EKWULO, EMMANUEL OSILEMME PG/Ph.D/10/57787 EMMANUEL... · I also thank the laboratory staff of the Department of Civil Engineering, RSUST for their support and assistance while carrying

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DEVELOPMENT OF LAYERED ELASTIC ANALYSIS PROCEDURE FOR

PREDICTION OF FATIGUE AND RUTTING STRAINS IN CEMENT -

STABILIZED LATERITIC BASE OF LOW VOLUME ROADS

Digitally Signed by: Content manager’s Name

DN : CN = Webmaster’s name

O = University of Nigeria, Nsukka

OU = Innovation Centre

Agboeze Irene E.

EKWULO, EMMANUEL OSILEMME

PG/Ph.D/10/57787

ENGNEERING

CIVIL ENGNEERING

ii

Ph.D DEFENCE

ON

DEVELOPMENT OF LAYERED ELASTIC ANALYSIS PROCEDURE FOR

PREDICTION OF FATIGUE AND RUTTING STRAINS IN CEMENT -

STABILIZED LATERITIC BASE OF LOW VOLUME ROADS

BY


PG/Ph.D/10/57787

SUPERVISOR:

PROF. J. C. AGUNWAMBA

DEPARTMENT OF CIVIL ENGINEERING, UNIVERSITY OF NIGERIA,

NSUKKA

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DECLARATION

I, Ekwulo, Emmanuel Osilemme do hereby declare that this research work

presented is my original research report and has not been previously submitted to

any University or similar institution.

……………………………………………..


PG/Ph.D/10/57787

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CERTIFICATION

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APPROVAL PAGE

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DEDICATION

This Thesis is dedicated to the Almighty God as He continues to grant me the

grace, wisdom and knowledge to contribute in the development our dear country

Nigeria.

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ACKNOWLEDGMENT

My sincere appreciation goes to Prof. J.C. Agunwamba, my supervisor for all his

guidance, encouragement and unalloyed support throughout this endavour.

I also thank the laboratory staff of the Department of Civil Engineering, RSUST for their

support and assistance while carrying out my laboratory work.

My profound gratitude goes to my wife and children for their understanding during the

period I was away in pursuit of this programme, I promise to make up for you all.

My appreciation also goes to the Managing Director of Liberty House, Hon. Henry

Wechie for his support during the period.

Special thank you to my “Mum” and mentor, Dr. (Mrs.) Emylia Jaja for her

encouragement, moral and financial support during the period, “Mum, you are just

wonderful”, God bless you.

I also thank my colleagues, Engr. Dr. S.B. Akpila, Engr. Dr. E.A. Igwe and Mrs. L. Barber

for their encouragement and support.

Many special thanks to my friends, Engr. Dennis Eme, Engr. Dr. Solomon Eluozor, Engr.

Emeka Nwaobakat, Mr. Kelechi Ogbonna and others who contributed one way or the

other to make this research a success, may God bless you all.

Above all, I thank God Almighty for His guidance, strength and provisions during this

period, may His name alone be glorified.

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ABSTRACT

It is generally known that the major causes of failure in asphalt pavement is fatigue

cracking and rutting deformation, caused by excessive horizontal tensile strain at the

bottom of the asphalt layer and vertical compressive strain on top of the subgrade due to

repeated traffic loading. In the design of asphalt pavement, it is necessary to investigate

these critical strains and design against them. This study was conducted to develop a

simplified layered elastic analysis and design procedure to predict fatigue and rutting

strain in cement-stabilized base, low-volume asphalt pavement. The major focus of the

study was to develop a design procedure which involves selection of pavement material

properties and thickness such that strains developed due to traffic loading are within the

allowable limit to prevent fatigue cracking and rutting deformation. Analysis were

performed for hypothetical asphalt pavement using the layered elastic analysis program

EVERSTRESS for four hundred and eighty pavement sections and three traffic

categories. A total of Ninety predictive regression equations were developed with thirty

equations for each traffic category for the prediction of pavement thickness, tensile

(fatigue) strain below asphalt layer and compressive (rutting) strain on top the subgrade.

The regression equations were used to develop a layered elastic analysis and design

program, “LEADFlex”. LEADFlex procedure was validated by comparing its result with

that of EVERSTRESS and measured field data. The LEADFlex-calculated and measured

horizontal tensile strains at the bottom of the asphalt layer and vertical compressive

strain at the top of the subgrade were calibrated and compared using linear regression

analysis. The coefficients of determination R2 were found to be very good. The

calibration of LEADFlex-calculated and measured tensile and compressive strains

resulted in minimum R2 of 0.992 and 0.994 for tensile (fatigue) and compressive (rutting)

strain respectively indicating that LEADFlex is a good predictor of fatigue and rutting

strains in cement-stabilized lateritic base for low-volume asphalt pavement. The result of

this research will enable pavement engineers to predict critical fatigue and rutting

strains in low-volume roads in order to prevent pavement failures.

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LIST OF TABLES

Page

Table 2.1.: Minimum Asphalt Pavement Thickness(TA) 22

Table 2.2: NCSA Design Index categories 22

Table 2.3: Inputs levels in layered elastic Design 32

Table 2.4: Default Resilient Modulus (Mr) Values for Pavement Materials 33

Table 2.5: Typical Poison’s Ratio Values for Pavement Materials 33

Table 2.6: Vehicle Classification 36

Table 2.7: Poisson’s Ratio Used by Various Agencies 44

Table 2.8: Critical Analysis Locations in a Pavement Structure 47

Table 2.9: Limiting Vertical Compressive Strain in Subgrade Soils by Various Agencies 53

Table 3.1: Traffic Categories 68

Table 3.2: Load and materials parameter for determination of critical wheel load 71

Table 3.3: Critical Loading Configuration Determination 71

Table 3.4: LEADFlex Pavement Load and materials parameter 72



Table 4.1a: Light Traffic – Pavement Response Analysis 85

Table 4.1b: Light Traffic - Pavement Response Data 87

Table 4.1c: Light Traffic - Pavement Response Regression Equations 89

Table 4.2a: Medium Traffic – Pavement Response Analysis 90

Table 4.2b: Medium Traffic - Pavement Response Data 92

Table 4.2c: Medium Traffic - Pavement Response Regression Equations 94

Table 4.3a: Heavy Traffic – Pavement Response Analysis 95

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Table 4.3b: Heavy Traffic - Pavement Response Data 97

Table 4.3c: Heavy Traffic - Pavement Response Regression Equations 100

Table 5.1a: Expected Traffic, subgrade CBR and Pavement Base Thickness data for light traffic 102 Table 5.1b: Base Thickness, subgrade CBR and Horizontal Tensile Strain data for light traffic 102 Table 5.1c: Base Thickness, subgrade CBR and Vertical Compressive Strain data for light traffic 103 Table 5.2a: Expected Traffic Repetitions, subgrade CBR and Base Thickness data for medium traffic 103 Table 5.2b: Base Thickness, subgrade CBR and Horizontal Tensile Strain data for medium traffic 103 Table 5.2c: Base Thickness, subgrade CBR and Vertical Compressive Strain data for medium traffic 104 Table 5.3a: Expected Traffic Repetitions, CBR and Base Thickness data for heavy traffic 104 Table 5.3b: Base Thickness, CBR and Horizontal Tensile Strain data for heavy traffic 104 Table 5.3c: Base Thickness, subgrade CBR and Vertical Compressive Strain data

for heavy traffic 105 Table 5.4a: Light Traffic LEADFlex Pavement Characteristic 106

Table 5.4b: Medium Traffic LEADFlex Pavement Characteristics 107

Table 5.4c: Heavy Traffic LEADFlex Pavement Characteristics 108

Table 5.5a: Comparison of LEADFlex and EVERSTRESS Result for LIGHT TRAFFIC 125

Table 5.5b: Comparison of LEADFlex and EVERSTRESS Result for

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MEDIUM TRAFFIC 127

Table 5.5c: Comparison of LEADFlex and EVERSTRESS Result for HEAVY TRAFFIC 129

Table 5.6a: R2 values for LEADFlex-computed and EVERESTERSS-computed Pavement Thickness, Tensile and Compressive Strain for Light Traffic 131

Table 5.6b: R2 values for LEADFlex-computed and EVERESTERSS-computed Pavement Thickness, Tensile and Compressive for Medium Traffic 131

Table 5.6c: R2 values for LEADFlex-computed and EVERESTERSS-computed Pavement Thickness, Tensile and Compressive for Heavy Traffic 131

Table 5.7a: Comparison of LEADFlex-Calculated and Measured Pavement

Response for Subgrade Modulus 4,500psi (31MPa) 132

Table 5.7b: Comparison of LEADFlex-Calculated and Measured Pavement


Table 5.7c: Comparison of LEADFlex-Calculated and Measured Pavement


Table 5.7d: Comparison of LEADFlex-Calculated and Measured Pavement


Table 5.7e: Comparison of LEADFlex-Calculated and Measured Pavement


Table 5.7f: Comparison of LEADFlex-Calculated and Measured Pavement


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LIST OF FIGURES

Page

Figure 2.1: Thickness Requirement for Asphalt Pavement Structure 21

Figure 2.2: NCSA Design Chart 23

Figure 2.3: The Nigerian CBR Design chart 24

Figure 2.4: Three-Layer Pavement System Showing Location of Stresses 31

Figure 2.5: Critical Analysis Locations in a Pavement Structure 47

Figure 2.6: Typical Fatigue Curves (Freeme et al, 1982) 51

Figure 2.7: Rutting Criteria by Various Agencies 54

Figure 3.1: Typical Single Wheel and Dual-wheel 70

Figure 3.2: Typical LEADFlex Pavement Section Showing Location of Strains 72

Figure 3.3: Flow Diagram for LEADFlex Procedure 78

Figure 5.1a: Expected Traffic – Pavement Thickness Relationship for

Light Traffic 109

Figure 5.1b: Expected Traffic – Pavement Thickness Relationship for

Medium Traffic 110

Figure 5.1c: Expected Traffic – Pavement Thickness Relationship for

Heavy Traffic 111

Figure 5.2a: Pavement Thickness – Horizontal Tensile Strain Relationship for

Light Traffic 112

Figure 5.2b: Pavement Thickness – Horizontal Tensile Strain Relationship for

Medium Traffic 113

Figure 5.2c: Pavement Thickness – Horizontal Tensile Strain Relationship for

Heavy Traffic 114

Figure 5.3a: Pavement Thickness – Vertical Compressive Strain Relationship for

Light Traffic 115

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Figure 5.3b: Pavement Thickness – Vertical Compressive Strain Relationship for

Medium Traffic 117

Figure 5.3c: Pavement Thickness – Vertical Compressive Strain Relationship for

Heavy Traffic 118

Figure 5.4a: Effect of subgrade CBR on Pavement Thickness for

Light Traffic 119

Figure 5.4b: Effect of subgrade CBR on Pavement Thickness for

Medium Traffic 120

Figure 5.4c: Effect of subgrade CBR on Pavement Thickness for

Heavy Traffic 120

Figure 5.5a: Calibration of Calculated and Measured Tensile Strain for 31MPa Subgrade Modulus 135

Figure 5.5b: Calibration of Calculated and Measured Compressive Strain for 42MPa

Subgrade Modulus 135

Figure 5.6a: Calibration of Calculated and Measured Tensile Strain for 41MPa














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Figure 5.11a: LEADFlex Program Start-up Window 141

Figure 5.11b: LEADFlex Traffic Data Window – Step 1 of 3 142

Figure 5.11c: Pavement Design Parameters Window – Step 2 of 3 142

Figure 5.11d: Pavement Response Window – Step 3 of 3 143

Figure 5.11e: Pavement Response Window – Rutting Criteria not meet

– Step 3 of 3 144

Figure 5.11f: Pavement Response Window – Rutting Criteria not meet

– Step 3 of 3 144

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TABLE OF CONTENT

Page

TITLE PAGE i

DECLARATION ii

CERTIFICATION iii

APPROVAL PAGE iv

DEDICATION v

ACKNOWLEDGMENT vi

ABSTRACT vii

LIST OF TABLES viii

LIST OF FIGURES xi

CHAPTER 1: INTRODUCTION 1

1.1 Background of Study 1

1.2 Definition of Problem 3

1.3 Research Justification 4

1.4 Objectives 5

1.5 Scope and Limitation 6

1.6 Methodology of Study 6

1.7 Purpose and Organization of Thesis 7

CHAPTER 2: LITERATURE REVIEW 9

2.1 Pavement Design History 9

2.2 Flexible Highway Pavements 10

2.3 Pavement Design and Management 11

2.4 Flexible Pavement Design Principles 14

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2.5 Pavement Design Procedures 15

2.5.1 Empirical Design Approach 16

2.5.2 CBR Design Methods 19

2.5.2.1 The Asphalt Institute CBR Method 20

2.5.2.2 The National Crushed Stone Association CBR Method 20

2.5.2.3 The Nigerian CBR Method 23

2.5.2.4 The AASHTO Pavement Design Guides 25

2.5.3 Mechanistic Design Approach 25

2.5.4. Mechanistic –Empirical Design Approach 26

2.5.5 Layered Elastic System 27

2.5.6 Finite Element Model 31

2.5.7 Mechanistic-Empirical Design Inputs 31

2.5.8 Traffic Loading 34

2.5.9 Material Properties 36

2.5.9.1 Elastic Modulus of Bituminous Materials 37

2.5.9.2 Prediction Model for Dynamic and Resilient Modulus of Asphalt Concrete 39

2.5.9.3 Elastic Modulus of Soils and Unbound Granular

Materials 41 2.5.9.4 Non-linearity of Pavement Foundation 43

2.5.9.5 Poisson’s Ratio 44

2.5.9.6 Climatic Conditions 44

2.6 Pavement Response Models 46

2.6.1 Layered Elastic Model 46

2.6.2 Finite Elements Model 48

2.7 Flexible Pavement M-E Distress Models (Failure Criteria) 48

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2.7.1 Fatigue Failure Criterion 49

2.7.2 Rutting Failure Criterion 52

2.8 Layered Elastic Analysis Programs 54

2.9 Validation with Experimental Data 57

CHAPTER 3: METHODOLOGY 59

3.1 Layered Elastic Analysis and Design Procedure for Cement Stabilized Low-Volume Asphalt Pavement 59

3.2 Empirical 59

3.2.1 Pavement Material Characterization 59

3.2.1.1 Asphalt Concrete Elastic Modulus 59

3.2.1.2 Mix Proportion of Aggregates 60

3.2.1.3 Specimen Preparation 60

3.2.1.4 Determination of Bulk Specific Gravity (Gmb) of Samples 61

3.2.1.5 Determination of Void of compacted mixture 62

3.2.1.6 Density of Specimens 62

3.2.1.7 Stability and Flow of Samples 62

3.2.1.8 Determination of Asphalt Concrete Elastic Modulus 63

3.2.2 Base Material 64

3.2.2.1 Soil Classification Test 64

3.2.2.2 Sieve Analysis 64

3.2.2.3 Compaction Test 65

3.2.2.4 Soil Classification 65

3.2.2.5. California Bearing Ratio (CBR) Test Specimen 66

3.2.3 Subgrade Material 66

3.2.4 Poison’s Ratio 68

3.2.5 Traffic and Wheel load Evaluation 68

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3.2.6 Loading Conditions 69

3.2.7 LEADFlex Pavement Model 71

3.2.8 Environmental Condition 72

3.2.9 Pavement Layer Thickness 73

3.2.10 Traffic Repetition Evaluation 73

3.2.10 Determination of Design ESAL 74

3.3 Analytical 76

3.4 Summary of the LEADFlex Procedure 76

CHAPTER 4: DEVELOPMENT OF LEADFLEX DESIGN PROCEDURE AND PROGRAM 79

4.1 Determination of Minimum Pavement Thickness 79

4.2 Layered Elastic Analysis of LEADFlex Pavement 79

4.3 Allowable Strains for LEADFlex Pavement 80

4.4 Traffic Repetitions to Failure 81

4.5 Damage Factor 81

4.6 Development of LEADFlex Regression Equations 81

4.7 Summary of LEADFlex Design Procedure 82

4.8 Developlemt of LEADFlex Program 101

4.8.1 Program Algorithm 101

4.8.2 LEADFlex Visual Basic Codes 101

CHAPTER 5: RESULTS AND DISCUSSION 102

5.1 Results 102

5.1.1 Light Traffic 102

5.1.2 Medium Traffic 103

5.1.3 Heavy Traffic 104

5.1.4 LEADFlex Pavement Characteristics 105

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5.2 Discussion of Result 109

5.2.1 Expected Traffic and Pavement Thickness Relationship 109

5.2.2 Pavement Thickness and Tensile Strain Relationship 112

5.2.3 Pavement Thickness and Compressive Strain Relationship 115

5.2.4 Effect of Subgrade CBR on Pavement Thickness 118

5.3 Validation of LEADFLEX Result 121

5.3.1 Coefficient of Determination 121

5.3.2 Comparison of LEADFlex with EVERSTRESS Results 122 5.3.3 Comparison with K-ATL measured field data 123

5.4: The LEADFlex Program 141

5.4.1: LEADFlex Program Application and Design Example 141

5.4.2: Adjustment of LEADFlex Pavement Thickness 143

CHAPTER 6: CONCLUSION AND RECOMMENDATION 145

6.1 Conclusion 145

6.2 Recommendation 145

REFERENCE 148

APPENDIX 157

APPENDIX A: LEADFlex Pavement Material Characterization 158

APPENDIX B: Determination of Minimum Pavement Thickness 171

APPENDIX C: Light Traffic SPSS Regression Analysis of LEADFlex Pavement 220

APPENDIX D: Medium Traffic SPSS Regression Analysis of LEADFlex

Pavement 251

APPENDIX E: Heavy Traffic SPSS Regression Analysis of LEADFlex

Pavement 282

APPENDIX E: Visual basic Codes 315

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CHAPTER 1

INTRODUCTION

1.1 Background of Study

Since the early 1800’s when the first paved highways were built, construction of roads

has been on the increase as well as improved method of construction. The need for

stronger, long-lasting and all-weather pavements has become a priority as result of rapid

growth in the automobile traffic and the development of modern civilization. Since the

beginning of road building, modeling of highway and airport pavements has been a

difficult task. These difficulties are due to the complexity of the pavement system with

many variables such as thickness, material technology, environment and traffic. Most

attention has been given to material technology and construction techniques and less

was given to material properties and their behaviour. Terzaghi was the first to introduce

the concept of subgrade modulus and plate load test to pavement studies. Given the

load (traffic) and the measurement of deflection under this load, the carrying capacity of

a pavement could be determined. Several other soil tests were developed, such as the

California Bearing Ratio (CBR), the triaxial test and the unconfined compression test.

Several theoretical developments followed in the different parts of the world, In Europe,

for flexible pavements, Shell adopted Burmister’s theoretical work to model and analyze

the pavement as an elastic layered system involving stress and strain (Claussen et al,

1977). In North America (USA), a comprehensive set of full-scale road tests were

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launched. The American Association of State Highway Official [AASHTO, 1993)

introduced its first guide in 1972 which was revised in 1986 and 1993. From these two

agencies, a conclusion can be drawn that the trend in pavement engineering was either

empirical or a mechanistic method. An empirical approach is one which is based on the

results of experiments or experience. This means that the relationship between design

inputs (loads, material, layer configuration and environment) and pavement failure

were arrived at through experience, experimentation or a combination of both. The

mechanistic approach involves selection of proper materials and layer thickness for

specific traffic and environmental conditions such that certain identified pavement

failure modes are minimized. In mechanistic design, material parameters for the analysis

are determined at conditions as close as possible to what they are in the road structure.

The mechanistic approach is based on the elastic or visco-elastic representation of the

pavement structure. In mechanistic design, adequate control of pavement layer

thickness as well as material quality are ensured based on theoretical stress, strain or

deflection analysis. The analysis also enables the pavement designer to predict with

some amount of certainty the life of the pavement.

It is generally accepted that highway pavements are best modeled as a layered system,

consisting of layers of various materials (concrete, asphalt, granular base, subbase etc.)

resting on the natural subgrade. The behaviour of such a system can be analyzed using

the classical theory of elasticity (Burmister, 1945). This theory was developed for

continuous media, but pavement engineers recognized very clearly that the material

used in the construction of pavements do not form a continuum, but rather a series of

particular layered materials.

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Modeling the uncracked pavement as a layered system, the following assumptions are

usually made:

1. Each layer is linearly elastic, isotropic and homogenous, hence are not

stressed beyond their elastic ranges.

2. Each layer (except the subgrade) is finite in thickness and infinite in the

horizontal direction.

3. The subgrade extends infinitely downwards

4. The loads are applied on top of the upper layer

5. There are no shear forces acting directly on the loaded surface

6. There is perfect contact between the layers at their interfaces.

Because of assumption (1), the constitutive relationship for such material involves

variables such as the modulus of elasticity (E) and the Poisson’s ratio (ν), Elastic

constants or bulk modulus (K) and shear modulus (G). While some authors;

(Domaschuck and Wade, 1969); (Naylor,1978); (Pappin and Brown,1980); (Bowles,1988)

feel that K and G are preferable to E and ν to characterize earth materials, it is

customary to use E and ν in all geotechnical and pavement engineering computations.

Because of the transient or repetitive nature of loading in pavement engineering, the

elastic modulus can be replaced by the resilient modulus (Mr). The resilient modulus is

defined as the recoverable strain divided by stress.

1.2 Definition of Problem

Road failures in most developing tropical countries have been traced to common causes

which can broadly be attributed to any or combination of geological, geotechnical,

design, construction, and maintenance problems (Ajayi, 1987). Several studies have been

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carried out to trace the cause of early road failures, studies were carried out by

researchers on the geological (Ajayi, 1987), geotechnical, (Oyediran, 2001), Construction

(Eze-Uzomaka, 1981) and maintenance (Busari, 1990) factors. However, the design factor

has not been given adequate attention. In Nigeria, the only design method for asphalt

pavement is the California Bearing Ratio (CBR) method. This method uses the California

Bearing Ratio and traffic volume as the sole design inputs. The method was originally

developed by the California Highway Department and modified by the U.S Corps of

Engineers (Corps of Engineers, 1958). It was adopted by Nigeria as contained in the

Federal Highway Manual (Highway Manual-Part 1, 1973). Most of the roads designed

using the CBR method failed soon after construction by either fatigue cracking or rutting

deformation or both. In their researches (Emesiobi, 2004, Ekwulo et al , 2009), a

comparative analysis of flexible pavements designed using three different CBR

procedures were carried out, result indicated that the pavements designed by the CBR-

based methods are prone to both fatigue cracking and rutting deformation. The CBR

method was abandoned in California 50 years ago (Brown, 1997) for the more reliable

mechanistic-empirical methods (Layered Elastic Analysis or Finite Element Methods). It

is regrettable that this old method is still being used by most designers in Nigeria and

has resulted in unsatisfactory designs, leading to frequent early pavement failures. In

Pavement Engineering, it is generally known that the major causes of failure of asphalt

pavement is fatigue cracking and rutting deformation, caused by excessive horizontal

tensile strain at the bottom of the asphalt layer and vertical compressive strain on top of

the subgrade due to repeated traffic loading (Yang, 1973; Saal and Pell, 1960; Dormon

and Metcaff, 1965; NCHRP, 2007)). In the design of asphalt pavement, it is necessary to

investigate these critical strains and design against them. There is currently no pavement

design method in Nigeria that is based on analytical approach in which properties and

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thickness of the pavement layers are selected such that strains developed due to traffic

loading do not exceed the capability of any of the materials in the pavement. The

purpose of this study therefore is to develop a layered elastic design procedure to

predict critical horizontal tensile strain at the bottom of the asphalt bound layer and

vertical compressive strain on top of the subgrade in cement-stabilized low volume

asphalt pavement in order to predict failure modes such as fatigue and rutting and

design against them.

1.3 Research Justification

A long lasting pavement can be designed using the developments in mechanistic-based

method (Monismith, 2004), hence, the transition of structural design of asphalt

pavements from the pure empirical methods towards a more mechanistic-based

approach is a positive development in pavement engineering (Brown, 1997; Ullidtz,

2002). The mechanistic-based design approach (Layered Elastic Analysis and Finite

Element) is based on the theories of mechanics and relates pavement structural

behaviour and performance to traffic loading and environmental influences. The CBR

design method developed by the California Highway Department has since been

abandoned for a more reliable mechanistic approach. Therefore the need to develop a

layered elastic analysis has become necessary in order to evaluate the response of

asphalt pavement due to traffic loading. Since the failure of asphalt pavement is

attributable to fatigue cracking and rutting deformation, caused by excessive horizontal

tensile strain at the bottom of the asphalt layer and vertical compressive strain on top of

the subgrade, in the design of asphalt pavement, it is necessary to investigate these

critical strains and design against them. The layered elastic analysis approach involves

selection of proper materials and layer thickness for specific traffic and environmental

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conditions such that certain identified pavement failure modes such as fatigue cracking

and rutting deformations are minimized. The use of the layered elastic analysis concept

is necessary in that it is based on elastic theory(Yang, 1973), and can be used to evaluate

excessive horizontal tensile strain at the bottom of the asphalt layer(fatigue cracking)

and vertical compressive strain on top of the subgrade (Rutting deformation) in asphalt

pavements. The major disadvantage of the CBR procedure is its inability to evaluate

fatigue and rutting strains in asphalt pavement and its use in Nigeria should be

discontinued. In the final analysis, the research will go along way in proffering solution

to one of the factors responsible for frequent early pavement failures which have been

attributed to unsatisfactory designs. The research will also be a noble contribution to the

review of the Nigerian Highway Manual proposed by the Nigeria Road Sector

Development Team in 2005.

1.4 Objectives

The summary of the main objectives of the research shall be as follows:

1. Develop a layered elastic analysis procedure for design of cement-stabilized low

volume asphalt pavement in Nigeria.

2. Develop design equations and charts for the prediction of pavement thickness,

critical tensile and compressive strains in cement-stabilized low volume asphalt

pavements using layered elastic analysis procedure.

3. Collect pavement response standard data from Literature.

4. Calibrate and verify developed equations using the collected data.

5. Develop a design tool (program) LEADFlex for design of cement-stabilized lateritic

base low-volume asphalt pavement.

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1.5 Scope and Limitations

Scope:

The study is to address one of the factors responsible for frequent early pavement

failures associated with Nigerian roads; the design factor, however, particular emphasis

will be on the adoption of the layered elastic analysis procedure to predict critical fatigue

and rutting strains in cement-stabilized low volume asphalt pavement. A design tool

(software) shall be developed for the procedure. The very popular layered elastic

analysis software, EVERSRESS (Sivaneswaran et al, 2001) developed by the Washington

State Department of Transportation (WSDOT) will be employed for pavement analysis.

Limitations:

i. Assumption of elasticity of pavement materials

ii. Assumptions of Poisson’s ratio of pavement materials

1.6 Methodology of Study

The method adopted in this study is to use the layered elastic analysis and design

approach to develop a procedure that will predict fatigue and rutting strains in cement-

stabilized low volume asphalt pavement. To achieve this, the study will be carried out in

the following order:

1. Characterize pavement materials in terms of elastic modulus, CBR/resilient

modulus and poison’s ratio.

2. Obtain traffic data needed for the entire design period.

3. Compute fatigue and rutting strains using layered elastic analysis procedure

based the Asphalt Institute response models.

86

4. Evaluate and predict pavement responses (tensile strain, compressive strain and

allowable repetitions to failure).

5. If the trial design does not meet the performance criteria, modify the design and

repeat the steps 3 through 5 above until the design meet the criteria.

The procedure shall be implemented in software (LEADFlex) in which all the above steps

are performed automatically, except the material selection. Traffic estimation is in the

form of Equivalent Single Axle Load (ESAL). The elastic properties (elastic modulus of

surface and base, resilient modulus of subgrade and Poisson’s ratio) of the pavement

material are used as inputs for design and analysis. The resilient modulus is obtained

through correlation with CBR. The layered elastic analysis software EVERSRESS

(Sivaneswaran et al, 2001) was employed in the analysis.

1.7 Purpose and Organization of Thesis

The purpose of the study is to use the layered elastic analysis approach to develop

procedure that will predict fatigue and rutting strains in cement-stabilized low volume

asphalt pavement. The study is presented in six chapters. Chapter One introduces the

research topic on the application of analytical approach in design in flexible pavement

and the need to develop an analytical approach for the Nigerian (CBR) method for

flexible pavement design. Chapter Two presents Literature Review on highway

pavements and design of flexible pavements. The use of empirical and mechanistic

(analytical) design procedure is presented in detail. Chapter Three outlines and

describes in details the procedure adopted in the research including material

characterization, design inputs and summary of the development of the design

procedure. Chapter Four presents details of the development of the layered elastic

87

analysis procedure for prediction of fatigue and rutting strains in cement-stabilized low

volume asphalt pavement. The developed equations, program algorithm, visual basic

codes and program interface and design are presented in details in this chapter. Chapter

Five will present the results and discussion of the results of the study. Effect of

pavement parameters on pavement response shall be discussed in this section. Finally,

Chapter Six will present the Conclusions and recommendations of the study.

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CHAPTER 2

LITERATURE REVIEW

2.1 Pavement Design History

Pavement design is a complex field requiring knowledge of both soil and paving

materials, and especially, their responses under various loadings and environmental

conditions. Pavement design methods can vary, and have evolved over the years in

response to changes in traffic and loading conditions, construction materials and

procedures. Design methods have progressed from rule-of-thumb methods, to empirical

methods and at present, towards a mechanistic approach.

In the United States, the majority of pavement designers use the AASHTO (American

Association of State Highway and Transportation Official ) Guide for design of

Pavement Structures (AASHTO, 1993). The AASHTO Guide was developed from

empirical performance equations based on observations from the AASHTO Road Test

conducted in Illinois from October, 1958 to November, 1960. Many significant changes in

loading conditions, construction materials and methods, and design needs have

occurred since the time of AASHTO Road Test, prompting development of new

mechanistic-empirical design procedures. This procedure allows the designer to

consider current site conditions such as realistic loading, climatic factors such as

temperature and moisture, material properties and existing pavement condition in the

design of a new pavement, rehabilitation of an existing pavement, or evaluation of an

existing pavement. This approach is described in more details in the Guide for

mechanistic-empirical Design of New and Rehabilitated Pavement Structures (NCHRP,

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2004). Additionally, mechanistic-empirical design procedure was developed such that

improvement could be made as technology advances.

Empirical methods of analysis are derived from experimental data and practical

experience. The mechanistic-empirical (M-E) design approach considers the three

necessary elements of rational design (Yoder and Witczak, 1975). The element of rational

design include (1) an assumed failure or distress parameter predictive theory (2)

evaluation of material properties in relationship to the theory selected and (3)

relationship determination between the performance level desired and the appropriate

parameter magnitude. The mechanistic-empirical design approach applies engineering

mechanics principles to consider these rational design elements.

The initial phase of the mechanistic design approach consist of proper structural

modeling of pavement structures (NCHRP, 2004). Pavement is modeled as multi-layered

elastic or viscoelastic on elastic or viscoelastic foundation. These models are used in

analysis to predict critical pavement responses (deflections, stresses and strains) due to

traffic loading and environmental conditions for selected trial or initial design. The

accuracy of the chosen model is validated by data from controlled-vehicle tests or other

types of tests where actual loading and environmental conditions are simulated. Where

predicted values agree with measured values, the level of confidence in the model

increases with increase data available for validation. Once an accurate structural

response model is developed, the responses are input into distress models to determine

pavement damage throughout the specific design period. Failure criteria are then

evaluated, and an iterative process continues until a final design is reached.

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2.2 Flexible Highway Pavements

The beginning of flexible pavement construction history to early 1900’s in United States

when experience dominated pavement design and construction. Through the experience

gained over the years, many design methods were developed for determining critical

features like thickness of the asphalt surface. As of 1990, there were millions of miles of

paved roads in the US, 94% of which are topped by asphalt (Huang, 1993). A typical

flexible pavement cross section consists of an asphalt concrete surface, base and subbase

resting on the natural subgrade.

Since the beginning of road building, three types of flexible pavement construction have

been used: conventional flexible pavement, full-depth asphalt and contained rock

asphalt mat (CRAM). As knowledge increased and other technologies developed, a

composite pavement made up of hot mix asphalt concrete (HMA) and Portland cement

concrete (PCC) beneath the HMA came into being with the most desirable

characteristics. However, the CRAM construction is still relatively rare and composite

pavement is very expensive, and hence seldom used in practice (Huang, 1993).

Various empirical methods have been developed for analyzing flexible pavement

structures. However, due to limitations of the analytical tools developed in the 1960s

and 1970s, the design of flexible pavements is still largely empirically-based. The

empirical method limits itself to a certain set of environmental and material conditions

(Huang, 1993), if the condition changes, the design is no longer valid. The mechanistic-

empirical method relates some inputs such as wheel loads to some outputs, such as

stress or strain. The mechanistic method is more reliable for the extrapolation from

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measured data than empirical methods. However, the effectiveness of any mechanistic

design method relies on the accuracy of the predicted stresses and strains. Due to their

flexibility and power, three-dimensional (3D) finite element methods are increasingly

being used to analyze flexible pavements.

2.3 Pavement Design and Management

Pavement engineering may be defined as the process of designing, construction,

maintenance, rehabilitation and management of pavement, in order to provide a desired

level of service for traffic. In the design stage of pavement design, engineers make a

number of assumptions about the construction methods and level of maintenance for the

pavement.

Flexible pavements are classified as a pavement structure having a relatively thin

asphalt wearing course, with layers of granular base and subbase being used to protect

the subgrade from being overstressed. This type of pavement design is based on

empiricism or experience, with theory playing only a subordinate role in the procedure.

However, the recent design and construction changes brought about primarily by

heavier wheel-loads, higher traffic levels, and recognition of various independent

distress modes contributing to pavement failure (such as rutting, shoving and cracking)

have led to the introduction and increased use of stabilized base and Subbase material.

The purpose of stabilizer material is to increase the structural strength of the pavement

by increasing rigidity. Roadway rehabilitation using asphalt without the need for

excavation of old, cracked and oxidized asphalt pavements with water-weakened, or

non-uniform support bases and subbases has often been attempted, usually with

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variable success. It was concluded (Johnson and Roger, 1992) that keeping water out of

the road base and sub-base is a major solution to prevent premature road failures.

The purpose of a pavement is to carry traffic safely, conveniently and economically over

its design life, by protecting the subgrade from the effects of traffic and climate and

ensuring that materials used in the pavement do not suffer from deterioration. The

pavement surface must provide adequate skid resistance. The structural part of the

pavement involves material sections that are suitable for the above purpose. The design

process consists of two parts: the determination of the pavement thickness layer that

have certain mechanical properties, and the determination of the composition of the

material that will provide these properties. The main structural layer of the pavement is

the road base, whose purpose is to distribute traffic loads so that stresses and strains

developed by them in the subgrade and subbase are within the capacity of the materials

in these layers.

Asphalt pavements are designed and constructed to provide an initial service life of

between 15 to 20 years (Gervais et al, 1992), however, this design life is rarely met,

largely because of more traffic, heavier axle loads, material problems, higher tire

pressure and extreme environmental conditions. These factors usually result in two

major modes of distress: surface cracking and rutting which, if allowed to progress too

far, will require major rehabilitation or complete reconstruction. Research work over the

past several decades had led to many recommended solutions. New asphalt mixes, use

of larger crushes aggregates, textile sheets, thicker asphalt layer, polymer modification

93

and reinforcement of various types have been tried in the field to minimize pavement

cracking or rutting.

In asphalt pavement, the term “reinforcement” generally means the inclusion of certain

material with some desired properties within other materials which lack these

properties. Within the entire pavement structure, the asphalt concrete layer receives

most of the load and non-load induced tensile stresses. However, it is known that

asphalt concrete lacks the ability to resist such stresses which makes it an ideal medium

for which reinforcement can be considered. If reinforcement is to be considered, two

basic features need to be considered (Haas, 1984):

1. Intended function of the reinforcement

i. reducing rutting

ii. reducing cracking

iii. reducing layer thickness

iv. extending pavement life/reducing maintenance

2. Reinforcement alternative

i. Types and possible locations in the pavement structure

ii. Major variables (pavement layer and reinforcement properties, traffic

loads and volume etc.

2.4 Flexible Pavement Design Principles

Before the 1920s, pavement design consisted basically of defining the thickness of

layered materials that would provide strength and protection to a soft subgrade.

94

Pavements were designed against subgrade shear failure. Engineers used their

experience based on successes and failures of previous projects. As experience evolved,

several pavement design methods based on subgrade shear strength were developed.

Ever since, there has been a change in design criteria as a result of increase in traffic

volume. As important as providing subgrade support, it is equally important to evaluate

pavement performance through ride quality and other surface distress that increase the

rate of deterioration of pavement structure. For this reason performance became the

focus of pavement designs. Methods based on serviceability (an index of the pavement

service quality) were developed based on test track experiments. The AASHTO Road

Test in 1960s as a seminal experiment from which the AASHTO design guide was

developed. Methods developed laboratory test data or test track experiments in which

model curves are fitted to data are typical example of empirical methods. Although they

may exhibit good accuracy, empirical methods are valid for only the materials and

climate conditions for which they were developed.

Meanwhile, new materials started to be used in pavement structures that provide better

subgrade protection, but with their own failure modes. New designs criteria were

required to incorporate such failure mechanisms such as fatigue cracking and

permanent deformation in the case of asphalt concrete. The Asphalt Institute method

(Asphalt Institute, 1982, 1991) and the Shell method (Claessen et al, 1977; Shook et al,

1982) are examples of procedures based on asphalts concrete’s fatigue cracking and

permanent deformation failure modes. These methods were the first to use linear elastic

theory of mechanics to compute structural response in combination with empirical

models to predict number of loads to failure for flexible pavements. The problem in the

use of the elastic theory is that pavement material do not exhibit the simple behaviour

95

assumed in isotropic linear elastic theory. Nonlinearities, time and temperature

dependency, and anisotropy are some of the complicated features often observed in

pavement materials. Therefore to predict pavement performance mechanistically,

advanced modeling is required. The mechanistic design approach is based on the

theories of mechanics and relates pavement structural behaviour and performance to

traffic loading and environmental influences. Progress has been made on isolated cases

of mechanistic performance prediction problem, but the reality is that fully mechanistic

methods are not yet available for practical pavement design (Schwartz and Carvalho,

2007).

Mechanistic-empirical approach is a hybrid approach. Empirical methods are used to fill

in the gaps that exist between the theory of mechanics and the performance of pavement

structures. Simple mechanistic responses are easy to compute with assumptions and

simplifications (that is homogenous material, small strain analysis, static loading as

typically assumed in linear elastic theory), but they themselves cannot be used to predict

performance directly: some type of empirical model is required to carryout the

appropriate correlation. Mechanistic-empirical methods are considered an intermediate

step between empirical and fully mechanistic methods.

2.5 Pavement Design Procedures

Studies in pavement engineering have shown that the design procedure for highway

pavement is either empirical or mechanistic. An empirical approach is one which is

based on the results of experiments or experience or both. This means that the

relationship between design inputs and pavement failure were arrived at through

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experience, experimentation or a combination of both. The mechanistic approach

involves selection of proper materials and layer thickness for specific traffic and

environmental conditions such that certain identified pavement failure modes are

minimized. The mechanistic approach involves the determination of material

parameters for the analysis, at conditions as close as possible to what they are in the road

structure. The mechanistic approach is based on the elastic or visco-elastic

representation of the pavement structure. In mechanistic design, adequate control of

pavement layer thickness as well as material quality are ensured based on theoretical

stress, strain or deflection analysis. The analysis also enables the pavement designer to

predict with some amount of certainty the life of the pavement (Schwartz and Carvalho,

2007).

2.5.1 Empirical Design Approach

An empirical design approach is one that is based solely on the result of experiment or

experience. Observations are used to establish correlations between the inputs and the

outcomes of a process, for example pavement design and performance. These

relationships generally do not have firm scientific basis, although they must meet the

tests of engineering reasonability. Empirical approaches are often used as an expedient

when it is too difficult to define theoretically the precise cause and effect relationships of

a phenomenon.

The principal advantages of empirical design approaches are that they are usually

simple to apply and are based on actual real-world data. Their principal disadvantage

is that the validity of the empirical relationships is limited to the conditions in the

underlying data from which they were inferred. New materials, construction

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procedures, and changed traffic characteristics cannot be readily incorporated into

empirical design procedures.

The first empirical method for flexible pavement design date to the mid 1920s when the

first soil classification were developed. One of the first to be published was the Public

Roads (PR) soil classification system (Huang, 2004). In 1929, the California Highway

Department developed a method using the California Bearing Ratio (CBR) strength test

(Porter, 1950; Huang, 2004). The CBR method relates the material’s CBR value to the

required thickness to provide protection against subgrade shear failure. The thickness

computed was defined for the standard crushed stone used in the definition of the CBR

test. The CBR test was improved by the US Corps of Engineers (USCE) during the World

War II and later became the most popular design method. In 1945 the Highway Research

Board(HRB) modified the PR classification. Soils were grouped in seven categories (A-1

to A-7) with indexes to differentiate soils within each group. The classification was

applied to estimate subbase quality and total pavement thickness (Huang, 2004).

Several methods based on subgrade shear failure developed after CBR method. Huang

(2004) used Terzaghi’s bearing capacity formula to compute pavement thickness, while

Huang (2004) applied logarithmic spirals to determine bearing capacity of pavements.

However, with increasing traffic volume and vehicle speed, new materials were

introduced in the pavement structure to improve performance and smoothness and

shear failure was no longer the governing design criterion.

The first attempt to consider a structural response as a qualitative measure of the

pavement structural capacity was measuring surface vertical deflection. A few methods

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were developed based on the theory of elasticity for soil mass. This method estimated

layer thickness based on a limit for surface deflection. The first published work on this

method was the one developed by the Kansa State Highway Commission, in 1947

(NCHRP, 2007), in which Boussinesg’s equation was used and the deflection of subgrade

was limited to 2.54mm. Later in 1953, the U.S. Navy applied Burmister’s two-layer

elastic theory and limited the surface deflection to 6.35mm. Other methods were

developed over the years, incorporating strength tests. More recently, resilient modulus

has been used (Huang, 2004) to establish relationships between the strength and

deflection limits for determining thickness of new pavement structures and overlays.

The deflection methods were most appealing to practitioners because deflection is easy

to measure in the field. However, failures in pavements are caused by excessive stress

and strain rather than deflection (NCHRP, 2007). In the early 1950s, experimental tracks

started to be used for gathering pavement performance data. Regression models were

developed linking the performance data to design inputs. The biggest disadvantage of

regression methods is the limitation on their application. As is the case for any empirical

method, regression methods can be applied only to the conditions similar to those for

which they were developed. The empirical AASHTO method (AASHTO, 1993), based on

the AASHTO Road Test from the late 1950s, is the most widely used pavement design

method today. The AASHTO design equation is a regression relationship between the

number of load cycles, pavement structural capacity, and performance measured in

terms of serviceability. The concept of serviceability was introduced in the AASHTO

method as an indirect measure of the pavement’s ride quality. The serviceability index is

based on surface distress commonly found in pavements.

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The AASHTO (1993) method has been adjusted several times over the years to

incorporate extensive modifications based on theory and experience that allowed the

design equations to be used under conditions other than those of the AASHTO Road

Test.

2.5.2 CBR Design Methods

The almost universal parameter used to characterize soils for pavement design purpose

is the California Bearing Ratio (CBR). This empirical index test was abandoned in

California over 50 years ago but, following its adoption by the US. Corps of Engineers in

World War II, it was gradually accepted World-wide as the appropriate test (Brown,

1997). Given that the test is at best, an indirect measurement of undrained shear strength

and the pavement design requires knowledge of soil resilience and its tendency to

develop plastic strains under repeated loading, the tenacity exhibited by generation of

highway engineers in regard to the CBR is somewhat surprising. Jim Porter, a Soil

Engineer for the State of California, introduced the “Soil Bearing Test” in 1929

commented nine years later, that the bearing values are not direct measure of the

supporting value of materials (Porter, 1938). In recognition that the CBR design curves

give a total thickness of pavement to prevent shear deformation in the soil, Turnbull

(1950) noted that the CBR is an index of shearing strength. The shear strength of soil is

not of direct interest to the road engineer, the soil should operate at stress levels within

100

the elastic range (Brown, 1997). The pavement engineer is therefore more concerned

with the elastic modulus of soil and the behaviour under repeated loading.

The CBR method of pavement design is an empirical design method and was first used

by the California Division of Highways as a result of extensive investigations made on

pavement failures during the years 1928 and 1929 (Corps of Engineers, 1958). To predict

the behaviour of pavement materials, the CBR was developed in 1929. Tests were

performed on typical crushed stone representative of base course materials and the

average of these tests designated as a CBR of 100 percent. Samples of soil from different

road conditions were tested and two design curves were produced corresponding to

average and light traffic conditions. From these curves the required thickness of

Subbase, base and surfacing were determined. The investigation showed that soils or

pavement material having the same CBR required the same thickness of overlying

materials in order to prevent traffic deformation. So, once the CBR for the subgrade and

those of other layers are known, the thickness of overlying materials to provide a

satisfactory pavement can be determined. The US corps of Engineers adopted the CBR

method for airfield at the beginning of the Second World War, since then, several

modifications of the original design curves have been made (Oguara, 2005). Some of the

common CBR design methods include the Asphalt Institute (Asphalt Institute, 1981)

method, the National Crushed Stone Association (NCSA) design method (NCSA, 1972),

the Nigerian (CBR) design procedure (Highway Manuel, 1973) etc.

2.5.2.1 The Asphalt Institute CBR Method

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Although the Asphalt institute has developed a new thickness design procedure based

on the mechanistic approach (Asphalt Institute, 1981), the original asphalt institute

thickness design procedure is based on the concept of full depth asphalt, that is using

asphalt mixtures for all courses above the subgrade or improved subgrade. Traffic

analysis is in terms of 80kN equivalent single axle load in the form of a Design Traffic

Number, DTN. The DTN is the average daily number of equivalent 80kN single-axle

estimated for the design period. The CBR, Resistance value or Bearing value from plate

loading test is used in subgrade strength evaluation. Figure 2.1 shows the Thickness

chart for Asphalt pavement structure. The recommended minimum total asphalt

pavement thickness (TA) is presented in Table 2.1

2.5.2.2 The National Crushed Stone Association CBR Method

The National Crushed Stone Association (NCSA) empirical design method (NCSA, 1972)

is based on the US Corps of Engineers pavement design. Traffic analysis is based on the

average number of 80kN single-axle loads per lane per day over a pavement life

expectancy of 20 years. The method incorporates a factor of traffic in the design called

Design Index (DI). Six design index categories are defined as presented in Table 2.2. In

the absence of traffic survey data, general grouping of vehicles can be obtained from

spot checks of traffic and placed in one of the three groups as follows:

Group 1: Passenger cars, panel and pickup trucks

Group 2: Two-axle trucks loaded or larger vehicles empty or carrying light

Loads.

Group 3: All vehicles with more than three loaded axles

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Subgrade strength evaluation is made in terms of CBR and compaction requirement is

provided to minimize permanent deformation due to densification under traffic.

Presented in Figure 2.2 is the NCSA design chart.

Figure 2.1: Thickness Requirement for Asphalt Pavement Structure (Source: Oguara, 2005)

103

Table 2.1.: Minimum Asphalt Pavement Thickness(TA) (Source: Oguara, 2005)

Traffic DTN Minimum TA(mm)

Light Less than10 100

Medium 10 - 100 125

Heavy 100 – 1000

More than

1000

150

175

Table 2.2: NCSA Design Index categories (Source: Oguara, 2005)

Design

Index

General Character Daily ESAL

DI-1 Light traffic (few vehicles heavier than

passenger cars, no regular use by

Group 2 or 3 vehicles)

5 or less

DI-2 Medium-light traffic (similar to DI-1,

maximum 1000 VPD including not

over 5% Group 2, no regular use by

Group 3 vehicles

6-20

DI-3 Medium traffic (maximum 3000VPD,

including not over 10% Group 2 and 3,

1% Group 3 vehicles)

21-75

104

DI-4 Medium – heavy traffic (maximum

6000VPD, including not over 15%

Group 2 and 3, 1% Group 3 vehicles)

76-250

DI-5 Heavy traffic (maximum 6000VPD,

may include 25% Group 2 and 3, 10%

Group 3 vehicles)

251-900

DI-6 Very heavy traffic (over 6000VPD,

may include over 25% Group 2 or 3

vehicles)

901-3000

Figure 2.2: NCSA Design Chart (Source: Oguara, 2005)

105

2.5.2.3 The Nigerian CBR Method

The Nigerian (CBR) design procedure is an empirical procedure which uses the

California Bearing Ratio and traffic volume as the sole design inputs. The method uses a

set of design curves for determining structural thickness requirement. The curves were

first developed by the US Corps of Engineers and modified by the British Transportation

and Road Research Laboratory (TRRL, 1970), it was adopted by Nigeria as contained in

the Federal Highway Manual (Highway Manuel, 1973). The Nigerian (CBR) design

method is a CBR-Traffic volume method, the thickness of the pavement structure is

dependent on the anticipated traffic, the strength of the foundation material, the quality

of pavement material used and the construction procedure. This method considers

traffic in the form of number of commercial vehicles/day exceeding 29.89kN (3 tons).

Subgrade strength evaluation is made in terms of CBR. The selection of pavement

structure is made from design curves shown in Figure 2.3.

106

The thickness of the pavement layers is dependent on the expected traffic loading.

Recommended minimum asphalt pavement surface thickness is considered in terms of

light, medium and heavy traffic as follows:

Light traffic - 50mm

Medium - 75mm

Heavy - 100mm

Figure 2.3: The Nigerian CBR Design chart (Source: Oguara, 2005)

107

2.5.2.4 The AASHTO Pavement Design Guides

The AASHTO Guide for Design of Pavement Structures is the primary document used

to design new and rehabilitated highway pavements. The Federal Highway

Administration's 1995-1997 National Pavement Design Review found that some 80

percent of states use the 1972, 1986, or 1993 AASHTO Guides (AASHTO, 1972; 1986;

1993), of the 35 states that responded to a 1999 survey by Newcomb and Birgisson

(1999), 65% reported using the 1993 AASHTO Guide for both flexible and rigid

pavement designs.

All versions of the AASHTO Design Guide are empirical methods based on field

performance data measured at the AASHO Road Test in 1958-60, with some theoretical

support for layer coefficients and drainage factors. The overall serviceability of a

pavement during the original AASHO Road Test was quantified by the Present

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Serviceability Rating (PSR; range = 0 to 5), as determined by a panel of highway raters.

This qualitative PSR was subsequently correlated with more objective measures of

pavement condition (e.g., cracking, patching, and rut depth statistics for flexible

pavements) and called the Pavement Serviceability Index (PSI). Pavement performance

was represented by the serviceability history of a given pavement - i.e., by the

deterioration of PSI over the life of the pavement. Roughness is the dominant factor in

PSI and is, therefore, the principal component of performance under this measure.

2.5.3 Mechanistic Design Approach

The mechanistic design approach represents the other end of the spectrum from the

empirical methods. The mechanistic design approach is based on the theories of

mechanics to relate pavement structural behavior and performance to traffic loading

and environmental influences. The mechanistic approach for rigid pavements has its

origins in Westergaard's (Westergaard, 1926) development during the 1920s of the slab

on subgrade and thermal curling theories to compute critical stresses and deflections in

a PCC slab. The mechanistic approach for flexible pavements has its roots in

Burmister's (Burmister, 1945) development during the 1940s of multilayer elastic theory

to compute stresses, strains, and deflections in pavement structures.

A key element of the mechanistic design approach is the accurate prediction of the

response of the pavement materials - and, thus, of the pavement itself. The elasticity-

based solutions by Boussinesq, Burmister, and Westergaard were an important first

step toward a theoretical description of the pavement response under load. However,

the linearly elastic material behavior assumption underlying these solutions means that

they will be unable to predict the nonlinear and inelastic cracking, permanent

109

deformation, and other distresses of interest in pavement systems. This requires far

more sophisticated material models and analytical tools. Much progress has been made

in recent years on isolated pieces of the mechanistic performance prediction problem.

The Strategic Highway Research Program during the early 1990s made an ambitious

but, ultimately, unsuccessful attempt at a fully mechanistic performance system for

flexible pavements. To be fair, the problem is extremely complex; nonetheless, the

reality is that a fully mechanistic design approach for pavement design does not yet

exist. Some empirical information and relationships are still required to relate theory to

the real world of pavement performance.

2.5.4. Mechanistic –Empirical Design Approach

The development of mechanistic-empirical design approaches dates back at least four

decades. As its name suggests, a mechanistic-empirical approach to pavement design

combines features from both the mechanistic and empirical approaches. The induced

state of stress and strain in a pavement structure due to traffic loading and

environmental conditions is predicted using theory of mechanics. Empirical models link

these structural responses to distress predictions. Huang (1993) notes that Kerkhoven

and Dormon (1953) were the first to use the vertical compressive strain on top of the

subgrade as a failure criterion to reduce permanent deformation. Saal and Pell (1960)

published the use of horizontal tensile strain at the bottom of the asphalt bound layer to

minimize fatigue cracking. The concept of horizontal tensile strain at the bottom of the

asphalt bound layer was first used by Dormon and Metcaff 1965) for pavement design.

The Shell method (Claussen et al, 1977) and the Asphalt Institute method (Shook et al,

1982; Asphalt Institute, 1992) incorporated strain-based criteria in their mechanistic-

empirical procedures. Several studies over the past fifteen years have advanced

mechanistic-empirical techniques. Most of the works, however, were based on variants

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of the same two strain-based criteria developed by Shell and the Asphalt Institute. The

Washington State Department of Transportation (WSDOT), North Carolina Department

of Transportation(NCDOT) and Minnesota Department of Transportation(MNDOT), to

name but a few, developed their own Mechanistic-Empirical procedures (Schwartz and

Carvalho, 2007). The National Cooperative Highway Research Program (NCHRP) 1-26

project report, Calibrated Mechanistic Structural Analysis Procedures for Pavements (1990),

provided the basic framework for most of the efforts made by state DOTs. WSDOT

(Pierce et al., 1993; WSDOT, 1995).

2.5.5 Layered Elastic System

The analysis of stresses, strains and deflections in pavement systems have been largely

derived from the Boussinesq equation originally developed for a homogeneous,

isotropic and elastic media due to a point load at the surface. According to Boussinesq,

the vertical stress σZ at any depth z below the earth’s surface due to a point load P at the

surface is given by (Oguara, 2005):

σZ = 2

.Z

Pk (2.0)

Where,

k = ( )[ ] 2

52

1

1

2

3

z

r+π (2.1)

and

r is the radial distance from the point of load application.

111

For stress on a vertical plate passing through the centre of a loaded plate:

σZ = ( )

+−

23

22

3

1zr

zP (2.2)

Where,

P is the unit load on a circular plate of radius r ( or of a tyre of known contact area and

pressure). Here the vertical stress is dependent on the depth z and radial distance r and

is independent of the properties of the transmitting medium.

Considering radial strains which is dependent on Poisson’s ratio µ, from equation (2.2)

and µ = 0.5, the Boussinesq equation for deflection, ∆ at the centre of a circular plate is

given as:

∆ = ( )

( ) 21

22

2

2

3

zrE

rP

+ (2.3)

This may be written as

∆ = FE

aP )( (2.4)

Where, F = ( )[ ] 2

12

1

1.

2

3

zr+

(2.5)

112

The term F reflects the depth-radius ratio. The value of F when taken at the contact

surface equals 1.5 and 1.18 for flexible and rigid plate respectively.

For flexible plate, the deflection at the centre of the loaded circular plate of radius “a” is

therefore given as:

∆ = E

Pa5.1 (2.6)

and for a rigid plate, the deflection is given as:

∆ = E

Pa18.1 (2.7)

From equations (2.6) and (2.7), the modulus of elasticity E of a soil or pavement can be

computed by measuring the deflection under a known load and contact area (Oguara,

2005). The fact that pavement deflection can be directly related to Hook’s law that says

stress σ is proportional to strain Є, or to the modulus of elasticity of the material, has

brought forth the use of elastic layered systems – a mechanistic approach in design of

pavements (Oguara, 1985)

The response of pavement systems to wheel loading has been of interest since 1926 when

Wetergaard used elastic layered theory to predict the response of rigid pavements

(Westergaard, 1926). It is generally accepted that pavements are best modeled as a

layered system, consisting of layers of various materials (concrete, asphalt, granular

113

base, subbase etc.) resting on the natural subgrade. The behaviour of such a system can

be analyzed using the classical theory of elasticity (Burmister, 1945). The Layered Elastic

Analysis (LEA) is a mechanistic-empirical procedure capable of determining pavement

responses (stress and strain) in asphalt pavement. The major assumptions in the use of

layered elastic analysis are that;

i. the pavement structure be regarded as a linear elastic multilayered system in

which the stress-strain solution of the material are characterized by the

Young’s modulus of Elasticity E and poison’s ratio µ.

ii. Each layer has a finite thickness h except the lower layer, and all are infinite in

the horizontal direction.

iii. The surface loading P can be represented vertically by a uniformly distributed

vertical stress over a circular area.

In three-layered pavement system, the locations of the various stresses are as shown in

Figure 2.4 (Yoder and Witczak, 1975). The horizontal tensile strain at the bottom of the

asphalt concrete layer and vertical compressive strain at the top of the subgrade are

given by equations 2.8 and 2.9 respectively;

Єr1 = 1

11

1

11

1

1

EEE

zrr σµ

σµ

σ−− (2.8)

Єz1 = ( )32

3

1rz

Eσσ − (2.9)

Where,

114

1zσ = vertical stress at interface 1 (bottom of asphalt concrete layer)

2zσ = vertical stress at interface 2

1rσ = horizontal stress at the bottom of layer 1

2rσ = horizontal stress at the bottom of layer 2

3rσ = horizontal stress at the top of layer 3

31 EandE are Modulus of elasticity of layer 1 and 3 receptively.

µ = Poisson’s ratio of the layer

P

µ1 = 0.5, h1, E1

µ2 = 0.5, h2, E2

µ1 = 0.5, h3, E2

a

σz1

σr1

σz2

σr2

σr3

Interface 1

Interface 2

Figure 2.4: Three-Layer Pavement System Showing Location of Stresses

115

2.5.6 Finite Element Model

The Finite Element Method (FEM) is a numerical analysis technique for obtaining

approximate solutions to engineering problems. In the finite element analysis of asphalt

pavements, the pavement and subgrade is descritized into a number of elements with

the wheel load at the top of the pavement. The FEM assumes some constraining values

at the boundaries of the region of interest (pavement and subgrade) and is used to

model the nonlinear response characteristic of pavement materials.

2.5.7 Mechanistic-Empirical Design Inputs

Inputs for M-E pavement design include traffic, material and subgrade characterization,

climate factors and performance criteria. Layered elastic models require a minimum

number of inputs to adequately characterize a pavement structure and its response to

loading. Some of the inputs include modulus of elasticity (E) and Poisson’s ratio (µ) of

material, pavement thickness(h) and the loading (P). In the Mechanistic-Empirical(M-E)

pavement design guide (AASHTO, 1993), three levels of material inputs are adopted as

shown in Table 2.3. Level 1 material input is obtained through direct laboratory testing

and measurements. This level of input uses the state of the art technique in

characterization of materials as well as characterization of traffic through collection of

data from weigh-in-motion (WIM) stations; Level 2 uses correlations to determine the

required material inputs, while Level 3 uses material inputs selected from typical

defaults values. Tables 2.4 and 2.5 shows typical input values for some pavement

materials. The outputs expected in layered elastic analysis are the pavement responses;

stresses, strains and deflections.

116

Table 2.3: Inputs levels in layered elastic Design

Material Input

Level 1

Input

Level 2

Input

Level 3

Asphalt Concrete Measured

Diametric Modulus

Estimated

Diametric Modulus

Default

Diametric Modulus

Portland Cement

Concrete

Measured

Elastic Modulus

Estimated

Elastic Modulus

Default

Elastic Modulus

Stabilized Materials Measured

Resilient Modulus

Estimated

Resilient Modulus

Default

Resilient Modulus

Granular Materials Measured

Resilient Modulus

Estimated

Resilient Modulus

Default

Resilient Modulus

Subgrades Measured

Resilient Modulus

Estimated

Resilient Modulus

Default

Resilient Modulus

Table 2.4: Default Resilient Modulus (Mr) Values for Pavement Materials

General Level of

Subgrade Support

AASHTO Soil Classification Broad Mr range and Mean

Mr at Optimum Moisture

Content

Very Good Coarse grained: Gravel and gravely soils;

A-1-a, A-1-b

172 to 310MPa

Mean = 269MPa

Good Coarse grained: Sand and Sandy soils

A-2-4, A-3

138 to 275MPa

Mean = 207MPa

117

Fair Fined grained: Mixed silt and clay

A-2-7, A-4, A-2-5, A-2-6

103 to 207MPa

Mean = 179MPa

Poor Fine grained: Low compressibility

A-5, A-6

69 to 172MPa

Mean = 124MPa

Very Poor Fine grained: High compressibility

A-7-5, A-7-6

34 to 103MPa

Mean = 69MPa

Crushed Stone 138 to 241MPa

Mean = 172MPa

NOTE: Subgrade properties for the above soil classes are as follows

Very Poor: (PI = 30, No. 200 = 85%, No. 4 = 95%, D60 = 0.02mm)

Poor: (PI = 15, No. 200 = 75%, No. 4 = 95%, D60 = 0.04mm)

Fair: (PI = 7, No. 200 = 30%, No. 4 = 70%, D60 = 1.0mm)

Good: (PI = 5, No. 200 = 20%, No. 4 = 61%, D60 = 3.0mm) – Meets most agencies spec for

subbase materials.

Very Good: (PI = 1, No. 200 = 5%, No. 4 = 47%, D60 = 8.0mm) Meets most agencies spec

for base material.

Table 2.5: Typical Poison’s Ratio Values for Pavement Materials (NCHRP, 2004; WSDOT, 2005)

Material µ Range Typicalµ

Clay (saturated) 0.4 - 0.5 0.45

Clay (unsaturated) 0.1 - 0.3 0.2

118

Sandy clay 0.2 - 0.3 0.25

Silt 0.3 - 0.35 0.325

Dense sand 0.2 - 0.4 0.30

Coarse-grained sand 0.15 0.15

Fine-grained sand 0.25 0.25

Bedrock 0.1 - 0.4 0.25

Crushed Stone 0.1 – 0.45 0.30

Cement Treated Fine-grain

Materials

0.15 – 0.45 0.40

2.5.8 Traffic Loading

An important factor affecting pavement performance is the number of load repetitions

and the total weight a pavement experiences during its lifetime. Although it is not too

difficult to determine a wheel or an axle load for an individual vehicle, it becomes quite

complicated to determine the number and types of wheel/ axle loads that a particular

pavement will be subjected to over its design life. Furthermore, it is not the wheel load

but rather the damage to the pavement caused by the load that is of primary concern.

The most common approach is to convert damage from wheel loads of various

magnitude and repetitions (“mixed traffic”) to damage from an equivalent number of

“standard” or “equivalent” loads. The most commonly used equivalent load is the

18,000lb (80kN) Equivalent single axle Load ESAL. As a result of variation in traffic

loading, many pavement design agencies have developed multiplying factors called

“load equivalency factors” as a means of reducing the variation in traffic loading to

single load conditions. The most widely used load equivalency factor are those

119

developed at the AASHTO Road Test (AASHTO, 1972). A “load equivalency factor”

represents the number of ESALs for the given weight-axle combination. The AASHTO

(2002) Guide for the Design of New and Rehabilitated Pavement Structures adopts the load

spectra approach in M-E design of pavements. In essence, the load spectra approach

uses the same data that ESAL approach uses only it does not convert the loads to ESALs

– it maintains the data by axle configuration and weight.

For Nigerian traffic condition, traffic analysis could be based on the number of axle

loads of commercial vehicles expressed in terms of an equivalent 80kN single axle load.

There are no load equivalency factors developed in Nigeria, therefore, the AASHTO

equivalency factors could be used in design. Traffic analysis procedure suggested by

Oguara (1985) involves the determination of the number of 80kN equivalent standard

axle load (ESAL) as follows:

ESAL = FV TxN∑ (2.10)

TF = ∑V

F

N

ExNA (2.11)

Where,

NV = number of commercial vehicles

NA = Number of axles

TF = Truck or commercial vehicle factor

120

EF = Load equivalency factors

The truck factors could be calculated from specific truck/ commercial vehicle axle and

weight data. Shook et al, (1982) presented typical truck factors for different classes of

highways and vehicles in the United States. AASHTO (1993) recommended the

estimation of design ESAL from traffic volume. This involves converting the daily traffic

volume into an annual ESAL amount. Pavements are typically designed for the critical

lane or “design lane”, which accounts for traffic distribution (Pavement interactive,

2008). The ESALs per year is given by:

ESALs per year = (Vehicle/day) x (Lane Distribution Factor) x (days/yr.) x

(ESALs/vehicle) (2.12)

The design ESAL is given by:

ESAL = ESALs per year x ( )

g

gn

11 −+ (2.13)

Where,

n = design period

g = annual growth rate.

The Nigerian Highway manual recommended a procedure for estimation of traffic

repetitions (Nanda, 1981) using Table 2.6.

121

Table 2.6: Vehicle Classification (Nanda, 1981)

Class Description

(Nanda, 1981)

Typical ESALs per Vehicle

1 Passenger cars, taxis, landrovers, pickups, and

mini-buses.

Negligible

2 Buses 0.333

3 2-axle lorries, tippers and mammy wagons 0.746

4 3-axle lorries, tippers and tankers 1.001

5 3-axle tractor-trailer units (single driven axle,

tandem rear axles)

3.48

6 4-axle tractor units (tandem driven axle, tandem

rear axles)

7.89

7 5-axle tractor-trailer units(tandem driven axle,

tandem rear axles)

4.42

8 2-axle lorries with two towed trailers 2.60

2.5.9 Material Properties

The ability to calculate the response of pavement structure due to vehicle load depends

on a proper understanding of the mechanical properties of the constituent materials. In

M-E pavement design, material characterization requires the determination of the

material stiffness as defined by the elastic modulus and Poisson’s ratio. The elastic

modulus can either be determined or correlated with conventional test. In many cases

where there is need for laboratory testing, the method of testing the modulus should

reproduce field conditions as accurately as possible. Generally, the dynamic modulus,

122

diametric resilient modulus, and indirect tensile test are used for asphalt concrete and

stabilized materials; the resilient modulus test is mainly used for granular materials.

2.5.9.1 Elastic Modulus of Bituminous Materials

The dynamic modulus test can be used to determine the linear viscoelastic properties of

bituminous materials. The dynamic modulus is derived from the complex modulus E*

defined as a complex number that relates stress to strain for a linear viscoelastic material

subjected to sinusoidal loading at a given temperature and loading frequency (Yorder

and Witczak, 1975). The dynamic complex modulus test accounts not only for the

instantaneous elastic response without delayed effects, but also the accumulation of

cyclic creep and delayed elastic effects with the number of cycles. The dynamic modulus

test does not allow time for any delayed elastic rebound during the test, which is the

fundamental difference from the resilient modulus test. The test is conducted as

specified in ASTM D3497-79 on unconfined cylindrical specimen100mm diameter by

200mm high using uniaxialy applied sinusoidal stress pattern. Strains are recorded using

bonded wire strain gauges and a-channel recording system.

By definition, the absolute value of the complex modulus *E is commonly referred to as

dynamic modulus.

E* = φε

σ

φε

σ

SinCos 0

0

0

0 + (2.14)

Where,

σ0 = stress amplitude (N/mm2)

ε0 = recoverable strain amplitude (mm/mm)

123

Ф = the phase lag angle (degrees)

For and elastic material, Ф = 0,, hence the dynamic modulus is calculated using equation

2.15(Yoder and Witczak, 1975)

E* = 0

0*ε

σ=E (2.15)

Thus the elastic or dynamic modulus of bituminous materials may be determined by

dividing the peak stress σ0 to strain amplitude ε0 from dynamic modulus test.

The elastic modulus of bituminous materials can also be determined by means of the

diametric resilient modulus device developed by Schmidt (Schmidt, 1972) which is a

repetitive load test on cylindrical specimen 100mm diameter by 63mm high, fabricated

either by marshal apparatus or Hveen Kneading compactor. The repeated load is

applied across the diameter, placing the specimen in a state of tensile stress along the

vertical diameter. Linear Variable Differential Transducers (LVDT) mounted on each

side of the horizontal specimen axis measure the lateral deformation of the specimen

under the applied load. One of the major difference between a resilient modulus test and

a dynamic complex modulus test for asphalt concrete mixtures is that the resilient

modulus test has a loading of one cycle per second (1 Hz) with a repeated 0.1 second

sinusoidal load followed by a 0.9 second rest period, while the dynamic modulus test

applies a sinusoidal loading without rest period.

Knowledge of the dynamic load and deformations allow the resilient modulus to be

calculated. Frocht (1948) gave expressions for the stresses σx and σy across the diameter

”d” perpendicular to the applied load P as:

124

Horizontal Diametral Plane:

+

−=

22

22

4

4

..

2

xd

xd

dt

Px

πσ (2.16)

−

+−= 1

4..

222

2

xd

d

dt

Py

πσ (2.17)

τxy = 0 (2.18)

Vertical Diametral Plane:

dt

Px

..

2

πσ = (2.19)

−

++

−−=

dydyddt

Py

1

2

2

2

2

..

2

πσ (2.20)

τxy = 0 (2.21)

where,

t is the specimen thickness and x and y are the distance from the origin along the

x and y-axis.

Thus, if the horizontal deformation across a cylindrical specimen resulting from an

applied vertical load is known the modulus of elasticity can be calculated.

125

2.5.9.2 Prediction Model for Dynamic and Elastic Modulus of Asphalt Concrete

To perform a dynamic modulus test is relatively expensive. Efforts were made by

asphalt pavement researchers to develop regression equation to estimate the dynamic

modulus for a specific hot mix design. One of the comprehensive asphalt concrete

mixture dynamic modulus models is the Witczak prediction model (Christensen et al,

2003). It is proposed in the AASHTO M-E Design Guide and the calculations were based

on the volumetric properties of a given mixture.

Witczak’s prediction equation is presented in equation 2.22a

[ ])22.2(

1

00547.0)(000017.0003958.00021.0871977.3

)(802208.0058097.0002841.0)(001767.0029232.0249937.1log

)log393532.0log313351.0603313.0(

34

2

38384

4

2

200200

*

ae

PPPP

VV

VVPPPE

f

abeff

beff

a

η−−−

+−+−+

+−−−−+−=

Where

*E = Dynamic modulus, in 105 Psi

η = Bituminous viscosity, in 106 Poise (at any temperature, degree of aging)

f = Load frequency, in Hz

Va = Percent air voids content, by volume

Vbeff = Percent effective bitumen content, by volume

P34 = Percent retained on 19mm sieve, by total aggregate weight(cumulative)

126

P38 = Percent retained on 9.51mm sieve, by total aggregate weight(cumulative)



Asphalt concrete elastic modulus can also be predicted using equation 2.22. Researches

have indicated that the dynamic modulus values of asphalt concrete measured at a

loading frequency of 4Hz is comparable with the elastic modulus values (FDOT, 2007;

TM 5-822-13/AFJMAN 32-1018, 1994). The elastic modulus can then be predicted by

modifying equation 2.22b as follows:

[ ])22.2(

1

00547.0)(000017.0003958.00021.0871977.3

)(802208.0058097.0002841.0)(001767.0029232.0249937.1log

)log393532.07919691.0(

34

2

38384

4

2

200200

be

PPPP

VV

VVPPPE

abeff

beff

a

η−−

+−+−+

+−−−−+−=

Where

E = Elastic modulus, in 105 Psi




P34 = Percent retained on 19mm sieve, by total aggregate weight(cumulative)


127



2.5.9.3 Elastic Modulus of Soils and Unbound Granular Materials

The elastic properties of subgrade soils and unbound granular materials for base and

subbase courses can be measured directly by the Resilient Modulus test using a triaxial

test device capable of applying repeated dynamic loads of controlled magnitude and

duration. The resilient (recoverable) deformation over the entire length of the specimen

could be measured with LVDT. The specimen size is normally 100mm in diameter by

200mm high. The Resilient modulus is calculated by dividing the repeated axial stress σd

(equal to the deviator stress) by the recoverable strain εr.

For unbound granular materials, the resilient modulus MR, which is stress dependent, is

given as (Shook et al, 1982):

MR = K1.θ.K2 (2.23)

Where, K1 and K2 are material constants experimentally determined and

θ = the sum of principal stresses.

If repeated load test equipment is not available, the Resilient Modulus of subgrade may

be estimated from CBR values by using the relationship developed by Heukelom and

Klomp, (1962) as:

128

MR(MPa) = 10.3 CBR (2.24a)

MR(psi) = 1500CBR (2.24b)

For subgrade soaked CBR value between 1 and 10%

For unbound base material layers, the resilient modulus may be assumed to be a

function of the thickness of the layer h and the modulus of the subgrade reaction MRs

(Emesiobi, 2000) as shown in equation (2.25)

MR = 0.2 x h0.45 x MRs (2.25)

Where,

h is in millimeters and MR must lie between 2 and 4 times MRs.

The AASHTO Guide for design of pavement structures (AASHTO, 1993) recommends a

standard method of calculating subgrade modulus. This method involves calculating a

weighted average subgrade resilient modulus based on the relative pavement damage.

Because lower values of subgrade resilient modulus result in more pavement damage,

lower values o subgrade resilient modulus is weighted more heavily. The relative

damage equation used in the 1993 AASHTO Guide is:

fu = (1.18 x 108)32.2−

RM (2.26)

Where,

129

fu = relative damage factor

MR = resilient modulus in psi

Therefore, over an entire year, the average relative damage is given by:

n

uuuu

fnff

f

+++=

...21 Where, n = 12.

When triaxial test equipment for resilient modulus is not available, the U.S Army Corps

of Engineers (Hall and Green, 1975) recommends the estimation of resilient modulus for

unbound granular material using equation 2.27.

MR(psi) = 5409(CBR)0.71 (2.27)

Researches have also revealed some useful relationship between CBR and resilient

modulus “E” of stabilized laterite (Ola, 1980) as follows;

For soaked specimen,

E(psi) = 250(CBR)1.2 (2.28)

For unsoaked specimen

E(psi) = 540(CBR)0.96 (2.29)

2.5.9.4 Non-linearity of Pavement Foundation

130

The non-linearity of pavement foundation has been demonstrated both from insitu

measurement of stress and strain (Brown and Bush, 1972; Brown and Pell, 1967) using

field instrumentation, and through back-analysis of surface deflections bowls measured

with the Falling Weight Deflectometer. These non-linearity characteristics have also been

extensively studied using repeated load triaxial facilities and various models proposed

for use in pavement analysis. Some of these are quite sophisticated.

For granular materials, the use of stress dependent bulk and shear modulus provides a

much more sounder basis for analysis than the simple “k-θ” model in which the resilient

modulus is expressed as a function of the mean normal stress and usually, a fixed value

of Poisson’s ratio is adopted, typically 0.3.

For fine grained soils, emphasis has been placed on the relationship between resilient

modulus and deviator stress following the early work done by Seed et al (1962). For

saturated silty- clay, Brown et al (1987) suggested the following model based on a series

of good quality laboratory tests;

Gr =

m

r

or

q

P

C

q

'

(2.30)

Where Gr = Resilient shear modulus

qr = Repeated deviator stress

P0’ = Mean normal effective stress

C, m = Constant for the particular soil

131

For partially saturated soils with degree of saturation in excess of 85%, the same

equation was valid with P0’ being replaced by the soil suction.

2.5.9.5 Poisson’s Ratio

The Poisson’s ratio µ is defined as the ratio of lateral strain εL to the axial strain εa caused

by a load parallel to the axis in which the strain is measured (Oguara, 1985). Values of

Poisson’s ratio are generally estimated, as most highway agencies use typical values as

design inputs in elastic layered analysis. Table 2.7 gives typical Poisson’s ratio values by

various agencies.

Table 2.7: Poisson’s Ratio Used by Various Agencies (Oguara, 2005)

Material Original Shell Oil

Company

Revised Shell

Oil Company

The Asphalt

Institute

Kentucky Highway

Department

Asphalt Concrete 0.5 0.55 0.40 0.40

Granular Base 0.5 0.53 0.45 0.45

Subgrade 0.5 0.35 0.45 0.45

If deformations are monitored from either static or dynamic test, an approximate µ value

could be obtained from equation (2.28):

µ =

∆−

0

11

2

1

V

V

aε (2.31)

Where,

132

V = volume of the material

2.5.9.6 Climatic Conditions

The mechanical parameters of both bounded and unbound layers in pavement

structures are seasonally affected. It is therefore important to understand their seasonal

variations in order to be able to predict their effect on pavement performance. In

mechanistic design, two climatic factors, temperature and moisture are considered to

influence the structural behaviour of the pavement, for instance, temperature influences

the stiffness and fatigue of bituminous materials and is the major factor in frost

penetration. Moisture conditions influence the stiffness and strength of base course,

subbase course and subgrade.

In most pavement design procedures, the effect of the environment is accounted for by

including them in the material properties. The mean annual air temperature MAAT or

mean monthly air temperature MMAT have been generally used in pavement design

analysis. Because the effect of freezing and thawing is very serious in temperate regions,

more attention has been directed towards design of pavement to resist spring thaw

effects. These efforts have several times led to loss of subgrade supporting capacity, a

phenomenon called spring break up.

In Mechanistic design, the effect of environmental factors is included in the analysis. The

moisture and temperature variation for each sub-layer within the pavement, or a

representative temperature need to be determined. In the Asphalt institute design

method, pavement temperature can be determined by (Witczak, 1972):

133

MMPT = MMAT( ) ( )

+

+−

++ 6

4

34

4

11

zz (2.32)

Where,

MMPT = mean monthly pavement temperature

MMAT = mean monthly air temperature

Z = depth below pavement surface (inches)

Pavement design is usually predicated on a subgrade which is assumed to be near-

saturation. The design may be based on subgrade with lower moisture content if

available field measurement indicates that the subgrade will not reach saturation. For

Nigerian climatic condition, the most damaging environmental factor is rainfall, which

unfortunately has not received as much attention as that of frost or freeze-thaw action.

Although the soaked CBR test has been used to simulate the worst environmental

conditions, this may be over conservative in the dry regions of Nigeria. The provision of

adequate drainage facility and proper compaction of pavement materials will go a long

way to alleviate the effect of the environment , especially rainfall on pavements (Oguara,

1985).

2.6 Pavement Response Models

Mechanistic-empirical design procedure requires calculation of the critical structural

responses (stresses, strains or displacements) within the pavement layers induced by

traffic and/ or environmental loading. These responses are used to predict damage in

134

the pavement system which is later related to the pavement distresses (cracking or

rutting). Basically, two types of mechanistic models are commonly used to model

flexible pavements; the layered elastic model (LEA) and the finite element model (FEM).

Both of these models can easily be run on personal computers and only require data that

can be realistically obtained.

2.6.1 Layered Elastic Model

A layered elastic model can compute stresses, strains and deflections at any point in a

pavement structure resulting from the application of a surface load. The layered elastic

model assumes that each pavement layer is homogenous, isotropic and linearly elastic

(Burmister, 1945) and could be used to analyze pavement distress (Peattie, 1963). The

layered elastic approach works with relatively simple mathematical models and thus,

requires some basic assumptions. These assumptions are:

i. Pavement layers extend infinitely in the horizontal direction.

ii. The bottom layer (usually the subgrade) extends infinitely downwards.

iii. Materials are not stressed beyond their elastic ranges.

Layered elastic models require a minimum number of inputs such as Thickness of the

pavement layers, Material properties (modulus of elasticity and Poisson’s ratio) and

Traffic loading (Weight, wheel spacing, and axle spacing) to adequately characterize a

pavement structure and its response to loading. The outputs of a layered elastic model

are the stresses, strains, and deflections in the pavements. Layered elastic computer

programs are used to calculate the theoretical stresses, strains and deflections anywhere

135

in a pavement structure. Table 2.8 and Figure 2.5 however, show few critical locations

that are often used in pavement analysis.

Table 2.8: Critical Analysis Locations in a Pavement Structure

Location Response Reason for Use

Pavement Surface Deflection Used in imposing load restrictions

during spring thaw and overlay

design

Bottom of HMA Layer Horizontal Tensile Strain Used to predict fatigue in the HMA

layer

Top of intermediate Layer

(Base or Surface)

Vertical Compressive Strain

Used to predict rutting failure in the

base or subbase

Top of Subgrade Vertical Compressive Strain Used to predict rutting failure in the

subgrade

1. Pavement surface deflection 2. Horizontal tensile strain at the bottom of bituminous layer 3. Vertical compressive strain at top of base 4. Vertical compressive strain at top of subgrade

Figure 2.5: Critical Analysis Locations in a Pavement Structure (Pavement Interactive, 2008)

136

2.6.2 Finite Elements Model

The Finite Element Method (FEM) is a numerical analysis technique for obtaining

approximate solutions to engineering problems. In a continuum problem (e.g., one that

involves a continuous surface or volume) the variables of interest generally posses

infinitely many values because they are functions of each generic point in the

continuum. For example the stress in a particular element of pavement cannot be solved

with one simple equation because the functions that describe its stresses are particular to

each location. However, the finite element method can be used to divide a continuum

(the pavement volume) into a number of small discrete volumes in order to obtain an

approximate numerical solution for each individual volume rather than an exact close-

form solution for the whole pavement volume. Fifty year ago the computations involved

in doing this were incredibly tedious, but today computers can perform them quite

readily. In the finite element analysis of flexible pavements, the pavement and subgrade

is discretized into a number of elements with the wheel load at the top of the pavement.

The FEM assumes some constraining values at the boundaries of the region of interest

(pavement and subgrade) and is used to model the nonlinear response characteristic of

pavement materials. The FEM approach works with more complex mathematical model

than the layered elastic approach so it makes fewer assumptions. Generally, FEM must

assume some constraining values at the boundaries of the region of interest.

2.7 Flexible Pavement M-E Distress Models (Failure Criteria)

The use of mechanistic approach requires models for relating the output from elastic

layered analysis (i.e stress, strain, or deflections) to pavement behaviour (e.g.

137

performance, cracking, rutting, roughness etc) as elastic theory can be used to compute

only the effect of traffic loads.

The main empirical portions of the mechanistic-empirical design process are the

equations used to compute the number of loading cycles to failure. These equations are

derived by observing the performance of pavements and relating the type and extent of

observed failure to an initial strain under various loads. Currently, two failure criteria

are widely recognized; one relating to fatigue cracking and the other to rutting

deformation in the subgrade. A third deflection-based criterion may be of special

applications (Pavement interactive, 2008). Most of the principles in mechanistic-

empirical design of highway pavements are based on limiting strains in the asphalt

bound layer (fatigue analysis) and permanent deformation (rutting) in the subgrade.

2.7.1 Fatigue Failure Criterion

Fatigue cracking is a phenomenon which occurs in pavements due to repeated

applications of traffic loads. Accumulation of micro damage after each pass on a

bituminous pavements leads to progressive loss of stiffness and eventually, to fatigue

cracking. Repeated load initiate cracks at critical locations in the pavement structure, i.e.

the locations where the excessive tensile stresses and strains occur. The continuous

actions of traffic cause these cracks to propagate through the entire bound layer. The

fatigue criterion in mechanistic-empirical design approach is based on limiting the

horizontal tensile strain on the underside of the asphalt bound layer due to repetitive

loads on the pavement surface, if this strain is excessive, cracking (fatigue) of the layer

will result.

138

The cracks in the asphalt layer may initiate at the bottom of the layer and propagate to

the top of the layer, or may initiate at the top surface of the asphalt layer and propagate

downwards. In Practice pavements are subjected to a wide range of traffic and axle

loads, to account for the contribution of the individual axle load applications, the linear

summation technique known as Miner’s hypothesis (Miner’s Law) is used to sum the

compound loading damage that occurs, so that the total damage can be computed as

follows:

∑=

=i

i f

i

N

nD

1

(2.33)

Where,

D = Total cumulative damage

ni = Number of traffic load application at strain level i

Nf = Number of application to cause failure in simple loading at strain level i

This equation indicates that the determination of fatigue life is based on the

accumulative damage level D. Failure occurs when D > 1 and a redesign may be in

order. When D is considerably less than unity, the section may be under designed. The

relationship shows that pavement sections can fail due to fatigue after a particular

number of load applications (Oguara, 2005).

139

Studies carried out by various researchers have shown that the relationship between

load repetitions to failure Nf and strain for asphalt concrete material is given as:

Nf =

b

t

a

ε

1 (2.34)

Where

Nf = Number of load applications to failure

tε = Horizontal tensile strain at the bottom of asphalt

bound layer

a and b = Coefficients from fatigue tests modified to reflect insitu

performance

Various equations and curves have been developed based on this relationship. Pell and

Brown (1972) used the following in developing their fatigue curves:

Nf =

8.3

11 1108.3

−

t

xε

(2.35)

Figure 2.6 shows typical fatigue curves from Freeme et al for layered elastic analysis

(Freeme et al, 1982).

Figure 2.6: Typical Fatigue Curves (Source: Oguara, 2005)

140

Many other equations have also been developed to estimate the number of repetitions to

failure in the fatigue mode for asphalt concrete. Most of these rely on the horizontal

tensile strain at the bottom of the HMA layer, εt and the elastic modulus of the HMA.

One commonly accepted criterion developed by Finn et al (1977) is:

Log Nf =

−

−

− 36 10log854.0

10log291.3947.15 ACt Eε

(2.36)

Where,

Nf = Number of cycles to failure

εt = Horizontal Tensile Strain at the bottom of the HMA layer

EAC = Elastic Modulus of the HMA

The above equation defines failure as fatigue cracking over 10 percent of the wheel path

area.

The Asphalt Institute (1982) developed a relationship between fatigue failure of asphalt

concrete and tensile strain at the bottom of the asphalt layer follows:

Nf 854.0291.3 )()(0796.0 −−= EItε (2.37)

Where,

Nf = Number of load repetitions to to prevent fatigue cracking

141

εt = Tensile Strain at the bottom of asphalt layer

EI = Elastic modulus of asphalt concrete (psi)

2.7.2 Rutting Failure Criterion

Permanent deformation or rutting is a manifestation of both densification and

permanent shear deformation of subgrade. As a mode of distress in highway pavements,

pavement design should be geared towards eliminating or reducing rutting in the

pavement for a certain period. Rutting can initiate in any layer of the structure, making it

more difficult to predict than fatigue cracking.

Current failure criteria are intended for rutting that can be attributed mostly to weak

pavement structure. This is typically expressed in terms of the vertical compressive

strain (εv) at the top of the subgrade layer as:

Nf =

4843.46

18 1010077.1

−

v

xε

(2.38)

Where,

Nf = Number of repetions to faulre

εv = Vertical compressive Strain at the top of the subgrade layer

The above equation defines failure as 12.5mm (0.5inch) depression in the wheel paths of

the pavement.

142

The relationship between rutting failure and compressive strain at the top of the

subgrade is represented by the number of load applications as suggested by Asphalt

Institute (1982) in the following form:

Nr 477.49 )(10365.1 −−= cx ε (2.39)

Where,

Nf = Number of load repetitions to limit rutting

εc = Tensile Strain at the bottom of asphalt layer

Rutting criterion is based on limiting the vertical compressive subgrade strain, if the

maximum vertical compressive strain at the surface of the subgrade is less than a critical

value, then rutting will not occur for a specific number of traffic loadings. Presented in

Table 2.9 are permissible vertical compressive subgrade strains for various number of

load applications by some agencies, Figure 2.7 shows 5 criterion for limiting vertical

compressive subgrade strain (Claessen et al, 1977). The Shell criterion (Shell Criterion,

1977) corresponds to an average terminal rut depth of 13mm, whereas the Monismith

and McLean criterion [Monismith and Mclean, 1971] is based on a terminal rut depth of

10mm.

Table 2.9: Limiting Vertical Compressive Strain in Subgrade Soils by Various Agencies (Source:

Oguara, 2005)

Number of load

Repetitions to

Original Kentucky TRRL Chevron Revised

Shell

California

143

Failure

Nf

(10-6)

Shell

Model

(10-6)

(10-6)

(10-6)

Model

(10-6)

Model

(10-6)

(10-6)

103 2700 790 3122 2400 4979 2700

104 1680 639 1639 1400 2800 1680

105 1050 502 860 800 1575 1050

106 650 364 451 500 885 650

107 420 227 237 300 498 420

108 260 89 124 170 280 260

Figure 2.7: Rutting Criteria by Various Agencies (Source: Oguara, 2005)

144

2.8 Layered Elastic Analysis Programs

A number of computer programs based on layered elastic theory (Burmister, 1945) have

been developed for layered elastic analysis of highway pavements. The program

CHEVRON (Warren and Dieckman, 1963) developed by the Chevron Research

Company is based on linear elastic theory. The program can accept more than 10 layers

and up to 10 wheel loads. Huang and Witczak (1981) modified the program to account

for material non-linearity and named it DAMA. The DAMA computer program can be

used to analyze a multi-layered elastic pavement structure under single or dual-wheel

load, the number of layers cannot exceed five. In DAMA, the subgrade and the asphalt

layers are considered to be linearly elastic and the untreated subbase to be non-linear,

instead of using iterative method to determine the modulus of granular layer, the effect

of stress dependency is included by effective elastic modulus computed according to

equation (2.39)

E2 = 10.447h1-0.471h2-0.041E1-0.139E3-0.287K10.868 (2.40)

Where, E1, E2, E3 are the modulus of asphalt layer, granular base and subgrade

respectively; h1, h2 are the thicknesses of the asphalt layer and granular base. K1 and K2

are parameters for K-θ model with k2 = 0.5

ELSYM5 developed at the University of California for the Federal Highway

Administration Washington, is a five layer linear elastic program for the determination

of stresses and strains in pavements (Ahlborn, 1972). The program can Analyze a

pavement structure containing up to five layers, 20 multiple wheel loads.

145

The KENLAYER computer program developed based on Burmister’s elastic layered

theory by Yang H. Huang at the University of Kentucky in 1985, incorporates the

solution for an elastic multiple-layered system under a circular load. KENLAYER can be

applied to layered system under single, dual, dual-tandem wheel loads with each layer

material properties being linearly elastic, non-linearly elastic or visco-elastic. It can be

used to compute the responses for maximum of 19 layers with an output of 190 points.

The WESLEA program was developed by U.S. Army Corps of Engineers. The current

version can analyze more than 10 layers with more than 10 loads.

The EVERSTRESS (Sivaneswaran et al, 2001) layered elastic analysis program developed

by the Washington State Department of Transportation at the University of Washington,

was developed from WESLEA layered elastic analysis program. The program can be

used to determine the stresses, strains, and deflections in a layered elastic system (semi-

infinite) under circular surface loads. The program is able to analyze up to five layers, 20

loads and 50 evaluation points. The program can analyze hot mix asphalt (HMA)

pavement structure containing up to five layers and can consider the stress sensitive

characteristics of unbound pavement materials. The consideration of the stress sensitive

characteristics of unbound materials can be achieved through adjusting the layer moduli

in an iterative manner by use of stress-modulus relationships in equations 2.40 and 2.41

Eb = K1θK2 for granular soils ( 2.41)

Es = K3σdK4 for fine grained soils (2.42)

146

Where,

Eb = Resilient modulus of granualar soils (ksi or MPa)

Es = Resilient modulus of fine grained soils (ksi or MPa)

θ = Bulk stress (ksi or MPa)

σd = (Deviator stress (ksi or Mpa) and

K1, K2, K3, K4 = Regression constants

K1, and K2, are dependent on moisture content, which can change with the seasons. K3,

and K4 are related to the soil types, either coarse grained or fine-grained soil. K2 is

positive and K4 is negative and remain relatively constant with the season.

The BISAR program was developed by the Shell Oil Company. The program was

developed based on linear elastic theory. BISAR 3.0 can be used to calculate

omprehensive stress and strain profiles, deflections, and slip between the pavement

layers via a shearspring compliance at the interface.

The proposed LEADFlex Program differed from the other layered elastic analysis

procedures in that while the other programs are capable of carrying out layered elastic

analysis to determine pavement stresses, strains and deflections using trial pavement

thickness as one of the inputs, the LEADFlex program is a comprehensive program that

is capable of computing pavement thickness and predict fatigue and rutting strains in

the asphalt pavement. In the final analysis, the program determines adequate pavement

147

thicknesses that will limit fatigue cracking of asphalt layer and permanent deformation

of subgrade, hence limit pavement failure.

2.9 Validation with Experimental Data

An appreciable amount of work has been performed to validate proposed models

with experimental data. Researchers Ullidtz and Zhang (2002) calculated longitudinal

and traverse strains at the bottom of asphalt, and vertical strains in the subgrade using

layered elastic theory, method of equivalent thickness, and finite element methods. The

authors assert various degrees of agreement between the computed values and values

from the Danish Road Testing Machine. They stated that the critical factor is treating the

subgrade as a non-linear elastic material.

Another study by Melhem and Sheffield (2000) carried out full instrumentation of

several pavement sections at three(3) stations at the South (SM-2A) and North (SM-2A)

lanes of the Kansas Accelerated Testing Laboratory (K-ATL). Tensile strains at the

bottom of the asphalt layer and compressive strains at the top of the subgrade were

calculated using ELSYM5 based on the multi-layer elastic theory while the measured

strains were determined using strain gauges. The relationship between measured and

calculated strains under FWD loading was compared using linear regression analysis.

The result indicated that coefficient of determination was very good and concluded that

the multilayer elastic theory for asphalt pavement is a good estimator of pavement

responses.

148

A significant study by Huang, et al. (2002) presented the results of various numerical

analyses performed with various structural models, both two and three dimensions and

considering both static and transient loading. Their calculated values were compared to

experimental values from the Louisiana Accelerated Loading Facility (ALF) from three

asphalt test values. The Authors concluded stress and strain responses obtained with the

three-dimensional finite element program ABAQUS with rate-dependent viscoplastic

models for the asphalt and elastoplastic models for the other layers were close to

experiment values.

Work done by the Virginia Tech Transportation Institute (Loulizi, et al., 2004) compared

measured pavement responses using layered linear elastic analysis subject a single tire

and one set of dual tires. The authors used several elastic layer programs and two finite

element approaches. They concluded that responses were underestimated at high

temperatures, but overestimated at low intermediate temperatures. They recognized the

need for more research considering dynamic loading, layer bonding, and anisotropic

material properties.

Pavement responses of horizontal tensile and vertical shear strains in the asphalt layers

were of interest in a study authored by Elseifi, et al. (2006). The field-measured

responses from the Virginia Smart Road were compared against finite element predicted

response incorporating a viscoelastic model using laboratory-determined parameters. In

addition, dimensions and vertical pressure measurements of each tire tread were used in

the simulation. The authors claim an average predictions error of less than 15% between

149

the calculated and field response values, and concluded elastic models under-predict

pavement response at intermediate and high temperatures.

150

CHAPTER 3

METHODOLOGY

3.1 Layered Elastic Analysis and Design Procedure for Cement Stabilized Low-

Volume Asphalt Pavement

This study is geared towards developing a layered elastic analysis and design procedure

for the prediction of fatigue and rutting strain in cement-stabilized lateritic base asphalt

pavement. This chapter described in detail, the procedure to be adopted in

characterization of LEADflex pavement material, traffic estimation and summary of the

LEADFlex procedure.

The design procedure comprises of two parts, namely; empirical and analytical.

3.2 Empirical

The empirical part involves material characterization, traffic estimation, computation of

pavement layer thicknesses and development of simple empirical relationship between

these parameters.

3.2.1 Pavement Material Characterization

Material characterization involves laboratory test on surface, base and subgrade

materials to determine the elastic modulus of the asphalt concrete, elastic modulus of the

cement-stabilized lateritic material and resilient modulus of the natural subgrade.

151

3.2.1.1 Asphalt Concrete Elastic Modulus

The following physical (rheological) property test were carried out on the bitumen

sample:

1. Specific gravity test

2. Consistency test such as;

i. Penetration Test

ii. Softening Point Test

iii. Ductility Test

iv. Viscosity Test

3. Gradation Analysis Test

The result of the specific gravity of aggregates and consistency test for binder are

presented in Tables 3.1A and 3.2A of Appendix A.

3.2.1.2 Mix Proportion of Aggregates

In order to meet the specification requirement for aggregate gradation, the proportion of

each aggregate mix was determined. The straight line method of aggregate combination

was used; this method involved plotting on a straight line the percent passing on each

sieve size with the corresponding sieve size for both aggregates on the same graph as

shown in Figure 3.3A of Appendix A. After which a mix proportion was obtained for

152

each aggregate by locating their point of intersection on the graph. The Specification

limits for aggregate in accordance with ASTM (1951: C136) and proportion of each

aggregate based on aggregate combination is presented in Table 3.5A of Appendix A.

From the aggregate gradation and combination, the proportion of coarse and fine

aggregates were determined as 58% for gravel and 42% for sand.

3.2.1.3 Specimen Preparation

Specimens were prepared using the Marshal mix design procedure for asphalt concrete

mixes as presented (NAPA, 1982; Roberts et al, 1996; Asphalt Institute, 1997). The

procedure involved the preparation of a series of test specimens for a range of asphalt

contents such that the test data curves showed well defined optimum values. Test were

scheduled on the basis of 0.5 percent increment of asphalt content with at least 3

asphalts contents above and below the optimum asphalt content. Three specimens were

prepared for each asphalt content, each specimen required approximately 1.2kg of the

total weight of the mixture and measures 64mm thick and 100mm diameter.

To prepare the test specimens, aggregates were first heated for about 5 minutes before

bitumen was added to allow for absorption into the aggregates. After which the mix was

poured into a mould and compacted on both faces with 35, 50, 75, 100, 125 and 150

blows using a rammer falling freely at 450mm and having a weight of 6.5kg. The

compacted specimens were subjected to the following test and analysis:

i. Bulk specific gravity

ii. Stability and Flow at the pavement temperature

153

iii. Density and voids

The maximum stability, unit weight and median of air voids were determined as 1700N,

2460kg/m3 and 5% at 4.5%, 4% and 5% binder content respectively. The optimum binder

content was obtained by taking the average of the binder contents at maximum stability,

unit weight, and median of air voids. Optimum binder content of 4.5% was obtained for

the bituminous mixes and was used to for the preparation of the asphalt concrete mix

(Asphalt Institute, 1997).

3.2.1.4 Determination of Bulk Specific Gravity (Gmb) of Samples

The bulk specific gravity of each specimen was obtained by measuring the weight of

each compacted specimen in air and its weight in water. The bulk specific gravity was

then determined as the ratio of the weight of the specimen in air to the difference in

weight of specimen in air and water as follows:

wa

a

mbWW

WG

−= (3.1)

where, Gmb = bulk specific gravity of compacted specimen

Wa = Weight air

Ww = Weight in water

3.2.1.5 Determination of Void of compacted mixture

154

The Air Voids consist of the small air spaces between the coated aggregate particles.

Voids Analysis involved the determination of both percent air voids and percent voids

in mineral aggregates of each specimen. The results of bulk specific gravity and

maximum specific gravity were used with already existing equations to determine the

percent airs voids and percent voids in mineral aggregates.

At the compactions levels of 35, 50, 75, 100, 125 and 150 blows using a harmer of weight

6.5kg falling freely at 450mm, the percent air voids “Va” were determined using

equation 3.2

Gmm

GGV mbmm

a

−= x 100% (3.2)

Where, Va = percent air voids content

Gmm = maximum specific gravity of compacted mixture

Gmb = bulk specific gravity of compacted mixture

3.2.1.6 Density of Specimens

The density of the specimens were determined by multiplying the bulk specific gravity

already determined by 1000kg/m3.

3.2.1.7 Stability and Flow of Samples

155

The Marshall Test Apparatus was used for the stability and flow test. The machine was

used to apply load at a constant rate of deformation of 50mm/minute until failure

occurred (Asphalt Institute, 1997). The point of maximum load was recorded as the

Marshall stability value for the specimen. The flow values in units of 0.25mm was also

obtained simultaneously at maximum load using the flow meter attached to the

machine.

3.2.1.8 Determination of Asphalt Concrete Elastic Modulus

The elastic modulus of the asphalt concrete was determined using the modified Witczak

model ((Christensen et al, 2003)) in equation 3.3.

[ ])3.3(

1

00547.0)(000017.0003958.00021.0871977.3

)(802208.0058097.0002841.0)(001767.0029232.0249937.1log

)log393532.07919691.0(

34

2

38384

4

2

200200

η−−

+−+−+

+−−−−+−=

e

PPPP

VV

VVPPPE

abeff

beff

a

Where

E = Elastic Modulus (Psi)




P34 = Percent retained on 3/4 in. sieve, by total aggregate weight(cumulative)

P38 = Percent retained on 3/8 in. sieve, by total aggregate weight(cumulative)

P4 = Percent retained on No. 4 sieve, by total aggregate weight(cumulative)

156

P200 = Percent retained on No. 200 sieve, by total aggregate weight(cumulative)

Using equation 3.3, the design elastic modulus of asphalt concrete was determined by

developing a regression equation relating the compaction levels and percents air voids

on one hand and the percents air voids and elastic modulus on the other hand. Table

3.6A of APPENDIX presents the compaction level, percent air voids and elastic modulus

of the asphalt concrete. Figures 3.4A and 3.5A of APPENDIX A shows the relationship

between compaction level and air voids, and air voids and elastic modulus

From Figures 3.4A and 3.5A of Appendix A, the design elastic modulus of 3450MPa can

be obtained for percentage air voids of 3.04% and compaction level of 90 blows.

3.2.2 Base Material

The base material used in the study is cement-treated laterite of elastic modulus of

329MPa. The elastic modulus was determined by correlation with CBR as presented in

equation 3.4 (Ola, 1980). From equation 3.5, elastic modulus of 329MPa corresponds

with CBR of 79.5% approximately 80% CBR. The study is based on cement stabilized

base of 80% CBR ie elastic modulus of 329MPa.

E(psi) = 250(CBR)1.2 (3.4)

157

3.2.2.1 Soil Classification Test

The following soil classification tests were carried out on the sample to obtain its

physical properties.

(i) Natural moisture content.

(ii) Atterberg limit (liquid and plastic limit)

(iii) Sieve analysis

(iv) Compaction (Moisture-density) tests.

3.2.2.2 Sieve Analysis

500g of an oven dried sample was used for sieve analysis. Wet sieving was carried out to

determine the accurate amount of silt and clay passing sieve 0.075(No. 200). The result of

the sieve analysis is shown in Table 3.7A of APPENDIX A and the Particle Size

Distribution is shown in Figure 3.6A of APPENDIX A.

Group index value of the sample was also obtained as follows:

Group index GI = 0.2a + 0.005ac + 0.01bd (3.5)

a = that portion of percentage passing No. 200 sieve greater than 35% and not

exceeding 75%, expressed as a positive whole number (1-40)

therefore a = 0; percentage passing No. 200 sieve is 22%, less than 35%

b = that portion of percentage passing No. 200 sieve greater than

158

15% and not exceeding 55% expressed as a whole number (1-40), therefore

b = 22-15 = 7

c = that portion of numerical liquid limit greater than 40 and not exceeding 60,

expressed as a positive whole number (1-20) therefore c =0; liquid limit = 32%, less

than 40%.

d = that potion of the numerical plasticity, index greater than 10 and not exceeding 30,

expressed as a positive whole number (1-20)

Therefore a = 16 – 10 = 6

GI = 0.2 x 0 + 0.005x0x0 + 0.01x 7x 6 = 0.42

3.2.2.3 Compaction Test

Compaction (Moisture-Density) test was carried out on the soil sample to determine the

optimum moisture content (OMC) and the corresponding maximum dry density (MDD)

of the sample. The test was carried out using a proctor mould of 100mm diameter by

115mm height and a 2.5kg hammer with a drop of 300mm. 3000g of the oven dried soil

was mixed with a specified amount of water and compacted in three layers in the

proctor mould, each layer being compacted with 25 blows of the hammer falling a

distance of 300mm. The result of the compaction test is shown in the Table 3.8A of

Appendix A and the moisture-density relation is shown in Figure 3.7A of APPENDIX A.

3.2.2.4 Soil Classification

159

From the classification tests, the material was found to posses the following physical

properties.

(i) Well graded

(ii) Natural moisture content = 11.31%

(iii) Liquid limit = 32%

(iv) Plasticity index = 15.51%

(v) Proctor maximum dry density = 1960kg/m3

(vi) Proctor optimum moisture content = 10.8%

Base on the AASHO (1993) classification system, the Sieve Analysis and Group index,

the soil was classified as A-2-6 (0.42). That is, the soil is silty or clayed gravely and sand

and it is rated as excellent to good as sub-grade materials

In accordance with Table 3.9A of APPENDIX A, the soil will require about 5 to 9%

cement for stabilization

3.2.2.5. California Bearing Ratio (CBR) Test Specimen

To obtain a cement treated laterite of 80% CBR, trial CBR test were carried out at varying

cement contents. The cement treated specimen for the CBR test were prepared in the

CBR mould 152.4mm (6.0in) in diameter and 177.8mm (7.0in) high with collar and base.

The soil- cement mixture was mixed with water at the optimum moisture content and

compacted in three layers with 50 blows per layer in the CBR mould using the modified

AASHTO hammer of 4.5kg falling a distance of 450mm. A set three specimens were

prepared for each fiber content. The compacted specimen in the mould was kept in an

air- tight water proof sack to prevent loss of moisture for 24 hours and tested using the

160

CBR machine. Table 3.10A of Appendix A presents the trial CBR tests result while Figure

3.8A of Appendix A shows the relationship between the cement content and CBR. From

Figure 3.8A of APPENDIX A, 80% CBR was obtained at cement of 5.4%.

3.2.3 Subgrade Material

The resilient modulus of subgrade was determined in accordance the AASHTO Guide

(AASHTO, 1993) in order to reflect actual field conditions. It is recommended that

subgrade samples be collected for a period of twelve (12) months in order to

accommodate the effect of seasonal subgrade variation on resilient modulus of

subgrades. In this study, samples were collected from January 2011 – December, 2011

(four samples per month). Average subgrade CBR for each month was determined as

presented in Table 3.11A of Appendix A. The resilient modulus (Mr) was determined

using correlation with CBR as shown equation (3.6) (HeuKelom and Klomp, 1962). The

CBR of subgrade material was determined using the procedure as earlier described in

section 3.2.2.4.

Mr (psi) = 1500 CBR (3.6)

In accordance with AASHTO Guide (AASHTO, 1993), the relative damage per month

were determined using equation 3.7.

fu = (1.18 x 108)32.2−

RM (3.7)

161

From equations 3.6 and 3.7

fu = (1.18 x 108)x(32.2

)1500 −CBR (3.8)

Where,

fu = relative damage factor

CBR = California Bearing Ratio (%)

Therefore, over an entire year, the average relative damage was determined using

equation 3.9 as follows:

:

n

uuuu

fnff

f

+++=

...21 Where, n = 12. (3.9)

=fu 0.53

Hence from equation 3.8, the average CBR is given by

CBR = 1500

)10847.0( 431.08 −−xux f (3.10)

= 2.64%

The study approximates CBR of subgrade to the nearest whole number, hence the CBR

of the subgrade is taken as 3%. However, for worse conditions a CBR of 2% may be

assumed.

162

3.2.4 Poison’s Ratio

In mechanistic-empirical design, the Poisson’s ratios of pavement materials are in most

cases assumed rather than determined (NCHRP, 2004). In this study, the Poisson’s ratios

of the materials were selected from typical values used by various pavement agencies as

presented in Literature (NCHRP, 2004; WSDOT, 2005).

3.2.5 Traffic and Wheel load Evaluation

The study considered traffic in terms of Equivalent Single Axle Load (ESAL) repetitions

for a design period of 20years (NCHRP, 2004). Traffic estimation is in accordance with

the procedure contained in the Nigerian Highway Manual part 1 (1973). For the purpose

of this study, three traffic categories; Light, medium and Heavy traffic were considered

in design as presented in Table 3.1.

Table 3.1: Traffic Categories (NCHRP, 2004)

Traffic

Category

Expected 20 yr

Design

ESAL

A.C. Surface

Thickness

(mm)

Stabilized Base

Thickness

(mm)

Light 1 x 104 – 5 x 104 50 ≥ 50

Medium 5 x 104 – 2.5 x 105 75 ≥ 75

Heavy 2.5 x 105 – 7.5 x 105 100 ≥ 100

Light Traffic

163

50,000 ESAL maximum – typical of local streets or low volume country roads with very

few trucks, approximately 4-5 per day, first year.

Medium Traffic

250,000 ESAL maximum – typical of collectors with fewer trucks and buses,

approximately 23 per day, first year.

Heavy Traffic

750,000 ESAL maximum – typical of collectors with significant trucks and buses,

approximately 70 per day first year.

3.2.6 Loading Conditions

The study considered a three layer pavement model. The static load(P) applied on the

pavement surface, the geometry of the load (usually specified as a circle of a given

radius), and the load on the pavement surface in form of Equivalent Single Axle load

(ESAL) was considered. The loading condition on pavement was obtained by

determining the critical load configuration. The critical load configuration was

determined by investigating the effect of single and multiple wheel loads on the tensile

strain below asphalt concrete layer and compressive strain at the top the subgrade. To

investigate this, the pavement system was subjected to three different loading cases as

shown in Figure 3.1. The first one will be single axle with single wheel (I), the second

one will be single axle with dual wheels (four wheels; II), and the last one will be tandem

axle with dual wheels (eight wheels; II + III). Each axle will be 80kN as assumed in

164

design. The pavement analysis was carried out using EVERSTRESS program

(Sivaneswaran et al, 2001) developed by the Washington State Department of

Transportation (WSDOT). Result of the analysis is shown in Table 3.3 while details of the

layered elastic analysis are presented in Tables 3.12A, 3.13A and 3.14A of Appendix A.

The LEADFlex pavement material parameters are as presented in Table 3.2. The

pavement was loaded as described in section 3.2.6 and the effect of single and multiple

wheel load configurations are as presented in Table 3.3. From Table 3.3, the critical

loading condition was determined to be the single, axle, single wheel since it recorded

the highest maximum stresses, strains and deflections.

Figure 3.1: Typical Single Wheel and Dual-wheel Tandem

200mm

200mm

1800mm

I

200mm

200mm

200mm

200mm

13

00

mm

1800mm

305m305m

305m305m

II

III

x

y

165

Table 3.2: Load and materials parameter for determination of critical wheel load

Wheel

Load

(kN)

Tire

Pressure

(kPa)

Pavement Layer

Thickness

(mm)

Pavement Material Moduli

(MPa)

Poison’s Ratio

A.C. Surface

T1

Base

layer

T2

A.C

Surface

E1

Base

E2

Subgrade

E3

A.C

Surface

Base Subgrade

40 690 100 300 3450 329 52 0.35 0.40 0.45

20 690 100 300 3450 329 52 0.35 0.40 0.45

20 690 100 300 3450 329 52 0.35 0.40 0.45

Table 3.3: Critical Loading Configuration Determination

Load Configuration Axle

Load

Pavement Response

Maximum Strain

(10-6)

Maximum Stress

(kPa)

Max. Deflection

(10-6mm)

Below

Asphalt

Layer

On Top

Subgrade

Layer

Below

Asphalt

Layer

On Top

Subgrade

Layer

Below

Asphalt

Layer

On Top

Subgrade

Layer

Single Axle, Single wheel

(I)

40kN 285.25 872.52 1372.89 48.85 699.903 587.450

Single Axle, Dual Wheel 20kN 247.61 652.76 1110.83 38.48 617.261 536.478

166

(II)

Tandem Axle, Dual Wheel

(II + III)

20kN 241.61 643.86 1090.00 39.47 779.429 699.840

3.2.7 LEADFlex Pavement Model

The LEADFlex pavement is a 3-layer pavement model (surface, base and subgrade) as

shown in Figure 3.2. The load and material parameters are as presented in Table 3.4,

Single Axle with single wheel load configuration was assumed. The study considered

application of 40kN load on a single tire having tire pressure of 690 kPa (AASHTO,

1993).

Figure 3.2: Typical LEADFlex Pavement Section Showing Location of Strains

µ3 = 0.45, E3 = 10 – 103MPa

εr1

P

µ1 = 0.35

E = 3450MPa

µ2 = 0.40

E =329MPa

a

εz2

h1≥50mm

h2 >50mm

167

Table 3.4: LEADFlex Pavement Load and materials parameter

Wheel

Load

(kN)

Tire

Pressure

(kPa)

Pavement Layer

Thickness

(mm)

Pavement Material Moduli

(MPa)

Poison’s Ratio

A.C. Surface

T1

Base

layer

T2

A.C

Surface

E1

Base

E2

Subgrade

E3

A.C

Surface

Base Subgrade

40 690 50 ≥ 50 3450 329 10-103 0.35 0.40 0.45

40 690 75 ≥ 75 3450 329 10-103 0.35 0.40 0.45

40 690 100 ≥100 3450 329 10-103 0.35 0.40 0.45

3.2.8 Environmental Condition

The two environmental parameters that influence pavement performance are

temperature and moisture. Temperature conditions for the particular site have to be

known to properly design an asphalt pavement, hence the test temperature should be

selected so that the asphalt concrete modulus in the test matches with that in the field

(Brown, 1997). In this study, the influence of temperature was accounted for by

characterization of asphalt concrete at the pavement temperature. In the Asphalt

Institute design method, pavement temperature can be correlated with air temperature

(Witczak, 1972) as follows:

MMPT = MMAT( ) ( )

+

+−

++ 6

4

34

4

11

zz (3.11)

168

Where,

MMPT = mean monthly pavement temperature

MMAT = mean monthly air temperature

Z = depth below pavement surface (inches)

The effect of moisture (seasonal variation) was accounted for by calculating a weighted

average subgrade resilient modulus based on the relative pavement damage over a one

year period as described in section 3.2.3.

3.2.9 Pavement Layer Thickness

Mechanistic-Empirical design combines the elements of mechanical modeling and

performance observations in determining the required pavement thickness for a set of

design conditions. The thicknesses of the asphalt layer for the various traffic categories

are as presented in Table 3.1. The minimum thicknesses of cement-stabilized base layer

were determined based on pavement response using the asphalt institute response

model (Asphalt Institute, 1982). The required minimum base thickness was determined

as that expected traffic and base thickness that resulted in a maximum compressive

strain and allowable repetitions to failure (Nr) such that the damage factor D is equal to

unity.

3.2.10 Traffic Repetition Evaluation

The study considered evaluation of future traffic and determination of axle load

repetition in the form of 80kN equivalent single axle load (ESAL). Vehicle classification

169

was in accordance with the procedure proposed for the new Nigerian Highway Manual

(1973) where vehicles are classified into 8 different classes as shown in Table 3.5.

Standard operational factors for single and tandem axles based on the AASHTO road

test were used (Nanda, 1981).

Table 3.5: Vehicle Classification (Source: Oguara, 2005)

Class Description

(Nanda, 1981)

Typical ESALs per Vehicle

1 Passenger cars, taxis, landrovers, pickups, and

mini-buses.

Negligible

2 Buses 0.333

3 2-axle lorries, tippers and mammy wagons 0.746

4 3-axle lorries, tippers and tankers 1.001

5 3-axle tractor-trailer units (single driven axle,

tandem rear axles)

3.48

6 4-axle tractor units (tandem driven axle, tandem

rear axles)

7.89

7 5-axle tractor-trailer units(tandem driven axle,

tandem rear axles)

4.42

8 2-axle lorries with two towed trailers 2.60

3.2.10 Determination of Design ESAL

The expected traffic was determined in accordance with the procedure outlined in the

Nigerian Highway Manual part 1 (1973). A typical example of the procedure for

computation of expected traffic repetitions is as presented in Table 3.6.

170

Highway Facility: 6-lane (3 lane in each direction)

Traffic Growth rate: 4%

Design Period: 20 year

Traffic Category

- Passenger cars, taxis, landrovers, pickups, and mini-buses: 1321veh/day

- Buses: 520 veh/day

- 2-axle lorries, tippers and mammy wagons: 5 veh/day

- 3-axle lorries, tippers and tankers: 3 veh/day

- 3-axle tractor-trailer units (single driven axle, tandem rear axles): 2 veh/day

- 4-axle tractor units (tandem driven axle, tandem rear axles): 3 veh/day

- 5-axle tractor-trailer units(tandem driven axle, tandem rear axles): 1 veh/day

- 2-axle lorries with two towed trailers: 1 veh/day

Procedure

Step 1: Enter vehicle class, equivalent operational factor and number of vehicles in 24

hours (as determined from traffic studies) in columns 1, 2 and 3 respectively.

Step 2: Determine total ESAL per day in column 4 by multiplying columns 2 and 3.

Step 3: Determine total ESAL per year in column 5 by multiplying column 4 by number

of days in a year

171

Step 4: Determined the ESAL per year for all the axle categories as shown in column 5

(FHWA, 2001). The design ESALs is obtained in column 7 for a given growth

rate by multiplying columns 5 with the multiplier in column 6.

The expected traffic repetition is therefore determined using equation 3.12.

Ni = ( )

g

gxxFxAADT

n11

365−+ (3.12)

Where,

Ni = Expected traffic repetition (ESAL)

F = Equivalent operational factor

g = growth rate in %

n = design period (20yrs)

Where growth rate data is not available, 4% growth rate is recommended for 20 year

design period for flexible (AASHTO, 1972).

From Table 3.6, ESAL = 2.55 x 105

172

Table 3.6: Vehicle Classification

Vehicle

Class

Equivalent

Operational

Factor

Number of

Vehicles in

24 hours

Total

ESAL per

day

(2) x (3)

Total ESAL per

Year

(4) x 365 days

Multiplier

( )g

gn

11 −+

Total

ESAL in

20 years

(1) (2) (3) (4) (5) (6) (7)

1 negligible 1321 - - - -

2 0.333 5 1.665 607.725 29.78 18098.05

3 0.746 3 2.238 816.87 29.78 24326.39

4 1.001 2 2.002 730.730 29.78 21761.14

5 3.48 3 10.44 3,810.6 29.78 113479.70

6 7.89 - - - - -

7 4.42 1 4.42 1,613 29.78 48044.07

8 2.60 1 2.60 949 29.78 28261.22

Total ESAL in 20 years 254666.5

3.3 Analytical

The analytical part involved the analysis and the design of the 3-layer pavement system,

evaluation and prediction of maximum horizontal tensile strain at the bottom of the

asphalt layer and maximum vertical compressive strain at the top of the subgrade using

the Layered Elastic Analysis (LEA) procedure. Pavement analysis was carried out using

173

the EVERSTRESS (Sivaneswaran et al, 2001) program developed by the Washington

State Department of Transportation.

3.5 Summary of the LEADFlex Procedure

The summary of LEADFlex Procedure is itemized below;

1. Material characterization of the asphalt concrete, cement stabilized lateritic base

and subgrade were carried out to determine the design elastic modulus and

resilient modulus of the layers.

2. The minimum pavement base thicknesses required to withstand the expected

traffic repetitions were determined using the layered elastic analysis program

EVERSTRESS (Sivaneswaran et al, 2001). The minimum pavement thickness is

referred to as the LEADFlex pavement section.

3. Having determined the required minimum pavement thickness, layered elastic

analysis of the LEADFlex pavement was carried out to compute pavement

response in terms of horizontal tensile strain at the bottom of the asphalt layer and

vertical compressive strain on top the subgrade.

4. Using regression analysis, simple regression equation were developed to establish

the relationship between traffic repetitions and pavement thickness, pavement

thickness and horizontal tensile strain, pavement thickness and vertical

compressive strain.

5. The Asphalt Institute response model (Asphalt Institute, 1982) was adopted to

compute the allowable tensile and horizontal strains, and number of repetitions to

failure in terms of fatigue and rutting criteria.

6. Damage factors D was computed for both fatigue and rutting criteria such that D

≤ 1.

174

7. The Procedure was validated using result of layered elastic analysis and

measured strain data from the Kansas Accelerated Testing Laboratory (K-ATL).

8. Algorithm were written using the developed regression equations and visual basic

codes were used to develop the LEADFlex Program for the design and analysis of

cement-stabilized lateritic base low volume asphalt pavements.

The flow diagram for the LEADFlex Procedure is as shown in Figure 3.1.

Figure 3.3: Flow Diagram for LEADFlex Procedure

Material

Inputs

Traffic

Inputs

Pavement

Layer Thickness

Yes

YE

NNO

Final Design

D>1?

D<<1?

LEADFlex Model

No

Allowable Load

Repetitions Expected Load

Repetitions

Is

Horizontal

Tensile Strain

Is

Vertical

Compressive

Strain

Pavement

Response

Compute Damage D

YE

Increase

Pavement

175

CHAPTER 4

DEVELOPMENT OF LEADFLEX DESIGN PROCEDURE AND PROGRAM

4.1 Determination of Minimum Pavement Thickness

Layered elastic analysis of the pavement sections in Figure 3.2 was carried to determine

minimum pavement thicknesses required to withstand the expected traffic repetitions

for light, medium and heavy traffic categories. Three trial analysis using EVERSTRESS

(Sivaneswaran et al, 2001) program were carried out for each subgrade modulus and

traffic repettiions. Regression equations were developed using SPSS (SPSS 14.0, 2005) to

determine the thickness of base (T) that will result in a damage factor (D) of 1. In this

study, layered elastic analysis of the pavement showed that the rutting criteria was the

cntrolling criteria, hence was used to develop the regression equations. Presented in

Tables 4.1.1B, 4.2.1B and 4.3.1B of APPENDIX B are pavement thickness layered elastic

analysis to determine minimum pavement base thickness for light, medium and heavy

traffic category respectively while Tables 4.1.2B, 4.2.2B and 4.3.2B presents the regression

equation used to determine the required minimum pavement base thickeness to

withstand expected traffic repetitions for light, medium and heavy traffic category

respectively.

4.2 Layered Elastic Analysis of LEADFlex Pavement Sections

Layered elastic analysis of the pavement sections determined in section 4.1 were carried

out to determine the pavement responses (fatigue and rutting strains, number of

repetitions to failure and damage factors) for each traffic category. The EVERSTRESS

176

(Sivaneswaran et al, 2001) program was used to apply a static load on a circular plate

placed on a single axle single wheel configuration. A tire load of 40kN and pressure of

690kpa (AASHTO, 1993) was adopted in the analysis. The results of the pavement

responses are presented in Tables 4.1a, 4.2a and 4.3a for light, medium and heavy traffic

categories respectively while Tables 4.1b, 4.2b and 4.3b presents summary of the

mimimum pavement thickness required to withstand the expected traffic, the maximum

tensile and compressive strains due to the expected traffic load repetitions for light,

medium and heavy traffic categories respectively.

4.3 Allowable Strains for LEADFlex Pavement

The Asphalt Institute failure criteria models in equations 4.1 and 4.2 were used to

develop allowable (limiting) horizontal tensile (fatigue) and vertical compressive

(rutting) strains for LEADFlex pavement by assuming the tensile and compressive

strains in equations 4.1 and 4.2 as the critical strain beyond which failure occurs.

Nf 854.0291.3 )()(0796.0 −−= EItε (4.1)

Nr 477.49 )(10365.1 −−= cx ε (4.2)

Where,

Nf, Nr = Number of load repetitions to failure in terms of fatigue and rutting

respectively

EI = Elastic modulus of asphalt concrete (psi)

177

εt, εc = Tensile strain at the bottom of asphalt layer and compressive strain on

top of subgrade respectively.

The allowable strains were determined by making the critical strains the subject of

equations 4.1 and 4.2 to obtain equations 4.3 and 4.4 respectively.

Єt 303.0854.0 ))(562.12( −= EN i (4.3)

Єc 223.08 )(1032.7 −= iNx (4.4)

Where, Єt = Allowable tensile strain

Єc = Allowable compressive strain

E = Elastic Modulus of asphalt concrete (psi)

Ni = Expected traffic repetitions

The allowable strains were taken as the maximum strain resulting from the passage of

the total expected traffic repetition within the design period.

4.4 Traffic Repetitions to Failure

The number of repetitions to failure for each expected traffic repetitions were

determined using the Asphalt Institute pavement response model in equation 4.1 and 4.2

for fatigue and rutting criteria respectively (Asphalt Institute, 1982).

178

4.5 Damage Factor

The total cumulative damage on the pavement is computed using the linear summation

technique known as Miner’s hypothesis as presented in equation 4.5

∑=

=i

i

i

N

nD

1

(4.5)

Where,

D = Total cumulative damage

ni = Number of traffic load application at strain level i

N = Number of application to cause failure in simple loading at strain level i

4.6 Development of LEADFlex Regression Equations

The pavement response data generated in Tables 4.1b, 4.2b and 4.3b of section 4.2 were

used to develop nonlinear regression equations between expected traffic and pavement

thickness; pavement thickness and maximum tensile strain at the bottom of the asphalt

layer; and pavement thickness and maximum compressive strain on top the subgrade.

The regression equations were developed based on the nonlinear general equations 4.6

and 4.7 using the SPSS program (SPSS 14, 2005). The relationships between expected

traffic and pavement thickness were best fitted using equation 4.6 while that of

pavement thickness and horizontal tensile strain, and pavement thickness and vertical

compressive strains were fitted using equation 4.7.

179

bxay 11 ln= (4.6)

cxay += )ln( 22 (4.7)

Where, y1 = pavement thickness (mm)

y2 = tensile or compressive strain (10-6)

x1 = expected traffic (ESAL)

x2 = pavement thickness (mm)

a, b and c are constants

Presented in Tables 4.3a, 4.3b and 4.3c are the developed LEADFlex pavement

regression equation for the various subgrade CBR for light, medium and heavy traffic

categories respectively. Details of the SPSS (SPSS 14, 2005) analysis for light, medium

and heavy traffic are presented in Appendix C, D and E respectively.

4.7 Summary of LEADFlex Design Procedure

The summary of Layered Elastic Analysis and Design of Flexible (LEADFlex) pavement

procedure are summarized as follows:

STEP 1 – COMPUTE EXPECTED TRAFFIC

180

Determine expected traffic (Ni) for all vehicle class for a design period of 20 years in

terms of Equivalent Single Axle Load (ESAL) using equation 4.8 and identify the traffic

category.

Ni = AADT x F x 365 x ( )

g

gn

11 −+ (4.8)

STEP 2 – COMPUTE MINIMUM PAVEMENT THICKNESS

For a particular subgrade CBR, determine minimum pavement thickness required to

withstand the expected traffic using the expected traffic – pavement thickness

relationship in Table 4.1c, 4.2c or 4.3c where applicable.

STEP 3: COMPUTE PAVEMENT RESPONSE

(a) For the same subgrade CBR, using the pavement thickness determined in STEP

2, compute pavement response in terms of maximum tensile strain at the

bottom of asphalt layer (fatigue strain) using the pavement thickness – tensile

strain relationship in Table 4.1c, 4.2c or 4.3c where applicable.

(b) For the same subgrade CBR, using the pavement thickness determined in STEP

2, compute pavement response in terms of maximum compressive strain at the

top of subgrade layer (rutting strain) using the pavement thickness –

compressive strain relationship in Table 4.1c, 4.2c or 4.3c where applicable.

181

(c) Evaluate allowable tensile/limiting strain at the bottom of the asphalt layer

using equation 4.9. This must be less than the actual tensile strain computed in

STEP 3(a).

Єt 303.0854.0 ))(562.12( −= EN i (4.9)

(d) Evaluate allowable/limiting compressive strain on top subgrade layer using

equation 4.10. This must be less than actual compressive strain computed in

STEP 3(b)

Єc 223.08 ))(1032.7( −= iNx (4.10)

(e) Evaluate number of traffic repetitions to failure (Nf) in terms of fatigue strain

using the asphalt institute model in equation 4.11

Nf 854.0291.3 )()(0796.0 −−= Etε (4.11)

(f) Evaluate number of traffic repetitions to failure (Nr) in terms of rutting strain

using the asphalt institute model in equation 4.12.

Nr477.49 )(10365.1 −−= cx ε (4.12)

(g) Evaluate damage factor (Df) in terms of fatigue using equation 4.13. This must

be less than or equal 1.

Df = Ni/Nf (4.13)

(h) Evalaute damage factor (Dr) in terms of rutting using equation 4.14. This must

be less than or equal to 1.

Dr = Ni/Nr (4.14)

182

Table 4.1a: Light Traffic – Pavement Response Analysis

A.C

Mod.

Base

Mod.

Sub

Mod.

Layer Thickness Expected

Repetitions

Ni

Fatigue Criterion Rutting Criterion

A.C

Surface

T1

(mm)

Stabilized

Base

T2

(mm)

Total

T

(mm)

E1

(MPa)

E2

(MPa)

E3

(MPa) Horizontal

Tensile

Strain

Allowable

Tensile

Strain

No. of

Repetition

to Failure

D.F

Vertical

Compressive

Strain

Allowable

Compressive

Strain

No. of

Repetition

to Failure

D.F

3450 329 10 50 313.9 363.9 1.00E+04 266.2E-6 955.5E-6 6.29E+05 0.02 1.335E-03 1.35E-03 1.00E+04 1.00

3450 329 10 50 348.4 398.4 2.00E+04 263.0E-6 774.5E-6 6.54E+05 0.03 1.145E-03 1.16E-03 2.00E+04 1.00

3450 329 10 50 369.4 419.4 3.00E+04 262.0E-6 684.9E-6 6.63E+05 0.05 1.048E-03 1.06E-03 3.00E+04 1.00

3450 329 10 50 385.6 435.6 4.00E+04 261.5E-6 627.8E-6 6.67E+05 0.06 9.814E-04 9.93E-04 4.00E+04 1.00

3450 329 10 50 398.1 448.1 5.00E+04 260.3E-6 586.7E-6 6.68E+05 0.07 9.340E-04 9.45E-04 5.00E+04 1.00

3450 329 21 50 275.2 325.2 1.00E+04 280.7E-6 955.5E-6 5.28E+05 0.02 1.338E-03 1.35E-03 1.00E+04 1.00

3450 329 21 50 308 358 2.00E+04 275.3E-6 774.5E-6 5.63E+05 0.04 1.146E-03 1.16E-03 2.00E+04 1.00

3450 329 21 50 328.2 378.2 3.00E+04 273.2E-6 684.9E-6 5.77E+05 0.05 1.047E-03 1.06E-03 3.00E+04 1.00

3450 329 21 50 343.3 393.3 4.00E+04 272.0E-6 627.8E-6 5.85E+05 0.07 9.810E-04 9.93E-04 4.00E+04 1.00

3450 329 21 50 354.8 404.8 5.00E+04 271.4E-6 586.7E-6 5.90E+05 0.08 9.345E-04 9.45E-04 5.00E+04 1.00

183

3450 329 31 50 252 302 1.00E+04 289.4E-6 955.5E-6 4.78E+05 0.02 1.339E-03 1.35E-03 1.00E+04 1.00

3450 329 31 50 284 334 2.00E+04 282.5E-6 774.5E-6 5.17E+05 0.04 1.148E-03 1.16E-03 200E+04 1.00

3450 329 31 50 303.6 353.6 3.00E+04 279.8E-6 684.9E-6 5.34E+05 0.06 1.047E-03 1.06E-03 3.00E+04 1.00

3450 329 31 50 318.1 368.1 4.00E+04 278.2E-6 627.8E-6 5.44E+05 0.07 9.808E-04 9.93E-04 4.00E+04 1.00

3450 329 31 50 328.1 378.1 5.00E+04 277.4E-6 586.7E-6 5.49E+05 0.09 9.387E-04 9.45E-04 5.00E+04 1.00

3450 329 41 50 233.9 283.9 1.00E+04 296.0E-6 955.5E-6 4.43E+05 0.02 1.338E-03 1.35E-03 1.00E+04 1.00

3450 329 41 50 265.4 315.4 2.00E+04 288.0E-6 774.5E-6 4.85E+05 0.04 1.144E-03 1.16E-03 200E+04 1.00

3450 329 41 50 284.2 334.2 3.00E+04 284.8E-6 684.9E-6 5.03E+05 0.06 1.046E-03 1.06E-03 3.00E+04 1.00

3450 329 41 50 297.9 347.9 4.00E+04 283.0E-6 627.8E-6 5.14E+05 0.08 9.824E-04 9.93E-04 4.00E+04 1.00

3450 329 41 50 309.3 359.3 5.00E+04 281.8E-6 586.7E-6 5.21E+05 0.10 9.332E-04 9.45E-04 5.00E+04 1.00

3450 329 52 50 217.1 267.1 1.00E+04 301.9E-6 955.5E-6 4.16E+05 0.02 1.337E-03 1.35E-03 1.00E+04 1.00

3450 329 52 50 247.6 297.6 2.00E+04 293.0E-6 774.5E-6 4.58E+05 0.04 1.146E-03 1.16E-03 200E+04 1.00

3450 329 52 50 266.4 316.4 3.00E+04 289.3E-6 684.9E-6 4.78E+05 0.06 1.046E-03 1.06E-03 3.00E+04 1.00

3450 329 52 50 279.8 329.8 4.00E+04 287.2E-6 627.8E-6 4.90E+05 0.08 9.819E-04 9.93E-04 4.00E+04 1.00

184

3450 329 52 50 290.7 340.7 5.00E+04 285.8E-6 586.7E-6 4.98E+05 0.10 9.337E-04 9.45E-04 5.00E+04 1.00

3450 329 62 50 203.6 253.6 1.00E+04 306.5E-6 955.5E-6 3.95E+05 0.03 1.338E-03 1.35E-03 1.00E+04 1.00

3450 329 62 50 233.4 283.4 2.00E+04 296.9E-6 774.5E-6 4.39E+05 0.05 1.148E-03 1.16E-03 2.00E+04 1.00

3450 329 62 50 252.0 302.0 3.00E+04 292.7E-6 684.9E-6 4.60E+05 0.07 1.047E-03 1.06E-03 3.00E+04 1.00

3450 329 62 50 265.7 315.7 4.00E+04 290.3E-6 627.8E-6 4.72E+05 0.08 9.807E-04 9.93E-04 4.00E+04 1.00

3450 329 62 50 275.9 325.9 5.00E+04 288.8E-6 586.7E-6 4.81E+05 0.10 9.348E-04 9.45E-04 5.00E+04 1.00

3450 329 72 50 191.4 241.4 1.00E+04 310.5E-6 955.5E-6 3.79E+05 0.03 1.338E-03 1.35E-03 1.00E+04 1.00

3450 329 72 50 221.5 271.5 2.00E+04 300.0E-6 774.5E-6 4.24E+05 0.05 1.145E-03 1.16E-03 2.00E+04 1.00

3450 329 72 50 239.9 289.9 3.00E+04 295.7E-6 684.9E-6 4.45E+05 0.07 1.047E-03 1.06E-03 3.00E+04 1.00

3450 329 72 50 252.6 302.6 4.00E+04 293.1E-6 627.8E-6 4.58E+05 0.09 9.818E-04 9.93E-04 4.00E+04 1.00

3450 329 72 50 263.2 313.2 5.00E+04 291.4E-6 586.7E-6 4.67E+05 0.11 9.333E-04 9.45E-04 5.00E+04 1.00

3450 329 82 50 180.5 230.5 1.00E+04 313.9E-6 955.5E-6 3.65E+05 0.03 1.337E-03 1.35E-03 1.00E+04 1.00

3450 329 82 50 210.2 260.2 2.00E+04 302.9E-6 774.5E-6 4.11E+05 0.05 1.145E-03 1.16E-03 2.00E+04 1.00

3450 329 82 50 228.1 278.1 3.00E+04 298.2E-6 684.9E-6 4.33E+05 0.07 1.046E-03 1.06E-03 3.00E+04 1.00

3450 329 82 50 241.0 291 4.00E+04 295.5E-6 627.8E-6 4.46E+05 0.09 9.813E-04 9.93E-04 4.00E+04 1.00

185

3450 329 82 50 251.4 301.4 5.00E+04 293.7E-6 586.7E-6 4.55E+05 0.11 9.331E-04 9.45E-04 5.00E+04 1.00

3450 329 93 50 169.0 219 1.00E+04 317.5E-6 955.5E-6 3.52E+05 0.03 1.338E-03 1.35E-03 1.00E+04 1.00

3450 329 93 50 198.2 248.2 2.00E+04 305.8E-6 774.5E-6 3.98E+05 0.05 1.147E-03 1.16E-03 2.00E+04 1.00

3450 329 93 50 216.3 266.3 3.00E+04 300.7E-6 684.9E-6 4.21E+05 0.07 1.046E-03 1.06E-03 3.00E+04 1.00

3450 329 93 50 229.2 279.2 4.00E+04 297.8E-6 627.8E-6 4.34E+05 0.09 981.2E-6 9.93E-04 4.00E+04 1.00

3450 329 93 50 239.0 289 5.00E+04 296.0E-6 586.7E-6 4.43E+05 0.11 9.352E-04 9.45E-04 5.00E+04 1.00

3450 329 103 50 159.2 209.2 1.00E+04 320.4E-6 955.5E-6 1.01E+06 0.01 1.339E-03 1.35E-03 1.00E+03 1.00

3450 329 103 50 188.8 238.8 2.00E+04 307.9E-6 774.5E-6 3.89E+05 0.05 1.146E-03 1.16E-03 2.00E+04 1.00

3450 329 103 50 206.6 256.6 3.00E+04 302.7E-6 684.9E-6 4.12E+05 0.07 1.046E-03 1.06E-03 3.00E+04 1.00

3450 329 103 50 219 269 4.00E+04 299.7E-6 627.8E-6 4.25E+05 0.09 982.4E-6 9.93E-04 4.00E+04 1.00

3450 329 103 50 229.2 279.2 5.00E+04 297.7E-6 586.7E-6 4.35E+05 0.11 9.341E-04 9.45E-04 5.00E+04 1.00

186

Table 4.1b: Light Traffic - Pavement Response Data (Ni = 1 x 104 – 5 x 104, T1 = 50mm)

Subgrade

Expected Traffic

(ESAL)

Pavement Thickness

(mm)

Horizontal Tensile

(Fatigue) Strain

(10-6

)

Vertical Compressive

(Rutting) Strain

(10-6

)

CBR

%

Modulus Surface

T1

Base

T2

Total

T

1 10 1.00E+04 50 313.9 363.9 266.2 1335.0

1 10 2.00E+04 50 348.4 398.4 263.0 1145.0

1 10 3.00E+04 50 369.4 419.4 262.0 1048.0

1 10 4.00E+04 50 385.6 435.6 261.5 981.40

1 10 5.00E+04 50 398.1 448.10 260.3 934.00

2 21 1.00E+04 50 275.2 325.2 280.7 1338.0

2 21 2.00E+04 50 308.0 358.0 275.3 1146.0

2 21 3.00E+04 50 328.2 378.2 273.2 1047.0

2 21 4.00E+04 50 343.3 393.3 272.0 981.00

2 21 5.00E+04 50 354.8 404.8 271.4 934.50

187

3 31 1.00E+04 50 252.0 302 289.4 1339.0

3 31 2.00E+04 50 284.0 334 282.5 1148.0

3 31 3.00E+04 50 303.6 353.6 279.8 1047.0

3 31 4.00E+04 50 328.1 368.1 278.2 980.80

3 31 5.00E+04 50 328.1 378.1 277.4 938.70

4 41 1.00E+04 50 233.9 283.9 296.0 1338.0

4 41 2.00E+04 50 265.4 315.4 288.0 1144.0

4 41 3.00E+04 50 284.2 334.2 284.8 1046.0

4 41 4.00E+04 50 297.9 347.9 283.0 982.40

4 41 5.00E+04 50 309.3 359.3 281.8 933.20

5 52 1.00E+04 50 217.1 267.1 301.9 1337.0

5 52 2.00E+04 50 247.6 297.6 293.0 1146.0

5 52 3.00E+04 50 266.4 316.4 289.3 1046.0

5 52 4.00E+04 50 279.8 329.8 287.2 981.90

5 52 5.00E+04 50 290.7 340.7 285.8 933.70

188

6 62 1.00E+04 50 203.6 253.6 306.5 1338.0

6 62 2.00E+04 50 233.4 283.4 296.9 1148.0

6 62 3.00E+04 50 252 302 292.7 1047.0

6 62 4.00E+04 50 265.7 315.7 290.3 980.70

6 62 5.00E+04 50 275.9 325.9 288.8 934.80

7 72 1.00E+04 50 191.4 241.4 310.5 1338.0

7 72 2.00E+04 50 221.5 271.5 300.0 1145.0

7 72 3.00E+04 50 239.9 289.9 295.7 1047.0

7 72 4.00E+04 50 252.6 302.6 293.1 981.80

7 72 5.00E+04 50 263.2 313.2 291.4 933.30

8 82 1.00E+04 50 180.5 230.5 313.9 1337.0

8 82 2.00E+04 50 210.2 260.2 302.9 1145.0

8 82 3.00E+04 50 228.1 278.1 298.2 1046.0

8 82 4.00E+04 50 241 291 295.5 981.30

189

8 82 5.00E+04 50 251.4 301.4 293.7 933.10

9 93 1.00E+04 50 169 219 317.5 1338.0

9 93 2.00E+04 50 198.2 248.2 305.8 1147.0

9 93 3.00E+04 50 216.3 266.3 300.7 1046.0

9 93 4.00E+04 50 229.2 279.2 297.8 981.20

9 93 5.00E+04 50 239 289.0 296.0 935.20

103 103 1.00E+04 50 159.2 209.2 320.4 1339.0

103 103 2.00E+04 50 188.8 238.8 307.9 1146.0

103 103 3.00E+04 50 206.6 256.6 302.7 1046.0

103 103 4.00E+04 50 219 269 299.7 982.40

103 103 5.00E+04 50 229.2 279.2 297.7 934.10

Table 4.1c: Light Traffic - Pavement Response Regression Equations (Ni = 1 x 104 – 5 x 104, T1 = 50mm)

A.C

Modulus

Base

Modulus

Subgrade Expected Traffic –

Pavement Thickness

Fatigue Criterion

Rutting Criterion

CBR Modulus

190

(MPa)

E1

(MPa)

(MPa)

E2

(MPa)

(%)

(MPa)

E3

(MPa)

Relationship Tensile Strain - Pavement

Thickness Relationship

(10-6)

Compressive Strain – Pavement


(10-6)

3450 329 1 10 T = 110.68(Ni)0.129

R² = 1

εt = -26.85ln(T) + 424.29

R² = 0.975

εc = -1930.98ln(T) + 12715.12

R² = 0.998

3450 329 2 21 T = 92.91(Ni)0.136

R² = 1

εt = -42.86ln(T ) + 528.09

R² = 0.974

εc = -1846.77ln(T) + 12014.21

R² = 0.998

3450 329 3 31 T = 83.29(Ni)0.140

R² = 0.999

εt = -53.71ln(T) + 595.49

R² = 0.980

εc = -1786.67ln(T) + 11536.74

R² = 0.999

3450 329 4 41 T = 74.342(Ni)0.146

R² = 1

εt = -60.73ln(T) + 638.39

R² = 0.982

εc = -1723.29ln(T) + 11066.66

R² = 0.998

3450 329 5 52 T = 66.65(Ni)0.151

R² = 1

εt = -66.50ln(T) + 672.79

R² = 0.985

εc = -1661.24ln(T) + 10614.46

R² = 0.999

3450 329 6 62 T = 60.35(Ni)0.156

R² = 1

εt = -70.92ln(T) + 698.39

R² = 0.987

εc = -1610.94ln(T) + 10250.97

R² = 0.999

191

3450 329 7 72 T = 54.88(Ni)0.161

R² = 0.999

εt = -73.73ln(T) + 714.29

R² = 0.988

εc = -1556.52ln(T) + 9873.81

R² = 0.999

3450 329 8 82 T = 50.12(Ni)0.166

R² = 0.999

εt = -75.83ln(T + 725.69

R² = 0.989

εc = -1509.57ln(T) + 9545.52

R² = 0.999

3450 329 9 93 T = 44.99(Ni)0.172

R² = 0.999

εt = -78.01ln(T) + 737.09

R² = 0.989

εc = -1454.94ln(T) + 9174.98

R² = 0.999

3450 329 10 103 T = 40.66(Ni)0.178

R² = 0.999

εt = -79.17ln(T) + 742.61

R² = 0.989

εc = -1406.04ln(T) + 8848.93

R² = 1

Table 4.2a: Medium Traffic – Pavement Response Analysis

A.C

Mod.

Base

Mod.

Sub

Mod.


Repetitions

Ni


A.C

Surface

T1

(mm)

Stabilized

Base

T2

(mm)

Total

T

(mm)

E1

(MPa)

E2

(MPa)

E3

(MPa) Horizontal

Tensile

Strain

Allowable

Tensile

Strain

No. of

Repetition

to Failure

D.F

Vertical

Compressive

Strain

Allowable

Compressive

Strain

No. of

Repetition

to Failure

D.F

192

3450 329 10 75 356.7 431.7 5.00E+04 282.6E-6 586.7E-6 5.16E+05 0.10 9.339E-04 9.45E-04 5.00E+04 1.00

3450 329 10 75 397.9 472.9 1.00E+05 277.7E-6 475.6E-6 5.47E+05 0.18 8.014E-04 8.09E-04 1.00E+05 1.00

3450 329 10 75 424.5 499.5 1.50E+05 275.6E-6 420.6E-6 5.61E+05 0.27 7.298E-04 7.40E-04 1.50E+05 1.00

3450 329 10 75 443.3 518.3 2.00E+05 274.4E-6 385.5E-6 5.69E+05 0.35 6.847E-04 6.94E-04 2.00E+05 1.00

3450 329 10 75 457.7 532.7 2.50E+04 273.7E-6 360.3E-6 5.74E+05 0.44 6.528E-04 6.60E-04 2.50E+05 1.00

3450 329 21 75 310.5 385.5 5.00E+04 292.2E-6 586.7E-6 4.63E+05 0.11 9.344E-04 9.45E-04 5.00E+04 1.00

3450 329 21 75 350.4 425.4 1.00E+05 285.7E-6 475.6E-6 4.98E+05 0.20 7.991E-04 8.09E-04 1.00E+05 1.00

3450 329 21 75 374.3 449.3 1.50E+05 283.0E-6 420.6E-6 5.14E+05 0.29 7.311E-04 7.40E-04 1.50E+05 1.00

3450 329 21 75 392.1 467.1 2.00E+05 281.3E-6 385.5E-6 5.24E+05 0.38 6.856E-04 6.94E-04 2.00E+05 1.00

3450 329 21 75 406.6 481.6 2.50E+05 280.2E-6 360.3E-6 5.31E+05 0.47 6.515E-04 6.60E-04 2.50E+05 1.00

3450 329 31 75 283.2 358.2 5.00E+04 297.7E-6 586.7E-6 4.35E+05 0.11 9.330E-04 9.45E-04 5.00E+04 1.00

3450 329 31 75 321.3 396.3 1.00E+05 290.4E-6 475.6E-6 4.72E+05 0.21 7.999E-04 8.09E-04 1.00E+05 1.00

3450 329 31 75 344.6 419.6 1.50E+05 287.2E-6 420.6E-6 4.90E+05 0.31 7.312E-04 7.40E-04 1.50E+05 1.00

3450 329 31 75 362.2 437.2 2.00E+05 285.2E-6 385.5E-6 5.01E+05 0.40 6.848E-04 6.94E-04 2.00E+05 1.00

3450 329 31 75 375.5 450.5 2.50E+05 284.0E-6 360.3E-6 5.08E+05 0.49 6.524E-04 6.60E-04 2.50E+05 1.00

193

3450 329 41 75 261.2 336.2 5.00E+04 301.8E-6 586.7E-6 4.16E+05 0.12 9.336E-04 9.45E-04 5.00E+04 1.00

3450 329 41 75 298.2 373.2 1.00E+05 293.9E-6 475.6E-6 4.54E+05 0.22 8.011E-04 8.09E-04 1.00E+05 1.00

3450 329 41 75 321.7 396.7 1.50E+05 290.3E-6 420.6E-6 4.73E+05 0.32 7.301E-04 7.40E-04 1.50E+05 1.00

3450 329 41 75 338.1 413.1 2.00E+05 288.2E-6 385.5E-6 4.84E+05 0.41 6.856E-04 6.94E-04 2.00E+05 1.00

3450 329 41 75 351.6 426.6 2.50E+04 286.8E-6 360.3E-6 4.92E+05 0.51 6.518E-04 6.60E-04 2.50E+05 1.00

3450 329 52 75 241 316 5.00E+04 305.5E-6 586.7E-6 4.00E+05 0.13 9.339E-04 9.45E-04 5.00E+04 1.00

3450 329 52 75 277.7 352.7 1.00E+05 296.8E-6 475.6E-6 4.39E+05 0.23 7.999E-04 8.09E-04 1.00E+05 1.00

3450 329 52 75 300 375 1.50E+05 293.0E-6 420.6E-6 4.58E+05 0.33 7.310E-04 7.40E-04 1.50E+05 1.00

3450 329 52 75 316.3 391.3 2.00E+05 290.8E-6 385.5E-6 4.70E+05 0.43 6.857E-04 6.94E-04 1.99E+05 1.00

3450 329 52 75 329.7 404.7 2.50E+05 289.2E-6 360.3E-6 4.79E+05 0.52 6.513E-04 6.60E-04 2.50E+05 1.00

3450 329 62 75 225.2 300.2 5.00E+04 308.1E-6 586.7E-6 3.88E+05 0.13 9.335E-04 9.45E-04 5.00E+04 1.00

3450 329 62 75 261.4 336.4 1.00E+05 299.0E-6 475.6E-6 4.29E+05 0.23 7.994E-04 8.09E-04 1.00E+05 1.00

194

3450 329 62 75 283.3 358.3 1.50E+05 295.0E-6 420.6E-6 4.48E+05 0.33 7.306E-04 7.40E-04 1.50E+05 1.00

3450 329 62 75 299.2 374.2 2.00E+05 292.6E-6 385.5E-6 4.60E+05 0.43 6.856E-04 6.94E-04 2.00E+05 1.00

3450 329 62 75 312.1 387.1 2.50E+05 291.0E-6 360.3E-6 4.69E+05 0.53 6.518E-04 6.60E-04 2.50E+05 1.00

3450 329 72 75 210.8 285.8 5.00E+04 310.4E-6 586.7E-6 3.79E+05 0.13 9.340E-04 9.45E-04 5.00E+04 1.00

3450 329 72 75 246.7 321.7 1.00E+05 300.9E-6 475.6E-6 4.20E+05 0.24 7.993E-04 8.09E-04 1.00E+05 1.00

3450 329 72 75 268.4 343.4 1.50E+05 296.7E-6 420.6E-6 4.40E+05 0.34 7.301E-04 7.40E-04 1.50E+05 1.00

3450 329 72 75 284.1 359.1 2.00E+05 294.2E-6 385.5E-6 4.52E+05 0.44 6.850E-04 6.94E-04 2.00E+05 1.00

3450 329 72 75 296.4 371.4 2.50E+05 292.5E-6 360.3E-6 4.61E+05 0.54 6.523E-04 6.60E-04 2.50E+05 1.00

3450 329 82 75 197.8 272.8 5.00E+04 312.4E-6 586.7E-6 3.71E+05 0.13 9.340E-04 9.45E-04 5.00E+04 1.00

3450 329 82 75 233.3 308.3 1.00E+05 302.5E-6 475.6E-6 4.13E+05 0.24 7.993E-04 8.09E-04 1.00E+05 1.00

3450 329 82 75 254.3 329.3 1.50E+05 298.2E-6 420.6E-6 4.33E+05 0.35 7.315E-04 7.40E-04 1.50E+05 1.00

3450 329 82 75 270.3 345.3 2.00E+05 295.5E-6 385.5E-6 4.46E+05 0.45 6.848E-04 6.94E-04 2.00E+05 1.00

3450 329 82 75 282.6 357.6 2.50E+05 293.8E-6 360.3E-6 4.55E+05 0.55 6.516E-04 6.60E-04 2.50E+05 1.00

3450 329 93 75 184.8 259.8 5.00E+04 314.1E-6 586.7E-6 3.65E+05 0.14 9.333E-04 9.45E-04 5.00E+04 1.00

195

3450 329 93 75 219.4 294.4 1.00E+05 304.0E-6 475.6E-6 4.06E+05 0.25 8.008E-04 8.09E-04 1.00E+05 1.00

3450 329 93 75 240.9 315.9 1.50E+05 299.4E-6 420.6E-6 4.27E+05 0.35 7.304E-04 7.40E-04 1.50E+05 1.00

3450 329 93 75 256 331.0 2.00E+05 296.8E-6 385.5E-6 4.39E+05 0.46 685.7E-6 6.94E-04 2.00E+05 1.00

3450 329 93 75 268.3 343.3 2.50E+05 295.0E-6 360.3E-6 4.49E+05 0.56 6.520E-04 6.60E-04 2.50E+05 1.00

3450 329 103 75 173.7 248.7 5.00E+04 315.5E-6 586.7E-6 3.59E+05 0.14 9.333E-04 9.45E-04 5.00E+04 1.00

3450 329 103 75 208.5 283.5 1.00E+05 305.0E-6 475.6E-6 4.02E+05 0.25 7.992E-04 8.09E-04 1.00E+05 1.00

3450 329 103 75 229.4 304.4 1.50E+05 300.4E-6 420.6E-6 4.22E+05 0.36 7.302E-04 7.40E-04 1.50E+05 1.00

3450 329 103 75 244.6 319.6 2.00E+05 297.7E-6 385.5E-6 4.35E+05 0.46 684.8E-6 6.94E-04 2.00E+05 1.00

3450 329 103 75 256.6 331.6 2.50E+05 295.8E-6 360.3E-6 4.44E+05 0.56 6.519E-04 6.60E-04 2.50E+05 1.0

Table 4.2b: Medium Traffic - Pavement Response Data (Ni = 5 x 104 – 2.5 x 105, T1 = 75mm)

Subgrade

Expected Traffic

(ESAL)

Pavement Thickness

(mm)

Horizontal Tensile Strain

(Fatigue)


(Rutting) Strain

196

CBR

%

Modulus Surface

T1

Base

T2

Total

T

(10-6)

(10-6)

1 10 5.00E+04 75 356.7 431.7 282.6 933.9

1 10 1.00E+05 75 397.9 472.9 277.7 801.4

1 10 1.50E+05 75 424.5 499.5 275.6 729.8

1 10 2.00E+05 75 443.3 518.3 274.4 684.7

1 10 2.50E+05 75 457.7 532.7 273.7 652.8

2 21 5.00E+04 75 310.5 385.5 292.2 934.4

2 21 1.00E+05 75 350.4 425.4 285.7 799.1

2 21 1.50E+05 75 374.3 449.3 283.0 731.1

2 21 2.00E+05 75 392.1 467.1 281.3 685.6

2 21 2.50E+05 75 406.6 481.6 280.2 651.5

3 31 5.00E+04 75 283.2 358.2 297.7 933.0

3 31 1.00E+05 75 321.3 396.3 290.4 799.9

3 31 1.50E+05 75 344.6 419.6 287.2 731.2

197

3 31 2.00E+05 75 362.2 437.2 285.2 684.8

3 31 2.50E+05 75 375.5 450.5 284.0 652.4

4 41 5.00E+04 75 261.2 336.2 301.8 933.6

4 41 1.00E+05 75 298.2 373.2 293.9 801.1

4 41 1.50E+05 75 321.7 396.7 290.3 730.1

4 41 2.00E+05 75 338.1 413.1 288.2 685.6

4 41 2.50E+05 75 351.6 426.6 286.8 651.8

5 52 5.00E+04 75 241.0 316.0 305.5 933.9

5 52 1.00E+05 75 277.7 352.7 296.8 799.9

5 52 1.50E+05 75 300.0 375.0 293.0 731.0

5 52 2.00E+05 75 316.3 391.3 290.8 685.7

5 52 2.50E+05 75 329.7 404.7 289.2 651.3

6 62 5.00E+04 75 225.2 300.2 308.1 933.5

6 62 1.00E+05 75 261.4 336.4 299.0 799.4

198

6 62 1.50E+05 75 283.3 358.3 295.0 730.6

6 62 2.00E+05 75 299.2 374.2 292.6 685.6

6 62 2.50E+05 75 312.1 387.1 291.0 651.8

7 72 5.00E+04 75 210.8 285.8 310.4 934.0

7 72 1.00E+05 75 246.7 321.7 300.9 799.3

7 72 1.50E+05 75 268.4 343.4 296.7 730.1

7 72 2.00E+05 75 284.1 359.1 294.2 685.0

7 72 2.50E+05 75 296.4 371.4 292.5 652.3

8 82 5.00E+04 75 197.8 272.8 312.4 934.0

8 82 1.00E+05 75 233.3 308.3 302.5 799.3

8 82 1.50E+05 75 254.3 329.3 298.2 731.5

8 82 2.00E+05 75 270.3 345.3 295.5 684.8

8 82 2.50E+05 75 282.6 357.6 293.8 651.6

9 93 5.00E+04 75 184.8 259.8 314.1 933.3

199

9 93 1.00E+05 75 219.4 294.4 304.0 800.8

9 93 1.50E+05 75 240.9 315.9 299.4 730.4

9 93 2.00E+05 75 256 331.0 296.8 685.7

9 93 2.50E+05 75 268.3 343.3 295.0 652.0

103 103 5.00E+04 75 173.7 248.7 315.5 933.3

103 103 1.00E+05 75 208.5 283.5 305.0 799.2

103 103 1.50E+05 75 229.4 304.4 300.4 730.2

103 103 2.00E+05 75 244.6 319.6 297.7 684.8

103 103 2.50E+05 75 256.6 331.6 295.8 651.9

Table 4.2c: Medium Traffic - Pavement Response Regression Equations (Ni = 5 x 104 – 2.5 x 105, T1 = 75mm)

A.C

Modulus

(MPa)

Base

Modulus

(MPa)


Pavement Thickness

Relationship

Fatigue Criterion

Rutting Criterion

CBR

(%)

Modulus

(MPa)

Tensile Strain - Pavement


Compressive Strain –

Pavement Thickness

Relationship

200

E1

(MPa)

E2

(MPa)

E3

(MPa)

(10-6) (10-6)

3450 329 1 10 T = 104.62(Ni)0.131

R² = 1

εt = -42.55ln(T) + 540.39

R² = 0.983

εc = -1339.96ln(T) + 9059.89

R² = 0.998

3450 329 2 21 T = 86.87(Ni)0.138

R² = 1

εt = -54.22ln(T) + 614.60

R² = 0.987

εc = -1274.29ln(T) + 8517.94

R² = 0.998

3450 329 3 31 T = 76.76(Ni)0.142

R² = 1

εt = -60.12ln(T) + 650.75

R² = 0.989

εc = -1226.63ln(T) + 8142.97

R² = 0.998

3450 329 4 41 T = 67.95(Ni)0.148

R² = 1

εt = -63.35ln(T) + 669.84

R² = 0.990

εc = -1186.13ln(T) + 7830.42

R² = 0.999

3450 329 5 52 T = 60.32(Ni)0.153

R² = 1

εt = -66.19ln(T) + 685.88

R² = 0.989

εc = -1145.03ln(T) + 7520.87

R² = 0.999

3450 329 6 62 T = 54.78(Ni)0.157

R² = 1

εt = -67.70ln(T) + 693.70

R² = 0.991

εc = -1110.62ln(T) + 7265.71

R² = 0.999

201

3450 329 7 72 T = 49.48(Ni)0.162

R² = 0.999

εt = -68.65ln(T) + 698.09

R² = 0.992

εc = -1077.81ln(T) + 7026.26

R² = 0.999

3450 329 8 82 T = 44.62(Ni)0.168

R² = 0.999

εt = -69.17ln(T) + 699.78

R² = 0.991

εc = -1045.53ln(T) + 6795.21

R² = 0.999

3450 329 9 93 T = 40.22(Ni)0.173

R² = 0.999

εt = -68.96ln(T) + 696.90

R² = 0.991

εc = -1011.61ln(T) + 6555.18

R² = 0.999

3450 329 10 103 T = 36.38(Ni)0.178

R² = 0.999

εt = -68.79ln(T) + 694.36

R² = 0.992

εc = -980.73ln(T) + 6340.81

R² = 0.999

Table 4.3a: Heavy Traffic – Pavement Response Analysis

A.C

Mod.

Base

Mod.

Sub

Mod.


Repetitions

Ni


A.C

Surface

T1

(mm)

Stabilized

Base

T2

(mm)

Total

T

(mm)

E1

(MPa)

E2

(MPa)

E3

(MPa) Horizontal

Tensile

Strain

Allowable

Tensile

Strain

No. of

Repetition

to Failure

D.F

Vertical

Compressive

Strain

Allowable

Compressive

Strain

No. of

Repetition

to Failure

D.F

3450 329 10 100 414.4 514.4 2.50E+05 249.9E-6 360.3E-6 7.74E+05 0.32 6.518E-04 6.60E-04 2.50E+05 1.00

202

3450 329 10 100 437.8 537.8 3.50E+05 247.6E-6 325.4E-6 7.98E+05 0.44 6.054E-04 6.12E-04 3.50E+05 1.00

3450 329 10 100 456.2 556.2 4.50E+05 246.2E-6 301.5E-6 8.13E+05 0.55 5.722E-04 5.79E-04 4.50E+05 1.00

3450 329 10 100 471.2 571.2 5.50E+05 245.1E-6 283.7E-6 8.25E+05 0.67 5.471E-04 5.53E-04 5.50E+05 1.00

3450 329 10 100 484.2 584.2 6.50E+05 244.3E-6 269.7E-6 8.34E+05 0.78 5.266E-04 5.33E-04 6.51E+05 1.00

3450 329 10 100 495.0 595.0 7.50E+05 243.7E-6 258.3E-6 8.41E+05 0.89 5.103E-04 5.17E-04 7.50E+05 1.00

3450 329 21 100 359.2 459.2 2.50E+05 256.3E-6 360.3E-6 7.12E+05 0.35 6.517E-04 6.60E-04 2.50E+05 1.00

3450 329 21 100 382 482 3.50E+05 253.5E-6 325.4E-6 7.38E+05 0.47 6.042E-04 6.12E-04 3.50E+05 1.00

3450 329 21 100 399.3 499.3 4.50E+05 251.7E-6 301.5E-6 7.56E+05 0.60 5.713E-04 5.79E-04 4.50E+05 1.00

3450 329 21 100 413.3 513.3 5.50E+05 250.4E-6 283.7E-6 7.69E+05 0.72 5.465E-04 5.53E-04 5.51E+05 1.00

3450 329 21 100 425.5 525.5 6.50E+05 249.4E-6 269.7E-6 7.79E+05 0.83 5.261E-04 5.33E-04 6.53E+05 1.00

3450 329 21 100 435.5 535.5 7.50E+05 248.6E-6 258.3E-6 7.87E+05 0.96 5.101E-04 5.17E-04 7.50E+05 1.00

3450 329 31 100 326.1 426.1 2.50E+05 260.0E-6 360.3E-6 6.79E+05 0.37 6.519E-04 6.60E-04 2.50E+05 1.00

3450 329 31 100 347.9 447.9 3.50E+05 256.9E-6 325.4E-6 7.07E+05 0.50 6.049E-04 6.12E-04 3.50E+05 1.00

3450 329 31 100 364.8 464.8 4.50E+05 254.6E-6 301.5E-6 7.28E+05 0.62 5.717E-04 5.79E-04 4.50E+05 1.00

3450 329 31 100 378.5 478.5 5.50E+05 253.4E-6 283.7E-6 7.40E+05 0.74 5.466E-04 5.53E-04 5.50E+05 1.00

203

3450 329 31 100 390.3 490.3 6.50E+05 252.2E-6 269.7E-6 7.50E+05 0.87 5.262E-04 5.33E-04 6.50E+05 1.00

3450 329 31 100 400 500 7.50E+05 251.4E-6 258.3E-6 7.59E+05 0.99 5.102E-04 5.17E-04 7.50E+05 1.00

3450 329 41 100 300 400 2.50E+05 262.7E-6 360.3E-6 6.57E+05 0.38 6.522E-04 6.60E-04 2.50E+05 1.00

3450 329 41 100 321.7 421.7 3.50E+05 259.3E-6 325.4E-6 6.86E+05 0.51 6.043E-04 6.12E-04 3.50E+05 1.00

3450 329 41 100 337.9 437.9 4.50E+05 257.1E-6 301.5E-6 7.05E+05 0.64 5.717E-04 5.79E-04 4.50E+05 1.00

3450 329 41 100 351.5 451.5 5.50E+05 255.5E-6 283.7E-6 7.19E+05 0.76 5.461E-04 5.53E-04 5.50E+05 1.00

3450 329 41 100 362.6 462.6 6.50E+05 254.4E-6 269.7E-6 7.30E+05 0.89 5.264E-04 5.33E-04 6.50E+05 1.00

3450 329 41 100 372.5 472.5 7.50E+05 253.4E-6 258.3E-6 7.59E+05 0.99 5.097E-04 5.17E-04 7.50E+05 1.00

3450 329 52 100 276.3 376.3 2.50E+05 264.9E-6 360.3E-6 6.39E+05 0.39 6.520E-04 6.60E-04 2.50E+05 1.00

3450 329 52 100 297.3 397.3 3.50E+05 261.4E-6 325.4E-6 6.68E+05 0.52 6.046E-04 6.12E-04 3.50E+05 1.00

3450 329 52 100 313.2 413.2 4.50E+05 259.1E-6 301.5E-6 6.87E+05 0.65 5.718E-04 5.79E-04 4.50E+05 1.00

3450 329 52 100 326.2 426.2 5.50E+05 257.4E-6 283.7E-6 7.02E+05 0.78 5.468E-04 5.53E-04 5.50E+05 1.00

3450 329 52 100 337.2 437.2 6.50E+05 256.2E-6 269.7E-6 7.13E+05 0.91 5.268E-04 5.33E-04 6.50E+05 1.00

3450 329 52 100 346.8 446.8 7.50E+05 255.1E-6 258.3E-6 7.55E+05 0.99 5.101E-04 5.17E-04 7.50E+05 1.00

204

3450 329 62 100 257.9 357.9 2.50E+05 266.5E-6 360.3E-6 6.27E+05 0.40 6.512E-04 6.60E-04 2.50E+05 1.00

3450 329 62 100 278.3 378.3 3.50E+05 262.8E-6 325.4E-6 6.55E+05 0.53 6.045E-04 6.12E-04 3.50E+05 1.00

3450 329 62 100 294.1 394.1 4.50E+05 260.4E-6 301.5E-6 6.75E+05 0.67 5.713E-04 5.79E-04 4.50E+05 1.00

3450 329 62 100 306.7 406.7 5.50E+05 258.8E-6 283.7E-6 6.90E+05 0.80 5.466E-04 5.53E-04 5.50E+05 1.00

3450 329 62 100 319.3 419.3 6.50E+05 257.2E-6 269.7E-6 7.04E+05 0.92 5.234E-04 5.33E-04 6.60E+05 1.00

3450 329 62 100 326.5 426.5 7.50E+05 256.4E-6 258.3E-6 7.11E+05 0.98 5.107E-04 5.17E-04 7.50E+05 1.00

3450 329 72 100 241 341 2.50E+05 267.8E-6 360.3E-6 6.16E+05 0.41 6.518E-04 6.60E-04 2.50E+05 1.00

3450 329 72 100 261.4 361.4 3.50E+05 264.0E-6 325.4E-6 6.46E+05 0.54 6.043E-04 6.12E-04 3.50E+05 1.00

3450 329 72 100 276.7 376.7 4.50E+05 261.6E-6 301.5E-6 6.66E+05 0.68 5.716E-04 5.79E-04 4.50E+05 1.00

3450 329 72 100 289.1 389.1 5.50E+05 259.9E-6 283.7E-6 6.81E+05 0.81 5.469E-04 5.53E-04 5.50E+05 1.00

3450 329 72 100 299.4 399.4 6.50E+05 258.5E-6 269.7E-6 6.92E+05 0.94 5.275E-04 5.33E-04 6.50E+05 1.00

3450 329 72 100 309.3 409.3 7.50E+05 257.4E-6 258.3E-6 7.21E+05 0.96 5.096E-04 5.17E-04 7.50E+05 1.00

205

3450 329 82 100 225.9 325.9 2.50E+05 268.9E-6 360.3E-6 6.08E+05 0.41 6.517E-04 6.60E-04 2.50E+05 1.00

3450 329 82 100 245.8 345.8 3.50E+05 265.0E-6 325.4E-6 6.38E+05 0.55 6.047E-04 6.12E-04 3.50E+05 1.00

3450 329 82 100 261.2 361.2 4.50E+05 262.5E-6 301.5E-6 6.58E+05 0.68 5.714E-04 5.79E-04 4.50E+05 1.00

3450 329 82 100 273.4 373.4 5.50E+05 260.7E-6 283.7E-6 6.73E+05 0.82 5.467E-04 5.53E-04 5.50E+05 1.00

3450 329 82 100 284.1 384.1 6.50E+05 259.3E-6 269.7E-6 6.85E+05 0.95 5.262E-04 5.33E-04 6.50E+05 1.00

3450 329 82 100 292.7 392.7 7.50E+05 258.3E-6 258.3E-6 7.50E+05 1.00 5.105E-04 5.17E-04 7.50E+05 1.00

3450 329 93 100 210.7 310.7 2.50E+05 269.8E-6 360.3E-6 6.01E+05 0.42 6.517E-04 6.60E-04 2.50E+05 1.00

3450 329 93 100 230.6 330.6 3.50E+05 265.9E-6 325.4E-6 6.31E+05 0.55 6.042E-04 6.12E-04 3.50E+05 1.00

3450 329 93 100 245.5 345.5 4.50E+05 263.3E-6 301.5E-6 6.51E+05 0.69 5.716E-04 5.79E-04 4.50E+05 1.00

3450 329 93 100 257.7 357.7 5.50E+05 261.5E-6 283.7E-6 6.67E+05 0.82 546.4E-6 5.53E-04 5.50E+05 1.00

3450 329 93 100 268 368 6.50E+05 260.1E-6 269.7E-6 6.79E+05 0.95 526.4E-6 5.33E-04 6.50E+05 1.00

3450 329 93 100 276.9 376.9 7.50E+05 259.0E-6 258.3E-6 7.50E+05 1.00 5.099E-04 5.17E-04 7.50E+05 1.00

3450 329 103 100 197.8 297.8 2.50E+05 270.5E-6 360.3E-6 5.96E+05 0.42 6.522E-04 6.60E-04 2.50E+05 1.00

3450 329 103 100 217.5 317.5 3.50E+05 266.5E-6 325.4E-6 6.26E+05 0.56 6.046E-04 6.12E-04 3.50E+05 1.00

206

3450 329 103 100 232.3 332.3 4.50E+05 263.9E-6 301.5E-6 6.47E+05 0.70 5.717E-04 5.79E-04 4.50E+05 1.00

3450 329 103 100 244.2 344.2 5.50E+05 262.1E-6 283.7E-6 6.62E+05 0.83 546.9E-6 5.53E-04 5.50E+05 1.00

3450 329 103 100 254.3 354.3 6.50E+05 260.7E-6 269.7E-6 6.74E+05 0.96 527.0E-6 5.33E-04 6.50E+05 1.00

3450 329 103 100 263.7 363.7 7.50E+05 259.6E-6 258.3E-6 7.54E+05 0.99 5.094E-04 5.17E-04 7.50E+05 1.00

Table 4.3b: Heavy Traffic - Pavement Response Data (Ni = 2.5 x 105 – 7.5 x 105, T1 = 100mm)

Subgrade

Expected Traffic

(ESAL)

Pavement Thickness

(mm)

Horizontal Tensile

(Fatigue) Strain

(10-6)


(Rutting) Strain

(10-6)

CBR

%

Modulus Surface

T1

Base

T2

Total

T

1 10 2.50E+05 100 414.4 514.4 249.9 651.8

1 10 3.50E+05 100 437.8 537.8 247.6 605.4

1 10 4.50E+05 100 456.2 556.2 246.2 572.2

1 10 5.50E+05 100 471.2 571.2 245.1 547.1

1 10 6.50E+05 100 484.2 584.2 244.3 526.6

1 10 7.50E+05 100 495.0 595.0 243.7 510.3

207

2 21 2.50E+05 100 359.2 459.2 256.3 651.7

2 21 3.50E+05 100 382 482 253.5 604.2

2 21 4.50E+05 100 399.3 499.3 251.7 571.3

2 21 5.50E+05 100 413.3 513.3 250.4 546.5

2 21 6.50E+05 100 425.5 525.5 249.4 526.1

2 21 7.50E+05 100 435.5 535.5 248.6 510.1

3 31 2.50E+05 100 326.1 426.1 260.0 651.9

3 31 3.50E+05 100 347.9 447.9 256.9 604.9

3 31 4.50E+05 100 364.8 464.8 254.6 571.7

3 31 5.50E+05 100 378.5 478.5 253.4 546.6

3 31 6.50E+05 100 390.3 490.3 252.2 526.2

3 31 7.50E+05 100 400 500.0 251.4 510.2

4 41 2.50E+05 100 300 400.0 262.7 652.2

4 41 3.50E+05 100 321.7 421.7 259.3 604.3

4 41 4.50E+05 100 337.9 437.9 257.1 571.7

208

4 41 5.50E+05 100 351.5 451.5 255.5 546.1

4 41 6.50E+05 100 362.6 462.6 254.4 526.4

4 41 7.50E+05 100 372.5 472.5 253.4 509.7

5 52 2.50E+05 100 276.3 376.3 264.9 652.0

5 52 3.50E+05 100 297.3 397.3 261.4 604.6

5 52 4.50E+05 100 313.2 413.2 259.1 571.8

5 52 5.50E+05 100 326.2 426.2 257.4 546.8

5 52 6.50E+05 100 337.2 437.2 256.2 526.8

5 52 7.50E+05 100 346.8 446.8 255.1 510.1

6 62 2.50E+05 100 257.9 357.9 266.5 651.2

6 62 3.50E+05 100 278.3 378.3 262.8 604.5

6 62 4.50E+05 100 294.1 394.1 260.4 571.3

6 62 5.50E+05 100 306.7 406.7 258.8 546.6

6 62 6.50E+05 100 319.3 419.3 257.2 523.4

6 62 7.50E+05 100 326.5 426.5 256.4 510.7

209

7 72 2.50E+05 100 241 341.0 267.8 651.8

7 72 3.50E+05 100 261.4 361.4 264.0 604.3

7 72 4.50E+05 100 276.7 376.7 261.6 571.6

7 72 5.50E+05 100 289.1 389.1 259.9 546.9

7 72 6.50E+05 100 299.4 399.4 258.5 527.5

7 72 7.50E+05 100 309.3 409.3 257.4 509.6

8 82 2.50E+05 100 225.9 325.9 268.9 651.7

8 82 3.50E+05 100 245.8 345.8 265.0 604.7

8 82 4.50E+05 100 261.2 361.2 262.5 571.4

8 82 5.50E+05 100 273.4 373.4 260.7 546.7

8 82 6.50E+05 100 284.1 384.1 259.3 526.2

8 82 7.50E+05 100 292.7 392.7 258.3 510.5

9 93 2.50E+05 100 210.7 310.7 269.8 651.7

210

9 93 3.50E+05 100 230.6 330.6 265.9 604.2

9 93 4.50E+05 100 245.5 345.5 263.3 571.6

9 93 5.50E+05 100 257.7 357.7 261.5 546.4

9 93 6.50E+05 100 268 368 260.1 526.4

9 93 7.50E+05 100 276.9 376.9 259.0 509.9

103 103 2.50E+05 100 197.8 297.8 270.5 652.2

103 103 3.50E+05 100 217.5 317.5 266.5 604.6

103 103 4.50E+05 100 232.3 332.3 263.9 571.7

103 103 5.50E+05 100 244.2 344.2 262.1 546.9

103 103 6.50E+05 100 254.3 354.3 260.7 527.0

103 103 7.50E+05 100 263.7 363.7 259.6 509.4

Table 4.3c: Heavy Traffic - Pavement Response Regression Equations (Ni = 2.5 x 105 – 7.5 x 105, T1 = 100cmm)

A.C

Modulus

(MPa)

Base

Modulus

(MPa)


Pavement Thickness

Relationship

Fatigue Criterion

Rutting Criterion

CBR

(%)

Modulus

(MPa) Tensile Strain - Pavement Compressive Strain –

211

E1

(MPa)

E2

(MPa)

E3

(MPa)


(10-6)

Pavement Thickness

Relationship

(10-6)

3450 329 1 10 T = 98.72(Ni)0.133

R² = 1

εt = -42.42ln(T) + 514.40

R² = 0.994

εc = -971.06ln(T) + 6712.19

R² = 0.999

3450 329 2 21 T = 80.77(Ni)0.140

R² = 1

εt = -49.90ln(T) + 561.97

R² = 0.996

εc = -920.61ln(T) + 6292.88

R² = 0.999

3450 329 3 31 T = 69.64(Ni)0.146

R² = 1

εt = -53.73ln(T) + 585.07

R² = 0.994

εc = -885.48ln(T) + 6011.51

R² = 0.999

3450 329 4 42 T = 61.11(Ni)0.151

R² = 1

εt = -55.69ln(T) + 596.13

R² = 0.995

εc = -855.38ln(T) + 5775.60

R² = 0.999

3450 329 5 52 T = 54.23(Ni)0.156

R² = 1

εt = -56.90ln(T) + 602.12

R² = 0.997

εc = -826.00ln(T) + 5549.02

R² = 0.999

3450 329 6 62 T = 48.24(Ni)0.161

R² = 0.999

εt = -57.22ln(T) + 602.67

R² = 0.996

εc = -800.57ln(T) + 5357.36

R² = 0.999

212

3450 329 7 72 T = 43.92(Ni)0.165

R² = 1

εt = -56.96ln(T) + 599.74

R² = 0.996

εc = -778.86ln(T) + 5192.70

R² = 1

3450 329 8 82 T = 39.58(Ni)0.170

R² = 1

εt = -56.79ln(T) + 597.23

R² = 0.996

εc = -757.22ln(T) + 5032.18

R² = 1

3450 329 9 93 T = 35.26(Ni)0.175

R² = 1

εt = -55.96ln(T) + 590.67

R² = 0.997

εc = -734.37ln(T) + 4864.99

R² = 1

3450 329 10 103 T = 31.57(Ni)0.181

R² = 1

εt = -54.68ln(T) + 581.70

R² = 0.996

y = -714.77ln(T) + 4722.76

R² = 1

102

4.8 Developlemt of LEADFlex Program

The LEADFlex programme was developed using algorithm, Visual Basic Codes and

program interface as presented in the following section.

4.8.1 Program Algorithm

1. Enter the traffic data, material and pavement layer thickness

2. Compute the Expected Traffic – Ni(ESAL)

3. Check if the Traffic Category is Light, Medium or Heavy Traffic

4. Compute the minimum pavement thickness

5. Compute the Maximum tensile and compressive Strain and

5.1 Check if maximum tensile strain is less than allowable

5.2 Check if maximum compressive strain is less than available

6. Compute number of traffic repetitions to failure for fatigue and rutting

7. Compute Damage Factor for fatigue and rutting

7.1.1 Check if the Damage Factor for fatigue Df is less than 1. If Df is less than 1

go to 8 otherwise go to 4 and increase pavement.

7.1.2 Check if the Damage Factor for rutting Dr is less than 1. If Dr is less than 1

go to 8 otherwise go to 4 and increase pavement.

8. Save Final Design.

4.8.2 LEADFlex Visual Basic Codes

The LEADFlex Visual Basic Codes are as presented in APPENDIX F

103

CHAPTER 5

RESULTS AND DISCUSSION

5.1 Results

The results of the developed LEADFlex pavement design procedure are presented in

sections 5.1.1, 5.1.2 and 5.1.3 for light, medium and heavy traffic categories respectively.

5.1.1 Light Traffic

Presented in Tables 5.1a, 5.1b and 5.1c are light traffic LEADFlex pavement thicknesses,

tensile and compressive strains respectively for particular traffic repetition and subgrade

CBR generated from the developed LEADFlex pavement regression equations in chapter

4.

Table 5.1a: Expected Traffic, Subgrade CBR and Pavement Thickness data for Light Traffic

Expected

Traffic

Ni

(ESAL)

Subgrade CBR (%)/Pavement Thickness (mm)

1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

1.00E+04 363.14 325.13 302.41 285.25 267.79 253.91 241.78 231.21 219.34 209.49

2.00E+04 397.10 357.27 333.22 315.63 297.34 282.90 270.32 259.41 247.11 237.00

3.00E+04 418.43 377.53 352.69 334.87 316.12 301.38 288.56 277.47 264.96 254.74

4.00E+04 434.25 392.59 367.18 349.24 330.15 315.21 302.24 291.04 278.40 268.12

5.00E+04 446.93 404.69 378.83 360.80 341.46 326.37 313.29 302.02 289.29 278.99

104

Table 5.1b: Pavement Thickness, Subgrade CBR and Horizontal Tensile Strain data for Light Traffic

Pavement

Thickness

(mm)

Subgrade CBR (%)/Horizontal Tensile Strain (10-6)

1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

209.49 280.79 299.02 308.43 313.81 317.37 319.35 320.23 320.40 320.15 319.48

268.85 274.09 288.32 295.03 298.66 300.78 301.65 301.83 301.49 300.69 299.73

328.21 268.73 279.77 284.31 286.54 287.51 287.50 287.12 286.36 285.13 283.94

387.57 264.27 272.65 275.38 276.45 276.46 275.71 274.87 273.75 272.16 270.77

446.93 260.44 266.54 267.73 267.79 266.98 265.61 264.36 262.94 261.04 259.49

Table 5.1c: Pavement Thickness, Subgrade CBR and Vertical Compressive Strain data for Light Traffic

Pavement

Thickness

(mm)

Subgrade CBR (%)/Vertical Compressive Strain (10-6)

1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

209.49 2394.66 2143.82 1987.57 1856.23 1735.67 1641.02 1554.71 1477.36 1398.80 1334.10

268.85 1912.92 1683.09 1541.83 1426.31 1321.23 1239.12 1166.40 1100.75 1035.82 983.33

328.21 1527.69 1314.66 1185.39 1082.51 989.81 917.74 855.87 799.59 745.56 702.82

387.57 1206.68 1007.65 888.37 796.03 713.64 649.93 597.11 548.64 503.69 469.08

446.93 931.50 744.48 633.76 550.45 476.91 420.37 375.30 333.52 296.35 268.71

5.1.2 Medium Traffic

Presented in Tables 5.2a, 5.2b and 5.2c are medium traffic LEADFlex pavement

thicknesses, tensile and compressive strains respectively for particular traffic repetition

105

and subgrade CBR generated from the developed LEADFlex pavement regression

equations in chapter 4.

Table 5.2a: Expected Traffic Repetitions, Subgrade CBR and Pavement Thickness data for Medium Traffic

Expected

Traffic

Ni

(ESAL)

Subgrade CBR (%)/ Pavement Thickness (mm)

1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

5.00E+04 431.70 386.66 356.77 337.01 315.79 299.47 285.54 274.76 261.44 249.62

1.00E+05 472.73 425.47 393.67 373.41 351.12 333.90 319.47 308.69 294.74 282.40

1.50E+05 498.52 449.96 417.00 396.51 373.60 355.85 341.16 330.46 316.16 303.53

2.00E+05 517.67 468.18 434.39 413.75 390.41 372.29 357.43 346.82 332.29 319.48

2.50E+05 533.02 482.82 448.38 427.65 403.97 385.57 370.59 360.07 345.37 332.43

Table 5.2b: Pavement Thickness, Subgrade CBR and Horizontal Tensile Strain data for Medium Traffic

Pavement

Thickness

(mm)

Subgrade CBR (%)/ Horizontal Tensile Strain (10-6)

1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

249.62 305.52 315.31 318.89 320.15 320.52 320.00 319.15 317.97 316.24 314.64

320.47 294.89 301.76 303.87 304.32 303.98 303.09 301.99 300.68 299.02 297.46

391.32 286.39 290.93 291.86 291.67 290.76 289.56 288.28 286.87 285.24 283.72

462.17 279.31 281.91 281.86 281.13 279.74 278.30 276.86 275.36 273.77 272.27

533.02 273.24 274.18 273.28 272.09 270.30 268.64 267.07 265.49 263.93 262.46

106

Table 5.2c: Pavement Thickness, Subgrade CBR and Vertical Compressive Strain data for Medium Traffic

Pavement

Thickness

(mm)


1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

249.62 1663.39 1483.94 1372.05 1283.05 1200.37 1135.15 1076.81 1023.95 971.15 927.24

320.47 1328.60 1165.56 1065.57 986.70 914.29 857.67 807.52 762.72 718.40 682.21

391.32 1060.96 911.03 820.57 749.79 685.58 635.84 592.25 553.89 516.35 486.32

462.17 837.99 698.98 616.45 552.41 495.04 451.02 412.89 379.91 348.01 323.12

533.02 646.87 517.24 441.50 383.23 331.73 292.62 259.17 230.79 203.73 183.24

5.1.3 Heavy Traffic

Presented in Tables 5.3a, 5.3b and 5.3c are heavy traffic LEADFlex pavement thicknesses,

tensile and compressive strains respectively for particular traffic repetition and subgrade

CBR generated from the developed LEADFlex pavement regression equations in chapter

4.

Table 5.3a: Expected Traffic Repetitions, CBR and Pavement Thickness data for Heavy Traffic

Expected

Traffic

Ni

(ESAL)

Subgrade CBR (%)/ Pavement Thickness (mm)

1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

2.50E+05 515.62 460.22 427.52 399.21 376.98 356.84 341.45 327.44 310.40 299.43

3.50E+05 539.22 482.41 449.05 420.02 397.30 376.71 360.94 346.71 329.23 318.24

4.50E+05 557.55 499.69 465.83 436.26 413.18 392.26 376.22 361.84 344.03 333.05

107

5.50E+05 572.63 513.93 479.68 449.68 426.32 405.14 388.89 374.40 356.32 345.37

6.50E+05 585.49 526.09 491.52 461.17 437.58 416.18 399.75 385.19 366.90 355.97

7.50E+05 596.74 536.73 501.90 471.24 447.45 425.88 409.31 394.67 376.20 365.31

Table 5.3b: Pavement Thickness, CBR and Horizontal Tensile Strain data for Heavy Traffic

Pavement

Thickness

(mm)

Subgrade CBR (%)/ Horizontal Tensile Strain (10-6)

1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

299.43 272.53 277.45 278.71 278.59 277.68 276.41 274.96 273.42 271.59 269.92

358.89 264.84 268.41 268.98 268.50 267.38 266.04 264.64 263.13 261.46 260.02

418.35 258.34 260.76 260.74 259.97 258.65 257.27 255.91 254.43 252.88 251.63

477.81 252.70 254.13 253.60 252.57 251.09 249.67 248.34 246.88 245.44 244.37

537.27 247.73 248.27 247.30 246.03 244.42 242.96 241.66 240.22 238.88 237.95

596.74 243.27 243.04 241.66 240.19 238.44 236.95 235.68 234.26 233.00 232.21

Table 5.3c: Pavement Thickness, Subgrade CBR and Vertical Compressive Strain data for Heavy Traffic

Pavement

Thickness

(mm)


1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

299.43 1175.32 1043.67 962.61 898.33 839.27 792.61 751.73 714.60 677.70 647.23

358.89 999.43 876.92 802.22 743.39 689.65 647.59 610.65 577.44 544.68 517.76

418.35 850.56 735.78 666.47 612.25 563.02 524.86 491.25 461.36 432.10 408.18

477.81 721.51 613.44 548.80 498.58 453.25 418.47 387.75 360.73 334.50 313.19

537.27 607.62 505.46 444.94 398.25 356.37 324.58 296.40 271.92 248.37 229.36

596.74 505.68 408.82 351.98 308.45 269.66 240.53 214.63 192.42 171.28 154.32

108

5.1.4 LEADFlex Pavement Characteristics

The LEADFlex pavement characteristics (pavement material properties, pavement

thickness, fatigue and rutting strain) are summarized in Tables 5.4a, 5.4b and 5.4c for

light medium and heavy traffic respectively.

106

Subgrade Minimum Pavement Thickness

(mm)

Fatigue Criteria

Rutting Criteria

CBR

(%)

Modulus

(MPa)

E3

(MPa)

Max.

Fatigue

Strain

εt

(10-6)

Allowable

Fatigue

Strain

Єt

(10-6)

No. of

Repetitions

to failure

Nf

Damage

Factor

Df

Max.

Rutting

Strain

εc

(10-6)

Allowable

Rutting

Strain

Єc

(10-6)

No. of

Repetitions

to failure

Nr

Damage

Factor

Dr

A.C.

Surface

Cement-

Stabilized

Base

Total

1 10 50 396.93 446.93 260.44 586.70 6.75 x 105 0.07 931.50 945.00 5.06 x 105 0.99

2 21 50 354.69 404.69 270.50 586.70 5.96 x 105 0.08 927.83 945.00 5.15 x 104 0.97

3 31 50 328.83 378.83 276.61 586.70 5.54 x 105 0.09 927.42 945.00 5.16 x 104 0.97

4 41 50 310.80 360.80 280.79 586.70 5.27 x 105 0.09 927.31 945.00 5.16 x 104 0.97

5 52 50 291.46 341.46 284.85 586.70 5.03 x 105 0.10 926.96 945.00 5.17 x 104 0.97

6 62 50 276.46 326.37 287.54 586.70 4.86 x 105 0.10 926.80 945.00 5.18 x 104 0.97

107

Table 5.4a: Light Traffic LEADFlex Pavement Characteristics - ( E1 = 500377psi (3450MPa), E2 = 329MPa, Ni = 5 x 104 max)

Table 5.4b: Medium Traffic LEADFlex Pavement Characteristics - (E1 = 500377psi (3450MPa), E2 = 329MPa, Ni = 2.5x105 max.)


(mm)

Fatigue Criteria

Rutting Criteria

CBR

(%)

Modulus

(MPa)

E3

(MPa)

Max.

Fatigue

Strain

εt

(10-6)

Allowable

Fatigue

Strain

Єt

(10-6)

No. of

Repetitions

to failure

Nf

Damage

Factor

Df

Max.

Rutting

Strain

εc

(10-6)

Allowable

Rutting

Strain

Єc

(10-6)

No. of

Repetitions

to failure

Nr

Damage

Factor

Dr

A.C.

Surface

Cement-

Stabilized

Base

Total

7 72 50 263.29 313.29 290.55 586.70 4.71 x 105 0.11 925.29 945.00 5.21 x 104 0.96

8 82 50 252.29 302.02 292.66 586.70 4.60 x 105 0.11 925.13 945.00 5.22 x 104 0.96

9 93 50 239.29 289.29 294.92 586.70 4.49 x 105 0.11 924.21 945.00 5.24 x 104 0.95

10 103 50 228.99 278.99 296.50 586.70 4.41 x 105 0.11 921.27 945.00 5.32 x 104 0.94

108

1 10 75 458.02 533.02 273.24 360.3 5.77 x 105 0.43 646.87 659.9 2.59 x 105 0.97

2 21 75 407.82 482.82 279.54 360.3 5.35 x 105 0.47 643.28 659.9 2.65 x 105 0.94

3 31 75 373.38 448.38 283.05 360.3 5.14 x 105 0.49 643.20 659.9 2.66 x 105 0.94

4 41 75 352.65 427.65 286.05 360.3 4.96 x 105 0.50 643.18 659.9 2.66 x 105 0.94

5 52 75 328.97 403.97 288.65 360.3 4.82 x 105 0.52 643.08 659.9 2.66 x 105 0.94

6 62 75 310.57 385.57 290.57 360.3 4.71 x 105 0.53 642.28 659.9 2.67 x 105 0.94

7 72 75 295.59 370.59 292.02 360.3 4.63 x 105 0.54 641.91 659.9 2.68 x 105 0.93

8 82 75 285.07 360.07 292.62 360.3 4.60 x 105 0.54 640.90 659.9 2.70 x 105 0.93

9 93 75 270.37 345.37 293.86 360.3 4.54 x 105 0.55 640.70 659.9 2.70 x 105 0.93

10 103 75 257.43 332.43 294.94 360.3 4.49 x 105 0.56 640.27 659.9 2.71 x 105 0.92

109

Table 5.4c: Heavy Traffic LEADFlex Pavement Characteristics (E1 = 500377psi (3450MPa), E2 = 329MPa, Ni = 7.5x105 max.)


(mm)

Fatigue Criteria

Rutting Criteria

CBR

(%)

Modulus

(MPa)

E3

(MPa)

Max.

Fatigue

Strain

εt

(10-6)

Allowable

Fatigue

Strain

Єt

(10-6)

No. of

Repetitions

to failure

Nf

Damage

Factor

Df

Max.

Rutting

Strain

εc

(10-6)

Allowable

Rutting

Strain

Єc

(10-6)

No. of

Repetitions

to failure

Nr

Damage

Factor

Dr

A.C.

Surface

Cement-

Stabilized

Base

Total

1 10 100 496.74 596.74 243.27 258.6 8.45 x 105 0.88 505.68 516.5 7.80 x 105 0.96

2 21 100 436.73 536.73 248.32 258.6 7.90 x 105 0.94 505.39 516.5 7.82 x 105 0.96

3 31 100 401.90 501.90 250.96 258.6 7.63 x 105 0.98 505.36 516.5 7.82 x 105 0.96

4 41 100 371.24 471.24 253.34 258.6 7.63 x 105 0.98 505.34 516.5 7.82 x 105 0.96

5 52 100 347.45 447.45 254.83 258.6 7.62 x 105 0.98 505.31 516.5 7.82 x 105 0.96

6 62 100 325.88 425.88 256.25 258.6 7.60 x 105 0.99 505.29 516.5 7.82 x 105 0.96

110

7 72 100 309.31 409.31 257.16 258.6 7.58 x 105 0.99 505.27 516.5 7.83 x 105 0.96

8 82 100 294.67 394.67 257.74 258.6 7.58 x 105 0.99 505.26 516.5 7.83 x 105 0.96

9 93 100 276.20 376.20 257.88 258.6 7.56 x 105 0.99 505.10 516.5 7.84 x 105 0.96

10 103 100 265.31 365.31 257.98 258.6 7.54 x 105 0.99 505.08 516.5 7.84 x 105 0.96

109

5.2 Discussion of Result

The relationship between traffic repetitions (expected traffic) and pavement

thickness; pavement thickness and tensile strain; pavement thickness and

compressive strain are presented in sections 5.2.1. 5.2.2 and 5.2.3 for light, medium

and heavy traffic categories respectively.

5.2.1 Expected Traffic and Pavement Thickness Relationship

The effect of traffic repetitions on pavement thickness are shown in Figures 5.1a, 5.1b

and 5.1c for light medium and heavy traffic respectively.

Figure 5.1a: Expected Traffic – Pavement Thickness Relationship for Light Traffic

LIGHT TRAFFIC

110

For the light traffic category, Figure 5.1a show that at 1% CBR, increasing the

expected traffic from 1.00E+04 to 5.00E+04 ESAL resulted in an increase in pavement

thickness from 363.14mm to 446.93mm while at 10% CBR, as the expected traffic

increased from 1.00E+04 to 5.00E+05, the pavement thickness also increased from

209.49mm to 278.99mm. The result indicates that for a subgrade CBR of 1%, a

minimum pavement thickness of 446.94mm is required to with stand the maximum

light traffic of 5.00E+04 ESAL while a subgrade of 10% CBR requires a minimum

pavement thickness of 278.99mm to with stand same traffic for design period of 20

years. Figure 5.1a shows that the pavement thickness increases as the expected traffic

repetition increases. This trend was observed for all subgrade CBR.

For the medium traffic category, Figure 5.1b shows that at 1% CBR, as the expected

traffic increased from 5.00E+04 to 2.50E+05, the pavement thickness increased from

431.70mm to 533.02mm while at 10% CBR, as the expected traffic increased from

Figure 5.1b: Expected Traffic – Pavement Thickness Relationship for Medium Traffic

MEDIUM TRAFFIC

111

5.00E+04 to 2.50E+05, the pavement thickness increased from 249.62mm to

332.43mm. The result indicates that for the medium traffic situation, a subgrade CBR

of 1% requires a minimum pavement thickness of 533.02mm to withstand the

maximum traffic of 2.5.0E+05 ESAL, while a subgrade CBR of 10% requires a

minimum pavement thickness of 332.43mm to withstand same traffic for design

period of 20 years. Figure 5.1b shows that the pavement thickness increases as the

expected traffic repetition increases. This trend was observed for all subgrade CBR.

In the case of the heavy traffic category, Figure 5.1c shows that at 1% CBR, as the

expected traffic increased from 2.50E+05 to 7.50E+05, the pavement thickness also

increased from 515.62mm to 596.74mm while at 10% CBR, the pavement thickness

increased from 299.43mm to 365.31mm as the expected traffic increases from

Figure 5.1c: Expected Traffic – Pavement Thickness Relationship for Heavy Traffic

HEAVY TRAFFIC

112

2.50E+05 to 7.50E+05 . The result indicates that a subgrade CBR of 1% requires a

minimum pavement thickness of 596.74mm to withstand the maximum traffic of

7.5.0E+05 ESAL, while subgrade CBR of 10% requires a minimum pavement

thickness of 365.31mm to withstand same traffic for design period of 20 years. This

trend was observed for all subgrade CBR.

Generally, for all traffic categories, this result indicates that for each subgrade CBR,

the pavement thickness increases as the expected traffic repetition increases. This

trend is in accordance with previous studies (Siddique et al, 2005; NCHRP, 2007).

5.2.2 Pavement Thickness and Tensile Strain Relationship

The effect of pavement thickness on horizontal tensile (fatigue) strain below asphalt

layer are shown Figures 5.2a, 5.2b and 5.2c for light medium and heavy traffic

categories respectively.

LIGHT TRAFFIC

Figure 5.2a: Pavement Thickness – Horizontal Tensile Strain Relationship for Light Traffic

113

Figure 5.2a shows the effect of pavement thickness on the fatigue strain for light

traffic category. The result shows that for subgrade CBR of 1%, as the pavement

thickness increased from 209.49mm to 446.93mm, the fatigue strain decreased from

280.79 x10-6 to 260.44 x 10-6 while for a subgrade CBR of 10%, as the pavement

thickness increased from 209.49 to 446.93mm, the fatigue decreased from 319.48 x 10-

6 to 259.49 x 10-6. This result indicates that for the light traffic situation, a subgrade

CBR of 1% requires a minimum pavement thickness of 209.49mm to withstand the

maximum fatigue strain of 280.79 x10-6 while a subgrade CBR of 10% requires a

minimum pavement thickness of 446.93mm to withstand the maximum fatigue

strain of 319.48 x 10-6. The same trend was observed for other subgrade CBR. This

result implied that for the light traffic category, about 113.34% increase in pavement

thickness resulted in a decrease in tensile strain of about 7.25%, 10.86%, 13.19%,

14.66%, 15.88%, 16.83%, 17.44%, 17.93%, 18.46% and 18.78% for subgrade CBR of 1%,

2%, 3%, 4%, 5%. 6%, 7%, 8%, 9% and 10% respectively.

Figure 5.2b: Pavement Thickness – Horizontal Tensile Strain Relationship for Medium Traffic

MEDIUM TRAFFIC

114

The effect of pavement thickness on the fatigue strain for medium traffic category is

as presented in Figure 5.2b. The result indicates that for a subgrade CBR of 1%, as

the pavement thickness increased from 249.62mm to 533.02mm, the fatigue strain

decreased from 305.52 x10-6 to 273.24 x 10-6 while for a subgrade of 10%, as the

pavement thickness increased from 249.62mm to 533.02mm, the fatigue strain

decreased from 314.64 x 10-6 to 262.46 x 10-6. This result shows that for the medium

traffic situation, a subgrade CBR of 1% requires a minimum pavement thickness of

249.62mm to withstand the maximum fatigue strain of 305.52 x10-6 while a subgrade

CBR of 10% will require a minimum pavement thickness of 249.62mm to withstand a

maximum fatigue strain of 314.64 x 10-6. The same trend was observed for other

subgrade CBR. This result indicates that for the medium traffic category, increasing

the pavement thickness by about 113.53% reduced the tensile strain by about 10.56%,

13.04%, 14.30%, 15.01%, 15.67%, 16.05%. 16.32%, 16.50%, 16.54% and 16.58% for for

subgrade CBR of 1%, 2%, 3%, 4%, 5%. 6%, 7%, 8%, 9% and 10% respectively

HEAVY TRAFFIC

Figure 5.2c: Pavement Thickness – Horizontal Tensile Strain Relationship for Heavy Traffic

115

In the case of heavy traffic category, the effect of pavement thickness on fatigue

strain is presented in Figure 5.2c. The result shows that for a subgrade CBR of 1%,

the fatigue strain decreased from 272.53 x10-6 to 243.27 x 10-6 as the pavement

thickness increased from 299.43mm to 596.74mm while for 10% subgrade CBR, the

fatigue decreased from 269.92 x 10-6 to 232.21 x 10-6 as the pavement thickness

increased from 299.43mm to 596.74mm. This result indicates that for the heavy traffic

situation, a subgrade CBR of 1% requires a minimum pavement thickness of

299.43mm to withstand the maximum fatigue strain of 272.53 x10-6 while a subgrade

of 10% CBR will require the minimum pavement thickness of 299.43mm to

withstand the maximum fatigue strain of 269.92 x 10-6. The same trend was observed

for other subgrade CBR. This result implies that for the heavy traffic category,

increasing the pavement thickness by 99.29% caused a decrease of about 10.74%,

12.40%, 13.29%, 13.52%, 14.13%, 14.28%, 14.29%, 14.32% 14.21% and 13.97% in tensile

strain for subgrade CBR of for subgrade CBR of 1%, 2%, 3%, 4%, 5%. 6%, 7%, 8%, 9%

and 10% respectively.

Generally, the result shows that for particular subgrade CBR, the horizontal tensile

strain below the asphalt layer decreases as the pavement thickness increases. This

trend is in accordance with previous studies (Dormon et al, 1965; Saal et al, 1960;

Siddique et al, 2005; NCHRP, 2007).

5.2.3 Pavement Thickness and Compressive Strain Relationship

The effect pavement thickness on vertical compressive (rutting) strain on top the

subgrade layer are shown in Figures 5.3a, 5.3b and 5.3c for light medium and heavy

traffic respectively.

116

Figure 5.3a presents the effect of pavement thickness on rutting strain for light traffic

category. Figure 5.3a shows that as the pavement thickness increased from

209.49mm to 446.93mm, the rutting strain decreased from 2,394.66 x10-6 to 931.50 x

10-6 and 1334.80 x 10-6 to 268.71 x 10-6 for subgrade CBR of 1% and 10% respectively.

The result indicates that for subgrade CBR of 1%, a minimum pavement thickness of

209.49mm is required to withstand a maximum rutting strain of 2,394.66 x10-6 while

a subgrade CBR of 10% requires a minimum pavement thickness of 209.49mm to

withstand a maximum rutting strain of 1334.80 x 10-6. The same trend was observed

for other subgrade CBR. This result also shows that for the light traffic category,

increasing the pavement thickness by 113.34% caused a decrease of about 61.10%,

65.27%, 68.11%, 70.34%, 72.52%, 74.38%, 75.86%, 77.42% 78.81% and 79.86% in

rutting strain for subgrade CBR of for subgrade CBR of 1%, 2%, 3%, 4%, 5%. 6%, 7%,

8%, 9% and 10% respectively.

Figure 5.3a: Pavement Thickness – Vertical Compressive Strain Relationship for Light Traffic

LIGHT TRAFFIC

117

The effect of pavement thickness on rutting strain for medium traffic category is as

presented in Figure 5.3b. Result shows that for 1% subgrade CBR, the rutting strain

decreased from 1663.39 x10-6 to 646.87 x 10-6 as the pavement thickness increased

from 249.62mm to 533.02mm while for 10% subgrade CBR, the rutting strain

decreased from 927.24 x 10-6 to 183.24 x 10-6 as the pavement thickness increased

from 249.62mm to 533.02mm. The result indicates that for subgrade CBR of 1%, a

minimum pavement thickness of 249.62mm is required to withstand a maximum

rutting strain of 1663.39 x10-6 while for a subgrade CBR of 10%, a minimum

pavement thickness of 249.62mm withstands a maximum rutting strain of 927.24 x

10-6. The same trend was observed for other subgrade CBR. The result further

indicated that for the medium traffic category, increasing the pavement thickness by

113.53% caused a decrease of about 61.11%, 65.14%, 69.82%, 70.13%, 72.36%, 74.22%,

75.93%, 77.46%, 79.02% and 80.24% in rutting strain for subgrade CBR of for

subgrade CBR of 1%, 2%, 3%, 4%, 5%. 6%, 7%, 8%, 9% and 10% respectively.

MEDIUM TRAFFIC

Figure 5.3b: Pavement Thickness – Vertical Compressive Strain Relationship for Medium Traffic

118

In the case of heavy traffic category, Figure 5.2c shows that for 1% subgrade CBR, the

rutting strain decreased from 1,175.32 x10-6 to 505.68 x 10-6 as the pavement thickness

increased from 299.43mm to 596.74mm while fort 10% subgrade CBR, the rutting

strain decreased from 647.23 x 10-6 to 154.32 x 10-6 as the pavement thickness

increased from 299.43mm to 596.74mm. The result indicates that for subgrade CBR of

1%, a minimum pavement thickness of 299.43mm is required to withstand the

maximum rutting strain of 1,175.32 x10-6 while for 10% subgrade CBR, a minimum

pavement thickness of 299.43mm is required to withstand a maximum rutting strain

of 647.23 x 10-6. The same trend was observed for other subgrade CBR. This result

shows that for the heavy traffic category, increasing the pavement thickness by

99.29% caused a decrease of about 56.98%, 60.83%, 63.43%, 65.66%, 67.87%, 69.65%,

71.45%, 73.07%, 74.72% and 76.16% in rutting strain for subgrade CBR of for

subgrade CBR of 1%, 2%, 3%, 4%, 5%. 6%, 7%, 8%, 9% and 10% respectively.

Figure 5.3c: Pavement Thickness – Vertical Compressive Strain Relationship for Heavy Traffic

HEAVY TRAFFIC

119

Generally, Figures 5.3a to 5.3c show that for particular subgrade CBR, the rutting

strain below the asphalt layer decreases as the pavement thickness increases. This

trend is in line with the result of previous researches (Huang, 1993; Kerkhoven et al,

1953; Siddique et al, 2005; NCHRP, 2007).

5.2.4 Effect of Subgrade CBR on Pavement Thickness

The effect of subgrade CBR on pavement thickness are shown in Figures 5.4a, 5.4b

and 5.4c for light, medium and heavy traffic respectively.

Figure 5.4a presents the effect of subgrade CBR on pavement thickness for light

traffic category. The result shows that for expected traffic of 1.00E+04 ESAL, the

pavement thickness decreased from 363.14mm to 209.49mm as the subgrade CBR

increased from 1% to 10%,. Similarly, for expected traffic of 5.00E+04 ESAL, the


increases from 1% to 10%. The result indicates a percentage decrease of about 39.50%

in pavement thickness as the subgrade CBR increased from 1% to 10%. The same

trend was observed for all ranges of traffic.

Figure 5.4a: Effect of subgrade CBR on Pavement Thickness for Light Traffic

LIGHT TRAFFIC

Expected Traffic

120

The effect of subgrade CBR on pavement thickness for medium traffic is presented in

Figure 5.4b. Result shows that for expected traffic of 1.00E+04 ESAL, the pavement

thickness decreased from 431.70mm to 249.62mm as the subgrade CBR increased

from 1% to 10%. Also, for expected traffic of 5.00E+04 ESAL, the pavement thickness

decreased from 533.02mm to 332.43mm as the subgrade CBR increases from 1% to

10% resulting in a percentage decrease of about 39.63% in pavement thickness as the

subgrade CBR increased from 1% to 10%. The same trend was observed for all

ranges of traffic.

Figure 5.4b: Effect of subgrade CBR on Pavement Thickness for Medium Traffic

MEDIUM TRAFFIC

Expected Traffic

121

For heavy traffic category, Figure 5.4c shows that for an expected traffic of 1.00E+04

ESAL, the pavement thickness decreased from 515.62mm to 299.43mm as the

subgrade CBR increased from 1% to 10%. Also, for expected traffic of 5.00E+04, the


increases from 1% to 10% resulting in a percentage decrease of about 40.14% in

pavement thickness. The same trend was observed for all ranges of traffic.

Generally, the result shows that increase in subgrade CBR from 1% to 10% resulted

in a percentage decrease of about 39.50%, 39.69% and 40.14% in pavement thickness

for light, medium and heavy traffic respectively, indicating that for particular traffic

repetition, pavement thickness decreases as subgrade CBR increases. This implies

Figure 5.4c: Effect of subgrade CBR on Pavement Thickness for Heavy Traffic

HEAVY TRAFFIC

Expected Traffic

122

that pavement thickness is dependent on subgrade CBR. This trend is in line with

previous studies (Nanda, 1981; Siddique et al, 2005; NCHRP, 2007).

5.3 Validation of LEADFLEX Result

The result of LEADFlex pavement design procedure was validated in three aspects:

i. Using the coefficient of determination R2 of the nonlinear regression analysis

using SPSS (SPSS 14.0, 2005),

ii. Comparison of the LEADFlex-calculated result with EVERSTRESS-calculated

result.

iii. Comparison of the LEADFlex-computed result with measured field result of

Kansas Accelerated Test Laboratory (K-ATL) Pavement Sections (Melhem et

al, 2000).

5.3.1 Coefficient of Determination

The result of the LEADFlex design procedure was validated in the first instance,

using the estimated R2 values of the nonlinear regression equations presented in

Tables 4.1c, 4.2c and 4.3c and APPENDIX C, D and E for light, medium and heavy

traffic respectively. The minimum estimated R2 values were 0.975, 0.983 and 0.994

for light, medium and heavy traffic respectively. This R2 values indicates that the

LEADFlex regression equations are good predictors (estimators) of pavement

thickness, fatigue and rutting strains in highway pavements.

123

5.3.2 Comparison of LEADFlex with EVERSTRESS Results

The LEADFlex results were also validated by comparing it with the results obtained

using the EVERTRESS (Sivaneswaran et al, 2001) Program. The ratio of the

LEADFlex-calculated and EVERSTRESS-calculated pavement thickness, fatigue and

rutting strains are presented in Tables 5.5a, 5.5b and 5.5c for light, medium and

heavy traffic respectively. The results show that the average ratio of LEADFlex-

calculated to EVERSTRESS-calculated pavement thicknesses were 0.99, 0.99, and 1.00

for light, medium and heavy traffic respectively. The average ratio of LEADFlex-

calculated to EVERSTRESS-calculated fatigue strain were 1.00, 0.99 and 0.99 for light,

medium and heavy traffic respectively while the ratio of LEADFlex-calculated to

EVERSTRESS-calculated rutting strain were 1.00, 1.00 and 0.99 for light, medium and

heavy traffic respectively. Calibration of LEADFlex-calculated and EVERSTRESS-

calculated pavement thickness using linear regression analysis shows that the

minimum coefficient of determination are 0.998, 0.999 and 0.999 for light, medium

and heavy traffic. Calibration of tensile (fatigue) strain resulted in minimum R2 of

0.971, 0.980 and 0.993 for light respectively, medium and heavy traffic respectively

while that of compressive (rutting) strain were 0.996, 0.996 and 0.998 for light,

medium and heavy traffic respectively. Similarly, linear regression analysis of

LEADFlex-calculated and EVERSTRESS-calculated pavement thickness resulted in

maximum R2 of 1.0. 0.999 and 1.0 for light, medium and heavy traffic respectively.

Calibration of tensile (fatigue) strain resulted in R2 of 0.982, 0.986 and 0.995 for light,

medium and heavy traffic respectively while that of compressive (rutting) strain

were 0.997, 0.997 and 0.998 for light, medium and heavy traffic respectively.

124

5.3.3 Comparison with K-ATL measured field data

The LEADFlex procedure was also validated using measured pavement response

data from three(3) stations at the South (SM-2A) and North (SM-2A) lanes of the K-

ATL (Melhem et al, 2000). Six (6) pavement test section were loaded using a falling

weight deflectometer load of 40kN. The pavement material consist of natural

subgrade with moduli 4.500psi (31MPa), 6000 psi (41MPa), 9,000psi (62MPa), 10,500

psi (72MPa), 13,500psi (93MPa) and 15,000psi (103MPa), aggregate base modulus of

47,717psi (329MPa) and asphalt concrete modulus of 500,377psi (3450MPa). The

pavement sections consist of 2-4in (50 – 100mm) asphalt concrete surface and 8 –

18in (200 – 450) aggregate base.

The horizontal tensile strain at the bottom of the asphalt bound layer and vertical

compressive strains at the top of the subgrade predicted by LEADFlex for the six (6)

pavement sections are as presented in Tables 5.7a to 5.7f. The average ratio of the

LEADflex-calculated and measured tensile and compressive strains were found to be

1.04 and 1.02 respectively for subgrade modulus of 31Mpa, 1.03 and 1.03 respectively

for subgrade modulus of 41MPa, 0.98 and 1.01 respectively for subgrade modulus of

62Mpa, 1.02 and 1.02 respectively for subgrade modulus of 72MPa, 1.04 and 1.00

respectively for subgrade modulus of 93MPa, and 1.03 and 1.03 respectively for

subgrade modulus of 103MPa .

The LEADFlex-calculated and measured horizontal tensile strains at the bottom of

the asphalt layer and vertical compressive strain at the top of the subgrade were

125

calibrated and compared using linear regression analysis as shown in Figure 5.5a

and 5.5b, 5.6a and 5.6b, 5.7a and 5.7b, 5.8a and 5.8b, 5.9a and 5.9b, and 5.10a and

5.10b for subgrade moduli of 31Mpa, 41Mpa, 62MPa, 72Mpa, 93MPa and 103MPa

respectively. The coefficients of determination R2 were found to be very good. The

calibration of LEADFlex-calculated and measured tensile and compressive strain

resulted in R2 of 0.999 and 0.994 respectively for subgrade modulus of 31MPa, 0.997

and 0.997 respectively for subgrade modulus of 41MPa, 0.996 and 0.999 respectively

for subgrade modulus of 62MPa, 0.992 and 0.995 respectively for subgrade modulus

of 72MPa, 0.999 and 0.998 respectively for subgrade modulus of 93MPa, and 0.999

and 0.999 respectively for subgrade modulus of 103MPa. The result indicates that the

LEADFlex procedure is a good estimator of horizontal tensile strain at the bottom of

asphalt layer and vertical compressive strain on top subgrade.

126

Table 5.5a: Comparison of LEADFlex and EVERSTRESS Result for LIGHT TRAFFIC

Expected

Traffic

(ESAL)

Subgrade

CBR/Modulus

Pavement Thickness

(mm)

Pavement Response

Tensile Strain

(10-6)

Compressive Strain

(10-6)

CBR

(%)

Modulus

(MPa)

LEADFlex

EVERSTRESS Ratio LEADFlex


EVERSTRESS Ratio

1.00E+04 1 10 363.14 363.9 0.9979 266.02 266.2 0.9993 1332.42 1335 0.9981

2.00E+04 1 10 397.10 398.4 0.9967 263.61 263.0 1.0023 1159.76 1145 1.0129

3.00E+04 1 10 418.43 419.4 0.9977 262.21 262.0 1.0008 1058.76 1048 1.0103

4.00E+04 1 10 434.25 435.6 0.9969 261.21 261.5 0.9989 987.10 981.4 1.0058

5.00E+04 1 10 446.93 448.1 0.9974 260.44 260.3 1.0005 931.52 934.0 0.9973

1.00E+04 2 21 325.13 325.2 0.9998 280.18 280.7 0.9981 1332.05 1338 0.9956

2.00E+04 2 21 357.27 358.0 0.998 276.14 275.3 1.0030 1157.96 1146 1.0104

3.00E+04 2 21 377.53 378.2 0.9982 273.77 273.2 1.0021 1056.13 1047 1.0087

4.00E+04 2 21 392.59 393.3 0.9982 272.10 272.0 1.0004 983.87 981 1.0029

5.00E+04 2 21 404.69 404.8 0.9997 270.80 271.4 0.9978 927.83 934.5 0.9929

127

1.00E+04 3 31 302.41 302.0 1.0014 288.71 289.4 0.9976 1331.68 1339 0.9945

2.00E+04 3 31 333.22 334.0 0.9977 283.50 282.5 1.0035 1158.30 1148 1.009

3.00E+04 3 31 352.69 353.6 0.9974 280.45 279.8 1.0023 1056.88 1047 1.0094

4.00E+04 3 31 367.18 368.1 0.9975 278.29 278.2 1.0003 984.92 980.8 1.0042

5.00E+04 3 31 378.83 378.1 1.0019 276.61 277.4 0.9971 929.11 938.7 0.9898

1.00E+04 4 41 285.25 283.9 1.0047 295.06 296 0.9968 1324.28 1338 0.9897

2.00E+04 4 41 315.63 315.4 1.0007 288.92 288 1.0032 1149.89 1144 1.0051

3.00E+04 4 41 334.87 334.2 1.002 285.32 284.8 1.0018 1047.87 1046 1.0018

4.00E+04 4 41 349.24 347.9 1.0039 282.77 283 0.9992 975.49 982.4 0.993

5.00E+04 4 41 360.80 359.3 1.0042 280.79 281.8 0.9964 919.35 933.2 0.9852

1.00E+04 5 52 267.79 267.1 1.0026 301.04 301.9 0.9972 1327.77 1337 0.9931

2.00E+04 5 52 297.34 297.6 0.9991 294.08 293 1.0037 1153.89 1146 1.0069

3.00E+04 5 52 316.12 316.4 0.9991 290.01 289.3 1.0025 1052.18 1046 1.0059

4.00E+04 5 52 330.15 329.8 1.0011 287.12 287.2 0.9997 980.02 981.9 0.9981

128

5.00E+04 5 52 341.46 340.7 1.0022 284.88 285.8 0.9968 924.05 933.7 0.9897

1.00E+04 6 62 253.91 253.6 1.0012 305.71 306.5 0.9974 1331.24 1338 0.9949

2.00E+04 6 62 282.90 283.4 0.9982 298.04 296.9 1.0038 1157.04 1148 1.0079

3.00E+04 6 62 301.38 302 0.9979 293.55 292.7 1.0029 1055.15 1047 1.0078

4.00E+04 6 62 315.21 315.7 0.9984 290.37 290.3 1.0002 982.85 980.7 1.0022

5.00E+04 6 62 326.37 325.9 1.0015 287.90 288.8 0.9969 926.77 934.8 0.9914

1.00E+04 7 72 241.78 241.4 1.0016 309.66 310.5 0.9973 1331.61 1338 0.9952

2.00E+04 7 72 270.32 271.5 0.9957 301.43 300 1.0048 1157.90 1145 1.0113

3.00E+04 7 72 288.56 289.9 0.9954 296.62 295.7 1.0031 1056.29 1047 1.0089

4.00E+04 7 72 302.24 302.6 0.9988 293.20 293.1 1.0004 984.20 981.8 1.0024

5.00E+04 7 72 313.29 313.2 1.0003 290.55 291.4 0.9971 928.28 933.3 0.9946

1.00E+04 8 82 231.21 230.5 1.0031 312.92 313.9 0.9969 1328.42 1337 0.9936

2.00E+04 8 82 259.41 260.2 0.9970 304.20 302.9 1.0043 1154.73 1145 1.0085

3.00E+04 8 82 277.47 278.1 0.9977 299.09 298.2 1.0030 1053.12 1046 1.0068

129

4.00E+04 8 82 291.04 291 1.0001 295.47 295.5 0.9999 981.03 981.3 0.9997

5.00E+04 8 82 302.02 301.4 1.0021 292.66 293.7 0.9965 925.12 933.1 0.9914

1.00E+04 9 93 219.34 219 1.0015 316.57 317.5 0.9971 1331.95 1338 0.9955

2.00E+04 9 93 247.11 248.2 0.9956 307.27 305.8 1.0048 1158.49 1147 1.01

3.00E+04 9 93 264.96 266.3 0.9950 301.83 300.7 1.0037 1057.03 1046 1.0105

4.00E+04 9 93 278.40 279.2 0.9971 297.97 297.8 1.0006 985.03 981.2 1.0039

5.00E+04 9 93 289.29 289 1.0010 294.97 296 0.9965 929.19 935.2 0.9936

1.00E+04 10 103 209.49 209.2 1.0014 319.48 320.4 0.9971 1334.09 1339 0.9963

2.00E+04 10 103 237.00 238.8 0.9925 309.71 307.9 1.0059 1160.61 1146 1.0127

3.00E+04 10 103 254.74 256.6 0.9927 304.00 302.7 1.0043 1059.13 1046 1.0126

4.00E+04 10 103 268.12 269 0.9967 299.95 299.7 1.0008 987.13 982.4 1.0048

5.00E+04 10 103 278.99 279.2 0.9992 296.80 297.7 0.9970 931.29 934.1 0.997

Average Ratio 0.9991 1.0002 1.0013

130

Table 5.5b: Comparison of LEADFlex and EVERSTRESS Result for MEDIUM TRAFFIC

Expected

Traffic

(ESAL)

Subgrade

CBR/Modulus

Pavement Thickness

(mm)

Pavement Response

Tensile Strain

(10-6)

Compressive Strain

(10-6)

CBR

(%)

Modulus

(MPa)

LEADFlex



EVERSTRESS Ratio

5.00E+04 1 10 431.69 431.7 0.9999 282.21 282.6 0.9986 929.38 933.9 0.9952

1.00E+05 1 10 472.73 472.9 0.9996 278.34 277.7 1.0023 807.71 801.4 1.0079

1.50E+05 1 10 498.52 499.5 0.998 276.08 275.6 1.0018 736.54 729.8 1.0092

2.00E+05 1 10 517.67 518.3 0.9988 274.48 274.4 1.0003 686.04 684.7 1.0020

2.50E+05 1 10 533.02 532.7 1.0006 273.24 273.7 0.9983 646.87 652.8 0.9909

5.00E+04 2 21 386.66 385.5 1.0030 291.58 292.2 0.9979 926.30 934.4 0.9913

131

1.00E+05 2 21 425.47 425.4 1.0002 286.40 285.7 1.0024 804.41 799.1 1.0066

1.50E+05 2 21 449.96 449.3 1.0015 283.36 283 1.0013 733.11 731.1 1.0027

2.00E+05 2 21 468.18 467.1 1.0023 281.21 281.3 0.9997 682.52 685.6 0.9955

2.50E+05 2 21 482.82 481.6 1.0025 279.54 280.2 0.9976 643.28 651.5 0.9874

5.00E+04 3 31 356.77 358.2 0.996 297.42 297.7 0.9991 933.95 933 1.001

1.00E+05 3 31 393.67 396.3 0.9934 291.50 290.4 1.0038 813.22 799.9 1.0167

1.50E+05 3 31 417.00 419.6 0.9938 288.04 287.2 1.0029 742.59 731.2 1.0156

2.00E+05 3 31 434.39 437.2 0.9936 285.58 285.2 1.0013 692.49 684.8 1.0112

2.50E+05 3 31 448.38 450.5 0.9953 283.68 284 0.9989 653.62 652.4 1.0019

5.00E+04 4 41 337.01 336.2 1.0024 301.14 301.8 0.9978 927.03 933.6 0.9930

1.00E+05 4 41 373.41 373.2 1.0006 294.64 293.9 1.0025 805.35 801.1 1.0053

1.50E+05 4 41 396.51 396.7 0.9995 290.84 290.3 1.0018 734.17 730.1 1.0056

2.00E+05 4 41 413.75 413.1 1.0016 288.14 288.2 0.9998 683.67 685.6 0.9972

2.50E+05 4 41 427.65 426.6 1.0025 286.05 286.8 0.9974 644.49 651.8 0.9888

132

5.00E+04 5 52 315.79 316 0.9993 304.95 305.5 0.9982 931.12 933.9 0.9970

1.00E+05 5 52 351.12 352.7 0.9955 297.93 296.8 1.0038 809.69 799.9 1.0122

1.50E+05 5 52 373.60 375 0.9963 293.82 293 1.0028 738.65 731 1.0105

2.00E+05 5 52 390.41 391.3 0.9977 290.91 290.8 1.0004 688.26 685.7 1.0037

2.50E+05 5 52 403.97 404.7 0.9982 288.65 289.2 0.9981 649.16 651.3 0.9967

5.00E+04 6 62 299.47 300.2 0.9976 307.67 308.1 0.9986 932.92 933.5 0.9994

1.00E+05 6 62 333.90 336.4 0.9926 300.31 299 1.0044 812.06 799.4 1.0158

1.50E+05 6 62 355.85 358.3 0.9932 296.00 295 1.0034 741.36 730.6 1.0147

2.00E+05 6 62 372.29 374.2 0.9949 292.94 292.6 1.0012 691.20 685.6 1.0082

2.50E+05 6 62 385.57 387.1 0.9960 290.57 291 0.9985 652.29 651.8 1.0007

5.00E+04 7 72 285.54 285.8 0.9991 309.92 310.4 0.9984 931.92 934 0.9978

1.00E+05 7 72 319.47 321.7 0.9931 302.21 300.9 1.0043 810.89 799.3 1.0145

1.50E+05 7 72 341.16 343.4 0.9935 297.70 296.7 1.0034 740.10 730.1 1.0137

2.00E+05 7 72 357.43 359.1 0.9954 294.50 294.2 1.001 689.87 685 1.0071

2.50E+05 7 72 370.59 371.4 0.9978 292.02 292.5 0.9984 650.90 652.3 0.9979

133

5.00E+04 8 82 274.76 272.8 1.0072 311.33 312.4 0.9966 923.61 934 0.9889

1.00E+05 8 82 308.69 308.3 1.0013 303.27 302.5 1.0026 801.86 799.3 1.0032

1.50E+05 8 82 330.46 329.3 1.0035 298.56 298.2 1.0012 730.64 731.5 0.9988

2.00E+05 8 82 346.82 345.3 1.0044 295.22 295.5 0.9990 680.11 684.8 0.9932

2.50E+05 8 82 360.07 357.6 1.0069 292.63 293.8 0.9960 640.92 651.6 0.9836

5.00E+04 9 93 261.44 259.8 1.0063 313.06 314.1 0.9967 924.37 933.3 0.9904

1.00E+05 9 93 294.74 294.4 1.0012 304.79 304 1.0026 803.06 800.8 1.0028

1.50E+05 9 93 316.16 315.9 1.0008 299.95 299.4 1.0018 732.10 730.4 1.0023

2.00E+05 9 93 332.29 331 1.0039 296.52 296.8 0.9990 681.76 685.7 0.9942

2.50E+05 9 93 345.37 343.3 1.0060 293.86 295 0.9961 642.71 652 0.9857

5.00E+04 10 103 249.62 248.7 1.0037 314.64 315.5 0.9973 927.24 933.3 0.9935

1.00E+05 10 103 282.40 283.5 0.9961 306.16 305 1.0038 806.24 799.2 1.0088

1.50E+05 10 103 303.53 304.4 0.9972 301.19 300.4 1.0026 735.45 730.2 1.0072

2.00E+05 10 103 319.48 319.6 0.9996 297.67 297.7 0.9999 685.23 684.8 1.0006

134

2.50E+05 10 103 332.43 331.6 1.0025 294.94 295.8 0.9971 646.28 651.9 0.9914

Average Ratio 0.9993 1.0002 1.0012

Table 5.5c: Comparison of LEADFlex and EVERSTRESS Result for HEAVY TRAFFIC

Expected

Traffic

(ESAL)

Subgrade

CBR/Modulus

Pavement Thickness

(mm)

Pavement Response

Tensile Strain

(10-6)

Compressive Strain

(10-6)

CBR

(%)

Modulus

(MPa)

LEADFlex



EVERSTRESS Ratio

2.50E+05 1 10 515.62 514.4 1.0024 249.47 249.9 0.9983 647.56 651.8 0.9935

3.50E+05 1 10 539.22 537.8 1.0026 247.57 247.6 0.9999 604.10 605.4 0.9979

4.50E+05 1 10 557.55 556.2 1.0024 246.16 246.2 0.9998 571.64 572.2 0.999

5.50E+05 1 10 572.63 571.2 1.0025 245.02 245.1 0.9997 545.73 547.1 0.9975

6.50E+05 1 10 585.49 584.2 1.0022 244.08 244.3 0.9991 524.15 526.6 0.9954

7.50E+05 1 10 596.74 595.0 1.0029 243.27 243.7 0.9982 505.67 510.3 0.9909

135

2.50E+05 2 21 460.22 459.2 1.0022 256.00 256.3 0.9988 647.98 651.7 0.9943

3.50E+05 2 21 482.41 482 1.0009 253.65 253.5 1.0006 604.61 604.2 1.0007

4.50E+05 2 21 499.69 499.3 1.0008 251.89 251.7 1.0008 572.22 571.3 1.0016

5.50E+05 2 21 513.93 513.3 1.0012 250.49 250.4 1.0004 546.36 546.5 0.9997

6.50E+05 2 21 526.09 525.5 1.0011 249.32 249.4 0.9997 524.83 526.1 0.9976

7.50E+05 2 21 536.73 535.5 1.0023 248.32 248.6 0.9989 506.38 510.1 0.9927

2.50E+05 3 31 427.52 426.1 1.0033 259.57 260 0.9984 647.27 651.9 0.9929

3.50E+05 3 31 449.05 447.9 1.0026 256.93 256.9 1.0001 603.77 604.9 0.9981

4.50E+05 3 31 465.83 464.8 1.0022 254.96 254.6 1.0014 571.28 571.7 0.9993

5.50E+05 3 31 479.68 478.5 1.0025 253.39 253.4 0.9999 545.34 546.6 0.9977

6.50E+05 3 31 491.52 490.3 1.0025 252.08 252.2 0.9995 523.74 526.2 0.9953

7.50E+05 3 31 501.90 500 1.0038 250.96 251.4 0.9982 505.24 510.2 0.9903

2.50E+05 4 41 399.21 400 0.9980 262.58 262.7 0.9995 652.31 652.2 1.0002

3.50E+05 4 41 420.02 421.7 0.9960 259.75 259.3 1.0017 608.85 604.3 1.0075

4.50E+05 4 41 436.26 437.9 0.9963 257.63 257.1 1.0021 576.39 571.7 1.0082

136

5.50E+05 4 41 449.68 451.5 0.9960 255.95 255.5 1.0017 550.47 546.1 1.008

6.50E+05 4 41 461.17 462.6 0.9969 254.54 254.4 1.0006 528.90 526.4 1.0047

7.50E+05 4 41 471.24 472.5 0.9973 253.34 253.4 0.9998 510.41 509.7 1.0014

2.50E+05 5 52 376.98 376.3 1.0018 264.58 264.9 0.9988 649.03 652 0.9954

3.50E+05 5 52 397.30 397.3 1.0000 261.59 261.4 1.0007 605.67 604.6 1.0018

4.50E+05 5 52 413.18 413.2 1.0000 259.36 259.1 1.0010 573.29 571.8 1.0026

5.50E+05 5 52 426.32 426.2 1.0003 257.58 257.4 1.0007 547.43 546.8 1.0012

6.50E+05 5 52 437.58 437.2 1.0009 256.10 256.2 0.9996 525.91 526.8 0.9983

7.50E+05 5 52 447.45 446.8 1.0015 254.83 255.1 0.9989 507.47 510.1 0.9948

2.50E+05 6 62 356.84 357.9 0.9970 266.37 266.5 0.9995 652.18 651.2 1.0015

3.50E+05 6 62 376.71 378.3 0.9958 263.27 262.8 1.0018 608.81 604.5 1.0071

4.50E+05 6 62 392.26 394.1 0.9953 260.96 260.4 1.0021 576.42 571.3 1.009

5.50E+05 6 62 405.14 406.7 0.9962 259.11 258.8 1.0012 550.55 546.6 1.0072

137

6.50E+05 6 62 416.18 419.3 0.9926 257.57 257.2 1.0014 529.02 523.4 1.0107

7.50E+05 6 62 425.88 426.5 0.9986 256.25 256.4 0.9994 510.57 510.7 0.9998

2.50E+05 7 72 341.45 341 1.0013 267.48 267.8 0.9988 649.46 651.8 0.9964

3.50E+05 7 72 360.94 361.4 0.9987 264.32 264 1.0012 606.22 604.3 1.0032

4.50E+05 7 72 376.22 376.7 0.9987 261.96 261.6 1.0014 573.92 571.6 1.0041

5.50E+05 7 72 388.89 389.1 0.9994 260.07 259.9 1.0007 548.14 546.9 1.0023

6.50E+05 7 72 399.75 399.4 1.0009 258.50 258.5 1.000 526.67 527.5 0.9984

7.50E+05 7 72 409.31 409.3 1.0000 257.16 257.4 0.9991 508.28 509.6 0.9974

2.50E+05 8 82 327.44 325.9 1.0047 268.34 268.9 0.9979 646.90 651.7 0.9926

3.50E+05 8 82 346.71 345.8 1.0026 265.09 265 1.0004 603.59 604.7 0.9982

4.50E+05 8 82 361.84 361.2 1.0018 262.67 262.5 1.0006 571.23 571.4 0.9997

5.50E+05 8 82 374.40 373.4 1.0027 260.73 260.7 1.0001 545.40 546.7 0.9976

6.50E+05 8 82 385.19 384.1 1.0028 259.12 259.3 0.9993 523.90 526.2 0.9956

7.50E+05 8 82 394.67 392.7 1.0050 257.74 258.3 0.9978 505.48 510.5 0.9902

138

2.50E+05 9 93 310.40 310.7 0.9990 269.58 269.8 0.9992 651.28 651.7 0.9993

3.50E+05 9 93 329.23 330.6 0.9958 266.28 265.9 1.0014 608.03 604.2 1.0063

4.50E+05 9 93 344.03 345.5 0.9957 263.82 263.3 1.002 575.74 571.6 1.0072

5.50E+05 9 93 356.32 357.7 0.9962 261.86 261.5 1.0014 549.95 546.4 1.0065

6.50E+05 9 93 366.90 368 0.997 260.22 260.1 1.0005 528.48 526.4 1.0039

7.50E+05 9 93 376.20 376.9 0.9981 258.82 259 0.9993 510.09 509.9 1.0004

2.50E+05 10 103 299.43 297.8 1.0055 269.92 270.5 0.9979 647.22 652.2 0.9924

3.50E+05 10 103 318.24 317.5 1.0023 266.59 266.5 1.0003 603.69 604.6 0.9985

4.50E+05 10 103 333.05 332.3 1.0022 264.10 263.9 1.0008 571.17 571.7 0.9991

5.50E+05 10 103 345.37 344.2 1.0034 262.12 262.1 1.0001 545.21 546.9 0.9969

6.50E+05 10 103 355.97 354.3 1.0047 260.46 260.7 0.9991 523.60 527 0.9935

7.50E+05 10 103 365.31 363.7 1.0044 259.05 259.6 0.9979 505.09 509.4 0.9915

Average Ratio 1.0004 0.9999 0.9994

139

Table 5.6a: R2 values for LEADFlex-computed and EVERESTERSS-computed Pavement Thickness, Tensile and Compressive Strain for Light Traffic

Calibrated Parameter CBR (%)/ Coefficient of Determination R2

1 2 3 4 5 6 7 8 9 10

Pavement Thickness 1 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.998

Tensile Strain 0.974 0.971 0.973 0.977 0.980 0.983 0.981 0.982 0.982 0.981

Compressive 0.997 0.997 0.996 0.996 0.997 0.997 0.997 0.997 0.997 0.997

Table 5.6b: R2 values for LEADFlex-computed and EVERESTERSS-computed Pavement Thickness, Tensile and Compressive for Medium Traffic


1 2 3 4 5 6 7 8 9 10

Pavement Thickness 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999

Tensile Strain 0.980 0.984 0.986 0.987 0.985 0.986 0.986 0.986 0.986 0.986

Compressive 0.997 0.997 0.997 0.997 0.997 0.997 0.996 0.997 0.997 0.997

Table 5.6c R2 values for LEADFlex-computed and EVERESTERSS-computed Pavement Thickness, Tensile and Compressive for Heavy Traffic

140


1 2 3 4 5 6 7 8 9 10

Pavement Thickness 1.0 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999

Tensile Strain 0.993 0.994 0.991 0.993 0.995 0.993 0.994 0.993 0.994 0.993

Compressive 0.999 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998

Table 5.7a: Comparison of LEADFlex-Calculated and Measured Pavement Response for Subgrade Modulus 4,500psi (31MPa)

Lane

Subgrade CBR/

Modulus

Pavement Thickness

(mm)

Pavement Response

Tensile Strain

(10-6)

Compressive Strain

(10-6)

CBR

(%)

Mod.

(psi)

Mod.

(MPa)

Surface Base Total LEADFlex-

Calculated

Measured Ratio LEADFlex-

Calculated

Measured

Ratio

South (SM-2A) - ST. 5 3 4,500 31 50 200 250 298.93 286 1.04 1671.71 1615 1.03

North (SM-2A) - ST. 5 3 4,500 31 50 250 300 289.14 274 1.05 1345.96 1360 0.98

South (SM-2A) - ST. 10 3 4,500 31 50 300 350 280.86 270 1.04 1070.55 975 1.09

North (SM-2A) - ST. 10 3 4,500 31 50 350 400 273.69 265 1.03 831.97 850 0.97

South (SM-2A) - ST. 15 3 4,500 31 50 400 450 267.36 254 1.05 621.53 590 1.05

141

North (SM-2A) - ST. 15 3 4,500 31 50 450 500 261.70 250 1.04 433.29 444 0.97

Average Ratio 1.04 1.02

Table 5.7b: Comparison of LEADFlex-Calculated and Measured Pavement Response for Subgrade Modulus 6,000psi (41MPa)

Lane

Subgrade CBR/

Modulus

Pavement Thickness

(mm)

Pavement Response

Tensile Strain

(10-6)

Compressive Strain

(10-6)

CBR

(%)

Mod.

(psi)

Mod.

(MPa)


Calculated


Calculated

Measured

Ratio

South (SM-2A) - ST. 5 4 6,000 41 75 200 275 314.02 318 0.98 1168.20 1119 1.04

North (SM-2A) - ST. 5 4 6,000 41 75 250 325 303.43 297 1.03 970.05 982 0.99

South (SM-2A) - ST. 10 4 6,000 41 75 300 375 294.37 285 1.04 800.32 772 1.03

North (SM-2A) - ST. 10 4 6,000 41 75 350 425 286.44 278 1.03 651.86 617 1.06

South (SM-2A) - ST. 15 4 6,000 41 75 400 475 279.39 268 1.05 519.93 525 0.99

North (SM-2A) - ST. 15 4 6,000 41 75 450 525 273.05 262 1.04 401.22 382 1.05

142


Table 5.7c: Comparison of LEADFlex-Calculated and Measured Pavement Response for Subgrade Modulus 9,000psi (62MPa)

Lane

Subgrade CBR/

Modulus

Pavement Thickness

(mm)

Pavement Response

Tensile Strain

(10-6)

Compressive Strain

(10-6)

CBR

(%)

Mod.

(psi)

Mod.

(MPa)


Calculated


Calculated

Measured

Ratio

South (SM-2A) - ST. 5 6 9,000 62 50 200 250 306.81 299 1.02 1356.23 1362 0.99

North (SM-2A) - ST. 5 6 9,000 62 50 250 300 293.88 295 0.99 1062.76 1056 1.01

South (SM-2A) - ST. 10 6 9,000 62 50 300 350 282.95 285 0.99 814.19 802 1.02

North (SM-2A) - ST. 10 6 9,000 62 50 350 400 273.48 281 0.97 599.08 605 0.99

South (SM-2A) - ST. 15 6 9,000 62 50 400 450 263.48 275 0.95 409.34 403 1.02

North (SM-2A) - ST. 15 6 9,000 62 50 450 500 257.65 268 0.96 239.34 230 1.04


143

Table 5.7d: Comparison of LEADFlex-Calculated and Measured Pavement Response for Subgrade Modulus 10,500psi (72MPa)

Lane

Subgrade CBR/

Modulus

Pavement Thickness

(mm)

Pavement Response

Tensile Strain

(10-6)

Compressive Strain

(10-6)

CBR

(%)

Mod.

(psi)

Mod.

(MPa)


Calculated


Calculated

Measured

Ratio

South (SM-2A) - ST. 5 7 10,500 72 100 200 300 274.85 281 0.97 750.25 766 0.97

North (SM-2A) - ST. 5 7 10,500 72 100 250 350 266.07 272 0.98 630.19 599 1.05

South (SM-2A) - ST. 10 7 10,500 72 100 300 400 258.47 249 1.03 526.18 503 1.04

North (SM-2A) - ST. 10 7 10,500 72 100 350 450 251.76 239 1.05 434.45 441 0.98

South (SM-2A) - ST. 15 7 10,500 72 100 400 500 245.76 234 1.05 352.39 334 1.05

North (SM-2A) - ST. 15 7 10,500 72 100 450 550 249.33 240 1.03 278.16 264 1.05


144

Table 5.7e: Comparison of LEADFlex-Calculated and Measured Pavement Response for Subgrade Modulus 13,500psi (93MPa)

Lane

Subgrade CBR/

Modulus

Pavement Thickness

(mm)

Pavement Response

Tensile Strain

(10-6)

Compressive Strain

(10-6)

CBR

(%)

Mod.

(psi)

Mod.

(MPa)


Calculated


Calculated

Measured

Ratio

South (SM-2A) - ST. 5 9 13,500 93 75 200 275 309.57 298 1.03 873.20 882 0.99

North (SM-2A) - ST. 5 9 13,500 93 75 250 325 298.05 285 1.04 704.20 691 1.02

South (SM-2A) - ST. 10 9 13,500 93 75 300 375 288.18 271 1.06 559.44 551 1.01

North (SM-2A) - ST. 10 9 13,500 93 75 350 425 279.55 265 1.05 432.83 443 0.97

South (SM-2A) - ST. 15 9 13,500 93 75 400 475 271.88 260 1.04 320.06 331 0.97

North (SM-2A) - ST. 15 9 13,500 93 75 450 525 264.98 251 1.05 219.06 210 1.04


145

Table 5.7f: Comparison of LEADFlex-Calculated and Measured Pavement Response for Subgrade Modulus 15,000psi (103MPa)

Lane

Subgrade CBR/

Modulus

Pavement Thickness

(mm)

Pavement Response

Tensile Strain

(10-6)

Compressive Strain

(10-6)

CBR

(%)

Mod.

(psi)

Mod.

(MPa)


Calculated


Calculated

Measured

Ratio

South (SM-2A) - ST. 5 10 15,000 103 50 200 250 305.49 296 1.03 1085.54 1065 1.01

North (SM-2A) - ST. 5 10 15,000 103 50 250 300 291.05 286 1.02 829.18 801 1.03

South (SM-2A) - ST. 10 10 15,000 103 50 300 350 278.85 270 1.03 612.44 600 1.02

North (SM-2A) - ST. 10 10 15,000 103 50 350 400 268.28 261 1.03 424.69 411 1.03

South (SM-2A) - ST. 15 10 15,000 103 50 400 450 258.95 251 1.03 259.08 245 1.05

North (SM-2A) - ST. 15 10 15,000 103 50 450 500 250.61 240 1.04 110.94 102 1.08


146

Figure 5.5a: Calibration of Calculated and Measured Tensile Strain for 31MPa Subgrade Modulus

Figure 5.5b: Calibration of Calculated and Measured Compressive Strain for 31MPa Subgrade Modulus

147



148



149



150

Figure 5.9a: Calibration of Calculated and Measured Compressive Strain for 93MPa Subgrade Modulus


151



152

5.4: The LEADFlex Program

The LEADFlex visual basic interface windows are shown in Figures 5.11a, 5.11b,

5.11c and 5.11d. Figure 5.11a shows the start-up window, Figure 5.11b is the traffic

data input window, Figure 5.11c shows the pavement layer parameter input window

while Figure 5.11d shows the pavement response and structural pavement section

window.

Figure 5.11a: LEADFlex Program Start-up Window

153

5.4.1: LEADFlex Program Application and Design Example

The application of LEADFlex program is in three steps as presented in Figures 5.11b,

5.11c and 5.11d. The traffic data in Table 3.6 of section 3.2.10 was used as a typical

design example. The steps involved in the design are as follows;

Step 1 of 3 – This involves the input of traffic data as illustrated in Figure 5.11b

Step 2 of 3 – This involves pavement material and layer parameter input– Figure

5.11c

Step 3 of 3 – The design pavement thickness is adjusted for convenience – Figure

5.11d

Figure 5.11b: LEADFlex Traffic Data Window – Step 1 of 3

154

Figure 5.11c: Pavement Design Parameters Window – Step 2 of 3

Figure 5.11d: Pavement Response Window – Step 3 of 3

155

5.4.2: Adjustment of LEADFlex Pavement Thickness

The design example as illustrated in Figure 5.11d resulted in a minimum pavement

thickness of 429mm in order to meet both the fatigue and rutting criteria. Adjusting

the pavement thickness to a value lower than the minimum results in unsatisfactory

design. For instance, Figure 5.11e shows that the minimum pavement thickness of

429mm was adjusted to down to 421mm resulting in unsatisfactory design in terms

of rutting criterion with allowable compressive strain and damage factor not

satisfactory. In Figure 5.11f, increasing the pavement thickness from 421mm to

426mm satisfied the allowable compressive strain, yet the damage factor

requirement was not satisfied thereby requiring a redesign.

156

Figure 5.11e: Pavement Response Window – Rutting Criteria not meet – Step 3 of 3

Figure 5.11f: Pavement Response Window – Rutting Criteria not meet – Step 3 of 3

157

CHAPTER 6

CONCLUSION AND RECOMMENDATION

6.1 Conclusion

The research presented the result of a study to develop a layered elastic analysis and

design procedure for cement-stabilized lateritic base low volume asphalt pavement

in Nigeria. The pavement analysis involved a linear elastic, static analysis of the

multilayered system using the EVERSTRESS program with layer moduli, layer

thickness and Poisson’s ratio as inputs. The process offers a precise and simple

framework for pavement design. The process starts with material characterization of

the asphalt concrete, cement stabilized base and natural subgrade to determine the

material elastic/resilient modulus and traffic analysis in the form of equivalent

single axle load (ESAL) to determine the expected traffic within the design period.

The study presented simple regression equations relating expected traffic repetitions

and pavement thickness, pavement thickness and tensile strain at the bottom of

asphalt layer, and pavement thickness and compressive strain at the top of the

subgrade. The input parameters for the design process are the expected traffic and

pavement thickness. The outputs are tensile strain at the bottom of asphalt layer,

horizontal strain at the top of subgrade layer, number of traffic repetitions to failure

and damage factors for fatigue and rutting criteria respectively. The relationship

between LEADFlex-calculated pavement thickness, tensile and compressive strains

were compared using measured data collected from K-ATL and with those of

EVERSTRESS using linear regression analysis. The coefficients of determination

158

were found to be very good. The result showed minimum coefficient of

determination R2 of 0.992 and 0.994 for tensile (fatigue) and compressive (rutting)

strain respectively indicating that LEADFlex is a good predictor of fatigue and

rutting strains in cement-stabilized lateritic base for low-volume asphalt pavements.

The study also developed a design tool (LEADFlex program) for the design process.

The advantages of the procedure over other procedures are that it encompasses both

design and analysis of the pavement. Also the structural pavement design process is

precise as it eliminates the common problem of trial thickness design which makes

design cumbersome.

The major findings and conclusions obtained from the study are as follows:

1. At a particular subgrade CBR/resilient modulus, the thickness of the

pavement increases with increase in the expected traffic repetitions.

2. At a particular subgrade CBR/resilient modulus, the tensile strain at the

bottom of asphalt layer decreases as the pavement thickness increases.

3. At a particular subgrade CBR/resilient modulus, the compressive strain at the

top of subgrade layer decreases as the pavement thickness increases.

4. For any value of expected traffic repetition, the pavement thickness decreases

as the subgrade CBR/Resilient modulus increases.

5. LEADFlex-calculated strains show good agreement with the EVERSTRESS-

calculated strains

6. LEADFlex-calculated strains compares well with measured strains.

159

The study showed that LEADFlex procedure is a good estimator of tensile strain

below asphalt layer and compressive strain at the top of subgrade in asphalt

pavement.

6.2 Recommendation

In this study, the available measured pavement response (tensile and compressive

strains) were limited. Although FWD test results are available, enough measured

strain data corresponding to the LEADFlex pavement material properties (asphalt

concrete elastic modulus, base elastic modulus and subgrade resilient modulus)

were not available. The researcher therefore recommends as follows:

i. FWD response data involving the LEADFlex pavement thickness and material

parameters should be collected for future research. This will further

strengthen the validity of this research.

ii. Elastic modulus, resilient modulus and Poisson’s ratio of pavement materials

should be determined in the laboratory, so that a comparison between the

moduli determined by correlation with CBR and tested modulu can be

conducted to check the accuracy of the assumed Poisson’s ratio and pavement

layer moduli derived by correlation with other parameters such as CBR.

iii. Further research should be carried out to incorporate all values pavement

layer moduli rather than limit the moduli to those considered in the present

study.

160

iv. LEADFlex procedure should be adopted in the design of asphalt pavement in

Nigeria.

161

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EKWULO, EMMANUEL OSILEMME PG/Ph.D/10/57787 EMMANUEL... · I also thank the laboratory staff of the Department of Civil Engineering, RSUST for their support and assistance while carrying