 4.7:M versus Field Moisture Content

85

0.00 10.00 20.00 30.00 40.00 50.00

Plasticity Index , PI (%)

0

2

4

6

8

Con

stra

ined

Mod

ulus

, M (M

Pa)

0

10

20

30

40

50

60

70

80

TSF



Figure 4.8: M versus PI

20.00 40.00 60.00 80.00 100.00

CL-CH (Zhang and Tumay) , (%)

0

2

4

6

8

Con

stra

ined

Mod

ulus

, M (M

Pa)

0

10

20

30

40

50

60

70

80

TSF



Figure 4.9: M versus Probability of CL-CH (Zhang and Tumay,2000)

4.2.2 Regression Modeling for Constrained Modulus (M)

All possible regressions procedures were used to select best subset of predictors. Akaike’s

(1973) Information criteria (AIC), R-Square, adjusted R-Square, SSE and Mallow’s CP

parameters were used as criteria to assess the best predictors. SAS® program and the sample

output for the regression models are presented in Appendix B. Once a preliminary models

were selected, detail statistical analysis such as significance of the model as whole (F test)

and significance of the partial multiple regression coefficient (t test) was carried out.

Residuals were plotted to examine homoscedasticity of variables and checked for normality

assumption. Possible outliers are identified by looking at residual plots and also by checking

RStudent criteria.

In addition to statistical significance of the model and influence of predictor, choice

and suitability of model is also guided by the practical consideration such as time and

convenience of obtaining predictor variable in the field, repeatability and reliability of such

test and theoretical or empirical models based on past experience. In this study, statistical

correlations were divided into two categories: direct and the indirect models. In the direct

methods, correlations are formed using the parameters that are measured directly from PCPT

tests such as qt, fs, u1 and u2. Indirect models incorporated other soil properties such as

moisture content, density and Atterberg limits which are estimated using laboratory testing or

86

in situ methods other than PCPT. Summary of the significant models based on this study are

presented in Table 4.1. Some of the major relationships are discussed further in the following

sections.

Table 4.1: Regression Models for M

SN Model n SSE R2 AdjR2 Normality MSE

W Pr

Direct Models

1 M=1.42+1.91qt 36 18.67 0.67 0.67 0.97 0.48 0.549

2 M=3.1qt 36 38.59 0.91 0.91 0.98 0.85 1.102

3 ln(M)=1.22+0.61ln(qt) 36 2.64 0.62 0.61 0.97 0.4 0.078

4 M=3.65+4.35*log(qt) 36 17.79 0.69 0.68 0.98 0.92 0.523

5 M=1.98+29.26fs 34 29.07 0.49 0.47 0.93 0.04 0.909

6 M=16.50√(fs) 34 28.21 0.93 0.92 0.95 0.11 0.855

7 M=0.61+13.61√(fs) 34 26.66 0.53 0.51 0.95 0.11 0.833

8 M=3.47*qt0.564 36 17.69 0.69 0.68 0.98 0.7 0.52

9 M=3.95*qt0.54fs

.045 34 15.19 0.73 0.71 0.97 0.59 0.49

10 M=3.90*qt0.58fs0.034u1

0.017u20.004 28 13.10 0.76 0.71 0.96 0.36 0.569

11 M=3.85*qt0.56fs

0.023u10.035 34 14.60 0.74 0.73 0.97 0.50 0.487

Indirect Models

12 M=1.69+1.89* (qt-σvo) 36 20.02 0.65 0.64 0.96 0.29 0.589

13 M=3.27 (qt-σvo) 36 49.28 0.88 0.87 0.98 0.84 1.408

14 M=3.68 (qt-σvo)0.51 36 18.17 0.69 0.68 0.97 0.42 0.534

15 M=2.52 (qt-σvo)+.027mc 36 29.50 0.93 0.92 0.98 0.91 0.868

16 M=2.51+1.58qt+2.61 u2-.032mc 29 9.64 0.82 0.80 0.96 0.29 0.386

17 M=2.15+1.69qt+0.43u1-0.021mc 36 15.10 0.74 0.71 0.98 0.73 0.472

18 M=2.48qt+0.022 mc 36 26.84 0.93 0.93 0.96 0.40 0.789

19 M=2.36qt+0.67 u1+0.016mc 36 22.85 0.94 0.93 0.96 0.16 0.692

20 M=2.4 (qt-σvo)+.036 PI 36 28.87 0.93 0.92 0.96 0.30 0.849

21 M=2.21(qt-σvo)+0.018 CL 36 22.38 0.95 0.94 0.96 0.30 0.658

22 M=1.63+30.5 fs+.07 SM 34 22.80 0.60 0.57 0.97 0.54 0.735

23 M=2.14+11.04 √(fs)-.029 mc 34 23.17 0.59 0.56 0.98 0.71 0.747

SM=Probability of sand (%), CL= Probability of clay (%),ML= Probability of silt (%), Zhang and Tumay (1999).

87

4.2.3 Models in Terms of Cone Tip Resistance

Buisman (1940, 1941) Kerisel (1969), Sanglerat et al. (1969), Bachelier and Parez (1965),

Kantey (1965), Meigh and Corbett (1969), Thomas (1968) Sanglerat et al. (1972, Jones and

Rust (1995), Abu-Farsakh (2003) proposed direct relationship between cone tip resistance

and compressibility of clay. A direct trend of M and cone tip resistance qt is observed in this

study (Figure 4.10). Also a non linear regression was performed to explore relation between

M and qt. As proposed by Sanglerat (1972) and others, value of αm varies for soil type as well

as magnitude of cone tip resistance. As such it is more rational to assume bi-linear relation

for M versus qt. Also, the scatter plot of M versus square root of qt gives more pronounced

linear trend. It is interesting to note that non linear correlations

564.047.3 tqM = (n= 36, R2=0.69) [85]

51.0)(68.3 votqM σ−= (n= 36, R2=0.69) [86]

are analogous to the empirical relation used to calculate elastic modulus for the

calculation of deformation of reinforced concrete structure derived from crushing strength of

cubes or cylinder

'σAE = [87]

where E and σ’ are in bar and, A is constant and σ’ is ultimate crushing strength.

In general it is observed that direct or indirect models using cone tip resistance gives

the better correlations. Owing to the simplicity and higher coefficient of determination,

relations

tqM 1.3= (n= 36, R2=0.91) [88]

)(27.3 votqM σ−= (n= 36, R2=0.88) [89]

are deemed as the best. However, comparison between Figure 4.10, 4.11, 4.12, 4.13, 4.14,

and 4.15 shows that relation [2] and [13] underestimate the most of M values at the lower

bounds of the regression line. Also, relatively higher scattering is evident on the upper bound

of direct linear regression line (equation [11], [12]). Non linear correlations such as {8] or

[9], on the other hand give better fit at the upper bound of regression line, but overestimate M

for the lower bound. As such, performance of the linear or non linear correlation may also

depend on the range of cone tip resistance and consequently constrained modulus (M) of the

soil layer. As more data are available for these ranges, especially on the upper bound, these

observations should be verified and relations re-calibrated.

88

M =

3.1

* qt

R2 =

0.9

1

0 2 4


0

2

4

6

8

Con

stra

ined

Mod

ulus

, M (M

Pa)

0 10 20 30 40TSF

0

10

20

30

40

50

60

70

80

TSF



M = 3.47* qt0.546

R2 = 0.69

Figure 4.10 Regression model for M versus qt

M =

3.2

7* (q

t - vo

)

R2 =

0.8

8

0 2 4

Net Cone Tip Resistance, (qt-σvo) (MPa)

0

2

4

6

8

Con

stra

ined

Mod

ulus

, M (M

Pa)

0 10 20 30 40TSF

0

10

20

30

40

50

60

70

80

TSF



M = 3.68* (qt - vo)

0.51

R2 = 0.69

Figure 4.11: Regression model for M versus (qt-vo)

M fit = 0.

92 M m.

R2 =

0..91

0 2 4 6 8

Measured M, (MPa)

0

2

4

6

8

Pred

icte

d M

, (M

Pa)

0 10 20 30 40TSF

0

10

20

30

40

50

60

70

80

TSF



Perfect

Fit

Figure 4.12: Measured versus Predicted M using relation [2]

M fit = 0.

88 M m.

R2 =

0.88

0 2 4 6 8

Measured M, (MPa)

0

2

4

6

8

Pred

icte

d M

, (M

Pa)

0 10 20 30 40 50 60 70 80TSF

0

10

20

30

40

50

60

70

80

TSF


EvangelenePearl RiverEast AirportBossier Perf

ect Fit

M fit = 3.27* (qt - vo) R2 = 0.88

Figure 4.13: : Measured versus Predicted M using relation [13]

89

M fit = 0.

96 M m.

R2 =

0.96

0 2 4 6 8

Measured M, (MPa)

0

2

4

6

8

Pred

icte

d M

, (M

Pa)

0 10 20 30 40TSF

0

10

20

30

40

50

60

70

80

TSF



ect Fit

M fit = 3.47* qt 0.546

R2 = 0.88

Figure 4.14: Measured versus Predicted M.

M fit = 0.

96 M m.

R2 =

0.96

0 2 4 6 8

Measured M, (MPa)

0

2

4

6

8

Pred

icte

d M

, (M

Pa)

0 10 20 30 40 50 60 70 80TSF

0

10

20

30

40

50

60

70

80

TSF



ect Fit

M fit = 3.47* qt0.58 * fs0.034* u1

0.017* u2 0.004

R2 = 0.88


M fit = 0.

96 M m.

R2 =

0.96

0 2 4 6 8

Measured M, (MPa)

0

2

4

6

8

Pred

icte

d M

, (M

Pa)

0 10 20 30 40 50 60 70 80TSF

0

10

20

30

40

50

60

70

80

TSF



ect Fit

M fit =2.51+1.69* qt + 0.43* u1- 0.021 * mcR2 = 0.74


M fit = 0.75M m.

R2 = 0.81

0 2 4 6 8 10

Measured M, (MPa)

0

2

4

6

8

10

Pred

icte

d M

, (M

Pa)

0 10 20 30 40 50 60 70 80 90 100TSF

0

10

20

30

40

50

60

70

80

90

100

TSF



Perfec

t Fit

M fit = 2.21* (qt - vo)+0.018*CLR2 = 0.95


90

4.2.4 Models in Terms of Sleeve Friction

As evident from the scatter plot (Figure 4.3) weak linear trend exist between M and fs for total

data set. However plot between M versus square root of fs shows better trend (figure 4.18).

Value of coefficient of determination (R2) was found to be 0.95 for linear regression with √fs.

As discussed in the section 2.4.2, sleeve friction is related to shear strength of the soil and

thus, its correlation with M may seem unreasonable. However, for the case of cohesionless

soil such as loose sands, Schmertmann and Sanglerat (1972) proposed that shear strength, can

be related to compressibility as it is greatly dependent on shear strength of sand. It is,

however, interesting to find similar observation in the saturated cohesive soils.

0.00 0.10 0.20 0.30 0.40

Sq. root Sleeve friction, √ fs (MPa)

0

2

4

6

8

Con

stra

ined

Mod

ulus

, M (M

Pa)

0 1 2 3 4TSF

0

10

20

30

40

50

60

70

80TS

F



M =16.50* sqrt

( f s)

R2 = 0.93

Figure 4.18: Regression model for M versus √fs

M fit = 0.

91 M m.

R2 =

0..92

0 2 4 6 8

Measured M, (MPa)

0

2

4

6

8

Pred

icte

d M

, (M

Pa)

0 10 20 30 40 50 60 70 80TSF

0

10

20

30

40

50

60

70

80

TSF



Perfect

Fit

M fit =16.50* fs 0.50

R2 = 0.92


4.2.5 Relationship between Cone Tip Resistance (qt) and Compression Index (Cc, Cr)

As shown in Figure 4.20 majority of compression index (Cc) plotted against qt falls in a

hyperbolic curve. Figure 4.21 shows the plot of recompression index (Cr) calculated as the

slope of initial portion of e versus log (σ'), where σ' is the stress smaller than preconsolidation

pressure (σ'p). Similarly, plot of recompression index (cr) calculated as the slope of loading-

unloading curve (Figure 2.1) beyond preconsolidation stress (σ'p) is presented in Figure 4.22.

Plot of compression ratio versus qt also defines the hyperbolic curve, as shown in Figure

4.23. Plot of recompression ration versus qt is presented in Figure 4.24. Symbol presented in

dark green color represents the recompression ratio calculated along loading-unloading curve.

As shown in Figure 4.25, graph of qt/ CR versus qt, plotted in a linear scale, gives a distinct

straight line (R2 = 0.91) which confirms the hyperbolic distribution of CR with respect to qt.

91

0 2 4 6 8


0.00

0.20

0.40

0.60

0.80

Com

pres

sion

Inde

x, C

c

0 10 20 30 40 50 60 70 80TSF



Figure 4.20: cc versus qt

0 2 4 6 8


0.00

0.04

0.08

0.12

0.16

0.20

Rec

ompr

essi

on In

dex,

Cr

0 10 20 30 40 50 60 70 80TSF



Figure 4.21: cr versus qt

0 2 4 6 8


0.00

0.20

0.40

0.60

0.80

Com

pres

sion

Inde

x, C

c

0 10 20 30 40 50 60 70 80TSF



Figure 4.22: Cr versus qt ( loading-unloading)

0 2 4 6 8


0.00

0.05

0.10

0.15

0.20

0.25

0.30

CR

=Cc/

(1+e

0)

0 10 20 30 40 50 60 70 80TSF



Figure 4.23: CR versus qt

92

0 2 4 6 8


0.00

0.02

0.04

0.06

0.08

RR

=Cr/(

1+e 0

)

0 10 20 30 40 50 60 70 80TSF



Figure 4.24: CR versus qt

0 2 4 6 8


0

40

80

120

160

q t/C

R

0 10 20 30 40 50 60 70 80TSF



q t /CR =

17.16

* qt- 4.6

6

R2 = 0.91

Figure 4.25: qt/CR versus qt

4.3 Statistical Analysis for Overconsolidation Ratio (OCR)

The preconsolidation pressures (σp') of different clay layers were determined using

Casagrande’s graphical interpretation method. Effective overburden pressure (σvo') was

estimated from bore log information. In addition to PCPT measurements (qt, fs, u1 and u2),

index properties of soil such as Atterberg limits, overburden pressure and neutral water

pressure (u0) were also used in regression. Scatter plot of OCR and various PCPT parameters

are presented in Figures 4.26 through 4.33. As seen from the Figures 4.26 and 4.27, no clear

trend exists with cone tip or sleeve friction measurements. However, plots between OCR and

pore pressure measurements (u1 or u2) shows weak non linear trends and it is found that

excess pore pressure generated during cone penetration is inversely proportional to OCR of

the soil layer (Figures 4.28 and 4.29). Similarly, Figure 4.30 shows the decreasing trend of

OCR with average overburden pressure (σvo). Also OCR is also found be to be affected by

soil index properties such as in situ moisture contents and plasticity index (PI) as shown in

Figure 4.31 and 4.32. Plot of OCR versus PI in linear scale shows the decreasing trend of

OCR with increasing PI, however, data are highly scattered. Similarly, plot between OCR

and probability of finding clay, CL-CH (Zhang and Tumay, 2000) shows no clear trend, as

shown in Figure 4.33.

93

0 2 4


0

2

4

6

8

10

12

14

16

18

OC

R

0 10 20 30 40TSF


EvangelenePearl R iverEast AirportBossier

Figure 4.26: OCR versus qt

0.00 0.05 0.10 0.15 0.20

Sleeve Friction, fs (MPa)

0

2

4

6

8

10

12

14

16

18

OC

R

0.0 0.4 0.8 1.2 1.6 2.0TSF



Figure 4.27: OCR versus fs

0.0 0.5 1.0 1.5 2.0

Type 1 Pore Pressure, u1 (MPa)

0

2

4

6

8

10

12

14

16

18

OC

R

0 5 10 15 20TSF



Figure 4.28: OCR versus u1

-0.20 0.00 0.20 0.40 0.60

Type 2 Pore Pressure, u2 (MPa)

0

2

4

6

8

10

12

14

16

18

OC

R

0 2 4 6TSF



Figure 4.29:OCR versus u2

94

0.00 0.10 0.20 0.30 0.40

σνο (MPa)

0

2

4

6

8

10

12

14

16

18

OC

R

0 1 2 3 4TSF



Figure 4.30: OCR versus σvo

10 20 30 40 50 60 70

Moisture Content , mc (%)

0

2

4

6

8

10

12

14

16

18

OC

R



Figure 4.31: M versus Field Moisture Content

0 10 20 30 40 50

Plasticity Index , PI (%)

0

2

4

6

8

10

OC

R



Figure 4.32: OCR versus PI

20 40 60 80 100

CL-CH (Zhang and Tumay) , (%)

0

2

4

6

8

10

OC

R



Figure 4.33: OCR versus Probability of CL-CH (Zhang and Tumay,2000)

95

4.3.1 Regression Modeling for OCR

Best suitable subset of predictor is selected using SAS® program as discussed in the previous

sections. Linear and non linear regression analyses were done to explore new regression

models and or calibrate and refine existing correlations that are discussed in literature review

section. Summary of the significant models based on this study are presented in Table 4.2.

Some of the important relationships are discussed in details below:

Table 4.2: Regression Models for OCR.

SN Model n SSE R2 AdjR2 Normality

MSE W Pr

Cone tip and sleeve friction

1 OCR=0.8+0.11* (qt-σvo)/σvo' 41 62.84 0.65 0.64 0.97 0.27 1.611

2 OCR=0.14* (qt-σvo)/σvo' 41 73.61 0.86 0.85 0.96 0.1 1.84

3 OCR=0.17* (qt+fs)/σvo 40 55.21 0.87 0.87 0.95 0.10 1.416

4 OCR=1.08+1.92* fs/σvo' 39 40.12 0.72 0.71 0.94 0.03 1.084

5 OCR=0.88+0.13* (qt+fs)/σvo 40 41.40 0.71 0.71 0.98 0.53 1.09

Pore water pressure measurements

6 log(OCR)=-0.27*log(u1-u0) 28 1.79 0.26 0.23 0.95 0.17 0.066

7 log(OCR)=0.13-0.37*log(u1-u0) 38 1.94 0.40 0.38 0.97 0.50 0.054

8 OCR=1.17+0.134*PPD 26 22.60 0.54 0.51 0.99 0.99 0.942

Cone tip, sleeve friction and pore pressure

9 OCR=1.18+0.11* (qt-u1)/σvo' 34 53.56 0.67 0.66 0.97 0.60 1.674

10 OCR=0.153* (qt-u1)/σvo' 32 74.32 0.83 0.81 0.93 0.04 2.397

11 OCR=0.14* (qt-u2)/σvo' 41 75.76 0.85 0.84 0.96 0.31 1.894

12 log(OCR)=0.75+0.43* log{fs/(u1-u0)} 35 1.31 0.55 0.54 0.97 0.42 0.04

13 log(OCR)=0.44+0.29* log{fs/(u2-u0)} 27 1.65 0.30 0.27 0.91 0.01 0.066

14 log(OCR)=-0.36+.48* log{(qt+fs)/uo} 31 0.67 0.70 0.69 0.98 0.83 0.023

15 OCR=1.46+0.025* (qt+fs)/uo 31 32.72 0.67 0.66 0.93 0.06 1.128

16 log(OCR)=0.18-0.40*log(Bq1) 37 1.49 0.53 0.51 0.93 0.02 0.043

17 log(OCR)=-0.57*log(Bq1) 37 2.24 0.68 0.68 0.90 0.03 0.062

18 OCR=1.50*Bq1-0.48 37 81.05 0.54 0.54 2.316

96

Table 4.2 (continued)


W Pr

Cone tip, sleeve friction and pore pressure

19 OCR=4.33*Bq1-0.55*PI-0..37 35 56.62 0.63 0.61 0.91 0.01 1.77

20 log(OCR)=-0.04-0.35*log(Bq2) 28 1.51 0.37 0.35 0.90 0.01 0.058

21 log(OCR)=-0.32*log(Bq2) 28 1.52 0.75 0.74 0.90 0.01 0.056

22 OCR=1.21*Bq2-0.31 28 92.61 0.29 0.27 3.562

23 log(OCR)=0.16-0.43*log(u1/qt) 39 1.56 0.51 0.51 0.93 0.01 0.042

24 log(OCR)=0.69-0.36* log{u1/fs} 40 1.50 0.53 0.52 0.97 0.46 0.04

25 log(OCR)=0.79-0.30* log{(u1-u0)/(fs-uo)} 25 1.09 0.49 0.47 0.97 0.58 0.047

26 log(OCR)=0.15-0.42*log{(u1-u0)/(qt-u0)} 38 1.59 0.51 0.49 0.93 0.02 0.044

27 log(OCR)=-0.021-0.295*log{u2-u0)/ (qt-u0)} 26 1.16 0.30 0.27 0.90 0.01 0.048

28 log(OCR)=0.15-0.41* log{(u1-u0)/fs} 36 1.67 0.46 0.43 0.95 0.07 0.049

29 log(OCR)=0.41-0.28* log{(u2-u0)/fs} 27 1.56 0.33 0.30 0.90 0.01 0.063

30

OCR=1.02 +1.66* fs/σvo'-0.83u1

+0.0004(CL+ML)/σvo' 38 26.01 0.78 0.75 0.96 0.21 0.765

4.3.2 OCR Models in Terms of Cone Tip Resistance and Sleeve Friction

Regression models were analyzed using intercept term (b0) and also restricting intercept to

zero. Restraining intercept term to zero redefines coefficient of determination (R2) and its

interpretation is different from the R2 for normal regression line. Usually, restricting intercept

term results in inflation of R2.

Good correlation between OCR and normalized cone tip and sleeve friction

measurements are found as shown in Figures 4.34 through Figure 4.39 and in Table 4.2. Net

cone tip resistance (qt-σvo) normalized with respect to σvo' is found to be good predictor of

OCR (R2=0.86, OCR fit/ OCR Meas=0.98), as shown in Figures 4.34 and 4.37. Also the total

cone resistance (qt+fs) normalized with respect to σvo gives good correlation (R2 =0.71,

Figure 4.35 and 4.38). Moreover, scattering is relatively reduced, when compared to Figure

4.28. Normalized sleeve friction (fs/σvo') is found to be indicative of OCR (Figures 4.36 and

4.39) although points are relatively scattered. The parameter (fs/σvo') may be considered as the

best estimate of in situ (Su/σvo') and thus can be used as a predictor of in situ OCR, as

discussed by Schemertmann (1974, 1975) and Ladd et al. 1977).

97

0 20 40 60 80

(qt-σνο)/σ'νο

0

2

4

6

8

10

OC

R



OCR = 0.14

* [ (

q t - σ vo

) / σ vo

' ]

R2 = 0.

86

Figure 4.34: OCR versus (qt-σvo)/σ’vo

0 20 40 60 80

(qt+fs)/σνο

0

2

4

6

8

10

OC

R



OCR = 0.88

+ 0.13

* [ (q

t + f s)/

σ vo ]

R2 = 0.

71

Figure 4.35: OCR versus normalized total cone resistance [(qt+fs)/σνο].

0 1 2 3 4 5

fs/σ'νο

0

2

4

6

8

10

OC

R



OCR = 1.0

8 + 1.

92 *

f s/ σ vo

'

R2 = 0.

72

Figure 4.36: OCR versus normalized sleeve friction

OCR fit =

0.98 O

CR m.

R2 = 0.85

0 2 4 6 8 10

Measured OCR

0

2

4

6

8

10

Pred

icte

d O

CR



Perfect

Fit

OCR fit = 0.14 * [ (qt - σvo) / σvo' ]R2 = 0.86

Figure 4.37: Measured versus predicted OCR

98

OCR fit =

1.05O

CR m.

R2 = 0.90

0 2 4 6 8 10

Measured OCR

0

2

4

6

8

10Pr

edic

ted

OC

RTest Sites:AlfLafourcheNew Iberia


Perfect

Fit

OCR fit = 0.88 + 0.13 * [ (qt + fs)/ σvo ] R2 = 0.71


OCR fit = 1.

05 O

CR m.

R2 = 0.86

0 2 4 6 8 10

Measured OCR

0

2

4

6

8

10

Pred

icte

d O

CR



ect F

it

OCR fit = 1.08 + 1.92 * fs / σvo'R2 = 0.71


4.3.3 OCR Models in Terms of Pore Water Pressure Measurements

OCR shows the decreasing trend with increasing excess pore pressure (um-uo), where um

represents u1 or u2. However, only weak correlation is found (R2=0.38) and the plot of PCPT

predicted versus measured laboratory estimated OCR shows that predicted OCR is highly

overestimated (Figure 4.40). Similarly, PPD (Sully et al., 1988) parameter also showed

increasing trend OCR but with relatively high scattering (R2=0.54) as shown in Figure 4.41.

It was found that parameters derived from pore pressure measurements are highly erratic

possibly due to error in the measurement such as poor calibration, unsaturated filters or other

filed conditions such as drainage conditions, dilatory response in high OCR soils (negative

u2) etc. In some cases, such erratic points were omitted as outliers and correlations were

based on fewer data. As evident from the scatter plot, u1 and u2 reference measurement are

influenced by OCR of the soil deposit, however no good relation was found. Figure 4.40

through Figure 4.43 presents some of the correlations obtained using pore pressure

measurements only.

4.3.4 OCR Models with Cone Tip, Sleeve Friction and Pore Pressure Measurements

As discussed in section 2.9, several theoretical as well as empirical models have been

established to correlate OCR, cone tip resistance and reference pore pressure measurements.

Good correlation was found between OCR and normalized (qt-um) parameter, where um

represents u1 or u2 measurement based on location of filter (Table 4.2 and Figure 4.44).

99

0.00 0.01 0.10 1.00 10.00 100.00

(u1-u0)

0.1

1.0

10.0

100.0

OC

RTest Sites:AlfLafourcheNew Iberia


Figure 4.40: OCR versus (u1-u0)

0.00 10.00 20.00 30.00 40.00

PPD=(u1-u2)/uo

0

2

4

6

8

10

OC

R



OCR = 1.17 + 0.134 * [ (u1 - u 2)/

u0 ]

R2 = 0.54

Figure 4.41: OCR versus PPD.

OCR

fit =

2.9

1 O

CRm

.

R2 =

0.7

4

0 2 4 6 8 10

Measured OCR, (MPa)

0

2

4

6

8

10

Pred

icte

d O

CR,

(MPa

)



Perfec

t Fit

log(OCR) fit =1.13 -0.37 *log [ (u1 - u2)]R2 = 0.40

where um represents u1 or u2


OCR fit =

1.11 O

CR m.

R2 = 0.81

0 2 4 6 8 10

Measured OCR

0

2

4

6

8

10

Pred

icte

d O

CR



Perfect

Fit

OCR = 1.17 + 0.134 * [ (u1 - u2)/ u0 ]R2 = 0.54


Derived parameters using sleeve friction measurement (fs) were also found to be good

estimator of OCR. Linear trend was observed between OCR and total cone resistance

normalized with respect to neutral pore water, (qt+fs)/u0 (R2 = 0.71, Figure 4.45). Bq1

parameter was found indicative of OCR of the clay deposits in Louisiana soils, however with

weak correlation (R2 = 0.53). However, models with Bq parameter were formulated with

limited observations and the data from the Alf site were discarded. B q parameter is found to

be influenced by PI of the soil deposit. Introduction of PI in the non linear regression model

improves the correlation coefficient (R2 =0.63), as shown in Figure 4.46 and 4.50. Also, the

100

best fit line for measured versus predicted data for this correlation gives the estimate of 1.01

with R2=0.86. Although, Bq2 parameter shows the decreasing trend with increasing OCR,

high scattering was observed along the regression line with low coefficient of correlation

(R2=0.37).

0 20 40 60 80

(qt-u1)/σ'νο

0

2

4

6

8

10

OC

R



OCR = 0.1

53 *

[ (q t -

u 1) / σ vo'

]

R2 =

0.83

Figure 4.44: OCR versus (qt-u1)/σ’vo

0 100 200 300

(qt+fs)/u0

0

2

4

6

8

10

OC

R



OCR = 1.46+0.025 * [

(qt + f s)

/ u 0 ]

R2 = 0.70

Figure 4.45: OCR versus (qt+fs)/u0

0.00 0.01 0.10 1.00 10.00

Bq=(u1-u0)/(qt-σνο)

0

1

10

100

OC

R



OCR = 1.50 * Bq1 0.48

R 2 = 0.54

Figure 4.46 OCR versus Bq1

0.00 0.01 0.10 1.00 10.00

u1/qt

0

1

10

100

OC

R



log(OCR) =0.16-0.43* u1 / q

t

R 2 = 0.51

Figure 4.47: OCR versus u1/qt

Pore pressure measurement normalized with respect to cone tip resistance (qt) or sleeve

friction (fs) also shows the decreasing trend with increasing OCR, however data are scattered

and coefficient of determination, R2 is found relatively lower (Table 4.2, Figures 4.47 and

4.48). Houlsby (1988) mentioned that initial pore pressure (u0) should always be subtracted

101

before pore pressure measurement (u1 or u2) are used. Plot of OCR versus (u1-u0)/ (qt-u0) also

shows the decreasing trend of OCR with increasing (u1-u0)/ (qt-u0) and data are less scattered,

however, overall R2 remains unchanged. Some important correlation using mixed parameters

are shown in the Figure 4.44 to Figure 4.51.

0.10 1.00 10.00 100.00

u1/fs

0

1

10

100

OC

R



log(OCR) =0.69-0.63* u1/ fsR2 = 0.53

Figure 4.48: OCR versus u1/fs

0.00 0.01 0.10 1.00 10.00

(u1-u0)/(qt-uο)

0

1

10

100

OC

R



OCR = 0.15 * log[(u1 - u

0) / (qt - u

0)]

R2 = 0.51

Figure 4.49: OCR versus (u1-u0)/(qt-u0)

OCR fit = 1.01

OCR m.

R2 =

0.86

0 2 4 6 8 10

Measured OCR, (MPa)

0

2

4

6

8

10

Pred

icte

d O

CR,

(MPa

)



Perfec

t Fit

OCR fit = 4.33 * Bq1 -0.55 * PI -0.37

R2 = 0.63


OCR fit = 1.03

OCR m.

R2 =

0.94

0 2 4 6 8 10

Measured OCR, (MPa)

0

2

4

6

8

10

Pred

icte

d O

CR, (

MPa

)



Perfec

t Fit

OCR fit = 1.02 + 1.66 * fs / σvo' - 0.83* u1+0.004*(CL+ML) R2 = 0.71


4.4 Regression Models for Coefficient of Consolidation

Linear and Non linear regression models were explored to formulate correlation between

laboratory estimated coefficient of consolidation in vertical direction (cv) and the PCPT

102

parameters such as qt , fs, u1, u2, Δu1, Δu2, as well as t50 and u50. The parameters t50 and u50 are

derived from dissipation curves while others are obtained during cone penetration tests itself.

Scatter plots of cv versus some influential PCPT derived parameters are presented in Figures

4.52 through 4.59. As seen from Figure 4.52, cv is inversely proportional to t50 and falls in a

narrow band when plotted in logarithmic scale. Similarly pore pressure measured at the

beginning of dissipation test (ui) and pore pressure corresponding to 50% dissipation (u50) are

also found indicative of cv (Figures 4.53 and 4.54). Similarly, measured cv increases with

increasing Δu1 or Δu2 and trend is more pronounced for latter (Figures 4.55 and 4.56).

Furthermore, cv is directly proportional to square root of qt and inversely proportional to

friction ratio (FR) as shown in Figures 4.57 and Figure 4.58. As discussed in section 2.10.2,

these two parameters are indicative of rigidity index (Ir) of the soil layer and thus confirm to

the theoretical model proposed by Teh and Houlsby (1988).

Best suitable subset of predictor is selected using SAS® program as discussed in the

previous sections. Summary of the significant models based on this study are presented in

Table 4.3. Some of the major relationships are discussed in details below.

Linear trend was found between cv and time corresponding to 50% dissipation of

excess pore pressure during dissipation test (t50) plotted in a logarithmic graph, However

coefficient of determination was found to be low (R2 = 0.14, Table 4.3, Figure 4.52).

Similarly, simple correlation using Δu1 or Δu2 gave scattered result and coefficient of

determination was low. Ratio of t50 with respect to ui and u50 gave slightly better correlation

(R2=0.32 and 0.23 respectively) as shown in Figures 4.59.

10 100 1000 10000

t50 (min)

1E-005

1E-004

1E-003

1E-002

Coe

ffici

ent o

f con

solid

atio

n, c

v (cm

2 /sec

)



log (cv) =2.34-0.32* log (t50)

R2 = 0.21

Figure 4.52: cv versus t50

0 0 1

u50 (MPa)

1E-005

1E-004

1E-003

1E-002

Coe

ffici

ent o

f con

solid

atio

n, c

v (cm

2 /sec

)



log (c v) =-2.79+0.56 log (u50)

R2 = 0.21

Figure 4.53: cv versus u50

103

0 0 1 10

uι (MPa)

1E-005

1E-004

1E-003

1E-002

Coe

ffici

ent o

f con

solid

atio

n, c

v (cm

2 /sec

)



Figure 4.54: cv versus ui

0.0 0.1 1.0

(u1-u0) (MPa)

1E-005

1E-004

1E-003

1E-002

Coe

ffici

ent o

f con

solid

atio

n, c

v (cm

2 /sec

)

Test Sites:AlfLa fourcheNew Iberia

EvangelenePearl RiverEast AirportB ossier

Figure 4.55: cv versus (u1- u0)

0.0 0.1 1.0

(u2-u0) (MPa)

1E-005

1E-004

1E-003

1E-002

Coe

ffici

ent o

f con

solid

atio

n, c

v (cm

2 /sec

)



Figure 4.56: cv versus (u2- u0)

0.0 1.0 2.0 3.0

√qt (MPa)

0E+000

1E-003

2E-003

3E-003

Coe

ffici

ent o

f con

solid

atio

n, c

v (cm

2 /sec

)



c v = 0.0008 * sqrt(q t

R2 = 0.81

Figure 4.57: : cv versus √qt

104

1 10

FR (%)

1E-005

1E-004

1E-003

1E-002

Coe

ffic

ient

of c

onso

lidat

ion,

cv (

cm2 /s

ec)



log (cv) =-2.78-0.30 log (FR)

R2 = 0.14

Figure 4.58: cv versus FR

10 100 1000 10000 100000

t50/ui (MPa)

1E-005

1E-004

1E-003

1E-002

1E-001

Coe

ffici

ent o

f con

solid

atio

n, c

v (cm

2 /sec

)



log (cv) =-2.23-0.30 log (t50 / u i )

R2 = 0.32

Figure 4.59: cv versus t50/ ui

0.0001 0.001 0.01 0.1 1

√qt/t50 (MPa)

1E-005

1E-004

1E-003

1E-002

1E-001

Coe

ffici

ent o

f con

solid

atio

n, c

v (cm

2 /sec

)



log (c v) =-2.12+0.41* log (√qt/t50)

R2 = 0.28

Figure 4.60: cv versus (√qt/ t50)

0.0001 0.001 0.01 0.1 1

1/(t50*√FR)

1E-005

1E-004

1E-003

1E-002

Coe

ffici

ent o

f con

solid

atio

n, c

v (cm

2 /sec

)



log (c v) =-2.12+0.37* log [1/( t50√FR) ]

R2 = 0.27

Figure 4.61: cv versus 1/( t50√FR)

105

Table 4.3: Regression Models for cv.


W Pr

1 log(cv)=-2.34-0.32*log(t50) 28 4.14 0.21 0.17 0.94 0.15 0.159

2 log(cv) =-2.9+0.42*log(Δu1) 26 3.56 0.22 0.18 0.97 0.50 0.148

3 log(cv) =-2.58+0.55*log(Δu2) 23 3.13 0.32 0.28 0.95 0.34 0.149

4 log(cv) =-2.28+0.34*log(√qt/t50) 28 3.77 0.28 0.25 0.95 0.09 0.145

5 log(cv) =-2.14+0.37*log[1/(t50√FR)] 27 3.82 0.27 0.24 0.94 0.09 0.153

6 log(cv) =-2.07+0.33*log[ui /(t50√FR)] 27 3.25 0.38 0.35 0.94 0.11 0.13

7 log(cv) =-1.99+0.33*log[u50 /(t50√FR] 26 3.26 0.30 0.27 0.94 0.09 0.13

9 log(cv) =-2.23-0.30*log(t50/ui) 28 3.55 0.32 0.30 0.95 0.17 0.137

10 log(cv) =-2.21-0.29*log(t50/u50) 27 3.57 0.23 0.21 0.95 0.13 0.143

Relations (4) through (7) in the Table 4.4.1 incorporate effect of soil rigidity index, as

discussed previously, and are analogous to theoretical model ( equation [62]) proposed by

Teh and Houlsby (1988)

tc

rIh

.2r*T=

as T* and r2 are constant for given cone type and corresponding degree of

consolidation (section 2.9). As it can be seen from Figures 4.60 through 4.65 data are

bounded by narrower band and R2 is slightly improved. Figure 4.63 presents the comparison

of predicted cv using Teh and Houlsby (1988) method plotted against laboratory estimated cv.

Data falls evenly on the both side of best fit line, but are slightly scattered especially in the

upper bound. Roberstson et al. (1992) method on the other hand seems to give the

overestimate of cv compared to laboratory estimated value (Figure 4.64). Figure 4.65 presents

the comparison of predicted cv using Teh and Houlsby (1988) versus cv predicted using

proposed regression model. As can be seen, data plots in narrow band around the best fit line.

It is noteworthy to mention that equation [62] requires input of Ir and further input of Cc/Cr

and kh/kv ratios for corrections (Baligh and Lavadoux, 1986). These parameters are in general

estimated through rigorous laboratory tests and are time consuming. Proposed correlations

(relations (4) through (9), Table 4.3) on the other hand include only PCPT obtained

parameters.

106

1E-005 0.0001 0.001 0.01 0.1

ui/(t50*√FR) (MPa)

1E-005

1E-004

1E-003

1E-002

Coe

ffici

ent o

f con

solid

atio

n, c

v (cm

2 /sec

)



log (cv) =-2.07+0.33* log (ui /t50√FR)]

R2 = 0.38

Figure 4.62: cv versus ui/( t50√FR)

1E-005 1E-004 1E-003 1E-002 1E-001

Measured, cv (cm2/sec)

1E-005

1E-004

1E-003

1E-002

1E-001

Pred

icte

d, c

v (cm

2 /sec

)



log (cv) fit= 1.05 log (cv) Meas

R2 = 0.86

Perfect

Fit

Figure 4.63: Measured versus predicted cv for Teh and Houlsby (1988) method.

1E-005 1E-004 1E-003 1E-002 1E-001 1E+000


1E-005

1E-004

1E-003

1E-002

1E-001

1E+000

Pred

icte

d, c

v (cm

2 /sec

)



Perfect

Fit

Figure 4.64: Measured versus predicted cv for Robertson et al. (1992) method.

1E-005 1E-004 1E-003 1E-002 1E-001

cv = ui/(t50*√FR)(cm2/sec)

1E-005

1E-004

1E-003

1E-002

1E-001

cv,

Teh

& H

ouls

by (1

988)

(cm

2 /sec

) Test Sites:AlfLafourcheNew Iberia

EvangelenePearl R iverEast AirportBossier

Perfect

Fit

Figure 4.65: Comparision of cv predicted using proposed correlation with predicted using Teh and Houlsby (1988) method.

107

4.5 Regression Modeling for Undrained Shear Strength

Linear and Non linear regression models were explored to formulate correlation between

Undrained shear strength (Su) and PCPT parameters such as qt , fs, u1, u2, Δ u1, Δu2, as well as

σvo. It is noteworthy to mention that undrained shear strength used in these equation were

determined by unconfined undrained compression test (UU) in the Shelby tube samples

obtained from laboratory and as reported in bore logs. Best suitable subset of predictor is

selected using SAS® program as discussed in the previous sections. Summary of the

significant models based on this study are presented in Table 4.4.

The empirical cone factor Nk for clay deposits in Louisiana is found be in between 16

and 17 (Table 4.4). Correlations using (qt-σvo) and (qt-u2) almost give the similar predictions

(R2 = 0.82, Nk=16.1) as shown in Figures 4.66 and 4.67. Correlations using (qt-u2) and (qt+fs-

σvo), on the other hand gave the higher cone factor (Nk = 17), as shown in Figures 4.68. Also,

good correlation was found for Su using sleeve friction (R2 = 0.86), as shown in Figure 4.69.

As can be inferred from the relation (5), Table 4.4, sleeve friction measurement is close to the

undrained shear strength of clayey soil in agreement with the observation of Tomilson (1957)

for piles. Also, Terzaghi and Peck (1967) proposed that the ultimate value of side friction is

almost equal to the half the unconfined compressive strength (qu), which in turn is equal to Su

for cohesive soils, when qu is less than 0.2 MPa, and this is regardless of the remolding and

disturbances caused by driving.

Table 4.4: Regression Models for Undrained Shear Strength (Su=qu/2)

SN Model n SSE R2 AdjR2 Normality Cone Factor

W Pr Nk

1 Su=0.0621* (qt-σvo) 32 0.02 0.82 0.81 0.96 0.32 16.10

2 Su=0.05803* (qt-uo) 32 0.02 0.83 0.82 0.96 0.29 17.23

3 Su=0.06193* (qt-u2) 32 0.02 0.82 0.82 0.95 0.14 16.15

4 Su=0.05808* (qt+fs-σvo) 32 0.02 0.83 0.82 0.95 0.19 17.22

5 Su=1.123* fs 32 0.01 0.86 0.85 0.96 0.33

108

0.00 0.40 0.80 1.20 1.60 2.00

(qt-σνο) MPa

0.00

0.04

0.08

0.12

0.16

Su (M

Pa)

0.0

0.4

0.8

1.2

1.6

TSF



S u = (qt - σvo) / 16.10R2 = 0.82

Figure 4.66: Su versus (qt-σvo)

0.00 0.40 0.80 1.20 1.60 2.00

(qt-u2) MPa

0.00

0.04

0.08

0.12

0.16

Su (M

Pa)

0.0

0.4

0.8

1.2

1.6

TSF



S u = (q t -

u o) / 16.15

R2 = 0.82

Figure 4.67: Su versus (qt-u2)

0.00 0.40 0.80 1.20 1.60 2.00

(qt+fs-σvo) MPa

0.00

0.04

0.08

0.12

0.16

Su (M

Pa)

0.0

0.4

0.8

1.2

1.6

TSF



S u = (q t+ f s -

σ vo ) / 17.21

R2 = 0.83

Figure 4.68: Su versus (qt+ fs-σvo)

0.00 0.04 0.08 0.12

fs (MPa)

0.00

0.04

0.08

0.12

0.16

Su (M

Pa)

0.0

0.4

0.8

1.2

1.6

TSF



S u = 1.123* f s

R2 = 0.86

Figure 4.69: Su versus fs

109

CHAPTER 5

5 SETTLEMENT ANALYSIS AND VERIFICATION OF STATISTICAL MODLES

This chapter presents the verification of statistical models developed earlier for

consolidation parameters using data from Juban North and Juban south embankment sites.

Also parameters estimated using proposed relations are compared with laboratory and back

calculated parameters from field settlement analyses.

5.1 Verification of Statistical Models

Data from the Juban north and south embankments are used to verify the statistical models

proposed in the previous section. These data were not used in the formulation of regression

models and thus gives the unbiased assessment of correlation between laboratory estimated

and PCPT predicted parameters. Comparison will be made between PCPT predicted,

laboratory estimated and back calculated parameters from field measurements.

5.1.1 Constrained Modulus (M)

The laboratory measured versus predicted value of constrained modulus for some of the

regression models is presented in Figure 5.1 to 5.10. As evident from statistical fit of the data

points, for most of the model, Mfit / Mmeas is greater than or close to one indicating over

estimation of laboratory values. Introduction of additional parameters improved the

correlations and the scattering of the points about the best fit line was reduced as observed

from the comparison of Figures 5.1 against 5.5.

M fit =

1.45

M m.

R2 =

0.8

0 2 4 6 8 10

Measured M, (MPa)

0

2

4

6

8

10

Pred

icte

d M

, (M

Pa)

0 20 40 60 80 100TSF

0

20

40

60

80

100

TSF

Perfec

t Fit

Test Sites:

Juban North

Juban South

M fit =3.15* qtR2 = 0.91

Figure 5.1: Measured versus Predicted M for Juban Road

M fit =

1.45M

m.

R2 =

0.81

0 2 4 6 8 10

Measured M, (MPa)

0

2

4

6

8

10

Pred

icte

d M

, (M

Pa)

0 20 40 60 80 100TSF

0

20

40

60

80

100

TSF

Perfect

Fit

M fit = 3.27* (qt - vo) R2 = 0.88

Test Sites:

Juban North

Juban South


110

0.00 0.10 0.20 0.30 0.40 0.50

√ fs (MPa)

0

2

4

6

8C

onst

rain

ed M

odul

us, M

(MPa

)0 1 2 3 4 5

TSF

0

20

40

60

80

TSF

M =16.50* sqrt(

f s)

R2 = 0.93

Test Sites:

Juban North

Juban South


M fit = 1.

08 Mm.

R2 =

0.88

0 2 4 6 8 10

Measured M, (MPa)

0

2

4

6

8

10

Pred

icte

d M

, (M

Pa)

0 20 40 60 80 100TSF

0

20

40

60

80

100

TSF

Perfec

t Fit

M fit = 3.47* qt0.58 * fs0.034* u1

0.017* u2 0.004

R2 = 0.88

Test Sites:

Juban North

Juban South


Also, non linear model in qt gave the better prediction of M ( Mfit/ Mm= 1.20, r2 = 0.89) and

predicted values (Mfit) fits close to best fit line especially for qt>1.5 MPa. Figures 5.7 through

figure 5.10 present the profiles of PCPT predicted constrained modulus with depth as

compared to laboratory measured M values.

M fit = 1.

26Mm.

R2 =

0.89

0 2 4 6 8 10

Measured M, (MPa)

0

2

4

6

8

10

Pred

icte

d M

, (M

Pa)

0 20 40 60 80 100TSF

0

20

40

60

80

100

TSF

Perfec

t Fit

M fit =2.51+1.69* qt + 0.43* u1- 0.021 * mcR2 = 0.74

Test Sites:

Juban North

Juban South


M fit =

1.45M

m.

R2 =

0.81

0 2 4 6 8 10

Measured M, (MPa)

0

2

4

6

8

10

Pred

icte

d M

, (M

Pa)

0 20 40 60 80 100TSF

0

20

40

60

80

100

TSF

Perfect

Fit

M fit = 3.27* (qt - vo) R2 = 0.88

Test Sites:

Juban North

Juban South


111

0 5 10 15 20 25 30 35 40

Constrained Modulus (MPa)

0

2

4

6

8

10

12

14

16

18

20

Dept

h (m

)

0 100 200 300 400TSF

Constraints Modulus (M)M=3.27(qt-σvo)

Lab Measured

SANDY LAYER

SANDY LAYER

Figure 5.7: PCPT predicted versus laboratory measured profile of M (Juban North)

0 5 10 15 20 25 30 35 40


0

2

4

6

8

10

12

14

16

18

20

Dept

h (m

)

0 100 200 300 400TSF

Constraints Modulus (M)M=3.15qt

Lab Measured

SANDY LAYER

SANDY LAYER

Figure 5.8: : PCPT predicted versus laboratory measured profile of M (Juban North)

0 5 10 15 20 25 30 35 40


0

2

4

6

8

10

12

14

16

18

20

Dept

h (m

)

0 100 200 300 400TSF

Constraints Modulus (M)M=3.27(q t-σvo)

Lab Measured

SANDY LAYER

SANDY LAYER

SANDY LAYER

Figure 5.9: PCPT predicted versus laboratory measured profile of M (Juban South)

0 5 10 15 20 25 30 35 40


0

2

4

6

8

10

12

14

16

18

20

Dept

h (m

)

0 100 200 300 400TSF

Constraints Modulus (M)M=3.15qt

Measured

SANDY LAYER

SANDY LAYER

SANDY LAYER

Figure 5.10: PCPT predicted versus laboratory measured profile of M (Juban South)

112

5.1.2 Overconsolidation ratio (OCR)

The plot of predicted versus laboratory measured values of OCR for Juban north and Juban

south embankments are presented in figure 5.11 to figure 5.16. While models based on cone

tip and sleeve frictions give fair predictions, high scatterings are noticeable for models based

on pore pressure measurements, such as Bq1. This is reflected by low coefficient of

determination (R2 = 0.54) and poor trend of data against the best fit line, as seen in Figure

5.14. Correlation based on the cone tip resistance such as in Figure 5.11, gives the better

prediction (OCRfit/ OCRMeas=1.01) however data are scattered with R2=0.86 for best fit

estimates. The profile of OCR with depth predicted using some PCPT methods compared

with laboratory estimated OCR for north and south embankment of Juban road site is

presented in Figures 5.17 through Figure 5.20. The prediction of OCR profile with depth

looks reasonable and in good agreement with laboratory estimated values. In general it is

found that PCPT correlation overestimate the laboratory estimated OCR values for top for

Juban North and Juban South embankment sites. Further the spikes in the PCPT predicted

OCR profiles are due to presence of lenses of sandy or silty soils where cone tip resistance

shows sharp increase.

OCR fit =

1.01 O

CR m.

R2 = 0.68

0 2 4 6 8 10

Measured OCR

0

2

4

6

8

10

Pred

icte

d O

CR

Perfect

Fit

OCR fit = 0.14 * [ (qt - σvo) / σvo' ]R2 = 0.86

Test Sites:

Juban North

Juban South

Figure 5.11 : Measured versus predicted OCR for Juban Road site

OCR fit = 0.82 O

CR m.

R2 = 0.86

0 2 4 6 8 10

Measured OCR

0

2

4

6

8

10

Pred

icte

d O

CR

Perfec

t Fit

OCR fit = 0.88 + 0.13 * (qt+ fs) / σvo R2 = 0.71

Test Sites:

Juban North

Juban South

Figure 5.12: Measured versus predicted OCR for Juban Road site

113

OCR fit =0.72 OCR m.

R2 = 0.83

0 2 4 6 8 10 12 14

Measured OCR

0

2

4

6

8

10

12

14

Pred

icte

d O

CR

Perfec

t Fit

OCR fit = 1.08 + 1.92 * fs / σvo'R2 = 0.71


OCR fit = 0.49 OCR m.

R2 = 0.80

0 2 4 6 8 10

Measured OCR

0

2

4

6

8

10

Pred

icte

d O

CR Per

fect Fit

OCR = 1.17 + 0.134 * [ (u1 - u2)/ u0 ]R2 = 0.54

Test Sites:

Juban North

Juban South


OCR fit = 0.86 O

CR m.

R2 = 0.61

0 2 4 6 8 10

Measured OCR

0

2

4

6

8

10

Pred

icte

d O

CR

Perfect

Fit

OCR fit = 4.33 * Bq1 -0.55 * PI -0.37

R2 = 0.63

Test Sites:

Juban North

Juban South


OCR fit = 0.82 O

CR m.

R2 = 0.90

0 2 4 6 8 10

Measured OCR

0

2

4

6

8

10

Pred

icte

d O

CR

Perfec

t Fit

OCR fit = 1.02 + 1.66 * fs / σvo' - 0.83* u1+0.004*(CL+ML) R2 = 0.71

Test Sites:

Juban North

Juban South


114

0 5 10

OCR

0

2

4

6

8

10

12

14

16

18

20

Dept

h (m

)

OCROCR=0.15(qt-u1)/σ'vo

Measured

Figure 5.17: OCR profile with depth (Juban North)

0 5 10

OCR

0

2

4

6

8

10

12

14

16

18

20

Dept

h (m

)

OCROC R= 0.14 (qt-σvo)/σ'vo

M easured

Figure 5.18: : OCR profile with depth (Juban North)

0 5 10

OCR

0

2

4

6

8

10

12

14

16

18

20

Dept

h (m

)

OCROCR=0.15(qt-u1)/σ'vo

Measured

SANDY LAYER

SANDY LAYER

Figure 5.19: OCR profile with depth (Juban South)

0 5 10

OCR

0

2

4

6

8

10

12

14

16

18

20

Dept

h (m

)

OCROCR=0.14(qt-σvo)/σ 'vo

Measured

SANDY LAYER

SANDY LAYER

Figure 5.20: OCR profile with depth (Juban South)

115

5.1.3 Coefficient of consolidation (Cv)

Plot of predicted versus measured value of cv for Juban north and Juban south embankment is

presented in figure 5.21 to figure 5.24. It is obvious from the plots that simple linear

regression or non linear regression produces poor correlation between coefficients of

consolidation obtained from oedometer test and PCPT parameters. But the data still follows

the trend and further analysis by comparing with back calculated parameter will be discussed

in subsequent sections.

log(Cvfit) = 1.103* log(Cvm)R2 = 0.96

1E-005 1E-004 1E-003 1E-002 1E-001


1E-005

1E-004

1E-003

1E-002

1E-001

Pred

icte

d, c

v (cm

2 /sec

)

Perfect

Fit

Test Sites:

Juban North

Juban South

log(C vfi

t) = -2

.34-0.

32 lo

g (t 50)

R2 = 0.

21

Figure 5.21: Measured versus predicted Cv for Juban Road Site

1E-005 1E-004 1E-003 1E-002 1E-001


1E-005

1E-004

1E-003

1E-002

1E-001

Pred

icte

d, c

v (cm

2 /sec

)

Perfect

Fit

Test Sites:

Juban North

Juban South

log( C v) = -2.9+0.42 *log (u 1-u 0)R2 = 0.81

Figure 5.22: : Measured versus predicted Cv for Juban Road Site

1E-005 1E-004 1E-003 1E-002 1E-001


1E-005

1E-004

1E-003

1E-002

1E-001

Pred

icte

d, c

v (cm

2 /sec

)

Perfect

Fit

Test Sites:Juban NorthJuban South

log (cv) =-2.07+0.33* log (ui /t50√FR)]R2 = 0.38

Figure 5.23:Measured versus predicted Cv for Juban Road Site

1E-005 1E-004 1E-003 1E-002 1E-001


1E-005

1E-004

1E-003

1E-002

1E-001

Pred

icte

d, c

v (cm

2 /sec

)

Teh and Houlsby (1988)

Perfect

Fit

Test Sites:

Juban North

Juban South

Figure 5.24: Measured versus predicted Cv using Teh and Houlsby (1986) for Juban

Road Site

116

5.2 Field Settlement Analysis and Back Calculation of Consolidation Parameters

5.2.1 Magnitude of Total Settlement

The Principle and theory of settlement analysis were discussed in details in section 2.1.

Following section describes the steps followed in estimating field settlement using both

laboratory and PCPT parameters.

(i) Soil profiling: Identification of compressible layers and the estimation of

consolidation characteristics of the layer is first and crucial step. Conventionally,

physical and mechanical characterizations of sub soil layers are usually estimated

using soil samples obtained from bore hole in the close proximity. But this method

has certain practical limitations (section 2.2). On the other hand, PCPT gives the

repeatable and near continuous profile of soil properties such as soil type and

undrained shear strength that can be used to identify the different sub layers. In this

study, Zhang and Tumay (1999) method was used to identify soft compressible clayey

layers from incompressible dense sandy or gravel soils.

(ii) Estimate of existing overburden and incremental stress: Existing overburden stress at

the mid depth of sub layer is determined using relation

mmiivo HH γγσ21'' += ∑

where i'γ and iH represents unit weight and the depth of individual sub layers above

the soil layer, m'γ and mH represents the unit weight and depth of the soil layer under

consideration. Incremental induced vertical stress (Δσv) due to embankment loading is

estimated using Gray’s relation (Gray, 1936, Poulos and Davis, 1973), variables defined in

Figure 5.25.

)}({ 22

bxR

za

xqv −−+=Δ

αβπ

σ

For laboratory method of settlement prediction,

(iii) Calculate consolidation parameters Cc, Cr, e0 and σ’p from laboratory test such as one

dimensional Oedometer test.

(iv) For each layer, settlement due to incremental load is calculated as

p

vvo

p

c

vo

prc e

Ce

CS

''

log)1(

'log

)1( 0 σσσ

σσ Δ+

++

+= For over consolidated state

( vo'σ < p'σ and vs'σ > p'σ )

117

z

x

β

α

q

Ro

R1R2

b

a

o

Figure 5.25 Elastic solution for the incremental stress under embankment loading (Poulos and Davis, 1973)

where e0 and ep are void ratio at in situ and preconsolidation stresses respectively,

( vvovs ''' σσσ Δ+= ) is the final stress. Other terms are defined elsewhere. Similarly,

vo

vvo

p

rc e

CS'

'log

)1( σσσ Δ+

+= For over consolidated state ( vo'σ < p'σ and vs'σ < p'σ )

vo

vvo

p

cc e

CS

''

log)1( σ

σσ Δ++

= For normally consolidated state ( vo'σ > p'σ )

In case of PCPT, coefficient of compressibility is obtained directly in terms of

constrained Modulus (M) and as such it is more convenient to use following relations:

(v) For each layer, calculate average qt, fs, u1 and u2 and other related parameters.

Calculate constrained modulus (Mi) for each layer using PCPT correlations as

discussed earlier.

(vi) Find the corrected constrained modulus (Mavi) for each layer, for the stress range vo'σ

vvo σσ Δ+' , where vo'σ and vσΔ are existing average overburden and induced

incremental stress, respectively, calculated at the mid depth of the individual soil

layers.

vo

vvoav MM

'2/'

σσσ Δ+

= (Senneset et al., 1988)

118

(vii) Settlement of each layer is then calculated using relation

avi

vci M

HiS

σΔ=

where Hi is the depth of individual soil layer. Total settlement is then the summation

of all the compressible soil layers, given as:

∑ Δ=

n

avi

vc M

HiS

σ

where n is the total number of sub layers.

5.2.2 Time Rate of Consolidation Settlement

Average degree of consolidation due to both vertical and radial drainage is given by

)1)(1(1 hv UUU −−−=

For any given time t, time factor Tv is defined as

2dtc

T vv =

where d= drainage path = H for single drainage and 2H

= for double drainage.

Average degree of vertical consolidation Uv is then approximated with reasonable

accuracy by the following

4

2v

vU

Tπ

= For Uv≤ 0.6

085.0)1log(933.0 −−−= vv UT For Uv≥ 0.6

In the field, the vertical flow of pore water under the influence of excess pore water

pressure occurs through soil layers having different cv and k values before dissipating through

free drainage layer, as shown in Figure 5.26. Under such condition, dissipation of excess pore

pressure within different layers at different time periods can be calculated using more

rigorous numerical solution such as finite difference method. However, for practical reasons,

the average degree of vertical consolidation can be reasonably estimated by substituting

single equivalent coefficient of consolidation (cva) and drainage length (de) for multi layer soil

stratum using the following relation (Absi 1970, Sanglerat 1985)

2

2

⎟⎟⎠

⎞⎜⎜⎝

⎛=

∑vi

i

eva

ch

HC

119

∑= ie hH

where hi and cvi indicates the depth and vertical coefficient of consolidation of each

soil layer.

cv1 h1

Free Draining layer

Free Draining layer

cv2 h2

cv3 h3

Figure 5.26: Layered soil with different permeability and consolidation characteristics

The degree of consolidation of specific layer due to horizontal drainage facilitated by

installation of prefabricated vertical drains (PVD) is determined using the following relation

(Barron, 1948; Hansbo, 1979; Reisner et al. 1986)

[ ]FTU hh /8exp1 −−=

where Th and F are defined below

2Dtc

T hh =

where D is the influence zone diameter of the drain and is a function of drain spacing

(S) and pattern of drain layout.

SD *128.1= For rectangular pattern

SD *505.1= For triangular pattern

Also,

rs FFnFF ++= )(

where,

Drain spacing factor, 43)ln()( −=

wdDnF

Factor for soil disturbance, )1)ln(ds/dw-kk

(s

h=sF

120

Factor for drain resistance, )(05.0]k

z)-(Lz

[ h nFq

Fw

r ≈=π

In the above expressions,

Equivalent diameter of the drain, )2

( bad w+

=

where a and b are the width and thickness of PVD and for most of the PVD types used

in North America 05.0≈wd to 0.075 m. Diameter of the smear zone ds is taken twice the

diameter of the mandrel used in installation of PVD whilst ks defines the coefficient of

permeability in the smear zone and could be assumed to be equal to the coefficient of

permeability in vertical direction. kh is the coefficient of permeability in horizontal direction,

L and qw are length and discharge capacity of PVD respectively. Z is the depth of PVD from

the free draining layers.

5.3 Settlement Curves and Back Calculation of Consolidation Parameters for Juban Road I-12 Intersection sites

5.3.1 Comparison with Horizontal Inclinometer Measurements

Total settlement profile along the width of the embankment calculated using the different

PCPT methods, laboratory estimated parameters and the observed settlement measured using

horizontal inclinometer are presented in Figures 5.27 and 5.28. As seen in the figures,

settlement calculated using laboratory estimated parameters and that using corrected cone tip

resistance, qt estimated field measurement closely. On the other hand, settlement estimated

using other PCPT correlation is higher than the actual settlement by 75%. The rate of

settlement predicted using the laboratory or dissipation tests (Teh and Houlsby, 1988)

matches fairly well with field measurements as shown in Figures 5.29 and 5.30.

5.3.2 Comparison with Vertical Extensometer Measurements

Table 5.1 presents the summary of back calculated constrained modulus (M) and the

corresponding α value from Juban south vertical extensometer observations. By recording the

relative movement of spider magnets, vertical compression of each layer was calculated for a

given incremental stress. Also for each layer, thickness of incompressible sandy layer, as

identified by, PCPT profile was deducted from total thickness. The end of primary

consolidation was estimated using rectangular hyperbola curve fitting method, RHM

(Sridharan et al, 1985). Settlement curves and presentation of curve fitting plots are given in

Appendix C. Comparison of some important PCPT correlation and back calculated

constrained modulus is given in Figure 5.31. Figure 5.32 presents the comparison of back

121

calculated cv with PCPT predicted and laboratory measure cv. As seen in figure, high

scattering is evident but most of the values fall within narrow band of order of magnitude of

one log cycle. Most important, in this case, parameters predicted using proposed correlations

using based on PCPT measurements only are fairly within the range of average coefficient of

consolidation.

0 40 80 120 160 200 240 280 320 360

Distance (feet)

0

2

4

6

8

Settl

emen

t (in

ches

)

Sett lementMeasured ( 6 months)Lab Predicted (Total)PCPT Predicted -M=3.15qt (Total)M=3.47qt

0.564

M=3.85qt0.56fs

0. 023u10. 035

M=16.50*√fs

20

15

10

5

0

Settl

emen

t (cm

)

0 10 20 30 40 50 60 70 80 90 100

H= 32.38'

B2= 118' B1= 100' B3= 118'

Figure 5.27: Comparison of predicted settlement profile with field measurement (North

Embankment).

122

0 40 80 120 160 200 240 280 320

Distance (feet)

10

8

6

4

2

0

Settl

emen

t (in

ches

)

SettlementMeasured ( 6 months)Lab Predicted (Total)PCPT Predicted -M=3.15qt (Total)M=3.47qt

0.564

M=3.85qt0.56fs

0. 023u10. 035

M=16.50*√fs

25

20

15

10

5

0

Settl

emen

t (cm

)

0 10 20 30 40 50 60 70 80 90

H= 29.5'

B2= 105' B1= 100' B3= 105'

Figure 5.28: Comparison of predicted settlement profile with field measurement (Juban Road South Embankment).

123

0 30 60 90 120 150 180 210 240 270 300 330 360

Days

0

5

10

15

20

25

30

35

Heig

ht o

f Lift

(fee

t)

0

2

4

6

8

10

12

Hei

ght (

m )

5/14/05 6/25/05 8/6/05 9/17/05 10/29/05 12/10/05 1/21/06 3/4/06 4/15/06 5/27/06

(a)

0 30 60 90 120 150 180 210 240 270 300 330 360

Days

0

1

2

3

4

5

6

Settl

emen

t (In

ches

)

SettlementLab (DOTD)Lab (LTRC)CPTHI (Field)

0

2.5

5

7.5

10

12.5

15

Settl

emen

t (cm

)

5/14/05 6/25/05 8/6/05 9/17/05 10/29/05 12/10/05 1/21/06 3/4/06 4/15/06 5/27/06

(b)

Figure 5.29: a) Lift schedule b) Rate of settlement for Juban Road North Embankment.

124

0 14 28 42 56 70 84 98 112 126 140 154 168 182 196 210 224 238 252

Days

0

5

10

15

20

25

30

35

Heig

ht o

f Lift

(fee

t)

0

2

4

6

8

10

12

Hei

ght (

m )

8/6/05 9/17/05 10/29/05 12/10/05 1/21/06 3/4/06 4/15/06

(a)

0 30 60 90 120 150 180 210 240

Days

0

1

2

3

4

5

6

Settl

emen

t (In

ches

)

SettlementLab (DOTD)CPTHI (Field)

0

2.5

5

7.5

10

12.5

15

Settl

emen

t (cm

)

8/6/05 9/17/05 10/29/05 12/10/05 1/21/06 3/4/06 4/15/06

(b) Figure 5.30: a) Lift schedule b) Rate of settlement for Juban South Embankment.

125

0 2 4 6 8 10


0

2

4

6

8

10

Dept

h (m

)

Constraints Modulus (M)Oedometerbck calM=3.90*qt

0. 58fs 0 .034u10.017u2

0. 004

M=2.52(qt-σ vo)+.027 mc

M=16.50 √fs

M=3.47 qt0. 546

M=2.21(qt-σ vo)+0.018 CL

M=3.15 qt

M=3.58(qt-σ vo)

M=3.85*qt0. 56fs 0 .023u1

0.035

Figure 5.31: Comparison of PCPT correlations with laboratory and back calculated constrained Modulus (M) (Juban South Embankment)

1E-005 1E-004 1E-003 1E-002 1E-001 1E+000

Coefficient of consolidation Cv (cm2/sec)

12

10

8

6

4

2

0

Dep

th (m

)

Cv (cm2/sec)Teh and Houlsby(1988)OedometerCv field

Cv field (Sridharan et.al. 1985)

log(cv)=-2.29+0.42*log(Δu2)

cv=-2.07+0.33log[ui/(t50√FR)]

log(cv)=-2.58-0.55*log(Δu2)

Figure 5.32: Comparison of PCPT correlations with laboratory and back calculated constrained Cv (Juban South Embankment)

126

Table 5.1: Summary of back calculated constrained Modulus (M).

Elevation

Thk Settl. Δσv qt Cal

Senneset's αcal from field αpred/ αmeas

Magnets (ft) (ft) (s) kPa MPa σvo M Corr. qc qt (qt-σvo) qt

(qt-σvo)

SM-5 and SM-6

30.5-36.4

6.11 0.152 135.2 0.85 0.008 5.4 1.78 2.11 2.09 2.11 1.51 1.70

SM-4 and SM-5

25.5-30.5

4.84

0.110z 134.9 0.85 0.030 5.9 2.95 3.51 3.47 3.59 0.91 1.00

SM-2 and SM-3

19.8-23.5

3.59 0.067 134.5 1.61 0.068 7.2 4.42 2.75 2.75 2.87 1.15 1.25

SM-1 and SM-2

10.4-19.8

6.45 0.104 133.6 1.6 0.105 8.3 5.67 3.55 3.55 3.79 0.89 0.94

BM-1 and SM-1

4.5-10.4

3.74 0.058 132.1 2.56 0.148 8.5 6.28 2.46 2.45 2.61 1.28 1.37

SM-5 and SM-2

30.5-19.8

9.05 0.186 134.1 1.17 0.05 6.5 3.72 3.21 3.19 3.32 0.99 1.08

SM-5 and SM-1

30.5-10.4

16.83 0.280 132.9 1.37 0.07 8.0 4.95 3.63 3.61 3.82 0.87 0.94

Mean 3.03 3.01 3.16

STDEV 0.60 0.59 0.65

127

CHAPTER 6

6 SOFTWARE DEVELOPMENT

Software application was developed to classify and calculate settlement under the

embankment loading. This chapter gives the demonstration of the Visual Basic program

package and describes the main features available in this package.

6.1 Introduction

Stand alone software package (Figure 6.1) coded in Visual Basic was developed to facilitate

the estimate of magnitude and time rate of embankment settlement in the field using PCPT

parameters. The program can be installed in any personal computer or laptops running on

processor and memory specification greater or equivalent of Intel PIII© and equipped with

WINDOWS©. Step by step demonstration of the software features is discussed next.

Figure 6.1: Embankment settlement program logo.

6.2 Startup Windows and Input Files

This program is coded in VB and is Graphical User Interface type package which means user

can input parameters and browse files using mouse and navigation buttons. Input windows

ask the user to locate the PCPT files and the dissipation files. CPT data and dissipation files

used in this program should be saved in .DAT format. If type 2 cone tests (with u2

measurement) are available and uploaded, this program also corrects cone tip resistance for

pore water pressure (section 2.6). Preview window is also provided to view file before

uploading. This feature helps to verify the type of cone used, check units as well as other

remarks (Figure 6.2).

128

Figure 6.2 : Opening window with navigation links and input parameters.

6.3 Project Information

Project information and other remarks are input in this window as shown in Figure

6.3. This information is used solely for project identification and display purpose only.

Figure 6.3 Project information window

129

6.4 Plot of PCPT Profile and Soil Classification

The first two columns in this window display qt and fs profiles with depth. Other two columns

display pore pressure measurements or soil classification depending upon user’s choice. Main

functions available in this window are

6.4.1 Classify Soil

Soil classification profile for the test site is plotted using probabilistic region estimating soil

classification method (Zhang and Tumay, 1999) as shown in Figure 7.1.4.

Figure 6.4 : Plot of PCPT profile and soil classification at the test site.

6.4.2 Soil Unit Weight

User can select either one average value for soil unit weight or can enter soil unit weights for

different layer from the borehole log information as shown in Figure 6.5. In addition, unit

weight for each soil layer can be estimated using CPT measurement (Robertson et al. 1986).

As overburden stress (σvo) is used in several PCPT correlations, options in the other windows

are disabled until selection is made in this menu.

6.4.3 Soil Properties

This menu allows choosing the display of profile of undrained shear strength (Su),

Constrained Modulus (M) and OCR with depth, estimated using PCPT correlations.

130

Figure 6.5: Soil unit weight input window.

6.4.4 Dissipation

Options are available for displaying dissipation curves (opens in separate window) or

showing profile of cv or ch value estimated using Teh and Houlsby (1988) method. Also

calculated value of cv and ch values can be exported in text formats (Figure 6.6)

Figure 6.6: Normalized dissipation curves for different depths.

6.4.5 Units

This menu allows user to choose English (ft-TSF) or metric (m-MPa) units.

131

6.4.6 Settlement

Steps for the analysis of the settlement under embankment loading were discussed in detail in

Chapter 5. Once the basic design input are entered, this program estimates the magnitude of

settlement under embankment loading based on PCPT estimated consolidation parameters.

Input window for this menu is as shown in Figure 6.7.

Settlement at any point under the embankment can be displayed by choosing

coordinate (x) of the point from the origin (from the left hand side of embankment). Also

display options for settlement profile along the embankment width with respect to time

(Figure 6.8) and time rate of settlement at the mid point (maximum settlement) as shown in

Figure 6.9.

6.4.7 Summary of Input Parameters

This window gives the summary of estimated consolidation parameters, soil classification

and location of drainage layers as used for settlement calculation (Figure 6.10). Also, at this

point, user can manually change or add the information based on his experience, engineering

judgment or other additional information such as results from close borehole drill. These

edited parameters are automatically updated by the program for its calculation and used to

furnish new settlement profile. This program can also be used to predict settlement profile for

laboratory estimated parameters by replacing CPT parameters in the table by laboratory

estimates.

6.4.8 Provision for Design of Surcharge Height and PVD Installation

In order to expedite the time rate of settlement in field, sometimes additional temporary fill,

known as surcharge is used. In some cases surcharge alone may not be sufficient and in that

case vertical drains such as sand drains or PVD are used to accelerate the dissipation of

excess pore water pressure and hence time of settlement. This program can also be used to

estimate the height of the surcharge and to design PVD parameters during early design stage.

User can manipulate different values of surcharge height and/or add PVD option to determine

optimum condition to get desired value of embankment settlement with in given time frame.

132

Figure 6.7: Input window for embankment dimension, fill characteristics and PVD design.

Figure 6.8: Progress of settlement profile along the width of embankment with time.

133

Figure 6.9: Comparison of time rate of settlement curve at the centre for with and with out surcharge condition.

Figure 6.10: Summary table for design parameters used in calculation.

134

CHAPTER 7

7 CONCLUSION AND RECCOMENDATIONS

The present study investigated the potential of PCPT method to evaluate and estimate

consolidation parameters of cohesive soils in Louisiana. The consolidation parameters

namely constrained modulus (M), overconsolidation ratio (OCR) and vertical coefficient of

consolidation (cv) were evaluated using PCPT correlations and comparisons were made with

laboratory estimated parameters. Back calculated consolidation parameters from settlement

monitoring instruments that includes horizontal inclinometer and vertical extensometer in

Juban Road I-12 intersection site were compared to that of laboratory and PCPT prediction

methods. In addition, magnitude and time rate of settlement estimated from laboratory and

PCPT parameters were compared with the settlement profiles obtained from horizontal

inclinometers placed under embankments

7.1 Conclusions • Several existing correlations were evaluated and calibrated for prediction of constrained

modulus, OCR and cv using simple linear, multiple and non linear regression analyses of

PCPT parameters with laboratory estimated consolidation parameters for seven sites in

Louisiana soils.

• PCPT correlations based on cone tip resistance are more reliable and accurate. Simple

correlations based on corrected cone tip resistance (qt) and or net cone tip resistance (qt-

σvo) gives the best prediction for M. Similarly, parameters [(qt-σvo)/σ’vo] and [(qt-u1)/σ’vo]

are deemed best based for prediction of OCR.

• Although correlations based on pore pressure measurements are indicative of M and

OCR, results obtained from these have, in general, lower coefficient of determination (R2)

compared to that based on cone tip resistance. This may be attributed largely to

inaccuracies in pore pressure measurements due to inadequate saturation, loss of

saturation during penetration, presence of thin sandy or silty lenses as well as theoretical

interpretation of pore pressure measurements.

• New correlations were developed with sleeve friction (fs) measurements. This study

found that sleeve friction measurement is close to undrained shear strength of cohesive

soils. Good correlations were also found for prediction of M and OCR using regression

models that includes sleeve friction measurements.

• Regression models based on pore pressure measurements were developed for estimating

vertical coefficient of consolidation.

135

• New correlations were developed to predict vertical coefficient of consolidation that

incorporated effect of rigidity index estimated using PCPT measurements. Comparison

with theoretical model proposed by Teh and Houlsby (1988) gave the fair match.

• Empirical cone factor (Nk) for prediction of undrained shear strength was found in

between 16 and 17.

• Horizontal inclinometers give the best performance as the field settlement monitoring

device. Magnetic extensometer, though provides excellent opportunity to monitor

settlements of individual layer, were marred by problems such as accidental breaking of

access pipe due to construction activities, hassles of adding extra pipe pieces as

embankment construction progresses etc.

• Stand alone Visual Basic program was developed to estimate magnitude and time rate of

consolidation settlement under embankment loading using PCPT correlations. The

program also has the feature to facilitate the design of surcharge and PVD to determine

optimum conditions to get desired value of settlement with in given time frame.

7.2 Recommendations • PCPT correlations obtained in this study are based only on data obtained from seven sites

in Louisiana. It is therefore recommended that the proposed correlations and coefficients

are only valid for this region or soils having similar geological or engineering properties.

• As more data are added, these correlations should be updated. This study also

recommends the scope of further research in the direction of evaluating reliability and

accuracy of PCPT predictions and use of statistical tools such as Bayesian analysis for

improving existing correlations.

• More in situ and field settlement monitoring tests are recommended to calibrate the

correlations directly with respect to back calculated parameters from in situ

measurements. Direct comparison with field performance will render further confidence

in practice of PCPT method to predict settlement.

• As cone tip resistance and sleeve friction measurements are found to be more reliable and

accurate for PCPT correlations, more attention should be given to calibrate and enhance

the performance of components recording these measurements.

136

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8

9

143

APPENDIX A

10 STRESS DISTRIBUTION DUE TO EXTERNAL LOADING

This section gives a brief review of the stress distribution with in an idealized elastic soil

mass due to different types of applied external loading. These relations are based on elastic

solutions proposed by Boussinesq and discussed elsewhere (Poulos and Davis, 1974; Aysen,

2000). Vertical stress under some of the common loading types in the field is given below:

(i) Concentrated Vertical Load

For any point located (r,z) from the concentrated load as shown in Figure A1, vertical

incremental stress is given as:

[ ] 2/522 1)/(23

+=Δ

zrzQ

vπ

σ

z

x

θ

Q

z R

r A

σz

σr

Figure A1: Concentrated load

(ii) Uniformly Loaded Circular Area

For any point located directly under the centre of uniformly loaded circular area as shown in

Figure A2, vertical incremental stress is given as:

⎥⎦

⎤⎢⎣

⎡+

−=Δ 2/32 ]1)/[(11

zRq

cvσ

z

x

q

z A

σz

Rc

Figure A2: Circular load

144

(iii) Uniformly Loaded infinite strip

[ ])2(cossin βαααπ

σ ++=Δq

v

where

( )[ ] ( )[ ]zbxzbx /tan/tan 11 −−+= −−α

( )[ ]zbx /tan 1 −= −β

x

β

α

q

Ro

R1

2b

o

σz

Figure A3: Infinite Strip loading

(iv) Embankment Loading of Infinite Length

For any point located (x,z) from the corner of the embankment loading, vertical incremental

stress is given as:

)}({ 22

bxR

za

xqv −−+=Δ

αβπ

σ

z

x

β

α

q

Ro

R1R2

b

a

o

Figure A4: Embankment Loading

145

APPENDIX B

11 SAS® PROGRAM AND SAMPLE OUTPUTS FOR REGRESSION ANALYSES

A brief description of SAS® program to analyze the data and perform regression analyses is

given in following sections.

(i) Importing data from Excel sheet and further data transformations dm 'log;clear;output;clear'; OPTIONS nodate nocenter pageno=1 ls=100 ps=66; Title1 'Regresssion Analysis for M'; PROC IMPORT OUT= WORK.MR DATAFILE= "D:\ROHIT\Desktop\Regression\M\data_112606" DBMS=EXCEL2000 REPLACE; SHEET="all_m_reg$"; GETNAMES=YES; RUN;

Following steps will create new data set MR2 that has additional transformed variables and

then displays the new data set in output window. Data MR2; set MR(drop=rem );lm=log(M);sqt=qt**.5;lgm=log10(M); lqt=log(qt);qt2=qt*qt;ltqt=log10(qt); lfs=log(fs); fsv=fs*CL;u10=U1-U0;u20=U2-U0;U22=U2*U2;U12=U1*U1;qu=qt*U1;run; PROC print data=MR2; RUN; Obs depth avs qt fs U1 U2 U0 efs M 1 0.4572 0.00740 0.56716 0.01154 0.03805 0.04293 0.00154 0.00586 1.80 2 1.3716 0.02229 0.63823 0.01769 0.02982 0.05296 0.01051 0.01178 2.66 3 2.2860 0.03696 0.59861 0.01883 0.04743 0.06640 0.01948 0.01747 1.30 4 4.1148 0.06651 0.75981 0.03464 0.03486 0.05009 0.03742 0.02909 1.92 5 5.0292 0.08167 1.00428 0.03501 0.03652 0.06324 0.04639 0.03528 3. 3

(ii) Selection of best models based on different criteria as discussed in chapter 4.

Models with intercept terms:

dm 'log;clear;output;clear'; proc reg data=MR2 outest=est; model M=qt fs avs efs U1 U2 SM ML mc PI / selection=adjrsq sse aic cp; output out=out p=p r=r; run;quit; dm 'log;clear;output;clear'; Models with intercept restricted to zero (lines passing through origin)

proc reg data=MR2 outest=est;

146

model M=qt fs avs efs U1 U2 SM ML mc PI / noint selection=adjrsq sse aic cp; output out=out p=p r=r; run;quit;

Sample Output The REG Procedure Model: MODEL1 Dependent Variable: M Adjusted R-Square Selection Method Number of Observations Read 37 Number of Observations Used 36 Number of Observations with Missing Values 1 Number in Adjusted Model R-Square R-Square C(p) AIC SSE Variables in Model 5 0.8075 0.8396 2.0168 -26.7893 8.87039 qt U1 U2 ML mc : 4 0.8034 0.8296 1.3237 -26.9192 9.42199 qt efs U2 mc 4 0.8024 0.8288 1.4340 -26.7663 9.46856 qt avs U2 mc 5 0.8008 0.8340 2.7481 -25.7290 9.17904 qt avs U1 U2 mc

6 0.8007 0.8406 3.8891 -24.9782 8.81652 qt efs U2 SM ML mc

:

4 0.3939 0.4747 47.8285 7.9859 29.04992 avs U1 SM mc 4 0.3926 0.4736 47.9694 8.0493 29.10938 avs U1 U2 mc

6 0.3918 0.5134 46.7497 9.6096 26.90634 avs efs U1 SM ML mc

(iii) Simple linear regression (SLR) model for M using cone tip resistance (qt) only

Robestreg procedure to check for outliers and other diagnostics (refer SAS help manual)

dm 'log;clear;output;clear'; proc robustreg data=MR; model M= qt/ diagnostics; run;

Model with intercept term

proc reg data=MR4; model M= qt /i r; output out=d2 predicted=yhat2 residual=resid2; run; options ls=64 ps=30; proc plot data=d2; plot M*qt='#' yhat2*qt='%'/overlay;run;options ls=64 ps=30; proc plot data=d2; plot resid2*qt;run;options ls=64 ps=30; proc plot data=d2; plot resid2*yhat2;run;options ls=64 ps=30; proc univariate data= d2 normal plot ;var resid2;run; options ls=100 ps=66;

For regression models without intercept term:

proc reg data=MR2; model M= qt /i r;restrict intercept; output out=d3 predicted=yhat3 residual=resid3; run;

147

Sample output Model: MODEL1 Dependent Variable: M Number of Observations Read 37 Number of Observations Used 36 Number of Observations with Missing Values 1 X'X Inverse, Parameter Estimates, and SSE Variable Label Intercept qt M Intercept Intercept 0.1016110351 -0.082694889 1.4225752272 qt qt -0.082694889 0.0926201145 1.9039535351 M M 1.4225752272 1.9039535351 18.670286608 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 39.13879 39.13879 71.27 <.0001 Error 34 18.67029 0.54913 Corrected Total 35 57.80907 Root MSE 0.74103 R-Square 0.6770 Dependent Mean 3.12250 Adj R-Sq 0.6675 Coeff Var 23.73196 Parameter Estimates Parameter Standard Variable Label DF Estimate Error t Value Pr > |t| Intercept Intercept 1 1.42258 0.23621 6.02 <.0001

qt qt 1 1.90395 0.22552 8.44 <.0001

Output Statistics Dependent Predicted Std Error Std Error Student Cook's Obs Variable Value Mean Predict Residual Residual Residual -2-1 0 1 2 D 1 1.8000 2.5024 0.1437 -0.7024 0.727 -0.966 | *| | 0.018 2 2.6600 2.6377 0.1362 0.0223 0.728 0.0306 | | | 0.000 3 1.3000 2.5623 0.1402 -1.2623 0.728 -1.735 | ***| | 0.056 4 1.9200 2.8692 0.1271 -0.9492 0.730 -1.300 | **| | 0.026 5 3.2300 3.3347 0.1260 -0.1047 0.730 -0.143 | | | 0.000

:

:

Sum of Residuals 0 Sum of Squared Residuals 18.67029 Predicted Residual SS (PRESS) 20.6048

Test for normality of residuals The UNIVARIATE Procedure Variable: resid2 (Residual) Moments N 36 Sum Weights 36 Mean 0 Sum Observations 0 Std Deviation 0.73036755 Variance 0.53343676 Skewness 0.44975193 Kurtosis -0.1914211 Uncorrected SS 18.6702866 Corrected SS 18.6702866 Coeff Variation Std Error Mean 0.12172793

Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.972234 Pr < W 0.4897 Kolmogorov-Smirnov D 0.081353 Pr > D >0.1500 Cramer-von Mises W-Sq 0.041656 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.304074 Pr > A-Sq >0.2500

148

(iv) Non Linear regression model for M using cone tip resistance (qt) only Proc nlin data=MR2 method=marquardt hougaard; parms a0=-2 to 2 a1=-5 to 5 ; model M = a0*(qt)**a1;output out=d2 predicted=yp2 residual=resid2; run; legend1 frame cframe=ligr label=none cborder=black position=center value=(justify=center); axis1 label=(angle=90 rotate=0) minor=none; axis2 minor=none; proc gplot; plot M*sqt yp2*sqt/frame cframe=ligr legend=legend1 vaxis=axis1 haxis=axis2 overlay ; run;

Sample Output The NLIN Procedure Dependent Variable M Method: Marquardt Iterative Phase Sum of Iter a0 a1 Squares 0 2.0000 1.0000 83.1052 1 3.5740 0.2522 31.3631 2 3.5284 0.5555 17.7989 3 3.4716 0.5641 17.6948 NOTE: Convergence criterion met. Estimation Summary Method Marquardt Iterations 3 R 6.319E-6 PPC(a1) 3.689E-6 RPC(a0) 0.016093 Object 0.005849 Objective 17.69475 Observations Read 37 Observations Used 36 Observations Missing 1 NOTE: An intercept was not specified for this model. Sum of Mean Approx Source DF Squares Square F Value Pr > F Model 2 391.1 195.6 375.76 <.0001 Error 34 17.6948 0.5204 Uncorrected Total 36 408.8 Approx Approximate 95% Parameter Estimate Std Error Confidence Limits Skewness a0 3.4716 0.1284 3.2107 3.7326 -0.00306 a1 0.5641 0.0643 0.4335 0.6947 0.0381

(v) Multiple Linear regression model for M using cone tip resistance (qt), u2 and mc dm 'log;clear;output;clear'; proc reg data=MR4; model M= qt U2 mc/i; output out=d2 predicted=yhat2 residual=resid2; run; proc univariate data= d2 normal plot ;var resid2;run; Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 44.14985 14.71662 38.16 <.0001 Error 25 9.64174 0.38567

149

Corrected Total 28 53.79159 Root MSE 0.62102 R-Square 0.8208 Dependent Mean 3.07069 Adj R-Sq 0.7992 Coeff Var 20.22422 Parameter Estimates Parameter Standard Variable Label DF Estimate Error t Value Pr > |t| Intercept Intercept 1 2.50816 0.50441 4.97 <.0001 qt qt 1 1.58134 0.23616 6.70 <.0001 U2 U2 1 2.61041 1.13227 2.31 0.0297 mc mc 1 -0.03231 0.01030 -3.14 0.0043

150

APPENDIX C

12 SETTLEMENT DATA FROM VERTICAL EXTENSOMETER

4.924.934.944.954.964.974.984.99

0 50 100 150t (days)

s (fe

et)

y = 13.998x + 756.44R2 = 0.9883

0500

10001500200025003000

0 50 100 150t (days)

t/s

BM1- SM1 Time -Set t lement Curve

9.389.4

9.429.449.469.48

0 50 100 150t (days)

s (fe

et)

y = 9.2198x + 716.55R2 = 0.9535

0

500

1000

1500

2000

2500

0 50 100 150t (days)

t/s

SM1-SM2

Time -Set t lement Curve

3.53.523.543.563.583.6

0 50 100 150t (days)

s (fe

et)

y = 11.453x + 390.17R2 = 0.9619

0

500

1000

1500

2000

2500

0 50 100 150t (days)

t/s

SM2-SM3 Time -Set t lement Curve

4.724.744.764.784.8

4.824.844.86

0 50 100 150t (days)

s (fe

et)

y = 7.3194x + 382.7R2 = 0.9983

0

500

1000

1500

2000

0 50 100 150t (days)

t/s

SM4-SM5

151

Time -Set t lement Curve

5.95

6

6.05

6.1

6.15

0 50 100 150t (days)

s (fe

et)

y = 5.3249x + 203.42R2 = 0.92

0200400600800

10001200

0 50 100 150t (days)

t/s

SM6-SM5 Time -Set t lement Curve

10.45

10.5

10.55

10.6

10.65

0 50 100 150t (days)

s (fe

et)

y = 4.3448x + 243.13R2 = 0.9101

0

200

400

600

800

1000

0 50 100 150t (days)

t/s

SM5-SM2

Time -Settlement Curve

19.85

19.9

19.9520

20.05

20.1

20.15

0 50 100 150t (days)

s (fe

et)

y = 2.8774x + 184.09R2 = 0.9373

0100200300400500600700

0 50 100 150t (days)

t/s

SM5-SM1

152

13 VITA

Rohit Raj Pant was born in September, 1979 in Mahakali Zone, Nepal, to Dr. Tek Raj Pant

and Ms. Kamala Devi Pant. He finished his school level education from Kanchan Vidhya

Mandir and intermediate in Science from Siddhanath Science Campus, Mahakali Zone,

Nepal. He attended Regional Engineering College, Rourkela, India from 1998 to 2002, under

student exchange scholarship program for Bachelor of Engineering degree in civil

engineering. After finishing Bachelor of Engineering degree, he was employed at Welink

Consultants, Kathmandu, Nepal, as a design engineer. He joined Louisiana State University,

Baton Rouge in the fall semester of 2005. He is anticipated to fulfill his requirements for the

master’s degree in civil engineering in August 2007.

evaluation of consolidation parameters of cohesive soils

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