EKWULO, EMMANUEL OSILEMME PG/Ph.D/10/57787

Transcription

1 i EKWULO, EMMANUEL OSILEMME PG/Ph.D/10/57787 DEVELOPMENT OF LAYERED ELASTIC ANALYSIS PROCEDURE FOR PREDICTION OF FATIGUE AND RUTTING STRAINS IN CEMENT - STABILIZED LATERITIC BASE OF LOW VOLUME ROADS CIVIL ENGNEERING ENGNEERING Agboeze Irene E. Digitally Signed by: Content manager s Name DN : CN = Webmaster s name O = University of Nigeria, Nsukka

2 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 EKWULO, EMMANUEL OSILEMME PG/Ph.D/10/57787 SUPERVISOR: PROF. J. C. AGUNWAMBA DEPARTMENT OF CIVIL ENGINEERING, UNIVERSITY OF NIGERIA, NSUKKA

3 iii 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... EKWULO, EMMANUEL OSILEMME PG/Ph.D/10/57787

4 CERTIFICATION iv

5 APPROVAL PAGE v

6 vi 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.

7 vii 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.

8 viii 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 R 2 were found to be very good. The calibration of LEADFlex-calculated and measured tensile and compressive strains resulted in minimum R 2 of and 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.

9 ix LIST OF TABLES 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 3.5: Vehicle Classification 74 Table 3.6: Vehicle Classification 76 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 Page

10 x 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

11 xi MEDIUM TRAFFIC 127 Table 5.5c: Comparison of LEADFlex and EVERSTRESS Result for HEAVY TRAFFIC 129 Table 5.6a: R 2 values for LEADFlex-computed and EVERESTERSS-computed Pavement Thickness, Tensile and Compressive Strain for Light Traffic 131 Table 5.6b: R 2 values for LEADFlex-computed and EVERESTERSS-computed Pavement Thickness, Tensile and Compressive for Medium Traffic 131 Table 5.6c: R 2 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 Response for Subgrade Modulus 6,000psi (41MPa) 132 Table 5.7c: Comparison of LEADFlex-Calculated and Measured Pavement Response for Subgrade Modulus 9,000psi (62MPa) 133 Table 5.7d: Comparison of LEADFlex-Calculated and Measured Pavement Response for Subgrade Modulus 10,500psi (72MPa) 133 Table 5.7e: Comparison of LEADFlex-Calculated and Measured Pavement Response for Subgrade Modulus 13,500psi (93MPa) 134 Table 5.7f: Comparison of LEADFlex-Calculated and Measured Pavement Response for Subgrade Modulus 15,000psi (103MPa) 134

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13 xiii LIST OF FIGURES 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 Page 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

14 xiv 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 Subgrade Modulus 136 Figure 5.6b: Calibration of Calculated and Measured Compressive Strain for 41MPa Subgrade Modulus 136 Figure 5.7a: Calibration of Calculated and Measured Tensile Strain for 62MPa Subgrade Modulus 137 Figure 5.7b: Calibration of Calculated and Measured Compressive Strain for 62MPa Subgrade Modulus 137 Figure 5.8a: Calibration of Calculated and Measured Tensile Strain for 72MPa Subgrade Modulus 138 Figure 5.8b: Calibration of Calculated and Measured Compressive Strain for 72MPa Subgrade Modulus 138 Figure 5.9a: Calibration of Calculated and Measured Tensile Strain for 93MPa Subgrade Modulus 139

15 xv Figure 5.9b: Calibration of Calculated and Measured Compressive Strain for 93MPa Subgrade Modulus 139 Figure 5.10a: Calibration of Calculated and Measured Tensile Strain for 103MPa Subgrade Modulus 140 Figure 5.10b: Calibration of Calculated and Measured Compressive Strain for 103MPa Subgrade Modulus 140 Figure 5.11a: LEADFlex Program Start-up Window 141 Figure 5.11b: LEADFlex Traffic Data Window Step 1 of Figure 5.11c: Pavement Design Parameters Window Step 2 of Figure 5.11d: Pavement Response Window Step 3 of Figure 5.11e: Pavement Response Window Rutting Criteria not meet Step 3 of Figure 5.11f: Pavement Response Window Rutting Criteria not meet Step 3 of 3 144

16 xvi TABLE OF CONTENT Page TITLE PAGE DECLARATION CERTIFICATION APPROVAL PAGE DEDICATION ACKNOWLEDGMENT ABSTRACT LIST OF TABLES LIST OF FIGURES i ii iii iv v vi vii viii xi CHAPTER 1: INTRODUCTION Background of Study Definition of Problem Research Justification Objectives Scope and Limitation Methodology of Study Purpose and Organization of Thesis 7 CHAPTER 2: LITERATURE REVIEW Pavement Design History Flexible Highway Pavements Pavement Design and Management Flexible Pavement Design Principles 14

17 xvii 2.5 Pavement Design Procedures Empirical Design Approach CBR Design Methods The Asphalt Institute CBR Method The National Crushed Stone Association CBR Method The Nigerian CBR Method The AASHTO Pavement Design Guides Mechanistic Design Approach Mechanistic Empirical Design Approach Layered Elastic System Finite Element Model Mechanistic-Empirical Design Inputs Traffic Loading Material Properties Elastic Modulus of Bituminous Materials Prediction Model for Dynamic and Resilient Modulus of Asphalt Concrete Elastic Modulus of Soils and Unbound Granular Materials Non-linearity of Pavement Foundation Poisson s Ratio Climatic Conditions Pavement Response Models Layered Elastic Model Finite Elements Model Flexible Pavement M-E Distress Models (Failure Criteria) 48

18 xviii Fatigue Failure Criterion Rutting Failure Criterion Layered Elastic Analysis Programs Validation with Experimental Data 57 CHAPTER 3: METHODOLOGY Layered Elastic Analysis and Design Procedure for Cement Stabilized Low-Volume Asphalt Pavement Empirical Pavement Material Characterization Asphalt Concrete Elastic Modulus Mix Proportion of Aggregates Specimen Preparation Determination of Bulk Specific Gravity (Gmb) of Samples Determination of Void of compacted mixture Density of Specimens Stability and Flow of Samples Determination of Asphalt Concrete Elastic Modulus Base Material Soil Classification Test Sieve Analysis Compaction Test Soil Classification California Bearing Ratio (CBR) Test Specimen Subgrade Material Poison s Ratio Traffic and Wheel load Evaluation 68

19 xix Loading Conditions LEADFlex Pavement Model Environmental Condition Pavement Layer Thickness Traffic Repetition Evaluation Determination of Design ESAL Analytical Summary of the LEADFlex Procedure 76 CHAPTER 4: DEVELOPMENT OF LEADFLEX DESIGN PROCEDURE AND PROGRAM Determination of Minimum Pavement Thickness Layered Elastic Analysis of LEADFlex Pavement Allowable Strains for LEADFlex Pavement Traffic Repetitions to Failure Damage Factor Development of LEADFlex Regression Equations Summary of LEADFlex Design Procedure Developlemt of LEADFlex Program Program Algorithm LEADFlex Visual Basic Codes 101 CHAPTER 5: RESULTS AND DISCUSSION Results Light Traffic Medium Traffic Heavy Traffic LEADFlex Pavement Characteristics 105

20 xx 5.2 Discussion of Result Expected Traffic and Pavement Thickness Relationship Pavement Thickness and Tensile Strain Relationship Pavement Thickness and Compressive Strain Relationship Effect of Subgrade CBR on Pavement Thickness Validation of LEADFLEX Result Coefficient of Determination Comparison of LEADFlex with EVERSTRESS Results Comparison with K-ATL measured field data : The LEADFlex Program : LEADFlex Program Application and Design Example : Adjustment of LEADFlex Pavement Thickness 143 CHAPTER 6: CONCLUSION AND RECOMMENDATION Conclusion 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

21 79 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

22 80 launched. The American Association of State Highway Official [AASHTO, 1993) introduced its first guide in 1972 which was revised in 1986 and 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.

23 81 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

24 82 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 CBRbased 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

25 83 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

26 84 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 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.

27 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 cementstabilized 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.

28 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

29 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.

30 88 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, 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,

31 ). 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.

32 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 mechanisticempirical 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

33 91 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

34 92 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

35 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. iii. iv. reducing cracking reducing layer thickness 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.

36 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

37 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

38 96 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) 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

39 97 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

40 98 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.

41 99 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 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

42 100 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 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 The Asphalt Institute CBR Method

43 101 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 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

44 102 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)

45 103 Table 2.1.: Minimum Asphalt Pavement Thickness(TA) (Source: Oguara, 2005) Traffic DTN Minimum TA(mm) Light Less than Medium Heavy More than Table 2.2: NCSA Design Index categories (Source: Oguara, 2005) Design Index DI-1 DI-2 DI-3 General Character Light traffic (few vehicles heavier than passenger cars, no regular use by Group 2 or 3 vehicles) Medium-light traffic (similar to DI-1, maximum 1000 VPD including not over 5% Group 2, no regular use by Group 3 vehicles Medium traffic (maximum 3000VPD, including not over 10% Group 2 and 3, 1% Group 3 vehicles) Daily ESAL 5 or less

46 104 DI-4 DI-5 DI-6 Medium heavy traffic (maximum 6000VPD, including not over 15% Group 2 and 3, 1% Group 3 vehicles) Heavy traffic (maximum 6000VPD, may include 25% Group 2 and 3, 10% Group 3 vehicles) Very heavy traffic (over 6000VPD, may include over 25% Group 2 or 3 vehicles) Figure 2.2: NCSA Design Chart (Source: Oguara, 2005)

47 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.

48 106 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)

49 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 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 , 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

50 108 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 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 elasticitybased 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

51 109 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 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 mechanisticempirical procedures. Several studies over the past fifteen years have advanced mechanistic-empirical techniques. Most of the works, however, were based on variants

52 110 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) 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): P σz = k. (2.0) Z 2 Where, k = and 3 2π r 2 [ 1+ ( ) ] z (2.1) r is the radial distance from the point of load application.

53 111 For stress on a vertical plate passing through the centre of a loaded plate: σz = 3 z ( ) P 1 (2.2) r + z 3 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: = 2E 2 3P( r ) ( r + z ) 2 (2.3) This may be written as = P ( a) F E (2.4) Where, F = r 2 [ 1+ ( ) ] z (2.5)

54 112 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: = 1.5Pa E (2.6) and for a rigid plate, the deflection is given as: = 1.18Pa E (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

55 113 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. iii. Each layer has a finite thickness h except the lower layer, and all are infinite in the horizontal direction. 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 = σ r1 E 1 σ σ r1 z1 µ 1 µ 1 (2.8) E1 E1 1 E Єz1 = ( σ ) 3 σ (2.9) z 2 r3 Where,

56 114 σ z1 = vertical stress at interface 1 (bottom of asphalt concrete layer) σ z2 = vertical stress at interface 2 σ r1 = horizontal stress at the bottom of layer 1 σ r 2 = horizontal stress at the bottom of layer 2 σ r3 = horizontal stress at the top of layer 3 E 1 and E 3 are Modulus of elasticity of layer 1 and 3 receptively. µ = Poisson s ratio of the layer P a µ 1 = 0.5, h 1, E 1 σ z1 σ r1 Interface 1 µ 2 = 0.5, h 2, E 2 σ z2 σ r2 σ r3 Interface 2 µ 1 = 0.5, h 3, E 2 Figure 2.4: Three-Layer Pavement System Showing Location of Stresses

57 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 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.

58 116 Table 2.3: Inputs levels in layered elastic Design Material Input Input Input Level 1 Level 2 Level 3 Asphalt Concrete Measured Estimated Default Diametric Modulus Diametric Modulus Diametric Modulus Portland Cement Measured Estimated Default Concrete Elastic Modulus Elastic Modulus Elastic Modulus Stabilized Materials Measured Resilient Modulus Estimated Resilient Modulus Default Resilient Modulus Granular Materials Measured Estimated Default Resilient Modulus Resilient Modulus Resilient Modulus Subgrades Measured Estimated Default Resilient Modulus Resilient Modulus Resilient Modulus Table 2.4: Default Resilient Modulus (M r) Values for Pavement Materials General Level of Subgrade Support Very Good Good AASHTO Soil Classification Coarse grained: Gravel and gravely soils; A-1-a, A-1-b Coarse grained: Sand and Sandy soils A-2-4, A-3 Broad M r range and Mean M r at Optimum Moisture Content 172 to 310MPa Mean = 269MPa 138 to 275MPa Mean = 207MPa

59 117 Fair Poor Very Poor Fined grained: Mixed silt and clay A-2-7, A-4, A-2-5, A-2-6 Fine grained: Low compressibility A-5, A-6 Fine grained: High compressibility A-7-5, A to 207MPa Mean = 179MPa 69 to 172MPa Mean = 124MPa 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 Typical µ Clay (saturated) Clay (unsaturated)

60 118 Sandy clay Silt Dense sand Coarse-grained sand Fine-grained sand Bedrock Crushed Stone Cement Treated Fine-grain Materials 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

61 119 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 = NV x TF (2.10) TF NA x E = N V F (2.11) Where, NV = number of commercial vehicles NA = Number of axles TF = Truck or commercial vehicle factor

62 120 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 ( + ) 1 g n 1 g (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.

63 121 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 axle lorries, tippers and mammy wagons axle lorries, tippers and tankers axle tractor-trailer units (single driven axle, tandem rear axles) 6 4-axle tractor units (tandem driven axle, tandem rear axles) 7 5-axle tractor-trailer units(tandem driven axle, tandem rear axles) axle lorries with two towed trailers 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,

64 122 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 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 D 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* = σ 0 σ 0 + (2.14) ε Cosφ ε 0Sinφ 0 Where, σ0 = stress amplitude (N/mm 2 ) ε0 = recoverable strain amplitude (mm/mm)

65 123 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* = σ 0 E * = (2.15) ε 0 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:

66 124 Horizontal Diametral Plane: + = x d x d d t P x π σ (2.16) + = x d d d t P y π σ (2.17) τxy = 0 (2.18) Vertical Diametral Plane: d t P x.. 2 π σ = (2.19) + + = d y d y d d t P y π σ (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.

67 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 log E + * = P 2 [ P P ( P ) P ] 1e ( P ( log f logη ) ) P V a V ( V beff beff + V a ) (2.22a) Where E * = Dynamic modulus, in 10 5 Psi η f = Bituminous viscosity, in 10 6 Poise (at any temperature, degree of aging) = 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)

68 126 P38 = Percent retained on 9.51mm sieve, by total aggregate weight(cumulative) P4 = Percent retained on 4.76mm sieve, by total aggregate weight(cumulative) P200 = Percent retained on 0.074mm sieve, by total aggregate weight(cumulative) Asphalt concrete elastic modulus can also be predicted using equation 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 /AFJMAN , 1994). The elastic modulus can then be predicted by modifying equation 2.22b as follows: log E + = P 2 [ P P ( P ) P ] 4 1e ( P 38 ( logη ) 200 ) P V 34 a V ( V beff beff + V a ) (2.22b) Where E = Elastic modulus, in 10 5 Psi η = Bituminous viscosity, in 10 6 Poise (at any temperature, degree of aging) 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) P38 = Percent retained on 9.51mm sieve, by total aggregate weight(cumulative)

69 127 P4 = Percent retained on 4.76mm sieve, by total aggregate weight(cumulative) P200 = Percent retained on 0.074mm sieve, by total aggregate weight(cumulative) 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:

70 128 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) Where, MR = 0.2 x h 0.45 x MRs (2.25) 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: u = (1.18 x 10 8 ) M (2.26) f 2.32 R Where,

71 129 u f = relative damage factor MR = resilient modulus in psi Therefore, over an entire year, the average relative damage is given by: u f = u f 1 + u f 2 + n... + u fn 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 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) Non-linearity of Pavement Foundation

72 130 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 = qr C ' Po q r m (2.30) Where Gr = Resilient shear modulus qr = Repeated deviator stress P0 = Mean normal effective stress C, m = Constant for the particular soil

73 131 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 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 Granular Base Subgrade If deformations are monitored from either static or dynamic test, an approximate µ value could be obtained from equation (2.28): 1 1 V µ = 1 2 ε a V0 (2.31) Where,

74 132 V = volume of the material 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):

75 MMPT = MMAT z + 4 z + 4 ( ) ( ) (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 nearsaturation. 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

76 134 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 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. iii. The bottom layer (usually the subgrade) extends infinitely downwards. 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

77 135 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)

78 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 closeform 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.

79 137 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 mechanisticempirical design of highway pavements are based on limiting strains in the asphalt bound layer (fatigue analysis) and permanent deformation (rutting) in the subgrade 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.

80 138 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: D = i i = 1 n N i f (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).

81 139 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 = 1 a ε t b (2.34) Where Nf = Number of load applications to failure ε t = 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 = x ε t (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)

82 140 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 = ε 3.291log t E log AC (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: = ( ε ) ( EI ) (2.37) Nf t Where, Nf = Number of load repetitions to to prevent fatigue cracking

83 141 εt = Tensile Strain at the bottom of asphalt layer EI = Elastic modulus of asphalt concrete (psi) 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 = x ε v (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.

84 142 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 = ( c ) x 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

85 143 Failure N f Shell Model Model Model (10-6 ) (10-6 ) (10-6 ) (10-6 ) (10-6 ) (10-6 ) (10-6 ) Figure 2.7: Rutting Criteria by Various Agencies (Source: Oguara, 2005)

86 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 = h h E E K (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.

87 145 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 (semiinfinite) 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)

88 146 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

89 147 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.

90 148 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

91 149 the calculated and field response values, and concluded elastic models under-predict pavement response at intermediate and high temperatures.

92 150 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 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.

93 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. iii. iv. Softening Point Test Ductility Test 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 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

94 152 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 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

95 153 iii. Density and voids The maximum stability, unit weight and median of air voids were determined as 1700N, 2460kg/m 3 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) 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: G mb a = (3.1) W a W W w where, Gmb = bulk specific gravity of compacted specimen Wa = Weight air Ww = Weight in water Determination of Void of compacted mixture

96 154 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 V a Gmm Gmb = x 100% (3.2) Gmm Where, Va = percent air voids content Gmm = maximum specific gravity of compacted mixture Gmb = bulk specific gravity of compacted mixture Density of Specimens The density of the specimens were determined by multiplying the bulk specific gravity already determined by 1000kg/m Stability and Flow of Samples

97 155 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 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. log E + = P 2 [ P P ( P ) P ] 4 1e Where E = Elastic Modulus (Psi) ( P 38 ( logη ) 200 ) P V 34 a V ( V beff beff + V a ) (3.3) η = Bituminous viscosity, in 10 6 Poise (at any temperature, degree of aging) Va = Percent air voids content, by volume Vbeff = Percent effective bitumen content, by volume 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)

98 156 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 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)

99 Soil Classification Test The following soil classification tests were carried out on the sample to obtain its physical properties. (i) (ii) (iii) (iv) Natural moisture content. Atterberg limit (liquid and plastic limit) Sieve analysis Compaction (Moisture-density) tests 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 ac bd (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

100 158 15% and not exceeding 55% expressed as a whole number (1-40), therefore b = = 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 = = 6 GI = 0.2 x x0x x 7x 6 = 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 Soil Classification

101 159 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/m 3 (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 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

102 160 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% 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 Mr (psi) = 1500 CBR (3.6) In accordance with AASHTO Guide (AASHTO, 1993), the relative damage per month were determined using equation 3.7. u = (1.18 x 10 8 ) M (3.7) f 2.32 R

103 161 From equations 3.6 and 3.7 u = (1.18 x 10 8 )x( 1500CBR ) (3.8) f 2.32 Where, u f = relative damage factor CBR = California Bearing Ratio (%) Therefore, over an entire year, the average relative damage was determined using equation 3.9 as follows: : u f = u f 1 + u f 2 + n... + u fn Where, n = 12. (3.9) u = 0.53 f Hence from equation 3.8, the average CBR is given by CBR = (0.847 xu f x10 ) (3.10) 1500 = 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.

104 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) 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 A.C. Surface Thickness Stabilized Base Thickness ESAL (mm) (mm) Light 1 x x Medium 5 x x Heavy 2.5 x x Light Traffic

105 163 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 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

106 164 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 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. 1800mm I 305m 305m y II 305m 305m 1300mm III 1800mm x Figure 3.1: Typical Single Wheel and Dual-wheel Tandem

107 165 Table 3.2: Load and materials parameter for determination of critical wheel load Wheel Tire Pavement Layer Pavement Material Moduli Poison s Ratio Load (kn) Pressure (kpa) Thickness (mm) (MPa) A.C. Surface Base A.C Base Subgrade A.C Base Subgrade layer Surface Surface T 1 T 2 E 1 E 2 E Table 3.3: Critical Loading Configuration Determination Load Configuration Axle Load Maximum Strain Pavement Response Maximum Stress Max. Deflection (10-6 ) (kpa) (10-6 mm) 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 40kN (I) Single Axle, Dual Wheel 20kN

108 166 (II) Tandem Axle, Dual Wheel 20kN (II + III) 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). P a µ 1 = 0.35 ε r1 h 1 50mm µ 2 = 0.40 ε z2 h 2 >50mm µ 3 = 0.45, E 3 = MPa Figure 3.2: Typical LEADFlex Pavement Section Showing Location of Strains

109 167 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 Base layer A.C Surface Base Subgrade A.C Surface Base Subgrade T 1 T 2 E 1 E 2 E 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: 1 34 MMPT = MMAT z + 4 z + 4 ( ) ( ) (3.11)

110 168 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 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 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

111 169 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 axle lorries, tippers and mammy wagons axle lorries, tippers and tankers axle tractor-trailer units (single driven axle, tandem rear axles) 6 4-axle tractor units (tandem driven axle, tandem rear axles) 7 5-axle tractor-trailer units(tandem driven axle, tandem rear axles) axle lorries with two towed trailers 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.

112 170 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

113 171 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 Ni = AADT x F x 365 x ( 1 + g) g n 1 (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 10 5

114 172 Table 3.6: Vehicle Classification Vehicle Class Equivalent Operational Factor Number of Vehicles in 24 hours Total ESAL per day Total ESAL per Year Multiplier ( + ) 1 g n 1 g Total ESAL in 20 years (2) x (3) (4) x 365 days (1) (2) (3) (4) (5) (6) (7) 1 negligible , , Total ESAL in 20 years 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

115 173 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.

116 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. Material Inputs Traffic Inputs Pavement Layer Thickness LEADFlex Model Increase Is Is Pavement YE Vertical Compressive Strain Pavement Response Horizontal Tensile Strain YE N Expected Load Repetitions Allowable Load Repetitions NO Compute Damage D D>1? Yes D<<1? No Final Design Figure 3.3: Flow Diagram for LEADFlex Procedure

117 175 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

118 176 (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. = ( ε ) ( EI ) (4.1) Nf t Nr = ( c ) x 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)

119 177 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 = ( E N i ( ) ) (4.3) Єc = 7.32 x 10 ( N i ) (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).

120 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 D = i i = 1 ni N (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.

121 179 b y1 a ln x1 = (4.6) y 2 = a ln( x 2 ) + c (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

122 180 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 ( + ) 1 g n 1 g (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.

123 181 (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 = ( E N i ( ) ) (4.9) (d) Evaluate allowable/limiting compressive strain on top subgrade layer using equation This must be less than actual compressive strain computed in STEP 3(b) Єc = (7.32 x 10 ( N i )) (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 = ( E ε t ) ( ) (4.11) (f) Evaluate number of traffic repetitions to failure (Nr) in terms of rutting strain using the asphalt institute model in equation Nr = x10 ( ε c ) (4.12) (g) Evaluate damage factor (Df) in terms of fatigue using equation This must be less than or equal 1. Df = Ni/Nf (4.13) (h) Evalaute damage factor (Dr) in terms of rutting using equation This must be less than or equal to 1. Dr = Ni/Nr (4.14)

124 182 Table 4.1a: Light Traffic Pavement Response Analysis A.C Mod. E1 (MPa) Base Mod. E2 (MPa) Sub Mod. E3 (MPa) A.C Surface T1 (mm) Layer Thickness Stabilized Base T2 (mm) Total T (mm) Expected Repetitions Ni Horizontal Tensile Strain Fatigue Criterion Allowable Tensile Strain No. of Repetition to Failure D.F Vertical Compressive Strain Rutting Criterion Allowable Compressive Strain No. of Repetition to Failure D.F E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

125 E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

126 E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

127 E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

128 186 Table 4.1b: Light Traffic - Pavement Response Data (N i = 1 x x 10 4, T 1 = 50mm) Subgrade Expected Traffic (ESAL) Pavement Thickness (mm) Horizontal Tensile (Fatigue) Strain Vertical Compressive (Rutting) Strain CBR % Modulus Surface T 1 Base T 2 Total T (10-6 ) (10-6 ) E E E E E E E E E E

129 E E E E E E E E E E E E E E E

130 E E E E E E E E E E E E E E

131 E E E E E E E E E E E Table 4.1c: Light Traffic - Pavement Response Regression Equations (N i = 1 x x 10 4, T 1 = 50mm) A.C Base Subgrade Expected Traffic Fatigue Criterion Rutting Criterion Modulus Modulus CBR Modulus Pavement Thickness

132 190 (MPa) (MPa) (%) (MPa) Relationship Tensile Strain - Pavement Thickness Relationship Compressive Strain Pavement Thickness Relationship E1 E2 E3 (10-6 ) (10-6 ) (MPa) (MPa) (MPa) T = (N i) R² = 1 ε t = ln(T) R² = ε c = ln(T) R² = T = 92.91(Ni) R² = 1 ε t = ln(T ) R² = ε c = ln(T) R² = T = 83.29(Ni) R² = T = (Ni) R² = 1 ε t = ln(T) R² = ε t = ln(T) R² = ε c = ln(T) R² = ε c = ln(T) R² = T = 66.65(Ni) R² = 1 ε t = ln(T) R² = ε c = ln(T) R² = T = 60.35(Ni) R² = 1 ε t = ln(T) R² = ε c = ln(T) R² = 0.999

133 T = 54.88(Ni) R² = ε t = ln(T) R² = ε c = ln(T) R² = T = 50.12(Ni) R² = ε t = ln(T R² = ε c = ln(T) R² = T = 44.99(Ni) R² = ε t = ln(T) R² = ε c = ln(T) R² = T = 40.66(Ni) R² = ε t = ln(T) R² = ε c = ln(T) R² = 1 Table 4.2a: Medium Traffic Pavement Response Analysis A.C Mod. E1 (MPa) Base Mod. E2 (MPa) Sub Mod. E3 (MPa) A.C Surface T1 (mm) Layer Thickness Stabilized Base T2 (mm) Total T (mm) Expected Repetitions N i Horizontal Tensile Strain Fatigue Criterion Allowable Tensile Strain No. of Repetition to Failure D.F Vertical Compressive Strain Rutting Criterion Allowable Compressive Strain No. of Repetition to Failure D.F

134 E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

135 E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

136 E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

137 E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E Table 4.2b: Medium Traffic - Pavement Response Data (Ni = 5 x x 10 5, T 1 = 75mm) Subgrade Expected Traffic (ESAL) Pavement Thickness (mm) Horizontal Tensile Strain (Fatigue) Vertical Compressive (Rutting) Strain

138 196 CBR Modulus Surface Base Total % T 1 T 2 T (10-6 ) (10-6 ) E E E E E E E E E E E E E

139 E E E E E E E E E E E E E E

140 E E E E E E E E E E E E E E

141 E E E E E E E E E Table 4.2c: Medium Traffic - Pavement Response Regression Equations (Ni = 5 x x 10 5, T 1 = 75mm) A.C Base Subgrade Expected Traffic Fatigue Criterion Rutting Criterion Modulus Modulus CBR Modulus Pavement Thickness Relationship (MPa) (MPa) (%) (MPa) Tensile Strain - Pavement Thickness Relationship Compressive Strain Pavement Thickness Relationship

142 200 E1 E2 E3 (10-6 ) (10-6 ) (MPa) (MPa) (MPa) T = (N i) R² = 1 ε t = ln(T) R² = ε c = ln(T) R² = T = 86.87(N i) R² = 1 ε t = ln(T) R² = ε c = ln(T) R² = T = 76.76(N i) R² = 1 ε t = ln(T) R² = ε c = ln(T) R² = T = 67.95(N i) R² = 1 ε t = ln(T) R² = ε c = ln(T) R² = T = 60.32(N i) R² = 1 ε t = ln(T) R² = ε c = ln(T) R² = T = 54.78(N i) R² = 1 ε t = ln(T) R² = ε c = ln(T) R² = 0.999

143 T = 49.48(N i) R² = ε t = ln(T) R² = ε c = ln(T) R² = T = 44.62(N i) R² = ε t = ln(T) R² = ε c = ln(T) R² = T = 40.22(N i) R² = ε t = ln(T) R² = ε c = ln(T) R² = T = 36.38(N i) R² = ε t = ln(T) R² = ε c = ln(T) R² = Table 4.3a: Heavy Traffic Pavement Response Analysis A.C Mod. E1 (MPa) Base Mod. E2 (MPa) Sub Mod. E3 (MPa) A.C Surface T1 (mm) Layer Thickness Stabilized Base T2 (mm) Total T (mm) Expected Repetitions N i Horizontal Tensile Strain Fatigue Criterion Allowable Tensile Strain No. of Repetition to Failure D.F Vertical Compressive Strain Rutting Criterion Allowable Compressive Strain No. of Repetition to Failure D.F E E E E E E E

144 E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

145 E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

146 E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

147 E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

148 E E E E E E E E E E E E E E E E E E E E E E E E E E E E Table 4.3b: Heavy Traffic - Pavement Response Data (N i = 2.5 x x 10 5, T 1 = 100mm) Subgrade Expected Traffic (ESAL) Pavement Thickness (mm) Horizontal Tensile (Fatigue) Strain Vertical Compressive (Rutting) Strain CBR % Modulus Surface T 1 Base T 2 Total T (10-6 ) (10-6 ) E E E E E E

149 E E E E E E E E E E E E E E E

150 E E E E E E E E E E E E E E E

151 E E E E E E E E E E E E E

152 E E E E E E E E E E E Table 4.3c: Heavy Traffic - Pavement Response Regression Equations (N i = 2.5 x x 10 5, T 1 = 100cmm) A.C Base Subgrade Expected Traffic Fatigue Criterion Rutting Criterion Modulus Modulus CBR Modulus Pavement Thickness Relationship (MPa) (MPa) (%) (MPa) Tensile Strain - Pavement Compressive Strain

153 211 E1 E2 E3 Thickness Relationship (10-6 ) Pavement Thickness Relationship (MPa) (MPa) (MPa) (10-6 ) T = 98.72(N i)0.133 R² = 1 ε t = ln(T) R² = ε c = ln(T) R² = T = 80.77(N i) R² = 1 ε t = ln(T) R² = ε c = ln(T) R² = T = 69.64(N i) R² = 1 ε t = ln(T) R² = ε c = ln(T) R² = T = 61.11(N i) R² = 1 ε t = ln(T) R² = ε c = ln(T) R² = T = 54.23(N i) R² = 1 ε t = ln(T) R² = ε c = ln(T) R² = T = 48.24(N i) R² = ε t = ln(T) R² = ε c = ln(T) R² = 0.999

154 T = 43.92(N i) R² = 1 ε t = ln(T) R² = ε c = ln(T) R² = T = 39.58(N i) R² = 1 ε t = ln(T) R² = ε c = ln(T) R² = T = 35.26(N i) R² = 1 ε t = ln(T) R² = ε c = ln(T) R² = T = 31.57(N i) R² = 1 ε t = ln(T) R² = y = ln(T) R² = 1

155 Developlemt of LEADFlex Program The LEADFlex programme was developed using algorithm, Visual Basic Codes and program interface as presented in the following section 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 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 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 LEADFlex Visual Basic Codes The LEADFlex Visual Basic Codes are as presented in APPENDIX F

156 103 CHAPTER 5 RESULTS AND DISCUSSION 5.1 Results The results of the developed LEADFlex pavement design procedure are presented in sections 5.1.1, and for light, medium and heavy traffic categories respectively 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 N i Subgrade CBR (%)/Pavement Thickness (mm) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% (ESAL) 1.00E E E E E

157 104 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% 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% 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

158 105 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 N i Subgrade CBR (%)/ Pavement Thickness (mm) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% (ESAL) 5.00E E E E E 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%

159 106 Table 5.2c: Pavement Thickness, Subgrade CBR and Vertical Compressive Strain data for Medium Traffic Pavement Thickness (mm) Subgrade CBR (%)/Vertical Compressive Strain (10-6 ) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 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 N i Subgrade CBR (%)/ Pavement Thickness (mm) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% (ESAL) 2.50E E E

160 E E E 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% Table 5.3c: Pavement Thickness, Subgrade CBR and Vertical Compressive Strain data for Heavy Traffic Pavement Thickness (mm) Subgrade CBR (%)/Vertical Compressive Strain (10-6 ) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

161 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.

162 106 Subgrade Minimum Pavement Thickness Fatigue Criteria Rutting Criteria (mm) CBR (%) Modulus (MPa) E3 (MPa) A.C. Surface Cement- Stabilized Base Total Max. Fatigue Strain ε t (10-6 ) Allowable Fatigue Strain Є t (10-6 ) No. of Repetitions to failure N f Damage Factor D f Max. Rutting Strain ε c (10-6 ) Allowable Rutting Strain Є c (10-6 ) No. of Repetitions to failure N r Damage Factor D r x x x x x x x x x x x x

163 x x x x x x x x Table 5.4a: Light Traffic LEADFlex Pavement Characteristics - ( E 1 = psi (3450MPa), E 2 = 329MPa, N i = 5 x 10 4 max) Table 5.4b: Medium Traffic LEADFlex Pavement Characteristics - (E 1 = psi (3450MPa), E 2 = 329MPa, N i = 2.5x10 5 max.) Subgrade Minimum Pavement Thickness Fatigue Criteria Rutting Criteria (mm) CBR (%) Modulus (MPa) E3 (MPa) A.C. Surface Cement- Stabilized Base Total Max. Fatigue Strain ε t (10-6 ) Allowable Fatigue Strain Є t (10-6 ) No. of Repetitions to failure N f Damage Factor D f Max. Rutting Strain ε c (10-6 ) Allowable Rutting Strain Є c (10-6 ) No. of Repetitions to failure N r Damage Factor D r

164 x x x x x x x x x x x x x x x x x x x x

165 109 Table 5.4c: Heavy Traffic LEADFlex Pavement Characteristics (E 1 = psi (3450MPa), E 2 = 329MPa, N i = 7.5x10 5 max.) Subgrade Minimum Pavement Thickness Fatigue Criteria Rutting Criteria (mm) CBR (%) Modulus (MPa) E3 (MPa) A.C. Surface Cement- Stabilized Base Total Max. Fatigue Strain ε t (10-6 ) Allowable Fatigue Strain Є t (10-6 ) No. of Repetitions to failure N f Damage Factor D f Max. Rutting Strain ε c (10-6 ) Allowable Rutting Strain Є c (10-6 ) No. of Repetitions to failure N r Damage Factor D r x x x x x x x x x x x x

166 x x x x x x x x

167 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 and for light, medium and heavy traffic categories respectively 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. LIGHT TRAFFIC Figure 5.1a: Expected Traffic Pavement Thickness Relationship for Light Traffic

168 110 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 mm to mm while at 10% CBR, as the expected traffic increased from 1.00E+04 to 5.00E+05, the pavement thickness also increased from mm to mm. The result indicates that for a subgrade CBR of 1%, a minimum pavement thickness of mm 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 mm 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. MEDIUM TRAFFIC Figure 5.1b: Expected Traffic Pavement Thickness Relationship for Medium Traffic 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 mm to mm while at 10% CBR, as the expected traffic increased from

169 E+04 to 2.50E+05, the pavement thickness increased from mm to mm. The result indicates that for the medium traffic situation, a subgrade CBR of 1% requires a minimum pavement thickness of mm to withstand the maximum traffic of 2.5.0E+05 ESAL, while a subgrade CBR of 10% requires a minimum pavement thickness of mm 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. HEAVY TRAFFIC Figure 5.1c: Expected Traffic Pavement Thickness Relationship for Heavy Traffic 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 mm to mm while at 10% CBR, the pavement thickness increased from mm to mm as the expected traffic increases from

170 E+05 to 7.50E+05. The result indicates that a subgrade CBR of 1% requires a minimum pavement thickness of mm to withstand the maximum traffic of 7.5.0E+05 ESAL, while subgrade CBR of 10% requires a minimum pavement thickness of mm 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) 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

171 113 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 mm to mm, the fatigue strain decreased from x10-6 to x 10-6 while for a subgrade CBR of 10%, as the pavement thickness increased from to mm, the fatigue decreased from x 10-6 to x This result indicates that for the light traffic situation, a subgrade CBR of 1% requires a minimum pavement thickness of mm to withstand the maximum fatigue strain of x10-6 while a subgrade CBR of 10% requires a minimum pavement thickness of mm to withstand the maximum fatigue strain of x The same trend was observed for other subgrade CBR. This result implied that for the light traffic category, about % 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. MEDIUM TRAFFIC Figure 5.2b: Pavement Thickness Horizontal Tensile Strain Relationship for Medium Traffic

172 114 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 mm to mm, the fatigue strain decreased from x10-6 to x 10-6 while for a subgrade of 10%, as the pavement thickness increased from mm to mm, the fatigue strain decreased from x 10-6 to x This result shows that for the medium traffic situation, a subgrade CBR of 1% requires a minimum pavement thickness of mm to withstand the maximum fatigue strain of x10-6 while a subgrade CBR of 10% will require a minimum pavement thickness of mm to withstand a maximum fatigue strain of x The same trend was observed for other subgrade CBR. This result indicates that for the medium traffic category, increasing the pavement thickness by about % reduced the tensile strain by about 10.56%, 13.04%, 14.30%, 15.01%, 15.67%, 16.05% %, 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

173 115 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 x10-6 to x 10-6 as the pavement thickness increased from mm to mm while for 10% subgrade CBR, the fatigue decreased from x 10-6 to x 10-6 as the pavement thickness increased from mm to mm. This result indicates that for the heavy traffic situation, a subgrade CBR of 1% requires a minimum pavement thickness of mm to withstand the maximum fatigue strain of x10-6 while a subgrade of 10% CBR will require the minimum pavement thickness of mm to withstand the maximum fatigue strain of x 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) 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.

174 116 LIGHT TRAFFIC Figure 5.3a: Pavement Thickness Vertical Compressive Strain Relationship for Light Traffic 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 mm to mm, the rutting strain decreased from 2, x10-6 to x 10-6 and x 10-6 to 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 mm is required to withstand a maximum rutting strain of 2, x10-6 while a subgrade CBR of 10% requires a minimum pavement thickness of mm to withstand a maximum rutting strain of x The same trend was observed for other subgrade CBR. This result also shows that for the light traffic category, increasing the pavement thickness by % 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.

175 117 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 x10-6 to x 10-6 as the pavement thickness increased from mm to mm while for 10% subgrade CBR, the rutting strain decreased from x 10-6 to x 10-6 as the pavement thickness increased from mm to mm. The result indicates that for subgrade CBR of 1%, a minimum pavement thickness of mm is required to withstand a maximum rutting strain of x10-6 while for a subgrade CBR of 10%, a minimum pavement thickness of mm withstands a maximum rutting strain of x The same trend was observed for other subgrade CBR. The result further indicated that for the medium traffic category, increasing the pavement thickness by % 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

176 118 In the case of heavy traffic category, Figure 5.2c shows that for 1% subgrade CBR, the rutting strain decreased from 1, x10-6 to x 10-6 as the pavement thickness increased from mm to mm while fort 10% subgrade CBR, the rutting strain decreased from x 10-6 to x 10-6 as the pavement thickness increased from mm to mm. The result indicates that for subgrade CBR of 1%, a minimum pavement thickness of mm is required to withstand the maximum rutting strain of 1, x10-6 while for 10% subgrade CBR, a minimum pavement thickness of mm is required to withstand a maximum rutting strain of x 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. HEAVY TRAFFIC Figure 5.3c: Pavement Thickness Vertical Compressive Strain Relationship for Heavy Traffic

177 119 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) 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 mm to mm as the subgrade CBR increased from 1% to 10%,. Similarly, for expected traffic of 5.00E+04 ESAL, the pavement thickness decreased from mm to mm as the subgrade CBR 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. LIGHT TRAFFIC Expected Traffic Figure 5.4a: Effect of subgrade CBR on Pavement Thickness for Light Traffic

178 120 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 mm to mm as the subgrade CBR increased from 1% to 10%. Also, for expected traffic of 5.00E+04 ESAL, the pavement thickness decreased from mm to mm 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. MEDIUM TRAFFIC Expected Traffic Figure 5.4b: Effect of subgrade CBR on Pavement Thickness for Medium Traffic

179 121 HEAVY TRAFFIC Expected Traffic Figure 5.4c: Effect of subgrade CBR on Pavement Thickness for Heavy Traffic For heavy traffic category, Figure 5.4c shows that for an expected traffic of 1.00E+04 ESAL, the pavement thickness decreased from mm to mm as the subgrade CBR increased from 1% to 10%. Also, for expected traffic of 5.00E+04, the pavement thickness decreased from mm to mm as the subgrade CBR 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

180 122 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 R 2 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) Coefficient of Determination The result of the LEADFlex design procedure was validated in the first instance, using the estimated R 2 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 R 2 values were 0.975, and for light, medium and heavy traffic respectively. This R 2 values indicates that the LEADFlex regression equations are good predictors (estimators) of pavement thickness, fatigue and rutting strains in highway pavements.

181 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 LEADFlexcalculated to EVERSTRESS-calculated pavement thicknesses were 0.99, 0.99, and 1.00 for light, medium and heavy traffic respectively. The average ratio of LEADFlexcalculated 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 EVERSTRESScalculated pavement thickness using linear regression analysis shows that the minimum coefficient of determination are 0.998, and for light, medium and heavy traffic. Calibration of tensile (fatigue) strain resulted in minimum R 2 of 0.971, and for light respectively, medium and heavy traffic respectively while that of compressive (rutting) strain were 0.996, and for light, medium and heavy traffic respectively. Similarly, linear regression analysis of LEADFlex-calculated and EVERSTRESS-calculated pavement thickness resulted in maximum R 2 of and 1.0 for light, medium and heavy traffic respectively. Calibration of tensile (fatigue) strain resulted in R 2 of 0.982, and for light, medium and heavy traffic respectively while that of compressive (rutting) strain were 0.997, and for light, medium and heavy traffic respectively.

182 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 ( ) 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

183 125 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 R 2 were found to be very good. The calibration of LEADFlex-calculated and measured tensile and compressive strain resulted in R 2 of and respectively for subgrade modulus of 31MPa, and respectively for subgrade modulus of 41MPa, and respectively for subgrade modulus of 62MPa, and respectively for subgrade modulus of 72MPa, and respectively for subgrade modulus of 93MPa, and and 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.

184 126 Table 5.5a: Comparison of LEADFlex and EVERSTRESS Result for LIGHT TRAFFIC Expected Traffic (ESAL) Subgrade CBR/Modulus Pavement Thickness (mm) Tensile Strain (10-6 ) Pavement Response Compressive Strain (10-6 ) CBR (%) Modulus (MPa) LEADFlex EVERSTRESS Ratio LEADFlex EVERSTRESS Ratio LEADFlex EVERSTRESS Ratio 1.00E E E E E E E E E E

185 E E E E E E E E E E E E E E

186 E E E E E E E E E E E E E E

187 E E E E E E E E E E E E Average Ratio

188 130 Table 5.5b: Comparison of LEADFlex and EVERSTRESS Result for MEDIUM TRAFFIC Expected Traffic (ESAL) Subgrade CBR/Modulus Pavement Thickness (mm) Tensile Strain (10-6 ) Pavement Response Compressive Strain (10-6 ) CBR (%) Modulus (MPa) LEADFlex EVERSTRESS Ratio LEADFlex EVERSTRESS Ratio LEADFlex EVERSTRESS Ratio 5.00E E E E E E

189 E E E E E E E E E E E E E E

190 E E E E E E E E E E E E E E E

191 E E E E E E E E E E E E E E

192 E Average Ratio Table 5.5c: Comparison of LEADFlex and EVERSTRESS Result for HEAVY TRAFFIC Expected Traffic (ESAL) Subgrade CBR/Modulus Pavement Thickness (mm) Tensile Strain (10-6 ) Pavement Response Compressive Strain (10-6 ) CBR (%) Modulus (MPa) LEADFlex EVERSTRESS Ratio LEADFlex EVERSTRESS Ratio LEADFlex EVERSTRESS Ratio 2.50E E E E E E

193 E E E E E E E E E E E E E E E

194 E E E E E E E E E E E E E

195 E E E E E E E E E E E E E E

196 E E E E E E E E E E E E Average Ratio

197 139 Table 5.6a: R 2 values for LEADFlex-computed and EVERESTERSS-computed Pavement Thickness, Tensile and Compressive Strain for Light Traffic Calibrated Parameter CBR (%)/ Coefficient of Determination R Pavement Thickness Tensile Strain Compressive Table 5.6b: R 2 values for LEADFlex-computed and EVERESTERSS-computed Pavement Thickness, Tensile and Compressive for Medium Traffic Calibrated Parameter CBR (%)/ Coefficient of Determination R Pavement Thickness Tensile Strain Compressive Table 5.6c R 2 values for LEADFlex-computed and EVERESTERSS-computed Pavement Thickness, Tensile and Compressive for Heavy Traffic

198 140 Calibrated Parameter CBR (%)/ Coefficient of Determination R Pavement Thickness Tensile Strain Compressive Table 5.7a: Comparison of LEADFlex-Calculated and Measured Pavement Response for Subgrade Modulus 4,500psi (31MPa) Lane Subgrade CBR/ Modulus Pavement Thickness (mm) Tensile Strain Pavement Response Compressive Strain (10-6 ) (10-6 ) CBR Mod. Mod. Surface Base Total LEADFlex- Measured Ratio LEADFlex- Measured Ratio (%) (psi) (MPa) Calculated Calculated South (SM-2A) - ST , North (SM-2A) - ST , South (SM-2A) - ST , North (SM-2A) - ST , South (SM-2A) - ST ,

199 141 North (SM-2A) - ST , Average Ratio Table 5.7b: Comparison of LEADFlex-Calculated and Measured Pavement Response for Subgrade Modulus 6,000psi (41MPa) Lane Subgrade CBR/ Modulus Pavement Thickness (mm) Tensile Strain Pavement Response Compressive Strain (10-6 ) (10-6 ) CBR Mod. Mod. Surface Base Total LEADFlex- Measured Ratio LEADFlex- Measured Ratio (%) (psi) (MPa) Calculated Calculated South (SM-2A) - ST , North (SM-2A) - ST , South (SM-2A) - ST , North (SM-2A) - ST , South (SM-2A) - ST , North (SM-2A) - ST ,

200 142 Average Ratio Table 5.7c: Comparison of LEADFlex-Calculated and Measured Pavement Response for Subgrade Modulus 9,000psi (62MPa) Lane Subgrade CBR/ Modulus Pavement Thickness (mm) Tensile Strain Pavement Response Compressive Strain (10-6 ) (10-6 ) CBR Mod. Mod. Surface Base Total LEADFlex- Measured Ratio LEADFlex- Measured Ratio (%) (psi) (MPa) Calculated Calculated South (SM-2A) - ST , North (SM-2A) - ST , South (SM-2A) - ST , North (SM-2A) - ST , South (SM-2A) - ST , North (SM-2A) - ST , Average Ratio

201 143 Table 5.7d: Comparison of LEADFlex-Calculated and Measured Pavement Response for Subgrade Modulus 10,500psi (72MPa) Lane Subgrade CBR/ Modulus Pavement Thickness (mm) Tensile Strain Pavement Response Compressive Strain (10-6 ) (10-6 ) CBR Mod. Mod. Surface Base Total LEADFlex- Measured Ratio LEADFlex- Measured Ratio (%) (psi) (MPa) Calculated Calculated South (SM-2A) - ST , North (SM-2A) - ST , South (SM-2A) - ST , North (SM-2A) - ST , South (SM-2A) - ST , North (SM-2A) - ST , Average Ratio

202 144 Table 5.7e: Comparison of LEADFlex-Calculated and Measured Pavement Response for Subgrade Modulus 13,500psi (93MPa) Lane Subgrade CBR/ Modulus Pavement Thickness (mm) Tensile Strain Pavement Response Compressive Strain (10-6 ) (10-6 ) CBR Mod. Mod. Surface Base Total LEADFlex- Measured Ratio LEADFlex- Measured Ratio (%) (psi) (MPa) Calculated Calculated South (SM-2A) - ST , North (SM-2A) - ST , South (SM-2A) - ST , North (SM-2A) - ST , South (SM-2A) - ST , North (SM-2A) - ST , Average Ratio

203 145 Table 5.7f: Comparison of LEADFlex-Calculated and Measured Pavement Response for Subgrade Modulus 15,000psi (103MPa) Lane Subgrade CBR/ Modulus Pavement Thickness (mm) Tensile Strain Pavement Response Compressive Strain (10-6 ) (10-6 ) CBR Mod. Mod. Surface Base Total LEADFlex- Measured Ratio LEADFlex- Measured Ratio (%) (psi) (MPa) Calculated Calculated South (SM-2A) - ST , North (SM-2A) - ST , South (SM-2A) - ST , North (SM-2A) - ST , South (SM-2A) - ST , North (SM-2A) - ST , Average Ratio

204 146 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

205 147 Figure 5.6a: Calibration of Calculated and Measured Tensile Strain for 41MPa Subgrade Modulus Figure 5.6b: Calibration of Calculated and Measured Compressive Strain for 41MPa Subgrade Modulus

206 148 Figure 5.7a: Calibration of Calculated and Measured Tensile Strain for 62MPa Subgrade Modulus Figure 5.7b: Calibration of Calculated and Measured Compressive Strain for 62MPa Subgrade Modulus

207 149 Figure 5.8a: Calibration of Calculated and Measured Tensile Strain for 72MPa Subgrade Modulus Figure 5.8b: Calibration of Calculated and Measured Compressive Strain for 72MPa Subgrade Modulus

208 150 Figure 5.9a: Calibration of Calculated and Measured Compressive Strain for 93MPa Subgrade Modulus Figure 5.9b: Calibration of Calculated and Measured Compressive Strain for 93MPa Subgrade Modulus

209 151 Figure 5.10a: Calibration of Calculated and Measured Tensile Strain for 103MPa Subgrade Modulus Figure 5.10b: Calibration of Calculated and Measured Compressive Strain for 103MPa Subgrade Modulus

210 : 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

211 : 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 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

212 154 Figure 5.11c: Pavement Design Parameters Window Step 2 of 3 Figure 5.11d: Pavement Response Window Step 3 of 3