Deterioration Modelling of Granular Pavements for Rural Arterial Roads

DETERIORATION MODELLING OF GRANULAR PAVEMENTS FOR RURAL ARTERIAL ROADS

By Nahla Hussein Aswad Alaswadko

Submitted in fulfillment of the requirements for the degree of Doctor of Philosophy

Faculty of Science, Engineering and Technology

Swinburne University of Technology

Melbourne, Australia

December 2016

ABSTRACT

To keep any network in service at an acceptable condition and maintain and preserve the network performance, the management system can be enhanced by models for predicting pavement conditions. Investigation into maintenance and rehabilitation of rural arterial roads is triggered when road condition reaches certain threshold levels of roughness, rutting and cracking. To assist road agencies in their long term planning, the aim of this research project is to develop powerful deterioration models for a rural arterial network, using novel approaches for data preparation and modelling.

The reliability and usefulness of such models in a pavement management system stem from using accurate datasets with suitable modelling approaches. Therefore, the study’s main goal is to use a new approach for preparing accurate condition data to use in developing pavement deterioration models utilising a new modelling approach. Pavement condition parameters modelled herein, include surface roughness, rutting and cracking.

To achieve the aim of this study, representative samples of highways from Victoria’s spray sealed rural network are considered. The selected sample network is from 40 highways with a combined length of more than 2,300 km. The network covers a large sample size with representative ranges of traffic loading, pavement strength, subgrade soil type and environmental factors for four road classes (M, A, B and C) which differ in quality and function. For each highway segment (100m), readily available historical time series data covering a number of years has been collected for use in models’ development and validation.

A great emphasis and effort has been put into the data preparation process because it is a vital step for the development of robust deterioration models. Therefore, a State of the Art approach for preparing condition data for use in developing pavement deterioration models is demonstrated. It involves: data alignment process, data cleaning process, data filtering process, boundary limits of data and compiling and splitting datasets.

The prepared panel datasets have hierarchical structure with four-levels of variation within the selected network. Time series observations are nested within segments which are nested within highways which are nested within the four road classes.

ABSTRACT

An exploratory analysis has been carried out using traditional linear regression model. The Durbin-Watson test from this analysis is used to test whether the residuals are positively correlated or not. The results have indicated that there is statistical evidence that the residuals are positively correlated in all datasets. Consequently, this meant that the traditional regression approach is inappropriate for analysing panel data because it allows for a single level of variation only. The aim is to apply a modelling approach that captures the effect of variance at all possible levels in modelling roughness and rutting progression and predicting the probability of pavement crack initiation and progression.

Multilevel analysis also called Hierarchical Linear Modelling (HLM) has been used to develop empirical deterministic models to predict pavement roughness and rutting progression over time as functions of a number of contributing variables. However, a Hierarchical Generalized Linear Models (HGLM) framework has been used to develop probabilistic models to predict crack initiation and progression. These types of analyses are used to allow for nesting of the data creating sample dependencies. This dependency violates the assumptions of traditional statistical models, including independence of errors and homogeneity of regression intercepts and slopes. Hence multilevel analysis can account for the correlation among time series data of the same segment and capture the effects of unobserved factors. As a result, the study demonstrates that unobserved heterogeneity is a critical aspect that should be considered not only between segments but between highways and road classes as well.

The study presented predicted roughness and rutting progression models for the whole network and the four road classes. The study has concluded that a separate model for each road class provides more realistic predictions than the overall network model, which would help researchers to better understand the effect of contributing factors. The models will also help road agencies in developing more efficient maintenance programs.

Accuracy and reliability of the developed models have been tested using simulation and validation processes. Further, assessments of the performance of all road classes are conducted by comparing their pavement conditions and factors affecting the rate of pavement deterioration. The results indicate that the effect of traffic loading is stronger than other factors on roughness progression for class M and class A; however, the effect of initial pavement strength is stronger than the other factors for class B and class C.

ABSTRACT

Also, it has been found that the effect of time is stronger than the effects of other contributing factors on rutting progression for all road classes. Another main observation is that the decrease in strength of sealed granular pavements has a stronger contribution to rutting progression than the increase in traffic loading.

The study estimates the probability of crack initiation at a certain time and predicts the probability of a pavement maintaining its current level of cracking. It has been found that the developed probabilistic model format for cracking data provide flexibility in the application of the model when triggers are set according to risk considerations. In addition, it is found that the effect of time is stronger than the effects of the other factors on crack initiation and progression. Also, the effect of traffic loading is stronger than the effect of initial pavement strength in crack initiation phase. However, the effect of pavement strength at any time is stronger than the effect of traffic loading in crack progression phase.

The study results indicate that different pavement segments within a network may deteriorate at the same rate but their roughness values could be different at the same time due to their different initial pavement condition, design standards, construction quality, or any other unobserved variables. Further, it has been observed that subgrade soil type and climate condition only affect roughness and rutting progressions of light duty pavements. The study also showed that class M roads have longer gradual phase of roughness progression than the other road classes. However, they have shorter rutting gradual phase than the other road classes.

From cracking observation data, the study has shown that there are less cracked observations in heavy duty pavements than light duty pavements due to more frequent crack sealing practice for the former pavements than the latter. Further, in all road classes the percent of observations of ‘insignificant affected area’ is higher than for the other categories, whereas the percent of observations of ‘significant affected area’ is lower than the other categories. Also, it shows that observations of the significant affected area for class C are higher than for the other road classes.

The study concludes that multilevel modelling approach is a successful approach to present advanced analysis of pavement deterioration models. The procedure outlined is quite general, and can be applied to any pavement condition variable that has continuous data or ordinal classification with data that has a hierarchical structure. With

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ABSTRACT accurate prediction models, the implications of optimum maintenance timing and rehabilitation strategies can be assessed with confidence and practical decisions can be made.

ACKNOWLEDGMENTS

This thesis would never have done without the guidance, encouragement and support from many people.

Special thanks must go to my main supervisor, A/Prof. Rayya Hassan for her continuous guidance and encouragement. Her support and enlightening discussions were essential for this research. This thesis would never have been possible without her valuable advice, critical review and useful suggestions.

I would also like to thank my associate supervisors, A/Prof. Denny Meyer for her helpful discussions in using HLM7 software and her recommendations in statistics, and Dr. Robert Evans for his early assistance with using In-House Excel based tool.

I would acknowledge the Iraqi Ministry of Higher Education and Scientific Research for granting me the scholarship to give me the opportunity to undertake this study research. The financial support provided by the Iraqi government for supporting this study is gratefully appreciated.

I acknowledge and appreciate Prof. Riadh Al-Mahaidi for his continuous support and encouragement, Dr. Sylvia Mackie for her always willing to help me with editing, VicRoads for supplying the data for this thesis, and Mr. Hunar Hamza and A/Prof. Everarda Cunningham for their early help with statistics.

I wish to express my love and deep gratitude to my husband, Bayar Mohammed, a friend who made everything possible to hold my hands through the smooth and the rough patches of this road. I could not have made it this far without him.

The biggest thank you is extended to my lovely daughters, Ara and Darya for granting me the power to pursue this study research and giving up their precious playtime with their mummy. Their patience with me through this bumpy and rough road of my life journey is highly appreciated.

My sincere gratitude is extended to my beloved sister, Mayson, and her husband, Abduljabbar Abdy for their never-ending precious assistance and continuous support. Without their help, this part of my lifespan would have been severely inflexible.

I would like to thank all my friends for their support, especially Nasreen Hussein, a friend who has always been there for me and to give me support and make my study years memorable!

Finally, I am grateful to my family and friends for their best wishes and tremendous support, although from thousands of miles away, were always there for me. I really acknowledge them for their encouragement throughout this long undertaking.

Nahla Hussein Aswad Alaswadko, 2016

PUBLICATIONS

PUBLICATIONS The following publications are based on the work presented in this thesis:

 Alaswadko, N. & Hassan, R. 2016. Rutting Progression Models for Light Duty Pavements. International Journal of Pavement Engineering, DOI:10.1080/ 10298436.2016.1155123.

 Alaswadko, N., Hassan, R. & Evans, R. 2015. Effect of Traffic and Environmental Factors on Roughness Progression Rate of Sealed Low Volume Arterials. In: proceedings of the 9th International Conference on Managing Pavement Assets (ICMPA9), 18-21 May 2015, Virginia, Washington DC. USA.

 Alaswadko, N., Hassan, R. & Evans, R. 2015. Absolute Deterministic Based Models for Pavement Deterioration of Low Volume Arterials in Victoria/ Australia. Presented in Conference of Australian Institutes of Transport Research (CAITR), February, 2015, Melbourne University, Victoria, Australia.

 Alaswadko, N., Hassan, R., Meyer, D. & Mohammed, B. 2016. Probabilistic Prediction Models for Crack Initiation and Progression of Spray Sealed Pavements. International Journal of Pavement Engineering, DOI: 10.1080/10298436. 2016.1244437.

 Alaswadko, N., Hassan, R., Meyer, D. & Mohammed, B. 2016. An Absolute Deterministic Model for Permanent Deformation of Low Volume Flexible Pavements. In: proceedings of the 27th ARRB conference, November, 2016, Melbourne, Victoria, Australia.

 Alaswadko, N., Hassan, R. & Mohammed, B. 2016. A New Approach for Estimating Pavement Rutting Progression. In: proceedings of the 2nd IRF Asia Regional Congress & Exhibition, October 16-20, 2016, Kuala Lumpur, Malaysia.

 Alaswadko, N., Hassan, R., Meyer, D. & Mohammed, B. 2016. Modelling Roughness Progression of Sealed Granular Pavements: A New Approach. International Journal of Pavement Engineering, (revised manuscript has been submitted).

 Alaswadko, N. & Hassan, R. 2016. Performance Comparison between Heavy and Light Duty Pavements. (Manuscript has been submitted to International Journal of Pavement Engineering).

DECLARATION

I hereby declare that this thesis contains no materials that has been accepted for the award to the candidate of any other degree or diploma, except where due reference has been made in the text of the examinable outcome.

To the best of my knowledge, this thesis contains no material previously published or written by another person except where due reference has been made in the text of the examinable outcome.

Nahla Hussein Aswad Alaswadko

December, 2016

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TABLE OF CONTENTS

ABSTRACT ...... I ACKNOWLEDGMENTS...... V PUBLICATIONS ...... VI DECLARATION ...... VII TABLE OF CONTENTS ...... VIII LIST OF FIGURES ...... XIV LIST OF TABLES ...... XIX LIST OF EQUATIONS ...... XXIII ABBREVIATIONS AND NOTATIONS ...... XXVI 1. CHAPTER ONE ...... 1 INTRODUCTION ...... 1 1.1 INTRODUCTION ...... 1 1.2 BACKGROUND ...... 1 1.3 PROBLEM STATEMENT ...... 4 1.4 RESEARCH AIM AND OBJECTIVES ...... 5 1.5 RESEARCH OUTCOMES AND SIGNIFICANCE ...... 6 1.6 THESIS ORGANISATION ...... 7 2. CHAPTER TWO ...... 10 LITERATURE REVIEW ...... 10 2.1 INTRODUCTION ...... 10 2.1.1 Pavement Types in Victoria ...... 10 2.2 PAVEMENT PERFORMANCE MEASURES ...... 12 2.2.1 Pavement Distress Modes...... 13 2.2.2 Pavement Distress Measurement ...... 14 2.2.2.1 Roughness ...... 14 2.2.2.2 Rutting ...... 17 2.2.2.3 Cracking ...... 18 2.2.3 Causes of Pavement Distress ...... 19 2.2.4 Phases of Pavement Deterioration ...... 20 2.2.4.1 Phases of Road Roughness ...... 20 2.2.4.2 Phases of Rutting ...... 21 2.2.4.3 Phases of Cracking ...... 22 2.3 FACTORS CONTRIBUTING TO PAVEMENT DETERIORATION ...... 22 2.3.1 Traffic Loading ...... 23 2.3.2 Climate ...... 26 2.3.3 Pavement Composition ...... 29 2.3.3.1 Pavement Materials ...... 29 2.3.3.2 Pavement Thickness ...... 30 2.3.4 Pavement Strength ...... 30 2.3.5 Subgrade Soil...... 32 2.3.6 Maintenance ...... 33 2.3.7 Pavement Age ...... 34 2.3.8 Drainage ...... 35 2.4 CLASSIFICATION OF DETERIORATION MODELS ...... 37 2.4.1 Deterministic Models ...... 39 2.4.1.1 Mechanistic Models ...... 39 2.4.1.2 Empirical Models ...... 40 2.4.1.3 Mechanistic - Empirical Models ...... 41 2.4.2 Probabilistic Models ...... 41 2.4.2.1 Survivor Curves ...... 42 2.4.2.2 Markov Models ...... 42 2.4.2.3 Semi-Markov Models ...... 43

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2.4.2.4 Continuous Models ...... 44 2.4.3 Other Models ...... 44 2.4.3.1 Artificial Neural Networks (ANN) ...... 44 2.4.3.2 Finite Element (FE) ...... 45 2.4.3.3 Data Mining (DM) ...... 45 2.4.3.4 Minimum Message Length (MML) ...... 46 2.4.3.5 Fuzzy Logic (FL) ...... 46 2.5 DETERIORATION MODELS FOR SEALED GRANULAR PAVEMENTS ...... 47 2.6 SUMMARY OF THE LITERATURE REVIEW ...... 54 3. CHAPTER THREE ...... 56 MODELLING REQUIREMENTS AND DATA COLLECTION PROCESS ...... 56 3.1 INTRODUCTION ...... 56 3.1.1 Road Types in Victoria ...... 56 3.2 MODEL REQUIREMENTS ...... 58 3.3 NETWORK SELECTION CRITERIA ...... 59 3.4 DATA COLLECTION PROCESS ...... 64 3.4.1 Condition Data / Performance Measures ...... 64 3.4.1.1 Roughness Data ...... 65 3.4.1.2 Rutting and Cracking Data ...... 65 3.4.2 Data Related to the Factors that Affect Pavement Performance ...... 66 3.4.2.1 Initial Surface Condition ...... 67 3.4.2.2 Traffic Loading...... 67 3.4.2.3 Climate Condition...... 69 3.4.2.4 Subgrade Soil Types ...... 71 3.4.2.5 Drainage Condition ...... 73 3.4.2.6 Pavement Types ...... 73 3.4.2.7 Maintenance Activities ...... 74 3.4.2.8 Road Geometry...... 75 3.4.2.9 Pavement Strength ...... 75 3.5 SUMMARY ...... 76 4. CHAPTER FOUR ...... 78 DATA PREPARATION ...... 78 4.1 INTRODUCTION ...... 78 4.2 ALIGNING CONDITION DATA ...... 78 4.2.1 Aligning Roughness Data ...... 78 4.2.2 Aligning Rutting and Cracking Data...... 82 4.3 CLEANING CONDITION DATA ...... 86 4.4 EXCLUDING MAINTENANCE EFFECT (DATA FILTERING) ...... 88 4.5 SETTING UP DATA BOUNDARY LIMITS ...... 89 4.6 COMPILING AND SPLITTING THE PREPARED DATASETS ...... 92 4.7 SUMMARY ...... 92 5. CHAPTER FIVE ...... 94 PRELIMINARY ANALYSIS AND MODELLING APPROACH...... 94 5.1 INTRODUCTION ...... 94 5.2 STRUCTURE OF PREPARED DATASETS ...... 94 5.2.1 Descriptive Statistics ...... 97 5.2.1.1 Roughness Dataset ...... 97 5.2.1.2 Rutting Dataset ...... 99 5.2.1.3 Cracking Dataset ...... 101 5.2.2 Transformation of Variables...... 105 5.2.3 Removing Prediction Bias ...... 106 5.2.4 Interpreting Transformed Variables ...... 107 5.3 MODELLING APPROACH ...... 107 5.3.1 Exploratory Analysis ...... 108 5.3.2 Multilevel Models Specifications ...... 111 5.3.2.1 Hierarchical Linear Model (HLM) Specifications ...... 112 5.3.2.2 Hierarchical Generalized (Logistic) Linear Model (HGLM) Specifications ...... 116 5.3.3 Multilevel Model Fit...... 122 5.3.3.1 Null Model ...... 122 5.3.3.2 Growth Model ...... 124

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5.3.3.3 Conditional Model ...... 124 5.3.4 Multicollinearity Issue in Multilevel Model ...... 124 5.4 MODEL EVALUATION ...... 125 5.5 MODEL ASSESSMENT ...... 126 5.6 MODEL VALIDATION PROCESS ...... 127 5.6.1 Apparent Validation Method ...... 127 5.6.2 Internal Validation Method ...... 128 5.7 MODEL SIMULATION PROCESS ...... 129 5.8 SUMMARY ...... 129 6. CHAPTER SIX ...... 131 DEVELOPMENT OF ROUGHNESS PROGRESSION MODELS ...... 131 6.1 INTRODUCTION ...... 131 6.2 WHOLE NETWORK (NW) ROUGHNESS PROGRESSION MODEL ...... 132 6.2.1 NW Roughness Null Model ...... 132 6.2.2 NW Roughness Growth Model ...... 134 6.2.3 NW Roughness Conditional Model ...... 135 6.3 CLASS M ROUGHNESS PROGRESSION MODEL ...... 138 6.3.1 Class M Roughness Null Model ...... 138 6.3.2 Class M Roughness Growth Model ...... 139 6.3.3 Class M Roughness Conditional Model ...... 140 6.4 CLASS A ROUGHNESS PROGRESSION MODEL ...... 142 6.4.1 Class A Roughness Null Model ...... 142 6.4.2 Class A Roughness Growth Model ...... 143 6.4.3 Class A Roughness Conditional Model ...... 144 6.5 CLASS B ROUGHNESS PROGRESSION MODEL ...... 146 6.5.1 Class B Roughness Null Model ...... 146 6.5.2 Class B Roughness Growth Model ...... 147 6.5.3 Class B Roughness Conditional Model ...... 148 6.6 CLASS C ROUGHNESS PROGRESSION MODEL ...... 150 6.6.1 Class C Roughness Null Model...... 150 6.6.2 Class C Roughness Growth Model...... 151 6.6.3 Class C Roughness Conditional Model ...... 152 6.7 ACCURACY EVALUATION OF ROUGHNESS MODELS ...... 154 6.8 ASSESSMENT OF DEVELOPED ROUGHNESS MODELS ...... 156 6.9 VALIDATION OF THE DEVELOPED ROUGHNESS MODELS ...... 158 6.9.1 Apparent Validation Method ...... 158 6.9.2 Internal Validation Method ...... 161 6.10 DETERMINISTIC SIMULATION FOR THE DEVELOPED ROUGHNESS MODELS ...... 164 6.11 SUMMARY ...... 169 7. CHAPTER SEVEN ...... 172 DEVELOPMENT OF RUTTING PROGRESSION MODELS ...... 172 7.1 INTRODUCTION ...... 172 7.2 WHOLE NETWORK (NW) RUTTING PROGRESSION MODEL ...... 173 7.2.1 NW Rutting Null Model ...... 173 7.2.2 NW Rutting Growth Model ...... 175 7.2.3 NW Rutting Conditional Model ...... 176 7.3 CLASS M RUTTING PROGRESSION MODEL ...... 178 7.3.1 Class M Rutting Null Model ...... 179 7.3.2 Class M Rutting Growth Model ...... 180 7.3.3 Class M Rutting Conditional Model ...... 181 7.4 CLASS A RUTTING PROGRESSION MODEL ...... 182 7.4.1 Class A Rutting Null Model ...... 182 7.4.2 Class A Rutting Growth Model ...... 183 7.4.3 Class A Rutting Conditional Model ...... 184 7.5 CLASS B RUTTING PROGRESSION MODEL ...... 186 7.5.1 Class B Rutting Null Model ...... 186 7.5.2 Class B Rutting Growth Model ...... 187 7.5.3 Class B Rutting Conditional Model ...... 188

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7.6 CLASS C RUTTING PROGRESSION MODEL ...... 190 7.6.1 Class C Rutting Null Model ...... 190 7.6.2 Class C Rutting Growth Model ...... 191 7.6.3 Class C Rutting Conditional Model ...... 192 7.7 ACCURACY EVALUATION OF RUTTING MODELS ...... 194 7.8 ASSESSMENT OF DEVELOPED RUTTING MODELS ...... 195 7.9 VALIDATION OF THE DEVELOPED RUTTING MODELS ...... 197 7.9.1 Apparent Validation Method ...... 197 7.9.2 Internal Validation Method ...... 200 7.10 DETERMINISTIC SIMULATION FOR THE DEVELOPED RUTTING MODELS ...... 203 7.11 SUMMARY ...... 208 8. CHAPTER EIGHT ...... 211 DEVELOPMENT OF CRACK INITIATION AND PROGRESSION MODELS ...... 211 8.1 INTRODUCTION ...... 211

8.2 WHOLE NETWORK (NW) CRACK INITIATION (CRINI) MODEL ...... 212 8.2.1 NW Crack Initiation Null Model ...... 213 8.2.2 NW Crack Initiation Growth Model ...... 215 8.2.3 NW Crack Initiation Conditional Model ...... 216

8.3 WHOLE NETWORK CRACK PROGRESSION (CRPRO) MODEL ...... 219 8.3.1 NW Crack Progression Null Model ...... 219 8.3.2 NW Crack Progression Growth Model ...... 222 8.3.3 NW Crack Progression Conditional Model ...... 224 8.4 ACCURACY EVALUATION OF CRACKING MODELS ...... 227 8.5 VALIDATION OF THE DEVELOPED CRACKING MODELS ...... 231 8.6 SIMULATION FOR THE DEVELOPED CRACKING MODELS ...... 233 8.6.1 Simulation for Crack Initiation Models ...... 234 8.6.2 Simulation for Crack Progression Models ...... 236 8.7 SUMMARY ...... 243 9. CHAPTER NINE ...... 246 COMPARISON BETWEEN RESULTS OF DEVELOPMED MODELS FOR THE FOUR ROAD CLASSES ...... 246 9.1 INTRODUCTION ...... 246 9.2 COMPARISON BETWEEN ROUGHNESS MODELS FOR THE FOUR ROAD CLASSES ...... 247 9.2.1 Comparison between Roughness Null Models ...... 247 9.2.2 Comparison between Roughness Growth Models ...... 248 9.2.3 Comparison between Roughness Conditional Models ...... 250 9.3 COMPARISON BETWEEN RUTTING MODELS FOR THE FOUR ROAD CLASSES ...... 252 9.3.1 Comparison between Rutting Null Models ...... 252 9.3.2 Comparison between Rutting Growth Models ...... 254 9.3.3 Comparison between Rutting Conditional Models...... 255 9.4 COMPARISON BETWEEN CRACKING CONDITION FOR THE FOUR ROAD CLASSES...... 257 9.5 SUMMARY ...... 258 10. CHAPTER TEN ...... 260 SUMMARY, CONCLUSIONS AND RECOMMENDATIONS ...... 260 10.1 INTRODUCTION ...... 260 10.2 SUMMARY AND FINDINGS ...... 260 10.2.1 Roughness Models ...... 264 10.2.2 Rutting Models ...... 268 10.2.3 Cracking Models ...... 271 10.3 CONCLUSIONS ...... 274 10.4 RECOMMENDATIONS ...... 276 11. REFERENCES ...... 278 A. APPENDIX - A ...... 294 LAYOUTS OF TYPICAL ERD FILE AND EVENT FILE ...... 294 A.1 SAMPLE OF ERD FILE ...... 294 A.2 SAMPLE OF EVENT FILE ...... 295

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B. APPENDIX - B ...... 296 DESCRIPTION OF WORKING PRINCIPLES OF CLIMATE TOOL AND SAMPLES OF CALCULATING SHEETS...... 296 C. APPENDIX - C ...... 300 DESCRIPTION OF WORKING SHEETS OF IN-HOUSE EXCEL BASED TOOL FOR ALIGNING ROW PROFILE DATA ...... 300 D. APPENDIX – D ...... 303 BRIFE DESCRIPTION OF WORKING PRINCIPLES OF LRP TOOL AND SAMPLE OF CALCULATING SHEET ...... 303 E. APPENDIX – E ...... 309 SAMPLES OF PREPARED DATASETS ...... 309 E.1 SAMPLE OF PREPARED ROUGHNESS DATASET ...... 309 E.2 SAMPLE OF PREPARED RUTTING DATASET ...... 312 E.3 SAMPLE OF PREPARED CRACKING DATASET ...... 314 F. APPENDIX – F ...... 316 TRANSFORMING OF MODEL VARIABLES ...... 316 F.1 ROUGHNESS DATASET ...... 316 F.1.1 Whole Network (NW): Transformation for Roughness Data ...... 316 F.1.2 Class M: Transformation for Roughness Data ...... 317 F.1.3 Class A: Transformation for Roughness Data ...... 318 F.1.4 Class B: Transformation for Roughness Data ...... 319 F.1.5 Class C: Transformation for Roughness Data ...... 320 F.2 RUTTING DATASET ...... 321 F.2.1 Whole Network (NW) ...... 321 F.2.1.1 Transformation for Rutting Data ...... 321 F.2.1.2 Transformation for Traffic Loading Data ...... 322 F.2.2 Class M ...... 323 F.2.2.1 Transformation for Rutting Data ...... 323 F.2.2.2 Transformation for Traffic Loading Data ...... 324 E.2.3 Class A: Transformation for Rutting Data ...... 325 F.2.4 Class B: Transformation for Rutting Data ...... 326 F.2.5 Class C ...... 327 F.2.5.1 Transformation for Rutting Data ...... 327 F.2.5.2 Transformation for Traffic Loading Data ...... 328 G. APPENDIX – G ...... 329 SAMPLE OF PREPARING DATASET FOR MULTILEVEL ANALYSIS ...... 329 G.1 SPSS INPUT FILES FOR MULTILEVEL MODEL ...... 329 G.2 WORKING WITH HLM7 SOFTWARE ...... 332 H. APPENDIX – H ...... 336 APPARENT VALIDATION PLOTS FOR ROUGHNESS MODELS ...... 336 H.1 APPARENT VALIDATION FOR CLASS M ...... 336 H.2 APPARENT VALIDATION FOR CLASS A...... 338 H.3 APPARENT VALIDATION FOR CLASS B ...... 340 H.4 APPARENT VALIDATION FOR CLASS C ...... 342 I. APPENDIX – I ...... 344 DETERMINISTIC SIMULATIONS FOR ROUGHNESS MODELS ...... 344 I.1 SIMULATION OF NW CONDITIONAL ROUGHNESS MODEL ...... 344 I.2 SIMULATION OF CLASS M CONDITIONAL ROUGHNESS MODEL ...... 345 I.3 SIMULATION OF CLASS A CONDITIONAL ROUGHNESS MODEL ...... 346 I.4 SIMULATION OF CLASS B CONDITIONAL ROUGHNESS MODEL...... 347 I.5 SIMULATION OF CLASS C CONDITIONAL ROUGHNESS MODEL...... 348 J. APPENDIX – J ...... 350

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APPARENT VALIDATION PLOTS FOR RUTTING MODELS ...... 350 J.1 APPARENT VALIDATION FOR CLASS M ...... 350 J.2 APPARENT VALIDATION FOR CLASS A ...... 352 J.3 APPARENT VALIDATION FOR CLASS B ...... 354 J.4 APPARENT VALIDATION FOR CLASS C ...... 356 K. APPENDIX – K ...... 358 DETERMINISTIC SIMULATIONS FOR RUTTING MODELS ...... 358 K.1 SIMULATION OF NW CONDITIONAL RUTTING MODEL ...... 358 K.2 SIMULATION OF CLASS M CONDITIONAL RUTTING MODEL ...... 359 K.3 SIMULATION OF CLASS A CONDITIONAL RUTTING MODEL ...... 360 K.4 SIMULATION OF CLASS B CONDITIONAL RUTTING MODEL ...... 361 K.5 SIMULATION OF CLASS C CONDITIONAL RUTTING MODEL ...... 363 L. APPENDIX – L ...... 365 SIMULATIONS FOR CRACKING MODELS ...... 365 L.1 SIMULATION OF NW CONDITIONAL CRACK INITIATION MODEL ...... 365 L.2 SIMULATION OF NW CONDITIONAL CRACK PROGRESSION MODEL ...... 366

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LIST OF FIGURES

Figure ‎2-1: Typical cross-sections of pavement types in Victoria (Rebbechi, 2006) ...... 11 Figure ‎2-2: Interactions of different distress modes (Reproduced after Paterson, 1987)...... 13 Figure ‎2-3: Phases of pavement deterioration (Roughness and rutting) (Freeme, 1983)...... 21 Figure ‎2-4: Phases of pavement deterioration (Cracking) (Reproduced after Paterson, 1987) ...... 22 Figure ‎2-5: Factors affecting pavement deterioration and their interactions (Haas, 2001) ...... 24 Figure ‎2-6: Rural highways showing drainage system for (a) dual carriageway (b) single carriageway ...36 Figure ‎2-7: Typical table drain diagram (Veith and Bennett, 2010) ...... 36 Figure ‎2- 8: Typical model forms (AASHTO, 2001) ...... 38 Figure ‎2-9: Roles of prediction models to predict future requirements (Haas et al., 1994) ...... 38 Figure ‎3-1: Typical cross-sections for four road classes (M, A, B and C) in Victoria/Australia (VicRoads, 2013b) ...... 57 Figure ‎3-2: Structure of selected sample network ...... 60 Figure ‎3-3: Number of sites and percentage of total length for each road class ...... 61 Figure ‎3-4: Map of Victoria with the locations of selected road sites ...... 62 Figure ‎3-5: TMI map which divides Victoria into 5 climate zones (Lopes and Osman, 2010) ...... 70 Figure ‎3-6: Expansive soil regions in Victoria (Mann, 2003) ...... 72 Figure ‎4-1: Profile plot for a section of road over five years before alignment ...... 79 Figure ‎4-2: Profile plot for a section of road over five years shows different chainages for the same spike (before alignment) ...... 80 Figure ‎4-3: Profile plot for a section of road over five years shows the same chainage for the same spike (after alignment) ...... 81 Figure ‎4-4: Profile plot for a section of road over five years after alignment ...... 81 Figure ‎4-5: Roughness data profiles for four consecutive survey years (before alignment) ...... 84 Figure ‎4-6: Roughness data profiles for four consecutive survey years (after alignment) ...... 84 Figure ‎4-7: Profile data underlining rapid changes in elevation of year 2010 (blue line) ...... 87 Figure ‎4-8: Profile data underlining unusual reading in elevation at the start of year 2008 (pink line) .....87 Figure ‎4-9: Profile data underlining unusual reading in elevation at the end of year 2006 (green line) .....88 Figure ‎5-1: Structure of network data ...... 96 Figure ‎5-2: Distribution of cracking status over time for observations in the whole network sample ..... 104 Figure ‎5-3: Distribution for cracking progression status over time for observations in the whole network sample ...... 104 Figure ‎6-1: Apparent validation for the developed roughness growth model for the NW, (a) Residual histogram and (b) Line of equality ...... 159 Figure ‎6- 2: Apparent validation for the developed roughness conditional model for the NW, (a) Residual histogram and (b) Line of equality ...... 160 Figure ‎6- 3: Deterministic simulation for the growth roughness progression models over time for the NW and the four road classes (M, A, B and C) ...... 165 Figure ‎6-4: Deterministic simulation for the NW conditional roughness progression model over time .. 166 Figure ‎6-5: Deterministic simulation for the class M conditional roughness progression model over time ...... 167

XIV

LIST OF FIGURES

Figure ‎6- 6: Deterministic simulation for the class A conditional roughness progression model over time ...... 167 Figure ‎6- 7: Deterministic simulation for the class B conditional roughness progression model over time ...... 168 Figure ‎6- 8: Deterministic simulation for the class C conditional roughness progression model over time ...... 168 Figure ‎7-1: Apparent validation for the developed rutting growth model for the NW, (a) Residual histogram and (b) Line of equality ...... 198 Figure ‎7-2: Apparent validation for the developed rutting conditional model for the NW, (a) Residual histogram and (b) Line of equality ...... 199 Figure ‎7- 3: Deterministic simulation for the growth rutting progression models over time for the NW and the four road classes (M, A, B and C) ...... 204 Figure ‎7- 4: Deterministic simulation for the NW conditional rutting progression model over time ...... 205 Figure ‎7- 5: Deterministic simulation for class M conditional rutting progression model over time ...... 206 Figure ‎7- 6: Deterministic simulation for class A conditional rutting progression model over time ...... 207 Figure ‎7- 7: Deterministic simulation for class B conditional rutting progression model over time ...... 207 Figure ‎7- 8: Deterministic simulation for class C conditional rutting progression model over time ...... 208 Figure ‎8- 1: Simulation for the probability of NW growth crack initiation model over time ...... 234 Figure ‎8- 2: Simulation for the probability of NW conditional crack initiation model over time ...... 235 Figure ‎8- 3: Simulation for the NW cumulative probabilities of growth crack progression models over time ...... 236 Figure ‎8- 4: Simulation for the NW probabilities of growth crack progression model over time ...... 237 Figure ‎8-5: Simulation for the NW cumulative probabilities of conditional crack progression models over time when all variables are at their mean values ...... 239 Figure ‎8- 6: Simulation for the NW cumulative probabilities of conditional crack progression models over time when all variables are at their maximum values ...... 239 Figure ‎8- 7: Simulation for the NW cumulative probabilities of conditional crack progression models over time when all variables are at their minimum values...... 240 Figure ‎8- 8: Simulation for the NW probabilities of conditional crack progression model over time when all variables are at their mean values ...... 241 Figure ‎8- 9: Simulation for the NW probabilities of conditional crack progression model over time when all variables are at their maximum values ...... 242 Figure ‎8- 10: Simulation for the NW probabilities of conditional crack progression model over time when all variables are at their minimum values ...... 242 Figure ‎9- 1: Predicted roughness for the four road classes ...... 248 Figure ‎9- 2: Predicted rutting for the four road classes ...... 253 Figure ‎9-3: Distribution for crack status for the four road classes ...... 257 Figure ‎9-4: Distribution for crack categories for the four road classes ...... 258 Figure ‎A-1: Sample of ERD file for Princes highway east site, section 2A, 2009 ...... 294 Figure ‎A-2: Sample of Event file for Hume highway site, section 3A, 2010 ...... 295 Figure ‎B-1: Query management form for climate tool ...... 297 Figure ‎B-2: Data Entry sheet for climate tool...... 298 Figure ‎B-3: Data output sheet for climate tool ...... 299 Figure ‎C-1: Data entry worksheet for In-House Excel based tool ...... 301

LIST OF FIGURES

Figure ‎C-2: Shifting worksheet for In-House Excel based tool ...... 302 Figure ‎D-1: ‘Latest’ deterioration estimate (for roughness example) (Martin and Hoque, 2006) ...... 304 Figure ‎D-2: Estimated deterioration post rehabilitation (for roughness example) (Martin and Hoque, 2006) ...... 304 Figure ‎D-3: Result sheet for LRP tool ...... 305 Figure ‎D-4: Example of segment with two cycles of pavement deterioration ...... 306 Figure ‎D-5: Example of segment with positive progression of deterioration ...... 306 Figure ‎D-6: Example of segment with negative progression of deterioration ...... 307 Figure ‎D-7: Example of segment with “Error! No Solution” ...... 307 Figure ‎D-8: Example of segment with “Error! Not Enough Points” ...... 308 Figure ‎F-1: Frequency histogram plots for the NW roughness data (a) before transformation and (b) after transformation ...... 316 Figure ‎F-2: Frequency histogram plots for class M roughness data (a) before transformation and (b) after transformation ...... 317 Figure ‎F-3: Frequency histogram plots for class A roughness data (a) before transformation and (b) after transformation ...... 318 Figure ‎F-4: Frequency histogram plots for class B roughness data (a) before transformation and (b) after transformation ...... 319 Figure ‎F-5: Frequency histogram plots for class C roughness data (a) before transformation and (b) after transformation ...... 320 Figure ‎F-6: Frequency histogram plots for the whole network rutting data (a) before transformation and (b) after transformation ...... 321 Figure ‎F-7: Frequency histogram plots for the whole network traffic loading data (a) before transformation and (b) after transformation ...... 322 Figure ‎F-8: Frequency histogram plots for class M rutting data (a) before transformation and (b) after transformation ...... 323 Figure ‎F-9: Frequency histogram plots for class M traffic loading data (a) before transformation and (b) after transformation ...... 324 Figure ‎F-10: Frequency histogram plots for class A rutting data (a) before transformation and (b) after transformation ...... 325 Figure ‎F-11: Frequency histogram plots for class B rutting data (a) before transformation and (b) after transformation ...... 326 Figure ‎F-12: Frequency histogram plots for class C rutting data (a) before transformation and (b) after transformation ...... 327 Figure ‎F-13: Frequency histogram plots for class C traffic loading data (a) before transformation and (b) after transformation ...... 328 Figure ‎G-1: The file menu for HLM window ...... 332 Figure ‎G-2: Dialog box for selecting type of Multilevel Data Matrix (MDM) ...... 333 Figure ‎G-3: Dialog box for making Multilevel Data Matrix (MDM) ...... 333 Figure ‎G-4: Dialog box for the basic model specifications in HLM7 software ...... 334 Figure ‎G-5: Example of four level rutting model window ...... 335 Figure ‎H-1: Apparent validation for the developed roughness growth model for the class M roads, (a) Residual histogram and (b) Line of equality ...... 336 Figure ‎H-2: Apparent validation for the developed roughness conditional model for the class M roads, (a) Residual histogram and (b) Line of equality ...... 337

XVI

LIST OF FIGURES

Figure ‎H-3: Apparent validation for the developed roughness growth model for the class A roads, (a) Residual histogram and (b) Line of equality ...... 338 Figure ‎H-4: Apparent validation for the developed roughness conditional model for the class A roads, (a) Residual histogram and (b) Line of equality ...... 339 Figure ‎H-5: Apparent validation for the developed roughness growth model for the class B roads, (a) Residual histogram and (b) Line of equality ...... 340 Figure ‎H-6: Apparent validation for the developed roughness conditional model for the class B roads, (a) Residual histogram and (b) Line of equality ...... 341 Figure ‎H-7: Apparent validation for the developed roughness growth model for the class C roads, (a) Residual histogram and (b) Line of equality ...... 342 Figure ‎H-8: Apparent validation for the developed roughness conditional model for the class C roads, (a) Residual histogram and (b) Line of equality ...... 343 Figure ‎I -1: Simulation for the NW conditional roughness progression model over time for changes in MESA ...... 344 Figure ‎I-2: Simulation for the NW conditional roughness progression model over time for changes in SNC0...... 344 Figure ‎I-3: Simulation for the class M conditional roughness progression model over time for changes in MESA ...... 345 Figure ‎I-4: Simulation for the class M conditional roughness progression model over time for changes in SNC0...... 345 Figure ‎I-5: Simulation for the class A conditional roughness progression model over time for changes in MESA ...... 346 Figure ‎I-6: Simulation for the class A conditional roughness progression model over time for changes in SNC0...... 346 Figure ‎I-7: Simulation for the class B conditional roughness progression model over time for changes in MESA ...... 347 Figure ‎I-8: Simulation for the class B conditional roughness progression model over time for changes in SNC0...... 347 Figure ‎I-9: Simulation for the class B conditional roughness progression model over time for changes in TMI ...... 348 Figure ‎I-10: Simulation for the class C conditional roughness progression model over time for changes in MESA ...... 348 Figure ‎I-11: Simulation for the class C conditional roughness progression model over time for changes in SNC0...... 349 Figure I‎ -12: Simulation for the class C conditional roughness progression model over time for changes in TMI ...... 349 Figure ‎J-1: Apparent validation for the developed rutting growth model for the class M, (a) Residual histogram and (b) Line of equality ...... 350 Figure ‎J-2: Apparent validation for the developed rutting conditional model for the class M, (a) Residual histogram and (b) Line of equality ...... 351 Figure ‎J-3: Apparent validation for the developed rutting growth model for the class A, (a) Residual histogram and (b) Line of equality ...... 352 Figure ‎J-4: Apparent validation for the developed rutting conditional model for the class A, (a) Residual histogram and (b) Line of equality ...... 353 Figure ‎J-5: Apparent validation for the developed rutting growth model for the class B, (a) Residual histogram and (b) Line of equality ...... 354 Figure ‎J-6: Apparent validation for the developed rutting conditional model for the class B, (a) Residual histogram and (b) Line of equality ...... 355

XVII

LIST OF FIGURES

Figure ‎J-7: Apparent validation for the developed rutting growth model for the class C, (a) Residual histogram and (b) Line of equality ...... 356 Figure ‎J-8: Apparent validation for the developed rutting conditional model for the class C, (a) Residual histogram and (b) Line of equality ...... 357 Figure ‎K-1: Simulation for the NW conditional rutting progression model over time for changes in MESA ...... 358

Figure ‎K-2: Simulation for the NW conditional rutting progression model over time for changes in SNCi ...... 358 Figure ‎K-3: Simulation for the NW conditional rutting progression model over time for changes in TMI ...... 359 Figure ‎K-4: Simulation for the class M conditional rutting progression model over time for changes in MESA ...... 359 Figure ‎K-5: Simulation for the class M conditional rutting progression model over time for changes in SNCi ...... 360 Figure ‎K-6: Simulation for the class A conditional rutting progression model over time for changes in MESA ...... 360 Figure ‎K-7: Simulation for the class A conditional rutting progression model over time for changes in SNCi ...... 361 Figure ‎K-8: Simulation for the class B conditional rutting progression model over time for changes in MESA ...... 361 Figure ‎K-9: Simulation for the class B conditional rutting progression model over time for changes in SNCi ...... 362 Figure ‎K-10: Simulation for the class B conditional rutting progression model over time for changes in TMI ...... 362 Figure ‎K-11: Simulation for the class C conditional rutting progression model over time for changes in MESA ...... 363 Figure ‎K-12: Simulation for the class C conditional rutting progression model over time for changes in SNCi ...... 363 Figure ‎K-13: Simulation for the class C conditional rutting progression model over time for changes in TMI ...... 364 Figure ‎L-1: Simulation for the NW conditional crack initiation model over time for changes in MESA 365

Figure ‎L-2: Simulation for the NW conditional crack initiation model over time for changes in SNC0 .. 365 Figure ‎L-3: Simulation for the NW conditional crack initiation model over time for changes in TMI .... 366 Figure ‎L-4: Simulation for the cumulative probability of NW conditional crack progression model for significant affected area category with changes in SNCi ...... 366 Figure ‎L-5: Simulation for the cumulative probability of NW conditional crack progression model for considerable affected area category with changes in SNCi ...... 367 Figure ‎L-6: Simulation for the cumulative probability of NW conditional crack progression model for limited affected area category with changes in SNCi ...... 367 Figure ‎L-7: Simulation for the probability of NW conditional crack progression model for significant affected area category with changes in SNCi ...... 367 Figure ‎L-8: Simulation for the probability of NW conditional crack progression model for considerable affected area category with changes in SNCi ...... 367 Figure ‎L-9: Simulation for the probability of NW conditional crack progression model for limited affected area category with changes in SNCi ...... 367 Figure ‎L-10: Simulation for the probability of NW conditional crack progression model for insignificant affected area category with changes in SNCi ...... 367

XVIII

LIST OF TABLES

Table ‎2.1: Roughness and rutting intervention level for each road type (Austroads/ AAPA, 2003 cited in Austroads, 2004b) ...... 15 Table ‎2.2: Summary of reviewed roughness prediction models ...... 50 Table ‎2.3: Summary of reviewed rutting prediction models ...... 52 Table ‎2.4: Summary of reviewed cracking prediction models ...... 53 Table ‎3.1: Selected sites with detailed information ...... 63 Table ‎3.2: Definition of the symbols used in Event file (Hassan, 2011) ...... 66 Table ‎3.3: Initial pavement deterioration conditions for each road class in Victoria (Toole et al., 2004) . 67 Table ‎3.4: TMI ranges with different climate zones in Victoria (Lopes and Osman, 2010) ...... 69 Table ‎3.5: Classification of subgrade soils in Victoria from integrated map (Mann, 2003) ...... 73 Table ‎4.1: Roughness, rutting and cracking data for the same 100m segments (before alignment) ...... 83 Table ‎4.2: Corrected roughness, rutting and cracking data for the same 100 m segments (after alignment) ...... 85 Table ‎4.3: Number of road segments before and after data cleaning, filtering and limiting the boundary 90 Table ‎4.4: Initial and terminal roughness and rutting values for each road class (Austroads, 1992, Smith et al., 1996 and Toole et al., 2004) ...... 91 Table ‎5.1: Classification of the ranges of affected area for crack status and crack categories ...... 97 Table ‎5.2: Descriptive statistics of continuous variables used when developing roughness models ...... 98 Table ‎5.3: Distribution of categorical variables used when developing roughness models...... 99 Table ‎5.4: Descriptive statistics of continuous variables used when developing rutting models ...... 100 Table ‎5.5: Distribution of categorical variables used when developing rutting models ...... 101 Table ‎5.6: Descriptive statistics of continuous variables used when developing cracking models ...... 102 Table ‎5.7: Distribution of categorical variables used when developing cracking models ...... 103 Table ‎5.8: Distribution for crack status and crack progression...... 103 Table ‎5.9: Results of Durbin-Watson test for all datasets ...... 110 Table ‎6.1: Estimation of the fixed effect variable and variance components (random effect variables) for the whole network roughness null model ...... 133 Table ‎6.2: Estimation of the fixed effect variables and variance components (random effect variables) for the whole network roughness growth model ...... 135 Table ‎6.3: Estimation of the fixed effect variables and variance components (random effect variables) for the whole network roughness conditional model ...... 136 Table ‎6.4: Estimation of the fixed effect variable and variance components (random effect variables) for the class M roughness null model ...... 139 Table ‎6.5: Estimation of the fixed effect variables and variance components (random effect variables) for the class M roughness growth model ...... 140 Table ‎6.6: Estimation of the fixed effect variables and variance components (random effect variables) for the class M roughness conditional model ...... 141 Table ‎6.7: Estimation of the fixed effect variable and variance components for the class A roughness null model...... 143 Table ‎6.8: Estimation of the fixed effect variables and variance components for the class A roughness growth model ...... 144

XIX

LIST OF TABLES

Table ‎6.9: Estimation of the fixed effect variables and variance components for the class A roughness conditional model...... 145 Table ‎6.10: Estimation of the fixed effect variable and variance components for the class B roughness null model ...... 147 Table ‎6.11: Estimation of the fixed effect variables and variance components for the class B roughness growth model ...... 148 Table ‎6.12: Estimation of the fixed effect variables and variance components for the class B roughness conditional model...... 149 Table ‎6.13: Estimation of the fixed effect variable and variance components for the class C roughness null model ...... 151 Table ‎6.14: Estimation of the fixed effect variables and variance components for the class C roughness growth model ...... 152 Table ‎6.15: Estimation of the fixed effect variables and variance components for the class C roughness conditional model...... 153 Table ‎6.16: Pseudo R2 values for developed roughness growth and conditional models ...... 155 Table ‎6.17: Deviance test results for predicted roughness progression models ...... 157 Table ‎6.18: Internal validation results for growth roughness progression models ...... 162 Table ‎6.19: Internal validation results for conditional roughness progression models ...... 163 Table ‎7.1: Estimation of the fixed effect variable and variance components for the NW rutting null model ...... 174 Table ‎7.2: Estimation of the fixed effect variables and variance components for the NW rutting growth model...... 176 Table ‎7.3: Estimation of the fixed effect variables and variance components for the NW rutting conditional model...... 177 Table 7.4:‎ Estimation of the fixed effect variable and variance components for the class M rutting null model...... 179 Table ‎7.5: Estimation of the fixed effect variables and variance components for the class M rutting growth model ...... 180 Table ‎7.6: Estimation of the fixed effect variables and variance components for the class M rutting conditional model...... 181 Table ‎7.7: Estimation of the fixed effect variable and variance components for the class A rutting null model...... 183 Table ‎7.8: Estimation of the fixed effect variables and variance components for the class A rutting growth model...... 184 Table ‎7.9: Estimation of the fixed effect variables and variance components for the class A rutting conditional model...... 185 Table 7.10:‎ Estimation of the fixed effect variable and variance components for the class B rutting null model...... 186 Table ‎7.11: Estimation of the fixed effect variables and variance components for the class B rutting growth model ...... 188 Table ‎7.12: Estimation of the fixed effect variables and variance components for the class B rutting conditional model...... 189 Table 7.13:‎ Estimation of the fixed effect variable and variance components for the class C rutting null model...... 191 Table ‎7.14: Estimation of the fixed effect variables and variance components for the class C rutting growth model ...... 192

LIST OF TABLES

Table ‎7.15: Estimation of the fixed effect variables and variance components for the class C rutting conditional model...... 193 Table ‎7.16: Pseudo R2 values for developed rutting growth and conditional models ...... 195 Table ‎7.17: Deviance test results for predicted rutting progression models ...... 196 Table ‎7.18: Internal validation results for growth rutting progression models ...... 201 Table ‎7.19: Internal validation results for conditional rutting progression models ...... 202 Table ‎8.1: Estimation of the fixed effect variable and random effect variables for the NW crack initiation null model ...... 213 Table ‎8.2: Estimation of the fixed effect variables and random effect variables for the NW crack initiation growth model ...... 216 Table ‎8.3: Estimation of the fixed effect variables and random effect variables for the NW crack initiation conditional model...... 217 Table ‎8.4: Estimation of the fixed effect variables and random effect variables for the NW crack progression null model ...... 220 Table ‎8.5: Estimation of the fixed effect variables and random effect variables for the NW crack progression growth model ...... 223 Table ‎8.6: Estimation of the fixed effect variables and random effect variables for the NW crack progression conditional model ...... 226 Table ‎8.7: Frequencies of observed and predicted probabilities of cracking status for growth crack initiation model ...... 228 Table ‎8.8: Frequencies of observed and predicted probabilities of cracking status for conditional crack initiation model ...... 229 Table ‎8.9: Frequencies of observed and predicted probabilities of cracking categories for growth crack progression model ...... 230 Table ‎8.10: Frequencies of observed and predicted probabilities of cracking categories for conditional crack progression model ...... 231 Table ‎8.11: Internal validation results for growth and conditional crack initiation models ...... 232 Table ‎8.12: Internal validation results for growth and conditional crack progression models ...... 233 Table ‎9.1: Comparison between the four road classes using roughness null model results...... 247 Table ‎9.2: Comparison between the four road classes using roughness growth model results ...... 249 Table ‎9.3: Comparison between the four road classes using roughness conditional model results ...... 251 Table ‎9.4: Comparison between the four road classes using rutting null model results ...... 253 Table ‎9.5: Comparison between the four road classes using rutting growth model results ...... 254 Table ‎9.6: Comparison between the four road classes using rutting conditional model results ...... 256 Table ‎10.1: Developed roughness growth models ...... 265 Table ‎10.2: Developed roughness conditional models ...... 265 Table ‎10.3: Developed rutting growth models ...... 269 Table 10.4:‎ Developed rutting conditional models ...... 269 Table ‎10.5: Developed cracking growth models ...... 271 Table ‎10.6: Developed cracking conditional models ...... 272 Table ‎E.1: Sample of prepared roughness dataset ...... 309 Table E.2:‎ Sample of prepared rutting dataset...... 312 Table ‎E.3: Sample of prepared cracking dataset ...... 314

XXI

LIST OF TABLES

Table ‎F.1: Statistics of roughness data and its transformed data for the whole network roughness dataset ...... 316 Table ‎F.2: Statistics of roughness data and its transformed data for class M roughness dataset ...... 317 Table ‎F.3: Statistics of roughness data and its transformed data for class A roughness dataset ...... 318 Table ‎F.4: Statistics of roughness data and its transformed data for class B roughness dataset ...... 319 Table ‎F.5: Statistics of roughness data and its transformed data for class C roughness dataset ...... 320 Table ‎F.6: Statistics of rutting data and its transformed data for the whole network rutting dataset ...... 321 Table ‎F.7: Statistics of traffic loading data and its transformed data for the whole network rutting dataset ...... 322 Table ‎F.8: Statistics of rutting data and its transformed data for class M rutting dataset ...... 323 Table ‎F.9: Statistics of traffic loading data and its transformed data for class M rutting dataset ...... 324 Table ‎F.10: Statistics of rutting data and its transformed data for class A rutting dataset ...... 325 Table ‎F.11: Statistics of rutting data and its transformed data for class B rutting dataset ...... 326 Table ‎F.12: Statistics of rutting data and its transformed data for class C rutting dataset ...... 327 Table ‎F.13: Statistics of traffic loading data and its transformed data for class C rutting dataset ...... 328 Table ‎G.1: Sample of Level-1 file ...... 329 Table ‎G.2: Sample of Level-2 file ...... 330 Table ‎G.3: Sample of Level-3 file ...... 331 Table ‎G.4: Sample of Level-4 file ...... 332

XXII

LIST OF EQUATIONS

‎Equation 2-1: Convert NAASRA roughness data to IRI data ...... 16 Equation 2-2: Defelection-structural number relationship for granular base pavements ...... 31 ‎Equation 2-3: Defelection-structural number relationship for cemented base pavements...... 31 ‎Equation 3-1: Number of heavy vehicles at time of construction ...... 68 ‎Equation 3-2: Cumulative growth factor ...... 68 ‎Equation 3-3: Cumulative traffic loading in terms of million equivalent standard axles ...... 68 ‎Equation 3-4: Cumulative growth factor over the design life...... 75 ‎Equation 3-5: Cumulative traffic loading at design life ...... 76 ‎Equation 3-6: Initial value of structural number at the time of pavement construction ...... 76 ‎Equation 3-7: Modified structural number at different ages...... 76 ‎Equation 5-1: Correction factor to remove bias...... 106 ‎Equation 5-2: Basic simple linear regression model ...... 112 ‎Equation 5-3: Linear four-level model with random intercept and slopes ...... 113 ‎Equation 5-4: Linear four-level model with time independent variable ...... 114 ‎Equation 5-5: Prediction of roughness value in terms of IRI ...... 114 ‎Equation 5-6: Prediction of rutting value in terms of RD ...... 115 ‎Equation 5-7: Logit of the odds ...... 117 ‎Equation 5-8: Probability of crack initiation ...... 117 ‎Equation 5-9: Logit of the odds via linear combination of predictors ...... 118 ‎Equation 5-10: Probability of crack initiation via linear combination of predictors ...... 118 ‎Equation 5-11: Binary logistic four-level model with random intercept and slopes ...... 119 ‎Equation 5-12: Prediction of the logit odds via linear combination of selected predictors ...... 119 ‎Equation 5-13: Cumulative probabilities for the four cracking progression categories ...... 120 ‎Equation 5-14: Probabilities for the four cracking progression categories ...... 121 ‎Equation 5-15: Prediction of the logit odds for the four cracking progression categories ...... 121 ‎Equation 5-16: Proportion of variance within time series observations within segments ...... 123 ‎Equation 5-17: Proportion of variance between segments within highways ...... 123 ‎Equation 5-18: Proportion of variance between highways within road classes ...... 123 ‎Equation 5-19: Proportion of variance between road classes within the network...... 123 ‎Equation 5-20: Coefficient of determination ...... 126 ‎Equation 5-21: Success rate of developed model ...... 126 ‎Equation 5-22: 99% confidence intervals ...... 129 ‎Equation 6-1: NW roughness null model ...... 132 ‎Equation 6-2: NW roughness growth model ...... 134 ‎Equation 6-3: NW roughness conditional model ...... 135 ‎Equation 6-4: Class M roughness null model ...... 138 ‎Equation 6-5: Class M roughness growth model ...... 139 ‎Equation 6-6: Class M roughness conditional model...... 140

XXIII

LIST OF EQUATIONS

‎Equation 6-7: Class A roughness null model ...... 142 ‎Equation 6-8: Class A roughness growth model...... 143 ‎Equation 6-9: Class A roughness conditional model ...... 144 ‎Equation 6-10: Class B roughness null model ...... 146 ‎Equation 6-11: Class B roughness growth model ...... 147 ‎Equation 6-12: Class B roughness conditional model...... 148 ‎Equation 6-13: Class C roughness null model ...... 150 ‎Equation 6-14: Class C roughness growth model ...... 151 ‎Equation 6-15: Class C roughness conditional model...... 152 ‎Equation 7-1: NW rutting null model ...... 173 ‎Equation 7-2: NW rutting growth model ...... 175 ‎Equation 7-3: NW rutting conditional model ...... 176 ‎Equation 7-4: Class M rutting null model ...... 179 ‎Equation 7-5: Class M rutting growth model ...... 180 ‎Equation 7-6: Class M rutting conditional model ...... 181 ‎Equation 7-7: Class A rutting null model ...... 182 ‎Equation 7-8: Class A rutting growth model ...... 183 ‎Equation 7-9: Class A rutting conditional model ...... 184 ‎Equation 7-10: Class B rutting null model ...... 186 ‎Equation 7-11: Class B rutting growth model ...... 187 ‎Equation 7-12: Class B rutting conditional model ...... 188 ‎Equation 7-13: Class C rutting null model ...... 190 ‎Equation 7-14: Class C rutting growth model ...... 191 ‎Equation 7-15: Class C rutting conditional model ...... 192 ‎Equation 8-1: NW crack initiation null model ...... 214 ‎Equation 8-2: NW crack initiation growth model ...... 215 ‎Equation 8-3: NW crack initiation conditional model ...... 217 ‎Equation 8-4: NW cumulative probability null model for significant category ...... 221 ‎Equation 8-5: NW cumulative probability null model for considerable category ...... 221 ‎Equation 8-6: NW cumulative probability null model for limited category ...... 221 ‎Equation 8-7: NW cumulative probability null model for insignificant category ...... 221 ‎Equation 8-8: NW cumulative probability growth model for significant category ...... 223 ‎Equation 8-9: NW cumulative probability growth model for considerable category ...... 223 ‎Equation 8-10: NW cumulative probability growth model for limited category ...... 224 ‎Equation 8-11: NW cumulative probability growth model for insignificant category ...... 224 ‎Equation 8-12: NW probability growth model for significant category ...... 224 ‎Equation 8-13: NW probability growth model for considerable category ...... 224 ‎Equation 8-14: NW probability growth model for limited category ...... 224 ‎Equation 8-15: NW probability growth model for insignificant category ...... 224 ‎Equation 8-16: NW cumulative probability conditional model for significant category...... 225

XXIV

LIST OF EQUATIONS

‎Equation 8-17: NW cumulative probability conditional model for considerable category ...... 225 ‎Equation 8-18: NW cumulative probability conditional model for limited category ...... 225 ‎Equation 8-19: NW cumulative probability conditional model for insignificant category ...... 225 ‎Equation 8-20: NW probability conditional model for significant category ...... 227 ‎Equation 8-21: NW probability conditional model for considerable category ...... 227 Equation 8-22: NW probability conditional model for limited category...... 227 ‎Equation 8-23: NW probability conditional model for insignificant category ...... 227

XXV

ABBREVIATIONS AND NOTATIOND

ABBREVIATIONS AND NOTATIONS

Abbreviations

AADT: Average Annual Daily Traffic AAPA: Australian Asphalt Pavement Association AASHTO: American Association of State Highway and Transportation Officials AC: Asphalt Concrete ALT: Accelerated Load Testing ANN: Artificial Neural Networks ARRB: Australian Road Research Board Austroads: Association of Australian and New Zealand Road Transport and Traffic Authorities CBR: Californian Bearing Ratio CDM: Coefficient of Developed Model CF: Correction Factor CGF: Cumulative Growth Factor CI: Confidence Interval CP: Cumulative Probability CR: Cracking

CRini: Crack Initiation

CRpro: Crack Progression CVM: Coefficient of Validated Model D: Deflection DF: Direction Factor DL: Design Life DM: Developed Model DRA: Drainage DV: Dependent Variable DW: Durbin-Watson

DWL: Lower critical Durbin-Watson

DWU: Upper critical Durbin-Watson ERD: Engineering Research Division ES: Expansive Soil ESA/HVAG: Equivalent Standard Axles per Heavy Vehicle Axle Group ESA: Equivalent Standard Axles EXP: Exponential FE: Finite Element FL: Fuzzy Logic GD: Good Drainage GF: Growth Factor GPS: Global Positioning Satellites

XXVI

ABBREVIATIONS AND NOTATIOND

HDM-3: Highway Design and Maintenance standards model HDM-4: Highway Development and Management tools HGLM: Hierarchical Generalized Linear Model HLM: Hierarchical Linear Model HLM7: Hierarchical Linear and Nonlinear Modelling software HV: Heavy Vehicle IRI: International Roughness Index IV: Independent Variable LB: Lower Bound LDF: Lane Distribution Factor LN: Natural Log transformation LOS: Level of Service LRP: Linear Rate of Progression LTPP: Long Term Pavement Performance LTPPM: Long Term Pavement Performance Maintenance MDM: Multilevel Data Matrix MESA: Million Equivalent Standard Axles MML: Minimum Message Length N.S.: Not Significant factor NAASRA: National Association of Australian State Road Authorities NES: Non-Expansive Soil NHVAG: Number of Heavy Vehicle Axle Group NRM: NAASRA Roughness Meter NW: Whole network P: Probability PD: Poor Drainage PMS: Pavement Management System PQL: Penalized Quasi Likelihood ProVAL: Profile Viewing and Analysis PVC: Proportion of variance between classes within the network PVH: Proportion of variance between highways within road classes PVO: Proportion of variance within time series observations PVS: Proportion of variance between segments within highways

RD: Rut Depth SN: Pavement Structural Number SNC: Modified Structural Number

SNC0: Modified Structural Number (Initial pavement strength)

SNCi: Modified Structural Number (Pavement strength at any age (i)) SNP: Adjusted Structural Number SPSS: Statistical Package for Social Sciences

XXVII

ABBREVIATIONS AND NOTATIOND

SRRS: State Road Reference System SST: Subgrade Soil Type Std. Dev.: Standard Deviation Time: Time variable TMI: Thornthwaite Moisture Index UB: Upper Bound V: Variance VicRoads: Victorian Road Authority VM: Validated Model

Notations

(1- P1): Probability of uncracked

(β0 + δ1): Second threshold value between considerable and limited categories

(β0 + δ2): Third threshold value between limited and insignificant categories

CPcon: Cumulative probability for at least considerable cracking

CPins: Cumulative probability for at least insignificant cracking

CPlim: Cumulative probability for at least limited cracking

CPsig: Cumulative probability for significant cracking df: Degree of freedom e: Residual or the error value (Level-1 random effect) H: Highway

LN_IRI: Natural log transformation (LN) function of roughness variable (IRI) LN_MESA: Natural log transformation (LN) function of traffic loading variable (MESA) LN_RD: Natural log transformation (LN) function of rutting variable (IRI) N: Sample size O: Observation

P1: Probability of cracked (crack initiation)

Pcon: Probability of considerable cracking

Pins: Probability of insignificant cracking

Plim: Probability of limited cracking

Psig: Probability of significant cracking r0 and r1: Level-2 random effects R2: Coefficient of determination S: Segment St: Street u00: Level-3 random effect v000: Level-4 random effect Ve: Variance of the residuals (e) or variance of level-1 random variable

Vr0: Variance of level-2 random variable

XXVIII

ABBREVIATIONS AND NOTATIOND

Vu00: Variance of level-3 random variable

Vv000: Variance of level-4 random variable X: Independent variable (predictor)

X1, X2, …., Xn: Independent variables Y: Dependent variable Z1: Climate zone 1 (wet area) Z2: Climate zone 2 (humid area) Z3: Climate zone 3 (sub-arid area) Z4: Climate zone 4 (semi-arid area) Z5: Climate zone 5 (arid area) β: Coefficient of the independent variable in the model

β0: Level-1 fixed effect coefficient (intercept)

β00 and β10: Level-2 fixed effect coefficients

β000: Level-3 fixed effect coefficient

β0000: Level-4 fixed effect coefficient

β01, β02 and β03: Level-2 fixed effect coefficients

β1, β2 and β3: Level-1 fixed effect coefficients η: Logit of the odds χ2: Chi-square Statistic

XXIX

CHAPTER ONE INTRODUCTION

1. CHAPTER ONE INTRODUCTION

1.1 Introduction

This chapter introduces useful information on the importance of the road pavement management system and the crucial role of pavement deterioration models to enhance the application of this system. Also presented here are the existing gaps in modelling pavement performance over time. Research objectives to achieve the aim are also stated. Finally, the thesis organisation is presented by way of chapter outlines.

1.2 Background

The road network is a vital component of the social activities and economic life of any community and it provides the platform for road transport and communication. Around the world, and especially in the developed countries, a great deal is spent by governments each year on highways’ construction, maintenance and administration.

The road agencies are responsible for the management of the road network in order to achieve an affordable, acceptable and sustainable level of performance. Road agencies conduct periodic maintenance and rehabilitation activities to sustain the condition and performance of road pavement in the long term. In Australia, many of the rural highways are built of locally available unbound material with a chip (sprayed) seal surface. The chips sealing techniques is common in rural areas because of its low cost and speed of construction; compared with other types of bituminous surfacing.

Ideally, maintenance works required in the management of a road network should be applied in a timely manner, i.e., at the time when the pavement needs to be repaired. Doing the right work at the right time and using the most efficient options will maintain suitable road conditions at minimum funds. However, even the best possible maintenance or rehabilitation program is subject to funding constraints or issues in matching demand with supply through the management of asset systems.

One of the primary components of a pavement management system (PMS) is the method of evaluating the rate of pavement deterioration over time, i.e. pavement

CHAPTER ONE INTRODUCTION

performance models. To keep any network in service at an acceptable condition and maintain and preserve the network performance, the management system can be enhanced by such models for predicting pavement distress or condition and estimating when it needs repair.

The development of reliable pavement deterioration prediction models has been a challenge facing pavement engineers, because it is an area that continually needs enhancement. Identifying the causes and rates of pavement deterioration can help in the adoption of accurate remedies and appropriate techniques with reasonable cost. Moreover, more effective pavement management at a network level relies on models which reliably predict the impact of different variables on pavement deterioration, such as axle load increases.

A pavement deterioration model is an equation that relates the time factor with other essential factors and performance parameters to simulate the deterioration process of pavement condition. With accurate prediction models, the implications of optimum maintenance timing and rehabilitation strategies can be assessed with confidence and practical decisions can be made.

Generally, there are numerous methods, concepts and measures used for assessing pavement performance. However, the way to evaluate pavement performance should be objective, economical and related to the long term functional and structural performance (Toole et al., 2009). Pavement condition parameters modelled in this study include surface roughness, rutting and cracking. These parameters are used for triggering investigation into pavement preservation and/or rehabilitation by road agencies in many countries including Australia.

The general condition of road pavement is objectively measured by its surface roughness, which is a very important condition parameter that is used in triggering investigation into rehabilitation work, in Australia and elsewhere. It is the most popular condition variable in pavement deterioration models, locally and internationally. Rough pavements can produce many problems which are sometimes difficult to quantify, such as decreasing the speed of traffic flow, causing damage to vehicles, increasing the number of traffic accidents and pavement damage due to dynamic wheel loads.

CHAPTER ONE INTRODUCTION

In addition to that, monitoring the transverse profile of a pavement surface in terms of rutting is important because it is an effective indicator of pavement strength (Roberts and Martin, 1996) in addition to its impact on road safety. Permanent deformation or rutting of flexible pavements has a major impact on structural and surface performance of flexible pavement under different conditions. It reduces the useful service life of the pavement as it affects pavement integrity, affects vehicle handling characteristics and the accumulation of rainwater in ruts leads to hydroplaning.

Another important pavement distress mode is surface cracking, which is considered a sign of surface failure in flexible pavement. The extended cracking in pavement surface layers speeds up pavement deterioration because it allows water ingress and weakens the pavement and subgrade layers (Paterson, 1987) by increasing the moisture content of their materials.

The causes of these principal modes of pavement distress can be categorised into three types: structure, environment and construction quality. In many cases, the primary cause of a particular defect is difficult to identify because more than one cause may contribute to pavement distress. Some of these causes include ingress of water into pavement layers, overloading of the pavement structure, moisture movement and volume change, particularly in expansive subgrade soils, ageing and hardening of pavement bituminous surface (oxidation), impact of climate such as temperature and rainfall, or inappropriate pavement design (Paterson, 1987, Moffatt and Hassan, 2007). These factors and their interactions influence the modelling of performance prediction at different rates through their effects on the initiation and progression phases of various pavement distress modes.

Indeed, the database for any network is unable to capture all possible variables affecting pavement deterioration process and therefore some critical factors may not be incorporated in predicting pavement deterioration model. To overcome this problem, it is important to develop models that are able to capture the effect of unobserved factors. Further, pavement performance variability should be included in model parameters and it is likely that the variability (i.e. the heterogeneity) may be due to observed variables or unobserved variables (factors beyond those included in a proposed model) in the network (Hong, 2007, Hong and Prozzi, 2010).

CHAPTER ONE INTRODUCTION

1.3 Problem Statement

Models for predicting pavement deterioration sometimes fail in two critical ways, which are:

1. Quality problems with the data: quality data input is essential if reliable accurate prediction models are to be developed. Generally, quality problems with the data stem from human subjectivity and automated surveys over time. 2. Incorrect statistical approaches for analysing the data: usually, observed historical condition data has a hierarchical structure, with time series observations nested within sections, which are nested within highways, which are nested within road classes (different functions). Therefore, the development of a network pavement deterioration model must allow for variation at all of these levels. In the framework of multilevel studies, using an adequate sample size is very important to generate unbiased and accurate estimates. Many of the existing reviewed models using time series data fail in addressing all these levels of variation.

To overcome these problems and develop more powerful models, modelling pavement deterioration at a network level needs to meet the following basic requirements:

 More accurate models should be based on a representative network and comprehensive field data.  More reliable models should include all possible influencing factors that have significant contributions.  True pavement performance models may be identified when all data used for models development and validation are cleaned from incorrect data using appropriate tools.  More accurate models should be developed by comparing condition of the same length of road over time.  More powerful and unbiased estimations can be obtained by selecting an appropriate analysis approach and functional form of the model which suits the network data structure.  More precise models should be assessed by validating their ability to predict future conditions accurately.

CHAPTER ONE INTRODUCTION

 More acceptable models need to be simple, and should require a reasonable amount of input data to ensure acceptance by practitioners.

These issues have been addressed in the current study which presents a new approach for preparing pavement condition data and for developing robust multilevel deterioration models.

1.4 Research Aim and Objectives

The main goal of this research is to apply a new approach for preparing condition data for use in developing pavement deterioration models using a new advanced modelling approach. Pavement condition parameters modelled in this study include surface roughness, rutting and cracking. Roughness and rutting have three distinct phases of deterioration; namely: initial, gradual and rapid; whereas cracking is characterised by separate phases of initiation and progression. In this study, only the gradual phase is modelled for roughness and rutting pavement conditions. For cracking, both the initiation and progression phases are modelled. The aim is to develop empirical deterministic models for roughness and rutting, and probabilistic models for cracking. This is to be achieved by applying a multilevel modelling approach that captures the effect of variance at all possible levels in modelling roughness and rutting progression and predicting the probability of pavement crack initiation and progression.

These models are expected to be used in a PMS for network level management. The sample network used for the application of these approaches has been selected from the rural arterial network of Victoria/Australia. The latter consists of four road classes with different functions, geometry and level of service standards, representing heavy and light duty pavements. The objectives to achieve the aims of the project are:

1. Develop a representative network covering the four road classes with wide ranges of traffic volumes, subgrade soil types, environmental and operating conditions. 2. Apply suitable adjustments to the longitudinal road surface profile data, rutting data and cracking data to ensure that the same sections are being compared over time. 3. Apply appropriate data cleaning and filtering techniques to remove irrelevant data and the influence of maintenance activities.

CHAPTER ONE INTRODUCTION

4. Develop empirical deterministic deterioration models for roughness and rutting and probabilistic deterioration models for cracking (using time series data) as a function of significant contributing factors. These include: time, traffic loading, soil type, pavement strength, climate and drainage. 5. Study the effect of variation (heterogeneity) among time series observations, segments, highways and road classes. 6. Study the contribution and significance of different influencing factors in predicting each condition parameter, associated level of accuracy for each road class and the variation between road classes. 7. Study the progression rates of roughness, rutting and cracking for the whole network and the different road classes. 8. Simulate the developed models to understand and assess their performance. 9. Validate the developed models to ensure their ability to predict future conditions accurately. 10. Compare the developed models of all road classes for each condition parameter.

1.5 Research Outcomes and Significance

The main outcomes of this research project are listed below:

 A State of the Art approach for preparing condition data for use in developing pavement deterioration models.  A State of the Art approach for developing pavement deterioration models.  Empirical deterministic regression models for pavement roughness and rutting progression within gradual deterioration phase for the whole network sample and for each of the four road classes (M, A, B and C).  Probabilistic models for pavement crack initiation and crack progression for the whole network sample.  An assessment of the effects of all possible contributing factors to the progression of roughness and rutting and the initiation and progression of cracking.  An assessment of the performance of the four road classes (M, A, B and C) by comparing their pavement conditions and factors affecting the rate of pavement deterioration from developed models.

CHAPTER ONE INTRODUCTION

Accurate deterioration models based on a comprehensive dataset can be used by road agencies for several fundamental applications in their PMS, including:

 Gap analysis i.e. predicting when a pavement needs to be maintained or rehabilitated before it actually fails, by using specific intervention thresholds to address the level of service (LOS), safety concerns or asset sustainability.  Evaluation of maintenance strategies and assessment of current and future financial decisions.  Evaluation of the best intervention options required for short and long term maintenance programs.  Assessment of overall network condition and how it is affected by budget constraints.

1.6 Thesis Organisation

This thesis has been organised into ten chapters. The introduction chapter presents a brief overview of this research study, including research background, problem statement, research aim and objectives, and research significant. The remaining chapters are organised as below:

 Chapter 2: Literature Review

The chapter covers pavement deterioration modes, causes, measurement, phases and the factors contributing to initiation and progression of the different modes. Thereafter, the chapter contains a brief overview of various pavement deterioration modelling approaches. A review of some existing models is also provided.

 Chapter 3: Modelling Requirements and Data Collection Process

The requirements for developing reliable models, the criteria for network selection and the data collection process are presented in this chapter. The chapter describes sources of available data related to the three performance condition parameters (roughness, rutting and cracking) and available data related to the different factors that contribute to the pavement deterioration.

CHAPTER ONE INTRODUCTION

 Chapter 4: Data Preparation

This chapter describes the approach used to prepare accurate datasets for modelling three pavement condition parameters (roughness, rutting and cracking). The data preparation process includes data alignment, cleaning, filtering, setting up the boundary limits of the data, and compiling and splitting the datasets.

 Chapter 5: Preliminary Analysis and Modelling Approach

This chapter presents details of the preliminary exploratory analysis and proposed research methodology. The structure of the prepared datasets for the three condition parameters (roughness, rutting and cracking) is presented. Descriptions of the data structure, and variables transformation, bias and interpretation are provided. Then, the process for selecting the appropriate modelling analysis approach for these condition parameters is presented. The chapter includes the results of initial exploratory analysis and the need for using multilevel analysis and relevant model specifications. Also, it provides the appropriate methods for model evaluation, model validation and model simulation process.

 Chapter 6: Development of Roughness Progression Models

In this chapter the developed models for roughness progression of the whole network and the four road classes are presented together with models’ evaluation, assessment, simulation and validation.

 Chapter 7: Development of Rutting Progression Models

This chapter provides a description of the developed models for rutting progression for the whole network and the four road classes. Models’ evaluation, assessment, simulation and validation are also presented.

 Chapter 8: Development of Crack Initiation and Progression Models This chapter provides the developed models for probabilities of crack initiation and progression for the whole network. Simulation of predicted models and evaluation of the models’ performance are also presented.

CHAPTER ONE INTRODUCTION

 Chapter 9: Comparison between Results of Developed Models for the Four Road Classes

This chapter includes a comparison between results of developed models for the four road classes. The three fitted models (null, growth and conditional) results for predicting roughness and rutting condition parameters are used to compare between the four road classes. Also, the four road classes are compared in terms of descriptions for cracking status and cracking progression categories.

 Chapter 10: Summary, Conclusions and Recommendations

This chapter presents the summary of the study and the conclusions based on the models’ outputs and major finding. Also, it provides recommendations for model application and future possible research.

CHAPTER TWO LITERATURE REVIEW

2. CHAPTER TWO LITERATURE REVIEW

2.1 Introduction

This chapter includes an overview of pavement deterioration and modelling relevant to the sample network, used herein, of rural highways of Victoria. It includes an overview of pavement types used in the sample network followed by an investigation of pavement deterioration modes considering herein their causes and measurement. It also includes a discussion on the factors contributing to pavement deterioration, and effects of their variation on rate of progression of the different condition measures considered herein. A brief overview of the different approaches for deterioration modelling, their accuracy and application is also provided. In addition, it provides a review of a number of existing prediction models that are relevant to this study. Finally, the chapter concludes with a summary of the key findings from the literature review.

2.1.1 Pavement Types in Victoria

Basically there are two types of pavements, namely, rigid pavements and flexible pavements. The former type normally uses Portland cement concrete as the basic structural layer, whereas the latter normally uses bituminous material for the surface, and sometimes for the underlying layers but mostly they are built of granular materials. Within Australia, flexible pavements can be classified into three categories according to their composition (Moffatt and Hassan, 2006) as shown in Figure 2-1; which are:

 Granular pavements with bituminous surface (chip seal or thin asphalt).  Bound pavements with bituminous surface (asphalt) and treated bases and /or sub-bases.  Full depth or deep lift asphalt pavements.

A large proportion of the Australian network is built of granular layers and surfaced with sprayed (chip) seals (Oliver, 1999). Generally, around 95 % of Australia’s rural

CHAPTER TWO LITERATURE REVIEW

arterial roads are sealed granular pavements (Oliver, 1999, ABS, 2001 cited in Martin, 2008).

Figure 2-1: Typical cross-sections of pavement types in Victoria (Rebbechi, 2006)

CHAPTER TWO LITERATURE REVIEW

Out of around 800,000 km of total length of road network, there is approximately 500,000 km of gravel surface and 307,000 km of sprayed seal or asphalt surface (Holtrop, 2008). In Victoria, the rural network is essentially spray sealed surface over natural gravels (Cossens, 2010). Road agencies practice for almost all rural roads is to prime or primeseal, followed by a single or double coat seal with one sized aggregate (size 10 or 14 mm) (VicRoads,1993a). The sprayed sealing technique is commonly used in rural areas because of its low cost and speed of construction, compared with other types of road pavement surfacing (Holtrop, 2008). Besides, sprayed sealing practice by applying a layer of bitumen followed by a layer of aggregate provides a road surface that is flexible, waterproof, with good ride quality and skid resistance (Holtrop, 2006). Asphalt surfacing is greatly preferred in high traffic volume areas (Holtrop, 2008) and more expensive than sprayed seals.

Victorian road agencies manage these two types of road surfacing, with around 75% of the network representing sprayed seal surface and 25% representing asphalt surface (Cossens, 2010). Road pavement deterioration is considered to be the main reason for resealing in Victoria, and cracking is considered the next most important reason (Oliver, 1999). Accordingly, this research study will focus on developing deterioration models for sprayed (chip) seal rural pavements in Victoria, Australia.

2.2 Pavement Performance Measures

Generally, there are numerous methods and measures used for assessing pavement performance. However, the way to evaluate pavement performance should be based on crucial aspects, which means that the method used must be objective, economical and related to the long term functional performance of road pavements (Toole et al., 2009). The following subsections provide the information relevant to granular pavement distress modes, their causes and measurement and phases of pavement deterioration.

CHAPTER TWO LITERATURE REVIEW

2.2.1 Pavement Distress Modes

Pavement distress modes can be broadly classified or evaluated by two main performance terms, functional performance and structural and surface performance (Foley, 1999, Bennett et al., 2005, Kadar, 2009); these are described as follows:

 Functional performance is concerned with parameters that affect safety measures and comfortable riding quality of road users. These are signified by distress modes of roughness, texture and skid resistance.  Structural and surface performance is concerned with the impact of wheel loads under different environmental conditions on pavement structure and surface layer(s). These take account of distress modes such as rutting and cracking.

All the above distress modes are measured in different ways and with varying degrees of success (Foley, 1999). The combined effects and interactions of these modes of pavement deterioration contribute to surface roughness, which is a key parameter in pavement deterioration modelling. Figure 2-2 shows the interactions of different distress modes (Paterson, 1987) that contribute to surface roughness.

Figure 2-2: Interactions of different distress modes (Reproduced after Paterson, 1987)

CHAPTER TWO LITERATURE REVIEW

2.2.2 Pavement Distress Measurement

The most common pavement condition parameters that are captured at a network level and used in pavement asset management include roughness, rutting, cracking, and texture (Foley, 1999). However, in the present case study only three of these parameters are adopted as dependent variables for pavement deterioration modelling, and include roughness, rutting and cracking. As mentioned earlier, the sample network used herein includes rural state arterials from Victoria/Australia, therefore, the details of roughness, rutting and cracking condition data are presented next, including their measurement, reporting and utilisation in PMS, in terms of the practice by road agencies in Victoria. Each year, half of Victoria’s major arterial road length is surveyed to collect data related to these parameters (VicRoads, 1998). They employ advanced equipment for measuring, quantifying and analysing the raw data (Papacostas and Bowman, 2003). Monitoring of these pavement condition parameters is always carried out when pavements are at their weakest. For this reason, the spring season is the best time for monitoring in the southern part of Australia (including Victoria) (Foley, 1999).

2.2.2.1 Roughness

Road roughness is defined as the irregularity of road surface that has adverse effects on riding quality criteria, dynamics of vehicle, operating costs, surface drainage, speed, safety and comfort of travel, which consequently impact on the performance of pavement and vehicle safety (Paterson, 1987, Bennett et al., 2005). The general condition of a road is objectively measured by pavement roughness (Austroads, 2001), and it is the most used condition variable in pavement deterioration models (Foley, 1999). The reasons are (Paterson, 1987, Mclean and Ramsay, 1996, Huang, 2004, Austroads, 2004b):

1) It is the primary indicator of the functional condition of pavement and combines the consequence of many modes of pavement deterioration. 2) It affects vehicle operating costs, which increase with increased roughness. 3) It affects drivers’ comfort, especially at high speed more than 70 km/hr.

CHAPTER TWO LITERATURE REVIEW

In Victoria, longitudinal road surface profile measurement is conducted using a multi- laser profilometer. This measurement meets the following requirements (Foley, 1999, VicRoads, 2002a, Papacostas and Bowman, 2003, Moffatt, 2007):

 The most common lane used by vehicles is usually surveyed, normally, the outer lane; if it is not clear, then the center lane is followed.  For each section, the longitudinal profile is measured in left and right wheel paths with a sampling interval of 50 mm.  Roughness data are reported in terms of the International Roughness Index (IRI) in m/km and/or NAASRA Roughness Meter (NRM) in counts/km.  100m length intervals by one lane are used for results processing and reporting purposes. Data is reported for each wheel path and average lane IRI (average of IRI of the two wheel paths).  The measurement frequency for the network is once every two years.  The intervention level for the desirable maximum value of road roughness depends on the road function as given in Table 2.1.

Table 2.1: Roughness and rutting intervention level for each road type (Austroads/ AAPA, 2003 cited in Austroads, 2004b)

Roughness limit for % Road length with Road function length >500m, IRI, m/km rut depth exceeding (NRM, counts/km) 20 mm

Freeways, and other high-class 3.5 (90) 10 facilities Highways and main roads (100 4.2 (110) 10 km/hr.) Highways and main roads (less 5.4 (140) 20 than 80 km/hr.) Other sealed local roads No defined limits 30

CHAPTER TWO LITERATURE REVIEW

Prem (1989) developed a relationship to convert NAASRA roughness data to IRI data, which has the following form:

NAAS A roughness . 9 1. 7 2-1

Roughness data has several applications in pavement asset management, either alone or in combination with other parameters. In Australia; including Victoria; the acquisition of roughness information is a fundamental activity in determining the following objectives (Moffatt, 2007):

 Monitoring of road network condition, involving performance measures.  Screening of candidate sections for further investigation or treatment.  Analysing the total life cycle costing and prioritization at network level.  Developing deterioration modelling and truck ride indicators.  Assessing the quality of new works at a project level.  Evaluating the road suitability for road users.  Estimating the cost of travelling on the road.  Evaluating the relative conditions of roads and networks.

Road roughness has been the most suitable measure for evaluating long-term functional performance of road pavements. Shiyab (2007) showed that an IRI of 3.4 can be selected as a terminal value where speed is more than 100 km/hr. for a major road. A number of studies were presented by many researchers to predict the performance of unbound granular pavements in terms of road roughness at network level under Australian conditions (Hunt and Bunker, 2004, Martin, 2008, Byrne et al., 2009). In addition, some studies present techniques to extract additional information on pavement roughness, such as long and short roughness wavebands (Brown et al., 2010, Sen et al., 2012, Evan, 2013).

However, road roughness may not always be an effective measure for evaluating pavement maintenance and rehabilitation requirements. Therefore, this is highlighted as a reason for assessing more appropriate pavement distress measures such as rutting and cracking for triggering intervention as well (Toole et al., 2009).

CHAPTER TWO LITERATURE REVIEW

2.2.2.2 Rutting

Pavement rutting is described as depression in the transverse profile of the road pavement surface (Haas et al., 1994). It arises from a permanent deformation in pavement layers and/or wearing courses or in the subgrade, which is caused by either consolidation or lateral movement of pavement materials (Huang, 2004). Monitoring the transverse profile of a pavement surface in terms of rutting is important because it is a major parameter in the design of pavements and an effective indicator of pavement strength (Roberts and Martin, 1996, Foley, 1999).

In Victoria, rut depth data is collected using a multi-laser profilometer and considering the following requirements (Foley, 1999, Papacostas and Bowman, 2003, Moffatt and Hassan, 2007):

 The lane that is used by the majority of traffic is surveyed (generally the left (outer) lane).  The maximum depth under a 1.2 m simulated straight-edge center at both wheel paths method is used.  The frequency of surveys of rutting network is once every two years.  For reporting purposes, 100 m length intervals by one lane should be utilised.  The section which is used for rutting measurements is based on a continuous profile at 50 mm intervals and an entire lane width with 13 observations.  The rutting items are reported in terms of mean rut depth and percent length.  The intervention level for the desirable maximum value of road rut depth depends on the road function as given in Table 2.1.

In order to manage road networks effectively and efficiently, rutting data is collected and used for the following purposes (Moffatt and Hassan, 2007):

 Monitoring the condition of the road networks.  Screening the entire network from treatment sections.  Managing maintenance contracts and using them as intervention triggers for routine maintenance works.  Developing and refining rutting performance prediction models.  Inputting as variables in pavement roughness progression models.

CHAPTER TWO LITERATURE REVIEW

 Assessing pavement structural strength and their health.  Evaluating road safety.  Analysing the total life cycle cost.  Deciding network level prioritization.  Determining the network performance measures by compounding them with other condition parameters.

2.2.2.3 Cracking

Cracking is a term used for the procedure of progress of a crack on the pavement; it represents an unexpected break in the integrity of the pavement surface. It is considered a sign of surface failure in flexible pavement (Moffatt and Hassan, 2006) and an important parameter for designing the thickness of a new pavement or for overlaying an existing pavement for rehabilitation purposes (VicRoads, 1993a). Cracks often occur for two main reasons, namely, traffic loading and environmental factors. The first cause is due to repeated loading or overstressing by traffic, while the second cause is due to moisture changes, differential movement of expansive subgrades, and oxidation or chemical shrinkage of the pavement surfacing materials (Moffatt and Hassan, 2006).

In addition, the extended cracking in pavement surface layers frequently speeds up pavement deterioration because it allows water ingress and weakens the pavement and subgrade layers (Paterson, 1987, VicRoads, 1993a) by increasing the moisture content of their materials. Therefore, at network level, monitoring of cracking data is needed to indicate pavement deterioration where rutting data is not extensive enough for any reason (Moffatt and Hassan, 2006).

Cracking data are collected in Victoria by video recording using cameras attached to the survey vehicle. The data is then recorded manually by relying on the following requirements (Foley, 1999, Moffatt and Hassan, 2006):

 Using visual system of rating surface cracking of a lane from an interpretation of digital video images of a moving vehicle in dry and daylight conditions.  Surveying a minimum of one lane for each carriageway in a preferred direction (generally the left lane).

CHAPTER TWO LITERATURE REVIEW

 Measuring the full lane width of the section, between the centers of the lane lines.  Using 100 m intervals in one lane for longitudinal sampling frequency.  Including all types of cracking (visible and repaired): transverse, longitudinal and crocodile cracking types, and reporting as percentage of cracking.  Surveying at a frequency equal to once every two years.

For the road network management issues, cracking data can be used for a range of applications, by either employing it by itself or using it with other parameters. A number of these applications are listed below (Foley, 1999, Moffatt and Hassan, 2006):

 Pavement condition monitoring at network level.  Selection of maintenance requirement for candidate sections that need treatment.  Development and improvement of pavement performance models.  Evaluation of pavement structural strength.  Management of the maintenance delivery of road pavement in performance-based contracts.  Life cycle costing analysis at project level, prioritization of projects and assessment of new works.

2.2.3 Causes of Pavement Distress

Many measurable distress modes can serve to identify pavement conditions such as rutting, roughness, potholing, raveling, cracking etc. These modes can result from different sources. The causes of the principal modes of pavement distress can be categorised into three types of defects, structural, environmental and construction quality. In many cases, the primary cause of the particular defect is difficult to identify because more than one cause may contribute to pavement distress (Paterson, 1987, Austroads, 2004b). A number of these causes are summarized below (Paterson, 1987, Austroads, 2004b, Moffatt and Hassan, 2007):

 Ingress of water into base, sub-base, and subgrade layers, either through the pavement surface or road edges.  Inadequate compaction or drainage, due to lack of quality construction control.  Inadequate pavement thickness.

CHAPTER TWO LITERATURE REVIEW

 Overloading of the pavement structure.  Inadequate quality of pavement or surfacing materials.  Moisture movement and volume change, particularly in expansive subgrade soil.  Fatigue of pavement structure due to high curvature value.  Ageing and hardening of pavement surface (oxidation).  Lack of bond between pavement layers and incorrect asphalt mix design.  Intrusion of plant roots into the subgrade or pavement layers.  Inappropriate stone size in seal or stone deterioration  Settlement of underground service or structure.  Use of naturally smooth aggregates.  Impact of climate such as temperature and rainfall.

2.2.4 Phases of Pavement Deterioration

Pavement deterioration has been categorised into phases by the trends of progression of distress modes, where roughness and rutting are characterised by continuous progression as shown in Figure 2-3 (Freeme, 1983), whereas cracking is characterised by separate phases of initiation and progression as shown in Figure 2-4 (Paterson, 1987). These phases are separately presented below for the distress modes of interest namely: roughness, rutting and cracking.

2.2.4.1 Phases of Road Roughness

Road roughness is developed progressively throughout the depth of road pavement; the three phases of roughness development are (Freeme, 1983, Paterson, 1987):

 Initial roughness: this is roughness value of road pavement after construction and during the initial densification phase.  Roughness progression: in this phase, the trend of deterioration is gradual and the rate of roughness progression depends on traffic loading level, pavement strength and environmental condition factors.

CHAPTER TWO LITERATURE REVIEW

 Rapid deterioration: in this stage, the roughness progression rises more rapidly by weakening of the pavement when some surface defects occur such as cracking, potholing, and patching. Also, dynamic wheel loading induces more pavement deterioration from the interaction between road surface roughness and heavy vehicle body (Austroads, 2001).

Figure 2-3: Phases of pavement deterioration (Roughness and rutting) (Freeme, 1983)

2.2.4.2 Phases of Rutting

Pavement materials are able to resist permanent deformation (rutting) based on several factors such as traffic loading, climate, construction methods and the structure of pavement. Generally, there are three phases (see Figure 2-3 ) for development of rutting on pavement surface (Freeme, 1983, Morosiuk et al., 2004):

 Initial densification or bedding-in phase: this densification occurs on newly constructed pavement after it is opened to traffic. Its degree depends on the level of compaction during construction and the applied traffic load.  Constant or stable rate of deformation phase: in this phase, the deformation rate constantly increases with traffic. This rate depends on several factors such as traffic loads, pavement strength and environmental conditions.

CHAPTER TWO LITERATURE REVIEW

 Accelerating deformation phase: in this final phase, the deformation rate rapidly increases depending on traffic loading, pavement strength and the environment.

2.2.4.3 Phases of Cracking

Cracking is characterised by two distinct phases (Paterson, 1987), as shown in Figure 2-4 and described below:

 Initiation phase: in this phase, the defects appear on the pavement surface after construction.  Progression phase: in this phase, the defects develop progressively, in extent over the surface area and in severity as individual cracks widen.

Figure 2-4: Phases of pavement deterioration (Cracking) (Reproduced after Paterson, 1987)

2.3 Factors Contributing to Pavement Deterioration

A wide range of factors contribute to structural and surface deterioration of pavements. These factors influence the modelling of performance prediction at different rates by

CHAPTER TWO LITERATURE REVIEW

affecting the initiation and progression phases of various pavement distress modes (Toole et al., 2009). There are three initial factors that affect the rate of pavement deterioration, including initial inadequate pavement design, quality and methods of initial construction, and materials used (Hassan et al., 1999). The initial type of pavement construction has a major impact on the future condition of pavement, and would be a significant input to pavement performance modelling (Roberts and Martin, 1998). Pavement distress modes are considered vital criteria in pavement design as well (Huang, 2004, Jameson, 2008). Hunt and Bunker (2001) indicated that there is no direct link between pavement design and pavement progression modelling, while all input variables for the former are considered important for the latter.

To allow inclusive performance modelling in the phases of pavement deterioration, many factors need to be considered with the aim of predicting the change over time (Toole et al., 2009). The variations and interactions among these factors affect the progression rate of the various deterioration modes over time, such as roughness, rutting and cracking, etc. This is illustrated in Figure 2-5 (Haas, 2001) and listed below and the effects of each are explained in the following sub-sections.

 Traffic loading  Climate  Pavement composition  Pavement strength  Subgrade soil  Maintenance  Pavement age  Drainage

2.3.1 Traffic Loading

Victoria has approximately 151,000 kilometers of roads used by general traffic and all roads carry freight to some extent. All declared arterial roads have the capacity to carry heavy traffic, while some roads clearly carry the bulk of the freight task (DOT, 2008). In 2008, approximately 606,000 freight vehicles were registered in Victoria. This

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number is expected to grow significantly by approximately 1.12 million freight vehicles (an increase of 85%) by 2030 (DOT, 2008).

Figure 2-5: Factors affecting pavement deterioration and their interactions (Haas, 2001)

According to Martin (2011), unbound granular sealed pavements in Australia are estimated to experience an increased amount of deterioration with an increase in axle loads and this is expected to double over the next 15 years, with around 90% of the freight task is carried on this sealed road network (Martin, 2009).

Existing high volume of heavy trucks causes accelerated deterioration of pavement condition in terms of roughness, rutting, cracking, etc. (Graves et al., 2005). Heavy vehicles impose a load on pavement structure, which causes pavement damage due to static and dynamic tyre forces. The amount of this pavement loading depends on several parameters, such as axle group type, tyre configuration, gross vehicle mass, suspension performance, and dynamic wheel loading and spatial repeatability (Cebon, 1999).

When pavement deteriorates as a result of the passage of a heavy vehicle, this deterioration not only depends on the gross weight of the heavy vehicle, but also on

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how this weight is distributed and applied on the pavement structure (Austroads, 2004a). Uneven loads result in high average tyre forces that lead to high stresses and strains and additional road surface damage (Cebon, 1999). Hence, the roughness of road surface is different and variable, and is based on the variability of vehicle loading on pavement structure and vehicle speed and weight as well (Mun et al., 2012). Furthermore, the primary function of pavement structure is to support the applied traffic loading and spread the concentrated wheel loads, within acceptable levels of riding quality and deterioration during design life. However, under repeated load, deformation of flexible pavement produces horizontal tensile strains which can induce cracking in bound layers, whereas the vertical compressive strains in the pavement and subgrade lead to rutting by producing deformations in asphalt and unbound layers (Sharp, 2009). This deformation is also influenced by the moisture of subgrade soil (Bae et al., 2008).

Traffic loading is a major contributor to deterioration progression in all types of pavement. Numerous studies have addressed the interaction between vehicle characteristics and pavement characteristics to estimate pavement performance. A recent study was conducted in Victoria by Sen (2012) to evaluate the impact of overloading or higher axle loads on pavement deterioration progression. The results revealed that sites carrying high traffic loading experience high progression rates in rutting and in certain roughness wavebands. This study supported that overloading of pavement structure is the main cause of longitudinal deformation in a wheel path (Austroads, 2004b). Also, Mun et al. (2012) demonstrated that an increase in vehicle loading by 8% causes a reduction in pavement remaining service life by 26.5%. Moreover, some authors (Salama et al., 2006, Zhang et al., 2009) have observed that rutting in flexible pavements increases under heavy loads more than roughness and cracking.

Early study of a long-term Austroads research project (Moffatt, 2013) examined the influence of multi axle group loads on pavement performance. The data obtained from this study shows constant increases in pavement deformation with increases in traffic loading and does not show high variability within different axle group loads. From similar studies, Cebon (1999) and Salama et al. (2006) highlighted that rutting damage appears from the effect of multiple axle loads more than single and tandem axles, whereas the latter tend to cause more cracking or fatigue damage. Sen (2012) also showed that rut progression rate increased with increasing tri-axles in the fleet. This

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indicates that different parameters have different affect and sensitivity in predictive pavement deterioration modelling. So in terms of sensitivity, Pradhan (2000) reports that traffic volume is a very sensitive parameter in all aspects of predictive modelling, whilst traffic growth and composition are not very sensitive to prediction modelling.

In addition, dynamic wheel loading is considered a necessary component for the evaluation of pavement performance under different conditions, because the dynamic tyre forces accelerate road deterioration by generating additional dynamic stresses and strains in road pavements from the vibration of heavy vehicle body (Cebon, 1999). Mclean and Ramsay (1996) reported that the dynamic component of truck axle loads increases with increasing road roughness. Another study conducted by Hassan (2003) demonstrated that roughness characteristics of the pavement surface and their dynamic interaction with heavy vehicles are strongly affected by the climate and reactivity of the subgrade soil. Further, statistical analysis of the structural performance of flexible pavements under dynamic loads and different pavement roughness conditions conducted by Mikhail and Mamlouk (1997) indicates that vehicle speed significantly affects pavement performance, where 20 km/hr. speed resulted in permanent displacement around 10 times than 130 km/hr. This is supported by findings of Loizos and Plati (2008), who found that driving speed and vehicle characteristics contribute to the ride quality and pavement roughness. Speed is known to affect comfort level while travelling on a rough surface and also affect dynamic wheel load.

All the above mentioned studies show that there is strong evidence that traffic loading in terms of different parameters has a strong effect on pavement performance; so traffic loading is an imperative factor to include for estimating reliable and applicable models for a road network (Paterson, 1987). Generally for highways, traffic data are collected at specific locations for several days per year and then expanded to estimate the Annual Average Daily Traffic (AADT) (Hudson et al., 1997).

2.3.2 Climate

Victorian natural environment is changing as a result of climate change. It is forecast to be hotter and drier over the coming decades (DOT, 2008). Victoria experiences a wide range of climatic conditions, from hot summers to snow storms in winter and from

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relatively dry to wet areas. So the direct and indirect impacts of climate change will have adverse effects economically and environmentally (Victoria, 2008). As well as the fact that temperature is expected to increase in Victoria, the annual average evaporation is expected to increase around 3% by 2030, with the greatest changes expected in winter. However, a slight diminution in the annual average humidity is expected by 2030, with the largest decreases expected in spring (Victoria, 2008).

Climate conditions have significant effects on road performance. An accurate knowledge of climatic trends plays an important role in developing road performance models (Byrne and Aguiar, 2010). Actually, road roughness is influenced by environmental factors, namely temperature and seasonal effects in terms of monthly rainfall, humidity or moisture regimes in terms of Thornthwaite’s moisture index (TM ), and other factors such as atmosphere and site geological conditions (Haas and Hudson, 1978, Paterson, 1987, Haas et al., 1994). TMI is defined as the combination of annual effects; these include precipitation, moisture deficit, evapotranspiration, soil water storage and runoff (Thornthwaite, 1948). TMI deals with engineering applications that lie on or beneath the ground surface, such as road pavements (Byrne and Aguiar, 2010).

Austroads guide to the design of rehabilitation treatments for road pavements (2004b) recommends that consideration needs to be given to the impact of pavement temperatures on its performance. For example, at high temperature, some pavement surfacing does not perform adequately in some circumstances such as high turning and braking stresses. Temperature has a major influence on pavement performance and its trends have an important role in the development of roughness and rutting in flexible road pavements (Austroads, 00 a , D’Apuzzo et al., 005) . This is due to its effects on the ageing/ oxidation rates and viscosity of the bitumen in the surface layers of road pavement (Roberts and Martin, 1998). Typically, fatigue cracking occurs when asphalt becomes stiff and brittle at low temperatures, while permanent deformation develops when it is soft and viscoelastic at high temperatures (Austroads, 2004a). The higher rate of pavement permanent deformation in terms of rutting occurs when its temperatures are higher than 40oC (Al-Khateeb and Basheer, 2009), because the stiffness of all bituminous materials decreases as their temperature becomes over the range (Croney and Croney, 1991). In addition, Zhang and others (2009) observed that, in higher summer temperature, rutting is considered one of the major distresses in asphalt surfaced pavements.

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Rainfall has a significant influence on the development of pavement distress in terms of intensity and distribution (Austroads, 2004b). Rainfall changes lead to changes in pavement moisture balance with consequent influence on pavement deterioration (Cechet, 2005). It has a considerable influence on pavement strength in a wet climate, especially with inadequately drained subgrade; while it has fairly little influence on pavement strength in a dry climate, even when the subgrade is poorly drained (Roberts and Martin, 1996). A study conducted by Incegul and Ergun (2011) reveals that pavement deterioration increases as the total amount of rain increases.

Some research has been conducted on seasonal variation effects on pavement. It has been found that the variations in subgrade water content in each season have a considerable impact on the remaining life of pavement (Zuo et al., 2007). In addition, Byrne et al. (2008) validated the hypothesis that road roughness levels increase with time, as a result of seasonal variation caused by the interaction of climatic and soil conditions. They found that dry pavements differ in seasonal variation for both types of soil, expansive and non-expansive. Also, they found that seasonal variation is greater in magnitude for wet pavements. A drying climate has great impact on pavement and structures foundation movements. As the depth of the soil drying zone increases, the seasonal foundation movements increase as well (Lopes and Osman, 2010).

According to Mann (2003), the majority of Victorian rough highways were found within a TMI band ranging between +5 and -30. High positive TMI values refer to the higher soil moistures in humid or wet zones, whilst negative TMI values refer to dry soils in arid zones. Zero TMI refers to a balance between soil moisture and environmental conditions (Lopes and Osman, 2010). In Victoria the TMI values in the wetter climates have changed more than in the drier climates, because the higher soil suctions and the lower percentage of rainfall change in the latter climates (Lopes and Osman, 2010).

In this study, TMI is used to represent climate condition due to the fact that TMI incorporates temperature and rainfall impacts (Martin et al., 2011) and it is the most used factor in pavement deterioration models (Martin, 2008, Martin et al., 2011, Sen, 2012, Choummanivong, and Martin, 2013).

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2.3.3 Pavement Composition

Information related to existing pavement composition such as material quality and pavement thickness is essential for determining pavement performance and making decisions about suitable pavement treatments (Austroads, 2004b). Also, in order to protect the pavement structure from the effects of traffic loading and environment, the pavement layer thickness and materials stiffness must be addressed (Sharp, 2009). Thus, the following subsections provide the role of pavement materials and pavement layer thickness on pavement deterioration.

2.3.3.1 Pavement Materials

Pavements consist of a semi-infinite variety of layers of materials that usually have different properties and therefore behave differently under load (Paterson, 1987). This load induces pavement strains which vary with the stiffness of different pavement layers. Asphalt layer stiffness varies with temperature changes, while base and subgrade layers stiffness varies with water content changes (Zuo et al., 2007). According to Austroads pavement technology guide (Rebecchi and Sharp, 2009), spray sealed pavement is most suitable for rural roads with design traffic more than one million equivalent standard axle loads, whilst thin asphalt pavement can be used successfully with adequate performance for all road classes when it is employed with good quality control of materials, construction processes, and maintenance.

In unbound granular and modified granular pavements, shear strength develops through particle interlock with no significant tensile strength. Therefore, a number of distress modes occur such as deformation through shear and densification, and disintegration through breakdown. However, in asphalt bound pavements, shear strength and cohesion develop through particle interlock with significant tensile strength. For this reason, permanent deformation and cracking appear through fatigue and overloading (Sharp, 2009).

According to the findings of Sen (2012), roads with granular pavement in Victoria exhibit higher rates of deterioration progression (roughness and rutting) than roads composed of asphalt pavement. Another study was carried out on Victorian seals by

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Oliver (2004), to predict the life of sprayed seals taking into account the effect of seal size. The study confirmed that an increase in seal size from 9.5 mm to 12.7 mm contributes to increasing the average seal life by 1.6 years, and also showed that the average seal life for 10, 14, and 19 mm seals are 10.3, 11.8, and 13.4 years respectively.

2.3.3.2 Pavement Thickness

Typically, each lower layer of pavement is thicker than the one above it. The thickness of the surface and binder course is fairly standard, while the road base thickness depends on the loading of traffic (Pearson, 2012).

Inadequate pavement thickness and quality of pavement or surfacing materials are significant reasons for rutting occurring in wheel paths of a lane or crocodile cracking confined to the wheel paths (Austroads, 2004b). To restrict rutting in pavement materials, the thickness of the base and sub-base layer materials need to be increased when the traffic loading increases (VicRoads, 1993a). In a study conducted by Bae and others (2008), it was found that the longitudinal roughness deterioration can be delayed, as the pavement thickness is increased. In addition, Mikhail and Mamlouk (1997) emphasized that pavement performance is influenced by the thickness of the pavement, where higher displacements and strains occur within thin pavement structure.

2.3.4 Pavement Strength

As described earlier, the pavement consists of different layers of materials that typically have different properties and behaviour under load. Improvement of pavement specification by 50% increase in strength can contribute to an increase in the equivalent standard axle load (ESA) life of a pavement by nearly 8 times. Therefore, the representation of pavement strength is a major factor in modelling pavement performance (Paterson, 1987).

Insufficient strength of pavement can contribute to the development of rutting. According to the findings of Koniditsiotis and Kumar (2004), there is a poor but qualitative relationship between pavement structural capacity and transverse profile

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shape (rutting). Also, the time to cracking initiation is significantly diminished by reducing pavement strength (Paterson, 1987, Rebecchi and Sharp, 2009). Mikhail and Mamlouk (1997) found that weak pavement may deteriorate faster than strong/stiff pavement, because the former produces more displacements and strains in the pavement structure. Further, a study conducted by Shiyab (2007) showed that when pavement modulus is about 20-35% of its original design value, cracking and patching area exceeds 17% of the total pavement section area, and the rut depth is more than 15 mm, then the pavement can be considered to be structurally failed and major reconstruction or rehabilitation should be applied.

Pavement structural condition is indicated by the pavement surface deflection under an applied load, which helps with the selection of appropriate maintenance treatments (Rebecchi and Sharp, 2009). For pavement design and performance purposes, pavement strength is represented by the Structural Number (SN), which is considered a general parameter of the pavement layer strength, but not essentially adequate. However, the modified structural number (SNC) is the most used strength parameter in roughness progression models (Paterson, 1987) and it was used in HDM-3 models. For roughness prediction application on different pavements, deflection data is used to estimate the modified structural number; to achieve this, the following deflection-structural number relationships are used (Paterson, 1987):

SN . D-0. (for granular base pavements) 2 - 2

-0. SN . D (for cemented base pavements) 2 - 3

Where: SNC = modified structural number for pavement / subgrade strength. D = maximum deflection.

Moreover, the latest pavement strength concept that was developed to identify the contribution of all pavement layers separately is called adjusted structural number (SNP) (Rolt and Parkman, 2000). This new concept is used in many models such as HDM-4 models (Morosiuk et al., 2004, Toole et al., 2004).

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2.3.5 Subgrade Soil

Subgrade soil provides support to the upper layers of road pavement and withstands the stresses applied to it under load (Sharp, 2009). Also, roads are constructed on different types of soils which control the rate at which seasonal moisture changes occur, and all of these roads are expected to deteriorate over time (Jameson, 2008). Yet, if roads are constructed on expansive subgrade soils, they can deteriorate at a faster rate than those with stable subgrade (Mann, 2003), particularly, areas with highly reactive soils tend to develop higher roughness contents and progress at high rates (Sen et al., 2012).

Reactivity of soils is an important parameter for maintenance and rehabilitation purposes of the Victorian road network since most of the network is built on expansive soils with different reactivity levels. Expansive soils are sensitive to moisture changes during seasonal variation cycles and this leads to volume changes and manifest in two major types of deterioration (VicRoads, 1993a, VicRoads, 1995, Austroads, 2004b):

 Loss of pavement shape (roughness).  Longitudinal cracking as a series of near parallel cracks.

The moisture variation in expansive subgrade soil leads to swelling or shrinkage phenomena, resulting in differential settlement of pavement (Jones and Jefferson, 2012). As the magnitude and variation of moisture increase, deterioration rate increases as well. Moreover, this moisture variation is likely to more influence longer and wider roughness wavebands (Bae et al., 2008).

In the study of Mann (2003), it was observed that the majority of rough roads in Victoria are on expansive soils. The study showed that the differential swelling of expansive subgrade soils forms long wavelength roughness. These long waves induce high vertical and longitudinal vibrations in heavy vehicles and detract from the ride quality experienced by the occupants (Hassan, 2003). Expansive soils can be found in arid, semi-arid or humid environments and cause significant damage to pavement in these regions (Jones and Jefferson, 2012).

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2.3.6 Maintenance

The main objective of pavement maintenance activities is to keep pavement condition at or above the minimum acceptable serviceability level, by improving pavement shape, ride quality (reduce roughness), waterproofing, or surface characteristics (VicRoads, 2002c). Generally, maintenance has two significant effects on improving the condition and performance of road pavement, namely (Paterson, 1987):

 An immediate impact on pavement condition, and  An impact on the future rate of pavement deterioration.

Different strategies of pavement maintenance treatment have a significant effect on the progression of roughness and rutting (Martin, 2004). There are three main activities or strategies to ensure adequate pavement performance by managing current assets and providing for future assets (Sharp and Toole, 2009):

 Routine maintenance activities: address minor defects on the carriageway and drainage to reduce pavement deterioration rates and ensure a base level of road safety. For particular roads or classes of roads, the road management plan sets out a priority order of standards for inspection, maintenance and repair of road infrastructure (Batchelor, 2004). Examples of these activities include crack sealing and potholes patching.  Periodic maintenance activities: timely surface interventions to reduce future pavement deterioration, limit the need for expensive rehabilitation, improve skid resistance and maintain general safety level. Examples include resealing (with spray seal) and surfacing (asphalt) with or without regulations and patching.  Rehabilitation activities: target roads which are significantly deteriorated and display inadequate structural capacity for traffic loading. Timely rehabilitation with appropriate solutions is required to ensure total of life cycle costs are reduced. In Victoria, investigation into rehabilitation is triggered by roughness to improve users’ comfort and reduce their costs. Examples include asphalt overlay, granular resheets and reconstruction.

Regular maintenance is a cost effective way of reducing pavement deterioration and postponing more expensive treatments. For instance, resealing a road costs around $2 per square meter, but if left untreated, rehabilitation costing $20 to $30 per square meter

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may be required over a few years (VicRoads, 1993b). In other words, by applying the right maintenance strategy at the right time, the pavement deterioration rates can be slowed significantly (VicRoads, 1993b). Moreover, for selecting appropriate treatment type and proper scheduling of maintenance and rehabilitation works, roughness indices such as IRI have been used effectively in PMS as predictors (Shiyab et al., 2006). Also, some studies (Wiyono et al., 2008, Wiyono, 2012) found that the prediction and modelling of cracking in flexible pavement can be used as guidance for maintenance intervention criteria and rehabilitation options.

Other criteria that are considered in developing maintenance strategies and selection of treatments include cost analysis, effective service life, risk assessment outcomes, traffic volumes, strength in addition to existing pavement condition (VicRoads, 2002b, VicRoads, 2002c). Many of the deterioration models in the literature consider maintenance and rehabilitation activities as important factors that affect pavement performance. In light of this, Lu (2011) developed pavement performance and preservation statistical models using pavement roughness in terms of IRI values as dependent variables. The study provided insight into improving pavement management systems and pavement preservation planning. Furthermore, Mandiartha et al. (2012) presented prediction models for pavement maintenance activities in the State of Victoria/Australia.

2.3.7 Pavement Age

Pavement age is observed by the original construction date (years) or last rehabilitation date (years) (Martin and Choummanivong, 2010). Road pavement is designed to provide satisfactory service over a specified period of time (typical flexible pavements design periods are 20-40 years) (Austroads, 2004a). Though sometime, this service cannot be expected because of the state of pavement changes with time, depending on the damage caused from a number of factors (e.g. traffic loading, climate, soil, etc.) (Freeme, 1983, Austroads, 2004a). Even so, the design period provides an initial input for the pavement rehabilitation or reconstruction works (Austroads, 2004a).

Many studies showed that deterioration prediction models are significantly dependent on pavement age. A study conducted by Shiyab and others (2006) shows that pavement

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age accounts for around 9 % of the models’ prediction of flexible pavement performance. Further, a study conducted by Mubaraki (2010) concludes that age is the most significant factor in predicting pavement deterioration because it is a common factor in the estimation of other factors such as traffic and effect of drainage over the life cycle period (i.e. age can be a surrogate for the effect of other factors).

So, as discussed above, in order to develop reliable and applicable models, it is imperative that the models include time effects for a wide range of circumstances (Paterson, 1987).

2.3.8 Drainage

Drainage has been identified as an important factor for both functional and structural condition of road pavement (Pearson, 2012). Performance of road pavements is directly influenced by drainage systems because they have a considerable impact on subgrade moisture conditions and bearing strength of pavement materials (NAASRA, 2000, Jameson, 2008). Moreover, porosity, permeability, or subjectivity are three main measures of ensuring adequate or good drainage which are recorded in terms of poor, fair, or good (Haas et al., 1994).

Pavement permeability contributes to several kinds of surface distresses by stripping the binder from the aggregate and causing loss of bond between pavement layers, which leads to fretting, raveling and delimitation of pavement surface. So, to provide support to the pavement structure and reduce the effect of natural water table fluctuation with seasons, to keep pavement and subgrade at equilibrium moisture content, a good drainage system is required (Pearson, 2012). Figure 2-6 presents examples of typical rural highways in Victoria showing the drainage systems.

Typically, the drainage system is a table drain (ditch) on both sides of the carriageway of an undivided highway. In divided highways, the water is drained via a table drain placed on the outer side of each carriageway and the depressed median between the two carriageways. Also, typically catch drains are used at top of cut batters as shown in Figure 2-7.

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(a)

(b)

Figure 2-6: Rural highways showing drainage system for (a) dual carriageway (b) single carriageway

Figure 2-7: Typical table drain diagram (Veith and Bennett, 2010)

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2.4 Classification of Deterioration Models

Pavement performance modelling aims at relating the performance indicators (condition parameters) to a set of causal variables. In the context of pavement performance modelling, the pavement condition parameters (roughness, rutting, cracking, etc.) are represented as “dependent” variables and the causal parameters (traffic, climate, soil, etc.) are represented as “independent” variables (Hudson et al., 1997, oberts and Martin, 1998, AASHTO, 2001). These performance models take several statistical forms; some of which are shown in Figure 2-8 (AASHTO, 2001). A study conducted by Ens (2012) involved a comparison between three types of progression models namely; linear, exponential and ordinal. He found that exponential models were the most suitable for predicting future asset conditions and to estimate funding requirements. Also, roughness-age models were developed by Shiyab (2007) as exponential and polynomial functions and were found to have good fitness with sufficient accuracy and good predictability when the value of coefficient of multiple determinations (R2) is high. Kharel (2006) developed a set of regression equations (linear, S-shape, exponent, power, logistic) and he found that more accurate prediction models can be obtained from nonlinear transformation functions such as power and exponent forms. However, linear model to predict pavement condition has been developed by many researchers (Hunt, 2002, Martin, 2008, Stephenson, 2010, Sen, 2012) considering the relationship between pavement condition (dependent variable) and each of the included factors (independent variables) is linear.

Moreover, intervention timing for pavement maintenance or rehabilitation can be estimated by applying pavement deterioration prediction models to existing sections of pavement as illustrated in Figure 2-9 (Haas et al., 1994). The figure also shows that post rehabilitation, the condition of section is improved but the level of improvement (works effects) and post rehabilitation deterioration rate vary, depending on the type of treatment applied.

Pavement performance is modeled by two main types of approaches, namely deterministic and probabilistic modelling (Lytton, 1987). In a survey for future distress prediction models in Australia, it was found that around 83% of the State Road Authority professionals prefer to use probabilistic pavement deterioration models, whereas 71% prefer to use deterministic models (Martin and Kadar, 2012). This

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indicated that both types of models, probabilistic and deterministic, are used to some extent in Australian road conditions. To ensure that the types of models are utilised in the right way, understanding and distinguishing the variation of the modelling fundamentals are needed. Available models which are applied to infrastructure deterioration modelling can be classified into three categories; namely, deterministic models, probabilistic models and other models. These categories are described briefly in the following sections.

Figure 2-8: Typical model forms (AASHTO, 2001)

Figure 2-9: Roles of prediction models to predict future requirements (Haas et al., 1994)

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2.4.1 Deterministic Models

Deterministic models predict a single value of pavement condition measurement and take no direct account of the stochastic nature of pavement performance. The following criteria apply to such models (Lytton, 1987, Hass et al., 1994, Martin, 1996, Toole et al., 2009, Ens, 2012):

 Significant quantities of pavement performance data are required.  Statistical relationships between pavement condition parameters (dependent variables) and the parameters influencing it (independent variables) are used.  Function forms are displayed: simple functions using linear regression (F test is used) or complex functions using non-linear regression, such as exponential formula (likelihood ratio test is used); the latter can generate more accurate results.  Pavement performance is related to primary response, functional, or structural, and damage level is predicted.

Many studies prefer to use deterministic approaches because they are the most popular models, of great practical value, and easy to use and understand (Lu, 2011). In addition, the most common example of deterministic models is the World Bank’s highway design and maintenance standards models (HDM). Both HDM-3 and HDM-4 programs contain pavement prediction models which are often implemented by Australian road authorities (Toole et al., 2009). Deterministic models are classified into three main types based on their derivation, namely, mechanistic models, empirical models and mechanistic-empirical models. These types of models are presented below.

2.4.1.1 Mechanistic Models

Mechanistic models are based on mechanistic responses of the pavement structure such as stress, strain, or deflection to predict future changes in this response caused by some factors (Lu, 2011). Therefore, these models depend on mechanics theories such as elastic layer theory, fracture mechanics, visco-elastic theory, and finite element analysis (AASHTO, 2001). The main features of these types of models are:

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 They are not appropriate for pavement condition data which include only surface data (Mubaraki, 2010).  They are cost effective models (Lytton, 1987).  They are not typically utilised in deterioration modelling, because they cannot account for deterioration that is caused by the interaction of various factors (Ens, 2012).  They have the advantage that they may be applied beyond the data range from which they were developed (Lytton, 1987).

In addition, a study conducted by Larsen and Ullidtz (1998) provided successful mechanistic deterioration models for rutting, roughness, and plastic strain in subgrade, which are based on Accelerated Load Testing (ALT) and complemented by laboratory testing.

2.4.1.2 Empirical Models

These models are developed from experimental or observed historical data of performance indicators and explanatory variables by using regression analysis. They are used when the mechanism of pavement performance is not purely present (Martin, 1996, Toole et al., 2009) and have the following features:

 They require a large amount of data (AASHTO, 2001).  They are unlikely to use data beyond the range from which they were developed (Lytton, 1987), that is, these models should not be used when the actual conditions are beyond development data limits.  They have a basic problem with multicolinearity, which means that there is correlation between some of the independent parameters used in the models, such as time and traffic variables which are highly correlated (Lytton, 1987).

In this dissertation, it is intended to consider empirical pavement deterioration models for evaluating deterioration behaviour (roughness and rutting) under the effect of various explanatory variables, because the only available data is observed field data.

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2.4.1.3 Mechanistic - Empirical Models

Mechanistic-empirical models combine both observational and theory evidence by mixing both mechanistic and empirical analysis to predict the pavement response in relation to observed conditions (Toole et al., 2009). These are carried out by evaluating the pavement material responses to the applied load and then predicting the pavement performance due to these responses (AASHTO, 2001). Indeed, the mechanistic- empirical models are developed by some researchers (Gramajo, 2005, Martin, 2008, Schram, 2008, Muhammet and Braimah, 2010) when both of the field data and experimental data are available.

These types of models are based on the following aspects (Lytton, 1987, Martin, 1996):

 They can be used in wider circumstances than the range of data from which they were developed.  They have a problem with multicolinearity between independent variables.  They are cost effective models.  They require less data than empirical models.

2.4.2 Probabilistic Models

Probabilistic models take into account the random nature of pavement performance with some errors in the assessment of pavement condition (Martin, 1996). That means the future pavement condition (i.e. the dependent variables) assigns various probability distributions, because the pavement and the different parameters (the independent variables) that affect their behaviour are essentially non-homogenous. For developing these types of models, minimum historical pavement performance data is needed (Lytton, 1987, Martin, 1996, Toole et al., 2009).

For example, Zheng (2005) proposed a probabilistic and adaptive methodological framework to capture the dynamic and stochastic nature of pavement deterioration processes. In this study both the ordered probit models and the sequential logit models were developed by using the AASHTO Road Test data. His models aimed to directly

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forecast pavement performance in terms of their condition states in relation to a number of variables such as traffic, pavement structure and environment.

The following subsections describe different types of probabilistic models commonly used in pavement asset management.

2.4.2.1 Survivor Curves

Survivor curve is defined as a graph of probability versus time or traffic. This probability drops off from one to zero and states the percentage of the remaining pavements in service after a number of years without maintenance or rehabilitation (Lytton, 1987). The slope of this curve defines a probability density function (PDF) for pavement survival (Toole et al., 2009). In addition, this curve represents the number of pavement sections that stay in service at a selected period (Lu, 2011) and assumes that the pavement performance represents its average life expectancy (Lytton, 1987). However, development of survivor curves at a network level requires intensive data at failure condition (Martin, 1996).

2.4.2.2 Markov Models

The Markov chain model is considered the most popular probabilistic modelling technique and is used broadly in modelling a variety of physical phenomena that are stochastic in nature (Yang et al., 2005, Ens, 2012). Also, it is a useful approach to show the uncertainty of pavement behaviour (Mandiartha et al., 2012). Markov models use a transition matrix which gives the probability that a pavement in a known condition state at a certain time will change in the next time period to another condition state (Toole et al., 2009, Lu, 2011). In other words, this type of model is based on the current state of the pavement for estimating the future state, regardless of the historical pavement state (Haas et al., 1994). This indicates that this model is a time-dependent or time- homogeneous model and ignores non-load or environmental effects (Lytton, 1987). Also, it is based on empirical information instead of historical data (Choummanivong and Martin, 2013).

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Nevertheless, a transition probability matrix should be developed for each combination of factors that influence pavement performance (Haas et al., 1994). Transitional probabilities in a Markov model can be estimated by using one of the following suitable methods (Toole et al., 2009):

 Non- Linear programming.  Maximum likelihood estimation.  Expert opinion.

The Markov transition model has been employed broadly for modelling pavement deterioration that is characterised as a random process, such as pavement crack condition. This is due to stochasticity in the cracking mechanism and non-linear pavement surface layer properties (Yang, 2004, Yang et al., 2005).

2.4.2.3 Semi-Markov Models

The Semi Markov model is a simple alteration to the Markov probabilistic model. It is based on a probability transition matrix for predicting future pavement condition when changing from one state of pavement condition to another (Toole et al., 2009).

However, the Semi Markov is non-homogeneous model and more realistic than the Markov model, because of the following reasons (Lytton, 1987, Martin, 1996, Toole et al., 2009, Ens, 2012):

 It recognises the pavement condition and changes on the traffic and weather conditions (independently distributed random variables are used).  It reduces the size of the problem by using random time intervals.  It requires adequate data for its additional parameters.  It demands more difficult implementation.

According to some research (Anderson, 1989, Tam and Bushby, 1995 cited in Toole et al., 2009), the Semi-Markov model is normally used in Australia when a probabilistic method is utilised for estimation of road pavement performance at a network level. This is suggested when adequate observational data is available.

CHAPTER TWO LITERATURE REVIEW

2.4.2.4 Continuous Models

This modelling approach estimates future pavement failure probability depending on a continuous curve failure probability (Martin and Kadar, 2012). Examples of using continuous probability curves are Bayesian regression techniques, Monte Carlo simulation approach and logistic models. The Bayesian model is developed from observed data with expert knowledge. It deals with observed data which are small in quantity and poor in quality (Pilson et al., 1998, George et al., 1998 cited in Toole et al., 2009).

Probability based on an existing road deterioration model using Monte Carlo (MC) simulation is used to estimate the normal probability distribution of the condition. In MC approach, the variation in the sample data is simulated from the input variable probability distribution. According to Martin and Kadar (2012), this approach can only be used when a known deterministic relationship exists and sufficient data is available. This method was used by Choummanivong and Martin (2013) to estimate the possible range of the dependent output variables.

However, logistic model form is another example of using continuous probability technique that has been used effectively by a number of recent studies in predicting defect initiation and progression (Henning, 2008, Henning and Roux, 2012, Wang, 2013, Kodippily et al., 2015, Hassan et al., 2015).

2.4.3 Other Models

Many different types of techniques with different features of analyses are used for developing road deterioration or performance models. Some of these models are listed below:

2.4.3.1 Artificial Neural Networks (ANN)

These models mimic the structure of human brain neurons which are able to send information back and forth to each other (AASHTO, 2001, Ens, 2012). Artificial neural

CHAPTER TWO LITERATURE REVIEW

network analysis is a huge field of study that can be used to develop models to predict pavement performance measures. Back propagation technique is the most common method for training an ANN with the observed data to obtain minimum error of prediction (AASHTO, 2001).

The biggest advantages of the ANN method are that they are able to learn from past examples and also they can produce correct responses from incomplete data. However, the disadvantages of this method are that they require (AASHTO, 2001):

 A large amount of good quality of data.  A great effort to explain the relationship to link the data.  Much effort to understand how input data affect the output data.

2.4.3.2 Finite Element (FE)

Finite element modelling is a flexible method that integrates more realistic relationships between boundary conditions and material constitutive. This type of model is more suitable for pavement structure when its modulus varies depending on the material stress conditions, such as unbound granular materials (Bodin et al., 2013).

This method is based on dividing the pavement into a large number of distinct elements which are linked together. Then, for each element, the specific stress condition is computed (Bodin et al., 2013). The FE approach has been used to develop models for integrating nonlinear behaviour of pavement granular materials to suit granular specific constitutive relationships (Gonzalez et al., 2012). Also, it is utilised to model laboratory testing conditions for unbound granular materials. In this case, the data obtained under wheel-tracking conditions and the applied stress is not uniform due to boundary conditions (Bodin et al., 2013).

2.4.3.3 Data Mining (DM)

The data mining method often mentioned as Machine Learning (ML) or Knowledge Discovery through Databases (KDD), is a technique widely used to analyse a large

CHAPTER TWO LITERATURE REVIEW

volume of data and to process this data to learn information, by utilising computer power to infer data which is based on relationships between variables instead of depending on human judgements (Byrne et al., 2005).

This method was employed by Hunter (2003) to search for association rules on pavement deterioration and apply a priori algorithm based approach. Generally, algorithm methods are used for complex optimization problems such as programming of non-linear, goal and interval problems (AASHTO, 2001). Furthermore, Byrne et al. (2005) demonstrated the applicability and feasibility of data mining method as a statistical modelling approach. This is supported by findings of Graves and others (2005), who strongly indicated that it is a successful method to present advanced analysis of pavement condition data.

2.4.3.4 Minimum Message Length (MML)

A number of studies have involved the application of minimum message length (MML) to develop pavement deterioration models. Byrne et al. (2006, 2008, and 2009) have developed deterioration models by using the MML approach within Australia dataset. According to Byrne et al. (2008), the MML model recognises particular patterns of variation for the selected variables, because the MML model ensures two main points, firstly, the optimal final model balances complication and precision; and secondly, the most advantageous explanation of the variables does not result in over fitting.

2.4.3.5 Fuzzy Logic (FL)

Fuzzy logic systems are numerical approaches which convert linguistic control strategies into automatic control strategies based on observed behaviour and knowledge (Saltan et al., 2007). The weakness of the FL model is that it is a difficult method due to complex interactions among the factors and the model’s quality depends on the quality of the data (AASHTO, 2001). However, this type of model can be used for predicting the surface deflection behaviour of the pavement that is subjected to dynamical loading, rather than using linear elastic theory and finite element methods which are considered more time consuming (Saltan et al., 2007).

CHAPTER TWO LITERATURE REVIEW

2.5 Deterioration Models for Sealed Granular Pavements

Around the world, a great deal of effort has been invested to develop models of pavement deterioration progression over time, with varying levels of complexity. This is because the first and the most essential concern for a pavement management program is modelling and predicting pavement performance. However, selection of the appropriate modelling approach depends upon data availability and the pavement management system (PMS) in place.

A comprehensive review of existing relevant pavement deterioration models indicates that different approaches and analysis methods have been proposed for predicting long life characteristics at network level. The majority of accepted approaches from the existing statistical prediction models are based on observed historical performance of pavements to estimate future pavement condition. Numerous studies have been developed using various linear or non-linear regression models or by using probability models based on individual distresses. Further, very few previous studies (Toole et al., 2004, Chen and Mastin, 2015) have focused on using accurate condition data in their analysis.

In the context of Australia’s and New Zealand’s network pavements, considerable effort on the part of many researchers has gone into developing deterioration models. In the literature, researchers adopt two kinds of road deterioration modelling efforts to describe pavement deterioration process related to spray sealed pavements. They include calibrating the available HDM-4 road deterioration models and newly developed models using local data.

Road agencies in a number of Australian states have adapted the HDM-4 performance models to Australian pavement conditions to use in their PMS. A number of research projects have been sponsored by Austroads for calibrating HDM-4 road deterioration models for roughness, rutting and cracking (Martin, 2004, Martin et al., 2004, Toole et al., 2004, Hoque and Martin, 2005, Martin and Choummanivong, 2008, Hoque et al., 2008). These projects were based on performance data derived from LTPP (Long Term Pavement Performance) and LTPPM (Long Term Pavement Performance Maintenance) data, ALT (Accelerated Load Testing) data, and additional data supplied by road agencies. The calibration results showed that there was consistent variation of the

CHAPTER TWO LITERATURE REVIEW

calibration coefficients from the default values of HDM-4 models. The outcomes of the latest calibration project (Hoque et al., 2008) were that there was strong correlation between the calibration coefficients and the predicted rates of observed deterioration.

In 2004, Toole et al. (2004b) reported a study on the calibration factors of HDM-4 road deterioration models for Victoria’s network. A total of 82 sites were calibrated based on historical data from database of relevant road agency. The calibration was performed using HDM-4 software models for roughness and rutting progression, and cracking initiation and progression in a recursive method. The results confirmed that there are significant differences occurring in the yearly rate of roughness progression and there has been considerable impact of environmental factors on performance. Also, there are differences in rutting behaviour depending on the material quality and moisture content. In addition, the differences in cracking behaviour are less clear due to regular crack sealing programs.

Nevertheless, there is still concern that the HDM-4 pavement deterioration models were developed based on asphalt pavement performance under significantly different conditions than the sealed granular pavements that comprise the majority of the Australian rural network, including Victoria (Martin, 2008).

On another hand, the newly developed deterioration models for sealed granular pavements under Australian and New Zealand’s network conditions have also some limitations; some of which are based on limited sample sizes or have used a few explanatory variables. The main observed problems in these studies have been presented in Section 1.3 of Chapter 1. The summaries of a number of reviewed performance modelling efforts for roughness progression, rutting progression, and crack initiation and progression for Australian and New Zealand’s networks are provided in Table 2.2 Table 2.3 and Table 2.4, respectively. In these tables, the type of modelling approach, sample size, included independent variables and main findings from the works of all the mentioned authors are provided. The overall observations from these pavement deterioration modelling efforts are summarized below:

 Different strategies and forms have been utilised to highlight the concept of road pavement deterioration and to study many parameters associated with pavement performance at a network level.

CHAPTER TWO LITERATURE REVIEW

 Different methods have been used to assess the precision and accuracy of the developed models.  The majority of the studies have used the observed historical performance of pavements to estimate future pavement conditions. That is, empirical models based on historical panel (time series) data for many different pavement sections were considered.  Different predictor factors have been included to represent their contribution to pavement deterioration. These factors generally were pavement age, traffic loading, climate, subgrade soil type, maintenance practice, and pavement and/or soil strength.  Road roughness in terms of IRI (International Roughness Index), rutting in terms of average rut depth and cracking in terms of affected area have been used as condition parameters.

However, none of these studies considered the structure of the network data or included the effect of unobserved heterogeneity in the modelling process. Also, very few studies have focused on using accurate condition data in their analysis. The importance of these issues is explained in detail in Chapter 5 . In the current study, new approaches for preparing pavement condition data and for developing robust pavement deterioration models are presented.

CHAPTER TWO LITERATURE REVIEW

ion ion of heavy vehicle oading oading and pavement Findings Findings

= 0.22). About 68.5% of the sites 2 = 0.56. The model can be applicable to 2

independent independent variables are highly significant with

erministic erministic model exist. The outcome is presented at three Environmental Environmental factors have roughness progression rate than l traffic the highest age. The contribution latter is found to be less to contribution on roughness than others. progression The analysis outcome estimates the likely distribution of the roughness forecasts with increasing the level of uncertainty with time. det The approach 90%). and 50% (10%, distributions percentiles is applicable when sound The model and all independent variables significant were with statistically R relatively high quality sealed road networks for strategic life cycle costing analysis and in the estimat wear. road All goodness of fit experienced (R roughness deterioration period. monitoring over the five year strategy maintenance road of level a that concluded The study in selected roads higher than routine maintenance is required conditions. road in worst

Carlo Carlo linear linear linear chains chains Monte Monte

Markov Markov analysis analysis analysis analysis Multiple Multiple Multiple approach approach nonlinear nonlinear regression regression regression regression Modelling Modelling simulation Linear and and Linear

357) 200 m) m) 200 m) 200 10 km) 10 km) ranging ranging ranging sections sections 500 sites 500 sites (included (included 2197 road road 2197 Sample size size Sample 127 sections 127 sections between 2.5 to to 2.5 between observations = observations between 100 to to 100 between to 150 between sample size, i.e. i.e. size, sample 10 sites (lengths (lengths 10 sites (lengths 27 sites ranging (lengths

strength

Table 2.2: Summary of reviewed roughness prediction models roughness of prediction reviewed models 2.2: Table Summary strength pavement type type pavement Predictor factors factors Predictor pavement strength strength pavement cumulative rutting, rutting, cumulative rutting, cumulative Traffic volume and and volume Traffic climate, cumulative cumulative climate, Traffic loading, age, age, loading, Traffic age, loading, Traffic age, loading, Traffic environmental factors factors environmental climate, maintenance, maintenance, climate, cracking and pavement pavement and cracking Traffic loading, age and age and loading, Traffic cumulative cracking and and cracking cumulative initial pavement initial climate, maintenance, and and maintenance, climate,

(2011), (2011), Australia Australia Australia Australia Australia Sen (2012), Sen (2012), Martin et al., al., et Martin Martin (2008), Martin (2008), (2012), Victoria/ Victoria/ (2012), Mandiartha et al. al. et Mandiartha of data collection data collection of Choummanivong, Choummanivong, Victoria/ Australia Victoria/ and Martin (2013), and Martin Author(s), Situation Situation Author(s),

CHAPTER TWO LITERATURE REVIEW

Also, it Also,

of of the include independent

Findings Findings ) was a reasonable value of 0.54 but 2

expansive soils. soils. expansive -

The The goodness of fit (R statistically significant based on likelihood ratio test. The model predicted that increased traffic load, decreased initial pavement strength, decreased annual maintenance expenditure, and wetter roughness. cumulative increased are climate, The study showed that complexity. of andleaves 60 accuracy 75% reveal models the results of was roughness progression found that and numberclimate vehicle (HV), heavy are AADT, performance the four most age. important variables of road The study found that the differ seasonal under variation wet and is dry climatic significant conditions. The and pavements in latter climate were found non and expansive to differ in seasonal variation for The study concluded that pavement segment is the unique and none roughness progression of variables each can accurately represent the roughness progression of pavements. network the whole

length length Linear Linear analysis analysis analysis message message approach approach Minimum Minimum regression regression Modelling Modelling Regression Regression Data mining Data

16,000 16,000 104,188 104,188 km each) km each) pavement pavement (each 1000 1000 (each Sample size size Sample (1 segments 28,838 rows rows 28,838 140 samples 140 samples meter chain) chain) meter observations

Table 2.2: Summary of reviewed roughness prediction models (Continued)roughness of prediction reviewed models 2.2:Table Summary age age age width width

strength strength Traffic, climate, climate, Traffic, Predictor factors factors Predictor loading, pavement pavement loading, Traffic volume and and volume Traffic type, subgrade soil, soil, subgrade type, type, geometry, and and geometry, type, Traffic loading, age, age, loading, Traffic pavement initial and climate, age, and seal seal and age, climate, climate, maintenance, maintenance, climate, and climate type, Soil speed limit, pavement limit, pavement speed

(2005), (2005), (2010), (2010), Australia Australia Australia Australia Australia Martin and and Martin Queensland/ Queensland/ Queensland/ Queensland/ Hunt (2002), Hunt (2002), of data collection data collection of Choummanivong, Choummanivong, Byrne et al. et Byrne (2008), al. et Byrne Author(s), Situation Situation Author(s),

CHAPTER TWO LITERATURE REVIEW

= 0.43). More 2

inty with time. The tributions (10%, 50% and 50% and (10%, tributions deterioration deterioration phase (initial axles axles cause higher rutting

cable to road networks for

Findings Findings

was was a fair value of 0.44 but statistically

) was a fair value of 0.45 but statistically 2) 2 = 0.07) was very poor and there was a high

carrying higher traffic loading experienced higher rutting

Roads progression rates. Also, trucks with rates. tri Pavement rate. age progression has the The highest analysis outcome estimates the likely distribution of contribution the rutting forecasts to with increasing rutting the level approach of is uncerta applicable when sound deterministic dis model percentiles atthree is presented outcome exist. The 90%). The goodness of fit (R significant the except thewas notof coefficient variable maintenance significant. The model analysis. costing can cycle life strategic be appli The model is acceptable with the goodness of fit (R realistic results were obtained when each densification, gradual independently. progression modeled and accelerated rutting) The goodness of be fit (R variability in the concludes that cumulative a reasonable prediction rutting can be produced if model. the data. develop to data used range of the input is within data However, the study The goodness of fit (R significant based on likelihood ratio test. The increased study predicted that traffic load rutting. cumulative increased and decreased initial pavement strength,

linear - Carlo Carlo linear linear Monte Monte Linear analysis analysis analysis Multiple Multiple approach nonlinear nonlinear regression regression regression regression non regression Modelling Modelling simulation simulation Linear and and Linear and Linear Regression Regression

514) 200 m) m) 200 size, i.e. i.e. size, 500 sites 500 sites 63 sections 63 sections Sample size size Sample 127 sections 127 sections 140 samples 2.5 to 10 km) km) 10 to 2.5 100 to 200 m) m) 200 to 100 observations = observations between 150 to to 150 between

(lengths 10 sites (lengths 27 sites ranging (lengths ranging between ranging between ranging between (included sample sample (included

Table 2.3: Summary of reviewed rutting prediction of models reviewed 2.3:Table Summary

c loading, loading, c (SNP) (SNP)

factors age and age and strength strength age, climate, age, climate, age, climate, age, climate, age, climate, environmental environmental Traffic loading, loading, Traffic Traffi loading, Traffic loading, Traffic loading, Traffic initial pavement pavement initial pavement initial Predictor factor Predictor maintenance, and and maintenance, and maintenance, and maintenance, and maintenance, strength pavement strength pavement strength pavement

Situation Situation (2011), (2011), (2010), Australia Australia Australia Australia Australia

and Martin Sen (2012), Sen (2012), Martin et al., Martin et New Zealand Zealand New Martin (2008), Martin (2008), Henning (2008), (2008), Henning of data collection data collection of Choummanivong, Choummanivong, Choummanivong, Victoria/ Australia Victoria/ and Martin (2013), and Martin Author(s), Author(s),

CHAPTER TWO LITERATURE REVIEW

The The

About 66% of 66% of About .

sed sed in the dataset. Only

0.33 which is considered . fit to thefit to data with increasing the level of

(up to 75%). to (up Findings Findings ) was 2 very poor very

model had model The The study results showed that tested data were compared, the when models developed had predicted and correlations significant The analysis outcome estimates the likely distribution of the rutting forecasts uncertainty with time. The is exist. The model outcome when sound deterministic approach is applicable presented at three percentiles distributions (10%, 50% 90%). and The model was not statistically significant based on the likelihood ratio test. Traffic pavement loading strength were and not significant initial because they could not be reliably asses significant. were climate age and cracking The the sites experienced cracking deterioration over the period monitoring five year significantand statistically found be to was The model consistent up to 50% of goodness cumulative of cracking. fit (R reasonable due to the stochastic data. nature of cracking

-linear -linear Linear Linear (Logit) on analysis analysis analysis analysis approach approach regression regression regression Modelling Modelling simulation N Regression Regression Regression Generalized Generalized Monte Carlo Carlo Monte

00 m) 00 (lengths (lengths (lengths (lengths

10 197 247) size, i.e. i.e. size, 500 sites 63 sections 63 sections Sample size size Sample 290 samples 290 samples 100 to 200 m) m) 200 to 100 observations = observations 100 to to 100 27 sites ranging between ranging between ranging between (included sample sample (included segments

and and

time crack , crack age age and age and , pavement , pavement Table 2.4: Summary of reviewed cracking prediction prediction modelscracking of reviewed 2.4: Table Summary

climate climate climate seal life seal life limate and and limate status status thickness strength, surface surface strength, Predictor factor Predictor Age, climate and and climate Age, C Cracking Cracking Cracking Traffic

phase phase Crack Crack Crack Crack Crack Crack initiation initiation Cracking Cracking

modelled progression progression progression progression

), ), of data of 3 4

(201 (2011), (201 , (2010), , (2010), Australia Australia Australia Australia Australia collection collection Author(s) Martin and and Martin and Martin, and Martin, , and Martin Martin and , Martin et al., Martin et New Zealand Zealand New Situation (2008), Henning Choummanivong Choummanivong Choummanivong

CHAPTER TWO LITERATURE REVIEW

2.6 Summary of the Literature Review

From all reviewed studies, the literature review confirms the following main points:

1. The majority of road pavements in Victoria’s rural arterial network are granular pavements with sprayed seal or thin asphalt surfacing. 2. Functional pavement performance can be assessed by evaluating the effect of roughness parameter, and the structural and surface performance can be addressed by evaluating the effect of rutting and cracking parameters. 3. Road roughness in terms of IRI (International Roughness Index) was found to be the most appropriate pavement distress measure for assessing overall pavement condition, because roughness combines the consequence of many modes of pavement deterioration. 4. An assessment of appropriate pavement distress measures in addition to roughness such as rutting and cracking is needed for triggering intervention and evaluating pavement maintenance and rehabilitation requirements. 5. Monitoring the transverse profile of a pavement surface in terms of rutting is important because it has a major impact on structural and surface performance of flexible pavement under different conditions. 6. Cracking is one of many measurable distress modes that can be used to assess pavement condition. Cracking is considered a sign of surface failure in flexible pavement and an important parameter for overlaying an existing pavement for maintenance and rehabilitation purposes. 7. Pavement deterioration has been categorised into phases using the trends of progression of distress modes. Roughness and rutting are characterised by continuous progression through three phases (initial, gradual and rapid), whereas cracking is characterised by separate phases of initiation and progression. 8. Different factors are contributing to pavement deterioration. Variations and interactions among various factors affect the progression rates of the various distress modes over time. These factors are usually selected to develop models based on their availability in the network databases, engineering experience or based on previous studies for similar networks. These factors include traffic loading, soil type, pavement age, climate condition, pavement surface type, pavement strength, and drainage condition.

CHAPTER TWO LITERATURE REVIEW

9. Basically there are three deterministic techniques in modelling absolute pavement deterioration. They are; mechanistic models, mechanistic-empirical models and empirical regression models. However, the latter will be used in this study for modelling roughness and rutting progression, considering the type of data available. The deterministic models are preferred for modelling roughness and rutting progression because they are used to predict a single value of pavement condition but with no direct account of the stochastic nature of pavement performance. 10. Basically there are four probabilistic techniques in modelling absolute pavement deterioration. They are; survivor curves, Markov models, semi-Markov models, and contentious logistic models. However, the latter will be used in this study for modelling crack initiation and progression, considering the type of data available. 11. The majority of accepted approaches from the existing statistical prediction models are based on observed historical performance of pavements to estimate future pavement condition. That is, empirical models based on historical panel data for many different pavement sections were considered. 12. In the context of Australian and New Zealand’s network pavements, researchers adopt two kinds of road deterioration modelling efforts to describe pavement deterioration process related to spray sealed pavements. They include calibrating the available HDM-4 road deterioration models and newly developed models using local observational data. Yet, there is concern that the HDM-4 pavement deterioration models were developed based on asphalt pavement performance under significantly different conditions than the sealed granular pavements. The newly developed deterioration models for sealed granular pavements reviewed herein have also some limitations. None of the existing models considered the structure of the network data or included the effect of unobserved heterogeneity in the modelling process. Also, very few studies have focused on using accurate condition data in their analysis.

` MODELLING REQUIREMENTS AND CHAPTER THREE DATA COLLECTION PROCESS

3. CHAPTER THREE MODELLING REQUIREMENTS AND DATA COLLECTION PROCESS

3.1 Introduction

In a practical application, an essential requirement to develop a powerful model is building a good database. The dataset that has been used in this study is selected from the rural arterial network of the State of Victoria, Australia. This chapter documents the characteristics of the four road types in Victoria/Australia, the requirements of reliable models, the criteria for network selection and data collection process for the purpose of this study. The chapter presents available data related to the three types of performance condition measures, namely: roughness, rutting and cracking (dependent variables) over a number of years. Also, available data related to the different factors (independent variables) that contribute to the development and progression of the three performance measures are presented.

3.1.1 Road Types in Victoria

All rural arterial roads in Victoria are identified by a simple system which is called the Statewide Route Numbering Scheme. Each road is specified by a letter followed by a number, which represents the quality and function of each road. These roads are classified into four types (M, A, B and C); with the characteristics and functions summarized below (VicRoads, 2013b):  Class M: this class refers to roads that have a high standard of driving conditions, including four traffic lanes, sealed shoulders, divided carriageways and visible line marking. Road of this class connects Melbourne (the capital of Victoria) with other capital cities and major provincial centers.  Class A: this class refers to roads that have a high standard of driving conditions with a single carriageway. These roads are used for a similar purpose as M class roads but carry less traffic.

` MODELLING REQUIREMENTS AND CHAPTER THREE DATA COLLECTION PROCESS

 Class B: this class has a high standard of guidepost delineation, two traffic lanes, and sealed type roads with shoulders. In addition, center and edge lines well marked, and they connect the major regions.  Class C: this class is two lane sealed type roads with shoulders. These roads are supply connections between population centers, and also links between these centers and the other parts of the primary transport network.

In general, road class (M) represents freeways and motorways, road class (A) represents major arterials, road class (B) represents main arterials which are state highways connecting major cities, and class (C) roads represent minor arterials which are rural roads connecting smaller towns (Hoque et al., 2008, Martin and Choummanivong, 2010). Typical cross-sections for these road classes are presented in Figure 3-1 (VicRoads, 2013b). Typically, class M and A roads are classified as heavy duty pavements and class B and C roads are classified as light duty pavements.

Figure 3-1: Typical cross-sections for four road classes (M, A, B and C) in Victoria/Australia (VicRoads, 2013b)

` MODELLING REQUIREMENTS AND CHAPTER THREE DATA COLLECTION PROCESS

Classes M and A have high standards of design and construction and frequently maintained. Their cross sections crowns are generally high, with deep table drains inverts and sub-soil drains may also be present, hence leaving little opportunity for water to gain access to the pavement (Toole et al., 2004). Classes B and C are of lower standards than the other classes in design and construction quality, with varying widths of sealed or unsealed shoulders. Their cross sections are generally low with little crown height unless embankment sections.

3.2 Model Requirements

According to AASHTO (2001), pavement deterioration models need the following basic requirements for reliability and accuracy (Darter, 1980):

 An acceptable database based on in-service sections  Consideration of all possible parameters/factors that affect pavement performance  Selection of an appropriate functional form of the model  Assessment of the precision and accuracy of the predicted model

However, from all reviewed studies, it is concluded that more accurate, powerful and acceptable pavement deterioration models at a network level should be based on the following criteria:

 A representative network and a comprehensive field data are selected.  All possible influencing factors that have significant contributions are included.  All data used for models development and validation are cleaned from incorrect data by using appropriate tools.  Pavement condition data of the same length of road is being compared over time.  An appropriate analysis approach and functional form of the model which suits the network data structure are selected.  The ability of developed model to predict future conditions accurately is validated.  Reasonable amount of input data is included to ensure acceptance by practitioners.

This study aims to develop absolute/aggregate models at a point in time, rather than incremental models which predict the change in condition from an initial state. The

` MODELLING REQUIREMENTS AND CHAPTER THREE DATA COLLECTION PROCESS absolute models predict the condition at a particular point in time as a function of a number of independent variables.

3.3 Network Selection Criteria

Representative samples of roads from Victoria’s rural arterial network are considered. The total number of selected sites is 40 highways with a combined length of more than 2,300 km. The selected sample network is distributed over the whole State and covers different soil types and environmental conditions. The network has the following characteristics:

 All pavement sections are granular pavements with bituminous surface (chip seal). These sections have granular bases and sub-bases with single or double coat spray/chip seals but have different thicknesses reflecting the different traffic loading to which they are subjected and designed for. A typical flexible granular pavement cross-section is presented in Figure 2-1.  Includes sections from four types of road classes, namely; (M, A, B and C).  The selected sections are built on eight types of subgrade soils, expansive and non- expansive. Expansive soils are sensitive to seasonal moisture variations that result in volume changes and results in distortion of the longitudinal profile of the road and cracking.  Drainage condition in terms of good and poor condition. As all roads considered herein are rural, their drainage systems consist of table drains or ditches.  Different climatic zones covering different ranges of Thornthwaite Moisture Index (TMI) values.

The flow chart in Figure 3-2 shows the structure of selected sample network. The figure illustrates the sample network selection criteria which are covering all above possible variables. They include only spray sealed pavement for four types of road classes (M, A, B and C) and each road class covers two types of soils (expansive and non- expansive). For segments in each class, two types of drainage conditions (good and poor) are considered which can be operating in any of the five climate zones, except for class M segments which operate in three climate zones.

` MODELLING REQUIREMENTS AND CHAPTER THREE DATA COLLECTION PROCESS

arid area), Z5: Climate zone 5 (arid area). area). 5 (arid zone Climate Z5: area), arid - GD: GD: Good drainage, PD: Poor drainage, Z1: Climate zone 1 (wet area), Z2: Climate zone 2 Figure 3-2: Structure of selected sample selected network of 3-2:sample Figure Structure arid area), Z4: Climate zone 4 (semi 4 zone Climate Z4: area), arid expansive expansive soil, - -

ES: Expansive soil, NES: Non

Note: 3 (sub zone Climate Z3: area), (humid

` MODELLING REQUIREMENTS AND CHAPTER THREE DATA COLLECTION PROCESS

The selected network includes 7 road sections of class M, 11 road sections of class A, 10 road sections of class B, and 12 road sections of class C, as shown in the pie chart in Figure 3-3. The figure shows the number of sites from each road class and their percentages of total length of the sample network (2308.87 km). Figure 3-4 illustrates the map of Victoria with the locations of selected road sites. This map shows that the selected network is distributed over the whole State. Table 3.1 presents detailed information of the selected sites. Accordingly, this research project has considered significant number of pavement segments, which are around 23,308 segments (each 100m length) from all parts of Victoria. Latimer et al. (2004) suggested that the smaller the segment length used, the more accurate the analysis outputs. It is expected that the extent of this coverage will overcome the limitations associated with previous modelling efforts of Victoria’s rural arterial network conditions.

Class M Class A Class B 7(7%) 12(27%) Class C 11(33%) 10(33%)

No. of sites (% of total length)

Figure 3-3: Number of sites and percentage of total length for each road class

` MODELLING REQUIREMENTS AND CHAPTER THREE DATA COLLECTION PROCESS

Map of Victoria with the locations of selected the of road with sites Victoria locations of Map Figure Figure 3-4 :

` MODELLING REQUIREMENTS AND CHAPTER THREE DATA COLLECTION PROCESS

Table 3.1: Selected sites with detailed information

Start End Road Site Class Length (km) chainage chainage Princes Highway East M 80624 90624 10 Princes Highway East M 388980 398980 10 Calder Freeway M 22314 83131 60.817 Hume Highway M 32477 42477 10 Hume Highway M 255611 265611 10 Hume Highway M 34600 44600 10 Goulburn Valley Highway M 100000 158699 58.699 Princes Highway West A 146042 212927 66.885 Princes Highway East A 164800 214578 49.778 Princes Highway East A 371190 410500 39.310 Western Highway A 285113 412931 127.818 Calder Freeway A 150740 209816 59.076 South Gippsland Highway A 135093 188661 53.568 Midland Highway A 0 73114 73.114 Sturt Highway A 0 116410 116.410 Henty Highway A 30225 87583 57.358 Henty Highway A 113300 214985 101.685 Goulburn Valley Highway A 158699 175300 16.601 Wimmera Highway B 135565 233193 97.628 Melba Highway B 0 64780 64.780 Northern Highway B 117070 164371 47.301 Murray Valley Highway B 373153 420533 47.380 Midland Highway B 388859 436916 48.057 Henty Highway B 217390 334990 117.600 Glenelg Highway B 179034 285389 106.355 Sunraysia Highway B 119579 210893 91.314 Great Alpine Road B 76271 183049 106.778 Great Alpine Road B 213330 240640 27.310 Wimmera Highway C 32075 125140 93.065 Kiewa Valley Highway C 0 78660 78.660 Wangaratta-Whitfield Road C 0 48970 48.970 Moe-Glengarry Road C 0 32825 32.825 Borung Highway C 98615 137655 39.040 Borung Highway C 56048 97820 41.772 Geelong - Ballan Road C 0 61075 61.075 Skipton Road C 0 29631 29.631 Mortlake - Ararat Road C 42820 92971 50.151 Mortlake - Ararat Road C 0 42820 42.820 Bendigo-Maryborough Road C 0 63422 63.422 Chalton-St Arnaud Road C 0 41630 41.630 Total 2308.87

` MODELLING REQUIREMENTS AND CHAPTER THREE DATA COLLECTION PROCESS

3.4 Data Collection Process

In any modelling exercise, the database is the key for formulating the models. Therefore, the accuracy, reliability and availability of this data are the most important factors in generating more powerful and reliable models.

The decisions about what prediction models to employ are directly affected by decisions about type of data available (AASHTO, 2001). Moreover, to obtain valid results from network data, it is necessary to consider time series data to evaluate the deterioration rates and to capture a generalization based on the greatest number of factors (Sayers and Karamihas, 1998, Kadar, 2009).

Therefore, a comprehensive time series dataset has been created from several sets of data to achieve the purpose of this study, because the most complex models are always the most accurate (Byrne et al., 2006). Different datasets related to two types of data are collected, which are:

1. Condition data/ performance measures (dependent variables), and 2. Data related to all possible factors that affect pavement performance (independent variables).

Collections of these datasets are discussed in detail in the following sub-sections.

3.4.1 Condition Data / Performance Measures

In Victoria, pavement condition data for each road section is collected biannually (i.e. once every two years) with half the network surveyed in each year. The condition data collected for this research project include:

1. Road roughness data, in terms of raw longitudinal profile measurements. 2. Pavement rut depth data. 3. Surface cracking data.

At time of this study, roughness data was available from 1998 to 2010, whereas rutting and cracking data was available from 2004 to 2011. The sites’ data is available in four, five or six years of condition data. This type of dataset is called panel data because it

` MODELLING REQUIREMENTS AND CHAPTER THREE DATA COLLECTION PROCESS consists of time series observations for many sections. Due to the nature of available observations for a number of years which differ from section to another (i.e. uneven spacing of time series observations) this type of data is called unbalanced panel data.

3.4.1.1 Roughness Data

Road roughness data in terms of the International Roughness Index (IRI) values have been determined from raw longitudinal surface profile data for the selected sites from 1998 to 2010. These profile data is collected using a multi-laser profilometer and for each site, profile data is represented by two files, and include ERD file and Event file.

The ERD (Engineering Research Division) file contains road profile elevation values (roughness data) for both left and right wheel paths with detailed information about start chainage, end chainage and sample interval. The Event file includes information to help with interpreting the profile of a road. There are many factors in the road environment that contribute to any high roughness readings, such as bridge abutments, rail crossings and roundabouts (Moffatt, 2007). These features are represented by symbols in the Event file (Hassan, 2011); the definitions of these symbols are shown in Table 3.2. Moreover, the Event file contains start chainage, end chainage, speed, km post and other reference marks. Samples of typical ERD and Event files are shown in Figure A-1 and Figure A-2, respectively, in Appendix-A.

3.4.1.2 Rutting and Cracking Data

Both rutting and cracking data have been extracted from database of relevant road agency for the selected sites from 2004 to 2011.

Rutting data is reported in terms of severity i.e. rut depth (RD) as average rut depth in both wheel paths and average lane rut depth. In addition, extent of rutting is reported in different series of rut depth bins for each wheel path, e.g. 10mm, 20mm and 25mm. However, only average lane rut depth is considered in this study.

` MODELLING REQUIREMENTS AND CHAPTER THREE DATA COLLECTION PROCESS

Cracking data is interpreted from digital video images of a moving vehicle and reported as percentage of surface cracking (CR) which includes all types of cracking, transverse, longitudinal and crocodile cracking.

Table 3.2: Definition of the symbols used in Event file (Hassan, 2011)

Event Definition Sample

PL Wheel over raised or sunken Pit lids, bridge joints or settlement at bridges

TL Crossing Tram or Train Line

SR Large grade changes due to Side Roads entering

RA Small radius roundabouts or sharp low speed right angle bend

VS Vehicle Stopped e.g. at Intersections (INT) or under speed

L1and L2 Lane change

3.4.2 Data Related to the Factors that Affect Pavement Performance

Through the literature review major parameters that contribute to pavement deterioration over time have been identified. The relevant data for these parameters were collected from relevant road agency. Based on the availability of information for the sample network sections, the variables considered in this study include the following parameters as the independent or predictor variables (the details of these data is described in the following subsections):

 Initial surface condition  Pavement surface type  Traffic loading  Maintenance activities  Climate condition  Road geometry  Subgrade soil type  Pavement strength  Drainage condition

` MODELLING REQUIREMENTS AND CHAPTER THREE DATA COLLECTION PROCESS

3.4.2.1 Initial Surface Condition

Based on typical construction standards, the initial surface conditions of a new pavement can be assumed (Toole et al., 2009). Toole and others (2004) recommended the initial post construction condition parameters for roughness and rutting shown in Table 3.3 for each road class (M, A, B and C) in Victoria. These initial condition values are used as boundary limits between the initial and gradual phases of roughness and rutting progression. Also, segments in rutting dataset with age 1 year or less is considered within initial phase as rutting due to initial densification that occurs within the first year after construction (Morosiuk et al., 2001, Henning, 2008).

Table 3.3: Initial pavement deterioration conditions for each road class in Victoria (Toole et al., 2004)

Road Class Pavement Conditions M A B and C Initial Roughness (m/km, IRI) 1.2 1.5 1.8

Initial Rut depth (mm, RD) 1 2 2

3.4.2.2 Traffic Loading

Traffic volume data in terms of annual average daily traffic (AADT) and the number of Heavy Vehicles (HV) for the different sections within the four road classes were extracted from the database of relevant agency for the relevant years. Heavy vehicles normally range in gross mass from 4 to 120 tones and generally travel at 100 km/hr. on rural arterials in Australia (Martin, 2011). In addition to this, the traffic volume information report presents road name, State Road Reference System (SRRS), road location, road chainages, traffic volume direction, and the relevant road administrative region.

` MODELLING REQUIREMENTS AND CHAPTER THREE DATA COLLECTION PROCESS

Estimation of traffic data for missing years (when condition data was available) was done for each highway by using the average growth factor for all its segments. HV numbers at the time of construction of different sections along each highway were estimated using current HV number, section age and relevant average growth rate (Equation 3-1). The cumulative growth factor (in each year for which condition data was available) was calculated using Equation 3-2. This data was then used to determine cumulative traffic loading in terms of million equivalent standard axles (MESA) (Jameson, 2012), for each year condition data was available; in conjunction with relevant parameters from Vic oads’ code of practice (VicRoads, 2013a) using Equation 3-3, as shown below:

HVcurrent HVat const 3-1 1+ G Age at current HV year

Where:

HVat const = number of heavy vehicles at time of construction

HVcurrent = number of heavy vehicles in any year of actual traffic is available GF = average annual growth rate of heavy vehicles Age = pavement age

(1+0.01G )Age 1 umulative Growth actor ( G ) 3-2 0.01G ESA MESA 5 HV D LD G NHVAG 10 3-3 at const HVAG Where: MESA = cumulative ESA (equivalent standard axle loads) from construction time to any year, condition data is available. DF = direction factor, (proportion of the two-way HV travelling in the direction of the design lane). LDF = lane distribution factor, (proportion of heavy vehicles in design lane). NHVAG = average number of axle groups per heavy vehicle. ESA/HVAG = average ESA per heavy vehicle axle group.

According to Vic oads’ code of practice (Vic oads, 01 a), the following typical values were adopted in the estimation of cumulative traffic loading in Equation 3-3 (i.e.

` MODELLING REQUIREMENTS AND CHAPTER THREE DATA COLLECTION PROCESS

DF = 1, LDF = 1, NHVAG = 3.1 and ESA/HVAG = 0.82 (class M and A) or 0.66 (class B and C)). According to this document, the value of LDF is considered as 1 when the number of road lanes is less than 3 lanes in one direction. Class M roads have two lanes in each direction, whereas class A, B, and C roads have one lane in each direction.

3.4.2.3 Climate Condition

A climate data extraction tool developed by Byrne and Aguiar (2010) was used to extract climate time series data in terms of the Thornthwaite Moisture Index (TMI). This tool allows easy access to a wide range of historical climate data from 1960 to 2007, and a range of simulated climate data between 2008 and 2099. It is provided as an Excel database and uses Global Positioning Satellites (GPS) (i.e. latitude and longitude) to access relevant data over time for each 100m road section. Historical climate time series data in terms of TMI for the selected sections, for every year condition data is available, was extracted for each 100m segment of the selected road network. Description of working principles of the climate tool and sample of calculating sheets are presented in Appendix-B. The Victorian climate has been divided into five zones with different ranges of TMI values as shown in Table 3.4, from wet to arid zones. Figure 3-5 also shows the TMI map which divides Victoria into the 5 climate zones with zone boundaries according to the changes of TMI values over a 20 year period (1988-2007) (Lopes and Osman, 2010).

Table 3.4: TMI ranges with different climate zones in Victoria (Lopes and Osman, 2010)

Climate Zone TMI Range Moisture Classification

1 ≥ + 10 Wet

2 +10 to -5 Humid

3 -5 to -15 Sub-arid

4 -15 to -25 Semi-arid 5 -25 to -40 Arid

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TMI map which divides Victoria into 5 climate zones (Lopes and Osman, 2010) (Lopes zones and which Victoria divides intoclimate 5 map TMI Figure 3-5Figure :

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3.4.2.4 Subgrade Soil Types

Pavement performance is considerably affected by the presence or absence of unstable materials or weak materials in the road pavement foundation such as expansive subgrade soils, which double the annual average rate of deterioration (Toole et al., 2004). More than half of Victorian road pavements are built on expansive subgrade soils with varying degrees of swell potential. The integrated colour-coded map of expansive soil regions in Victoria is shown in Figure 3-6 and the classification of these soils is presented in Table 3.5 (Mann, 2003). The map was used in conjunction with AutoCAD software to establish the type of subgrade soils for all selected sites with reference to their start and end chainages. The different colours in the map represent different soil types with different swell potential levels. The colours brown, burgundy, orange and pink represent moderate to highly swell potential soils and the colours yellow, light brown, green and white represent low levels of swell potential soils or non-expansive soils. For the purpose of this study, only two groups of subgrade swell potential were considered. The first group with moderate to high potential was considered as expansive soils and the second group of non-expansive and low potential was considered as non- expansive soils.

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potential

potential potential

swell

swell swell

Low Medium High

Expansive soil regions in Victoria (Mann, 2003) Victoria soil regions in Expansive Figure 3-6Figure :

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Table 3.5: Classification of subgrade soils in Victoria from integrated map (Mann, 2003) Level of swell Colour Type of soil potential White Non Gray brown highly calcareous loamy earth, and Yellow hard-setting loamy soils with mottled yellow Low clayey sub soils Leached sand soils and sandy soils with mottled Light brown Low yellow clayey sub soils Green Friable loamy soils Low Hard-setting loamy soils with mottled yellow Orange Medium clayey and red clayey sub soils Friable loamy soils and friable (highly structured) Pink Medium porous earths Cracking clay soils and mottled (brown, dark, red Burgundy High and yellow) clayey sub soils Dark brown Cracking clay soils High

3.4.2.5 Drainage Condition

The conditions of drainage system for the selected sections were extracted from the database of relevant agency based on 2010 network condition data. Drainage condition was rated as good or poor.

3.4.2.6 Pavement Types

The two most common pavement surface types in rural Victoria are thin/thick asphalt wearing course and sprayed seal on granular base and sub-base. In this study, sections with spray sealed surface granular pavement were only considered and all pavement sections with thin asphalt surface were excluded from the datasets. The sections with thin asphalt are mainly located at intersections and their performance is different to the other sections in the dataset due to turning movements and geometry. This is in addition

` MODELLING REQUIREMENTS AND CHAPTER THREE DATA COLLECTION PROCESS to uncertainty about the accuracy of their condition data due to slowing down or stoppage of survey vehicle. Further, sections with thick asphalt make up a very small part of the dataset hence were removed.

3.4.2.7 Maintenance Activities

Maintenance data for all selected highways have been obtained over the time frame of 1997 to 2010 from the annual maintenance program database of relevant road agency. This database includes different treatment activities such as resealing, re-sheeting, resurfacing, periodic maintenance, major rehabilitation and some routine maintenance. In addition to that, km post values of each treated section are provided. Typically, two sources of uncertainty could be found in maintenance records of the sample network:

 Maintenance activities listed in the annual maintenance programs are related to works planned rather than performed for each year.  The start and end chainages of road sections in the maintenance records are different from the chainages of sections in the condition survey data due to changes in geometry resulting in different chainages for reference markers. This made it hard to identify the exact locations of the sections that were treated.

Since the actual maintenance activities applied to the different sections in the sample network could not be identified, it was decided to remove the effect of maintenance from the model. The prediction model should account for the maintenance activities which affect the condition and the rate of deterioration, in a positive or a negative way. However, this influence should be removed from the model, if information on maintenance activities is not available or not accurate (AASHTO, 2001).

The sections that were subjected to maintenance over the study period (relevant survey years) were removed using the Linear Rate of Progression (LRP) tool (Martin and Hoque, 2006). The output of this tool includes the sections (100m) with positive progression only together with their progression rates. Details of removing the effects of maintenance works and using LRP tool are presented in Chapter 4.

` MODELLING REQUIREMENTS AND CHAPTER THREE DATA COLLECTION PROCESS

3.4.2.8 Road Geometry

The database (1998-2011) includes the following road geometry information that helped in identifying the relevant data for all selected sites:

 Lane width  Shoulder seal width  Surface layer type  Road type, name and number  Start and end chainages for each section  Km post and other reference marks information  Start and end latitude and longitude.

3.4.2.9 Pavement Strength

The representation of pavement strength is a major factor in modelling pavement performance (Paterson, 1987). As pavement deflection data for the selected sections was not available to calculate pavement strength, the following steps were used to estimate the modified structural number (SNC) at different ages.

1. Number of heavy vehicles at time of construction (HVat const) was calculated using Equation 3-1 which is presented in Section 3.4.2.2.

2. Cumulative Growth Factor (CGFDL) over the design life (DL) was estimated using Equation 3-4 where DL = 30 years for class M and DL = 20 years for class A, B and C (VicRoads, 2013a).

(1+0.01G )DL 1 umulative Growth actor at DL ( G DL) 3-4 0.01G

Where: GF = average annual growth rate of heavy vehicle.

3. Cumulative traffic loading data at design life (MESADL) was calculated using

Equation 3-5 with CGFDL from previous step.

` MODELLING REQUIREMENTS AND CHAPTER THREE DATA COLLECTION PROCESS

ESA MESADL 5 HV D LD G DL NHVAG 10 3-5 at const HVAG

Where all terms as defined previously in Section 3.4.2.2.

4. Initial value of structural number (SNC0) at the time of pavement construction (Age = 0) was calculated using the following expression (Equation 3-6) derived from NAASRA (1979) and Hodges et al. (1975) (cited in Chen and Martin, 2012).

This expression is based on the cumulative traffic loading (MESADL) that was expected to be experienced over the nominal pavement design life.

MESADL SN 0 0.55 Log10 ( 10 ) + 0. 3-6 1 0

Where:

SNC0 = initial pavement strength, at time of pavement construction (Age = 0).

5. Modified structural number (SNCi) at different ages (i) was estimated from SNC0, pavement age (Age) and design life (DL), using the following relationship (Equation 3-7) (Martin, 2008).

0. Age SN 0.9 SN 0 Exp ( ) 3-7 DL

Where:

SNCi = pavement strength at age (i).

3.5 Summary

In this chapter, the main requirements to develop more precise and robust pavement deterioration models at a network level are presented. They include a representative network, a comprehensive field data, all possible contributing factors, an accurate data preparation process, and appropriate analysis/modelling approaches.

epresentative samples of highways from Victoria’s rural arterial network are considered. The selected sample network is from 40 highways with a combined length of more than 2,300 km. The coverage of the network sites in terms of relevant modelling parameters is presented. This coverage includes only spray sealed granular

` MODELLING REQUIREMENTS AND CHAPTER THREE DATA COLLECTION PROCESS pavements, different climatic zones covering different ranges of Thornthwaite Moisture Index (TMI), four types of road classes (M, A, B and C) with different functions, different subgrade soil types (expansive and non-expansive), and drainage condition in terms of good or poor.

The various datasets used to collect the required data to facilitate the development of reliable and accurate pavement deterioration models have been also described. These are summarized below:

 Unbalanced panel pavement roughness data is obtained in terms of raw profile data from 1998 to 2010, whereas rutting and cracking data have been collected from 2004 to 2011.  All relevant data related to the factors contributing to pavement deterioration, including traffic loading, subgrade soil type, climate condition, pavement strength, drainage condition and pavement type are collected from various sources. Traffic loading in terms of (MESA) and pavement strength in terms of modified structural number (SNC) are calculated based on pavement age, number of heavy vehicles and average growth factor. Climate data is obtained using climate data extraction tool. The integrated colour-coded map of expansive soil regions in Victoria is used in conjunction with AutoCAD software to classify pavement subgrade soils in terms of swell potential.

The following chapter deals with the preparation of the collected data to use for models’ development and validations, then followed with the details of the modelling approaches used herein, namely empirical deterministic approach and probabilistic approach.

CHAPTER FOUR DATA PREPARATION

4. CHAPTER FOUR DATA PREPARATION

4.1 Introduction

The data preparation process is a critical step for the development of robust deterioration models. Quality problems with the condition data stem from human subjectivity and automated surveys over time. This step is essential if reliable accurate prediction models are to be developed. This chapter describes the approach used to prepare accurate datasets for modelling the three pavement condition parameters (roughness, rutting and cracking). The data preparation process includes data alignment, cleaning, filtering, setting up the boundary limits of the data, and compiling and splitting the datasets. The approach used in this thesis to prepare accurate datasets, as much as possible, is described in the following sub-sections.

4.2 Aligning Condition Data

Time series data for all condition data should be aligned for enabling the same road section condition data to be accurately compared over time (Evans and Arulrajah, 2011, Evans, 2013). The alignment process for roughness, rutting and cracking condition data is presented in the following sub-sections.

4.2.1 Aligning Roughness Data

Road roughness data in terms of the IRI is calculated from longitudinal surface profile data for the selected highway sections between 1998 and 2010. The profiles of each highway from different years are first aligned to ensure that the same sections are assessed over time, because any section of the road needs accurate data for analysing the trend of roughness (Moffatt, 2007). Time series data for raw road longitudinal profile are viewed and compared, using ProVAL (Profile Viewing and Analysis) software (ProVAL, 2014). It is observed that the chainages of these profiles for different years do not match as shown in Figure 4-1 (left elevation is chosen for viewing the

CHAPTER FOUR DATA PREPARATION

profile data). Therefore, there is a requirement to align these profile data for a number of years. The alignment process requires two main steps, namely: offset process and shifting process. The offset process is done by making the profile chainages start from the same point for all selected years. One year is considered as the reference, and then the other years are moved either negatively or positively to match the start point of the reference year (usually the last year of available condition data is considered as the reference year).

Figure 4-1: Profile plot for a section of road over five years before alignment

An In-House Excel based tool developed by Evans (2013) is used to do the shifting process for alignment of profile data over the different years. The program needs detailed information for the selected road where a separate file is prepared for each year. This information includes start and end chainages, the number of profile data lines, the interval value, the road name and the ERD file name, which are obtained from the ERD file. The data entry and shifting worksheets for the In-House Excel based tool are shown in Figure C-1 and Figure C-2 of Appendix-C. The shifting process is done using a

CHAPTER FOUR DATA PREPARATION

number of trials for inputting the required shifting value and changing the sample interval value for each year with respect to the reference year until they matched.

A clear example of the alignment process is illustrated in Figure 4-2 and Figure 4-3. From Figure 4-2, the year 2010 is selected as the reference year and the arrows from the spikes at years 2010, 2008, 2006, 2004 and 1998, which are the orange, pink, green, blue and red lines, respectively, shows that there are different positions (chainage values) for the same spike in all years.

Figure 4-2: Profile plot for a section of road over five years shows different chainages for the same spike (before alignment)

However, Figure 4-3 shows the profile data after the offset and shifting processes, which illustrates that the same spikes for all years are matched, where the same spikes have the same position (chainage value) in the different years. Figure 4-4 shows the whole length of the profile over five years after the alignment process. After this alignment process for the selected 40 highway sections, time series data for road longitudinal adjusted profiles are processed in ProVAL to calculate roughness in IRI (m/km) values for every 100m segment.

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Figure 4-3: Profile plot for a section of road over five years shows the same chainage for the same spike (after alignment)

Figure 4-4: Profile plot for a section of road over five years after alignment

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4.2.2 Aligning Rutting and Cracking Data

Rutting and cracking data for the sample network are extracted from relevant database of responsible road agency. Due to the variation in chainages between different years, rutting and cracking data is aligned and adjusted by checking the start and end chainages of each 100m segment over consecutive survey years. In order to have all years starting with the same reference point and all chainages matched in along a road section for the different years, corresponding road roughness data extracted from the same database, is plotted and their profiles are aligned i.e. matching the variation in roughness values over time. The final correct chainages for all 100m segments are then used to extract the corresponding rutting and cracking data.

Table 4.1 shows a typical example of roughness, rutting and cracking data for the same 100m segments over consecutive survey years (2005, 2007, 2009 and 2011) for a number of segments of Princes highway east. The roughness data is plotted to match the elevations for the same section over time. The last year of data (2011) is used as a reference to have all years starting with the same reference point and all chainages matched in along a road section for the other years. In Figure 4-5 , from chainage 393185 to chainage 394185 (shaded cells); it is observed that there is a variation in chainages of roughness data over four consecutive survey years. For this road section, roughness data for the year 2005 needs to shift one segment ahead and in year 2007, it needs to shift six segments ahead. Then, the process involved adjusting the roughness data from these two years to ensure they start and end at the same chainages as the reference year (2011). Accordingly, the same required shifting is used to match rutting and cracking data over time. Figure 4-6 shows roughness data after the aligning process for all relevant years. The required shifting for years 2005 and 2007 data is applied to rutting and cracking data as presented in Table 4.2.

CHAPTER FOUR DATA PREPARATION

Table 4.1: Roughness, rutting and cracking data for the same 100m segments (before alignment)

Roughness (NRM) Rutting (mm) Cracking (% of area)

Chainage 2005 2007 2009 2011 2005 2007 2009 2011 2005 2007 2009 2011

392585 48 52 45 45 3 3 1 8 7 12 12 17 392685 31 34 32 32 9 46 0 2 16 10 13 15 392785 36 33 37 34 12 0 0 0 12 9 18 23 392885 58 60 68 68 16 0 1 8 10 10 14 16 392985 53 61 49 51 22 0 1 0 20 8 7 10

393085 35 31 31 31 21 0 0 0 20 6 7 9 34 29 30 31 6 0 0 2 16 7 9 12 393185 393285 36 30 33 31 15 0 0 0 16 15 9 13

393385 27 30 28 27 11 0 0 2 18 12 7 12

393485 30 31 31 31 1 0 0 2 5 12 10 15 393585 30 30 33 31 0 2 0 2 4 13 9 11

393685 38 39 39 39 1 0 1 0 4 8 12 17

393785 34 33 33 33 1 0 1 0 6 6 11 15

393885 45 44 53 52 1 0 0 0 6 6 12 14 393985 40 43 35 37 1 0 0 0 8 7 11 11

394085 30 35 28 31 0 0 0 2 7 7 14 14

394185 29 31 33 34 0 0 1 0 8 7 14 15

394285 26 31 28 28 1 0 1 0 9 6 11 11

394385 28 30 39 32 3 0 0 0 9 7 13 14 394485 32 30 31 33 1 0 0 0 7 10 9 10 394585 33 33 36 35 3 2 1 0 7 10 10 12

394685 32 36 32 31 0 2 1 0 8 8 11 12

394785 34 31 36 36 0 0 0 0 9 10 11 12

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Figure 4-5: Roughness data profiles for four consecutive survey years (before alignment)

Figure 4-6: Roughness data profiles for four consecutive survey years (after alignment)

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Table 4.2: Corrected roughness, rutting and cracking data for the same 100 m segments (after alignment)

Roughness (NRM) Rutting (mm) Cracking (% of area)

Chainage 2005 2007 2009 2011 2005 2007 2009 2011 2005 2007 2009 2011

392585 45 45 1 8 12 17

392685 48 32 32 3 0 2 7 13 15

392785 31 37 34 9 0 0 16 18 23

392885 36 68 68 12 1 8 12 14 16

392985 58 49 51 16 1 0 10 7 10

393085 53 31 31 22 0 0 20 7 9

393185 35 52 30 31 21 3 0 2 20 12 9 12

393285 34 34 33 31 6 46 0 0 16 10 9 13

393385 36 33 28 27 15 0 0 2 16 9 7 12

393485 27 60 31 31 11 0 0 2 18 10 10 15

393585 30 61 33 31 1 0 0 2 5 8 9 11

393685 30 31 39 39 0 0 1 0 4 6 12 17

393785 38 29 33 33 1 0 1 0 4 7 11 15

393885 34 30 53 52 1 0 0 0 6 15 12 14

393985 45 30 35 37 1 0 0 0 6 12 11 11

394085 40 31 28 31 1 0 0 2 8 12 14 14

394185 30 30 33 34 0 2 1 0 7 13 14 15

394285 29 39 28 28 0 0 1 0 8 8 11 11

394385 26 33 39 32 1 0 0 0 9 6 13 14

394485 28 44 31 33 3 0 0 0 9 6 9 10

394585 32 43 36 35 1 0 1 0 7 7 10 12

394685 33 35 32 31 3 0 1 0 7 7 11 12

394785 32 31 36 36 0 0 0 0 8 7 11 12

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4.3 Cleaning Condition Data

The incorrect data or data points caused by errors in measurement (not related to previous or later measurement) should be removed from the dataset. In this study, road features and abnormalities in road profile data which lead to obtaining incorrect data are removed from the datasets. Using ProVAL, road surface profile data for each section is plotted, inspected and then cleaned from these abnormalities as listed below:

1. Using the features which result in irrelevant values in the Event file (see Table 3.2) of the relevant survey. These features include unusual peaks from stoppage and slowing down of survey vehicle, pit lids, bridge joints and patched trenches (Hassan, 2011). 2. Unnatural spikes are observed due to rapid change in elevation in the data of one or more year/s, as shown in Figure 4-7. 3. Unusual readings are observed in elevation at the start and end of profile data for all relevant years with the same chainages, as shown in Figure 4-8 and Figure 4-9, respectively.

In addition, for roughness, rutting and cracking datasets, as the road sites are divided into 100 m length segments, any last segment that ends up with less than a 50 m length is excluded. Also, segments that have less than three years data are excluded from the prepared datasets. As a result, a significant number of segments are excluded from prepared roughness, rutting and cracking datasets.

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Figure 4-7: Profile data underlining rapid changes in elevation of year 2010 (blue line)

Figure 4-8: Profile data underlining unusual reading in elevation at the start of year 2008 (pink line)

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Figure 4-9: Profile data underlining unusual reading in elevation at the end of year 2006 (green line)

4.4 Excluding Maintenance Effect (Data Filtering)

The key objective of pavement maintenance activities is to keep pavement condition at or above the minimum acceptable serviceability level. As mentioned in chapter three of this thesis, the prediction model should account for the maintenance activities or their influence should be removed from the model, if information on maintenance activities is not available or not accurate (AASHTO, 2001).

Also, further consideration should be given to major maintenance and rehabilitation activities while building the datasets to develop deterioration models because some significant activities such as granular resheets, asphalt overlay and major patching result in improved pavement condition and reset the pavement age to zero (Schram, 2008, Martin, 2008). In this study, the effects of periodic maintenance and rehabilitation works are excluded for the above reasons. The data filtering process is focused on the changes in pavement deterioration progression rate for all road sections. The road sections with positive progression in deterioration only are included in the analysis, while the road sections with negative progression in deterioration are excluded to remove the effects of significant maintenance and rehabilitation activities. The Linear

CHAPTER FOUR DATA PREPARATION

Rate of Progression (LRP) tool (Martin and Hoque, 2006) is used to determine deterioration progression rates of 100 m segments from available years.

The LRP tool contains three separate excel files that are used to predict the LRP from time series data of roughness, rutting and cracking rate of progression, separately, for each pavement segment included in a dataset. For any of the above condition parameters, the result sheet of the tool includes early LRP, latest LRP, minimum number of valid points and first and last points of LRP for early and latest estimated deterioration rate. Brief description of the working principles of LRP tool and a sample of calculating sheets are provided in Appendix-D. As a result of cleaning condition data and excluding maintenance effect, Table 4.3 shows that a significant number of segments are excluded from datasets of the three pavement condition parameters, however, the remaining number of segments after these two processes for roughness, rutting and cracking are 18852, 17673 and 10775 respectively. It can be noticed that the remaining number of segments for cracking dataset is less than roughness and rutting datasets due to the frequent crack sealing practice by road agency in Victoria.

4.5 Setting Up Data Boundary Limits

Road roughness and/or rutting develop progressively throughout the depth of road pavement. The three phases of roughness and rutting development are initial, gradual and rapid deterioration phases, as shown in Figure 2-3. In this study, roughness and rutting progression is modelled during the gradual phase only. The initial phase considers the first deterioration in road pavement after construction. The initial values in Table 4.4 (Toole et al., 2004) are considered as boundary limits to establish the gradual phase. Predicting pavement deterioration during the rapid phase is considered unreliable because the pavement condition would not be acceptable to road users beyond the gradual phase and the pavement needs to be maintained or rehabilitated before reaching the rapid deterioration phase (Martin, 2009). For this reason and lack of observational data within the rapid phase, this phase was not modelled in this study and only the gradual phase was considered.

CHAPTER FOUR DATA PREPARATION

Table 4.3: Number of road segments before and after data cleaning, filtering and limiting the boundary

No. of segments No. of segments in roughness No. of segments in rutting m)

in cracking dataset after dataset after dataset after

Class M roads Total no. of of no. Total the the the leaning leaning leaning iltering imiting iltering imiting iltering F F F L L C C C segments (100 segments boundary boundary Princes East -1 100 100 50 22 100 8 5 100 100 Princes East -2 100 100 60 46 100 7 5 100 93 Calder -1 608 548 462 347 575 549 548 575 383 Hume -1 100 100 83 82 100 95 95 100 22 Hume -2 100 79 69 55 100 98 98 100 45 Hume -3 100 99 83 70 100 104 104 100 64 Goulburn Valley -1 587 584 467 401 587 482 482 587 423 Class A roads Princes West 669 668 440 198 669 499 480 669 372 Princes East -3 498 497 365 323 496 387 375 496 235 Princes East -4 393 353 268 203 393 329 320 393 163 Western 1278 1278 1089 735 1278 1113 1047 1278 611 Calder -2 591 588 541 442 590 420 330 590 461 South Gippsland 536 532 407 324 536 458 447 536 192 Midland -1 731 731 690 456 731 609 492 731 286 Sturt 1164 1164 947 846 1160 800 765 1160 286 Henty -1 574 574 486 108 573 435 188 574 249 Henty -2 1017 1017 868 619 1017 772 744 1016 527 Goulburn Valley -2 166 165 153 126 166 133 132 166 119 Class B roads Wimmera -1 976 976 758 440 976 832 751 976 305 Melba 648 647 454 170 647 611 372 647 300 Northern 473 472 359 209 471 390 374 471 249 Murray Valley 474 473 398 117 474 357 347 474 188 Midland -2 481 458 414 241 480 356 341 480 197 Henty -3 1176 1154 1003 815 572 472 459 572 274 Glenelg 1064 1059 959 388 1063 806 779 1063 516 Sunraysia 913 913 769 415 907 753 490 907 388 Great Alpine -1 1068 1041 848 385 1066 722 680 1066 727 Great Alpine -2 273 269 204 188 273 201 200 273 136 Class C roads Wimmera -2 931 872 721 575 930 669 634 930 309 Kiewa Valley 787 784 690 366 784 676 624 784 244 Wangaratta whitfield 490 490 378 309 490 281 253 490 285 Moe-Glengarry 328 328 209 180 328 258 245 328 190 Borung -1 390 389 368 334 390 300 285 390 183 Borung -2 418 417 379 326 417 344 320 417 275 Geelong - Ballan 611 589 561 421 611 537 525 611 303 Skipton 296 273 227 6 296 210 4 296 152 Mortlake -Ararat -1 502 494 403 205 501 418 391 501 256 Mortlake -Ararat -2 428 424 372 261 428 371 357 428 195 Bendigo-Maryborough 634 614 475 298 634 439 290 634 314 Chalton-St Arnaud 416 398 375 312 415 372 329 415 158 Total 23089 22711 18852 12364 22424 17673 15707 22424 10775

Note: Each number represents 100 m segment

CHAPTER FOUR DATA PREPARATION

According to Austroads (1992) and Smith et al. (1996), the transition from gradual deterioration phase to the rapid deterioration phase is limited for each road class by their terminal roughness and rutting values. These terminal values are shown in Table 4.4 . In the current study, the initial and terminal condition values are used to establish boundary limits for the gradual deterioration phase. Hence, all segments with roughness and rutting values within the initial phase (below or at the values) are removed to ensure pavement deterioration had passed the initial phase and entered the gradual phase.

Also segments with roughness and rutting data that had passed the terminal condition values (above or at the values) are removed to ensure pavement deterioration did not enter the rapid phase. Also, segments in rutting dataset with age 1 year or less is excluded as rutting due to initial densification that occurs within the first year after construction (Morosiuk et al., 2001 and Henning, 2008). Accordingly, a number of segments are excluded from each dataset and the remaining number of segments after constraining boundary limits for roughness and rutting are 12364 and 15707, respectively, as shown in Table 4.3 . All cracking data after the filtering process is considered because both of cracking phases, namely: initiation and progression are modelled in this study.

Table 4.4: Initial and terminal roughness and rutting values for each road class (Austroads, 1992, Smith et al., 1996 and Toole et al., 2004)

Initial Terminal Initial Terminal Road class roughness, IRI roughness, IRI rutting, mm rutting, mm

M 1.2 4.2 1 20

A 1.5 4.2 2 20

B 1.8 5.71 2 25

C 1.8 6.65 2 25

CHAPTER FOUR DATA PREPARATION

4.6 Compiling and Splitting the Prepared Datasets

Data for the available variables are extracted from different databases. Hence for each 100 m segment, the chainages of condition data are treated as the base and chainages of data related to contributing factors (i.e. traffic loading, pavement strength, climate condition, soil types and drainage condition) are matched to them for all relevant years. Samples of prepared datasets for the three pavement condition parameters (roughness, rutting and cracking) are presented in Appendix-E. Good and Hardin (2003) recommended that one-fourth to one-third of the data should be set aside for validation purposes. Using SPSS (Statistical Package for Social Sciences) software (SPSS, 2015), random dataset split is utilised to divide the dataset into two parts; approximately 70% of the data to use for model development and the remaining 30% of the data to use for model validation.

4.7 Summary

In this chapter, great effort has been put into data preparation process because it is particularly a vital step for the development of robust deterioration models. The approach used to prepare road condition data involved the following steps:

 Data alignment: time series data for the three condition parameters (roughness, rutting and cracking) are aligned to ensure that the same road segments are compared over time. Raw roughness profile data from a number of condition surveys has been aligned using ProVAL software and an In-House Excel based tool. Rutting and cracking data has been aligned using aligned roughness data profiles extracted from the same database for the same segments over time.  Data cleaning: cleaning of roughness data involved removing anomalous values resulting from features such as pit lids, bridge joints, stop/start of survey vehicle and similar features that result in unusual spikes in the profile data. Cleaning rutting and cracking datasets involved removing the segments that are less than 100 m long for one or more year/s and segments that have less than three years of data.  Data filtering: the effects of periodic maintenance and rehabilitation works are excluded from the datasets. The road segments with only positive progression in

CHAPTER FOUR DATA PREPARATION

deterioration are taken into account using the Linear Rate of Progression (LRP) tool.  Boundary limits of data: the initial and terminal condition values of roughness and rutting data are used to establish boundary limits for the gradual deterioration phase.  Compiling and splitting datasets: for each 100 m segment, the chainages of condition data and chainages of data related to contributing factors are matched for all relevant years. Random dataset split is utilised to divide the dataset into two parts; around 70% of the data for model development and the remaining 30% of the data for model validation.

PRELIMINARY ANALYSIS AND CHAPTER FIVE MODELLING APPROACH

5. CHAPTER FIVE PRELIMINARY ANALYSIS AND MODELLING APPROACH

5.1 Introduction

This chapter presents details of the preliminary exploratory analysis and proposed research methodology. Firstly, the structure of the prepared datasets for the three condition parameters (roughness, rutting and cracking) is presented. The description of the data structure, and variables transformation, bias and interpretation are provided. Then, the appropriate modelling analysis approach for these condition parameters is presented. The chapter includes the results of the initial exploratory analysis and explains the need for using multilevel analysis and the relevant model specifications. Also, it provides the appropriate methods for model evaluation, model validation and model simulation process.

5.2 Structure of Prepared Datasets

The prepared datasets for the three pavement condition parameters, roughness, rutting and cracking consist of panel data which includes historical time series data (observations) and cross sectional data for many 100m segments. As mentioned before, the sample of network panel data is collected from 40 rural highway sections from four different road classes.

When using historical time series data for many pavement segments (panel data) in estimating future condition, examining the cause of heterogeneity across segments data is an essential step (Greene, 2004). This heterogeneity may be due to differences in construction quality, subgrade soil type, climate condition and maintenance activities applied, in different ways at different times. There are also differences between the highways from which the road segments are extracted which may be caused by variations in material properties. Finally, there are also differences between pavement classes, due to factors such as design standards and class duty function (light or heavy duty pavement). Therefore the data structure is hierarchical with four levels of variation within the selected network. Time series observations (level-1) are nested within

PRELIMINARY ANALYSIS AND CHAPTER FIVE MODELLING APPROACH segments (level-2) which are nested within highways (level-3) which are nested within road classes (level-4). Therefore, the development of a network pavement deterioration model must allow for variation at all four levels. The flowchart in Figure 5-1 shows the hierarchal structure for the nesting of the network data. In this hierarchy chart, H represents highway, S represents segment, and O represents one observation of a time series. According to Hong (2007) and Hong and Prozzi (2010), the variability (i.e. heterogeneity) in pavement condition can be categorised as:

1) Observed heterogeneity, which can be captured by including identified causal variables in the deterioration models (i.e. observed variables). 2) Unobserved heterogeneity, which arises from factors beyond the identified causal variables (i.e. unobserved variables).

Pavement performance variability due to the above two types of heterogeneity should be allowed for in the model parameters. In the current study, the observed heterogeneity is included using available observed variables such as traffic loading, pavement strength, climate condition, soil type, and drainage condition. However, the effect of unobserved heterogeneity can be accounted for by allowing randomness over the model parameters (Raudenbush and Bryk, 2002). This is explained in details in the model specification section of this chapter.

Further, cracking data are mostly reported as predominant cracking type, cracking severity or extent of cracking (percentage of affected area). However, the cracking data used for this study was reported in terms of extent only and considered as continuous data. Wang (2013) recommended that categorizing cracking data from a continuous variable into a discrete categorical variable would help smooth out abnormality in the dataset. Accordingly, this continuous cracking extent data is divided into two categories, namely cracked and uncracked to predict crack initiation. However, four discrete categories are used to predict crack progression in terms of the probability of a pavement falling into each category. The four categories of crack extent have been identified as insignificant, limited, considerable and significant affected area, with the ranges shown in Table 5.1 (Moffatt and Hassan, 2006). Additional details about the prepared datasets and the included variables are presented in the following sub-sections, which include descriptive statistics, variables transformation, prediction bias, and an interpretation of observed relationships found to be significant.

PRELIMINARY ANALYSIS AND CHAPTER FIVE MODELLING APPROACH

Structure of network data of Structure : Figure 5-1Figure

PRELIMINARY ANALYSIS AND CHAPTER FIVE MODELLING APPROACH

Table 5.1: Classification of the ranges of affected area for crack status and crack categories

Range of affected Cracking Category description Cracking status area category

Insignificant affected area 0% to 1% Uncracked Insignificant

Limited affected area 1% to < 5% Cracked Limited

Considerable affected area 5% to < 15% Cracked Considerable

Significant affected area ≥ 15% Cracked Significant

5.2.1 Descriptive Statistics

Descriptive statistics are used simply to describe the main characteristics of the variables in the dataset. They provide simple summaries and useful information about the data samples for the whole network and each class separately. The statistics for the continuous and categorical variables in the three datasets (roughness, rutting and cracking), used in developing models for all road classes (M, A, B and C) and the network as a whole (NW), are investigated. In addition to the relevant condition variable, roughness (IRI), rutting (RD) or cracking (CR); continuous variables in these datasets include traffic loading (MESA), initial pavement strength (SNC0), pavement strength at any age (SNCi), pavement age (Age), and climate condition (TMI). The categorical variables include subgrade soil type (SST) which is represented as expansive or non-expansive and drainage condition (DRA) which is represented as good or poor.

5.2.1.1 Roughness Dataset

Descriptive statistics for the continuous variables used in developing roughness models within the gradual phase of deterioration, for the whole network (NW) and the four road classes, are presented in Table 5.2. Table 5.2 presents the range for each variable within the training sample of data used for model development (i.e. 70% of the roughness

PRELIMINARY ANALYSIS AND CHAPTER FIVE MODELLING APPROACH dataset). The distributions for each categorical variable for all road classes are provided in Table 5.3.

Table 5.2: Descriptive statistics of continuous variables used when developing roughness models

Range of variables Descriptive Dataset statistics IRI MESA SNC0 SNCi TMI Age

Sample size 8686 8686 8686 8686 8686 8686 Mean 2.80 2.13 2.90 2.18 -2 13 Standard 0.84 3.14 0.38 0.51 26.3 5.09 NW deviation Minimum 1.21 0.01 1.49 1.31 -38 4 Maximum 6.61 34.78 4.14 3.95 100 39 Sample size 724 724 724 724 724 724 Mean 1.94 8.14 3.62 3.19 6 10 Class Standard 0.56 5.21 0.12 0.24 18.92 3.86 M deviation Minimum 1.21 1.34 3.42 2.50 -13 4 Maximum 4.20 34.78 4.14 3.95 94 23 Sample size 3088 3088 3088 3088 3088 3088 Mean 2.55 3.17 3.04 2.31 -5 13 Class Standard 0.63 3.03 0.32 0.40 24.69 4.24 A deviation Minimum 1.51 0.02 1.91 1.28 -38 4 Maximum 4.20 19.72 3.45 3.16 53 25 Sample size 2357 2357 2357 2357 2357 2357 Mean 2.90 0.91 2.77 2.11 2 13 Class Standard 0.78 0.87 0.27 0.35 34.79 4.33 B deviation Minimum 1.8 0.02 1.49 1.23 -28 5 Maximum 5.7 5.95 3.36 3.05 100 30 Sample size 2517 2517 2517 2517 2517 2517 Mean 3.20 0.52 2.65 1.85 -3 16 Class Standard 0.89 0.48 0.20 0.41 19.42 5.91 C deviation Minimum 1.81 0.01 1.61 1.13 -26 5 Maximum 6.61 3.37 2.99 2.71 81 39

PRELIMINARY ANALYSIS AND CHAPTER FIVE MODELLING APPROACH

Table 5.3: Distribution of categorical variables used when developing roughness models

classification of variables

SST DRA

Dataset - non % of xpansive drainage drainage % of expansive e % good of % poor of

NW 40.8 59.2 74.9 25.1

Class M 62.6 37.4 47.9 52.1

Class A 44.3 55.7 82.5 17.5

Class B 35.3 64.7 63.4 36.6

Class C 35.6 64.4 84.1 15.9

5.2.1.2 Rutting Dataset

Descriptive statistics for continuous variables used in developing the rutting models within the gradual phase of deterioration for the whole network (NW) and the four road classes are presented in Table 5.4 . The distributions of the categorical variables for the rutting dataset are provided in Table 5.5 . Both tables refer only to the training sample of data used for model development (i.e. 70% of the rutting dataset).

PRELIMINARY ANALYSIS AND CHAPTER FIVE MODELLING APPROACH

Table 5.4: Descriptive statistics of continuous variables used when developing rutting models

Range of variables Descriptive Dataset statistics RD MESA SNC0 SNCi TMI Age

Sample size 10978 10978 10978 10978 10978 10978 Mean 6 2.99 2.97 2.54 1 10 Standard 2.82 3.08 0.35 0.50 26.76 5.12 NW deviation Minimum 1 0.01 1.43 1.22 -38 1 Maximum 25 36.22 4.08 3.73 100 47 Sample size 925 925 925 925 925 925 Mean 5 7.66 3.64 3.28 4 8 Class Standard 2.46 5.88 0.10 0.16 9.91 2.63 M deviation Minimum 1 0.91 3.40 2.79 -13 2 Maximum 20 36.22 4.08 3.73 93 18 Sample size 3713 3713 3713 3713 3713 3713 Mean 6 2.94 3.13 2.54 -2 10 Class Standard 2.86 2.63 0.23 0.31 26.14 3.47 A deviation Minimum 2 0.51 2.11 2.09 -38 1 Maximum 20 16.48 3.46 3.25 53 25 Sample size 3359 3359 3359 3359 3359 3359 Mean 6 0.87 2.83 2.32 4 10 Class Standard 2.77 0.78 0.27 0.35 34.98 3.84 B deviation Minimum 2 0.01 1.43 1.52 -26 1 Maximum 22 5.10 3.38 3.10 100 30 Sample size 2981 2981 2981 2981 2981 2981 Mean 6 0.50 2.71 2.03 -1 13 Class Standard 2.90 0.47 0.22 0.49 19.55 6.74 C deviation Minimum 2 0.01 1.48 1.22 -26 1 Maximum 25 3.99 3.15 3.13 63 47

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Table 5.5: Distribution of categorical variables used when developing rutting models

classification of variables

SST DRA

Dataset - % of drainage drainage % non of expansive Expansive % good of % poor of

NW 39.1 60.9 78.8 21.2

Class M 53.9 46.1 52.2 47.8

Class A 41.4 58.6 83.8 16.2

Class B 35.1 64.9 74.8 25.2

Class C 36.1 63.9 85.4 14.6

5.2.1.3 Cracking Dataset

Descriptive statistics for the continuous variables used to develop cracking models within the initiation and progression phases of deterioration for the whole network (NW) and the four road classes are presented in Table 5.6. The distributions for the categorical variables are provided in Table 5.7.

As mentioned earlier, the continuous cracking extent data is divided into two cracking categories, namely cracked and uncracked, allowing the modelling of crack initiation. For modelling of cracking progression, four distinct categories of cracking are used; insignificant, limited, considerable and significant affected area. Table 5.8 shows that the whole network training sample contains 43% uncracked observations and 57% cracked observations. Also, the cracked status for class C roads (61%) is more than for the other classes, followed by class B (58%), then class A (56%) and class M (49%). The table also shows that in all road classes the percent of insignificant affect area

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PRELIMINARY ANALYSIS AND CHAPTER FIVE MODELLING APPROACH cracking observations is higher than for the other categories, whereas the percent of significant affected area observations is lower than the other categories.

Table 5.6: Descriptive statistics of continuous variables used when developing cracking models

Range of variables Descriptive Dataset statistics CR* MESA SNC0 SNCi TMI Age

Sample size 6952 6952 6952 6952 6952 6952 Mean 4.82 2.02 2.97 2.40 2 11 Standard 8.98 2.84 0.37 0.54 27.78 5.13 NW deviation Minimum 0 0.01 1.59 1.49 -38 1 Maximum 100 31.28 4.19 3.96 100 47 Sample size 782 782 782 782 782 782 Mean 3.79 6.50 3.64 3.28 12 8 Standard Class M 7.33 4.14 0.13 0.18 28.06 2.64 deviation Minimum 0 0.93 3.41 2.73 -13 3 Maximum 91 31.28 4.19 3.96 94 19 Sample size 2325 2325 2325 2325 2325 2325 Mean 4.79 2.71 3.10 2.51 -3 10 Standard Class A 8.77 2.66 0.25 0.33 24.13 3.50 deviation Minimum 0 0.01 2.09 1.67 -38 1 Maximum 98 15.49 3.46 3.32 53 25 Sample size 1961 1961 1961 1961 1961 1961 Mean 4.43 0.82 2.82 2.32 7 10 Standard Class B 7.56 0.77 0.27 0.35 36.05 3.74 deviation Minimum 0 0.01 1.59 1.49 -27 2 Maximum 100 5.91 3.37 3.10 100 28 Sample size 1884 1884 1884 1884 1884 1884 Mean 5.69 0.51 2.70 1.96 -2 15 Standard Class C 10.86 0.45 0.20 0.49 19.11 6.83 deviation Minimum 0 0.01 1.70 1.50 -26 1 Maximum 100 3.99 3.15 3.11 64 47 *Notes: CR represents the percent of affected area.

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Table 5.7: Distribution of categorical variables used when developing cracking models

classification of variables

SST DRA

Dataset - non

% of drainage drainage % of expansive Expansive % good of % poor of NW 37.8 62.2 79.4 20.6

Class M 54.5 45.5 54.0 46.0

Class A 35.1 64.9 81.5 18.5

Class B 36.6 63.4 78.6 21.4

Class C 35.4 64.4 88.1 11.9

Table 5.8: Distribution for crack status and crack progression

% of crack status % of crack categories Dataset Insignificant Uncracked Cracked Significant Considerable Limited (uncracked) NW 42.6 57.4 8.9 23.4 25.1 42.6

Class M 50.9 49.1 4.8 25.9 18.3 50.9

Class A 43.6 56.4 9.2 22.2 25.0 43.6

Class B 41.7 58.3 8.1 23.4 26.9 41.7

Class C 38.9 61.1 10.9 23.9 26.2 38.9

Graphical descriptions for cracking status and cracking progression for the whole network are also presented in Figure 5-2 and Figure 5-3, respectively. Figure 5-2 shows that the percent of cracked road segments increased with time, over the selected analysis

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PRELIMINARY ANALYSIS AND CHAPTER FIVE MODELLING APPROACH period. Figure 5-3 indicates that a decrease in insignificant and limited cracking categories over time, which is associated with an increase in the other two categories.

Figure 5-2: Distribution of cracking status over time for observations in the whole network sample

Figure 5-3: Distribution for cracking progression status over time for observations in the whole network sample 104

PRELIMINARY ANALYSIS AND CHAPTER FIVE MODELLING APPROACH

5.2.2 Transformation of Variables

The aim of this study is to develop empirical regression models; requiring that certain assumptions is use. The assumptions that residuals are normally distributed with constant variance (homogeneity) are two of these conditions (Francis, 2012, Garson, 2013). In order to comply with this assumption, the analysis might be improved by using some of the continuous variables have been transformed in order to reduce the level of skewness in their distributions and to reduce heterogeneity.

In any regression analysis, transforming the dependent variable (DV) is often essential. Transforming the independent variable/s (IVs) may also be necessary in order to ensure linear relationships.

The form of these transformations needs to be considered carefully, because some transformations can make the model more difficult to interpret (Francis, 2012). A log transformation is useful for data which exhibits moderate right skewness (positively skewed) (Francis, 2012). The log transformation has been used in this study because all considered variables are positively skewed. Parameter estimates are easily interpreted in this case.

The roughness data is positively skewed for the whole network dataset and all classes. Accordingly, the DV (roughness, IRI) is transformed using a natural log transformation (LN) function. For the whole network dataset (NW) and each of the four road classes (M, A, B and C), the statistics of roughness data and its transformed data are presented in Appendix-F in Table F.1, Table F.2, Table F.3, Table F.4 and Table F.5, respectively. The frequency histograms before and after transformations are shown in Figure F-1, Figure F-2, Figure F-3, Figure F-4 and Figure F-5, respectively in Appendix-F. These histograms show that the transformed roughness variable (LN_IRI) is much closer to the normal distribution than the original roughness (IRI) data. This suggests that model residuals will also be close to normal in distribution with constant variance.

The rutting (RD) variable is positively skewed in all datasets (NW, M, A, B and C) and the traffic loading (MESA) variable is also positively skewed for the NW, class M and class C datasets. Hence, these variables are transformed using natural log transformed (LN) function of RD (LN_RD) and natural log of MESA (LN_MESA). For the NW, class M, class A, class B and class C datasets, the statistics of rutting data and its

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PRELIMINARY ANALYSIS AND CHAPTER FIVE MODELLING APPROACH transformed data are presented in Appendix-F in Table F.6, Table F.8 , Table F.10, Table F.11 and Table F.12, respectively. The statistics of traffic loading data and its transformed data are presented in Appendix-F in Table F.7, Table F.9 and Table F.13 for the NW, class M and class C, respectively. The frequency histograms before and after transformations of rutting data are shown in Figure F-6 , Figure F-8, Figure F-10, Figure F-11 and Figure F-12, for the NW, class M, class A, class B and class C datasets, respectively. Also, the frequency histograms before and after transformations of traffic loading data are shown in Figure F-7 , Figure F-9 and Figure F-13, for the NW, class M and class C datasets, respectively. These histograms show that the transformed rutting variable (LN_RD) is much closer to the normal distribution than RD data before transformation, suggesting that the associated model residuals will also tend to be more normal in distribution with constant variance.

According to Raudenbush et al. (2011), the assumption of normality is applicable when the dependent variable is continuous. They emphasized that the normality assumption is not realistic when the dependent variable involves binary categories or multi-categories. Therefore, cracking data does not need to be transformed.

5.2.3 Removing Prediction Bias

The main two necessary properties of any parameter of the developed model are that it is unbiased and its variance is as small as possible (Uriel, 2013). The latter is achieved by fitting appropriate models. In order to remove bias caused by fitting the model to the log transformed data, predictions of transformed condition data (IRI and RD) are multiplied by the usual correction factor (CF), which is based on the variance (V) of the residuals (e) as shown in Equation 5-1 (Stow et al. 2006):

V 5-1 Exp ( )

Where: CF: is the correction factor Exp: is the exponential function Ve: is the variance of the residuals (e).

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5.2.4 Interpreting Transformed Variables

Parameter interpretations assume that the model can be defended, that the regression diagnostics are satisfactory and the data is from a valid source. The typical interpretation of a regression slope parameter is that a one unit increase in the predictor (IV) is associated with a β (coefficient of the IV in the model) unit increase in the expected value of the dependent variable (DV), while holding all the other predictors constant. There are three possible combinations of transformation involving logarithms to interpret log-transformed parameter estimates in regression models (Benoit, 2011), as listed below:

1. If only the DV is log-transformed, the interpretation is: One unit increase in the IV is associated with a [EXP (β) -1]*100 percent increase in DV. 2. If only the IV is log-transformed, the interpretation is: One percent increase in IV is associated with a [β * LN (101/100)] unit increase in DV. 3. If both the DV and IV are log-transformed, the interpretation is: One percent increase in IV is associated with a [(1.01^ β) - 1]*100 percent increase in DV.

5.3 Modelling Approach

A comprehensive review of existing pavement condition models indicates that different approaches and analysis methods have been proposed for predicting performance over time. Basically there are three deterministic techniques in modelling absolute pavement deterioration. They are; mechanistic models, mechanistic-empirical models and empirical regression models. The latter modelling approach has been used in this project for modelling roughness and rutting progression, due to the type of data available and for the following reasons (Haas et al., 1994, Giummarra et al., 2007, Mubaraki, 2010):

1. It is the most widely used method to predict pavement deterioration because it can be easily incorporated in a PMS. 2. It does not need elaborate mechanistic structural testing. 3. It has the capability to capture the effects of as many factors as available and necessary. 4. It has the capability to use the data very efficiently.

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5. It has the capacity to create models which readily transfer to other similar conditions when covering a wide range of independent variables.

However, the main disadvantages of regression models are that they need a large dataset for a more powerful model in terms of the number of predictors used, and that they can be used only within the range of input data (independent variables) used in their development.

The most common probabilistic approaches that have been used for predicting the probability of pavement performance are Markov or semi-Markov chain models, survival analysis and continuous probability models. As the cracking data in this study is converted from a continuous variable into a discrete categorical variable, a logistic regression is an appropriate type of model. The logistic regression modelling approach is an example of using a continuous probability technique that has been used effectively by a number of recent studies in predicting crack initiation (Henning, 2008, Henning and Roux, 2012) and the probability of crack progression (Khraibani et al., 2012, Lorino et al., 2012, Zouch et al., 2012, Wang, 2013, Choummanivong and Martin, 2014).

5.3.1 Exploratory Analysis

Different analysis approaches have different underlying assumptions. In all the reviewed studies, two types of regression analysis, in terms of the effect of variance in network data, have been used. A significant number of previous studies have employed only one level of variance in linear and nonlinear traditional regression analyses for their pavement deterioration models (Salama et al., 2006, Mulandi et al., 2007, Stephenson, 2010, Mubaraki, 2010, Martin et al., 2011, Sunitha et al., 2012, Sen, 2012, Wang, 2013, Azevedo et al., 2015, Alaswadko and Hassan, 2016). The main assumptions of this approach are that the deterioration of all pavement sections is due to same process and only depends on the predictors that are included in the regression analysis. In statistical terms, this approach assumes that the intercept term is the same for all pavement segments, both the intercept and slope are homogeneous (rather than random), and errors are independent.

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In addition to this, a number of studies have successfully developed regression deterioration models that included two levels of variances (Archilla and Madanat, 2000, Prozzi, 2001, Prozzi and Madanat, 2002, Onar et al., 2006, Hong, 2007, Hong and Prozzi, 2010, Gao et al., 2011, Christofa and Madanat, 2010, Zouch et al., 2012, Lorino et al., 2012, Khraibani et al., 2012). These studies incorporated the effect of observed and unobserved variables by incorporating the effect of variance between time series observations, within segments and between segments. In other words, they demonstrated that unobserved heterogeneity often exists in most network panel datasets and that residuals are correlated within segments across the years.

Initially, the relationships between the DV and relevant IVs in the datasets of this study are investigated for each dataset to check which of the above analysis approaches is more appropriate. Therefore, an exploratory analysis has been carried out using the most popular estimation technique which is the application of traditional linear regression model (i.e. ordinary least squares method) for pavement deterioration based on one level of variance. This regression analysis is performed for the whole network and for each of the four road classes for roughness, rutting and cracking datasets using SPSS software (SPSS, 2015). In this type of analysis, an assumption of residual independence is made. Durbin-Watson (DW) statistics is used to test for correlation between consecutive residuals. The value of this test statistics can vary between 0 and 4 with a value of close to 2 suggesting that consecutive residuals are uncorrelated. A value greater or below 2 indicates that there is correlation between errors (Field, 2009). A DW value greater than 2 indicates a negative correlation between consecutive residuals whereas a DW value below 2 indicates a positive correlation. In regressions, this can indicate an underestimation of the level of statistical significance.

In the NW and all classes’ datasets, it was found that the Durbin-Watson values are below 2 which mean that the errors are positively correlated in all datasets, as shown in Table 5.9 . To test for positive correlation, the test statistic DW is compared to lower and upper critical values (DWL and DWU), as below:

 If DW < DWL, there is statistical evidence that the residuals are positively correlated.

 If DW > DWU, there is no statistical evidence that the residuals are positively correlated.

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 If DWL < DW < DWU, the test is inconclusive.

The critical values for the Durbin-Watson test are available at Stanford website (Stanford, 2016). The size of DW statistic depends upon the number of observations (sample size of the dataset) and the number of predictors in the model (includes the intercept).

Table 5.9: Results of Durbin-Watson test for all datasets

Critical value of Durbin- Number DW* Dependent Sample Dataset Watson of Lower Upper variable size (DW) test predictors value value (DWL) (DWU) NW 1.028 8686 6 1.921 1.931

Class M 1.717 724 6 1.861 1.890

Roughness Class A 1.022 3088 6 1.921 1.931

Class B 0.985 2357 6 1.921 1.931

Class C 0.809 2517 6 1.921 1.931

NW 1.493 10978 5 1.922 1.930

Class M 1.563 925 5 1.885 1.902

Rutting Class A 1.203 3713 5 1.922 1.930

Class B 0.341 3359 5 1.922 1.930

Class C 1.362 2981 5 1.922 1.930

NW 0.586 6952 6 1.921 1.931

Class M 0.200 782 6 1.871 1.896

Cracking Class A 0.862 2325 6 1.921 1.931

Class B 0.162 1961 6 1.920 1.931

Class C 0.941 1884 6 1.919 1.930 *Note: the maximum sample size in the tables of the Stanford website is 2000; therefore, for sample size more than 2000, the critical values are based on values for 2000 observations.

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In this study, the number of predictors included for roughness and cracking for all datasets (NW, class M, class A, class B and class C) is six predictors (intercept, MESA, TMI, SNC, SST and DRA). The number of predictors included for rutting for all datasets is five predictors (intercept, MESA, TMI, SNC and DRA). From the number of predictors and sample size for each dataset, the lower and upper critical values

(DWL and DWU) at significance 5% are extracted from Stanford website (Stanford,

2016) and presented in Table 5.9 . It can be noticed that the DW < DWL in all cases. This indicates that there is statistical evidence that the residuals are positively correlated in all datasets. Consequently, this means that regression assumption of residual independence is not supported.

The traditional regression approach is inappropriate for analysing panel data (nested data) because it allows only a single level of variation (i.e. only variance between observations). As recommended by many statistical studies (Raundebush and Bryk, 2002, Kwok et al., 2007, Kwok et al., 2008 , Niehaus et al., 2013), when the available data have a hierarchical structure, it is necessary to account for variance at higher levels. To overcome the previous fundamental problem, one of the most useful techniques for analysing nested data is the hierarchical linear modelling (HLM) approach. It is a statistical modelling approach that captures the effects of variation at multiple levels (Raudenbush, 1993, Raudenbush and Bryk, 2002, Field, 2009, Woltman et al., 2012, Anderson, 2012, Niehaus et al., 2013, Garson, 2013), hereafter referred to as multilevel model. HLM explicitly models the dependency between observations, thereby obtaining more stable estimate of intercepts and slopes , and producing unbiased standard errors, especially when there is unbalanced data or missing data (Field, 2009, Niehaus et al., 2013). The specifications of two types of multilevel models are presented in the following sub-sections.

5.3.2 Multilevel Models Specifications

The two types of multilevel models considered here: are the Hierarchical Linear Model (HLM) and Hierarchical Generalized (logistic) Linear Model (HGLM). HLM has been used to develop roughness and rutting models and HGLM has been used for developing cracking models. The specifications for these two types of multilevel model are described below. The formulae and detailed approach or process described in these

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PRELIMINARY ANALYSIS AND CHAPTER FIVE MODELLING APPROACH sections are found in Raudenbush and Bryk (2002), Greene (2004), Field (2009), Raudenbush et al. (2011) and Snijders and Bosker (2012).

5.3.2.1 Hierarchical Linear Model (HLM) Specifications

The basic simple linear regression model is generally represented in the following form:

β + β X + 5-2

Where: Y: is the dependent variable X: is the independent variable (predictor) e: is the error value (random variable)

β0 and β1: are fixed and unknown coefficients, where β0 is the intercept and β1 is the slope.

In the above Equation 5-2, there is only one independent variable (X) to explain the dependent variable (Y) and all the other factors that affect Y are jointly captured by the error value (e). In other words, the error value represents factors other than X that affect Y. However, it is assumed that the variance of the errors (e) is constant.

In the context of pavement prediction models, as mentioned before, it is expected that there are four levels of variance within the panel datasets prepared for the analysis, and nesting of the network data is required to capture this variance. The HLM modelling approach handles models with datasets that have at most a four level nested structure. Hence, in this study, the four levels of random variation (heterogeneity) include the following:

1) Level-1 (e): Variation among time series observations within the same segments.

2) Level-2 (r0): Variation among pavement segments within the same highways.

3) Level-3 (u00): Variation among highways within the same road classes.

4) Level-4 (v000): Variation among road classes within selected network.

The effect of heterogeneity can be captured by allowing randomness over the model parameter(s). There are three types of random models, the random intercept model, the random slope model and the random intercept and slope model (random parameters).

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According to Field (2009), the latter is the most realistic condition in which both intercepts and slopes are assumed to vary for each individual pavement segment model. This approach was followed by Hong (2007). In the current study, the random parameter approach is utilised by allowing the intercepts to vary at level-2, level-3 and level-4, and the slope to vary only at level-2.

The above simple linear model (Equation 5-2 ) can be extended to the following four- level model (multilevel model) with random intercepts at level-2 (β0), level-3 (β00) and level-4 (β000) and random slope at level-2 (β1):

Level-1: Y = β0 + β1 X + e

Level-2: β0 = β00 + r0

β1 = β10 + r1

Level-3: β 00 = β000 + u00

Level-4: β000 = β0000 + v000

The final mixed model is given in Equation 5-3 :

β + β X + X + + + + 5-3

Where:

Y, X, β0 and β 1: are as defined previously e: is the level-1 random effect r0 and r1: are the level-2 random effects u00: is the level-3 random effect v000: is the level-4 random effect

β00 and β10: are level-2 fixed coefficients

β000: is level-3 fixed coefficient

β0000: is level-4 fixed coefficient

Formally there are i 1, , …..,O time series observations, which are nested within each of j 1, , …..,S segments that are nested within each of k 1, , …..,H highways which are nested within each of f 1, , ….., road classes within the network. For this study,

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PRELIMINARY ANALYSIS AND CHAPTER FIVE MODELLING APPROACH in Equation 5-3, if Y is some measure of pavement condition and X is a time factor (as time is an important predictor for this time series data), the final mixed model is given below:

β + β Time + Time + + + + 5-4

In Equation 5-4, only time is included as a predictor in the model. The coefficient β10 estimates the average change per year so it could be referred to as a growth model.

By incorporating all available variables that are considered in this study, the above multilevel model can be extended by including variables that vary over time within each segment (Time, MESA, SNCi and TMI) at level-1and variables that vary from one segment to another (SNC0, SST and DRA) in the level-2 intercept.

To develop a model for each condition variable (DV), the independent variables are identified based on availability, engineering experience and previous research studies. Hence, to develop a roughness multilevel model, the considered independent variables are Time, MESA, TMI, SNC0, SST and DRA. The roughness model is expressed as follows for the whole network dataset:

Level-1: Y = β0 + β1 Time + β2 MESA + β3 TMI + e

Level-2: β0 = β00 + β01 SNC0 + β02 SST + β03 DRA + r0

β1= β10 + r1

Level-3: β00 = β000 + u00

Level-4: β000 = β0000 + v000

The final mixed model is:

Y = β0000 + β10 Time + β2 MESA + β3 TMI + β01 SNC0 + β02 SST + β03 DRA + 5-5 Time r1 + e + r0 + u00 + v000

Where: Y: Predicted roughness value in terms of International Roughness Index (IRI, m/km).

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Time: is time variable in years within roughness gradual phase (coded as, 1998 =0, 1999 =1, 2000 =2, 2001 =3, …………….. and 2010 =12). MESA: is traffic loading variable in terms of Million Equivalent Standard Axles load /lane. TMI: is climate condition variable in terms of Thornthwaite Moisture Index.

SNC0: is initial pavement strength variable at time of pavement construction, in terms of modified structural number. SST: is subgrade soil type variable (coded as, non-expansive = 0 and expansive = 1). DRA: is drainage condition variable (coded as, good = 0 and poor = 1).

β2, β3: are level-1 fixed effect coefficients.

β01, β02 and β03: are level-2 fixed effect coefficients. All other variables are as defined previously.

The final roughness mixed model in Equation 5-5 that incorporates all possible available variables is referred to as a conditional model. β0000, β10, β2, β3, β01, β02 and β03 are fixed effect parameters, whereas, e, r1, r0, u00, v000 are random variables in the above model.

To develop a rutting multilevel model, the considered independent variables are Time,

MESA, TMI, SNCi and DRA. The rutting model is expressed as the following four levels for the whole network dataset:

Level-1: Y = β0 + β1 Time + β2 MESA + β3 TMI + β4 SNCi + e

Level-2: β0 = β00 + β01 DRA + r0

β1= β10 + r1

Level-3: β00 = β000 + u00

Level-4: β000 = β0000 + v000

The final mixed model is:

Y = β0000 + β10 Time + β2 MESA + β3 TMI + β4 SNCi + β01 DRA + Time r1 + e 5-6 + r0 + u00 + v000

Where: Y: Predicted rutting progression value in terms of RD (mm).

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SNCi: is the pavement strength variable at time (i), in terms of modified structural number. Time: is time variable in years within rutting gradual phase (coded as, 2004 =0, 2005 1, 00 , …………. and 011 7). All other variables are as defined previously.

The final mixed model in Equation 5-6 that incorporates all IVs is also referred to as a conditional model. β000, β10, β2, β3, β4 and β01 are fixed effect parameters, whereas, e, r1, r0, u00 are random variables.

According to Paterson (1987), in order to develop reliable and applicable models, it is imperative that the models include time effects for a wide range of circumstances. Pavement age is a common factor in the estimation of other factors such as traffic i.e. age can be a surrogate for the effect of other factors (Mubaraki, 2010). As stated in the literature review in Section 2.3.7, a number of previous studies indicated that the pavement age is an important factor in deterioration prediction models. However, in this study, to avoid double counting, pavement age is not included as a predictor because it is included in calculating pavement strength and traffic loading. However, the time variable in above models does not replace age because there could be young and old pavements that have the same progression rate at a certain time.

Further, when there is a significant proportion of variance explained by the four road classes (M, A, B and C) in the whole network panel dataset, then a separate multilevel regression model is required for each road class to predict its pavement conditions more accurately. These models can consider more efficiently the significant influencing variables for each road class.

5.3.2.2 Hierarchical Generalized (Logistic) Linear Model (HGLM) Specifications

Typically, binary logistic regression is employed when there is a binary outcome (two categories of dependent variable). This type of model was therefore used for the crack initiation model, cracked (coded as 1) and uncracked (coded as 0). Ordinal logistic regression models are employed when there are more than two categories of the dependent variable and there is a natural order between these categories. In the context

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PRELIMINARY ANALYSIS AND CHAPTER FIVE MODELLING APPROACH of pavement cracking extent, the progress of the affected area has an ordered structure starting from an insignificant affected area, progressing to limited affected area and then considerable and finally a significant affected area. This means that the four categories of cracking data have an ordinal structure relating to cracking progression over time. Hence, the ordinal logistic model was used to predict the cumulative probability of reaching each category.

In traditional logistic regression, the logit of the odds, denoted (η), serves as the dependent variable (logit link function). The logit in a binary regression model is the natural logarithm of the odds that an event occurs. In this study, the event is crack initiation. The general form of this model is described below:

η = LN [odds (cracked)]

Probability (cracked) η LN ( ) Probability (uncracked)

P1 η LN ( ) 5-7 1 P1

Where: LN: is the natural logarithm

P1: is the probability of cracked (crack initiation)

(1 - P1): is the probability of uncracked.

The predicted log-odds can be used to derive the probability of crack initiation (P1) by computing:

1 P 5-8 1 1+ Exp ( η)

The log-odds (η) and P1 can be estimated via a linear combination of predictor(s) X1,

X2….. Xn:

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η β + β X + β X +…………+ β X 5-9

1 P1 5-10 1+ Exp ( β + β X + β X +…………+ β X )

Where:

X1, X2, …., Xn: are the independent variables.

β0, β1, β2, ….., βn: are fixed and unknown coefficients, where β0 is the intercept and β1,

β2 a d βn are the slopes.

In terms of multilevel modelling, the logistic regression is extended to include multiple levels of nesting and is known as hierarchical generalized linear modelling (HGLM). As mentioned earlier in this chapter, it is expected that there are four levels of random variation (heterogeneity) within the existing panel dataset, including Level-1 (e) variation among time series observations within the same segments, Level-2 (r0) variation among pavement segments within the same highways, Level-3 (u00) variation among highways within the same road classes, and Level-4 (v000) variation among road classes within the selected network.

For the cracking datasets, the effect of heterogeneity is captured by implementing the random intercept approach which is used by allowing the intercepts to vary at level-2, level-3 and level-4. The multilevel model (four-level model) for the binary logistic regression depending on one predictor can be presented as follow:

Level-1: η = β0 + β1 X1 + e

Level-2: β0 = β00 + r0

Level-3: β00 = β000 + u00

Level-4: β000 = β0000 + v000

The final mixed model is given in Equation 5-11 below:

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η β + β X + + + + 5-11

Where:

η, X1, β0 and β 1: are as defined previously. e, r0, u00, and v000: are the random variables for level-1, level-2, level-3 and level-4, respectively.

β00, β000 and β0000: are the fixed intercept coefficients for level-2, level-3 and level-4, respectively.

By incorporating other network variables considered in this study, the above multilevel model can be extended by including variables that vary over time within segments (Time, MESA, SNCi and TMI) at level-1, and variables that vary from one segment to another (SNC0, SST and DRA) at level-2. The extended model for crack initiation model would include the following variables:

Level-1: η = β0 + β1 Time + β2 MESA + β3 TMI + e

Level-2: β0 = β00 + β01 SNC0 + β02 SST + β03 DRA + r0

Level-3: β00 = β000 + u00

Level-4: β000 = β0000 + v000

The mixed model that incorporates all the above levels is referred to as the conditional model below:

η = β0000 + β1 Time + β2 MESA + β3 TMI + β01 SNC0 + β02 SST + β03 DRA + e 5-12 + r0 + u00 + v000

Where: η: is the predicted logit odds. Time: is the time variable in years, for all cracking datasets coded as (2004 =0, 2005 =1, 00 , …………. and 011 7). MESA: is the traffic loading variable in terms of Million Equivalent Standard Axles load /lane.

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TMI: is the climate condition variable in terms of Thornthwaite Moisture Index.

SNC0: is the initial pavement strength variable at time of pavement construction (age = 0), in terms of modified structural number. SST: is the subgrade soil type variable (coded as, non-expansive = 0 and expansive = 1). DRA: is the drainage condition variable (coded as, good = 0 and poor = 1). All other variables are as defined previously.

It is important to note that, in order to avoid double counting of pavement strength, it is assumed that SNC0 is a more valuable predictor in crack initiation phase, whereas SNCi is a more valuable predictor in the crack progression phase. SNCi is the pavement strength at time (i) in terms of modified structural number.

In ordinal logistic regression, multiple logit functions are utilised to yield the predicted cumulative probability (CP) of each cracking category. As clarified before, four discrete categories can be used to describe crack progression in terms of the probability (P) of pavement falling into each category, as presented below:

CPsig = Psig

CPcon = Psig + Pcon

CPlim = Psig + Pcon + Plim

P ins Psig+Pcon+ Plim+Pins 1 5-13

Where:

CPsig: is the cumulative probability for significant cracking

CPcon: is the cumulative probability for at least considerable cracking

CPlim: is the cumulative probability for at least limited cracking

CPins: is the cumulative probability for at least insignificant cracking

Psig: is the probability of significant cracking

Pcon: is the probability of considerable cracking

Plim: is the probability of limited cracking

Pins: is the probability of insignificant cracking

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From the above formulae, the probability of each cracking category can be obtained as follows:

Psig = CPsig

Pcon = CPcon - CPsig

Plim = CPlim - CPcon

Pins 1 P lim 5-14

The set of cumulative predicted probabilities in Equation 5-13 has one redundant probability (CPins) due to the constraint that the sum of probabilities equals one, so only three equations are needed. Hence, the log-odds can be predicted via the linear combination of predictors for the first three categories which are separated by the threshold value (δ) as the following formulae show:

η (CPsig) = β0 + β1 X1 + β2 X2 +…………+ βn Xn

η (CPcon) = β0 + β1 X1 + β2 X2 +…………+ βn Xn + δ1

η ( P lim) β + β X + β X +…………+ β Xn + δ 5-15

Where:

β0: is the first threshold value between significant and considerable categories.

(β0 + δ1): is the second threshold value between considerable and limited categories.

(β0 + δ2): is the third threshold value between limited and insignificant categories. All other variables are as defined previously.

More details of the general model forms required to build up the final four-level model are provided in the Hierarchical Linear and Nonlinear Modeling manual (Raudenbush et al., 2011).

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5.3.3 Multilevel Model Fit

In this study, the analysis is performed using Hierarchical Linear and Nonlinear Modelling (HLM7) software (HLM7, 2015) and Statistical Package for Social Sciences (SPSS) software (SPSS, 2015). An example of a prepared dataset for multilevel analysis is provided in Appendix-G. The example is for four levels of analysis and shows that four separate SPSS input files of data are prepared for use in HLM7 software. Also, the appendix shows some basic dialog boxes for using HLM7 software to develop multilevel models. According to Raudenbush et al. (2011), in multilevel model, three types of parameter estimates are obtained; empirical Bayes estimates of randomly varying coefficients at level-1, level-2 and level-3, maximum likelihood estimates of the level-4 coefficients via generalized least squares estimates, and maximum likelihood estimates of the variance-covariance components. In this study, to develop pavement deterioration models, three types of models are fitted for each condition variable, null models (only intercept model), growth models (including only time as predictor), and conditional models (including additional predictor variables). These three models are fitted for different purposes as explained in the following sub-sections.

5.3.3.1 Null Model

This model predicts the condition variable (DV) with no specified predictors. As recommended in many studies (Raudenbush and Bryk, 2002, Field, 2009, Garson, 2013), the null model should be created first as a preliminary step in a hierarchical data analysis to serve three main purposes:

 To provide an estimate of the grand mean of the DV.  To use as a baseline model for model comparisons when adding predictors to the model, based on a deviance statistic test.  To estimate the proportion of variance at each level in the dataset used to predict the DV and to test whether multilevel modelling is needed. The proportion of variance could be estimated using the following formulas (Raudenbush and Bryk, 2002):

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1. Proportion of variance within level-1 (time series observations within segments), PVO:

V PVO 5-16 V + V + V +V

2. Proportion of variance within level-2 (between segments within highways), PVS:

V PVS 5-17 V + V + V +V

3. Proportion of variance within level-3 (between highways within road classes), PVH:

V PVH 5-18 V + V + V +V

4. Proportion of variance within level-4 (between road classes within the network), PVC:

V PV 5-19 V + V + V +V

Where: Ve: is the variance of level-1 random variable

Vr0: is the variance of level-2 random variable

Vu00: is the variance of level-3 random variable

Vv000: is the variance of level-4 random variable

It is suggested that a PVS value greater than 5% provides justification for level-2 of HLM, a PVH value greater than 5% provides justification for level-3 of HLM, and a PVC value greater than 5% provides justification for level-4 of HLM.

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5.3.3.2 Growth Model

This model predicts the condition variable as a function of the time variable in order to study the progression rate over time. As time is the most important factor in time series data, the growth model is estimated with only time as a predictor, with the intercept and slope regarded as random, whenever possible. The model estimates the average growth of DV per year, therefore, if there is no significant change over time, further model testing would not be performed (Shek and Ma, 2011, West et al., 2014).

5.3.3.3 Conditional Model

In this model available independent variables are added to the growth model as predictors. A backward variable selection procedure can be followed, in which all included predictors are added to the model simultaneously and evaluated together. Then, any non-significant fixed effects are removed one at a time to determine which variables to include in the final model formula.

5.3.4 Multicollinearity Issue in Multilevel Model

Multicollinearity occurs when there is strong correlation between two or more independent variables, contributing similar information in a regression equation. According to Hong (2007), there are two ways to treat the multicollinearity issue, which are:

 Removing one of the two correlated variable(s).  Using a large sample size to minimise the influence of multicollinearity.

This issue is avoided in this study due to the following facts:

 Large sample sizes of datasets for the three pavement condition (roughness, rutting and cracking) are prepared for the analysis to develop models in this study.  A number of previous studies (Sen, 2012, Martin, 2008, Henning, 2008) indicated that pavement age is an important factor affecting pavement deterioration. However, in this study, to avoid multicollinearity problems, pavement age is not included as a

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predictor because it is strongly correlated with pavement strength and traffic loading and the time variable.

HLM7 software automatically identifies multicollinearity between IVs. The HLM7 software prompts error messages when there is any issue in the analysis related to the data. These messages relate to overfitting (e.g. multicollinearity or too many random effects) as shown below:

 ‘There is a problem in the fixed portion of the model. A near singularity is likely. Possible sources are a collinearity or multicollinearity among the predictors’.  ‘HLM is unable to compute starting values based on the specified model. Every level-1 predictor matrix is near singular. One (or more) of the random effects should be either deleted from the model or treated as fixed’.  ‘There are no degrees of freedom to estimate sigma squared. Set sigma squared to a constant, or deletes one or more of the random effects from the model’.  ‘HLM is unable to estimate covariance components for the model specified. It is likely that either: one or more of the variance components is very close to zero and the reliability of the associated random effect is also close to zero, or there is a collinearity or multicollinearity among the random effects. In this case, the estimated correlations among the random effects would be close to 1.0, or the model should be re-specified. One (or more) of the random effects must be either deleted from the model or treated as fixed’.

5.4 Model Evaluation

Probably the most general measure of fit in regression modelling is the coefficient of determination (R2). It provides a simple and clear explanation, taking values between 0 and 1, and increasing with better model fits (Shtatland et al., 2002). Pseudo R2 statistics also provide an indication of the amount of variance accounted for by the predictor variables in the model (Raudenbush and Bryk, 2002). In multilevel model, the Pseudo R2 is estimated by comparing the variance component in a null model to the same variance component in a restricted model (growth or conditional model). In other

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PRELIMINARY ANALYSIS AND CHAPTER FIVE MODELLING APPROACH words, the variance explained is examined by the reduction in null model variance as predictors are added. The following formula is applied for calculating the variance explained by the roughness and rutting progression models from their level-1 variance (Ve):

V (null) V (restricted) 5-20 V (null)

Normally, the R2 is not useful for evaluating logistic models. Therefore, the logistic models for cracking data are evaluated by testing classification accuracy. Cross- tabulation analysis is used to test the ability of the models to correctly predict crack initiation and crack progression. The analysis result is a table in a matrix format that shows the frequency distribution of the predicted and observed cracking data. The numbers of observations that are being correctly or wrongly predicted in the dataset are used to determine the success rate of the developed model (Wuensch, 2014), as expressed in the Equation 5-21 when an estimated probability of above 0.5 results in a cracking prediction.

orrectly predicted observations % Success rate 5-21 Total observations

5.5 Model Assessment

The deviance statistic test is based on the maximum likelihood estimation procedure and is used to compare two nested models (Anderson, 2012). The null model is compared with the growth and conditional models to determine if a set of explanatory variables (independent variables) improve the fit of the model or not. The difference between the deviances for any two models follows an approximate chi-squared distribution with degrees of freedom computed as the difference of the models’ degrees of freedom. The greater the reduction in the deviance value, the greater the improvement in fit. Significant p-values for these likelihood ratio tests indicate that there is evidence in the data to suggest an association between the DV and the included

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IVs in the growth and conditional models, i.e. the model fit is significantly improved by adding the Time and other independent variables (Garson, 2013).

5.6 Model Validation Process

The developed models should be tested to ensure their ability to predict future conditions reasonably. Generally, there are three methods to validate developed model (Harrell, 2001), which are:

 Apparent validity: tests the model in sample data used to develop model.  Internal validity: tests the model in new data, randomly selected from underlying population.  External validity: tests the model in new data, randomly selected from a different population.

In this study, only the first two of the above methods for model validation are used to test the developed models. The external validity method is not used due to the reason that no comparable data was available for another network. The apparent and internal methods are conducted as described in below sub-sections.

5.6.1 Apparent Validation Method

The apparent validation method is applied by checking the fundamental assumptions of the initial regression model. The best way is to check the assumptions on the random errors using residuals and to use diagnostic plots to evaluate the model fit.

The regression model assumes that the residuals (i.e. the differences between the predicted values and the observed values for the dependent variable) (Raudenbush and Bryk, 2002):

 Are independent and normally distributed,  Have a zero mean within each section, and

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 Have a constant variance for all settings of the independent variables within each section.

The residual plots allow for the graphical evaluation of the goodness of fit of the selected model. Residuals also point to possible outliers in the dataset or any problem with the regression model. When the residuals display a clear pattern, a different regression model is suggested. Checks for residual normality can be done with histograms and normal probability plots. Thus, two plots are examined to evaluate each model fit. Tests for linearity are performed with a plot of observed DV versus predicted DV. The line of equality is a line through the origin at 45 degrees to the axes, when observed and predicted values are similar, the assumption of linearity is supported.

5.6.2 Internal Validation Method

The data splitting strategy is a simple technique for validating the developed model to ensure its ability to predict future conditions accurately. As stated before in Section 4.6 in previous chapter, Good and Hardin (2003) recommended that one-fourth to one-third of the dataset should be set aside for validation purposes. In this study, before developing the models, a random dataset split is used to divide the dataset into two parts; roughly 70% of the data is used for model development and the remaining 30% of the data is used for model validation.

This dataset is used to develop a validation model with the same variables that are used for the developed models (Berry and Linoff, 1997). Multiple statistical testing using a Bonferroni correction (Field, 2009) is applied when checking whether the coefficients of the validation model fall within the 99% confidence intervals for the coefficients of the developed model. The confidence interval estimate (CI) provides a range of likely values for each of the model parameters. Based on the general form of a confidence interval, the lower and upper bounds of the 99% confidence intervals are calculated using the following formula assuming a normal distribution for all parameter estimates (Field, 2009):

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99% onfidence interval Estimated parameter . 57 Standard error 5-22

5.7 Model Simulation Process

Model simulation is used to test whether a model can reproduce real networks and conceptual systems (Ptolemaeus, 2014). A deterministic simulation is used for the purpose of understanding the behaviour of the developed model under different selected conditions.

In this study, this simulation is done for the growth and conditional models over time and a range of traffic loadings. In this simulation, sets of model inputs are sampled from statistical distributions to describe multiple simulation scenarios to allow an overall understanding of the range of behaviours that can be expected over time. Different typical combination of predictor values are used to check the reasonableness of outputs in terms of engineering judgement.

5.8 Summary

In this chapter, details of the preliminary analysis and proposed modelling approach are presented. The prepared panel datasets have hierarchical structure with four-levels of variation within the selected network. The following main aspects related to the prepared datasets have been described:

 Descriptive statistics for the whole network and the four road classes are presented.  Roughness (IRI) and rutting (RD) variables are positively skewed in all datasets (NW, M, A, B and C) and the traffic loading (MESA) variable is also positively skewed for NW, class M and class C rutting datasets. Hence, these variables are transformed using natural log transformed (LN) function.  The method of removing prediction bias caused by fitting models to log transformed data is presented.

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 Methods for interpreting parameter estimates for models using log transformations are outlined.

Due to the nature of the data, an empirical linear regression modelling approach is used for modelling roughness and rutting progression and logistic regression is used for modelling crack initiation and progression. The following steps have been followed in order to establish the appropriate methods of analysis:

 Exploratory analysis: the Durbin-Watson test from traditional regression analysis is used to establish that consecutive residuals are positively correlated. This means that regression assumption of residual independence is not supported.  Multilevel model: hierarchical linear modelling (HLM) approach that captures the effects of variation at multiple levels is selected to use for developing multilevel models. Justification for HLM modelling is provided using the percent variation explained at each level. Three types of models have been described (null, growth and conditional models). Further, the importance of avoiding multicollinearity problem between independent variables in HLM7 software is presented.  Model evaluation: the coefficient of determination (R2) for evaluating linear regression models has been presented. Also, the classification success rate for evaluating logistic regression models has been presented.  Model assessment: the process of comparing null, growth and conditional multilevel models based on the deviance statistic test has been presented.  Model validation: Descriptions of two methods of validations, apparent validity and internal validity, have been provided. Apparent validity tests the model with the same sample data used to develop the model, whereas, internal validity tests the model in new data. Each original dataset was randomly split into a training set of data and a validation set of data.  Model simulation: Descriptions of deterministic simulation for the purpose of understanding the behaviour of the regression models under different conditions have been provided.

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6. CHAPTER SIX DEVELOPMENT OF ROUGHNESS PROGRESSION MODELS

6.1 Introduction

This chapter presents a new approach for developing robust multilevel roughness models of sealed granular pavements. As stated in the previous chapter, historical time series data for many different pavement sections located in Victoria, Australia, have been collected and prepared for use in a multilevel regression analysis. This type of analysis is selected to ensure that the hierarchical structure in the dataset is not ignored and the model can account for the variation between segments, highways and road classes. Thereby the models would be able to account for the effect of unobserved factors. Modelling parameters include road roughness in terms of IRI as the performance parameter and traffic loading (MESA), swell potential of subgrade soil (SST), climate condition (TMI), condition of drainage system (DRA) and initial pavement strength (SNC0) as predictor parameters. The range of independent variables’ values of datasets used in developing roughness model within the gradual phase for all road classes (M, A, B and C) and the network as a whole are presented in Table 5.2 and Table 5.3 in Chapter 5. The study period is 13 years (from 1998 to 2010) as shown in Section 3.4.1.1.

Roughness progression models within the gradual phase of deterioration have been developed for the whole network (NW) data and for each of the four road classes (M, A, B and C) separately. These models are presented and discussed in this chapter. Models’ evaluation, assessment, simulation and validation are also presented. The first step to develop a regression model is to assess the normality of the dependent variable (Garson, 2013). In the current datasets, it is observed that the DV (IRI) is positively skewed. The natural log of IRI (LN_IRI) is found to be the most appropriate transformation function in that skewness is minimised. The statistics and frequency histograms for the transformed variables are presented in Appendix-F.

Multilevel analysis, assuming normality, is used to develop empirical deterministic models to predict pavement roughness progression over time as a function of a number of contributing variables, depending on full maximum likelihood estimation. The

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DEVELOPMENT OF ROUGHNESS CHAPTER SIX PROGRESSION MODELS analysis is performed using Hierarchical Linear and Nonlinear Modelling (HLM7) software (HLM7, 2015) and Statistical Package for Social Sciences (SPSS) software (SPSS, 2015).

In a multilevel model, three types of parameter estimates are obtained; empirical Bayes estimates of randomly varying coefficients at level-1, level-2 and level-3, maximum likelihood estimates of the level-4 coefficients via generalized least squares estimates, and maximum likelihood estimates of the variance-covariance components. To develop roughness progression model, three types of models are fitted, null models (only intercept model), growth models (including only time as a predictor) and conditional models (including additional predictor variables). These three models are fitted for different purposes as presented in the following sections.

6.2 Whole Network (NW) Roughness Progression Model

A four level model is utilised to find the results of the three fitted models which are presented below:

6.2.1 NW Roughness Null Model

The results of the fixed and random effects parameters for the roughness null model are shown in Table 6.1. The table presents the fixed and random variables for the whole network roughness dataset. The final mixed model is:

LN_IRI = β0000 + e + r0 + u00 + v000

Estimated roughness null model is:

LN 0.901 6-1

Where: LN_IRI: is the natural logarithm of roughness variable in terms of IRI

β0000: is level-4 fixed coefficient, intercept e: is the level-1 random effect

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r0: is the level-2 random effect u00: is the level-3 random effect v000: is the level-4 random effect

In order to remove bias caused by fitting the model to the log transformed roughness data, predictions of roughness are multiplied by the correction factor (CF), which is expressed as CF = Exp (Ve / 2) (Equation 5 -1). Based on Ve (0.0088), the CF for the null model is 1.004 (Exp (0.0088/2)). The roughness null model in Equation 6-1 estimated that the roughness (IRI) grand mean value for the network sample is 2.47 m/km (Exp (0.901)*1.004). The four variance components (Ve, Vr 0, Vu00 and Vv000) are highly significant (p <0.001).

Table 6.1: Estimation of the fixed effect variable and variance components (random effect variables) for the whole network roughness null model

NW roughness null model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df)

I t c pt,(β0000) 0.901 0.1019 8.85 3 <0.05 Variance Degree of Random effect Standard Chi-Statistic component freedom 2 p-value* variable deviation (χ ) (V) (df) e 0.0939 0.0088

r0 0.2294 0.0526 8641 213258.52 <0.001

u00 0.0853 0.0073 35 1039.29 <0.001

v000 0.2016 0.0407 3 176.56 <0.001 * All predictors are statistically significant (p < 0.05) with 95% level of confidence

Based on Equations 5-16, 5-17 , 5-18 and 5-19, the proportions of variances at each level are calculated using variance components (for random effect variables) from the NW roughness null model results, as shown below:

1. Proportion of variance within time series observations is: PVO = 8.04% 2. Proportion of variance between segments within highways is: PVS = 48.08% 3. Proportion of variance between highways is: PVH = 6.67%

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4. Proportion of variance between classes is: PVC = 37.21%

These results indicate that there is a high variance between segments within highways (PVS = 48%) and a high variance between classes (PVC = 37%). Also, 8% of the variance is found within time series observations, and around 7% between highways. These results indicate that there is a significant variance between observations, segments, highways and road classes for roughness condition variable. This confirms that there is statistical justification for using multilevel analysis approach rather than depending on traditional regression analysis to produce a roughness progression model, by capturing the variance between levels correctly.

6.2.2 NW Roughness Growth Model

The results of roughness growth model for the whole network are shown in Table 6.2. Allowing only for the time predictor, the final growth mixed model is:

LN_IRI = β0000 + β10 Time + Time r1 + e + r0 + u00 + v000

The estimated NW growth roughness progression model is:

LN 0.7517 + 0.0185 Time 6-2

Where: r1: is the level-2 random effect

β10: is level-2 fixed coefficient Time: is time variable in years With all other variables are as defined previously.

The NW roughness growth model suggested that for each additional year, the log IRI increased by 0.0185 m/km. The IRI value (on average) increased by 1.87% [(EXP (0.0185) -1)* 100%] for every additional year. Highway segments differed significantly in their intercepts and slopes, as indicated in Table 6.2 . Based on Ve (0.0036), the correction factor (CF) for the growth model is 1.002 (Exp (0.0036/2)) which must be applied to the IRI predictions. For example, if Time =15 years then the predicted IRI = [Exp (0.7517+ 0.0185*15)]* 1.002 = 2.80 m/km.

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Table 6.2: Estimation of the fixed effect variables and variance components (random effect variables) for the whole network roughness growth model

NW roughness growth model Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 0.7517 0.1070 7.03 3 <0.05 Time 0.0185 0.0002 99.49 8641 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom 2 p-value* deviation (χ ) variable (V) (df) e 0.0597 0.0036

r0 0.2496 0.0623 8641 92662.95 <0.001

r1 0.0126 0.0002 8685 20935.56 <0.001

u00 0.0908 0.0083 35 1139.21 <0.001

v000 0.2016 0.0448 3 171.54 <0.001 * All predictors are statistically significant (p < 0.05) with 95% level of confidence

6.2.3 NW Roughness Conditional Model

The results of the fixed and random effects parameters of predicted NW roughness conditional model for the whole network are shown in Table 6.3 . The final developed roughness progression model as a function of the available contributing variables is presented below:

LN_IRI = β0000 + β10 Time + β2 MESA + β01 SNC0 + β02 SST + Time r1 + e + r0 + u00 + v000

The estimated NW conditional roughness progression model is:

LN . 5 5 + 0.01 Time + 0.008 MESA 0.5 7 SN 0 + 0.05 1 SST 6-3

Where: MESA: is traffic loading variable in terms of Million Equivalent Standard Axles load /lane.

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SNC0: is initial pavement strength variable at time of pavement construction, in terms of modified structural number. SST: is subgrade soil type variable (non-expansive = 0 and expansive = 1).

β2: is level-1 fixed effect coefficient.

β01 and β02: are level-2 fixed effect coefficients. All other variables are as defined previously.

Table 6.3: Estimation of the fixed effect variables and variance components (random effect variables) for the whole network roughness conditional model

NW roughness conditional model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 2.3535 0.0471 49.95 3 <0.001 Time 0.0166 0.0002 78.53 8639 <0.001 MESA 0.0086 0.0006 15.41 17370 <0.001

SNC0 -0.5374 0.0149 -36.06 8639 <0.001 SST 0.0541 0.0073 7.43 8639 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom p-value* deviation (χ2) variable (V) (df) e 0.0509 0.0035

r0 0.2252 0.0507 8639 79717.66 <0.001

r1 0.0115 0.0001 8685 19972.88 <0.001

u00 0.0820 0.0067 35 1277.93 <0.001

v000 0.0516 0.0127 3 17.23 <0.001 * All predictors are statistically significant (p < 0.001) with 95% level of confidence

The p-values in Table 6.3 for the Likelihood Ratio Chi-Square test show that the variables time, traffic loading (MESA), initial pavement strength (SNC0), and subgrade soil type (SST) have significantly influenced pavement roughness. Also, there are significant variance components within the random effects variables. However, climate condition (TMI) and drainage condition (DRA) are not significant, hence excluded from the model.

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The model indicates that MESA and Time are positively related to roughness progression (i.e. log IRI increases with Time and MESA), whereas SNC0 is negatively related to roughness progression (i.e. roughness decreases with increases in SNC0). The positive sign of SST indicates that increased swell potential of subgrade soil leads to increased roughness.

The correction factor for predicting roughness value from Equation 6-3 is 1.002 (Exp (0.0035/2)). The t-ratios are the regression coefficients divided by their standard errors and their absolute values represent the effect size of each predictor. The t-ratios suggest that the effect of Time is stronger than SNC0 and effect of SNC0 is stronger than the traffic loading on roughness progression, controlling for other factors in the model. However, the effect of swell potential of subgrade is limited compared to the other factors. The effect of each factor on roughness progression from the whole network conditional model can be explained as provided below. It is important to note that different units are used for each factor and a comparison between the effects of different factors is not possible due to this fact. For interpretation, see Section 5.2.4.

 On average, the roughness (IRI) value increases by 1.67% [(EXP (0.0166) - 1)*100%] for every additional year, when all other variables in the model are held constant. It can be noticed that the rate of roughness progression per year for the conditional model (1.67%) is less than in the growth model (1.87%) due to the fact that in the growth model the effect of Time factor incorporates the effect of traffic loadings which is the only variable that changes with time.  For a one MESA increase in traffic loading, a 0.86% [(EXP (0.0086) -1)*100%] increase in roughness value is expected, when all other variables in the model are held constant.

 For a one SNC0 unit decrease in pavement strength, about 41.57% [(1- EXP (- 0.5374))*100%] increase in roughness value is expected, when all other variables in the model are held constant.  Roughness value will be, on average, 5.56% [(EXP (0.0541) -1)*100%] higher for pavements built on expansive subgrade soils than for pavements built on non-expansive subgrade soils.

As presented in Section 6.2.1, there is a high proportion of roughness variance (PVC = 37%) among the four road classes (M, A, B and C), a separate model for each road class

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DEVELOPMENT OF ROUGHNESS CHAPTER SIX PROGRESSION MODELS is required to predict roughness progression. In this instance, the model could consider more efficiently the significant influencing variables for each road class. Therefore, separate multilevel regression models are developed for each of the four road classes.

6.3 Class M Roughness Progression Model

Only a three-level model is used to consider the effect of variation between time series observations for different segments that are nested within different highways of class M roads. A multilevel regression model is developed with roughness as the DV and the same IVs which are used in the whole network model.

6.3.1 Class M Roughness Null Model

The fixed and random effect parameters for the regression statistics of the developed null model are presented in Table 6.4. The final estimated class M roughness null model is:

LN 0.577 6-4

Based on Ve (0.0062) for the above null model, the correction factor (CF) is 1.003 (Exp (0.0062/2)). The null model results indicate that the roughness grand mean value for class M sample is 1.79 m/km (Exp (0.5772)* 1.003). The three variance components

(Ve, Vr0 and Vu00) are highly significant (p< 0.001) and indicate that there is significant variance between observations, segments, and highways for the roughness condition variable. Using Equations 5-16, 5-17 and 5-18, the proportion of variance results indicate that there is a high variance between segments within highways (PVS = 84%). Also, 9% of the variance is found within time series observations, and around 7% between highways.

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Table 6.4: Estimation of the fixed effect variable and variance components (random effect variables) for the class M roughness null model

Class M roughness null model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 0.5772 0.0296 19.52 6 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom p-value deviation (χ2) variable (V) (df) e 0.0788 0.0062

r0 0.2463 0.0607 717 25779.66 <0.001

u00 0.0698 0.0049 6 70.66 <0.001 * All predictors are statistically significant (p < 0.001) with 95% level of confidence

6.3.2 Class M Roughness Growth Model

The results of roughness growth model for the class M roads are shown in Table 6.5. Allowing only for the time predictor, the final estimated growth class M roughness progression model is:

LN 0.5181 + 0.018 Time 6-5

With both variables as defined previously.

The roughness growth model estimates that, for each additional year, the log IRI increases by 0.0183 m/km. On average, the IRI value increases by 1.85% [(EXP (0.0183) -1) * 100%] for every additional year. Chi-square (χ2) results also indicate that highway segments differ significantly in their intercepts and slopes. Based on Ve (0.0028) for the growth model, the CF is 1.001 (Exp (0.0028/2)). This CF must be applied to IRI predictions from the growth model in Equation 6-5.

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Table 6.5: Estimation of the fixed effect variables and variance components (random effect variables) for the class M roughness growth model

Class M roughness growth model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 0.5181 0.0300 17.25 6 <0.001 Time 0.0183 0.0008 23.86 716 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom 2 p-value* deviation (χ ) variable (V) (df) e 0.0528 0.0028

r0 0.2478 0.0614 717 18655.58 <0.001

r1 0.0153 0.0002 723 1669.15 <0.001

u00 0.0710 0.0050 6 76.33 <0.001 * All predictors are statistically significant (p < 0.001) with 95% level of confidence

6.3.3 Class M Roughness Conditional Model

The results of the fixed and random effects parameters of predicted class M roughness conditional model are shown in Table 6.6 . The final developed roughness progression model for class M roads as a function of the available contributing variables is presented below:

LN . 55 + 0.00 7 Time + 0.0115 MESA 0.78 SN 0 6-6

Where:

All variables are as previously defined.

From the developed conditional model, the significant p-values < 0.001 for the

Likelihood Ratio test show that the variables Time, MESA and SNC0 significantly influence pavement roughness progression with significant variance components within

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DEVELOPMENT OF ROUGHNESS CHAPTER SIX PROGRESSION MODELS random effects variables. However, TMI, SST and DRA are not significant and are excluded from the model. The model indicates that MESA and Time are positively related to roughness progression, whereas SNC0 is negatively related to roughness progression. The following results are observed from the class M roughness conditional model:

 On average, IRI value increases by 0.67% [(EXP (0.0067) -1) * 100%] for every additional year, when all other variables in the model are held constant.  For a one MESA increase in traffic loading, about a 1.16% [(EXP (0.0115) -1)* 100%] increase in roughness value is expected, when all other variables in the model are held constant.

 For a one SNC0 unit decrease in pavement strength, about a 54.43% [(1- EXP (- 0.786)) * 100%] increase in roughness value is expected, when all other variables in the model are held constant.

Table 6.6: Estimation of the fixed effect variables and variance components (random effect variables) for the class M roughness conditional model

Class M roughness conditional model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 3.3552 0.3983 8.42 6 <0.001 Time 0.0067 0.0015 4.57 715 <0.001 MESA 0.0115 0.0012 9.29 1167 <0.001

SNC0 -0.7860 0.1076 -7.30 715 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom 2 p-value* deviation (χ ) variable (V) (df) e 0.0527 0.0027

r0 0.2269 0.0515 716 16000.74 <0.001

r1 0.0154 0.0002 723 1696.07 <0.001

u00 0.0415 0.0017 6 19.22 <0.05 * All predictors are statistically significant (p < 0.05) with 95% level of confidence

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The t-ratios suggest that the effect of MESA is stronger than SNC0 and Time on roughness progression in class M due to the high volume of heavy trucks which cause accelerated deterioration of pavement. Based on Ve (0.0027) for the conditional model, the CF is 1.001 (Exp (0.0027/2)). This CF must be applied to IRI predictions from the conditional model in Equation 6-6. These results indicate that different variables influence the deterioration progression for road class M than for the whole network. This confirms that a separate model is necessary for each road class.

6.4 Class A Roughness Progression Model

A multilevel regression model is developed with roughness as the DV and the same IVs which are used in the whole network model, using a three-level model to consider the effect of variation between time series observations for different segments that are nested within different highways of class A roads. The three fitted models for this class are presented in the following sub-sections.

6.4.1 Class A Roughness Null Model

The fixed and random effect parameters for the regression statistics of the developed class A roughness null model are presented in Table 6.7 and the final mixed model is shown in equation below:

LN 0.89 1 6-7

Based on Ve (0.01) for the above null model, the correction factor (CF) is 1.005 (Exp (0.01/2)). The null model results indicate that the roughness grand mean value for class

A is 2.46 m/km (Exp (0.8961)* 1.005). The three variance components (Ve, Vr0 and Vu00) are highly significant (p <0.001) and indicate that there is significant variance between observations, segments, and highways for the roughness condition variable for class A roads. The proportion of variance results show that there is a high variance at level-2, between segments within highways (PVS = 78%). Also, 16% of the variance is

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DEVELOPMENT OF ROUGHNESS CHAPTER SIX PROGRESSION MODELS found within time series observations at level-1, and around 6 % between highways at level-3.

Table 6.7: Estimation of the fixed effect variable and variance components for the class A roughness null model

Class A roughness null model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 0.8961 0.0173 51.71 10 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom p-value deviation (χ2) variable (V) (df) e 0.1002 0.0100

r0 0.2197 0.0483 3077 61200.22 <0.001

u00 0.0552 0.0034 10 219.57 <0.001 * All predictors are statistically significant (p < 0.001) with 95% level of confidence

6.4.2 Class A Roughness Growth Model

The results of roughness growth model for the class A roads are shown in Table 6.8. The estimated class A roughness growth model is:

LN 0.7 + 0.0177 Time 6-8

With both variables as defined previously.

The roughness growth model estimates that, for each additional year, the log IRI increases by 0.0177 m/km. On average, the IRI value increases by 1.79% [(EXP (0.0177) -1) * 100%] for every additional year. Chi-square (χ2) results indicate that highway segments differ significantly in their intercepts and slopes. Based on Ve (0.0039) for the growth model, the CF is 1.002 (Exp (0.0039/2)). This CF must be applied to IRI predictions from the above growth model.

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Table 6.8: Estimation of the fixed effect variables and variance components for the class A roughness growth model

Class A roughness growth model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 0.7633 0.0180 42.38 10 <0.001 Time 0.0177 0.0003 64.32 3076 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom 2 p-value* deviation (χ ) variable (V) (df) e 0.0625 0.0039

r0 0.2330 0.0543 3077 32559.69 <0.001

r1 0.0109 0.0001 3087 7203.21 <0.001

u00 0.0571 0.0033 10 231.04 <0.001 * All predictors are statistically significant (p < 0.001) with 95% level of confidence

6.4.3 Class A Roughness Conditional Model

The predicted class A roughness conditional model result is shown in Table 6.9 . The developed roughness progression model for class A roads as a function of the contributing independent variables is presented below in Equation 6-9.

LN . 9 + 0.0115 Time + 0.0 1 MESA 0. 898 SN 0 6-9

Where:

All variables are as previously defined.

The above developed conditional model with the significant p-values < 0.001 for the

Likelihood Ratio test show that the variables Time, MESA and SNC0 significantly influence pavement roughness progression with significant variance components within random effects variables for class A roads. However, TMI, SST and DRA are not

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DEVELOPMENT OF ROUGHNESS CHAPTER SIX PROGRESSION MODELS significant and are excluded from the model. The model shows that MESA and Time are positively related to roughness progression, whereas SNC0 is negatively related to roughness progression. The following results are observed from the class A roughness conditional model:

 On average, IRI value increases by 1.16% [(EXP (0.0115 ) -1)* 100%] for every additional year, when all other variables in the model are held constant.  For a one MESA increase in traffic loading, about a 2.34% [(EXP (0.0231 ) -1)* 100%] increase in roughness value is expected, when all other variables in the model are held constant.

 For a one SNC0 unit decrease in pavement strength, about a 38.73% [(1- EXP (- 0.4898))*100%] increase in roughness value is expected, when all other variables in the model are held constant.

Table 6.9: Estimation of the fixed effect variables and variance components for the class A roughness conditional model

Class A roughness conditional model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 2.2292 0.0824 27.07 10 <0.001 Time 0.0115 0.0004 27.85 3075 <0.001 MESA 0.0231 0.0011 20.57 6003 <0.001

SNC0 -0.4898 0.0258 -18.96 3075 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom p-value* deviation (χ2) variable (V) (df) e 0.0626 0.0035

r0 0.2070 0.0429 3076 26563.14 <0.001

r1 0.0108 0.0001 3087 7040.79 <0.001

u00 0.0810 0.0066 10 534.18 <0.001 * All predictors are statistically significant (p < 0.001) with 95% level of confidence

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The t-ratios for included variables indicate that the effect of Time is stronger than

MESA and SNC0 on roughness progression in class A roads. Depending on Ve (0.0035), the CF is 1.002 (Exp (0.0035/2)) which should be applied to IRI predictions from the developed conditional model. These results also indicate that different factors impact the deterioration progression for class A roads than for the whole network. Hence, a separate model is necessary for each road class.

6.5 Class B Roughness Progression Model

For class B roads, a multilevel (three-level) roughness progression model is developed with IRI as the DV and all the same IVs which are used in the NW roughness model. The final estimated three fitted models (null, growth and conditional) are presented below.

6.5.1 Class B Roughness Null Model

The detail of regression statistics of the developed model is summarized in Table 6.10. The final estimated model is:

LN 1.009 6-10

To remove bias from the above null model, the correction factor (CF) is 1.005 (Exp (0.0094/2)) . The null model results in Table 6.10 indicate that the roughness grand mean value for road class B sample is 2.76 m/km (Exp (1.009)* 1.005). The three variance components (Ve, Vr 0 and Vu00) are statistically significant (p <0.001) and indicate that there is significant variance between observations, segments, and highways for the roughness condition variable. The proportion of variance results indicate that there is a high variance among segments within highways (PVS = 76%). Yet, only 14% of the variance is found within time series observations, and 10 % between highways in these class roads.

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Table 6.10: Estimation of the fixed effect variable and variance components for the class B roughness null model

Class B roughness null model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df)

Intercept 1.009 0.0255 39.50 9 <0.001 Variance Degree of Random Standard Chi-Statistic component freedom p-value* effect variable deviation (χ2) (V) (df) e 0.0971 0.0094

r0 0.2223 0.0494 2347 50470.31 <0.001

u00 0.0790 0.0062 9 273.68 <0.001 * All predictors are statistically significant (p < 0.001) with 95% level of confidence

6.5.2 Class B Roughness Growth Model

The results of roughness growth model for the class B roads are shown in Table 6.11. The estimated class B roughness growth model is:

LN 0.87 7 + 0.017 Time 6-11

With both variables as defined previously.

Using variance component at level-1 for the above model (Ve (0.0039)), the CF is 1.002 (Exp (0.0039/2)) . The model estimates that for each additional year, the log IRI increases by 0.0176 m/km. The IRI value (on average) increases by 1.78% [(EXP (0.0176) -1)*100%] for every additional year. Chi-square (χ2) tests also indicate that highway segments differ significantly in their intercepts and slopes.

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Table 6.11: Estimation of the fixed effect variables and variance components for the class B roughness growth model

Class B roughness growth model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 0.8737 0.0271 32.27 9 <0.001 Time 0.0176 0.0003 56.36 2346 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom p-value* deviation (χ2) variable (V) (df) e 0.0626 0.0039

r0 0.2291 0.0525 2347 23432.31 <0.001

r1 0.0104 0.0001 2356 5079.15 <0.001

u00 0.0837 0.0070 9 301.70 <0.001 * All predictors are statistically significant (p < 0.001) with 95% level of confidence

6.5.3 Class B Roughness Conditional Model

The results of developed conditional roughness progression model for class B roads as a function of the contributing independent variables are presented in Table 6.12 and the model formula is presented below in Equation 6-12.

LN 1.8199 + 0.01 Time + 0.0 1 MESA 0. SN 0 + 0.09 SST 6-12 + 0.000 TM

Where:

All variables are as defined previously.

All included variables (Time, MESA, TMI, SST and SNC0) except (DRA), have a significant influence on pavement roughness progression for class B roads. The model indicates that MESA, SST, TMI and Time are positively related to roughness progression, whereas SNC0 is negatively related to roughness progression. The

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DEVELOPMENT OF ROUGHNESS CHAPTER SIX PROGRESSION MODELS observed positive trend for TMI indicates that pavement in wet areas experience higher roughness progression than pavement in dry areas. The positive trend of SST indicates that increased swell potential of subgrade soil leads to increased roughness progression. The majority of these highway sections are built on expansive soils that are located within climate zones that are prove to having problems due to seasonal moisture variation.

Table 6.12: Estimation of the fixed effect variables and variance components for the class B roughness conditional model

Class B roughness conditional model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 1.8199 0.0806 22.59 9 <0.001 Time 0.0146 0.0005 30.76 2344 <0.001 MESA 0.0421 0.0041 10.28 4572 <0.001

SNC0 -0.3626 0.0283 -12.82 2344 <0.001 SST 0.0923 0.0150 6.16 2344 <0.001 TMI 0.0004 0.0002 2.13 4572 <0.05 Random Variance Degree of Standard Chi-Statistic effect component freedom p-value* deviation (χ2) variable (V) (df) e 0.0627 0.0037

r0 0.2160 0.0466 2345 21588.97 <0.001

r1 0.0107 0.0001 2356 5192.53 <0.001

u00 0.0675 0.0046 9 232.80 <0.001 * All predictors are statistically significant (p < 0.05) with 95% level of confidence

Depending on Ve (0.0037) for this conditional model, the CF is 1.002 (Exp (0.0037/2)). This CF must be applied to IRI predictions from the conditional model in Equation 6-12 to remove the bias from the log transformed model. The t-ratios refer that the effect of

Time is stronger than MESA and SNC0 on roughness progression. However, the effects of SST and TMI are low compared to other factors. The following results are observed from the developed class B roughness conditional model:

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 On average, the roughness (IRI) value increase by 1.47% [(EXP (0.0146)-1)* 100%] for every additional year, when all other variables in the model are held constant.  For a one MESA increase in traffic loading, about a 4.30% [(EXP (0.0421)-1)* 100%] increase in roughness value is expected, when all other variables in the model are held constant.

 For a one SNC0 unit decrease in pavement strength, about a 30.41% [(1- EXP (- 0.3626))*100%] increase in roughness value is expected, when all other variables in the model are held constant.  Roughness value will be on average 9.67% [(EXP (0.0923)-1)*100%] higher for pavements built on expansive subgrade soils than for pavements built on non- expansive subgrade soils.  On average, for a one unit increase in TMI, about a 0.04% [(EXP (0.0004)- 1)*100%] increase in roughness value is expected, when all other variables in the model are held constant.

6.6 Class C Roughness Progression Model

For class C roads, a multilevel (three-level) roughness progression model is developed with roughness as the DV and all the same IVs which are used in the NW roughness model. The final estimated three fitted models (null, growth and conditional) are presented below.

6.6.1 Class C Roughness Null Model

The details of regression statistics of the developed model are summarized in Table 6.13. The final estimated model is:

LN 1.1 6-13

Based on Ve (0.0073) for the above null model, the correction factor (CF) is 1.004 (Exp (0.0073/2)). The null model results indicate that the roughness grand mean value for

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DEVELOPMENT OF ROUGHNESS CHAPTER SIX PROGRESSION MODELS class C sample is 3.08 m/km (Exp (1.1224)* 1.004). The three variance components

(Ve, V r0 and Vu00) are statistically significant (p <0.001) and indicate that there is significant variance between observations, segments, and highways for the roughness condition variable. The proportion of variance results indicate that there is a high variance among segments within highways (PVS = 76%). Also, 10% of the variance is found within time series observations, and 14% among highways.

Table 6.13: Estimation of the fixed effect variable and variance components for the class C roughness null model

Class C roughness null model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df)

Intercept 1.1224 0.0315 35.66 11 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom p-value* deviation (χ2) variable (V) (df) e 0.0856 0.0073

r0 0.2416 0.0584 2505 85683.39 <0.001

u00 0.1043 0.0109 11 447.85 <0.001

* All predictors are statistically significant (p < 0.001) with 95% level of confidence

6.6.2 Class C Roughness Growth Model

The results of roughness growth model for class C roads are shown in Table 6.14. The estimated class C roughness growth model is:

LN 0.9 + 0.0 07 Time 6-14

With both variables as defined previously.

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Based on Ve (0.0032) for the growth model, the CF is 1.002 (Exp (0.0032/2)). The roughness growth model estimates that for each additional year, the log IRI increases by 0.021 m/km. On average, the IRI value increases by 2.09% [(EXP (0.0207) -1)*100%] for every additional year. Chi-square (χ2) tests also indicate that highway segments differ significantly in their intercepts and slopes.

Table 6.14: Estimation of the fixed effect variables and variance components for the class C roughness growth model

Class C roughness growth model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 0.9600 0.0349 27.52 11 <0.001 Time 0.0207 0.0004 52.86 2504 <0.001 Random Variance Standard Degree of Chi-Statistic effect component p-value* deviation freedom (df) (χ2) variable (V) e 0.0561 0.0032

r0 0.2798 0.0783 2505 31973.57 <0.001

r1 0.0142 0.0002 2516 6859.83 <0.001

u00 0.1155 0.0133 11 520.30 <0.001 * All predictors are statistically significant (p < 0.001) with 95% level of confidence

6.6.3 Class C Roughness Conditional Model

The results of developed conditional roughness progression model for class C roads as a function of the contributing independent variables are presented in Table 6.15 and the model is expressed below in Equation 6-15.

LN . 9 91 + 0.00 9 Time + 0. 7 9 MESA 1.1 77 SN 0 + 0.0 9 SST 6-15 + 0.0005 TM

Where:

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All variables are as previously defined.

Time, MESA, TMI, SST and SNC0 have a significant influence on pavement roughness progression for class C roads. The model indicates that MESA, SST, TMI and Time are positively related to roughness progression, whereas SNC0 is negatively related to roughness progression. The observed positive trend for TMI indicates that pavement in wet zones experience higher roughness progression than dry zones. The former could be attributed to the fact that shoulders of these roads are either unsealed or partially sealed (just compacted). Further, the majority of these sections that are built on expansive soils are located within climate zones that are prove to having problems due to seasonal moisture variation.

Table 6.15: Estimation of the fixed effect variables and variance components for the class C roughness conditional model

Class C roughness conditional model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 3.9291 0.0580 67.69 11 <0.001 Time 0.0049 0.0006 8.04 2502 <0.001 MESA 0.3749 0.0081 46.46 5627 <0.001

SNC0 -1.1677 0.0202 -57.90 2502 <0.001 SST 0.0639 0.0086 7.40 2502 <0.001 TMI 0.0005 0.0002 1.87 5627 <0.05 Random Variance Degree of Standard Chi-Statistic effect component freedom p-value* deviation (χ2) variable (V) (df) e 0.0560 0.0031

r0 0.1917 0.0367 2503 16946.19 <0.001

r1 0.0196 0.0004 2516 10873.80 <0.001

u00 0.0749 0.0056 11 676.82 <0.001 * All predictors are statistically significant (p < 0.05) with 95% level of confidence

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Based on Ve (0.0031) for the conditional model, the CF is 1.002 (Exp (0.0031/2)). This CF must be applied to IRI predictions from the conditional model in Equation 6-15. The t-ratios suggest that the effect of SNC0 is stronger than MESA and Time on roughness progression. However, the effects of Time, SST and TMI are much lower than SNC0 and MESA. The following results are observed from the class C roughness conditional model:

 On average, the roughness (IRI) value increase by 0.49% [(EXP (0.0049)-1)* 100%] for every additional year, when all other variables in the model are held constant.  For a one MESA increase in traffic loading, about a 45.48% [(EXP (0.3749)-1)* 100%] increase in roughness value is expected, when all other variables in the model are held constant.

 For a one SNC0 unit decrease in pavement strength, about a 68.89% [(1- EXP (- 1.1677)) * 100%] increase in roughness value is expected, when all other variables in the model are held constant.  Roughness value will be on average 6.60% [(EXP (0.0639)-1)*100%] higher for pavements built on expansive subgrade soils than for pavements built on non- expansive subgrade soils.  On average, for a one unit increase in TMI, about a 0.05% [(EXP (0.0005)- 1)*100%] increase in roughness value is expected, when all other variables in the model are held constant.

6.7 Accuracy Evaluation of Roughness Models

Pseudo R2 statistics provide an indication of the amount of variance accounted for by the predictor variables in the model (Raudenbush and Bryk, 2002). The Pseudo R2 is estimated by comparing the variance component in a null model to the same variance component in a restricted model (growth or conditional model). This means that, in a multilevel model, the explained variance is tested by the reduction in null model variance as predictors are added to the growth model or conditional model.

Based on random variance component at level-1 (V e) for each model, Pseudo R2 values are calculated for evaluating the accuracy of developed models using the formula

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DEVELOPMENT OF ROUGHNESS CHAPTER SIX PROGRESSION MODELS presented in Equation 5-20 in chapter five. It is worth noting that these Pseudo R2 values are for log-transformed roughness values. Pseudo R2 values are presented as percentages to represent the amount of variance accounted for by the predictor variable/s in the models. Table 6.16 shows that more than half of the variance in level-1 is accounted for by the Time factor in growth models for the whole network (59%), class M (55%), class A (61%), class B (58%) and class C (56 %). Also, more than half of the percentage of explainable variance is accounted for by the predictors in the conditional models for the whole network (60%), class M (56%), class A (65%), class B (61%) and class C (58%).

Table 6.16: Pseudo R2 values for developed roughness growth and conditional models

Dataset Model fit Pseudo R2

Growth model 59% NW Conditional model 60%

Growth model 55% Class M Conditional model 56%

Growth model 61% Class A Conditional model 65%

Growth model 58% Class B Conditional model 61%

Growth model 56% Class C Conditional model 58%

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6.8 Assessment of Developed Roughness Models

As stated before in chapter five, the deviance statistic test is based on the maximum likelihood estimation procedure and is used to compare two nested models (Anderson, 2012). The null model is compared with the growth and conditional models to determine if a set of IVs improve the fit of the model or not.

The difference between the deviances for any two models follows an approximate chi- squared distribution with degrees of freedom computed as the difference of the models’ degrees of freedom. The greater the reduction in the deviance value, the greater the improvement in fit.

Table 6.17 shows the results of the deviance statistic test for predicted null, growth and conditional roughness models for NW, class M, class A, class B and class C. In this table, it should be noticed that there is always a reduction in deviance from the null model to the growth model and from the growth model to the conditional model. The likelihood ratio tests show that these changes are all significant with p < 0.001. The significant p-values for chi-square (χ2) test indicate that there is evidence in the data to suggest an association between roughness progression and the included IVs, i.e. the model fit is significantly improved by adding these variables. In other words, these results indicate that the time variable in the growth models and all IVs in the conditional models have improved the models’ descriptions of the data.

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Table 6.17: Deviance test results for predicted roughness progression models

Model comparison test with null model Number of Deviance p-value (at Dataset Model fit estimated Degrees test (χ2) χ2 95% parameters of statistic confidence freedom interval) Null model -37966.94 5 - - - Growth -53916.13 8 15949.19 3 <0.001 NW model Conditional -55214.10 11 17247.16 6 <0.001 model Null model -3274.88 4 - - - Growth Class -4204.25 7 929.37 3 <0.001 M model Conditional -4328.71 9 1054.81 5 <0.001 model Null model -12275.54 4 - - - Growth Class -18352.71 7 6077.18 3 <0.001 A model Conditional -19032.03 9 6756.49 5 <0.001 model Null model -9731.83 4 - - - Growth Class -14157.21 7 4425.37 3 <0.001 B model Conditional -14375.91 11 4644.08 7 <0.001 model Null model -13270.64 4 - - - Growth Class -17828.89 7 4558.25 3 <0.001 C model Conditional -19587.09 11 6316.45 7 <0.001 model

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6.9 Validation of the Developed Roughness Models

Using both apparent and internal validation methods, the developed models are tested to ensure their ability to predict future conditions accurately. These two methods are conducted as described in the following sections.

6.9.1 Apparent Validation Method

The apparent validation method is applied by checking the fundamental assumptions of the initial developed regression model. Two plots have been examined to evaluate growth and conditional models fit for the whole network and each road class. The first is the frequency histogram and normal probability plot of residuals to check for residual normality. The second is the line of equality plot of observed DV versus predicted DV to test for linearity.

Figure 6-1 and Figure 6-2 illustrate the diagnostic plots to evaluate the growth model and conditional model fits for the NW, respectively. Part (a) of these figures shows that the residuals are normally distributed with mean very close to zero, small standard deviation (less than 0.05), and limited range of residuals (from -0.2 IRI to 0.2 IRI), for a large sample size (N = 34,787). Part (b) of both figures shows that the predicted against observed roughness values are very close to the line of equality with very high correlation (R2 = 97%) which means that the observed values and predicted values are very close. These results indicate that the assumptions of normality and linearity are supported.

This apparent validation is also conducted for the growth and conditional models of all road classes (M, A, B and C) and presented in Figure H-1, Figure H-2, Figure H-3, Figure H-4, Figure H-5, Figure H-6, Figure H-7 and Figure H-8 of Appendix-H. All figures show that the assumptions of normality and linearity are supported which means that all developed models exhibit apparent validity.

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(a)

R2 = 97%

(b)

Figure 6-1: Apparent validation for the developed roughness growth model for the NW, (a) Residual histogram and (b) Line of equality

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(a)

R2 = 97%

(b)

Figure 6-2: Apparent validation for the developed roughness conditional model for the NW, (a) Residual histogram and (b) Line of equality

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6.9.2 Internal Validation Method

As mentioned before in this study, approximately one-third of the data (30%) is selected randomly and set aside to use for model validation. This dataset is used to develop a validation model with the same variables that are used for the developed models. Multiple statistical testing using a Bonferroni correction is applied when checking whether the coefficients of the validation model fall within the 99% confidence intervals for the coefficients of the developed model. The confidence interval (CI) estimate provides a range of likely values for each of the model coefficients. The lower and upper bounds of the 99% confidence intervals are calculated using the formula given in Equation 5-22 .

The internal validation results for the growth and conditional roughness progression models for the NW and the four road classes (M, A, B and C) are presented in Table 6.18 and Table 6.19, respectively. The results of internal validation for all developed models indicate that all coefficients of the models based on the validation datasets fall within the upper and lower bound intervals for the coefficients of the developed models. This means that all the developed models exhibit internal validity.

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Table 6.18: Internal validation results for growth roughness progression models

99% 99% 1 p-value Standard 3 3 2 p-value Variables CDM 6 CI CI CVM 7 (DM ) Error 4 5 (VM ) Dataset LB UB

Intercept 0.756 <0.05 0.1081 0.477 1.034 0.752 <0.05

NW Time 0.018 <0.001 0.0003 0.018 0.019 0.019 <0.001

Intercept 0.518 <0.001 0.030 0.441 0.595 0.520 <0.001

Class M Class Time 0.018 <0.001 0.001 0.016 0.020 0.019 <0.001

Intercept 0.763 <0.001 0.018 0.717 0.810 0.760 <0.001

Class A Class Time 0.018 <0.001 0.0003 0.017 0.018 0.018 <0.001

Intercept 0.874 <0.001 0.027 0.804 0.943 0.878 <0.001

Class B Class Time 0.018 <0.001 0.0003 0.017 0.018 0.017 <0.001

Intercept 0.960 <0.001 0.035 0.870 1.050 0.974 <0.001

Class C Class Time 0.021 <0.001 0.000 0.020 0.022 0.020 <0.001 1: Coefficient of developed model 2: Coefficient of validated model 3: Confidence Interval 4: Lower Bound 5: Upper Bound 6: Developed model 7: Validated model

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Table 6.19: Internal validation results for conditional roughness progression models

99% 1 p-value Standard 99% 3 2 p-value Variables CDM 6 3 4 CI CVM 7 (DM ) Error CI LB 5 (VM ) Dataset UB Intercept 2.353 <0.001 0.047 2.232 2.475 2.365 <0.001 Time 0.017 <0.001 0.0002 0.016 0.017 0.017 <0.001

MESA 0.009 <0.001 0.001 0.007 0.010 0.008 <0.001 NW

SNC0 -0.537 <0.001 0.015 -0.576 -0.499 -0.542 <0.001 SST 0.054 <0.001 0.007 0.035 0.073 0.056 <0.001 Intercept 3.365 <0.001 0.398 2.329 4.381 2.646 <0.05

Time 0.007 <0.001 0.001 0.003 0.011 0.007 <0.05 MESA 0.011 <0.001 0.001 0.008 0.015 0.011 <0.001 Class M Class

SNC0 -0.788 <0.001 0.108 -1.063 -0.509 -0.598 <0.001 Intercept 2.229 <0.001 0.092 1.991 2.467 1.999 <0.001

Time 0.011 <0.001 0.0004 0.010 0.013 0.012 <0.001 MESA 0.023 <0.001 0.001 0.020 0.026 0.020 <0.001 Class A Class

SNC0 -0.490 <0.001 0.030 -0.567 -0.413 -0.415 <0.001 Intercept 1.820 <0.001 0.081 1.612 2.027 1.943 <0.001 Time 0.015 <0.001 0.000 0.013 0.016 0.014 <0.001

MESA 0.042 <0.001 0.004 0.032 0.053 0.048 <0.001

SNC0

Class B Class -0.363 <0.001 0.028 -0.435 -0.290 -0.409 <0.001 SST 0.092 <0.001 0.015 0.054 0.131 0.094 <0.001 TMI 0.0004 <0.05 0.0002 0.000 0.001 0.001 <0.05 Intercept 3.929 <0.001 0.058 3.780 4.079 3.855 <0.001 Time 0.005 <0.001 0.001 0.003 0.007 0.005 <0.001

MESA 0.375 <0.001 0.008 0.351 0.396 0.351 <0.001

SNC0 -1.168 <0.001 0.020 -1.220 -1.116 -1.133 <0.001 Class C Class SST 0.064 <0.001 0.009 0.042 0.086 0.053 <0.001 TMI 0.0005 <0.05 0.0002 -0.0002 0.0011 0.0005 0.171 1: Coefficient of developed model 2: Coefficient of validated model 3: Confidence Interval 4: Lower Bound 5: Upper Bound 6: Developed model 7: Validated model

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6.10 Deterministic Simulation for the Developed Roughness Models

A deterministic simulation is used for the purpose of understanding the behaviour of the developed models under different selected conditions. This simulation is conducted for the growth and conditional roughness models over time and a range of traffic loadings, for the whole network and the four road classes (M, A, B and C).

Figure 6-3 illustrates the deterministic simulation of the outputs from the growth roughness models over time, using Equations 6-2, 6-5, 6-8, 6-11and 6-14 for simulating growth model for the NW, class M, class A, class B and class C, respectively. The figure shows that for the given data one can estimate the roughness progression rate over time, when considering only the effect of time factor. It could be noticed that class C roads have higher roughness values than other classes, followed by class B then class A and class M. This is due to the higher design standards, for the latter two road classes and better quality materials than the former two classes. This is also confirmed by the roughness grand mean values from null models for all classes (M= 1.79, A= 2.46, B= 2.76 and C= 3.08 m/km). However, the figure also confirms that the rate of roughness progression per year for all classes is very close (0.02 m/km per year) and this is also supported by the results from the growth models for all classes (M= 1.87%, A= 1.85%, B= 1.79% and C= 2.09% m/km per year). Further, the figure also shows that the whole network growth model, almost represents the average of all classes and that it is almost a match to the class A model results, considering the close roughness grand mean (NW= 2.47 and class A= 2.46 m/km). This highlights that separate model for each road class is preferable.

In this simulation analysis for conditional roughness models, mean, maximum and minimum values (from the datasets used for developing the models) for MESA, TMI and SNC0 are used with different soil types (non-expansive soil and expansive soil), where relevant. Details of the descriptive statistics of continuous variables (MESA,

TMI and SNC0) used for simulating conditional models of the NW and the four road classes (M, A, B and C) are presented in Table 5.2.

Outputs from the conditional models are presented in Figure 6-4, Figure 6-5, Figure 6-6, Figure 6-7 and Figure 6-8 to test the sensitivity of the NW, class M, class A, class B and

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class C models for different MESA and SNC0 values using Equations 6-3, 6-6, 6-9, 6-12 and 6-15, respectively.

Figure 6-3: Deterministic simulation for the growth roughness progression models

over time for the NW and the four road classes (M, A, B and C)

It is observed that the predicted roughness progression changes significantly when varying the levels of included independent variables over time. All figures show that higher roughness values are expected when all factors at their minimum values than factors at their maximum values, especially in datasets that their analyses shows the effect of SNC0 is stronger than the effect of MESA (i.e. NW, class B and class C). Also, the figures, that include the effect of soil, illustrate that road sections in expansive soil areas are associated with higher roughness values than sections in non-expansive soil areas.

In addition, all conditional models have been simulated to show the predicted changes to roughness progression when one variable varies from its minimum to maximum values, while all other independent variables are at their mean value for the dataset. This

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DEVELOPMENT OF ROUGHNESS CHAPTER SIX PROGRESSION MODELS is conducted for the NW and the four road classes and presented in Appendix-I. The changes of SNC0 in all figures (in Appendix-I) show that the rates of deterioration is increasing with time for pavements that have the minimum SNC0 values than the maximum SNC0 values. This is more obvious in datasets that their analysis indicate that the effect of SNC0 is stronger than MESA (i.e. NW, class B and class C). The changes of MESA in all figures show that higher roughness values are expected with higher MESA values, particularlly in class C roads.This is due to the fact that the pavement has been deisgned to hold the expected traffic loading and class C are low volume roads which its standards of design and construction are considerably lower than other road classes (Toole et al., 2004). In addition, TMI has a clear effect only when very wet areas. All models’ simulations show that they are responded well on varying levels for the included variables, hence making them ideal for sensitivity analyses to investigate the effect of changing these variables.

Overall, the different combinations of predictor values for simulating the models show reasonable outputs in terms of engineering judgement.

Figure 6-4: Deterministic simulation for the NW conditional roughness progression

model over time

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Figure 6-5: Deterministic simulation for the class M conditional roughness

progression model over time

Figure 6-6: Deterministic simulation for the class A conditional roughness

progression model over time

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Figure 6-7: Deterministic simulation for the class B conditional roughness

progression model over time

Figure 6-8: Deterministic simulation for the class C conditional roughness

progression model over time

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6.11 Summary

Presented in this chapter are the developed roughness progression models within the gradual phase of deterioration for the whole network (NW) data and for each of the four road classes (M, A, B and C). Multilevel analysis (a new approach) is used to develop empirical deterministic models to predict pavement roughness progression over time as a function of a number of contributing variables, depending on full maximum likelihood estimation.

Modelling parameters include road roughness in terms of IRI as the performance parameter and traffic loading (MESA), swell potential of subgrade soil (SST), climate condition (TMI), condition of drainage system (DRA) and initial pavement strength

(SNC0) as predictor parameters. The DV (IRI) is positively skewed and the natural log of IRI (LN_IRI) is found to be the most appropriate transformation function in that the skewness is minimised. To remove bias caused by fitting the model to the log transformed data, the correction factor for each developed model is calculated and presented.

Three types of roughness models are fitted for different purposes, null models (only intercept model), growth models (including only time as predictor) and conditional models (including additional predictor variables).

For the whole network and the four road classes, null models show that there are significant variances between time series observations, segments, highways and road classes. This indicates that the heterogeneity (variation) is a critical aspect of the data that should be considered not only between segments but also between highways and road classes. This highlighted that a separate model for each road class is preferable. The roughness grand mean values from null models for all classes (M= 1.79, A= 2.46, B= 2.76 and C= 3.08 m/km) indicate that class C roads have higher roughness values than the other road classes followed by class B, then class A and class M. Further, the whole network growth model shows that it is representing the average of all classes and it is coinciding with class A results due to their close roughness grand means (NW= 2.47 and class A= 2.46 m/km).

All the developed growth models indicate that the Time factor is significant and confirm that the rate of roughness progression per year for all road classes is very close

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(0.02 m/km per year) where the roughness rate for class M= 0.0185 , class A= 0.0179, class B= 0.0178 and class C= 0.0209 m/km per year.

For the whole network and the four road classes, roughness conditional models are presented and the contribution and significance of relevant influencing factors in predicting roughness progression are also presented and explained. Except for the Time factor effect, the effect of SNC0 is stronger than the other factors for NW, class B and class C. This is due to lower standards of design and construction quality for class B and class C roads than the other road classes. Yet, the effect of MESA is stronger than the other factors for class M and class A due to higher traffic loading in these classes than the others. The effects of SST and TMI are significant in class B and class C roads, whereas both factors are not significant in class M and A roads. The reason behind that is the latter two classes have high standards of design and construction, well maintained, and generally exhibit high levels of smoothness. Also, road cross sections’ crowns are generally high, with deep table drain inverts and sub-soil drains may also be present, and therefore there is a little opportunity for water to gain access to the pavement (Toole et al., 2004).

Pseudo R2 values are calculated for evaluating the accuracy of developed models and showed that more than half of the variance is accounted for by the Time factor in growth models for the NW (59%), class M (55%), class A (61%), class B (58%) and class C (56%). Also, more than half of the percentage of explainable variance is accounted for by the predictors in the conditional models for the NW (60%), class M (56%), class A (65%), class B (61%) and class C (58%). Although the conditional models have slightly better R2 values than the growth models, the latter could be used when information relevant to contributing variables are not available.

The developed models are assessed using the deviance statistic test and the results indicated that the time variable in the growth models and all IVs in the conditional models have improved the models’ descriptions of the data.

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DEVELOPMENT OF ROUGHNESS CHAPTER SIX PROGRESSION MODELS observed roughness values are very close to the line of equality with very high correlation (R2) ranging from 96% to 98%. These validation results indicate that the assumptions of normality and linearity are supported, which means that all developed models exhibit apparent validity. Also, internal validation for all developed models is performed using another dataset from the same network and the results indicate that all the developed models exhibit internal validity. Multiple simulation scenarios from different combinations of predictor values are also presented. The simulation results show reasonable outputs in terms of engineering judgement.

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7. CHAPTER SEVEN DEVELOPMENT OF RUTTING PROGRESSION MODELS

7.1 Introduction

This chapter documents the development of multilevel rutting progression models for the gradual deterioration phase at a network level. They have been developed for the whole network and for each road class. The datasets that are used to develop rutting progression models are based on the following criteria:

 The observed rutting data is within the gradual deterioration phase. This data is greater than the assumed initial values and limited to the maximum observed values of rut depth shown in Table 4.4.  The rate of rutting progression is increasing over the period of available observed rutting data (i.e. rutting deterioration rate > zero).  The available independent variables that are expected to influence rutting

progression are traffic loading (MESA), pavement strength at any age (SNCi), climate condition (TMI) and drainage condition (DRA). The ranges of these independent variables are shown in Table 5.4 and Table 5.5.  The study period is 8 years (from 2004 to 2011) as shown in Section 3.4.1.2.  The pavement age is greater than 1 year to ensure the pavement segments have passed the initial densification phase.  Rut depth (RD), the dependent variable, is positively skewed in all datasets (NW, M, A, B and C) and the traffic loading (MESA) variable is also positively skewed for the NW, class M and class C datasets. These variables are transformed using natural log transformation (LN) functions of RD (LN_RD) and MESA (LN_MESA) as presented in Section 5.2.2. To remove bias caused by fitting the model to the log transformed data, predictions of rutting are multiplied by the correction factor (CF), which is expressed in Equation 5-1.  Two-third of the data (70%) is selected for model development and one-third of the data (30%) which is selected randomly and set aside, is used for internal model validation.

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Multilevel analysis is used to develop empirical deterministic models to predict pavement rutting progression over time as a function of the above mentioned variables, using full maximum likelihood estimation. The analysis is performed using Hierarchical Linear and Nonlinear Modelling (HLM7) software (HLM7, 2015) and the Statistical Package for Social Sciences (SPSS) software (SPSS, 2015). To develop rutting progression model, three types of models are fitted, namely; null models, growth models and conditional models. These three models are fitted as presented in the following sections. This chapter then presents the details of models’ evaluation, assessment, validation and simulation.

7.2 Whole Network (NW) Rutting Progression Model

A four level HLM model is utilised to find the results of the three rutting fitted models which are presented below:

7.2.1 NW Rutting Null Model

The results of the fixed and random effects parameters for the rutting null model are shown in Table 7.1. The final mixed model is:

LN_RD = β0000 + e + r0 + u00 + v000

Estimated rutting null model is:

LN D 1. 7-1

Where: LN_RD: is the natural logarithm of rutting variable in terms of average rut depth (RD)

β0000: is level-4 fixed coefficient, intercept e: is the level-1 random effect r0: is the level-2 random effect u00: is the level-3 random effect v000: is the level-4 random effect

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Based on Ve (0.0833) for the null model, the CF is 1.043 (Exp (0.0833/2)). The null model in Equation 7-1 estimated that RD grand mean value for the sample network is 5.34 mm (Exp (1.6334)*1.043). The four variance components (Ve,

Vr0, Vu00 and Vv000) are statistically significant (p<0.001).

Table 7.1: Estimation of the fixed effect variable and variance components for the NW rutting null model

NW rutting null model Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 1.6334 0.0223 73.23 3 <0.001 Variance Degree of Random effect Standard Chi-Statistic component freedom 2 p-value* variable deviation (χ ) (V) (df) e 0.2887 0.0833

r0 0.3637 0.1323 10933 76781.62 <0.001

u00 0.1333 0.0178 35 937.08 <0.001

v000 0.1056 0.0143 3 20.60 <0.001 * All predictors are statistically significant (p < 0.001) with 95% level of confidence

Using Equations 5-16, 5-17, 5-18 and 5-19, the proportions of variances at each level are calculated using variance components (for random effect variables) from the null model results, as shown below:

1. Proportion of variance within time series observations (level-1) is: PVO = 34%. 2. Proportion of variance between segments within highways (level-2) is: PVS = 53%. 3. Proportion of variance between highways (level-3) is: PVH = 7%. 4. Proportion of variance between road classes (level-4) is: PVC = 6%.

These results indicate that there is a high variance among segments within highways (PVS = 53%) and a high variance within time series observation (PVC = 34%). Also, 7% of the variance was found between highways, and around 6% between road classes. These results indicate that there is a significant variance between observations,

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DEVELOPMENT OF RUTTING CHAPTER SEVEN PROGRESSION MODELS segments, highways and road classes for rutting condition variable. This confirms that there is statistical justification for using multilevel analysis approach rather than depending on traditional regression analysis to produce a rutting progression model, by capturing the variance between levels correctly. Due to significant variance (Vv000) between the four road classes (M, A, B and C), a separate model for each road class is required to predict rutting progression.

7.2.2 NW Rutting Growth Model

The results of NW rutting growth model are shown in Table 7.2. Including only time as predictor, the final growth mixed model is:

LN_RD = β0000 + β10 Time + Time r1 + e + r0 + u00 + v000

The estimated NW rutting growth model is:

LN D 1. 175 + 0.08 1 Time 7-2

Where: r1: is the level-2 random effect

β10: is level-2 fixed coefficient Time: is time variable in years With all other variables are as defined previously.

This growth model is statistically significant and highway segments differed significantly in their intercepts and slopes. The model suggests that for each additional year, the log RD increased by 0.0841 mm, i.e. on average, the RD value increases by 8.77% [(EXP (0.0841) -1) * 100%] for every additional year. Based on Ve (0.0444), the correction factor (CF) for the growth model is 1.022 (Exp (0.0444/2)) which must be applied to rutting predictions. For example, if Time=12 years then the predicted RD = [Exp (1.3175 + 0.0841 * 12)]* 1.022 = 10.47 mm.

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Table 7.2: Estimation of the fixed effect variables and variance components for the NW rutting growth model

NW rutting growth model Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 1.3175 0.0210 62.73 3 <0.001 Time 0.0841 0.0006 152.08 10933 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom 2 p-value* deviation (χ ) variable (V) (df) e 0.2108 0.0444

r0 0.4415 0.1949 10933 52248.89 <0.001

r1 0.0172 0.0003 10977 12576.87 <0.001

u00 0.1249 0.0156 35 920.34 <0.001

v000 0.1054 0.0215 3 20.03 <0.001 * All predictors are statistically significant (p < 0.001) with 95% level of confidence

7.2.3 NW Rutting Conditional Model

The results of the fixed and random effects parameters for this model are shown in Table 7.3 . The final developed rutting progression model as a function of the available contributing variables is presented below:

LN_RD = β0000 + β10 Time + β2 LN_MESA + β3 SNCi + β4 TMI + Time r1 + e + r0 + u00 + v000

The estimated NW conditional rutting progression model is:

LN D . 5 + 0.05 1 Time + 0.050 LN M ESA 0. 795 SN + 7-3 0.001 TM

Where: LN_MESA: is the natural logarithm of traffic loading variable in terms of Million Equivalent Standard Axles load (MESA) /lane.

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SNCi: is the pavement strength variable at time (i), in terms of modified structural number. TMI: is the climate condition variable in terms of Thornthwaite Moisture Index.

β2, β3 and β4 are fixed effect coefficients. All other variables are as defined previously.

Table 7.3: Estimation of the fixed effect variables and variance components for the NW rutting conditional model

NW rutting conditional model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 2.3652 0.0701 33.72 3 <0.001 Time 0.0561 0.0011 50.13 10933 <0.001 LN_MESA 0.0503 0.0051 9.93 19653 <0.001

SNCi -0.3795 0.0122 -31.14 19653 <0.001 TMI 0.0014 0.0005 2.91 19653 <0.05 Random Variance Degree of Standard Chi-Statistic effect component freedom 2 p-value* deviation (χ ) variable (V) (df) e 0.2064 0.0406

r0 0.4146 0.1719 10933 48222.08 <0.001

r1 0.0266 0.0007 10977 13144.53 <0.001

u00 0.1567 0.0246 35 1453.91 <0.001

v000 0.1111 0.0123 3 21.33 <0.001 * All predictors are statistically significant (p < 0.05) with 95% level of confidence

The model is statistically significant with p -values in Table 7.3 for the Likelihood Chi-

Square test which show that the variables Time, MESA, SNCi and TMI have significantly influenced pavement rutting. Also, there are significant variance components within the random effects variables. However, drainage condition (DRA) is not significant (p>0.05), hence it has been excluded from the model.

The model indicates that MESA and Time are positively related to rutting progression

(i.e. log RD increases with Time and MESA), whereas SNCi is negatively related to

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rutting progression (i.e. rutting increases with decreases in SNCi). The positive sign of TMI indicates that pavements in wet zones experience higher rutting progression than in dry zones.

The correction factor for predicting rutting value from Equation 7-3 is 1.021 (Exp (0.0406/2)). The t-ratios are the regression coefficients divided by their standard errors and their absolute values represent the effect size of each predictor. The t-ratios suggest that the effect of Time is stronger than SNCi and effect of SNCi is stronger than the effect of traffic loading on rutting progression. However, the effect of climate is limited compared to the other variables. The effect of each factor on rutting progression from the conditional model can be explained as provided below. It is important to note that different units are used for each factor and a comparison between the effects of different factors is not possible due to this fact. For interpretation, see Section 5.2.4.

 On average, for every additional year, RD value increases by 5.77% = [(EXP (0.0561)-1)*100%], when controlling all other variables in the model.  For a one percent increase in MESA, a 0.05% = [(((1.01) ^ (0.0503)) -1)*100] increase in RD value is expected, when all other variables are held constant.

 For a decrease of one SNCi unit, about 31.58% = [(1-EXP (-0.3795))*100%] increase in RD value is expected, when controlling all other variables.  On average, for a one unit increase in TMI, about a 0.14% = [(EXP (0.0014)-1) * 100%] increase in RD value is expected, when all other variables in the model are held constant.

7.3 Class M Rutting Progression Model

Multilevel regression models are developed with LN_RD as the DV and the same IVs which are used in the NW model using three-level model to consider the effect of variation between time series observations for different segments that are nested within different highways of class M roads.

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7.3.1 Class M Rutting Null Model

The fixed and random effect parameters for the regression statistics of the developed rutting null model are presented in Table 7.4. The final estimated null model is:

LN D 1.5 1 7-4

As the Ve for the above null model is 0.104, the correction factor (CF) is 1.053 (Exp (0.104/2). The model results indicate that the rutting grand mean value for class M sample is 5.02 mm (Exp (1.5613)* 1.053)). The model is statistically significant and the variance components are highly significant (p<0.001) which indicate that there is significant variance between observations, segments, and highways for the rutting condition variable. Using Equations 5-16, 5-17 and 5-18 , the proportion of variance results indicate that there is a high variance between segments within highways (PVS = 44%) and a high variance within time series observations (PVO = 32%), and (24%) between highways.

Table 7.4: Estimation of the fixed effect variable and variance components for the class M rutting null model

Class M rutting null model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 1.5613 0.0977 15.99 6 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom p-value* deviation (χ2) variable (V) (df) e 0.3225 0.1040

r0 0.2749 0.0756 918 3438.90 <0.001

u00 0.2401 0.0576 6 291.03 <0.001 * All predictors are statistically significant (p < 0.001) with 95% level of confidence

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7.3.2 Class M Rutting Growth Model

The results of rutting growth model for class M roads when allowing only for time as predictor are shown in Table 7.5. The final estimated growth model is:

LN D 1. + 0.0957 Time 7-5

With both variables are as defined previously.

The model estimates that, for each additional year, the log RD increases by 0.0957 mm. On average, the RD value increases by 10.04% [(EXP (0.0957) -1)*100%] for every additional year. Chi-square results indicate that highway segments differ significantly in their intercepts and slopes. Using Ve (0.0446) for the growth model, the CF is 1.023 (Exp (0.0446/2)) which must be applied to RD predictions from the model in Equation 7-5.

Table 7.5: Estimation of the fixed effect variables and variance components for the class M rutting growth model

Class M rutting growth model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 1.2442 0.0982 12.67 6 <0.001 Time 0.0957 0.0017 55.59 917 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom p-value* deviation (χ2) variable (V) (df) e 0.2112 0.0446

r0 0.3533 0.1248 918 4128.04 <0.001

r1 0.0137 0.0002 924 1051.20 <0.05

u00 0.2419 0.0585 6 255.79 <0.001 * All predictors are statistically significant (p < 0.05) with 95% level of confidence

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7.3.3 Class M Rutting Conditional Model

The results of the fixed and random effects parameters of predicted class M rutting conditional model are shown in Table 7.6. The final estimated rutting model as a function of the available contributing variables is presented below:

LN D . 0 9 + 0.05 1 Time + 0.0975 LN M ESA 0.5 7 SN 7-6

Where: All variables are as previously defined.

From the developed conditional model, the significant p-values < 0.05 for the

Likelihood Ratio test show that the variables Time, MESA and SNCi significantly influence pavement rutting progression with significant variance components within random effects variables. The model indicates that RD increases with increases in Time and MESA, whereas rutting increases with decreases in SNCi. However, TMI and DRA are not significant (p >0.05), hence they have been excluded from the model.

Table 7.6: Estimation of the fixed effect variables and variance components for the class M rutting conditional model

Class M rutting conditional model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 3.0669 0.4974 6.17 6 <0.001 Time 0.0561 0.0063 8.87 917 <0.001 LN_MESA 0.0975 0.0351 2.78 1643 <0.05

SNCi -0.5674 0.1310 -4.33 1643 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom p-value* deviation (χ2) variable (V) (df) e 0.2119 0.0428

r0 0.3395 0.1153 918 3886.37 <0.001

r1 0.0128 0.0002 924 1044.41 <0.05

u00 0.2667 0.0711 6 344.08 <0.001 * All predictors are statistically significant (p < 0.05) with 95% level of confidence

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The CF for predicting rutting value from Equation 7-6 is 1.022 (Exp (0.0428/2)). The t- ratios indicate that the effect of Time is stronger than SNCi and effect of SNCi is stronger than the effect of MESA on rutting progression. The following results are observed from class M rutting conditional model:

 On average, for every additional year, the rutting value increases by 5.77% = [(EXP (0.0561)-1)*100%], when controlling all other variables in the model.  For a one percent increase in MESA, a 0.1% = [((1.01) ^ (0.0975)) -1)*100] increase in rutting value is expected, when controlling all other variables.

 For a decrease of one SNCi unit, about 43.3% = [(1-EXP (-0.5674))*100%] increase in rutting value is expected, when controlling all other variables.

7.4 Class A Rutting Progression Model

Three-level regression models are developed to consider the effect of variation between time series observations for different segments that are nested within different highways of class A roads.

7.4.1 Class A Rutting Null Model

The fixed and random effect parameters for the developed rutting null model are presented in Table 7.7. The final estimated null model is:

LN D 1. 71 7-7

As the Ve for this null model is 0.0942, the correction factor (CF) is 1.048 (Exp (0.0942/2)). The model results indicate that the rutting grand mean value for class A sample is 5.57 mm (Exp (1.671)* 1.048). The model is statistically significant with significant p-values (< 0.001) for the variance components which mean that there is significant variance between observations, segments, and highways for the rutting condition variable. The proportion of variance results indicate that there is a high

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DEVELOPMENT OF RUTTING CHAPTER SEVEN PROGRESSION MODELS variance between segments within highways where PVS = 52% and a high variance within time series observations where PVO = 41%, and only 7% between highways.

Table 7.7: Estimation of the fixed effect variable and variance components for the class A rutting null model

Class A rutting null model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 1.6710 0.0394 42.36 10 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom p-value* deviation (χ2) variable (V) (df) e 0.3069 0.0942

r0 0.3462 0.1198 3702 21208.31 <0.001

u00 0.1285 0.0165 10 410.78 <0.001 * All predictors are statistically significant (p < 0.001) with 95% level of confidence

7.4.2 Class A Rutting Growth Model

The results of rutting growth model for the class A roads when allowing only for the time predictor are presented in Table 7.8. The final estimated growth model is:

LN D 1. 8 + 0.087 Time 7-8

With both variables are as defined previously.

The model estimates that, for each additional year, the log RD increases by 0.0876 mm. On average, the RD value increases by 9.16% [(EXP (0.0876) -1) * 100%] for every additional year. Chi-square (χ2) results indicate that highway segments differ significantly in their intercepts and slopes. Using Ve (0.0496) for the growth model, the CF is 1.025 (Exp (0.0496/2)) which must be applied to RD predictions from this model.

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Table 7.8: Estimation of the fixed effect variables and variance components for the class A rutting growth model

Class A rutting growth model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 1.3348 0.0362 36.89 10 <0.001 Time 0.0876 0.0020 89.27 3701 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom 2 p-value* deviation (χ ) variable (V) (df) e 0.2227 0.0496

r0 0.4256 0.1811 3702 14975.70 <0.001

r1 0.0164 0.0003 3712 4092.30 <0.001

u00 0.1163 0.0135 10 364.42 <0.001 * All predictors are statistically significant (p < 0.001) with 95% level of confidence

7.4.3 Class A Rutting Conditional Model

The results of the fixed and random effects parameters of predicted class A rutting conditional model are shown in Table 7.9 . The final estimated rutting model as a function of the available contributing variables is presented below:

LN D . 1 5 + 0.05 5 Time + 0.0 MESA 0. 7 SN 7-9

Where: All variables are as previously defined.

From the above conditional model, the significant p-values < 0.05 for the Likelihood

Ratio test in Table 7.9 show that the variables Time, MESA and SNCi significantly influence pavement rutting progression with significant variance components within random effects variables. The model indicates that rutting increases with increases in

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Time and MESA, whereas rutting increases with decreases in SNCi. Nevertheless, TMI and DRA are not significant (p >0.05), hence have been excluded from the model.

Table 7.9: Estimation of the fixed effect variables and variance components for the class A rutting conditional model

Class A rutting conditional model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 2.3165 0.0886 26.13 10 <0.001 Time 0.0565 0.0020 28.47 3701 <0.001 MESA 0.0262 0.0033 8.01 6402 <0.001

SNCi -0.3674 0.0283 -12.98 6402 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom p-value* deviation (χ2) variable (V) (df) e 0.2236 0.0419

r0 0.3972 0.1578 3702 13446.80 <0.001

r1 0.0112 0.0001 3712 3959.92 <0.05

u00 0.1239 0.0153 10 401.96 <0.001 * All predictors are statistically significant (p < 0.05) with 95% level of confidence

The CF for predicting rutting value from above conditional model to remove bias is 1.021 (Exp (0.0419/2)). The t-ratio values indicate that the effect of Time is stronger than SNCi and the effect of SNCi is stronger than the effect of MESA on rutting progression. The following results are observed from the class A rutting conditional model:

 On average, for every additional year, the rutting value increases by 5.81% = [(EXP (0.0565) -1)*100%], when controlling all other variables in the model.  For a one MESA increase in traffic loading, a 2.65% [(EXP (0.0262) -1)*100%] increase in rutting value is expected, when all other variables in the model are held constant.

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 For a decrease of one SNCi unit, about 30.75% = [(1-EXP (-0.3674))*100%] increase in rutting value is expected, when controlling all other variables.

7.5 Class B Rutting Progression Model

Three-level rutting models are developed to consider the effect of variation between time series observations for different segments that are nested within different highways of class B roads. These models are presented in the following sub-sections.

7.5.1 Class B Rutting Null Model

The results of the fixed and random effects parameters for rutting null model are presented in Table 7.10. Rutting estimated null model can be expressed as:

LN D 1. 5 7-10

Table 7.10: Estimation of the fixed effect variable and variance components for the class B rutting null model

Class B rutting null model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 1.6546 0.0262 63.16 9 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom p-value* deviation (χ2) variable (V) (df) e 0.2630 0.0692

r0 0.3801 0.1445 3349 29019.29 <0.001

u00 0.0794 0.0163 9 128.06 <0.001 * All predictors are statistically significant (p < 0.001) with 95% level of confidence

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The correction factor (CF) for this null model is 1.035 (Exp (0.0692/2)). The model results indicate that the RD grand mean value for class B sample is 5.41 mm (Exp

(1.6546)* 1.035 ). In Table 7.10, the three variance components (Ve, Vr0, and Vu00) for the null model are highly significant (p<0.001) and indicate that there is significant variance between observations, segments, and highways for the RD. This also confirms that there is statistical justification for using the multilevel analysis approach. The proportion of variance results indicate that there is a high variance between segments within highways (PVS = 63%). Also, PVO = 30% of the variance is found within time series observations, and PVH = 7% between highways.

7.5.2 Class B Rutting Growth Model

The rutting growth model results are shown in Table 7.11. The model is estimated with only time as a predictor with the intercept and slope regarded as random. The estimated growth rutting progression model is:

LN D 1. 8 + 0.07 Time 7-11

With both variables are as defined previously.

The above model is statistically significant and suggests that for each additional year, the LN_RD increases by 0.0716 mm and RD value (on average) increases by 7.42% [(EXP (0.0716) -1)*100%] for every additional year. Highway sections differ significantly in their intercepts and slopes, as indicated in Table 7.11.

Based on Ve (0.0396), the CF for the growth model is 1.02 (Exp (0.0396/2)) which must be applied to RD predictions. For example, if Time=10 then the predicted RD based on above growth model is [Exp (1.3864+ (0.0716 *10))]* 1.02 = 8.35 mm.

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Table 7.11: Estimation of the fixed effect variables and variance components for the class B rutting growth model

Class B rutting growth model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 1.3864 0.0335 41.32 9 <0.001 Time 0.0716 0.0009 77.10 3348 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom 2 p-value* deviation (χ ) variable (V) (df) e 0.1991 0.0396

r0 0.4487 0.2013 3349 19642.44 <0.001

r1 0.0144 0.0002 3358 3753.99 <0.001

u00 0.1022 0.0104 9 230.91 <0.001 * All predictors are statistically significant (p < 0.001) with 95% level of confidence

7.5.3 Class B Rutting Conditional Model

The results of the fixed and random effects parameters of predicted class B rutting conditional model are shown in Table 7.12 . The final estimated rutting model as a function of the contributing variables is presented below:

LN D .900 + 0.0 5 Time + 0.0 19 MESA 0. 01 SN + 0.00 1 TM 7-12

Where: All variables are as previously defined.

The significant p-values < 0.05 for the Likelihood Ratio test in Table 7.12 show that the variables Time, MESA and SNCi significantly influence pavement rutting progression with significant variance components within random effects variables. The model indicates that rutting increases with increases Time and MESA, whereas rutting

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increases with decreases in SNCi. The positive sign of TMI indicates that pavement in wet zones experience higher rutting progression than in dry zones. Nevertheless, DRA is not significant (p >0.05), hence excluded from the model.

Table 7.12: Estimation of the fixed effect variables and variance components for the class B rutting conditional model

Class B rutting conditional model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 2.9004 0.1059 27.40 9 <0.001 Time 0.0353 0.0019 18.37 3348 <0.001 MESA 0.0219 0.0055 4.01 5627 <0.05

SNCi -0.6012 0.0386 -15.59 5627 <0.001 TMI 0.0031 0.0008 3.96 5627 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom p-value* deviation (χ2) variable (V) (df) e 0.2003 0.0301

r0 0.4023 0.1619 3349 16367.12 <0.001

r1 0.0117 0.0001 3358 3763.71 <0.001

u00 0.2360 0.0557 9 1303.83 <0.001 * All predictors are statistically significant (p < 0.05) with 95% level of confidence

In order to remove bias caused by fitting the model to the log transformed rutting data, predictions of RD are multiplied by a correction factor (CF). The CF for predicting RD is 1.015 (Exp (0.0301/2)). The t-ratios suggest that the effect of Time is the strongest followed by SNCi, MESA then TMI. The effect of each IV in the conditional model can be explained as follows:

 On average, for every additional year, RD value increases by 3.59% [(EXP (0.0353)-1)*100%], when controlling all other variables in the model.  For a one MESA increase in traffic loading, a 2.21% [(EXP (0.0219)-1)*100%] increase in RD is expected, when all other variables are held constant.

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 For a one SNCi unit decrease in pavement strength, about 45.18% [(1-EXP (- 0.6012))*100%] increase in RD is expected, when controlling all other variables.  On average, for a one unit increase in TMI, about a 0.31% [(EXP (0.0031)-1) * 100%] increase in RD value is expected, when all other variables in the model are held constant.

7.6 Class C Rutting Progression Model

For each of the following three fitted models, a three-level model is utilised to estimate the LN_RD to consider the effect of variation between time series observations for different segments that are nested within different highways of class C roads.

7.6.1 Class C Rutting Null Model

The results of the fixed and random effects parameters for class C rutting null model are presented in Table 7.13. The estimated rutting null model is:

LN D 1. 0 7 7-13

The CF for this null model is 1.041 (Exp (0.0795/2)), where Ve = 0.0795. The null model estimates that RD grand mean value for class C sample is 5.18 mm (Exp

(1.6037)* 1.041). The three variance components (Ve, Vr0, and Vu00) are highly significant (p<0.001) and indicate that there is significant variance between observations, segments, and highways for the rutting condition variable.

The proportion of variance results indicate that there is a high variance between segments within highways (PVS = 62%). Also, PVO = 32% of the variance is found within time series observations, and PVH = 6% between highways.

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Table 7.13: Estimation of the fixed effect variable and variance components for the class C rutting null model

Class C rutting null model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 1.6037 0.0342 46.91 11 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom p-value* deviation (χ2) variable (V) (df) e 0.2819 0.0795

r0 0.3889 0.1513 2969 25636.15 <0.001

u00 0.1115 0.0144 11 197.69 <0.001

* All predictors are statistically significant (p < 0.001) with 95% level of confidence

7.6.2 Class C Rutting Growth Model

The rutting growth model results are shown in Table 7.14. The model is estimated with only time as a predictor with the intercept and slope regarded as random. The estimated model is:

LN D 1. 97 + 0.090 Time 7-14

With both variables are as defined previously.

This growth model is statistically significant and the model suggests that LN_RD increases by 0.0903 mm for each additional year. The RD value (on average) increases by 9.45% [(EXP (0.0903)-1) * 100%] for every additional year. Based on Ve (0.0423), the CF for the growth model is 1.021 (Exp (0.0423/2)).

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Table 7.14: Estimation of the fixed effect variables and variance components for the class C rutting growth model

Class C rutting growth model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 1.2397 0.0293 42.37 11 <0.001 Time 0.0903 0.0011 80.58 2968 <0.001 Random Variance Degree of Standard Chi-Statistic effect component freedom p-value* deviation (χ2) variable (V) (df) e 0.2057 0.0423

r0 0.4679 0.2190 2969 13835.84 <0.001

r1 0.0206 0.0004 2980 3490.55 <0.001

u00 0.0920 0.0085 11 162.94 <0.001 * All predictors are statistically significant (p < 0.001) with 95% level of confidence

7.6.3 Class C Rutting Conditional Model

The results of the fixed and random effects parameters of predicted class C rutting conditional model are shown in Table 7.15. The final estimated rutting model as a function of the available contributing variables is presented below:

LN D .0 7 + 0.058 Time + 0.1 18 LN M ESA 0. 5 SN + 0.00 TM 7-15

Where: All variables are as previously defined.

The model is statistically significant and the significant p-values <0.05 for the Likelihood Ratio Chi-Square test in Table 7.15 show that the variables Time, MESA,

SNCi, and TMI significantly influence pavement rutting progression. Also, there are significant variance components within the random effects variables.

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Table 7.15: Estimation of the fixed effect variables and variance components for the class C rutting conditional model

Class C rutting conditional model

Fixed effect Standard Degree of Coefficient t-ratio p-value* variable error freedom (df) Intercept 2.0274 0.0523 38.76 11 <0.001 Time 0.0582 0.0018 32.22 2968 <0.001 LN_MESA 0.1218 0.0094 13.02 5978 <0.001

SNCi -0.2645 0.0169 -15.67 5978 <0.001 TMI 0.0020 0.0008 2.39 5978 <0.05 Random Variance Degree of Standard Chi-Statistic effect component freedom p-value* deviation (χ2) variable (V) (df) e 0.2054 0.0322

r0 0.4157 0.1728 2969 11637.07 <0.001

r1 0.0179 0.0003 2980 3390.73 <0.001

u00 0.1217 0.0148 11 310.59 <0.001 * All predictors are statistically significant (p < 0.05) with 95% level of confidence

Drainage condition (DRA) is not significant and has been excluded from the model. The CF for predicting RD from Equation 7-15 is 1.016 (Exp (0.0322/2)). The t-ratios suggest that the effect of Time is the strongest followed by SNCi, MESA then TMI. The effect of each IV in the conditional model can be explained as follows:

 On average, for every additional year, RD value increases by 5.99% [(EXP (0.0582) -1)*100%], when controlling all other variables in the model.  For a one percent of MESA increase in traffic loading, a 0.12% [((1.01) ^ (0.1218)) -1)*100] increase in RD is expected, when all other variables are held constant.

 For a one SNCi unit decrease in pavement strength, about 23.24% [(1-EXP (- 0.2645))*100%] increase in RD is expected, when controlling all other variables.

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 On average, for a one unit increase in TMI, about a 0.2% [(EXP (0.002)-1) * 100%] increase in RD value is expected, when all other variables in the model are held constant.

7.7 Accuracy Evaluation of Rutting Models

The accuracy of the developed rutting models can be evaluated based on Pseudo R2 value which provides an indication of the amount of variance accounted for by the predictor variables in the model. The Pseudo R2 is estimated by comparing the variance component for level-1 (V e) in a null model to the same variance component in a restricted model (growth or conditional model) using the formula given in Equation 5-20.

In all developed rutting models, these calculated Pseudo R2 values are for log- transformed rutting values. Pseudo R2 values are presented as percentages to represent the amount of variance accounted for by the predictor variable/s in the models.

Table 7.16 shows that more than 40% of the variance is accounted for by the Time factor in growth models for the NW (47%), class M (57%), class A (47%), class B (43%) and class C (47%). Also, more than half (50%) of the percentage of explainable variance is accounted for by the predictors in the conditional models for the NW (51%), class M (59%), class A (56%), class B (57%) and class C (60%).

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Table 7.16 : Pseudo R2 values for developed rutting growth and conditional models

Dataset Model fit Pseudo R2

Growth model 47% NW Conditional model 51%

Growth model 57% Class M Conditional model 59%

Growth model 47% Class A Conditional model 56%

Growth model 43% Class B Conditional model 57% Growth model 47% Class C Conditional model 60%

7.8 Assessment of Developed Rutting Models

The null model is compared with the growth and conditional rutting models for the NW and the four road classes to determine if the set of IVs improves the fit of each model or not. Deviance statistic test is based on the maximum likelihood estimation procedure and is normally used to compare two nested models in multilevel analysis. The difference between the deviances for any two models follows an approximate chi- squared distribution with degrees of freedom computed as the difference of the models’ degrees of freedom. The greater the reduction in the deviance value, the greater the improvement in fit.

The results of the deviance statistic test for predicted null, growth and conditional rutting models for all datasets are shown in Table 7.17. In this table, it should be noticed that there is always a reduction in deviance from the null model to the growth model and from the growth model to the conditional model.

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Table 7.17: Deviance test results for predicted rutting progression models

Model comparison test with null model Number of Deviance p-value (at Dataset Model fit estimated Degrees test (χ2) 95% parameters χ2 statistic of confidence freedom interval) Null model 36123.49 5 - - - Growth 17554.80 8 18568.69 3 <0.001 NW model Conditional 16583.04 11 19540.45 6 <0.001 model Null model 3254.87 4 - - - Growth Class 1128.64 7 2126.23 3 <0.001 M model Conditional 1088.03 9 2166.84 5 <0.001 model Null model 13075.63 4 - - - Growth Class 6788.72 7 6286.91 3 <0.001 A model Conditional 6482.53 9 6593.10 5 <0.001 model Null model 9315.38 4 - - - Growth Class 4410.39 7 4904.99 3 <0.001 B model Conditional 3948.83 10 5366.56 6 <0.001 model Null model 10071.90 4 - - - Growth Class 4726.21 7 5345.69 3 <0.001 C model Conditional 4230.75 10 5841.15 6 <0.001 model

The likelihood ratio tests show that these changes are all significant with p < 0.001. The significant p-values for chi-square (χ2) test indicate that there is evidence in the data to suggest an association between rutting progression and the included independent

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DEVELOPMENT OF RUTTING CHAPTER SEVEN PROGRESSION MODELS variable/s. These results mean that the time variable in the growth models and all IVs in the conditional models have improved the models’ descriptions of the data.

7.9 Validation of the Developed Rutting Models

Using both apparent and internal validation methods, the developed growth and conditional rutting models are tested to ensure their ability to predict future conditions accurately. The results of the two methods are presented in the following sub-sections.

7.9.1 Apparent Validation Method

In this validation method, the fundamental assumptions of the developed regression model are tested. Two plots have been examined to evaluate growth and conditional models for the NW and each road class. The frequency histogram and normal probability plot of residuals are plotted to check for residual normality. The line of equality plot of observed DV versus predicted DV is also plotted to test for linearity.

For the NW, the diagnostic plots to evaluate the growth model and conditional model fits are illustrated in Figure 7-1 and Figure 7-2, respectively. Part (a) of both figures shows that the rutting residuals are normally distributed with the mean very close to zero, standard deviation less than 0.2, and a limited range of residuals (from -0.5 mm to 0.5 mm), for a large sample size (N = 41,656). Part (b) of both figures shows that the predicted against observed rutting values are very close to the line of equality with very high correlation, R2 = 87% for the growth model and R2 = 88% for the conditional model. It can be noticed that there is very small number of observations which are underestimated, otherwise, the observed values and predicted values are very close. The underestimated observations are considered as outliers or incorrect data, therefore, they are removed from the dataset and the model has been re-estimated. However, all estimated model results did not change due to very small number of underestimated observations (compared to the large sample size). Overall, the results indicate that the assumptions of normality and linearity are supported.

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(a)

R2 = 87%

(b)

Figure 7-1: Apparent validation for the developed rutting growth model for the NW, (a) Residual histogram and (b) Line of equality

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(a)

R2 = 88%

(b)

Figure 7-2: Apparent validation for the developed rutting conditional model for the

NW, (a) Residual histogram and (b) Line of equality

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The apparent validation is also conducted for the rutting growth and conditional models of all road classes (M, A, B and C) and presented in Figure J-1, Figure J-2 , Figure J-3, Figure J-4 , Figure J-5, Figure J-6, Figure J-7 and Figure J-8 of Appendix-J. All these figures illustrate that the assumptions of normality and linearity are supported which means that all developed models reveal apparent validity.

7.9.2 Internal Validation Method

The one-third of the data (30%), which is selected randomly and set aside, has been used for internal model validation. This dataset is used to develop a rutting validation model with the same variables (Time, MESA, SNCi and TMI) that have been used for the developed rutting model. The confidence interval estimate provides a range of possible values for the model coefficients. Multiple statistical testing using a Bonferroni correction is applied when checking whether the coefficients of the validation model fall within the 99% confidence intervals for the coefficients of the developed model. The lower and upper bounds of the 99% confidence intervals are calculated using the formula given in Equation 5-22.

Results of the internal validation for the growth and conditional rutting models for the NW and the four road classes (M, A, B and C) are presented in Table 7.18 and Table 7.19, respectively. The results of internal validation for all developed growth rutting models indicate that the intercept and Time coefficients of the models, based on the validation datasets, fall within the upper and lower bound intervals for the coefficients of the developed models, as shown in Table 7.18. This means that all the developed growth models exhibit internal validity.

The results of internal validation for all developed conditional rutting models in Table 7.19 indicate that all coefficients of the models based on the validation datasets fall within the upper and lower bound intervals for the coefficients of the developed models, except for class M dataset. The bold cells in the table show that, for class M dataset, coefficients of the intercept and SNCi of the model based on the validation dataset do not fall within the upper and lower bound intervals for the coefficients of the developed models. It can be noticed that both coefficients are not significant (p>0.05) in the validation model which could be due to the small sample size dataset for class M

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DEVELOPMENT OF RUTTING CHAPTER SEVEN PROGRESSION MODELS validation model (only 412 segments). Although both modelling and validation datasets have the same ranges of each variable, it is possible that due to the smaller size of the validation set that the variation within each variable is not that evident.

Table 7.18: Internal validation results for growth rutting progression models

99% 99% 1 p-value Standard 3 3 2 p-value Variables CDM 6 CI CI CVM 7 (DM ) Error 4 5 (VM ) Dataset LB UB

Intercept 1.318 <0.001 0.021 1.263 1.372 1.326 <0.001

NW Time 0.084 <0.001 0.001 0.083 0.086 0.083 <0.001

Intercept 1.244 <0.001 0.098 0.991 1.497 1.159 <0.001

Class M Class Time 0.096 <0.001 0.002 0.091 0.100 0.095 <0.001

Intercept 1.335 <0.001 0.036 1.242 1.428 1.376 <0.001

Class A Class Time 0.088 <0.001 0.002 0.083 0.092 0.083 <0.001

Intercept 1.386 <0.001 0.034 1.473 1.387 <0.001 1.300

Class B Class Time 0.072 <0.001 0.001 0.074 0.073 <0.001 0.069

Intercept 1.240 <0.001 0.029 1.164 1.315 1.232 <0.001

Class C Class Time 0.090 <0.001 0.001 0.087 0.093 0.090 <0.001 1: Coefficient of developed model 2: Coefficient of validated model 3: Confidence Interval 4: Lower Bound 5: Upper Bound 6: Developed model 7: Validated model

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Table 7.19: Internal validation results for conditional rutting progression models

99% 99% 1 p-value Standard 3 3 2 p-value Variables CDM 6 CI CI CVM 7 (DM ) Error 4 5 (VM ) Dataset LB UB

Intercept 2.365 <0.001 0.070 2.185 2.546 2.287 <0.001 Time 0.056 <0.001 0.001 0.053 0.059 0.058 <0.001

LN_MESA 0.050 <0.001 0.005 0.037 0.063 0.044 <0.001 NW

SNCi -0.379 <0.001 0.012 -0.411 -0.348 -0.350 <0.001 TMI 0.001 <0.05 0.0005 0.0002 0.003 0.001 <0.05 Intercept 3.067 <0.001 0.497 1.785 4.348 1.598 0.077

Time 0.056 <0.001 0.006 0.040 0.072 0.064 <0.001 LN_MESA 0.098 <0.05 0.035 0.007 0.188 0.150 <0.05 Class M Class

SNCi -0.567 <0.001 0.131 -0.905 -0.230 -0.192 0.338 Intercept 2.316 <0.001 0.089 2.088 2.545 2.110 <0.001

Time 0.057 <0.001 0.002 0.051 0.062 0.060 <0.001 MESA 0.026 <0.001 0.003 0.018 0.035 0.018 <0.001 Class A Class

SNCi -0.367 <0.001 0.028 -0.440 -0.294 -0.295 <0.001 Intercept 2.900 <0.001 0.106 2.628 3.173 2.854 <0.001

Time 0.035 <0.001 0.002 0.030 0.040 0.040 <0.001 MESA 0.022 <0.05 0.008 0.001 0.044 0.001 <0.05 Class B Class SNCi -0.601 <0.001 0.029 -0.675 -0.528 -0.575 <0.001 TMI 0.003 <0.001 0.001 0.001 0.005 0.002 <0.05 Intercept 2.027 <0.001 0.052 1.893 2.162 2.062 <0.001

Time 0.058 <0.001 0.002 0.054 0.063 0.057 <0.001 LN_MESA 0.122 <0.001 0.009 0.098 0.146 0.127 <0.001 Class C Class SNCi -0.265 <0.001 0.017 -0.308 -0.221 -0.280 <0.001 TMI 0.002 <0.05 0.001 -0.001 0.004 0.001 0.259 1: Coefficient of developed model 2: Coefficient of validated model 3: Confidence Interval 4: Lower Bound 5: Upper Bound 6: Developed model 7: Validated model Note: Bold numbers mean that CVM do not fall within the UB and LB intervals for CDM.

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7.10 Deterministic Simulation for the Developed Rutting Models

A deterministic simulation is used for the purpose of understanding the behaviour of the developed rutting models under different selected conditions. This simulation is conducted for the growth and conditional models over time, for the whole network and the four road classes (M, A, B and C).

Figure 7-3 shows the simulation of the outputs from the growth rutting models over time, using Equations 7-2, 7-5, 7-8 , 7-11 and 7-14 for simulating growth model for the NW, class M, class A, class B and class C, respectively. The figure illustrates that, when considering only the effect of time factor, for the given data, one can estimate the rutting progression values over time. It could be noticed that the rates of rutting progression for all road classes are relatively the same with slow uniform deterioration rate over time. However, these rates increase rapidly close to 20 mm rut depth which is expected, i.e. that the pavements enter the rapid deterioration phase at in later years of service. This is supported by findings of Martin (2008), who found that it is expected that a pavement would normally deteriorate during its early period of life at a slow uniform rate and then increases towards the later years of service life. This is clear in Figure 7-3 that all four road classes have similar rates up to year 20 where the rate of progression varies with class M having the highest followed by A and C classes and the lowest for class B. This is also confirmed by the rutting grand mean values (range from 5 to 5.5 mm) from null models for all classes showing very close values of rut depth. Also, the results from the growth models for all classes indicate that the rate of rutting progression per year for all classes is very close (on average, 0.1 mm per year).

For simulating conditional rutting models, mean, maximum and minimum values (from the datasets used for developing the models) for MESA, SNCi and TMI are used. Details of the descriptive statistics of these continuous variables which are used for simulating the conditional models of the NW and the four road classes (M, A, B and C) are presented in Table 5.4.

Outputs from all rutting conditional models are presented in Figure 7-4, Figure 7-5, Figure 7-6, Figure 7-7 and Figure 7-8 to test the sensitivity of the NW, class M, class A, class B and class C models for different pavement conditions, using Equations 7-3 , 7-6, 7-9 , 7-12 and 7-15, respectively.

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Figure 7-3: Deterministic simulation for the growth rutting progression models over time for the NW and the four road classes (M, A, B and C)

It can be noticed that the predicted rutting progression changes significantly when varying the levels of included independent variables over time and in all simulations the rates of rutting increases with time. Also, all figures show that higher rutting values are expected when all the above variables are at their minimum values than when at their maximum values, except for class C model. This indicates that the pavements exhibit higher rutting when the strength is low, even with low traffic loading. This is supported by models’ results when the effect of SNCi is stronger than the effect of MESA. However, class C model shows that higher rutting values are expected when all variables are at their maximum values which could be due to very low traffic loading in this class that pavement could hold it even at low pavement strength.

Figure 7-4 indicates that a section with high strength and loading located in wet climate has lower rut depths than a section with low strength and loading but located in dry climate. This is opposite to what would be expected. However, as mentioned before the effect of climate is limited and much lower than that of SNCi and MESA. So the trends

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DEVELOPMENT OF RUTTING CHAPTER SEVEN PROGRESSION MODELS in this figure actually highlight the effects of the latter two rather than climate. A pavement subject to high traffic loads is designed for these loads hence the high strength and low values of rut depth.

Figure 7-4: Deterministic simulation for the NW conditional rutting progression model over time

Additionally, all rutting conditional models have been simulated to show the predicted changes to rutting progression when one variable varies from its minimum to maximum values, while all other independent variables are at their mean value for the dataset. This is conducted for the NW and the four road classes and presented in Appendix-K. In all figures, the changes of SNCi exhibit higher rutting values than the changes of MESA due to stronger effect of the former than the latter on rutting progression for all datasets. The changes of MESA in class B roads show there is no obvious changes in rutting values. This is due to the fact that the class B roads are light duty pavements (with maximum MESA=5 in available data) but have a better standard designs and construction qualities than class C roads (with maximum MESA= 4 in available data). In addition, TMI has a clear effect on rutting progression only when very wet areas in

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DEVELOPMENT OF RUTTING CHAPTER SEVEN PROGRESSION MODELS light duty pavements (class B and class C). The climatic effects across selected network are less significant than expected.

The models’ simulations show that they are responded well on varying levels for the included variables, hence making them ideal for sensitivity analyses to investigate the effect of changing these variables. Overall, the different combinations of predictor values for simulating the models show reasonable outputs in terms of engineering judgement.

Figure 7-5: Deterministic simulation for class M conditional rutting progression

model over time

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Figure 7-6: Deterministic simulation for class A conditional rutting progression model

over time

Figure 7-7: Deterministic simulation for class B conditional rutting progression model

over time

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Figure 7-8: Deterministic simulation for class C conditional rutting progression model

over time

7.11 Summary

Presented in this chapter are the developed rutting progression models within the gradual phase of deterioration of sealed granular pavements for the whole network (NW) and for each of the four road classes (M, A, B and C). Empirical deterministic models are developed to predict pavement rutting progression over time as a function of a number of contributing variables, using multilevel analysis, based on full maximum likelihood estimation. Modelling parameters include pavement rutting in terms of average rut depth (RD, mm) as the performance parameter and traffic loading (MESA), pavement strength (SNCi), climate condition (TMI) and drainage condition (DRA) as predictor parameters. The rutting (RD) dependent variable is positively skewed in all datasets (NW, M, A, B and C) and the traffic loading (MESA) variable is also positively skewed for the NW, class M and class C datasets. Both variables are transformed using natural logarithm transformation function (LN) of RD (LN_RD) and MESA

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(LN_MESA). The correction factor (CF) for each developed model is calculated to remove bias caused by fitting the model to the log transformed data.

For each dataset, three types of rutting models are fitted for different purposes, null models, growth models and conditional models. For the whole network and the four road classes, rutting null models show that there are significant variances between time series observations, segments, highways and road classes. This indicates that the heterogeneity (variation) is a critical aspect of the data that should not be ignored to include the effects of unobserved variables. The rutting grand mean values from null models for all datasets (NW= 5.34, M= 5.02, A= 5.57, B= 5.42 and C= 5.17 mm) indicate that their means are very close (around 5 mm). This confirms that all road classes have been designed according to the expected impacts of contributing factors to rutting progression. All the developed growth models indicate that the time factor is significant and confirm that the rate of rutting progression per year for all road classes is very close (0.1 mm per year), where the rutting rate for class M= 0.1, class A= 0.09, class B= 0.07 and class C= 0.09 mm per year. This implies that the Victorian pavements have a good performance in terms of rutting.

For the whole network and the four road classes, rutting conditional models are presented and the contribution and significance of relevant influencing factors in predicting rutting progression are also presented and explained. In all conditional models, the effect of Time is stronger than other factors on rutting progression, followed by SNCi then MESA and TMI (where relevant). The effect of TMI is only significant in class B and class C roads. This means that the climate has an effect only on light duty pavements. The reason is that, the standards of design and construction are considerably lower for classes B and C than other road classes, with varying sealed widths and unsealed shoulders. Also, road cross sections are generally low, with little crown height unless on embankment sections (Toole et al., 2004). In all conditional models, the effect of DRA is not significant due to the good condition of drainage systems for most of the network roads. Another reason is that the conditions of drainage system for the selected segments are extracted from database based on 2010 network condition survey (see Section 3.4.2.5); therefore, its effect is considered as a fixed variable for each segment.

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Pseudo R2 values are calculated for evaluating the accuracy of developed models and showed that more than half of the percentage of explainable variance is accounted for by the predictors in the conditional models for the NW (51%), class M (59%), class A (56%), class B (57%) and class C (60%).

The developed models are also assessed using the deviance statistic test and the results indicated that the time variable in the growth models and all IVs in the conditional models have improved the models’ descriptions of the data.

The diagnostic plots for apparent validations of the growth and conditional models’ fits show that the residuals are normally distributed with means very close to zero, small standard deviations (less than 0.2), and limited ranges of residuals (between -0.5 to 0.5 mm rut depth). Also, they show that the predicted rutting values against observed rutting values are very close to the line of equality with very high correlation (R2) ranging from 84% to 88%. These validation results indicate that the assumptions of normality and linearity are supported, which means that all developed models exhibit apparent validity. Also, internal validation for all developed models has been performed using another dataset from the same network and the results indicate that all the developed models exhibit internal validity. Multiple simulation scenarios from different combinations of predictor values are also presented. Overall simulation results show reasonable outputs in terms of engineering judgement.

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8. CHAPTER EIGHT DEVELOPMENT OF CRACK INITIATION AND PROGRESSION MODELS

8.1 Introduction

The purpose of this chapter is to present the application of a multilevel modelling approach (Hierarchical Generalized (logistic) Linear Model (HGLM)) to predict the probability of pavement crack initiation and progression and to capture the effects of variances at high levels through logistic models. Also, presented are the effects of several factors on pavement crack initiation and progression. This involves predicting the probability of pavement cracks occurring using a binary logistic model and cracks progression over time using an ordinal logistic regression model. The development of these models to take into account the effect of variations between time series observations, between segments and between highways, has been presented. This chapter also presents the details of models’ evaluation, validation and simulation.

The dataset that is used to develop probabilistic cracking models is based on the following criteria:

 Cracking data includes all types of cracking: transverse, longitudinal and crocodile cracking and is reported as a percent of the affected area.  The rate of cracking progression is increasing over the period of available observed cracking data (i.e. cracking deterioration rate > zero).  The available independent variables that are expected to influence crack initiation and progression are traffic loading (MESA), pavement strength (SNC), swell potential of subgrade soil (SST), climate condition (TMI) and drainage condition (DRA). The ranges of these independent variables are shown in Table 5.6 and Table 5.7.  The study period is 8 years (from 2004 to 2011) as shown in Section 3.4.1.2.

 It is assumed that initial pavement strength (SNC0) is a more valuable predictor

in crack initiation phase, whereas pavement strength at any age (SNCi) is a more valuable predictor in the crack progression phase.

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 Cracking data has been converted from a continuous variable into a discrete categorical variable to help smooth out abnormality in the dataset. Hence, the continuous cracking extent data is divided into two categories, namely cracked and uncracked to predict crack initiation. However, four discrete categories are used in modelling crack progression in terms of the probability of a pavement falling into each category. The four categories of crack extent have been identified as insignificant, limited, considerable and significant affected areas, with the ranges shown in Table 5.1.  The progress of the affected area has an ordered structure starting from an insignificant affected area, progressing to limited affected area, then considerable and finally a significant affected area. This means that the four categories of cracking data have an ordinal structure relating to cracking progression over time.  A random data split is used to divide the dataset into two parts; approximately 70% of the data is used for model development and the remaining 30% of the data is used for model validation.

The cracking models have been developed for the network dataset (NW) only for reasons explained in Section 8.2.1. The analysis is performed using Hierarchical Linear and Nonlinear Modelling (HLM7) software and Statistical Package for Social Sciences (SPSS). To develop crack initiation and progression models, three types of models are fitted for each, namely; null model, growth model and conditional model. These three models are fitted as presented in the following sections.

8.2 Whole Network (NW) Crack Initiation (CRini) Model

The CRini model is estimated using a Generalized HLM model with a logit link function. The model parameters are estimated using binary logistic regression model based on the full PQL (Penalized Quasi Likelihood) method (Raudenbush et al., 2011). The three fitted models are presented in the following sub-sections.

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8.2.1 NW Crack Initiation Null Model

A four-level binary logistic model is used to consider the effect of variation over time for different segments that are nested within a particular highway and road class, as they differ in their condition relative to segments nested in other highways or in other classes. The results of the random effects parameters for the null model indicated that the variance components at level-2 (r0) and level-3 (u00) are highly significant (p

<0.001). However, the level-4 variance component (v000) is not significant (p >0.05). This suggests that no heterogeneity exists between road classes in terms of crack initiation condition. Hence, the effect of variance at level-4 (between road classes) is ignored.

Only a three-level model that explains variation over time, nested within segments and segments within highways is used. The null model estimated that the variance of error components for levels 2 and 3 (r0 and u00) are highly significant (p <0.001), as shown in Table 8.1. The standard logistic distribution has a variance of π2/3 = 3.29, which is the level-1 variance (Ve) (Hedeker, 2007, Grilli and Rampichini, 2012, Snijders and Bosker, 2012).

Table 8.1: Estimation of the fixed effect variable and random effect variables for the NW crack initiation null model

NW crack initiation null model Fixed Odds Coefficient Standard t- p- effect df ratio, CI (β) error ratio value* variable Exp(β) Intercept, 1.293- 0.5406 0.1407 3.84 39 <0.001 1.717 β0 2.280 Random Variance Chi- Standard p- effect component df Statistic deviation value* variable (V) (χ2) Level-2, 0.3016 0.0910 6912 7262.96 <0.05 r0 Level-3, 0.8740 0.7638 39 1275.31 <0.001 u00 *: All predictors are statistically significant (p < 0.05) with 95% level of confidence. df: degree of freedom CI: confidence interval

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The proportion of variance can be estimated at each level using Equations 5-16, 5-17, 5-18 and 5-19. The results are:

 Proportion of variance within level-1 (time series observation), PVO = 79%  Proportion of variance within level-2 (between segments within highways), PVS = 2%  Proportion of variance within level-3 (between highways), PVH = 19%

These results indicate that there is a high variance among time series observations (PVO = 79%). Only 2% of the variance is found within segments, and around 19% between highways. The significant variances between observations, segments and highways confirm that there is statistical justification for using multilevel logistic analysis approach, rather than the traditional logistic regression analysis to capture the variance between datasets efficiently. The estimated null model yields a prediction for the average crack initiation rate (CRini) as shown below:

1 P ( ) ini 1+ Exp ( η)

η β + + +

The estimated NW crack initiation null model is:

1 P ( ) 0. 8-1 ini 1+ Exp ( 0.5 0 )

Where:

P (CRini): is the probability of crack initiation η: is the predicted logit odds e, r0 and u00: are the random variables for level-1, level-2 and level-3, respectively

β0: is the fixed intercept coefficient.

Thus, approximately 63% (0.632*100) of observations within segments in the selected network are expected to exhibit crack initiation during the study period. Yet, the average probability of uncracked pavement is 37% [(1-0.632)*100]. The odds of cracked pavement are defined as the ratio of the probability of cracked over the

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DEVELOPMENT OF CRACK CHAPTER EIGHT INITIATION AND PROGRESSION MODELS probability of uncracked pavement. Hence, the odds for a cracked pavement are 2 (0.63/0.37), i.e. the odds of cracked pavement are 2 to 1.

Due to the non-significant variance (Vv000) between the four road classes (M, A, B and C), a separate model for each road class is not required to predict the probability of crack initiation.

8.2.2 NW Crack Initiation Growth Model

The results of crack initiation growth model for the whole network are shown in Table 8.2. Allowing only for the time predictor, the final growth mixed model is:

1 P ( ) ini 1+ Exp ( η)

η β + β Time + + +

The estimated NW crack initiation growth model is:

1 P ( ) 8-2 ini 1+ Exp ( ( 1. 7 + 0.5715 Time ))

Where:

β1: is level-2 fixed coefficient Time: is time variable in years With all other variables are as defined previously.

The model is statistically significant and predicts that the probability of CRini increases with time. The variance components are highly significant (p<0.001) at 95% confidence interval and indicate that there is significant variance between observations, segments, and highways for the crack initiation condition variable. Chi-square (χ2) results also indicate that highway segments differ significantly in their intercepts.

An odds ratio is a measure of the change in event odds resulting from a unit change in the predictor. The odds ratio for the Time variable is also presented in Table 8.2. The

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DEVELOPMENT OF CRACK CHAPTER EIGHT INITIATION AND PROGRESSION MODELS odds ratio value for Time indicates that a one year increase in time increases the predicted odds of crack initiation 1.771 times on average with a 95% confidence interval (1.742 1.8 times).

Table 8.2: Estimation of the fixed effect variables and random effect variables for the NW crack initiation growth model

NW crack initiation growth model Fixed Odds Coefficient Standard p- effect t-ratio df ratio, CI (β) error value* variable Exp(β) 0.186 Intercept -1.3374 0.1695 -7.89 39 <0.001 0.263 0.370 1.742 Time 0.5715 0.0084 68.40 18683 <0.001 1.771 1.800 Random Variance Chi- Standard p- effect component df Statistic deviation value* variable (V) (χ2) Level-2, 0.8986 0.8075 6912 10530.24 <0.001 r0 Level-3, 1.0373 1.0760 39 1202.26 <0.001 u00 *: All predictors are statistically significant (p < 0.001) with 95% level of confidence. df: degree of freedom CI: confidence interval

8.2.3 NW Crack Initiation Conditional Model

To test the predictors effect on crack initiation, independent variables including time

(Time), traffic loading (MESA), initial pavement strength (SNC0), climate condition (TMI), subgrade soil type (SST) and drainage condition (DRA) are added to the model as predictors. The estimated parameters for this conditional model are shown in Table 8.3 . The final estimated model is:

1 P ( ) ini 1+ Exp ( η)

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η = β0 + β1 Time + β2 MESA + β01 SNC0 + β02 SST + β3 TMI + e + r0 + u00

The estimated NW crack initiation conditional model is:

P (CRini) 1/ (1+ Exp (- (1.5848 + 0.5365 Time + 0.1819 MESA 1.1439 SNC0 8-3 + 0.2248 SST + 0.0071 TMI)))

Table 8.3: Estimation of the fixed effect variables and random effect variables for the NW crack initiation conditional model

NW crack initiation conditional model Fixed Odds Coefficient Standard p- effect t-ratio df ratio, CI (β) error value* variable Exp(β) 1.992- Intercept 1.5848 0.4428 3.58 39 <0.001 4.878 11.947 1.680- Time 0.5365 0.0090 59.47 18681 <0.001 1.710 1.740 1.159- MESA 0.1819 0.0174 10.42 18681 <0.001 1.199 1.241 0.244- SNC -1.1439 0.1358 -8.42 6910 <0.001 0.319 0 0.416 1.120- SST 0.2248 0.0569 3.95 6910 <0.001 1.252 1.400 1.002- TMI 0.0071 0.0026 2.693 18681 <0.05 1.007 1.012 Random Variance Chi- Standard p- effect component df Statistic deviation 2 value* variable (V) (χ ) Level-2, 0.8654 0.7489 6910 10260.15 <0.001 r0 Level-3, 1.1259 1.2677 39 1235.66 <0.001 u00 *: All predictors are statistically significant (p < 0.05) with 95% level of confidence. df: degree of freedom CI: confidence interval

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Where: η: is the predicted logit odds. Time: is the time variable in years. MESA: is the traffic loading variable in terms of Million Equivalent Standard Axles load /lane. TMI: is the climate condition variable in terms of Thornthwaite Moisture Index.

β1, β2, β3, β01, β02: are fixed coefficients. All other variables are as defined previously.

The analysis results indicate that all the estimated parameters (except for the drainage condition) are statistically significant with p-values of <0.001. Time, MESA, TMI and

SST are positively related to the probability of CRini, whereas, SNC0 is negatively related to the probability of CRini. In other words, the model predicts that the probability of CRini increases with time and with traffic loading increases. The observed positive trends for TMI and SST indicate that the probability of CRini for pavements in wet zones and built on expansive soils is higher than in dry zones and non-expansive soils.

However, the probability of CRini decreases with increased initial pavement strength.

The t-ratios are the regression coefficients divided by their standard errors and their absolute values represent the effect size of each predictor. The t-ratios suggest that the effect of Time is stronger than the other variables, followed by MESA and SNC0, then SST and TMI.

An odds ratio is a measure of the change in an event odds resulting from a unit change in the predictor. The odds ratios for the predictors of the conditional model are also presented in Table 8.3. The main inferences from the crack initiation model (Equation 8-3) in terms of the odds ratios can be summarized as follows:

 After statistically controlling for the other factors, a one year increase in time increases the predicted odds of crack initiation 1.71 times on average with a 95% confidence interval (1.68 1.74 times).

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 If all the other factors remain the same, an increase of traffic loading by one MESA results in the odds of crack initiation being increased by 1.2 times on average with a 95% confidence interval (1.159 1.241 times).  If all the other factors remain the same, an increase of initial pavement strength

by one unit of SNC0 results in the odds of crack initiation being reduced by 68% ([1-0.319]*100%) on average with a 95% confidence interval (76% 58%).  Predicted probability of crack initiation is 25% higher (or 1.25 times) on average for a pavement with expansive subgrade soil than for a pavement with non- expansive soil.  A one unit increase in TMI (wetter climate), on average, increases the predicted odds of crack initiation by 1.01 times, after controlling all other factors, with a 95% confidence interval (1.002 1.012 times).

8.3 Whole Network Crack Progression (CRpro) Model

The CRpro model is estimated using an ordinal logistic regression model based on the full PQL (Penalized Quasi Likelihood) method (Raudenbush et al., 2011). A three-level model is used to predict the probability of crack progression in terms of the probability of a pavement falling into each of four discrete categories. The four categories of crack extent have been identified as insignificant, limited, considerable and significant affected area, with the ranges shown in Table ‎5.1.

8.3.1 NW Crack Progression Null Model

The parameters for the null model are summarized in Table 8.4. The null model indicates that the variance components for r0 and u00 are highly significant (p<0.001). The proportion of variance over time within segments is very high (PVO = 77%). Around 16% of the variance is found between segments, and around 7% between highways. The significant variance between observations, segments and highways confirms that there is statistical justification for using a multilevel logistic analysis approach to predict the probability of crack progression in order to capture the variance between levels efficiently. In ordinal logistic regression, multiple logit functions are

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DEVELOPMENT OF CRACK CHAPTER EIGHT INITIATION AND PROGRESSION MODELS utilised to yield the predicted cumulative probability (CP) of each cracking category, as presented below:

1 P 1+ Exp ( η)

η ( P sig) β + + +

η ( P con) β + δ + + +

η ( P lim) β + δ + + +

The estimated null models for the CP of cracking progression for the four categories are:

Table 8.4: Estimation of the fixed effect variables and random effect variables for the NW crack progression null model

NW crack progression null model Fixed Odds Coefficient Standard p- effect t-ratio df ratio, CI (β) error value* variable Exp(β) 0.070- Intercept -2.4686 0.0926 -26.67 39 <0.001 0.085 0.102 Threshold, 5.913- 1.8205 0.0221 82.28 18682 <0.001 6.175 δ1 6.449 Threshold, 19.595- 3.0237 0.0247 122.35 18682 <0.001 20.568 δ2 21.589 Random Variance Chi- Standard p- effect component df Statistic deviation 2 value* variable (V) (χ )

Level-2, r0 0.8328 0.6936 6912 11966.47 <0.001 Level-3, 0.5548 0.3078 39 1032.60 <0.001 u00 *: All predictors are statistically significant (p < 0.001) with 95% level of confidence. df: degree of freedom CI: confidence interval

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DEVELOPMENT OF CRACK CHAPTER EIGHT INITIATION AND PROGRESSION MODELS

1 P 0.0787 8-4 sig 1+ Exp ( ( . 8 ) )

1 P 0. 8-5 con 1+ Exp ( ( . 8 + 1.8 05) )

1 P 0. 5 8-6 lim 1+ Exp ( ( . 8 + . 0 7) )

P ins 8-7

Where:

CPsig: is the cumulative probability for significant cracking

CPcon: is the cumulative probability for at least considerable cracking

CPlim; is the cumulative probability for at least limited cracking

CPins: is the cumulative probability for at least insignificant cracking

β0: is the first threshold value between significant and considerable categories

(β0 + δ1): is the second threshold value between considerable and limited categories

(β0 + δ2): is the third threshold value between limited and insignificant categories All other variables are as defined previously.

The cumulative predicted probabilities in above equations have one redundant probability (CPins=1) due to the constraint that the sum of probabilities equals one, so only three equations are needed. Hence, the log-odds can be predicted via the linear combination of predictors for the first three categories which are separated by the threshold values (δ). Transforming the above predicted cumulative probabilities (CP) to the probabilities (P) of cracking for each category using the formulas in Equation 5-14; it is found that on average:

Psig = 0.0787*100 = 8% of the observations within segments in the selected network are expected to exhibit significant cracking during the study period.

Pcon = 34% - 8% = 26% of the observations within segments are expected to exhibit considerable affected cracking areas.

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DEVELOPMENT OF CRACK CHAPTER EIGHT INITIATION AND PROGRESSION MODELS

Plim = 63% - 34% = 29% of the observations within segments are expected to exhibit limited affected cracking areas.

Pins = 100% 63% = 37% of the observations within segments in the selected network are expected to reveal insignificant affected areas (uncracked) during the study period.

Where:

Psig: is the probability of significant cracking

Pcon: is the probability of considerable cracking

Plim: is the probability of limited cracking

Pins: is the probability of insignificant cracking

8.3.2 NW Crack Progression Growth Model

Table 8.5 summarizes the parameters for the growth model when allowing only for Time as a predictor. The model is statistically significant and predicts that the probability of CRpro increases with time. The growth model also indicates that the variance components for r0 and u00 are highly significant (p <0.001) at 95% confidence interval and indicates that there are significant variances between observations, segments, and highways for the crack progression condition variable. Chi-square (χ2) results also indicate that highway segments differ significantly in their intercepts. The final growth mixed models for the predicted cumulative probability (CP) of the four cracking categories are presented below:

1 P 1+ Exp ( η)

η ( P sig) β + β + + +

η ( P con) β + β + δ + + +

η ( P lim) β + β + δ + + +

Where:

β1: is level-2 fixed coefficient

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Time: is time variable in years With all other variables are as defined previously.

Table 8.5: Estimation of the fixed effect variables and random effect variables for the NW crack progression growth model

NW crack progression growth model Fixed Odds Coefficient Standard p- effect t-ratio df ratio, CI (β) error value* variable Exp(β) 0.003- Intercept -5.6654 0.1250 -45.33 39 <0.001 0.003 0.004 1.875- Time 0.6429 0.0074 87.02 18681 <0.001 1.902 1.930 Threshold, 10.978- 2.4526 0.0289 84.78 18681 <0.001 11.618 δ1 12.296 Threshold, 62.141- 4.1947 0.0333 125.99 18681 <0.001 66.331 δ2 70.803 Random Variance Chi- Standard p- effect component df Statistic deviation value* variable (V) (χ2)

Level-2, r0 1.5204 2.3117 6912 20946.46 <0.001

Level-3, 0.7146 0.5106 39 860.71 <0.001 u00 *: All predictors are statistically significant (p < 0.001) with 95% level of confidence. df: degree of freedom CI: confidence interval

The estimated growth models for the CP of cracking progression for each category are:

1 P 8-8 sig 1+ Exp ( ( 5. 5 + 0. 9 Time))

1 P 8-9 con 1+ Exp ( ( 5. 5 + 0. 9 Time + . 5 ) )

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1 P 8-10 lim 1+ Exp ( ( 5. 5 + 0. 9 Time + . 19 7) )

P ins 8-11

The three models presented in Equations 8-8, 8-9 and 8-10 have the same estimated slopes for the Time predictor with estimated thresholds of (-5.6654), (-5.6654 + 2.4526) and (-5.6654 + 4.1947), respectively. The odds ratio value for the Time variable indicates that for every additional year in time, the odds of greater cracking (significant cracking category) as opposed to less cracking (insignificant cracking category) increase 1.9 times on average with a 95% confidence interval (1.875 1.93 times).

From the cumulative probabilities in Equations 8-8 to 8-11 , the probability (P) of each cracking category can be obtained using formulas in Equation 5-14. These probabilities are as follows:

1 Psig 8-12 1+ Exp( ( 5. 5 + 0. 9 Time))

1 1 Pcon 8-13 1+Exp( ( 5. 5 + 0. 9 Time+ . 5 ) ) 1+ Exp( ( 5. 5 + 0. 9 Time))

1 1 Plim 8-14 1+Exp( ( 5. 5 + 0. 9 Time+ . 19 7)) 1+Exp( ( 5. 5 + 0. 9 Time+ . 5 ))

1 8-15 Pins 1 1+Exp( ( 5. 5 +0. 9 Time+ . 19 7))

8.3.3 NW Crack Progression Conditional Model

Available independent variables are added to the growth model as predictors to estimate the conditional predicted cumulative probability (CP) for each cracking category. The estimated parameters for the conditional crack progression model are shown in Table

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8.6. The final mixed models for the CP of significant, considerable, limited and insignificant categories are presented below:

P sig 1 (1+Exp ( ( . 00 7+ 0.5759 Time+0.0 58 MESA 1.0 9 SN +0. SST+ 8-16 0.0018 TM )))

P con 1 (1+Exp ( ( . 00 7+0.5759 Time+0.0 58 MESA 1.0 9 SN +0. SST+ 8-17 0.0018 TM + . 517 )))

P lim 1 (1+Exp ( ( . 00 7+ 0.5759 Time+0.0 5 8 MESA 1.0 9 SN +0. SST+ 8-18 0.0018 TM + . 19 )))

P ins 1 8-19

The analysis results show that the variances for the random errors (r0 and u00) and the fixed parameters for Time, SNCi and SST are statistically significant with p-values less than 0.001. MESA and TMI coefficients are statistically significant with p-values less than 0.05. Drainage condition (DRA) is not significant hence was excluded from the model. Time, MESA, TMI and SST are positively related to the probability of CRpro, whereas, SNCi is negatively related to the probability of CRpro.

The three models estimated in Equations 8-16, 8-17 and 8-18 have the same estimated slopes for all predictors with estimated thresholds of (-3.0047), (-3.0047+2.4517) and (- 3.0047+4.1942), respectively.

The absolute values of t-ratios indicate that the effect of Time is stronger than the effects of other variables on crack progression, followed by SNCi. Yet, MESA, TMI and SST have smaller effects on CRpro. The odds ratios for the predictors of the CRpro conditional model are presented in Table 8.6 and the effects of odds ratios can be explained as follows:

 For every additional year in time, the odds of greater cracking (significant cracking category) as opposed to less cracking (insignificant cracking category) increase 1.8 times on average when the other factors are statistically controlled.

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Table 8.6: Estimation of the fixed effect variables and random effect variables for the NW crack progression conditional model

NW crack progression conditional model Fixed Odds Coefficient Standard p- effect t-ratio df ratio, CI (β) error value* variable Exp(β) 0.030- Intercept -3.0047 0.2522 -11.91 39 <0.001 0.050 0.083 1.748- Time 0.5759 0.0089 64.86 18678 <0.001 1.779 1.810 0.998- MESA 0.0258 0.0141 1.83 18678 <0.05 1.026 1.055 0.297- SNC -1.0694 0.0739 -14.48 18678 <0.001 0.343 i 0.397 1.094- SST 0.2232 0.0683 3.27 6911 0.001 1.250 1.429 0.996- TMI 0.0018 0.0031 0.60 18678 <0.05 1.002 1.008 Threshold, 10.968- 2.4517 0.0289 84.69 18678 <0.001 11.608 δ1 12.285 Threshold, 62.104- 4.1942 0.0333 125.77 18678 <0.001 66.299 δ2 70.777 Random Variance Chi- Standard p- effect component df Statistic deviation value* variable (V) (χ2)

Level-2, r0 1.4759 2.1783 6911 20185.40 <0.001

Level-3, 0.9122 0.8321 39 1227.81 <0.001 u00 *: All predictors are statistically significant (p < 0.05) with 95% level of confidence. df: degree of freedom CI: confidence interval

 For every additional MESA in traffic loading, the odds of greater cracking as opposed to less cracking increase 1.03 times on average when the other factors are statistically controlled.  If all the other factors remain the same, the decrease of pavement strength by one unit of SNCi results in increasing the odds of greater cracking as opposed to less cracking by 66% ([1-0.343]*100%).

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 After controlling all other factors, the odds of greater cracking as opposed to less cracking is 25% higher (or 1.25 times) for the pavements built on expansive subgrade soil than for pavements built on non-expansive soil.  For every additional unit in TMI the odds of greater cracking as opposed to less cracking increase 1.002 times on average when the other factors are statistically controlled.

From the cumulative probability (CP) in Equations 8-16 to 8-19, the probability (P) of each cracking category can be obtained using formulae in Equation 5-14. These probabilities are presented below:

Psig 1 (1+Exp ( ( . 00 7+0.5759 Time+0.0 58 MESA 1.0 9 SN +0. SST+ 8-20 0.0018 TM )))

Pcon 1 (1+Exp ( ( . 00 7 +0.5759 Time+0.0 58 MESA 1.0 9 SN +0. SST+

0.0018 TM + . 517 ))) ( 1 (1+Exp ( ( . 00 7+ 0.5759 Time+0.0 5 8 MESA 1.0 9 SN 8-21

+0. SST+0.0018 TM ))))

Plim 1 (1+Exp ( ( . 00 7 +0.5759 Time+0.0 58 MESA 1.0 9 SN +0. SST+

0.0018 TM + . 19 ))) ( 1 (1+Exp ( ( . 00 7+ 0.5759 Time+0.0 5 8 MESA 1.0 9 SN 8-22

+0. SST+0.0018 TM + . 51 7))))

Pins 1 (1 (1+Exp ( ( . 00 7+ 0.5759 Time+0.0 58 MESA 1.0 9 SN +0. SST+ 8-23 0.0018 TM + . 19 ))))

8.4 Accuracy Evaluation of Cracking Models

The developed logistic models for cracking data are evaluated by testing the classification accuracy. Cross-tabulation analysis is used to test the ability of the models

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DEVELOPMENT OF CRACK CHAPTER EIGHT INITIATION AND PROGRESSION MODELS to correctly predict crack initiation and crack progression. The analysis result is a table in a matrix format that shows the frequency distribution of the predicted and observed cracking data. In this matrix, the columns are the frequencies of predicted probabilities of cracking observations, while the rows are the frequencies of observed (actual) probabilities of cracking observations. The numbers of observations that are being correctly or wrongly predicted in the dataset are used to determine the success rate of the developed model, by using Equation 5-21.

The developed growth and conditional crack initiation and progression models are tested using the network data to determine the predicted probability of cracking data and the frequencies of cracking condition results based on 50% estimated probability.

Table 8.7 and Table 8.8 present the results of cross- tabulation analysis for growth and conditional crack initiation models, respectively. The bold figures in Table 8.7 indicate that 8120 out of 10933 (74%) observations are correctly assigned to the uncracked status using the 50% predicted probability. For cracked status, 12957 out of 14743 (88%) observations are correctly assigned. In the same way, from bold figures in Table

8.8, the correctly predicted observations are obtained for conditional CRini model.

Table 8.7: Frequencies of observed and predicted probabilities of cracking status

for growth crack initiation model

Frequency of predicted probability of cracking status Total Uncracked Cracked

Uncracked 8120 2813 10933 bserved o Cracked 1786 12957 14743 Frequency probability of cracking cracking status

Total 9906 15770 25676

Note: Bold numbers are number of observations which are correctly predicted

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Table 8.8: Frequencies of observed and predicted probabilities of cracking status

for conditional crack initiation model

Frequency of predicted probability of cracking status Total Uncracked Cracked

Uncracked 8079 2854 10933 bserved o Cracked 1830 12913 14743 Frequency probability of cracking cracking status

Total 9909 15767 25676

Note: Bold numbers are number of observations which are correctly predicted

The overall success rates of both predicted CRini models using Equation 5-21 are as follows:

81 0 + 1 957 % Success rate of growth 8 % ini 5 7

8079 + 1 91 % Success rate of conditional 8 % ini 5 7

Table 8.9 and Table 8.10 show the results of cross- tabulation analysis for growth and conditional crack progression models, respectively. The first table shows that out of the 2284 observations as significant affected area category, only 884 (39%) are correctly assigned to that category using the predicted probability. Out of the 6015 observations as considerable affected area category, 4076 (68%) are correctly assigned. For the observations of limited affected area category, 2615 out of 6444 (41%) are correctly assigned. For the observations as insignificant affected area category, 9282 out of 10933 (85%) are correctly assigned. In same way, from bolded data in Table 8.10, the correctly predicted observations are obtained for conditional CRpro model.

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Table 8.9: Frequencies of observed and predicted probabilities of cracking categories for growth crack progression model

Frequency of predicted probability of cracking category

Total Limited Limited Significant Significant Considerable Considerable Insignificant Insignificant

Significant 884 1208 98 94 2284

bserved cracking cracking Considerable 164 4076 1539 236 6015 of of o

category Limited 1 1217 2615 2611 6444

Insignificant 0 232 1419 9282 10933 Frequency Frequency probability

Total 1049 6733 5671 12223 25676

Note: Bold numbers are number of observations which are correctly predicted

The overall success rates of both predicted CRpro models are as follows:

88 + 07 + 15 + 9 8 % Success rate of growth % pro 5 7

8 + 05 + 0 + 9 77 % Success rate of conditional 5% pro 5 7

With the 50% estimated probability, it is considered that 82% success rates of the crack initiation models for two categories (cracked and uncracked) refer to well estimated models. Also, with the 50% estimated probability, it is considered that 65% success rates of the crack progression models for the four categories (significant, considerable, limited and insignificant) refer to well estimated models.

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Table 8.10: Frequencies of observed and predicted probabilities of cracking categories for conditional crack progression model

Frequency of predicted probability of cracking category

Total Limited Limited Significant Significant Insignificant Insignificant Considerable Considerable

Significant 866 1227 95 96 2284

bserved cracking cracking Considerable 179 4053 1537 246 6015 of of o

category Limited 0 1216 2604 2624 6444

Insignificant

Frequency Frequency probability 0 245 1411 9277 10933

Total 1045 6741 5647 12243 25676

Note: Bold numbers are number of observations which are correctly predicted

It is important to note that this percent success rate is for 50% estimated probability and that this rate increases with higher estimated probability. For example, as the percent success rate for CRini model is 82% correctly predicted observations with 50% estimated probability, the percent success rate for CRini model becomes 98% correctly predicted observations with 60% estimated probability. Also, the percent success rate for CRpro model becomes 78% correctly predicted observations with 60% estimated probability.

8.5 Validation of the Developed Cracking Models

Internal validation method is used to ensure that the developed models have the ability to predict future conditions accurately. As mentioned before, around one-third of the data (30%) is set aside to use for model validation. This dataset is used to develop

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DEVELOPMENT OF CRACK CHAPTER EIGHT INITIATION AND PROGRESSION MODELS validation models (VM) with the same variables that have been used for the developed models (DM). Multiple statistical testing using a Bonferroni correction is applied when checking whether the coefficients for the validation models do fall within the 99% confidence intervals for the coefficients of the developed models, or not. The confidence interval (CI) estimate provides a range of likely values for each of the models’ parameters. Using the formula given in Equation 5-22 which is the general form of a confidence interval, the lower and upper bounds of the 99% confidence intervals are calculated based on the standard error of the coefficient of the developed model. The internal validation results for the growth and conditional crack initiation models are presented in Table 8.11 and those for crack progression models are presented in Table 8.12 . The results of both tables indicate that all parameters of the models based on the validation datasets fall within the upper and lower bound intervals for the parameters of the developed models. This means that both probability models exhibit internal validity.

Table 8.11: Internal validation results for growth and conditional crack initiation models

p- p- 1 Standard 99% 99% 2

fit Variable CDM value CVM value Error CI3 LB4 CI3 UB5 Model Model (DM6) (VM7)

Intercept -1.3374 <0.001 0.1695 -1.7741 -0.9007 -1.5023 <0.001 model Growth Time 0.5715 <0.001 0.0084 0.5500 0.5930 0.5794 <0.001

Intercept 1.5848 <0.001 0.4428 0.4443 2.7254 0.5935 0.334

Time 0.5365 <0.001 0.0090 0.5132 0.5597 0.5506 <0.001

MESA 0.1819 <0.001 0.0174 0.1369 0.2268 0.1597 <0.001

SNC0 -1.1439 <0.001 0.1358 -1.4937 -0.7942 -0.9024 <0.001

Conditional Conditional model SST 0.2248 <0.001 0.0569 0.0783 0.3712 0.3343 <0.001

TMI 0.0071 <0.05 0.0026 0.0003 0.0139 0.0089 <0.05

1: Coefficient of Developed Model 2: Coefficient of Validated Model 3: Confidence Interval 4: Lower Bound 5: Upper Bound 6: Developed Model 7: Validated Model

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Table 8.12: Internal validation results for growth and conditional crack progression models

fit p- p-

1 Standard 99% 99% 2 Variables CDM value 3 4 3 5 CVM value 6 Error CI LB CI UB 7

Model (DM ) (VM )

Intercept -5.6654 <0.001 0.1250 -5.9873 -5.3434 -5.6940 <0.001

Time 0.6429 <0.001 0.0074 0.6238 0.6619 0.6391 <0.001 Threshold, 2.4526 <0.001 0.0289 2.3780 2.5271 2.3846 <0.001 δ1

Growth model Threshold, 4.1947 <0.001 0.0333 4.1089 4.2804 4.1276 <0.001 δ2 Intercept -3.0047 <0.001 0.2522 -3.6544 -2.3550 -3.4534 <0.001

Time 0.5759 <0.001 0.0089 0.5530 0.5987 0.5648 <0.001

MESA 0.0258 <0.05 0.0141 -0.0105 0.0621 0.0577 <0.05

SNCi -1.0694 <0.001 0.0739 -1.2596 -0.8791 -1.0453 <0.001

SST 0.2232 <0.001 0.0683 0.0474 0.3990 0.3909 <0.001

TMI 0.0018 <0.05 0.0031 -0.0060 0.0097 0.0064 0.06 Conditional Conditional model Threshold, 2.4517 <0.001 0.0289 2.3771 2.5262 2.3865 <0.001 δ1 Threshold, 4.1942 <0.001 0.0333 4.1083 4.2801 4.1292 <0.001 δ2 1: Coefficient of Developed Model 2: Coefficient of Validated Model 3: Confidence Interval 4: Lower Bound 5: Upper Bound 6: Developed Model 7: Validated Model

8.6 Simulation for the Developed Cracking Models

For the purpose of understanding the performance of the predicted probability of crack initiation and progression under different selected conditions, a deterministic simulation is used. In this simulation, sets of model inputs are sampled from statistical distributions to describe multiple simulation scenarios to make an overall understanding of the range of behaviours that can be expected over time.

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8.6.1 Simulation for Crack Initiation Models

The probability of growth crack initiation model is simulated over time as shown in Figure 8-1, based on the model in Equation 8-2. The figure shows that about 50% of the predicted probability of being cracked occurs after the second year. Also, it shows that there is 100% probability of crack initiated after 10 years on the selected network.

Figure 8-1: Simulation for the probability of NW growth crack initiation model over time .

The probability of conditional crack initiation model is also simulated over time as shown in Figure 8-2, based on the model in Equation 8-2. The assumptions that are used to illustrate model simulations are based on the values of independent variables from the dataset that is used for developing the model. The mean, maximum and minimum values for MESA, SNC0 and TMI are used. Details of the descriptive statistics of these continuous variables which are used for simulating conditional CRini model of the NW are presented in Table 5.6 . The figure illustrates that for the given data, it is possible to estimate the probability of crack initiation over time, under different conditions.

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In all simulation scenarios, it can be noticed that road sections in expansive soil areas are slightly associated with early crack initiation than sections in non-expansive soil areas. Also, it is expected that about 50% of the predicted probability of being cracked occurs after the second year when all variables are at their mean values (MESA=2.02,

SNC0=2.97 and TMI=2). Further, about 50% of predicted probability of being cracked occurs after the first year when all variables are at their minimum values (MESA=0.01,

SNC0=1.59 and TMI=-38). However, Figure 8-2 also shows that more than 95% of predicted probability of being cracked occurs during the first year when all variables are at their maximum values (MESA=31.28, SNC0=4.19 and TMI=100). These simulations analyses demonstrate that the effect of traffic loading during crack initiation period is stronger than the effects of initial pavement strength and climate condition.

Figure 8-2: Simulation for the probability of NW conditional crack initiation model over time

Additionally, the crack initiation conditional model has been simulated to show the predicted probability changes of crack initiation when one variable varies from its

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DEVELOPMENT OF CRACK CHAPTER EIGHT INITIATION AND PROGRESSION MODELS minimum to maximum values, while all other independent variables are at their mean values for the dataset. This is conducted for the NW dataset and presented in Appendix- L. In all figures, the changes of MESA exhibit early crack initiation than the changes of

SNC0 due to stronger effect of the former than the latter on crack initiation. In addition, TMI has a clear effect on prediction probability of being cracked, occurs only in very wet climate.

8.6.2 Simulation for Crack Progression Models

Based on the three models in Equations 8-8 , 8-9 and 8-10, the cumulative probabilities of crack progression growth models are simulated over time for the three cracking categories, significant, considerable and limited affected areas, respectively. Figure 8-3 shows the cumulative probabilities of crack progression to stay at a certain cracking category or below it over time.

Figure 8-3: Simulation for the NW cumulative probabilities of growth crack

progression models over time

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The figure shows that there is a 50% probability that the pavement would have a significant affected area or lower at time=9 years, and this probability increases to about 100% at time=15 years. There is a 50% probability that the pavement would have a considerable affected area or lower at time=5 years, and this probability increases to about 100% at time=11 years. Also, there is a 50% probability that the pavement would have a limited affected area or lower (insignificant affected area) after 2 years, and this probability increases to about 100% at time=8 years.

Also, on the basis of Equations 8-12 through 8-15, the change of the probability of crack progression for the four categories with time is plotted as illustrated in Figure 8-4. From this figure it can be estimated that, at any time, the probability of a pavement section to be in any of the four cracking category. The cracking category with the highest probability is the most likely cracking state for that section.

Figure 8-4: Simulation for the NW probabilities of growth crack progression model over time

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The inference from Figure 8-4 is that a section say at year 5, has a 15% probability of having insignificant affected area, a 35% probability of having limited affected area, a 42% probability of having considerable affected area and an 8% probability of having significant affected area. Therefore, due to the highest probability of considerable cracking category, it is the most likely cracking state for that section.

In addition, it shows that the highest condition probability for sections within 2 years or less is insignificant cracking, those within 3 and 4 years have a high probability of being in limited cracking condition, considerable condition between 5 and 8 years and significant condition for 9 years and more.

Conditional crack progression models are simulated based on values of MESA, SNCi, and TMI (from Table 5.6) with expansive and non-expansive soils. The cumulative probabilities of conditional crack progression to stay at a certain cracking category or below are simulated over time based on Equations 8-16 to 8-19 . Different simulation scenarios are presented as shown in Figure 8-5 when all variables are at their mean values, in Figure 8-6 when all variables are at their maximum values, and in Figure 8-7 when all variables are at their minimum values. The curves in these figures show that at any given time, the probability of any cracking category or lower can be estimated.

For example, the NW cumulative probabilities of conditional crack progression models over time show that there is a 50% probability that the pavement would have a significant affected area or lower after 9 years when all variables are at their mean values. This time increases to 11 years when all variables are at their maximum values, and decreases to 8 years when all variables are at their minimum values, as shown in Figure 8-5, Figure 8-6 and Figure 8-7, respectively.

In all simulation scenarios, it can be noticed that road sections in expansive soil areas are marginally associated with early crack progression times than sections in non- expansive soil areas.

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Figure 8-5: Simulation for the NW cumulative probabilities of conditional crack progression models over time when all variables are at their mean values

Figure 8-6: Simulation for the NW cumulative probabilities of conditional crack progression models over time when all variables are at their maximum values

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Figure 8-7: Simulation for the NW cumulative probabilities of conditional crack progression models over time when all variables are at their minimum values

Also, on the basis of Equations 8-20 to 8-23, the change of probability of crack progression for the four categories with time is plotted for different combinations of contributing factors as presented in Figure 8-8, Figure 8-9 and Figure 8-10. From these figures, it can be estimated, at any time, the probability of a pavement section to be in any of the four cracking category. The cracking category with the highest probability is the most likely cracking state for that section. Figure 8-8 shows the probabilities of crack progression when all variables are at their mean values. The inference from this figure is that a section say at year 5 has a 15% probability of having insignificant affected area, a 35% probability of having limited affected area, a 42% probability of having a considerable affected area and an 8% probability of having significant affected area. Therefore, due to the highest probability of considerable cracking category, it is the most likely cracking state for that section.

Figure 8-9 shows the probabilities of crack progression when all variables are at their maximum values. The inference from this figure is that a section say at year 5 has a

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28% probability of having insignificant affected area, a 41% probability of having limited affected area, a 27% probability of having considerable affected area and a 4% probability of having significant affected area. Therefore, due to the highest probability of limited cracking category, it is the most likely cracking state for that section.

Further, Figure 8-10 shows the probabilities of crack progression when all variables are at their minimum values. The inference from this figure is that a section say at year 5 has an 8% probability of having insignificant affected area, a 24% probability of having limited affected area, a 53% probability of having considerable affected area and a 15% probability of having significant affected area. Therefore, due to the highest probability of considerable cracking category, it is the most likely cracking state for that section.

Figure 8-8: Simulation for the NW probabilities of conditional crack progression model over time when all variables are at their mean values

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Figure 8-9: Simulation for the NW probabilities of conditional crack progression model over time when all variables are at their maximum values

Figure 8-10: Simulation for the NW probabilities of conditional crack progression model over time when all variables are at their minimum values

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Furthermore, the crack progression conditional model has been simulated to show the predicted probability changes of crack progression when SNCi varies from its minimum to maximum values, while all other independent variables are at their mean values for the dataset. The cumulative probabilities and probabilities for the four cracking categories are simulated and presented in Appendix-L. In all figures, the changes of

SNCi show that an early crack progression is expected with a weak pavement (with minimum SNCi value) than a strong pavement (with maximum SNCi value).

All the above observations could be more or less in different conditions when considering various values of MESA and SNCi with wet or dry climate conditions and expansive or non-expansive soils. Overall, simulation plots for the developed models indicate that the models reasonably predict the expected crack initiation and progression over time, under the selected conditions.

8.7 Summary

The application of multilevel analysis using HLM for modelling the probability of pavement crack initiation and progression has been demonstrated in this chapter. The procedure outlined is quite general, and can be applied to any pavement condition variable that has ordinal classification with data that has a hierarchical structure. Particularly, the chapter presents multilevel hierarchical generalized linear models that can account for the correlation among time series data of the same segment and capture the effect of unobserved factors.

From the analysis approach performed for the sets of network segments used in this study, it is found that it is a successful approach to present advanced analysis of pavement cracking dataset. Further, the results indicate that unobserved heterogeneity is a critical aspect that should be considered between segments and between highways for modelling cracking. However, the heterogeneity between road classes for the selected network does not exist within the dataset used herein. For this reason separate models for the four road class are not presented.

Almost 63% of the observations within segments in the selected network are expected to exhibit crack initiation during the study period (from 2004 to 2011). Yet, the average

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DEVELOPMENT OF CRACK CHAPTER EIGHT INITIATION AND PROGRESSION MODELS probability of uncracked pavement is 37%. Hence, the odds of cracked pavement are 2 to 1.

The study found that about 8% of the observations within segments in the selected network are expected to exhibit significant cracking during the study period, 26% of them are expected to have considerable affected cracking areas, 29% of them are expected to have limited affected cracking areas, and 37% of them are expected to have insignificant affected areas (uncracked) during the study period.

The time to initiation of pavement cracking significantly decreases when the rate of traffic loading and other factors increases (Paterson, 1987). The developed conditional crack initiation and progression models for the whole network dataset are statistically significant and the parameter estimates are significant and have correct signs. The developed conditional models for crack initiation and progression indicate that time, traffic loading, climate condition and swell potential of subgrade soil have positive contributions to crack initiation and progression. However, pavement strength has negative contribution to crack initiation and progression. Drainage condition has no significant contribution to pavement cracking in the selected network.

The effect of time is stronger than the other variables on crack initiation and progression. The effect of traffic loading is stronger than the effect of initial pavement strength in crack initiation phase. However, the effect of pavement strength at any time is stronger than the effect of traffic loading in crack progression phase.

The developed logistic models for cracking data are evaluated by testing classification accuracy using cross-tabulation analysis. It is found that with the 50% estimated probability; about 82% of the observations are correctly predicted by the crack initiation model for the two categories (cracked and uncracked) which indicates a well estimated model. Also, with the 50% estimated probability, it is found that there is 65% success rate of the crack progression model for the four categories (significant, considerable, limited and insignificant) which also refers to a well estimated model. These rates increase to 98% for CRini model and to 78% for CRpro model, when the estimated probability increases to 60%. In addition, internal validation results show that all predicted probability models exhibit internal validity and have the ability to predict future conditions accurately.

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Further, the simulation plots for the developed models indicate that the models reasonably predict the probability of crack initiation and progression over time under different selected conditions. Hence, this is making them ideal for sensitivity analyses to investigate the effect of changing contribution variables. It is found that about 50% of the predicted probability of being cracked occurred after the second year. Also, there is 100% probability of crack initiated after 10 years in the selected network.

In all simulation scenarios, it has been noticed that road sections in expansive soil areas are associated with slightly earlier crack initiation than sections in non-expansive soil areas. Also, TMI effect on prediction probability of being cracked occurred only in very wet climate.

The cumulative probabilities of crack progression to stay at a certain cracking category or below over time shows that there is a 50% probability that the pavement would have a significant affected area or lower at time=9 years, and this probability increases to about 100% at time=15 years. There is a 50% probability that the pavement would have a considerable affected area or lower at time=5 years, and this probability increases to about 100% at time=11 years. Also, there is a 50% probability that the pavement would have a limited affected area or lower (insignificant affected area) after 2 years, and this probability increases to about 100% at time 8 years.

In addition, it has been found that the highest condition probability for sections within 2 years or less is insignificant cracking, those within 3 and 4 years have a high probability of being in limited cracking condition, considerable condition between 5 and 8 years and significant condition at 9 years and beyond.

To sum up, the probabilistic model format provides such flexibility in the application of the model. For example, for low traffic loading roads, maintenance intervention may be scheduled at a higher risk profile, whereas lower risk would be more suitable for high traffic loading roads. In this case, maintenance intervention for the former roads may be planned at say 65% probability, while the equivalent level would be say 40% for the latter roads. This indicates that the models can be implemented to set triggers according to risk considerations.

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9. CHAPTER NINE COMPARISON BETWEEN RESULTS OF DEVELOPMED MODELS FOR THE FOUR ROAD CLASSES

9.1 Introduction

Victoria’s freeway and arterial roads network covers approximately 151,000 kilometers, which are all used by general traffic and carry freight. The coverage of the network sites includes four types of road classes (M, A, B and C) which differ in qualities, functions, duties, geometric standards, and traffic volumes and loadings. Road class M represents freeways and motorways, road class A represents major arterials, road class B represents main arterials which are state highways connecting major cities, and class C roads represent minor arterials which are rural roads connecting smaller towns (Hoque et al., 2008, VicRoads, 2013b). Usually, class M and A roads are classified as heavy duty pavements and class B and C roads are classified as light duty pavements. The total length of selected network sample is 2308.87 km and includes 7 road sections of class M, 11 road sections of class A, 10 road sections of class B, and 12 road sections of class C.

This chapter aims to assess the performance of all road classes by comparing their pavement conditions and factors affecting the rate of pavement deterioration from the developed models in previous chapters. The sub-sections below provide a comparison for the three developed fitted models (null, growth and conditional) for two pavement condition parameters; roughness and rutting. Due to the observed non-significant variation between the four road classes in terms of pavement cracking, no separate models have been developed for each class (see Section 8.2.1). Therefore, the four road classes are compared only in terms of descriptions for cracking status and cracking progression.

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9.2 Comparison between Roughness Models for the Four Road Classes

The outputs of the analyses from null, growth and conditional models of roughness (in chapter six) are used to compare between the performances of the four road classes, as presented in the following sub-sections.

9.2.1 Comparison between Roughness Null Models

The null models’ results for all road classes indicate that the three variance components

(Ve, Vr0 and Vu00) are highly significant (p< 0.001) and indicate that there is significant variance between time series observations, segments, and highways for the roughness condition variable. The proportion of variance results indicate that there is a high variance between segments within highways (PVS) for all classes, followed by the proportion of variance within time series observations (PVO), and the proportion of variance between highways (PVH), as shown in Table 9.1 . However, in class C roads, the PVH is higher than the PVO, which could be due to the higher numbers of highway sections for class C set than those of other road classes (see Section 3.3).

Table 9.1: Comparison between the four road classes using roughness null model results

% of proportion of variance Road class PVO PVS PVH

Class M 9 84 7

Class A 16 78 6

Class B 14 76 10

Class C 10 76 14

Figure 9-1 shows that the predicted roughness grand mean values for all classes (M= 1.79, A= 2.46, B= 2.76 and C= 3.08 m/km) indicate that class C has, on overage, higher roughness values than the other road classes followed by class B, then class A and class

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M roads. This is due to higher design standards and better quality materials for the class M followed by class A, then class B and class C roads (Toole et al., 2004, VicRoads, 2013b).

Figure 9-1: Predicted roughness for the four road classes

9.2.2 Comparison between Roughness Growth Models

The results of roughness growth models for the four road classes indicate that highway segments differ significantly in their intercepts and slopes. Also, they indicate that the time factor is significant. All roughness growth models confirm that the rate of roughness progression per year for all road classes is very close (0.02 IRI/year) where the roughness rate for class M= 0.0185, class A= 0.0179 , class B= 0.0178 and class C= 0.0209 IRI/year, as shown in Table 9.2.

Considering that only segments within gradual deterioration phase are included to develop roughness models, the roughness value for each road class at the start of the gradual phase is determined from the growth models by considering the first year for gradual phase is when time is zero in this model. This is because the first year within the gradual deterioration phase is coded as zero when the models are developed. For example, if Time= 0 in class M roughness growth model (LN_IRI = 0.5181 + 0.0183

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Time) then the predicted IRI= [Exp (0.5181+ 0.0183*0 )]*CF = 1.68 m/km, where CF is correction factor for class M= 1.001.

Table 9.2 presents the predicted roughness values for the four road classes at the start of the gradual deterioration phase. It could be noticed that class C has higher roughness value at the start of the gradual phase than the other road classes followed by class B, then class A and class M roads. It is anticipated that these values are related to that the initial pavement condition for class C is higher than the other classes (see Table 4.4). For example, the initial roughness value after construction for class C (1.8 IRI) is higher than that for class M (1.2 IRI).

It is worth mentioning that, the conditional roughness model is not used for the purpose of predicting roughness value when the gradual phase starts, due to the fact that the

included independent factors (such as MESA and SNC0) in the conditional model are unknown and cannot be zero when the time is zero (which is the first year within the gradual phase).

Table 9.2: Comparison between the four road classes using roughness growth model results

Rate of Roughness value Assumed IRI Time spent Road roughness when gradual intervention within gradual class progression phase started level (trigger) phase (year) (IRI/year) (IRI) Class M 0.0185 1.68 3.5 40

Class A 0.0179 2.15 4.2 38

Class B 0.0178 2.40 4.5 36

Class C 0.0209 2.62 5.4 35

Moreover, the models can be used to determine the duration of the gradual phase by setting intervention triggers for each class. Table 9.2 shows IRI intervention levels for each road type given in Table 2.1 . Implementing the growth models with these triggers, shows that class M roads have longer gradual phase than the other classes which could

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COMPARISON BETWEEN RESULTS OF CHAPTER NINE DEVELOPMED MODELS FOR THE FOUR ROAD CLASSES be due to more frequent maintenance of class M than the other classes (Toole et al., 2004). Also, class M roads have been designed for longer life than the other classes.

9.2.3 Comparison between Roughness Conditional Models

Factors considered in the conditional models are time (Time), traffic loading (MESA), initial pavement strength (SNC0), subgrade soil type (SST), climate (TMI), and drainage (DRA). However, the analysis results for each road class show that different factors influence the deterioration progression of each road class.

In all conditional roughness models, the effect of DRA is not significant. The reason behind that could be related to the limited variation in the condition of the drainage systems of the network, or due to the fact that its effect is considered as a fixed variable for each segment.

Also, it is observed that subgrade soil type and climate condition affect the performance of light duty pavements (class B and class C), whereas their effects on heavy duty pavements (class M and class A) are not significant. The reasons could be that, the latter pavements are of high standard in design and construction, well maintained, and generally exhibit high levels of smoothness. In addition to that, road cross sections are generally high, with deep table drain inverts and available sub-soil drains. Therefore, there is a little opportunity for water to gain access to these types of pavement (Toole et al., 2004), i.e. better drainage system.

As class M carries more traffic loading than the other classes, the effect of traffic loading is stronger than other factors in this class. However, the effect of initial pavement strength is stronger than the other factors in class C due to lower quality pavement materials than other classes. The effect of time is stronger than the other variables for classes A and B as they have lower traffic loadings compared to class M and better initial pavement strengths than class C. The order of the effects of contributing factors for the four road classes is presented in Table 9.3. In this table, it can be noticed that, irrespective of the time factor, the effect of traffic loading is stronger than the other factors in heavy duty pavements (class M and class A) and the

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COMPARISON BETWEEN RESULTS OF CHAPTER NINE DEVELOPMED MODELS FOR THE FOUR ROAD CLASSES effect of initial pavement strength is stronger than other factors on light duty pavements (class B and class C).

Table 9.3: Comparison between the four road classes using roughness conditional model results

Order of the strongest factor effect on roughness progression Road class Time MESA SNC0 SST TMI

Class M 3 1 2 N.S. N.S.

Class A 1 2 3 N.S. N.S.

Class B 1 3 2 4 5

Class C 3 2 1 4 5

% of roughness progression for one unit increase/decrease of Road class factor

Time MESA SNC0 SST* TMI

Class M 0.67 1.16 54.43 N.S. N.S.

Class A 1.16 2.34 38.73 N.S. N.S.

Class B 1.47 4.30 30.41 9.67 0.04

Class C 0.49 45.48 68.89 6.60 0.05

Note: N.S. refers to non-significant factor. * % of roughness that will be higher for pavements built on expansive soils than for pavements built on non-expansive subgrade soils.

Moreover, the percent of roughness progression for a one unit increase/decrease of each included significant factor for all classes is also shown in Table 9.3 . It can be seen that for every additional year the effect of Time on roughness progression for class A and class B is more than its effect on M and C classes.

The table also shows that for a one MESA increase in traffic loading, the percent of roughness progression value increases for class C more than the other road classes

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COMPARISON BETWEEN RESULTS OF CHAPTER NINE DEVELOPMED MODELS FOR THE FOUR ROAD CLASSES followed by class B, then class A and class M roads. This finding is expected because a one MESA increase in traffic loading has more impact on roughness progression for class C that carries low traffic loading with a MESA range of (0.01 - 3.37 ) than class M which carries high traffic loading with a MESA range of (1.34 - 34.78). The ranges of

MESA for all classes are given in Table 5.2. Also, it can be noticed that a one SNC0 unit decrease in pavement strength, the percent of roughness progression value increases for class C more than the other road classes. The reason is that class C has lower pavement strength compared to other classes.

As mentioned earlier, SST and TMI only affect roughness progression for class B and class C. The percent of roughness progression is higher for pavements built on expansive soils than for pavements built on non-expansive subgrade soils for both classes. A one TMI unit increase in climate condition, the percent of roughness progression value increases only by 0.04 and 0.05 for class B and class C, respectively. This low percent of roughness progression is due to the wide range of TMI values for class B (-28 to 100) and class C (-26 to 81). Therefore, it is more reasonable to say that for 10 units increase in climate condition, the percent of roughness progression value increases by 0.4 and 0.5 for class B and class C, respectively.

9.3 Comparison between Rutting Models for the Four Road Classes

The outputs of the analyses from null, growth and conditional rutting models (in chapter seven) are used to compare between the performances of the four road classes, as presented in the following sub-sections.

9.3.1 Comparison between Rutting Null Models

The results of rutting null models for all road classes indicate that the three variance components (Ve, Vr 0 and Vu00) are highly significant (p< 0.001) and indicate that there is significant variance between time series observations, segments, and highways for the rutting condition variable. Table 9.4 shows that for all classes, the higher proportion of variance is between segments within highways (PVS) followed by the proportion of

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COMPARISON BETWEEN RESULTS OF CHAPTER NINE DEVELOPMED MODELS FOR THE FOUR ROAD CLASSES variance within time series observations (PVO), and the proportion of variance between highways (PVH).

Table 9.4: Comparison between the four road classes using rutting null model results

% of proportion of variance Road class PVO PVS PVH

Class M 32 44 24

Class A 41 52 7

Class B 30 63 7

Class C 32 62 6

Figure 9-2 shows that the predicted rutting grand mean values for all classes (M= 5, A= 5.5, B= 5.4 and C= 5.1 mm) have very close values. This confirms that all road classes have been designed according to the expected impacts of contributing factors to rutting progression and they have nearly the same initial rutting values (see Table 4.4).

Figure 9-2: Predicted rutting for the four road classes

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COMPARISON BETWEEN RESULTS OF CHAPTER NINE DEVELOPMED MODELS FOR THE FOUR ROAD CLASSES

9.3.2 Comparison between Rutting Growth Models

The results of rutting growth models for the four road classes indicate that the time factor is significant and the highway segments differ significantly in their intercepts and slopes. Rutting growth models confirm that the rate of rutting progression per year for all road classes is very close (0.1 mm per year), where the rutting rate for class M= 0.1, class A= 0.09, class B= 0.07 and class C= 0.09 mm per year, as shown in Table 9.5.

As the rutting models have been developed within the gradual deterioration phase, the growth models have been used to determine rutting values for all road classes when the gradual phase is initiated. As the first year within the gradual phase is coded as ‘zero’ when the models are developed, it is assumed that the rutting value when the gradual phase starts is when the Time factor is zero. For example, if Time= 0 in class A rutting growth model (LN_RD = 1.3348 + 0.0876 Time) then the predicted RD = [Exp (1.3348 + 0.0876*09)]*CF = 3. mm, where CF is correction factor for class A= 1.025. Table 9.5 presents the predicted rutting values for the four road classes when the gradual deterioration phase is initiated. It can be observed that the rutting values at the start of gradual phase, are very close (about 4 mm) for all road classes. It is expected that this similarity is related to the fact that initial pavement rutting for all road classes are nearly the same (see Table 4.4).

Table 9.5: Comparison between the four road classes using rutting growth model results

Rate of rutting Rutting value Intervention Duration of Road class progression when gradual level of gradual phase (mm/year) phase started (mm) rutting (mm) (year)

Class M 0.1004 3.5 10 11

Class A 0.0916 3.9 15 16

Class B 0.0742 4.1 20 22

Class C 0.0945 3.5 25 22

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Furthermore, the models can be used to determine the duration of the gradual phase for each road class by using relevant intervention levels, shown in Table 9.5. The durations of rutting gradual phase range from 11 years for class M to 16 years for class A and 22 years for B and C classes.

9.3.3 Comparison between Rutting Conditional Models

Factors considered in rutting conditional models are time (Time), traffic loading

(MESA), pavement strength (SNCi), climate (TMI), and drainage (DRA). However, the analysis results for each road class show that different factors influence rutting progression of each road class.

In all conditional rutting models, the effect of DRA is not significant. Also, it is observed that TMI affects the performance of light duty pavements (class B and class C), whereas its effect on heavy duty pavements (class M and class A) is not significant.

For all road classes, the effect of Time factor is stronger than the other factors on rutting progression, followed by SNCi then MESA and TMI (where relevant), as shown in Table 9.6. This means that all factors that change with time have a strong effect on rutting progression. Also, the conditional models’ results indicate that a decrease in pavement strength of sealed granular pavement has a stronger contribution to rutting progression than the increase in traffic loading.

Furthermore, Table 9.6 also presents the percent of rutting progression associated with one unit increase/decrease of each of the included significant factors for all road classes. It can be seen that for every additional year the effect of Time on rutting progression, for all classes, is the same (about 6%), except for class B which has less rutting progression with time. It can be also noticed that with one SNCi unit decrease in pavement strength, the percent of rutting progression value increases for class B more than the other road classes.

No comparison could be made between the four classes in terms of the contribution of traffic loading on rutting progression, since MESA contribution is measured in different

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COMPARISON BETWEEN RESULTS OF CHAPTER NINE DEVELOPMED MODELS FOR THE FOUR ROAD CLASSES ways (one unit of MESA for A and B classes, and one percent of MESA for M and C classes are used for predicting relative change in rut depth).

Furthermore, a one TMI unit increase in climate condition, the percent of rutting progression value increases only in class B and class C. This means that the climate condition has a significant effect only on light duty pavements.

Table 9.6: Comparison between the four road classes using rutting conditional model results

Order of the strongest factor effect on rutting Road class progression

Time SNCi MESA TMI

Class M 1 2 3 N.S.

Class A 1 2 3 N.S.

Class B 1 2 3 4

Class C 1 2 3 4 % of rutting progression for one unit Road class increase/decrease of factor

Time SNCi MESA TMI

Class M 5.77 43.30 0.097* N.S.

Class A 5.81 30.75 2.65 N.S.

Class B 3.59 45.18 2.21 0.31

Class C 5.99 23.24 0.121* 0.20

Note: N.S. refers to non-significant factor. * The number represents the percent increase in rutting value for a one percent increase in MESA due to the log-transformed of MESA data in the model.

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9.4 Comparison between Cracking Condition for the Four Road Classes

Due to the non-significant variance between the four road classes (M, A, B and C), separate models have not been developed to predict the probability of crack initiation or progression (see Section 8.2.1). Therefore, the four road classes are compared only in terms of the observed distributions of cracking status and cracking progression.

As the continuous cracking extent data is divided into two cracking categories, namely cracked and uncracked, Figure 9-3 shows the distribution for crack status for the four road classes. The figure illustrates that the cracked status for class C roads (61%) is more than for the other classes, followed by class B (58%), then class A (56%) and class M (49%). The uncracked status is the opposite order to cracked status. This indicates that there are less cracked observations in heavy duty pavements than light duty pavements due to more frequent crack sealing practice for the former pavements than the latter.

Figure 9-3: Distribution for crack status for the four road classes

For modelling of cracking progression, four distinct categories of cracking are used; insignificant, limited, considerable and significant affected area. Figure 9-4 shows that in all road classes the percent of insignificant affected area observations is higher than

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COMPARISON BETWEEN RESULTS OF CHAPTER NINE DEVELOPMED MODELS FOR THE FOUR ROAD CLASSES for the other categories, whereas the percent of significant affected area observations is lower than the other categories. Also, it shows clearly the significant affected area observations for class C is higher than the other road classes.

Figure 9-4: Distribution for crack categories for the four road classes

9.5 Summary

This chapter presented a comparison between the models of the four road classes for roughness and rutting. The comparison covered the three fitted models (null, growth and conditional) for roughness and rutting condition. Also, it covered a comparison of observed cracking status and categories between the four road classes.

From all fitted roughness models, the study has shown that class C has higher roughness values than the other road classes followed by class B, then class A and class M roads. Also, it confirms that the rate of roughness progression per year for all road classes is very close (0.02 IRI/year). These results indicate that different pavement segments within a network may deteriorate at the same rate but their roughness values could be different at the same time due to their different initial pavement condition, design standard, construction quality or any other unobserved variables.

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The study also showed that class M roads have longer gradual phase of roughness progression than the other classes. Further, it has been observed that subgrade soil type and climate condition only affect roughness progression of light duty pavements (class B and class C). The effect of traffic loading is stronger than other factors on heavy duty pavements (class M and class A) and the effect of initial pavement strength is stronger than the other factors on roughness progression of light duty pavements (class B and class C).

From all rutting fitted models, the study has shown that the predicted rutting grand mean values for all classes are very close (ranged from 5 to 5.5 mm) and the rate of rutting progression per year for all road classes is very close (0.1 mm per year). Also, it has been observed that the rutting values at the start of gradual phase, are very close (about 4 mm) for all road classes. These results confirm that all road classes have been designed according to the expected impacts of contributing factors to rutting and they have nearly same initial rutting values. In addition to that the study has shown that class M roads have shorter rutting gradual phase than the other classes. Also, TMI only affects the performance of light duty pavements. Another main study observation is that the decrease in strength of sealed granular pavements has a stronger contribution to rutting progression than the increase in traffic loading.

From cracking observation data, the study has shown that there are less cracked observations in heavy duty pavements than light duty pavements due to more frequent crack sealing practice for the former pavements than the latter. Further, in all road classes the percent of observations of insignificant affected area is higher than for the other categories, whereas the percent of observations of significant affected area is lower than the other categories. Also, it shows that observations of the significant affected area for class C are higher than the other road classes. This is due to lower standards of design and less resealing practice for class C roads than the other road classes.

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10. CHAPTER TEN SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

10.1 Introduction

The main goal of this research study is to apply a new approach for preparing condition data for use in developing network-level pavement deterioration models using a new modelling approach, for sealed granular pavement. This chapter briefly summarises the research process, outcomes and findings. This is then followed by major conclusions of the research and recommendations for further research.

10.2 Summary and Findings

To assist road agencies in their long term planning, the aim of this research project is to develop deterioration models for pavement roughness, rutting and cracking for rural arterial network. With accurate prediction models, the implications of optimum maintenance timing and rehabilitation strategies can be assessed with confidence and practical decisions can be made.

As presented in Chapter 1, the main goal of this research is about applying a new approach for preparing condition data for use in developing pavement deterioration models using a new modelling approach. Pavement condition parameters modelled in this study include surface roughness, rutting and cracking. These parameters are used for triggering investigation into pavement preservation and/or rehabilitation by road agencies in many countries including Australia. The aim is to apply a multilevel modelling approach that captures the effect of variance at all possible levels in modelling roughness and rutting progression and predicting the probability of pavement crack initiation and progression. Deterioration models can be used by road agencies for several fundamental applications in their PMS, including:

 Gap analysis i.e. predicting when a pavement needs to be maintained or rehabilitated before it actually fails.

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 Evaluation of maintenance strategies to assess the current and future financial decisions.  Assessment of the best intervention options required for short and long term maintenance programs.  Assessment of overall network condition and how it is affected by budget constraints.

As noted in the literature review, roughness and rutting have three distinct phases of deterioration; namely: initial, gradual and rapid; whereas cracking is characterised by separate phases of initiation and progression. In this study, only the gradual phase is modelled for roughness and rutting pavement conditions. For cracking, both the initiation and progression phases are modelled.

More effective pavement management requires models which reliably predict the impact of several variables on pavement deterioration. The impact of different factors on pavement deterioration is discussed in detail in Chapter 2. These factors are usually selected to develop models based on their availability in the network datasets, engineering experience or based on previous studies for similar networks. The main factors include traffic loading, soil type, pavement age, climate condition, pavement type, pavement strength, and drainage condition.

As discussed in Chapter 2, in the context of Australian and New Zealand’s network pavements, researchers adopt a number of road deterioration modelling efforts to describe pavement deterioration process related to spray sealed pavements. Yet, there is concern by road agencies that the developed deterioration models for sealed granular pavements have some limitations and have been found to be impractical in some cases.

To achieve the aim of this study, representative samples of highways from Victoria’s spray sealed rural network are considered. The selected sample network is from 40 highways with a combined length of more than 2,300 km.The network covers a large sample size with representative ranges of traffic loading, pavement strength, subgrade soil type and environmental factors. The various datasets used to collect the required data to facilitate the development of reliable and accurate pavement deterioration models have been described in Chapter 3.

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In this study, before developing the models, great emphasis and effort have been put into data preparation process because it is a vital step for the development of robust deterioration models. Therefore, a State of the Art approach for preparing condition data for use in developing pavement deterioration models was demonstrated in Chapter 4. The approach used to prepare accurate road condition data involves the following steps:

 Data alignment: time series datasets for the three condition data (roughness, rutting and cracking) are aligned to ensure that the same road segments are compared over time. Raw roughness profile data has been aligned using ProVAL software and an In-House Excel based tool. Rutting and cracking data has been aligned using aligned roughness data profiles extracted from the same database for the same segments over time.  Data cleaning: abnormalities in road profile data which lead to incorrect data are removed from the datasets.  Data filtering: the effects of periodic maintenance and rehabilitation works are excluded from the datasets. Road segments with only positive progression in roughness, rutting or cracking are taken into account using the Linear Rate of Progression (LRP) tool.  Boundary limits of data: the initial and terminal condition values of roughness and rutting data are used to establish boundary limits for the gradual deterioration phase.  Compiling and splitting datasets: for each 100m segment, the chainages of condition data and chainages of data related to contributing factors are matched for all relevant years. Then, random dataset split is utilised to divide the dataset into two parts; around 70% of the data is used for model development and the remaining 30% of the data is used for model validation.

The prepared panel datasets have hierarchical structure with four-levels of variation within the selected network. Time series observations (level-1) are nested within segments (level-2) which are nested within highways (level-3) which are nested within road classes (level-4). Therefore, the development of a network (NW) pavement deterioration model must allow for variation at all four levels. Due to the nature of the data, an empirical linear regression modelling approach is selected to use for modelling

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SUMMARY, CONCLUSIONS CHAPTER TEN AND RECOMMENDATIONS roughness and rutting progression and logistic regression is selected for modelling crack initiation and progression. Further discussion is provided in Chapter 5.

Roughness (IRI) and rutting (RD) variables were positively skewed in all datasets (NW, M, A, B and C) and the traffic loading (MESA) variable was also positively skewed for NW, class M and class C rutting datasets. Hence, these variables were transformed using natural log transformed (LN) function, making the models’ residuals close to normal in distribution with constant variance.

An exploratory analysis was carried out using the most popular estimation technique which is the application of traditional linear regression model (i.e. ordinary least squares method), for pavement deterioration based on one level of variance. This regression analysis was performed for the whole network and for each of the four road classes (M, A, B and C) for roughness, rutting and cracking datasets using SPSS software. The Durbin-Watson test from traditional regression analysis is used to test whether the residuals are correlated or not. The results of the exploratory analysis indicated that there is statistical evidence that the residuals are positively correlated in all datasets. Consequently, this meant that the traditional regression approach is inappropriate for analysing panel data (nested data) because it allows only for a single level of variation (i.e. only variance between observations).

Therefore, multilevel modelling approach that captures the effects of variation at multiple levels is selected to use for developing the models. It includes the effect of unobserved heterogeneity in the modelling process. The State of the Art approach for developing pavement deterioration models is presented in Chapter 5.

The study analysis has been performed using Hierarchical Linear and Nonlinear Modelling (HLM7) software and Statistical Package for Social Sciences (SPSS) software. The main outcomes of this research are listed below:

 Empirical deterministic regression models for pavement roughness and rutting progression within the gradual deterioration phase for the whole network sample (NW) and for each of the four road classes (M, A, B and C), as presented in Chapters 6 and 7 for roughness and rutting datasets, respectively.  Probabilistic models for pavement crack initiation and crack progression for the whole network sample, as presented in Chapter 8.

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 An assessment of the effects of all possible contributing factors to the progression of roughness and rutting and the initiation and progression of cracking, as presented in Chapters 6, 7 and 8, respectively.  An assessment of the performance of the four road classes (M, A, B and C) by comparing their pavement conditions and factors affecting the rate of pavement deterioration from the developed models, as presented in Chapter 9.

Three types of models have been fitted to each dataset for different purposes, and include null models (only intercept model), growth models (including only time as predictor) and conditional models (including additional predictor variables). The main outcomes and findings from roughness, rutting and cracking modelling are presented in the following sub-sections.

10.2.1 Roughness Models

The outcomes from modelling roughness datasets for the whole network (NW) and the four road classes (M, A, B and C) are presented in Table 10.1 and Table 10.2. Table 10.1 presents the developed roughness growth models, whereas Table 10.2 presents the developed roughness conditional models. Both tables provide R2 values and correction factors (CF) for each developed model. The CF for developed model is calculated and should be applied to the model prediction to remove bias caused by fitting the model to log transformed data. All developed models are statistically significant and the parameter estimates are also significant at the 95% confidence level with expected directions (signs). For the sets of network road sections used herein, the following results and findings can be drawn from the analysis approach performed:

 For the whole network and the four road classes, results of null models indicate that there are significant variances between time series observations, segments, highways and road classes. This indicates that the heterogeneity (variation) is a critical aspect of the data that should be considered not only between segments but also between highways and road classes. This also highlights that a separate model for each road class is preferable.

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Table 10.1: Developed roughness growth models

Dataset Predicted roughness growth model R2 CF

NW LN_IRI = 0.7517 + 0.0185 Time 59% 1.002

Class M LN_IRI = 0.5181 + 0.0183 Time 55% 1.001

Class A LN_IRI = 0.7633 + 0.0177 Time 61% 1.002

Class B LN_IRI = 0.8737 + 0.0176 Time 58% 1.002

Class C LN_IRI = 0.96 + 0.0207 Time 56% 1.002

Table 10.2: Developed roughness conditional models

Dataset Predicted roughness conditional model R2 CF

LN_IRI = 2.3535 + 0.0166 Time + 0.0086 MESA NW 60% 1.002 - 0.5374 SNC0 + 0.0541 SST

LN_IRI = 3.3552 + 0.0067 Time + 0.0115 MESA Class M 56% 1.001 - 0.786 SNC0

LN_IRI = 2.2292 + 0.0115 Time + 0.0231 MESA Class A 65% 1.002 - 0.4898 SNC0

LN_IRI = 1.8199 + 0.0146 Time + 0.0421 MESA Class B 61% 1.002 - 0.3626 SNC0 + 0.0923 SST + 0.0004 TMI

LN_IRI = 3.9291 + 0.0049 Time + 0.3749 MESA Class C 58% 1.002 - 1.1677 SNC0 + 0.0639 SST + 0.0005 TMI

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 Roughness grand mean values indicate that class C roads have higher roughness values than the other road classes followed by class B, then class A and class M. Also, it is found that class M roads have longer gradual phase of roughness progression than the other classes.  All developed roughness growth models indicate that the Time factor made a significant contribution to roughness progression and confirmed that the rates of roughness progression per year for all road classes are very close (0.02 IRI/year) where the roughness rate for class M= 0.0185, class A= 0.0179, class B= 0.0178 and class C= 0.0209 IRI/year. This indicates that different pavement segments within a network may deteriorate at the same rate but their roughness values could be different at the same time span due to their different initial pavement condition, design standards, construction quality or any other unobserved variables.  The whole network growth model indicates that it represents the average of all classes and it coincides with class A results due to their close roughness grand means (NW= 2.47 and class A= 2.46 m/km).  All developed conditional models indicate that time and traffic loading have positive contributions to roughness progression; however, initial pavement strength has negative contributions to roughness progression. Also, conditional models for the whole network, class B and class C roads indicate that sections in expansive soils are associated with higher roughness values than those in non-expansive subgrade soils. Climate condition is only significant in class B and class C models and indicates that higher roughness values are more likely in wet areas than in dry ones. Drainage condition has no significant contribution to roughness progression in the selected network.  For the whole network dataset, the most important predictor of pavement roughness progression is Time, followed by initial pavement strength then traffic. However, this is not true for the individual road classes. Except for the Time factor effect, the

effect of SNC0 was stronger than the other factors for class B and class C. This is due to lower standards of design and construction quality for these roads than the other road classes. Yet, the effect of MESA is stronger than the other factors for class M and class A due to higher traffic loading in these classes than the others. The effects of SST and TMI are significant in class B and class C roads, whereas both factors are not significant in class M and A roads. The reasons are the latter

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two classes have high standards of design and construction, well maintained, and generally exhibit high levels of smoothness. Also, road cross sections are generally high, with deep table drain inverts and sub-soil drains may also be present, and therefore there is a little opportunity for water to gain access to the pavement (Toole et al., 2004).  Pseudo R2 values have been calculated for evaluating the accuracy of the developed models and shown that more than half of the variance is accounted for by the Time factor in growth models for the NW (59%), class M (55%), class A (61%), class B (58%) and class C (56%). Also, more than half of the percentage of explainable variance is accounted for by the predictors in the conditional models for the NW (60%), class M (56%), class A (65%), class B (61%) and class C (58%). Although the conditional models have slightly better R2 values than the growth models, the latter could be used when information relevant to contributing variables are not available.  The developed models have been also assessed using the deviance statistic test and the results indicate that the time variable in the growth models and all IVs in the conditional models have improved the models’ descriptions of the data.  The diagnostic plots for apparent validations of the growth and conditional models fits exhibit that the residuals are normally distributed with means very close to zero, with small standard deviations (equal or less than 0.05), and limited ranges of residuals (between -0.2 IRI to 0.2 IRI). Also, they show that the predicted roughness values against observed values are very close to the line of equality with very high correlation with R2 ranging from 96% to 98%. These validation results indicate that the assumptions of normality and linearity are supported, which mean that all developed models exhibit apparent validity. Also, internal validation for all developed models has been performed using another dataset from the same network and the results indicate that all the developed models exhibit internal validity.  Multiple simulation scenarios from different combinations of predictor values have been performed and show reasonable outputs in terms of engineering judgement where the models predict the expected roughness progression over time under different assumed typical conditions.

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10.2.2 Rutting Models

The developed rutting progression models within the gradual phase of deterioration for sealed granular pavements of the NW data and for each of the four road classes (M, A, B and C) are presented in Table 10.3 and Table 10.4. Table 10.3 presents the developed rutting growth models, whereas Table 10.4 presents the developed rutting conditional models. Both tables present the R2 values and correction factors (CF) for each model. All models are statistically significant and the parameter estimates are also significant at the 95% confidence level with expected directions (signs). For the datasets used herein for modelling rutting progression, the following is a summary of findings:

 For the NW and the four road classes, rutting null models showed that there are significant variances between time series observations, segments, highways and road classes. This indicates that the heterogeneity is a critical aspect of the data that should not be ignored to include the effects of unobserved variables.  The developed models are statistically significant and the parameter estimates are also significant and have correct signs.  More than half of the percentage of explainable variance in the log transformed rutting values is accounted for by the predictors in the conditional model with R2 value more than 50%.  The rutting grand mean values from null models for all datasets (NW= 5.34, M= 5.02, A= 5.57, B= 5.42 and C= 5.17 mm) indicate that their means are very close (around 5 mm). This confirms that all road classes have been designed according to the expected impacts of contributing factors to rutting progression.  All the developed growth models indicate that the Time factor is significant and confirm that the rate of rutting progression per year for all road classes is very close (0.1 mm/year), where the rutting rate for class M= 0.1, class A= 0.09, class B= 0.07 and class C= 0.09 mm/year. This implies that the Victorian pavements have a good performance in terms of rutting. Also, it is found that class M roads have shorter rutting gradual phase than the other classes.  All conditional models indicate that Time, MESA and TMI have positive

contributions to rutting progression within the gradual phase. However, SNCi has negative contribution to rutting progression. Drainage condition has no significant contribution to pavement rutting in the selected network.

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Table 10.3: Developed rutting growth models

Dataset Predicted rutting growth model R2 CF

NW LN_RD = 1.3175 + 0.0841 Time 47% 1.022

Class M LN_RD = 1.2442 + 0.0957 Time 57% 1.023

Class A LN_RD = 1.3348 + 0.0876 Time 47% 1.025

Class B LN_RD = 1.3864 + 0.0716 Time 43% 1.020

Class C LN_RD = 1.2397 + 0.0903 Time 47% 1.021

Table 10.4: Developed rutting conditional models

Dataset Predicted rutting conditional model R2 CF

LN_RD = 2.3652 + 0.0561 Time + 0.0503 LN_MESA NW 51% 1.021 - 0.3795 SNCi + 0.0014 TMI

LN_RD = 3.0669 + 0.0561 Time + 0.0975 LN_MESA Class M 59% 1.022 - 0.5674 SNCi

LN_RD = 2.3165 + 0.0565 Time + 0.0262 MESA - Class A 56% 1.021 0.3674 SNCi

LN_RD = 2.9004 + 0.0353 Time + 0.0219 MESA - Class B 57% 1.015 0.6012 SNCi + 0.0031 TMI

LN_RD = 2.0274 + 0.0582 Time + 0.1218 LN_MESA Class C 60% 1.016 - 0.2645 SNCi + 0.002 TMI

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 In all developed conditional models, the effect of Time factor is stronger than the

other factors on rutting progression, followed by SNCi then MESA and TMI (where relevant). The effect of TMI is only significant in class B and class C roads. This confirms that the climate has an effect only on light duty pavements, considering their lower standards of design and construction than the other road classes, with varying sealed widths and unsealed shoulders. Also, road cross sections are generally low, with little crown height unless when on embankment sections. In all the conditional models, the effect of DRA is not significant due to the good condition of the drainage system in all network roads. Another reason for this is that the conditions of drainage system for the selected segments have been extracted from a database based on 2010 network condition data; therefore, its effect is considered as a fixed variable for each segment.  It is observed that the decreases in pavement strength of sealed granular pavements have stronger contribution to rutting progression than the increases in traffic loading.  The deviance statistic test results indicate that the Time variable in the growth models and all IVs in the conditional models have improved the models’ descriptions of the data.  The diagnostic plots for apparent validations of the growth and conditional models fits show that the residuals are normally distributed with means very close to zero, small standard deviations (less than 0.2), and with limited ranges of residuals (between -0.5 to 0.5 mm rut depth). Also, they show that the predicted roughness values against observed values are very close to the line of equality with very high correlation and R2 values ranging from 84% to 88%. This validation results indicate that the assumptions of normality and linearity are supported, which means that all developed models exhibit apparent validity. Also, internal validations for all developed models have been performed using another dataset from the same network and the results indicate that all the developed models exhibit internal validity.  Deterministic simulation plots for the developed growth and conditional models indicate that the models predict the expected rutting progression over time under different selected conditions.

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10.2.3 Cracking Models

The predicted probabilities for crack initiation and progression phases of sealed granular pavements for the NW data are presented in Table 10.5 and Table 10.6. Table 10.5 presents the predicted probabilities for cracking growth models, whereas Table 10.6 presents the predicted probabilities for cracking conditional models. All developed models are statistically significant and the parameter estimates are also significant at the 95% confidence level with expected correct signs. For the datasets used herein for modelling crack initiation and progression, the results from the analysis approach performed are summarized below:

Table 10.5: Developed cracking growth models

Predicted cracking growth model phase Crack Crack

1 P ini 1+ Exp ( ( 1. 7 + 0.5715 Time )) phase Initiation

1 P sig 1+ Exp( ( 5. 5 + 0. 9 Time))

1 1 P con 1+Exp( ( 5. 5 +0. 9 Time+ . 5 )) 1+ Exp( ( 5. 5 + 0. 9 Time))

1 1 P lim 1+Exp( ( 5. 5 +0. 9 Time+ . 19 7)) 1+Exp( ( 5. 5 +0. 9 Time+ . 5 )) Progression Progression phase

1 P 1 ins 1+Exp( ( 5. 5 + 0. 9 Time+ . 19 7) )

 The null model results indicate that unobserved heterogeneity is a critical aspect that should be considered between segments and between highways for modelling cracking. However, the heterogeneity between road classes for the selected network

271

SUMMARY, CONCLUSIONS CHAPTER TEN AND RECOMMENDATIONS

does not exist within the dataset used herein. For this reason separate models for each road class are not needed.  About 63% of the observations within segments in the selected network are expected to exhibit crack initiation during the study period. The average probability of uncracked pavements is 37%; hence, the odds of cracked pavement are 2 to 1.

Table 10.6: Developed cracking conditional models

Predicted cracking conditional model phase Crack Crack

Pini 1/ (1+ Exp (- (1.5848 + 0.5365 Time + 0.1819 MESA 1.1439 SNC0 + 0.2248 SST

+ 0.0071 TMI))) phase Initiation

Psig 1 (1+Exp ( ( . 00 7+0.5759 Time+0.0 58 MESA 1.0 9 SN +0. SST+

0.0018 TM )))

Pcon 1 (1+Exp ( ( . 00 7+ 0.5759 Time+0.0 58 MESA 1.0 9 SN +0. SST+

0.0018 TM + . 517 ))) ( 1 (1+Exp ( ( . 00 7+ 0.5759 Time+0.0 5 8 MESA 1.0 9 SN

phase + 0. SST+0.0018 TM ))))

Plim 1 (1+Exp ( ( . 00 7 +0.5759 Time+0.0 58 MESA 1.0 9 SN +0. SST+ Progression Progression

0.0018 TM + . 19 ))) ( 1 (1+Exp ( ( . 00 7+ 0.5759 Time+0.0 5 8 MESA 1.0 9 SN

+0. SST+0.0018 TM + . 51 7))))

Pins 1 (1 (1+Exp ( ( .00 7+0.5759 Time+0.0 58 MESA 1.0 9 SN +0. SST+

0.0018 TM + . 19 ))))

272

SUMMARY, CONCLUSIONS CHAPTER TEN AND RECOMMENDATIONS

 The study has shown that about 8% of the segments in the selected network are expected to exhibit significant cracking during the study period, 26% of them are expected to have considerable affected cracking areas, 29% of them have limited affected cracking areas, and 37% of them are expected to show insignificant affected areas (uncracked) during the study period.  From cracking observation data, the study shows that less cracked observations are expected in heavy duty pavements than light duty pavements due to more frequent crack sealing practice for the former pavements. Further, for all road classes the percent of insignificant affected area with cracking is higher than the other categories, with the percent of significant affected area being the lowest. Also, it shows that the significant affected area for class C is higher than for the other road classes, due to lower standards of design and less crack sealing operations.  The developed conditional models for crack initiation and progression indicate that Time, MESA, TMI and SST have positive contributions to crack initiation and

progression. However, SNC0 and SNCi have negative contributions to crack initiation and progression, respectively. Drainage condition has no significant contribution to pavement cracking in the selected network.  The effect of Time is stronger than the other variables on crack initiation and

progression. The effect of MESA is stronger than the effect of SNC0 in crack

initiation phase and the effect of SNCi is stronger than the effect of MESA in the crack progression phase.  The developed logistic models for cracking data have been evaluated by testing classification accuracy of cracking affected areas using cross-tabulation analysis. It is found that with the 50% estimated probability; about 82% of the observations are correctly predicted by the crack initiation model for the two categories (cracked and uncracked) which indicate a well estimated model. Also, with the 50% estimated probability, it is found that there is 65% success rate of the crack progression model for four categories (significant, considerable, limited and insignificant affected areas) which also indicates a well estimated model. These rates increase to 98% for crack initiation model and to 78% for crack progression model, when the estimated probability is increased to 60%. In addition, internal validation results show that all predicted probability models exhibit internal validity and have the ability to predict future conditions accurately.

273

SUMMARY, CONCLUSIONS CHAPTER TEN AND RECOMMENDATIONS

 The simulation plots for the developed models indicate that the models reasonably predict the probability of crack initiation and progression over time under different selected conditions. Hence, making them ideal for use in sensitivity analyses to investigate the effects of changing the included variables. It is found that about 50% of the predicted probability of being cracked occurs after the second year. Also, there is 100% probability of cracking being initiated after 10 years on the selected network. In all simulation scenarios, it is noticed that road sections in expansive soil areas are associated with slightly earlier crack initiation times than sections in non- expansive soil areas. Also, TMI has a clear effect on prediction probability of being cracked in very wet climates.  The cumulative probabilities of crack progression to stay at a certain cracking category or below over time show that there is a 50% probability that the pavement would have a significant affected area or lower at 9 years, and this probability increases to about 100% at 15 years. There is a 50% probability that the pavement would have a considerable affected area or lower at 5 years, and this probability increases to about 100% at 11 years. Also, there is a 50% probability that the pavement would have a limited affected area or lower (insignificant affected area) after 2 years, and this probability increases to about 100% at 8 years.  It is found that the highest condition probability for sections within 2 years or less is insignificant cracking, those within 3 and 4 years have a high probability of being in limited cracking condition, considerable condition between 5 and 8 years and significant condition at 9 years and beyond.

10.3 Conclusions

The following conclusions can be drawn from the analysis approach, testing and validation used in the development of deterioration models in this study:

 Multilevel modelling approach is a successful approach for advanced analysis of pavement deterioration models. The procedure outlined is quite general, and can be applied to any pavement condition variable that has continuous data or ordinal classification with data that has a hierarchical structure.

274

SUMMARY, CONCLUSIONS CHAPTER TEN AND RECOMMENDATIONS

 The data preparation process is an extremely important stage for the development of robust performance models; hence, strong emphasis should be put into data aligning, screening and filtering. Before developing pavement deterioration models that are based on time series data, all condition data should be aligned to allow condition data of the same road segments to be accurately compared over time. This is due to the variation in chainages of pavement condition over different years.  The development of pavement deterioration models that are based on historical time series data for many pavement segments (panel data); to estimate future condition, require an examination for the cause of heterogeneity across segments data. The study demonstrated that unobserved heterogeneity is a critical aspect that should be considered not only between segments but between highways and road classes as well.  The effects of observed and unobserved variables are incorporated into the models by incorporating the effect of variance between time series observations, segments, highways and road classes.  The study has concluded that a separate model for each road class provides more realistic predictions than the overall network model, which would help researchers to better understand the effect of contributing factors. The models will also help road agencies in developing more efficient maintenance programs.  The probabilistic model format for cracking data provides such flexibility in the application of the model when triggers are set according to risk considerations.  Different pavement segments within a network may deteriorate at the same rate but their roughness values could be different at the same time span due to their different initial pavement condition, design standards, construction quality or any other unobserved variables.  Light duty pavements have higher roughness values than the heavy duty pavements but both have very close rutting values. Also, the heavy duty pavements have longer roughness gradual phase and shorter rutting gradual phase.  The effect of initial pavement strength on roughness progression is stronger than the other factors for light duty pavements. Yet, the effect of traffic loading is stronger than the other factors for heavy duty pavements.  Road sections on expansive subgrade soils are associated with higher roughness values and cracking area than those in non-expansive subgrade soils. Also, higher

275

SUMMARY, CONCLUSIONS CHAPTER TEN AND RECOMMENDATIONS

roughness, rutting and cracking are more likely in wet climate areas than in dry areas.  The environmental factors such as climate condition and subgrade soil type have an impact on roughness and rutting progressions for only light duty pavements only.  The decreases in pavement strength of sealed granular pavements have stronger contribution to rutting progression than the increases in traffic loading.  The effect of time is stronger than the other variables on rutting progression, crack initiation and crack progression.  Light duty pavements exhibit higher percent of cracking areas ‘significant affected areas’ than heavy duty pavements.  The effect of traffic loading is stronger than the effect of initial pavement strength in crack initiation phase. However, the effect of pavement strength at any age is stronger than the effect of traffic loading in the crack progression phase.  The highest condition probability for sections within 2 years or less is insignificant cracking ‘insignificant affected areas’, those within 3 and 4 years have a high probability of being in limited cracking condition ‘limited affected areas’, considerable condition ‘considerable affected areas’ between 5 and 8 years and significant condition ‘significant affected areas’ at 9 years and beyond.

10.4 Recommendations

For more conclusive results and to further improve the pavement deterioration models, the following recommendations are proposed:

 All the developed models in this research study are empirical regression models. The main disadvantage of regression models is that they can be used only within the range of input data (independent variables) used in their development. Therefore, it is recommended that the developed models should be used only within the data limits and only for spray sealed pavements.  Although the results of NW cracking models show that there are no significant variances among the four road classes (M, A, B and C) for the selected sample network, it is recommended that a separate model for light and heavy duty pavements be developed to study the effect of contribution factors.

276

SUMMARY, CONCLUSIONS CHAPTER TEN AND RECOMMENDATIONS

 This research has demonstrated that only the main effects of all available independent variables are included in the models. However, it is recommended that the interaction between the independent variables should be investigated with future models.  With the availability of longer time span for time series pavement condition data; more powerful models could be developed.  Further development of models should be undertaken for the initial and rapid deterioration phases of roughness and rutting to further improve the understanding of pavement deterioration process within whole pavement design life.  It is anticipated that more sound deterioration models could be estimated by including more independent variables such as pavement thickness, material quality and road geometry.

277

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APPENDIX - A

A. APPENDIX - A LAYOUTS OF TYPICAL ERD FILE AND EVENT FILE A.1 Sample of ERD File

Figure A-1 shows the ERD file for section 2A of Princes highway east site in year 2009. The figure illustrates that the file contains road profile elevation values for both left and right wheel paths with detailed information about start chainage (80624), end chainage (90624) and data interval (0.04972).

Figure A-1: Sample of ERD file for Princes highway east site, section 2A, 2009

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A.2 Sample of Event File

Figure A-2 shows the Event file for section 3A of Hume highway site in year 2010. The figure illustrates that the file contains information about features that contribute to any inaccurate road profile elevation reading.

Figure A-2: Sample of Event file for Hume highway site, section 3A, 2010

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B. APPENDIX - B

DESCRIPTION OF WORKING PRINCIPLES OF CLIMATE TOOL AND SAMPLES OF CALCULATING SHEETS

The Excel based climate tool is used to extract the required climate time series data for performance prediction (Byrne and Aguir, 2010). In this tool, the following working sheets are used:

1. Query Management Form

This form is shown in Figure B-1. From this form the majority of the work is performed and it is designed to ask queries of the climate database. The query requests time series climate data for each GPS coordinate (latitude and longitude) provided by the user. As there are multiple climate types and a large range of years, the user can be quite specific about the data they wish extracted by the query. In this study, Thornthwaite method 2 was selected with the historical and simulated years (for which condition data is available for each road section).

2. Data Input

From the query management form, there are two options to input data which are import GPS and check data. The latter option is used in this study. Rather than importing through a prepared text file it is required to copy data directly into the Data Entry sheet as shown in Figure B-2. Before analysis the check data button must be pressed so that the software can identify the amount of data imported and check which GPS coordinates are suitable for analysis. The number of coordinates is restricted to 250. Therefore, it was required to run the tool more than one time for each road section depending on the number of 100m segments.

3. Data Output

The output of selected historical and simulated climatic time series data is obtained as shown in output sheet in Figure B-3.

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Figure B-1: Query management form for climate tool

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Figure B-2: Data Entry sheet for climate tool

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Figure B-3: Data output sheet for climate tool

299

APPENDIX - C

C. APPENDIX - C

DESCRIPTION OF WORKING SHEETS OF IN-HOUSE EXCEL BASED TOOL FOR ALIGNING ROW PROFILE DATA

In-House Excel based tool contains a number of working sheets which are used for alignment and synchronization of longitudinal road profile data. In this study, only two spread sheets were used for alignment process. Figure C-1 shows the required data entry from ERD data file for one year of profile data for one section.

Figure C-2 shows worksheet for shifting start and end points of profile data to obtain the new spacing interval between these data after a number of trials.

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Figure C-1: Data entry worksheet for In-House Excel based tool

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Figure C-2: Shifting worksheet for In-House Excel based tool

302

APPENDIX - D

D. APPENDIX – D

BRIFE DESCRIPTION OF WORKING PRINCIPLES OF LRP TOOL AND SAMPLE OF CALCULATING SHEET

1. Principles of estimating pavement deterioration from LRP tool:

The following principles were observed from the time series of the three condition data (roughness, rutting and cracking) to select segments with positive progression of deterioration (Martin and Hoque, 2006):  Deterioration estimates measure the underlying rate of the latest deterioration, that is, the deterioration of the pavement that is not influenced by the immediate impact of maintenance treatments (Figure D-1 for roughness example).  Deterioration estimates are made from data post the latest rehabilitation treatment (Figure D-2 for roughness example).  Estimates are based on an absolute minimum of three consecutive valid data points, although four consecutive points are more reliable.  Some allowance for noise in the data must be considered, including identifying outliers that are errors in measurement and not related to previous or later measurements.

2. Main observations from using Linear Rate of Progression (LRP) tool:

From Figure D-3, it can be noticed that two sets of results are given in LRP result sheet; one for early deterioration and one for latest deterioration. The latest one is usually more valid and should be selected for the analysis. The two results are most expected to be different if there are two cycles of pavement deterioration, as shown in Figure D-4. For the case of single cycle of pavement deterioration, the early and latest deterioration results are exactly the same. In the results sheet, the results of a record are given only when the trend of the data for that record exists, either positive or negative rate of deterioration (as shown in Figure D-5 and Figure D-6); otherwise the “Error! No Solution” message is displayed (i.e. there is no change in pavement deterioration over time), as shown in Figure D-7 . In addition to that, the “Error! Not Enough Points” message is displayed when the record sample size is less than 3 observations as shown in Figure D-8.

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Figure D-1: ‘Latest’ deterioration estimate (for roughness example) (Martin and Hoque, 2006)

Figure D-2: Estimated deterioration post rehabilitation (for roughness example) (Martin and Hoque, 2006)

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Result sheet for LRP tool for LRP sheet Result Figure D-3Figure :

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Figure D-4: Example of segment with two cycles of pavement deterioration

Figure D-5: Example of segment with positive progression of deterioration

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Figure D-6: Example of segment with negative progression of deterioration

Figure D-7: Example of segment with “Error! No Solution”

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Figure D-8: Example of segment with “Error! Not Enough Points”

308

APPENDIX - E

E. APPENDIX – E

SAMPLES OF PREPARED DATASETS E.1 Sample of Prepared Roughness Dataset

. Table E.1: Sample of prepared roughness dataset E.1: preparedTable of roughness Sample

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dataset (Continued)

roughness

prepared of .1: Sample E

Table

310

APPENDIX - E

Table E.1: Sample of prepared roughness dataset prepared of E.1:roughness Table (Continued) Sample

311

APPENDIX - E

E.2 Sample of Prepared Rutting Dataset

prepared of datasetE.2: rutting Table Sample

312

APPENDIX - E

prepared of datasetE.2:rutting Table (Continued) Sample

313

APPENDIX - E

E.3 Sample of Prepared Cracking Dataset

dataset

: Sample of prepared of cracking : Sample 3 . E Table Table

314

APPENDIX - E

Table E.3: Sample of prepared of E.3:cracking dataset Table (Continued) Sample

315

APPENDIX - F

F. APPENDIX – F

TRANSFORMING OF MODEL VARIABLES

F.1 Roughness Dataset

F.1.1 Whole Network (NW): Transformation for Roughness Data

Table F.1: Statistics of roughness data and its transformed data for the whole network roughness dataset

Transformed roughness Statistics Roughness (IRI) (LN_IRI)* Number of observations 34789 34789 Mean 2.797 0.986 Standard deviation 0.835 0.292 Variance 0.698 0.085 Skewness 0.799 0.072 *LN_IRI is the natural log of IRI

(a) (b)

Figure F-1: Frequency histogram plots for the NW roughness data (a) before transformation and (b) after transformation

316

APPENDIX - F

F.1.2 Class M: Transformation for Roughness Data

Table F.2: Statistics of roughness data and its transformed data for class M roughness dataset

Transformed roughness Statistics Roughness (IRI) (LN_IRI)* Number of observations 2623 2623 Mean 1.943 0.628 Standard deviation 0.555 0.263 Variance 0.308 0.069 Skewness 1.206 0.562 *LN_IRI is the natural log of IRI

(a) (b)

Figure F-2: Frequency histogram plots for class M roughness data (a) before transformation

and (b) after transformation

317

APPENDIX - F

F.1.3 Class A: Transformation for Roughness Data

Table F.3: Statistics of roughness data and its transformed data for class A roughness dataset

Transformed roughness Statistics Roughness (IRI) (LN_IRI)* Number of observations 12191 12191 Mean 2.549 0.905 Standard deviation 0.630 0.247 Variance 0.397 0.061 Skewness 0.409 0.001 *LN_IRI is the natural log of IRI

(a) (b)

Figure F-3: Frequency histogram plots for class A roughness data (a) before transformation and (b) after transformation

318

APPENDIX - F

F.1.4 Class B: Transformation for Roughness Data

Table F.4: Statistics of roughness data and its transformed data for class B roughness dataset

Transformed roughness Statistics Roughness (IRI) (LN_IRI)* Number of observations 9300 9300 Mean 2.904 1.033 Standard deviation 0.778 0.253 Variance 0.606 0.064 Skewness 0.957 0.437 *LN_IRI is the natural log of IRI

(a) (b)

Figure F-4: Frequency histogram plots for class B roughness data (a) before transformation and (b) after transformation

319

APPENDIX - F

F.1.5 Class C: Transformation for Roughness Data

Table F.5: Statistics of roughness data and its transformed data for class C roughness dataset

Transformed roughness Statistics Roughness (IRI) (LN_IRI)* Number of observations 10675 10675 Mean 3.196 1.124 Standard deviation 0.893 0.274 Variance 0.798 0.075 Skewness 0.659 0.118 *LN_IRI is the natural log of IRI

(a) (b)

Figure F-5: Frequency histogram plots for class C roughness data (a) before

transformation and (b) after transformation

320

APPENDIX - F

F.2 Rutting Dataset

F.2.1 Whole Network (NW) F.2.1.1 Transformation for Rutting Data

Table F.6: Statistics of rutting data and its transformed data for the whole network rutting dataset

Transformed rutting Statistics Rutting (RD) (LN_RD)* Number of observations 41659 41659 Mean 5.750 1.637 Standard deviation 2.823 0.479 Variance 7.972 0.229 Skewness 1.254 -0.048 *LN_RD is the natural log of RD

(a) (b)

Figure F-6: Frequency histogram plots for the whole network rutting data (a) before transformation and (b) after transformation

321

APPENDIX - F

F.2.1.2 Transformation for Traffic Loading Data

Table F.7: Statistics of traffic loading data and its transformed data for the whole network rutting dataset

Transformed traffic loading Statistics Traffic loading (MESA) (LN_MESA)* Number of observations 41659 41659 Mean 2.021 -0.259 Standard deviation 3.076 1.559 Variance 9.464 2.431 Skewness 3.533 -0.464 *LN_MESA is the natural log of MESA

(a) (b)

Figure F-7: Frequency histogram plots for the whole network traffic loading data (a) before transformation and (b) after transformation

322

APPENDIX - F

F.2.2 Class M F.2.2.1 Transformation for Rutting Data

Table F.8: Statistics of rutting data and its transformed data for class M rutting dataset

Transformed rutting Statistics Rutting (RD) (LN_RD)* Number of observations 3502 3502 Mean 5.190 1.542 Standard deviation 2.463 0.461 Variance 6.065 0.212 Skewness 1.272 -0.060 *LN_RD is the natural log of RD

(a) (b)

Figure F-8: Frequency histogram plots for class M rutting data (a) before transformation and (b) after transformation

323

APPENDIX - F

F.2.2.2 Transformation for Traffic Loading Data

Table F.9: Statistics of traffic loading data and its transformed data for class M rutting dataset

Transformed traffic loading Statistics Traffic loading (MESA) (LN_MESA)* Number of observations 3502 3502 Mean 7.664 1.794 Standard deviation 5.881 0.684 Variance 34.588 0.468 Skewness 1.654 0.255 *LN_MESA is the natural log of MESA

(a) (b)

Figure F-9: Frequency histogram plots for class M traffic loading data (a) before transformation and (b) after transformation

324

APPENDIX - F

E.2.3 Class A: Transformation for Rutting Data

Table F.10: Statistics of rutting data and its transformed data for class A rutting dataset

Transformed rutting Statistics Rutting (RD) (LN_RD)*

Number of observations 13841 13841

Mean 5.940 1.670

Standard deviation 2.861 0.478

Variance 8.185 0.229 Skewness 1.109 -0.108 *LN_RD is the natural log of RD

(a) (b)

Figure F-10: Frequency histogram plots for class A rutting data (a) before transformation and (b) after transformation

325

APPENDIX - F

F.2.4 Class B: Transformation for Rutting Data

Table F.11: Statistics of rutting data and its transformed data for class B rutting dataset

Transformed rutting Statistics Rutting (RD) (LN_RD)*

Number of observations 12358 12358

Mean 5.840 1.658

Standard deviation 2.771 0.468

Variance 7.676 0.219 Skewness 1.160 -0.095 *LN_RD is the natural log of RD

(a) (b)

Figure F-11: Frequency histogram plots for class B rutting data (a) before transformation and (b) after transformation

326

APPENDIX - F

F.2.5 Class C F.2.5.1 Transformation for Rutting Data

Table F.12: Statistics of rutting data and its transformed data for class C rutting dataset

Transformed rutting Statistics Rutting (RD) (LN_RD)* Number of observations 11958 11958 Mean 5.610 1.604 Standard deviation 2.904 0.490 Variance 8.432 0.240 Skewness 1.490 0.064 *LN_RD is the natural log of RD

(a) (b)

Figure F-12: Frequency histogram plots for class C rutting data (a) before transformation and (b) after transformation

327

APPENDIX - F

F.2.5.2 Transformation for Traffic Loading Data

Table F.13: Statistics of traffic loading data and its transformed data for class C rutting dataset

Transformed traffic loading Statistics Traffic loading (MESA) (LN_MESA)* Number of observations 11958 11958 Mean 0.503 -1.054 Standard deviation 0.469 0.081 Variance 0.220 0.177 Skewness 2.178 -0.233 *LN_MESA is the natural log of MESA

(a) (b)

Figure F-13: Frequency histogram plots for class C traffic loading data (a) before transformation and (b) after transformation

328

APPENDIX - G

G. APPENDIX – G

SAMPLE OF PREPARING DATASET FOR MULTILEVEL ANALYSIS

G.1 SPSS Input Files for Multilevel Model

Samples of preparing SPSS input files for multilevel analysis are shown in the following tables. Level-1 file in Table G.1 shows only time series data for the first two sections of the first highway in the first road class. This table containes only variables which are changed over time.

Table G.1: Sample of Level-1 file

Class No. Highway No. Section No. Time series IRI Time MESA TMI SNCi LN_IRI LN_MESA

1 1 1 1 1998 2 1 1 1 1999 1.83 1 0.302 -15 2.54 0.61 -1.197 3 1 1 1 2000 4 1 1 1 2001 1.9 3 0.417 -16 2.437 0.64 -0.875 5 1 1 1 2002 6 1 1 1 2003 1.91 5 0.435 -16 2.372 0.65 -0.832 7 1 1 1 2004 8 1 1 1 2005 1.94 7 0.651 -20 2.222 0.66 -0.429 9 1 1 1 2006 10 1 1 1 2007 2.02 9 0.781 -20 2.169 0.7 -0.247 11 1 1 1 2008 12 1 1 1 2009 2.55 11 0.952 -21 2.009 0.94 -0.049 13 1 1 1 2010 14 1 1 2 1998 15 1 1 2 1999 2.02 1 0.291 -15 2.858 0.7 -1.234 16 1 1 2 2000 17 1 1 2 2001 2.31 3 0.39 -15 2.458 0.84 -0.942 18 1 1 2 2002 19 1 1 2 2003 2.4 5 0.506 -16 2.353 0.88 -0.681 20 1 1 2 2004 21 1 1 2 2005 2.23 7 0.74 -20 2.133 0.8 -0.301 22 1 1 2 2006 23 1 1 2 2007 2.37 9 0.858 -20 2.017 0.86 -0.153 24 1 1 2 2008 25 1 1 2 2009 2.42 11 0.977 -21 1.897 0.88 -0.023 26 1 1 2 2010

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APPENDIX - G

Level-2 file in Table G.2 shows only the first twenty sections of the first highway in the first road class. This table containes only variables which are changed from section to another.

Table G.2: Sample of Level-2 file

Class No. Highway No. Section No. Drainage Soil SNCo

1 1 1 1 Poor Expansive 2.794 2 1 1 2 Poor Expansive 2.793 3 1 1 4 Poor Expansive 2.798 4 1 1 6 Poor Expansive 2.798 5 1 1 11 Poor Expansive 2.799 6 1 1 14 Poor Expansive 2.795 7 1 1 16 Poor Expansive 2.793 8 1 1 18 Poor Expansive 2.79 9 1 1 19 Poor Expansive 2.791 10 1 1 21 Poor Expansive 2.791 11 1 1 22 Poor Expansive 2.788 12 1 1 23 Poor Expansive 2.79 13 1 1 24 Poor Expansive 2.79 14 1 1 27 Poor Expansive 2.79 15 1 1 29 Poor Expansive 2.791 16 1 1 30 Poor Expansive 2.791 17 1 1 31 Poor Expansive 2.79 18 1 1 34 Poor Expansive 2.794 19 1 1 35 Poor Expansive 2.792 20 1 1 38 Poor Expansive 2.788

Level-3 file in Table G.3 shows the selected forty highways in the four road class. The table does not containe any variable because no data avaible which could be considered they are different in one highway to another. Also, Level-4 file in Table G.4 shows the four road class in the network. This last file does not included in three level model. It can be note that the average rate variable is included in Table G.3 and Table G.4 to help for administrating the analysis.

330

APPENDIX - G

Table G.3: Sample of Level-3 file

Class No. Highway No. Average rate 1 1 1 0.44 2 1 2 1.30 3 1 3 2.91 4 1 4 2.46 5 1 5 0.74 6 1 6 2.00 7 1 7 0.97 8 2 8 3.51 9 2 9 3.68 10 2 10 3.84 11 2 11 0.01 12 2 12 0.18 13 2 13 1.34 14 2 14 1.51 15 2 15 0.68 16 2 16 0.84 17 2 17 0.01 18 2 18 1.18 19 3 19 1.34 20 3 20 1.52 21 3 21 0.35 22 3 22 0,790 23 3 23 0.87 24 3 24 2.40 25 3 25 1.46 26 3 26 1.60 27 3 27 0.59 28 3 28 2.66 29 4 29 1.64 30 4 30 1.60 31 4 31 1.57 32 4 32 1.53 33 4 33 1.49 34 4 34 1.46 35 4 35 1.42 36 4 36 1.39 37 4 37 1.35 38 4 38 1.32 39 4 39 0.87 40 4 40 2.40

331

APPENDIX - G

Table G.4: Sample of Level-4 file

Class No. Average rate 1 1 0.44 2 2 1.18 3 3 1.34 4 4 2.40

G.2 Working with HLM7 Software

Figure G-1, Figure G-2, Figure G-3, Figure G-4 and Figure G-5 show some basic dialog boxes for HLM7 software. More details to build up the multilevel model are illustrated in the Hierarchical Linear and Nonlinear Modeling manual (Raudenbush et al., 2011).

Figure G-1: The file menu for HLM window

332

APPENDIX - G

Figure G-2: Dialog box for selecting type of Multilevel Data Matrix (MDM)

Figure G-3: Dialog box for making Multilevel Data Matrix (MDM)

333

APPENDIX - G

Figure G-4: Dialog box for the basic model specifications in HLM7 software

334

APPENDIX - G

Figure G-5: Example of four level rutting model window

335

APPENDIX - H

H. APPENDIX – H

APPARENT VALIDATION PLOTS FOR ROUGHNESS MODELS

H.1 Apparent Validation for Class M

(a)

2 R = 98%

(b)

Figure H-1: Apparent validation for the (b)developed roughness growth model for the class M roads, (a) Residual histogram and (b) Line of equality

336

APPENDIX - H

(a)

R2 = 98%

(b)

Figure H-2: Apparent validation for the developed roughness conditional model for the class M roads, (a) Residual histogram and (b) Line of equality

337

APPENDIX - H

H.2 Apparent Validation for Class A

(a)

R2 = 96%

(b)

Figure H-3: Apparent validation for the developed roughness growth model for the class A roads, (a) Residual histogram and (b) Line of equality

338

APPENDIX - H

(a)

R2 = 96%

(b)

Figure H-4: Apparent validation for the developed roughness conditional model for the class A roads, (a) Residual histogram and (b) Line of equality

339

APPENDIX - H

H.3 Apparent Validation for Class B

(a)

2 R = 96%

(b)

Figure H-5: Apparent validation for the developed roughness growth model for the class B roads, (a) Residual histogram and (b) Line of equality

340

APPENDIX - H

(a)

2 R = 96%

(b)

Figure H-6: Apparent validation for the developed roughness conditional model for the class B roads, (a) Residual histogram and (b) Line of equality

341

APPENDIX - H

H.4 Apparent Validation for Class C

(a)

2 R = 97%

(b)

Figure H-7: Apparent validation for the developed roughness growth model for the

class C roads, (a) Residual histogram and (b) Line of equality

342

APPENDIX - H

(a)

R2 = 98%

(b)

Figure H-8: Apparent validation for the developed roughness conditional model for the class C roads, (a) Residual histogram and (b) Line of equality

343

APPENDIX - I

I. APPENDIX – I

DETERMINISTIC SIMULATIONS FOR ROUGHNESS MODELS

I.1 Simulation of NW Conditional Roughness Model

Figure I-1: Simulation for the NW conditional roughness progression model over time

for changes in MESA

Figure I-2: Simulation for the NW conditional roughness progression model over time

for changes in SNC0

344

APPENDIX - I

I.2 Simulation of Class M Conditional Roughness Model

Figure I-3: Simulation for the class M conditional roughness progression model over

time for changes in MESA

Figure I-4: Simulation for the class M conditional roughness progression model over

time for changes in SNC0

345

APPENDIX - I

I.3 Simulation of Class A Conditional Roughness Model

Figure I-5: Simulation for the class A conditional roughness progression model over

time for changes in MESA

Figure I-6: Simulation for the class A conditional roughness progression model over

time for changes in SNC0

346

APPENDIX - I

I.4 Simulation of Class B Conditional Roughness Model

Figure I-7: Simulation for the class B conditional roughness progression model over

time for changes in MESA

Figure I-8: Simulation for the class B conditional roughness progression model over

time for changes in SNC0

347

APPENDIX - I

Figure I-9: Simulation for the class B conditional roughness progression model over

time for changes in TMI

I.5 Simulation of Class C Conditional Roughness Model

Figure I-10: Simulation for the class C conditional roughness progression model over

time for changes in MESA

348

APPENDIX - I

Figure I-11: Simulation for the class C conditional roughness progression model over

time for changes in SNC0

Figure I-12: Simulation for the class C conditional roughness progression model over

time for changes in TMI

349

APPENDIX - J

J. APPENDIX – J

APPARENT VALIDATION PLOTS FOR RUTTING MODELS

J.1 Apparent Validation for Class M

(a)

R2 = 86%

(b)

Figure J-1: Apparent validation for the developed rutting growth model for the class M, (a) Residual histogram and (b) Line of equality

350

APPENDIX - J

(a)

R2 = 86%

(b)

Figure J-2: Apparent validation for the developed rutting conditional model for the class M, (a) Residual histogram and (b) Line of equality

351

APPENDIX - J

J.2 Apparent Validation for Class A

(a)

R2 = 85%

(b)

Figure J-3: Apparent validation for the developed rutting growth model for the class A, (a) Residual histogram and (b) Line of equality

352

APPENDIX - J

(a)

R2 = 84%

(b)

Figure J-4: Apparent validation for the developed rutting conditional model for the class A, (a) Residual histogram and (b) Line of equality

353

APPENDIX - J

J.3 Apparent Validation for Class B

(a)

R2 = 87%

(b)

Figure J-5: Apparent validation for the developed rutting growth model for the class B, (a) Residual histogram and (b) Line of equality

354

APPENDIX - J

(a)

R2 = 87%

(b)

Figure J-6: Apparent validation for the developed rutting conditional model for the class B, (a) Residual histogram and (b) Line of equality

355

APPENDIX - J

J.4 Apparent Validation for Class C

(a)

R2 = 88%

(b)

Figure J-7: Apparent validation for the developed rutting growth model for the class C, (a) Residual histogram and (b) Line of equality

356

APPENDIX - J

(a)

2 R = 88%

(b)

Figure J-8: Apparent validation for the developed rutting conditional model for the class C, (a) Residual histogram and (b) Line of equality

357

APPENDIX - K

K. APPENDIX – K

DETERMINISTIC SIMULATIONS FOR RUTTING MODELS

K.1 Simulation of NW Conditional Rutting Model

Figure K-1: Simulation for the NW conditional rutting progression model over time

for changes in MESA

Figure K-2: Simulation for the NW conditional rutting progression model over time

for changes in SNCi

358

APPENDIX - K

Figure K-3: Simulation for the NW conditional rutting progression model over time

for changes in TMI

K.2 Simulation of Class M Conditional Rutting Model

Figure K-4 : Simulation for the class M conditional rutting progression model over

time for changes in MESA

359

APPENDIX - K

Figure K-5: Simulation for the class M conditional rutting progression model over

time for changes in SNCi

K.3 Simulation of Class A Conditional Rutting Model

Figure K-6: Simulation for the class A conditional rutting progression model over

time for changes in MESA

360

APPENDIX - K

Figure K-7: Simulation for the class A conditional rutting progression model over

time for changes in SNCi

K.4 Simulation of Class B Conditional Rutting Model

Figure K-8: Simulation for the class B conditional rutting progression model over

time for changes in MESA

361

APPENDIX - K

Figure K-9 : Simulation for the class B conditional rutting progression model over

time for changes in SNCi

Figure K-10: Simulation for the class B conditional rutting progression model over

time for changes in TMI

362

APPENDIX - K

K.5 Simulation of Class C Conditional Rutting Model

Figure K-11: Simulation for the class C conditional rutting progression model over

time for changes in MESA

Figure K-12: Simulation for the class C conditional rutting progression model over

time for changes in SNCi

363

APPENDIX - K

Figure K-13: Simulation for the class C conditional rutting progression model over

time for changes in TMI

364

APPENDIX - L

L. APPENDIX – L

SIMULATIONS FOR CRACKING MODELS

L.1 Simulation of NW Conditional Crack Initiation Model

Figure L-1: Simulation for the NW conditional crack initiation model over time for

changes in MESA

Figure L-2: Simulation for the NW conditional crack initiation model over time for

changes in SNC0

365

APPENDIX - L

Figure L-3: Simulation for the NW conditional crack initiation model over time for

changes in TMI

L.2 Simulation of NW Conditional Crack Progression Model

Figure L-4 : Simulation for the cumulative probability of NW conditional crack

progression model for significant affected area category with changes in SNCi

366

APPENDIX - L

Figure L-5 : Simulation for the cumulative probability of NW conditional crack progression model for considerable affected area category with changes in SNCi

Figure L-6: Simulation for the cumulative probability of NW conditional crack

progression model for limited affected area category with changes in SNCi

367

APPENDIX - L

Figure L-7: Simulation for the probability of NW conditional crack progression

model for significant affected area category with changes in SNCi

Figure L-8 : Simulation for the probability of NW conditional crack progression

model for considerable affected area category with changes in SNCi

368

APPENDIX - L

Figure L-9 : Simulation for the probability of NW conditional crack progression

model for limited affected area category with changes in SNCi

Figure L-10: Simulation for the probability of NW conditional crack progression

model for insignificant affected area category with changes in SNCi

369