.15.)? 5:3 .. . :3 35% .9... f. i ‘1‘... n.‘ lllllllllllllllllllllllllllllllHllllllllllllll c" _ 193 01779 2080 LIBRARY Michigan State University This is to certify that the dissertation entitled FRAMEWORK FOR INCORPORATING RUTTING PREDICTION MODEL IN THE RELIABILITY-BASED DESIGN OF FLEXIBLE PAVEMENTS presented by Hyung Bae Kim has been accepted towards fulfillment of the requirements for Ph .D . degree in Civil Engineering Major professor Date A //5 //€l Ci MS U is an Affirmative Action/Equal Opportunity Institution 0-12771 PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINB return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 1M animus-m4 FRAMEWORK FOR INCORPORATING RUTTING PREDICTION MODEL IN THE RELIABILITY-BASED DESIGN OF FLEXIBLE PAVEMENTS By Hyung Bae Kim A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTER OF PHILOSOPHY Department of Civil and Environmental Engineering 1 999 ME“ OR RE 3105151 Procedures {'0 usmo 9“ mechanistic-en" transfer fundiC and control 0 imations in m model bias This 51! predmion mod element analysi flexible pa'vemf flexible pax‘eme; The men the combination fattors such as Cemporium Th ABSTRACT FRAMEWORK FOR INCORPORATING RUTTING PREDICTION MODEL IN THE RELIABILITY-BASED DESIGN OF FLEXIBLE PAVEIVIENTS By Hyung Bae Kim Most state highway agencies (SHA’s) are being encouraged to change their design procedures for flexible pavements from an empirical-based procedure such as the AASHTO guide to mechanistic-based approaches. A successfiil implementation of mechanistic-empirical (M-E) pavement design requires i) the development of robust transfer functions to accurately predict pavement performance, and ii) the characterization and control of the uncertainties associated with M-E design procedures, including variations in material and cross-sectional properties, inaccuracy of traffic estimation, and model bias. This study presents the procedure and results of calibrating the existing rutting prediction model in MICHPAVE, a computer program for linear and non-linear finite element analysis of the pavement structure, using field data from thirty-nine in-service flexible pavement sections in Michigan, and a framework for a reliability-based M-E flexible pavement design approach using the calibrated rutting prediction model. The new rutting prediction model has a nonlinear form developed by considering the combination of mechanistic factors such as primary pavement responses and empirical factors such as pavement material and cross-sectional properties and environmental components. The model is validated using data from eleven in-service flexible pavements and the data fr Performance (1 In the 1 the reliability engineering p procedure are Variation. lmpr error The firs into uncenaint Based Fitment pep PTOcedures arr RESlSiance Fat 158 design pror- fir“ Order Cc paraIITEIers an: theorem“ Saf Professional fa use a“ “flame manages to z: and the data from twenty four general pavement sections from the Long Term Pavement Performance (LTPP-GPS) database. In the reliability analysis of pavement performance, a model to accurately evaluate the reliability of flexible pavement structure is introduced by incorporating practical engineering probabilistic techniques. The uncertainties associated with the design procedure are categorized into four parts based on the sources of uncertainty: spatial variation, imprecision in quantifying site conditions and traffic, model bias, and statistical error. The first two are integrated into uncertainties of design parameters; the latter two into uncertainties that stem from systematic errors. Based on the probabilistic techniques introduced in the reliability analysis of pavement performance, two practical reliability-based M-E flexible pavement design procedures are introduced; Reliability Factor Design (RFD) approach and Load and Resistance Factor Design (LRFD) approach. In order to characterize the uncertainties of the design procedure, the RFD approach employs the overall standard deviation that is the first order combination of the standard deviations due to uncertainties of design parameters and systematic errors in the design model, while the LRFD approach considers the overall safety factor based on the partial safety factors of all design variables and a professional factor, which is a ratio of measured to predicted rut-depth. Both approaches use an iterative algorithm where the computation is continued until the limit-state function converges to zero in order to produce an optimal pavement cross-section. This work is d $4.1ng Kim. \ emOriana} and t DEDICATION This work is dedicated to my parents, Hyun-Suk Kim and Soo-Ja Choi, and my sister, Sung-Ii Kim, without whom this work would have not been possible. Their ceaseless emotional and financial support has been invaluable. Thank you for everything and God bless you. iv 1 “DUI and guidance ' 1 also ‘ hold. and Dr wouid have not hh‘aPF illDOT) and ti Innersity for Si [would like it isfleaometer tes coil eCtion of field I would a works on derelc coneetion factor 1 hi research it orl; ACknowle j c, ‘ l «Min 011 Jin~ ACKNOWLEDGEMENTS I would first like to express my best gratitude to Dr. Neeraj Buch for his support and guidance throughout my research career at Michigan State University. I also wish to thank Dr. Gilbert Baladi, Dr. Ronald Harichandran, Dr. Thomas Wolfl‘, and Dr. Vince Melfi who are my PhD. guidance committee members. This work would have not been completed without their valuable advice. My appreciation is extended to the Michigan Department of Transportation (MDOT) and the Pavement Research Center of Excellence (PRCE) at Michigan State University for sponsoring this research work and providing financial support. In addition, I would like to thank MDOT personnel for performing coring and falling weight deflectometer testing as well as providing the necessary traffic control for carrying out the collection of field data. I would also like to give my sincere gratitude to Mr. Dong-Yeob Park for his works on developing a pavement temperature prediction model and a temperature correction factor for backcalculated moduli. His research results have fully contributed to this research work. Acknowledgment is given to Jung-Kyu Yu (President), Kyung-Won Cho (CEO), Eu-Jin Oh, Jin-Kyu Song, and Jin-Ho Jung (Executive Directors) of Yoo-Shin ov- Ido" ~ Imu‘w-;~mm.‘: w h. ”a. -‘i_4_'.»r ~ Engineering C eaduate stud) Finally engineering fo. Engineering Corporation, Seoul, Korea, for their willingness to allow me to continue my graduate study without any inconvenience. Finally, thanks to Korean students in the department of civil and environmental engineering for their valuable supports during my graduate study. vi ....- - . n "w’l‘ul' 47‘ J "IR‘ LIST OF TABI. LIST OF FIGIT CHIPTER l TNTROI.) (j P Dl> Mt TABLE OF CONTENTS LIST OF TABLES ..................................................................................................... x LIST OF FIGURES ..................................................................... ’ .............................. xii CHAPTER I INTRODUCTION ......................................................................................... 1 General ............................................................................................... 1 Problem Statement ............................................................................. 1 Background ........................................................................................ 2 Objectives of the Research ................................................................. 4 Organization ....................................................................................... 4 II LITERATURE REVIEW General .............................................................................................. 5 Mechanics of Permanent Deformation (Rut) ..................................... 9 Factors Affecting Rutting of Asphalt Surfaced Pavements ............... 11 Tire Inflation and Tire-Pavement Contact Pressure ............... 11 Environmental Factors ........................................................... 12 Permanent Deformation (Rutting) Prediction Models ....................... 13 Mechanistic Rutting Prediction Model .............................................. 13 Review of Mechanistic-Based Rutting Prediction Models ................ 15 VESYS Model .......................................................... - ............. 15 Revised VESYS Model with the Consideration of Actual Field Condition ...................................................................... 18 Calibrated VESYS Model with LTPP Database .................... l9 Advantages of Mechanistic-Based Rutting Prediction Models ......... 20 Disadvantages of Mechanistic-Based Rutting Prediction Models ..... 21 Rutting Prediction Models Based on Mechanistic-Empirical Approach ............................................................................................ 22 Mechanistic-Empirical Rutting Prediction Models ........................... 23 Type I ..................................................................................... 23 Type II .................................................................................... 23 Advantages of Mechanistic-Empirical Rutting Prediction Models ...26 Type I ..................................................................................... 26 Type II .................................................................................... 27 Disadvantages of Mechanistic-Empirical Rutting Prediction Models ................................................................................................ 27 Type I ..................................................................................... 27 Type II .................................................................................... 28 vii CMWER 3 R m FELDS TijCD—tmtfi ’ r-“ W MODEL 1 F v. u Fra Sn Hm FLEXIBU Me. CHAPTER Page Mechanistic-Empirical Flexible Pavement Design ............................ 28 Research Work Needed ...................................................................... 32 III FIELD STUDY — DATA COLLECTION .................................................... 34 Data Collection Criteria ....................................... ' .............................. 34 Site Selection ..................................................................................... 34 Types of Field Data Collected ........................................................... 39 Overview of Long Term Pavement (LTPP) Database ....................... 40 Data Acquisition from LTPP Database .............................................. 42 Preliminary Data Analysis ................................................................. 42 Backcalculation ...................................................................... 42 Temperature Correction Procedure ........................................ 45 Primary Pavement Responses ................................................ 46 Estimation of Cumulative Traffic Volume ............................ 46 IV MODEL DEVELOPMENT AND SENSITIVITY ANALYSIS ................... 55 Validation of Existing Rut Prediction Model .................................... 55 Proposed Rut Prediction Model ......................................................... 57 Framework for Calibration and Modification of Rut Prediction Model ................................................................................................ 57 Variable Selection .............................................................................. 59 Basic Concept of the Model ............................................................... 59 Nonlinear Regression Approach ........................................................ 61 Sensitivity Analysis ........................................................................... 62 Validation with Field Data Collected in Michigan 1998 ..... ‘ ............. 7O Validation with LTPP Database ......................................................... 70 V RELIABILITY-BASED APPROACH TO M-E FLEXIBLE PAVEMENT ANALYSIS ................................................................................................ 75 General ............................................................................................... 75 Reliability Concept ............................................................................ 76 Sources of Uncertainties in the M-E Flexible Pavement Design ....... 80 Practical Engineering Reliability Technique ..................................... 81 First Order Second Moment (FOSM) Method ....................... 81 Point Estimate Method (PEM) ............................................... 83 First Order Reliability Method (FORM) ................................ 84 Framework for Developing Reliability Model for Pavement Structural Analysis ............................................................................. 85 Illustrative Example ........................................................................... 87 VI DEVELOPMENT OF PRACTICAL RELIABILITY-BASED M-E FLEXIBLE PAVEMENT DESIGN ALGORITHMS ................................... 100 General ............................................................................................... 100 Method 1: Reliability Factor Design (RFD) Approach ..................... 100 viii CHAPTER REFERENCES . CHAPTER Page Modeling and Analysis of the Uncertainties in RFD Approach ........ 101 M-E Flexible Pavement Design Procedure Using RFD Approach....106 Sample Experimental Design Matn'x ................................................. 107 Illustration of RFD Approach .............................. ‘ .............................. 111 Method 2: Load and Resistance Factor Design (LRFD) Approach...114 Modeling and Analysis of the Uncertainties in LRF D Approach ...... 116 M-E Flexible Pavement Design Procedure Using LRFD Approach .117 Illustration of LRFD Approach .......................................................... 119 Sensitivity Analysis of RFD and LRFD Analysis ............................. 124 VII SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS ................. 129 Summary ............................................................................................ 129 Conclusions ........................................................................................ 132 Recommendations for Future Research ............................................. 135 REFERENCES .......................................................................................................... 137 ix Pax'emer‘ Summ . Temperat Summar} Summar} SUlear} Summar} Summary Assumpti‘ COrrelatio Statistical Experime, Rutting I) Variabilit; Summary 5mm a? Spreadshc LIST OF TABLES TABLE ‘ Page 1 Summary of Coefficients of Type I Rutting Prediction Models ................... 24 2 Pavement Selection Criterion ........................................................................ 35 3 Summary of Selected Sites ............................................................................ 37 4 Temperature History of Major Cities in Michigan ........................................ 41 5 Summary of Selected LTPP-GPS Sections .................................................... 43 6 Summary of Backcalculated Moduli of Test Sites ........................................ 47 7 Summary of Pavement Responses in Test Sites ............................................ 49 8 Summary of Traffic in Test Sites ................................................................... 52 9 Summary of Statistics of Analyzed Variables ............................................... 53 10 Assumptions for Kinematic Viscosity and Air Void ..................................... 56 11 Correlation Matrix of Pavement Variables ............ 6O 12 Statistical Results of Nonlinear regression Analysis ..................................... 63 13 Experimental Design Matrix for Sensitivity Analysis ................................... 66 14 Rutting Development at Test Sites with Increase of Traffic .......................... 72 15 Variability Components in M-E Flexible Pavement Design ......................... 8O 16 Summary of Variables Used in Example Pavement Sections ....................... 88 17 Summary of the Statistics of AC Thickness Cored in Michigan Sections ....89 18 Spreadsheet of Reliability Analysis of Pavement Performance (on Example Pavement Section 2) (a) F OSM or the lSt Iteration in FORM ......................................................... 93 i '3 ”‘2 -;:_v’cw"' lw Viv-1, . 'mm TABLE (b)End« 19 Spreadst L'sing P1 20. Summer: for Payer 21 Relationi Reliabilit 33 Factorial (AC Thic 33 Standard 24 Summ”) No.35..... 35. SUInmar} Reliabiliti 36 C0“Slant I TABLE Page 19 20 21 22 23 24 25 26 (b) End of the Iteration in FORM .................................................................. 94 Spreadsheet of Reliability Analysis of Pavement Performance Using PEM ..................................................................................................... 95 Summary of the Result of Reliability Analysis for Pavement Performance ............................................................................. 99 Relationship between Tangent Reliability Level and Its Corresponding Reliability Index ............................................................................................. 102 Factorial Experiment Matrix with Major Design Variables (AC Thickness, Subgrade Modulus, and Traffic) .......................................... 109 Standard Deviations Associated with Parameter Uncertainties ..................... 110 Summary of Computations for Partial and Overall Safety Factors at Cell No. 35 ............................................................................................................. 120 Summary of Partial and Overall Safety Factors with Various Target Reliabilities ....................................................................................... ............ 121 Constant Design Parameters in the Sensitivity Analysis ............................... 126 xi FIGURE 1 fl FIOWDII'igri Framew Transver Framewt h-l-E Fle.‘ Distribut Descnpti Conceptu Measure Measured Sensitivit) Rut-Dept} Measured Trpicar R1 Measured Data set... Probabrm; Geometric, Integrated ,‘ Helele Pd LIST OF FIGURES FIGURE Page 1 Framework for the Calibration of Existing Rut Prediction Model ................ 5 2 Transverse Profile of Loops 4 and 6 of the AASHO Road Test .................... 9 3 Framework of a M-E Flexible Pavement Design Model ............................... 30 4 M-E Flexible Pavement Design Flowchart in Minnesota Practice ................ 31 5 Distribution of Test Sites across the State of Michigan ................................. 36 6 Description of Typical Test Site .................................................................... 38 7 Conceptual Configuration of FWD Test ........................................................ 39 8 Measured vs. Predicted Rut-Depth Using Existing Model ............................ 58 9 Measured vs. Predicted Rut-Depth Using Revised Model ............................ 64 10 Sensitivity of Pavement Rutting to pavement design variables ..................... 67 11 Rut-Depth Development with Increase of Traffic ......................................... 69 12 Measured vs. Predicted Rut-Depth Based on ’98 Michigan Data Set ........... 71 13 Typical Rutting Development with Increase of Traffic ................................. 73 14 Measured vs. Predicted Rut-Depth Based on Selected LTPP-GPS Data set ........................................................................................................... 74 15 Probability of Unsatisfactory Performance with Specified Variables ........... 78 16 Geometrical Illustration of Hasofer and Lind’s Reliability Index ................. 78 17 Integrated Presentation of Types of Uncertainties Associated with M-E Flexible Pavement Analysis ........................................................................... 82 18 Flow Diagram for Pavement Reliability Analysis ........................................ 86 xii FIGURE 19 Approac Pavemei 30 Flowcha Approac 21 lllustrati. 22 F lowchai Approacl 23 Illustratid 34 Variation Variation FIGURE Page 19 Approach to Identifying the Optimum Reliability Level for a Given Pavement ........................................................................................................ 103 20 Flowchart for M-E Flexible Pavement Design Procedure Using RFD Approach ........................................................................................................ 108 21 Illustration of M-E Flexible Pavement Design Using RFD Approach .......... 112 22 Flowchart for M-E Flexible Pavement Design Procedure Using LRFD Approach ........................................................................................................ 1 1 8 23 Illustration of M-E Flexible Pavement Design Using LRFD Approach ........ 122 24 Variations of AC Thickness with Various Traffic Levels ............................. 127 25 Variations of AC Thickness with Various Target Reliability Levels ............ 128 xiii General The et'olutionar expanded b. The proper and interrela b} laboratog efforts regard rational new d IESIEIling flexi meChaniSth-em imparted pm munch-e5 ma}. more reasonable W01 Various PTOblem Staten), The AIICJL cl, - . “aging I“ dGSia CHAPTER I INTRODUCTION General The structural design of flexible pavements and bituminous overlays has been an evolutionary process, based primarily on the experience and judgment of engineers, and expanded by empirical relationships developed through research and field observations. The proper design of flexible pavements requires the consideration of several complex and interrelated factors. In previous research efforts, these factors were mainly identified by laboratory and field investigations, and combined with statistical analysis. Recent efforts regarding the interaction of these factors have resulted in the development of rational new design models employing mechanistic theories. Today, design methods for designing flexible pavements and overlays can be divided into two groups, empirical and mechanistic-empirical. Since both methods typically incorporate deterministic inputs and simplified procedure, the uncertainties of design parameters and design procedures themselves may have significant effects on the accuracy of design outputs. Therefore, more reasonable design procedures require comprehensive reliability techniques to control various uncertainties of pavement design and produce a consistent pavement performance level. Problem Statement The Michigan Department of Transportation (MDOT) is in the process of changing its design procedures of flexible pavements from one based on the AASHTO grade ‘° ‘ incHBAC are intend MICHPAV mp0nses. « There is a obsen'aron5 (PMS). and < effects of chE Background In rece change their c mediods (AAS perform this Obj ofM-E design a] depend on set'era l. The accuram pavem ent. I ~- The accurate layers. ‘ l -- {:6 .Selectior ctions. I 4. The accliracr etenoratiori r guide to a mechanistic approach. MICHPAVE, for flexible pavement design, and MICHBACK, for back-calculation of pavement layer moduli from FWD deflection data, are intended to be cornerstones of MDOT’s mechanistic design procedure [1]. MICHPAVE has linear and non-linear finite element models to predict primary responses, and field-derived fatigue and rut models to predict the secondary response. There is a need to verify/calibrate the distress models in MICHPAVE using field observations and the distress database in the MDOT Pavement Management System (PMS), and establish a mechanistic flexible pavement design procedure that considers the effects of changing design inputs and bias of the design model. Background In recent years, most state highway agencies (SHA’s) recognized the need to change their current flexible pavement design practices which are based on empirical methods (AASHTO) to mechanistic based approaches [2]. In order to successfully perform this objective, many SHA’s have conducted studies to determine the feasibility of M-E design approaches. In general, the success of the new design practice is known to depend on several factors: 1. The accuracy of the pavement structural model to obtain primary responses of the pavement. 2. The accurate characterization of the material properties in the different pavement layers. 3. The selection of reasonable design criterion based on functional and structural functions. 4. The accuracy of the mechanistic-based pavement performance models to predict the deterioration of these functions. ‘J! 31 (I) T the State change tk and desi g1 MICHBAi (NDT) dat considerabl accuracy in Verified wit} COUnty. Mic} With 1 development c “Sponges of th ImIOH include hundred pai't‘me meChitttistioemp Ifil’mtoq. data frd intently Com p l I \ afiecting pawn)? ll mod OIIOUr vec‘ 5. The application of reliability concept to treat uncertainties of the design procedure The solutions related to first and second items have been successfully achieved in the State of Michigan; Two computer programs have been developed in an effort to change the state’s design practice. One is a nonlinear finite element pavement analysis and design program, called MICHPAVE [3], and the other is a computer program, called MICHBACK, for backcalulation of layer moduli from nondestructive deflection testing (NDT) data [4]. Since the development of the program in 1988, MICHPAVE has had considerable reputation both within and outside the United States of America with the accuracy in computed results. The results from MICHPAVE and MICHBACK have been verified with the field test conducted at two pavement sections along I-96 in Ingham County, Michigan [5]. With reliable results from the computer programs that are commented above, the development of the pavement performance model that is based on mechanistic primary responses 4 of the pavement such as strains and deflections is required. The MICHPAVE version includes rut and fatigue distress models that were derived from about five hundred pavement sections in Michigan and five neighboring states. These models have mechanistic-empirical features in the sense that they are based on a combination of inventory data from the PMS database, field distress data, and mechanistic responses. In a recently completed three-year study aimed at identifying asphalt concrete mix factors affecting pavement rutting and fatigue cracking, field data were collected from sixty four Michigan pavement sections (forty nine flexible and fifteen composite sections) over a period of four years [6]. It is intended that, in addition to other pavement sections and PMS distress purpose ofca Objectives of The oh 1. Verifyr‘cali spectrum «I model ifnt 3. Develop th empirical (.‘ ..‘J . DeveIOp th; cross-sectio organization This the ' In chapter flitting fact mechanistic. In Chapter 3 raw field dat Chapter 4 d Wan-m [I In Chapter 5‘ flexible PaVe: [Ethnjques (e. PMS distress data, most of these pavement sections will be monitored over time for the purpose of calibrating the distress models in MICHPAVE. Objectives of the Research The objectives of this research are to: l. Verify/calibrate the rut prediction model in MICHPAVE using field data from a spectrum of in-service flexible pavement in the state of Michigan or improve the model if necessary. Figure 1 summarizes the calibration process. 2. Develop the reliability analysis model for evaluating uncertainties in the mechanistic- empirical (M-E) flexible pavement design procedure. 3. Develop the reliability-based pavement design algorithms that can output pavement cross-sections satisfying distress thresholds at a desired level of reliability. Organization This thesis is divided into seven chapters, including the introduction. 0 In chapter 2, a comprehensive literature review on the mechanics of pavement rutting, factors affecting pavement rutting, existing rut prediction models, and the mechanistic-empirical design procedures is presented. 0 In chapter 3, the data collection procedure is explained, and preliminary analysis of raw field data is described. 0 Chapter 4 describes the revision of the rut prediction model. The chapter also summarizes model validation results. 0 In chapter 5, a reliability analysis model for evaluating uncertainties in the M-E flexible pavement design procedure is introduced employing practical probabilistic techniques (e.g. F OSM, PEM, and FORM). v" to Cross . . 3 Data so Deflectr I Modul” . Pavement l 3.x ‘hlechanistic l ! Of the P3V€m( \ \ ;' Physmal P Bituminou \ I\ FigUre 0 Cross Sectional Data 0 Deflection Data l MICHBACK Moduli of the Pavement Layers MICHPAVE/ CHEVRONX Mechanistic Responses. of the Pavement 0 Physical Properties of Bituminous Mixture o Enviromnental Data r Traffic Data I Measured Distress Data (RBI D6pth)2 RDmcasured RDmeasured z RDprcdicted Pavement Distress (Rut Depth) from Predictive Model: RDpredictcd Install the Model in MICHPAVE Figure 1 Framework for the Calibration of Existing Rut Prediction Model Calibrate/Revise Existing Model No In chapu the revis introduce quantifyir . In chaptt provided. In chapter 6, two reliability-based M-E flexible pavement design procedures using the revised rut prediction model as a major performance/transfer fimction are introduced. In the two design procedures, different reliability methodologies for quantifying uncertainties of the M-E design components are exhibited. In chapter 7, the results of the research are summarized and conclusions are provided. Finally, recommendations for future research are proposed. General The 1‘ load over the ‘ pavements: Rut ‘ RL concrete SUIIaC‘ b)‘ environrnenI pavement mate“ Fatigue ‘ by fatigue failur n‘hc loading. It accelerated by en thinned by usi Ctr ' mimetion pract CHAPTER II LITERATURE REVIEW General The load-carrying capacity of flexible pavements is brought about by the load distributing characteristics of the individual layers. In general, flexible pavements consist of multiple layers with the highest strength material placed at near the surface. Hence, the pavement strength is derived from building up thick layers and thereby distributing the load over the roadbed soil. Two types of load related distress can be found in flexible pavements: Rut - Rut can be defined as the sum of the permanent deformation in the asphalt concrete surface, base, subbase and roadbed soil. Rut is a load-related distress accelerated by environmental factors. In general, rutting can be minimized by using the appropriate pavement materials, proper design thickness, and construction practices [6]. Fatigue - Fatigue or alligator cracking is a series of interconnecting cracks caused by fatigue failure of the asphalt concrete surface (or stabilized base) under repeated traffic loading. It is a load-associated distress that can be found in both wheel paths and is accelerated by environmental factors. Fatigue cracking potential of any pavement can be minimized by using the appropriate pavement materials, proper design procedure, and construction practices [6]. uflj‘w'vmv<— ~ 'VV 4.?" It Sl’lt rotting due tr theoretical a layer is main. 1. Engineered Plastic yiel" AC layer. 2- Balanced p; the C0mpres 10p Of the r0 1a.“ers. 3 G ‘ 00d consti I'aI-lOLlS paVe EXlSllng equations derii It should be noted that the contribution of the AC layer to the total pavement rutting due to densification is negligible, since this layer is typically compacted to near its theoretical maximum density during construction. Permanent deformation in the AC layer is mainly the result of lateral distortion due to repeated shear deformation. Rut potential of pavements can be minimized by taking balanced engineering steps during the material design (asphalt mix design), the cross-section design process and construction, These steps include: 1. Engineered asphalt mix design that can withstand the expected traffic loading without plastic yielding and resist repeated shear deformation that causes lateral distortion of AC layer. 2. Balanced pavement design process that provides adequate layer thickness to reduce the compressive stresses induced at the top of the base and subbase layers, and at the top of the roadbed soil. These stresses cause permanent deformation (rut) in pavement layers. 3. Good construction practices that deliver adequate and uniform compaction to the various pavement layers. Existing flexible pavement design methods can be divided into two categories: empirical and mechanistic-empirical. Most empirical methods are based on statistical equations derived from field observations of pavement rutting and roughness. Mechanistic-empirical design methods, on the other hand, are mainly based on two criteria: 1. Minimizing the rut potential of each pavement layer by limiting the magnitude of the compressive stress induced at the top of that layer by a moving wheel load. 2. Maximizing the fatigue life of the AC layer by minimizing the induced tensile stress at the bottom of the layer due to a moving wheel load. I Mechanics o Perm. wheel paths. pavement up noticeable on pennanent de soil. the subb magnitude of I. Constructi 01’ compac - ASphalt n Cement. hr tJ 3. Envirom and hi gh lllfldeQuaj 4' III? factc AS 5 AC: base. St the my,“ “idem the UBMbutior defending ‘ Mechanics of Permanent Deformation (Rut) Permanent deformation in flexible pavements manifests itself as rutting in the wheel paths, thereby causing permanent distortion in the transverse profile. In addition, pavement uplift may occur along the sides of the rut channel. In many instances, ruts are noticeable only after a rainfall, when the wheel paths are filled with water. Nevertheless, permanent deformation of the pavement surface is the result of rutting of the roadbed soil, the subbase and base layers, and the AC surface. Several other factors affect the magnitude of the rut and its time rate of accumulation. These factors include: 1. Construction factors, including inadequate compaction (either low compaction effort or compaction at lower temperatures than those specified). 2. Asphalt mix factors, which include soft (low viscosity or high penetration) asphalt cement, high air voids, rounded aggregate, and excess sand in the mix. 3. Environmental factors, which include high temperatures, which soften the AC layer, and high moisture content or saturation of the lower layers (base and subbase) due to inadequate drainage. 4. Tire factors, such as studded tires and high tire pressure. As stated earlier, pavement rutting is the sum of permanent deformations in the AC, base, subbase layers, and in the roadbed soil. Figure 2 shows the results of a study of the transverse profile of loops 4 and 6 at the AASHO Road Test [7]. From the figure, it is evident that rutting has occurred in all pavement layers and roadbed soil. The contribution of each layer to the total pavement rut varies from one pavement to another depending on material properties of layers. Loop 6 6—3—8 Desrgn 30 Kip Single Axle Load . , . . Original Profile Pavement Q fl/W .30 '7, 5:“; 9 /Z, / . :"' ' ., "’/ W'é:‘vv '0" < ll I I t I 4 .1?" 0 2 4 6 B 10 12 Loop 6 6—3—12 Design 30 Kip Single Axle Load W t ,. . u . -( V x»??? t is = v I A!» - ' ”e tsAgsfsfixu.‘ [:] SURFACING Ea BASE Loop 4 5—3-4 Desrgn Q soamse 32 Kip Tandem Axle Load Slow PATCH Transverse Direction, Feet Figure 2 Transverse Profile of Loops 4 and 6 of the AASHO Road Test [7] 10 Factors Aft 0 Tire ln‘| In tI rotting and i III the state I ha increase of I30psi is average tire (1069kPa) [E T)pi magnitude 0 and at the to tire pressure UPC and fit Concluded [} l. The €er PICSSUre increase inflation percem i mechani: MICHP; Factors Affecting Rutting of Asphalt Surfaced Pavements 0 Tire Inflation and Tire-Pavement Contact Pressure In the USA. asphalt surfaced pavement are in general, experiencing premature rutting and fatigue cracking due to increased traffic load and truck tire pressure. Surveys in the state of Illinois and Texas indicate that, over the last few decades, the tire pressure has increased substantially. An average tire pressure of 96psi (662kPa), with a maximum of 130psi (896kPa) was recorded in the Illinois survey. The Texas survey showed an average tire pressure of llOpsi (758kPa), with a maximum tire pressure of 155psi (1069kPa) [8]. Typically, the rut potential of a flexible pavement is evaluated on the basis of the magnitude of the compressive strains induced at the top of the base and subbase layers and at the top of the roadbed soil due to an 18kip (80kN) single axle load and a constant tire pressure (typically 85psi (586kPa)). An experimental study about the influence of tire type and tire pressure on pavement performance conducted by Smith and Bonquist concluded that [9]: 1. The effect of wheel load on pavement response is greater than the effect of tire pressure. The measured pavement responses (stresses and strains) doubled for an increase in load from 94001b (42kN) to 190001b (84.5kN), while increasing the tire inflation pressure from 76psi (524kPa) to 140psi (965kPa) resulted in a less than 10 percent increase in the measured response. This conclusion supports the results of mechanistic analysis of flexible pavement structures by Baladi, who used MICHPAVE, linear/nonlinear finite element computer program, to analyze the stresses and strains induced in the pavement layers due to various wheel loads and tire ll inflation i induced . wheel 10. I“) . The etTe. thin pave sections ( 3. Higher [c Wheel loa fatigue Cl' Environmen EXpo Strains affilia function of t aSphalt film I and material during mixin that early pax when it is Op, inflation pressures [10]. He reported that the effects of increasing tire pressure on the induced stresses and strains in the pavement are much smaller than those of increasing wheel load. 2. The effects of tire pressure and wheel load on pavement rutting are much higher for thin pavement sections (less than 2-inch (5cm) AC surface) than for typical or thick sections (more than 4-inch (10cm) thick AC surface). 3. Higher temperatures cause higher rut potential. Hence, the magnitude of tire pressure, wheel load, temperatures, and AC thickness are key to the deterioration of rutting and fatigue cracking in asphalt surfaced pavements. Environmental Factors Exposure to the environment causes bituminous materials to harden over time. As time goes by, the bituminous binder becomes so brittle that it can no longer sustain the strains affiliated to daily temperature changes and traffic loads. The rate of hardening is a function of the oxidation resistance of the binder, temperature, and thickness of the asphalt fihn [10]. Therefore, the rate of hardening varies with the binder type, climate, and material design. It should be noted that most of the asphalt hardening takes place during mixing, agitating, transporting, and construction. Hughes and Maupin reported that early pavement rutting is a function of the pavement temperature of the pavement when it is opened to traffic [8]. They suggested that pavement temperatures of less than ISOOF (66°C) lead to a stable asphalt mix under traffic. 12 Permanent1 Pa“ I fiffOUTBDCt life. or the l that must b prediction l mechanistic elasticity. p1 model can 1 bccause of it wbemade “ith the mec resfearches 10 tuning. In an 3531mm that magnitude 0, Strain and the Hechallistic As ”It Permanent Deformation (Rutting) Prediction Models Pavement design and pavement performance systems have to include the performance prediction models. Such models should address rate of deterioration, service life, or the remaining service life of the pavement structures. Rut is one type of distress that must be predicted in the pavement design and analysis procedures. Current rut prediction models can be divided into two categories: ( 1) mechanistic, and (2) mechanistic/empirical. The mechanistic models are based on either the theory of elasticity, plasticity, or visco-elasticity. Even though nonlinear plastic or visco-elastic model can provide more accurate results, the use of this model has been restricted because of its complex nature. In other words, the pavement rutting prediction is difficult to be made directly from plastic stress-strain relationships. The complexities involved with the mechanistic prediction models using nonlinear plastic or visco-elastic theory led researches to develop simplified mechanistic/empirical models for predicting pavement rutting. In an effort to develop practical alternatives for predicting rutting, it is generally assumed that the initial elastic strain and the number of load repetitions can explain the magnitude of cumulative plastic deformation. The relationship between the initial elastic strain and the number of load repetitions can be obtained from both laboratory tests and field observations using linear or nonlinear elastic theory. Mechanistic Rutting Prediction Model As mentioned above, rutting on the surface of a pavement due to a specific traffic can be defined as the sum of cumulative permanent deformations in the pavement layers. The cumulative permanent deformation of a layer can be calculated by integrating the 13 plastic strai total rut-dc; layers. The calculated. applications task to an correspondii Beca estimating including m elastic soluti “'thh the dc COmp0nents: Where: plastic strain in the layer due to the amount of applied traffic load [1 1]. So, theoretically, total rut-depth of a pavement can be estimated by integrating plastic strains through the layers. Therefore, if the plastic strain of each layer per cyclic load (traffic) can be calculated, one can exactly predict the total rut-depth due to the number of load applications at a given time. However, it is an extremely difficult and time-consuming task to analytically calculate plastic strains with time-series material properties corresponding to the number of load repetitions. Because of the reasons stated above, it is necessary to find alternatives for estimating the plastic strain with common analysis tools in pavement engineering, including multi-layered elastic theory and finite element analysis with elastic and visco- elastic solution. To this end, many researchers have suggested elastoplastic theory in which the deformation under loading from the load is assumed to be composed of two components: the elastic and plastic, or the recoverable and the unrecoverable [12]. Thus, the total strains can be expressed by the following equation; a = 6“, + 8p (1) where: e = total strain, 8: = elastic strain, and e = plastic strain p From equation 1, the plastic strain can be expressed: 5,, = a — a, (2) If the total stress is assumed to be constant, the plastic strain can be estimated by calculating the elastic strain. In order to avoid complex procedure for calculating elastic strains at loading stages with different resilient moduli, another assumption needs to be 14 made. Whit due to repc model illus: where: Several atter model based Ro’iew of M ° VESYS The method i based on the [l I] The “3'0 made, which is the rate of increase of permanent strain in each element of a given layer due to repeated wheel loads is proportional to the resilient strain. The general form of the model illustrating this assumption is followed as [12]; as 7 __p — —a (3) — .9 av #N r where: 8p = permanent strain, gr = resilient strain, N = number of load repetitions, and a and 11 = permanent strain parameters. Several attempts have been made to develop the mechanistic-based rutting prediction model based on these theories and assumptions. Review of Mechanistic-Based Rutting Prediction Models 0 VESYS Model The method incorporated in the VESYS computer program for predicting the rut depth is based on the assumption that the permanent strain is proportional to the resilient strain [11]. The two are related as follows: 8p(N) = pan/‘0‘ (4) in which 5,, (N) is the permanent or plastic strain due to a single load application, i.e., at the nth application; a is the elastic or resilient strain at the 200th repetition; N is the load application number; p is a permanent deformation parameter representing the constant of proportionality between permanent and elastic strains; and a is a permanent deformation parameter indicating the rate of decrease in permanent deformation as the number of load 15 application equation 4 From equat: So the sl0pe The intercep' T0 determine for the indit-j Strains due t. 7 . . "00m r epetm. inwhich e ( aillallOn 4 in tilde]. the 53 applications increase. The total permanent deformation can be obtained by integrating equation 4 l—a a, = fap(N)dN=gp11V (5) From equation 5 logsp =10g£16fl )+(1—a)logN (6) So the slope of the straight line S=1-a, or a : l-S (7) The intercept at N=1, 1:811/ (1 ~00, or a To determine the permanent deformation parameters of the layer system, am and #03 , for the individual layers, it is further assumed that the sum of permanent and recoverable strains due to each load application is a constant and equals to the elastic strain at the 200th repetition. This means that after the 200th repetition a = £p(N) + £,(N) (9) in which £r( N) is the recoverable strain due to each load application. Substituting equation 4 into equation 9, we obtain £,(N) =£(1—,uN‘“) (10) Under the same stresses, strains are inversely proportional to the moduli, so equation 10 can be rewritten as follows: 16 in which E: loading at ti individual 1 These mice different val in Which w i eqmtion. 4. . in Which y “hen the j acellITlulatec' mlfigranng f exl'«‘TC‘Ss,§-c] a E = EN“ (11) l-flN‘“ N“-# in which Er(N) is the elastic modulus due to unloading and E is the elastic modulus due to Er(N): loading at the 200th repetitions. Note that Er(N), which is the unloading modulus for each individual layer, is not a constant but increases with the increasing of load applications. These unloading moduli are used to determine the recoverable deformation wr(N) at different values of N. The permanent deformation wp(N) can then be computed by ; w, =w-w,(N) (12) in which w is the elastic deformation due to loading at the 200th applications. Similar to equation. 4, wp(N) can be expressed by mm = yaw-“w 03> in which 'uw and a.” are permanent deformation parameters of a pavement system. When the number of traffic load applications, It, is applied on a pavement, the accumulated permanent deformation of a layer of the pavement can be obtained by integrating equation 13 with respect to n; nl—am wp (n) = wpsys —— (14) l-am So, the sum of rut depths of all layers due to the number of load applications, 11, can be expressed as; 1 nl—asysl. Rut Depth = 2 Wuusys. ————- (15) l — i=1 1 asys, 17 o Revise For a layer rut-depth. c “here: p e h. 1 According tr and 0.006 to b." Ihfim hav Parameters, . commm ma e(Nation 15. palement. Where 3 0 Revised VESYS Model with the Consideration of Actual Field Condition. For a layer of pavement structure, the vertical compression, which is related to the true rut-depth, can be calculated using equation 14. This equation can be rewritten as [13]; ] l-a, p.- =1iht sifa’N (16) where: ’0~ = vertical compression in layer i, 5,, = resilient vertical strain in layer i, and hi = thickness of layer i. According to Leahy and Witczack, typical values for or and 1* range from 0.006 to 0.92 and 0.006 to 8.82, respectively [14]. Furthermore, results from extensive laboratory work by them have shown that or and [l are significantly influenced by mix design and test parameters, which is a background of the assumption that or and p are constant for common material specification of each layer. Based on this assumption and from equation 15, the following regression can be used to predict rut-depth in a flexible pavement. 1 1—a,~ C3 1 RUT = QAC2 2 h,- Niai'f" (17) i=1 where : RUT = rut depth due to vertical compression [in], A = a scaling variable related to the environment and the permanent strain coefficient, , and Cl,C2,C3 = regression coefficients obtained from field data. An important requirement for using this model is a simple procedure for obtaining the compressive strain in the pavement layers. This requires establishing locations for the 18 strains to applied lo; portion of '1" into three t calculatede 1. AC laye 2. Base lay 3. Subgradt Fina Strain calcc det‘el0ped f “here: AGE strains to ensure that they properly reflect the average strain responses from a given applied load, and do not result in over or underestimation of the permanent deformation portion of the layer. Owusu-Antwi, et a1. suggests that pavement layers should be divided into three courses of AC, base and subgrade and the critical strains for those layers be calculated at the following locations [13]; 1. AC layer -at the middle of the AC surface layer thickness 2. Base layer - at the middle of the base layer thickness 3. Subgrade - at the top of the subgrade. Finally, using data from Long Term Pavement Performance (LTPP) database and strain calculated at the critical location of each layer, the following equation was developed for predicting the total rut-depth, RUT, in flexible pavements [13]; 1 l-al 1 1—a2 1 1.03 077 RUT: 0.29.4050” ha, 21,5531 +17,“ mam +h,,,, 3,831,333,. (18) where: AGE = age of pavement, years (1.1 = 0.6, (12 = 0.7, and 013 = 0.7 The relevant statistics of the model are as follows; 1. Number of data points, N =80 2. Coefficient of determination, R2 = 0.35 3. Standard error estimate, SEE = 0.1 o Calibrated VESYS Model with LTPP Database Ali, et al. suggest a basic equation for predicting rut-depth in which the permanent deformation of each layer by various axle groups can be estimated [15]; 19 where: With a calit the followin r 0.022 I: Sub AdvantageS ' The Inc L 1 ““1 pl- Pp=2_3h11_a (EW nil—a1) (19) J: J where Pp = cumulative permanent deformation in all layers, from all load groups (rut-depth), gei‘j = vertical compressive strain in the middle of layer j, due to a passage of an axle of group i, and h. = thickness of layer j. The subgrade may be divided into several layers and the calculations performed until the vertical elastic strain approaches zero, the subgrade thickness is determined accordingly. With a calibration procedure of a and u for each layer using the data in LTPP database, the following equation is introduced as a final form of the model; k 0.9 k 0.05 pp = 0.00011 hAC[i§1ni(gel-’AC)LIHJ + 23 .26 * hbm [Elni(£e,~,base )20] 0.356 .81 "i (gensubg )2 J (20) "Mar _ + 0.022 12mg [ Advantages of Mechanistic-Based Rutting Prediction Models . The models follow mechanistic fundamentals without any physical violation. It means that a mechanistic design procedure adopting this model has a potential to satisfy various regional conditions. . The contribution of each layer to total rut-depth can be quantified in a reasonable manner. It means that the model can allow one to have various options for controlling rutting in pavement design by changing material properties of layers and layer thickness. . The models can account for rate-hardening (load applications vs. rut-depth) in the progression of rutting with increased load applications. 20 Dhadvant: Then Chang patent. The ea materia in labor in field The TCCI Vertical load. In Vadafior the Critic EVenrh. load SPC The models consider the rut-depth as performance function and hence can easily change failure criteria like rut-depth of 0.4in (1cm) or 0.51n (1.3cm). It means that pavements can be designed at various terminal service levels using this model. Disadvantages of Mechanistic-Based Rutting Prediction Models The early models such as VESYS model require laboratory tests to determine basic material properties of all layers in the pavement. The material properties determined in laboratory tests vary in accordance with test methods and are different from those in field full-scale tests. The recent models such as the revised VESYS assume that the locations of critical vertical strains are equivalent to the average strain responses from a given applied load. In multi-layered elastic analysis or finite element analysis, one can see a high variation of vertical strain along the thickness in each layer. So, “determining where the critical strain can be measur ” greatly affects the amount of total rut-depth. Even though the rut-depth prediction model is developed considering the actual axle load spectrum, there are some limits to estimate the effects of multiple wheels, which can cause the model to under or overestimate actual rut-depth. In the models developed by Ali et. al., the model has been formulated considering the contribution of various axle load groups to total rut-depth [15]. Definitely, axle load groups’ effects on the pavement should be separately evaluated since the change in load groups’ configuration cannot be linearly related to that of the damage amount to the pavement. For example, the AASHO road test verified that one passage of tandem axles is not equivalent to two passages of single axles, but 1.38 passages [16]. The 21 . \ ;.~ .4. .- ’L'mu Jr. w n ”V J 17‘ fit mech.‘ layere actual variou. patent Accord comput practica The ru tempera aSphalt- t“'0 cor develoy the mot be EXpr mechanistic pavement analysis algorithms using finite element method, multi- layered elastic analysis method, and so on can compute vertical strains considering actual wheel configurations of vehicles in order to correctly consider effects of various load groups. Unfortunately, most computer programs currently available for pavement analysis calculate vertical strains based on the superposition principle. According to this principle, principal stress and strain under multiple wheels are computed by superimposing those due to each single wheel load [12]. Thus, it is not practical to consider the actual axle load spectrum in rut-depth prediction. . The rutting prediction model proposed in the section above should include temperature or seasonal variations because the material properties of especially, asphalt-aggregate mixtures are highly sensitive to temperature variation. There are two common ways for the addition of temperature consideration to the model: (1) develop a temperature correction factor for the surface layer modulus and add it to the model, and (2) consider seasonal traffic damage. A conceptual model for this can be expressed as; llu k l l-aj_,,, J m 2 ( ]_ :2 2h,- —_(‘_1ni,m 631,13»: ) “M j (21) "3:11.31 aj’m where: an = number of load applications of load group i in seasonal term, m, and (1m , mm = permanent strain coefficients of layer j in seasonal term, m. Rutting Prediction Models Based on Mechanistic-Empirical Approach In general, mechanistic-empirical modeling approach can be divided into two categories. One approach is to simplify the prediction model with a few components and 22 emphasize vertical Stt mechanisti tiolating p Mechanist 0 Type I Where: 8., Table l sum ' T."Pe 11 Allen Ct. al. the payem e1 ”WOT rutti layers is 6X] Where: N f‘) (‘3 J [.11 (on, 1:! M '-i emphasize on the key phenomenon of the rutting mechanism such as the magnitude of vertical strain at the top of subgrade (type I), and the other is to statistically organize mechanistic, material, geometric, environmental, and traffic components without violating physical rules (type II). Mechanistic-Empirical Rutting Prediction Models 0 Type I Nd : .fl (8v )“f2 (22) where: 3, = vertical compressive strain at the top of subgrade. Table 1 summarizes the values of f1 and f2 used by several agencies [12]. 0 Type II Allen et, al. performed a comprehensive laboratory testing program to determine where in the pavement structure and to what extent rutting occurs and to determine the factors that control rutting [17]. As a result of the tests, the model for predicting plastic strains (8p) of layers is expressed as follows: log a, = C0 + CI (log N)+ C2 (log N)2 + C, (log N)’ (23) where N = number of stress repetitions in the asphalt layer C3 = 0.00938, C2 = 0.10392, C1 = 0.63974 C0 (-0.000663T2+0. 1 52 l T-l 3 .304) +[(1 .46-0.00572T)(logol)] T = temperature (F), and 61 = stress (psi) 23 Table 1 Su K Asphalt Ir "\ Shel] ( revi \ 50% Reli \ 858; Reli \ 959-2. Reli hmmmq \ Belgian R( \ Table 1 Summary of Coefficients of Type I Rutting Prediction Models [12] Agency f 1 f2 Rut Depth (in.) Asphalt histitute 1.365*10-9 4.477 0.5 50% Reliability 6.15"‘10-7 4.0 0.5 85& Reliability l.94"‘10-7 4.0 , 0.5 95% Reliability 1.05"'10‘7 4.0 0.5 UK. Transport & Road Research . . 6.18‘108 3.95 0.4 Laboratory (85% Reliability) Belgian Road Research Center 3.05‘10-9 4.35 0.4 24 for a dens I” ._.. mmpm 01 in the subgr w m (Dr‘m' p 01 03 Thus. b- Baladi COTlecte model a Losth *0.15*1 0.7a]0g “here: Pl) AV KY for a dense-graded aggregate base layer C3 = 0.0066-0.004log(w), C2 = -0. 142+0.09210g(w), C1 = 0.72 Co = [-4.41+(0.173+0.003w)(m)] -[(0.00075+0.0029w) (63)] w — moisture content (percent) m = deviator stress (psi), and 03 = confining pressure (psi) in the subgrade C3 = 0.007+0.001(logW), C2 = 0.018(logW), C1 : 10(-l.l+0.lw) c0 = [(-6.5+0.38w)-(1.llogo-3)]+(13610803) w = moisture content (percent) 61 = deviator stress (psi), and 03- = confining pressure (psi) Thus, Prowl = gPAC + 8PM“ + 8pmgm‘ (24) b. Baladi and Harichandran suggest a rut-depth prediction model based on data collected from field sites in Michigan and Indiana. Equation 25 summarizes the model attributes [l 8]: Log(RD)=-l .6+0.067*AV-1 .4*log(TAC)+0.07*AAT-0.000434*KV +0.15 * log(ESAL)-O.4*log(MRRB)-0.5 *log(MRB)+0.1 *lo g(SD)+0.01 *log(CS)- 0.7*log(TBEQ)+0.09*log[50—(TAC+ TBEQ)] (25) where: RD = rut depth (in.), AV = air void, KV = kinematic viscosity (centistroke), 25 ESAL so cs AAT TAC raw 11R“ MR. c. Carper field 51 RLT : —0 +0.05238. + 0.0004 1 (, there: RLT 40.430 STAB 011F840 AYEHOT ESAL Adl'an‘ages ”the! ‘ One Ca: Hitting a easily Ct lOadS. E] ESAL SD CS AAT TAC TBEQ MR. the number of 18-kip ESALS at which the rut depth is being calculated, pavement surface deflection (in.), compressive strain at the bottom of AC, average annual temperature (0F), thickness of AC, equivalent thickness of base material, resilient modulus of the roadbed soil, and resilient modulus of base material c. Carpenter suggests a rut-depth prediction model based on field data collected from field sites in Illinois [19]. RUT = —0.040930187(—40 + 80)”)349 — 0.0002569715(STAB) + 0.083705(DIFFS 40) + 0.0523817(A VEHOT) + 0.3 13578(ESAL)°-°‘”" —1.27453(-200)"-2“m (26) + 0.0004 1937(1)) + 0.0106828(RDEN)— 1.38669 where: RUT -40+80 STAB DIFFS40 AVEHOT ESAL -200 D RDEN rut-depth (in.), percent passing the No. 40 seive, retained on the No. 80 sieve of the surface mix (%), Marshall stability of the surface mixture (1b.), hump in the FHWA 0.45 power gradation curve on the No. 40 sieve in the surface mixture (%), average of the maximum monthly temperature during June, July, and August (0C), cumulative 18-kip ESALS using the overlay since placement (millions), percent passing the No. 200 sieve in the binder level mix (%), theoretical maximum density (pet), and relative density of the surface mixture (%). Advantages of Mechanistic-Empirical Rutting Prediction Models a. Type I . One can have a simple design criterion. By using a unique relationship between rutting and a pavement response such as the strain at the top of subgrade, one can easily control the magnitude of rutting amount in a pavement due to given traffic loads. Effects of various factors on pavement rutting can be integrated and quantified 26 in the the e magni pavem b. Type II . This In analysis asphalt c moisture Performai 0 The Effect monthly te Disadvantages ”.l'Pel 0 The mOde] Universal a 1 in the Star]: \‘ariabje is r mode] Predj. in the vertical strain at the t0p of subgrade soil. If a pavement designer understands the effects of various material properties and environmental conditions on the magnitude of vertical strain at the top of roadbed soil, he/she can easily design a pavement structure that successfully meets a mechanistic design criterion of rutting. b. Type II This type of rutting prediction model can be used very effectively in the pavement analysis for evaluating the effects of asphalt mix variables (i.e. air void, viscosity, asphalt content, aggregate angularity and so on) or subgrade soil properties (i.e. moisture content, relative density, and so on) on overall pavement rutting performance. The effect of environmental factor such as ambient annual temperature or maximum monthly temperature on asphalt modulus can be incorporated. Disadvantages of Mechanistic Empirical Rutting Prediction Models a. Type I The models are based on statistical analysis of observed field or laboratory data. Universal applicability of such models is somewhat limited. In the statistical analysis of this type of rutting prediction model, the independent variable is not rut-depth but the number of load applications. As seen in Table 1, the model predicts the number of load applications corresponding to the design criterion of rut-depth. It means that whenever a pavement design engineer wants to change the design criteria of rut-depth, he/she must find different model parameters that 27 corre I l paran' Asph to the . ln pat most ( subgra vertica '1 Type II o Applica 0 Variablt highly ‘ model. comm)L MechaniStit in 0 AASHTQ r dellecrim1 in or moismrg pavement mfldeled by correspond to the design criteria. For instance, when the design criterion in the Asphalt Institute model is changed from 0.5 inch of rut-depth to 0.3 inch, the parameters in the model should be changed, otherwise the model cannot be applied to the changed criterion. In pavements with thick asphalt-concrete layer that is subjected to heavy traffic load, most of permanent deformation occurs in the bituminous layer, rather than in the subgrade [6]. In such cases, it is difficult to control the pavement rutting only by vertical compressive strain on the top of roadbed soil. b. Type II Applicability is somewhat limited. Variables assigned in a rutting mechanistic-empirical prediction model may be highly correlated with each other, which may lead to high multi-colinearity of the model. These multi-colinearity effects can prevent the model from showing the contributions of highly correlated variables to total rut-depth. Mechanistic-Empirical Flexible Pavement Design In order to overcome the shortcomings from empirical design such as the AASHTO method [16], the numerical capability to calculate the stress, strain, or deflection in a pavement, when subjected to external loads or the effects of temperature or moisture, has been developed. However, various investigators have recognized that pavement performance is likely to be influenced by many factors that cannot be precisely modeled by mechanistic methods. Hence, it is necessary to calibrate the models with 28 observed developet E) desigr procedure available empirical related to Thickness-1 procedure. Specificatim assurance ; Considered. NCI PTOCCdme a for a mecha Ih”transfer Imodels 10 l milling Cra empirical de mOde] 1hr 01 observed performance data, i.e. empirical correlation. So, the procedure that is being developed as a new design method of the pavement is called mechanistic-empirical (M- E) design procedure. The current effort of developing mechanistic-empirical design procedures does not require new technology but assessing, evaluating, and applying available mechanistic-empirical technology. It should be noted that a mechanistic- empirical design procedure cannot adequately address all pertinent factors and issues related to load responses, distresses development, and ultimate system performance. Thickness-related factors are most readily addressed by mechanistic-empirical design procedure. Some other important factors such as material selection process and material specification, construction policy and specifications, quality control and quality assurance procedures, and maintenance and rehabilitation practices should also be considered. NCHRP 1-26 reports that the major inputs to the mechanistic-empirical design procedure are structural models, transfer functions, and reliability [20]. The framework for a mechanistic empirical model is illustrated in Figure 3. The report also concludes that transfer functions which relate the pavement responses determined from mechanistic models to pavement performance as measured by the type and severity of distress (rutting, cracking, roughness, and so on) are the weakest part in the mechanistic- empirical design procedure [20]. Hence, the achievement of rigorous distress prediction model through extensive field calibration and verification is the most important requirement in the complete implementation of M-E design procedure. In Phase I of NCHRP 1-26 project, it was concluded that the available flexible pavement structural models and computer codes (such as MICHPAVE, ILLIPAVE, CHEVRONX, ELSYMS, 29 Inputs Material Characterization Structural Model ‘ ‘ Paving Materials - Subgrade Soil Traffic Climate Pavement Response 0982A Transfer Functions Design Reliability ‘ ' Pavement Distress/Performance Figure 3 Framework of a M-E Flexible Pavement Design Model [20] 30 Layer Thickness. Tk Material Properties. Mi it t )1 Change Material Properties Change Layer Thickness Start over with initial i.j No Last Load Confi guration'? (Last j?) Load Configuration. Pj A Change Load Configuration Compute Damage. D“ ['1 ii =X—‘- Nfljk <—-———1 Traffic. nii Yes ( Pavement Failure) Yes (Pavement Over-designed) Design Thickness Figure 4 M-E Flexible Pavement Design Flowchart in Minnesota Praetice [21] 31 BISAK " developm design prt which the flowchart Research Based on t C AlthOL Structu rutting the m mecha: flexiblt tamper; mechar: many 1'. both prl man.) i prOCCdU l0ad-rel (— mechani 1 BISAR, WESLEA and so on) for mechanistic analysis are adequate for supporting the development and initiating the implementation of M-E thickness design procedures [20]. Currently, some of SHA’s are in the process of piloting M-E flexible pavement design procedures. Recently, Minnesota DOT has proposed a M-E design procedure in which the major design components have been calibrated to regional conditions. A flowchart regarding this design procedure is shown in Figure 4 [21]. Research Work Needed Based on the literature review presented above the following conclusions are drawn: . Although great amount of research efforts have been conducted to develop pavement structural performance models in terms of mechanistic-oriented distress such as rutting, or fatigue cracking, less effort has been devoted towards the applicability of the models to various regional and environmental conditions by combining mechanistic and non-mechanistic factors. It is obvious that fatigue and rutting of the flexible pavements are highly affected by non-mechanistic factors such as temperature, specific regional condition, and material properties as well as primary mechanistic factors (i.e. deflection, loading pressure, etc.). The models suggested by many investigators have not had enough success to accommodate systematically both primary mechanistic factors and non-mechanistic factors, which prevented many SHA’s from adopting mechanistic-empirical flexible pavement design procedure. Therefore, in brief, there is an urgent need to develop comprehensive load-related pavement distress prediction models that include both primary mechanistic factors and non-mechanistic factors in a reasonable manner, as 32 pave apprt M-E deter theorr analyfi desigrl affect be n compr design pavement design procedure is moving from empirical to mechanistic-empirical approaches. M-E design procedures presently suggested by many researchers incorporate deterministic design parameters and simplification of exact formula based on theoretical assumptions such as perfect elasticity, homogeneity, or two-dimensional analysis. The present M-E design procedure cannot prevent the uncertainties from design input variables and pragmatic simplification of the design from significantly affecting the accuracy of design outputs. In conclusion, it is necessary that in order to be more reasonable and practical, M-E design procedures must contain comprehensive reliability techniques to control various uncertainties of pavement design and produce a consistent pavement performance level. 33 Data Coll OJ pavement included 1 TrafT Asph Cross Road PaVerl Distre Table 2 pr Pal'emem 5 Site Select Has The length Presented ir Types of FT FOI- mcmgx Cl CHAPTER III FIELD STUDY - DATA COLLECTION Data Collection Criteria One of the first tasks of this study was to select test sites from in-service highway pavements in Michigan. A set of criterion for choosing the sites was developed and it included the following variables: Traffic volume and load Asphalt course thickness Cross-sections Roadbed type Pavement surface age Distress(rutting) severity Table 2 provides a list of the combination of variables used to prioritize the various pavement sections. Site Selection Based on the above criteria and variables, thirty-nine test sections were selected. The length of each section ranged from 300 to 500-ft. The locations of these sites are presented in Figure 5. The detailed information of selected sections is shown in Table 3. Types of Field Data Collected For each selected pavement section, the distress data (e. g. rut-depth, fatigue cracking), cross-sectional properties, traffic, and deflection data were collected and stored 34 Table 2. l 1‘ Pavel Table 2. Pavement Selection Criterion Selection Criteria Level Traffic Volume Light Medium Heavy HMAC Thickness Thin < 3inch Medium z 3 inch ~6 inch Thick > 6inch Cross-Section 3 layers 4 layers Roadbed Soil Stiff Sofi . Pavement Age Less than 3 years since last rehabilitation New construction Old pavement Pavement Distress (Rutting) Severity High Medium Low 35 .’1 *' fly / i 1"" L ,, K) -- _, 1 * ' —/ 1" * * ——* 4""; * * * ‘ W m__%\ f. . g l/ g \___ . l' v '\\- 1k P” a .1; n. __ P ~\* .. I - / [ Rik-H <9 * "W ’ r a- -1 g \\ xv. \ x/rJ \ / \ \\ 1 a 1‘ ‘ 1 :1) l l * * * *\ I xxx /' \\ ”3 1;’/ \‘x i/ * it ( 1/ \‘z \\ ‘\‘\.\\,/i * \ l / * a \ a ‘t \l * * \ \1. ‘ * \ I 52..- 5 91 \___\ _ I 96 /r’)\ \ / / ___*\ A \l _’ l ‘7’, Th :-——\N \ ,{i l l * ”rift; l * _ 1942/! 199/1"; [I g” ”(‘1 '— I) _ ,/”‘ * . .- — * l * ,{f ‘l , ,,,,, ,4. * . .,—_ firm?) “’TZL—rfik Figure 5 Distribution of Test Sites across the State of Michigan 36 Table 3 5 District No. ‘1_-—-——-"'——'--""' SuEnm’ Grand North North North North Sumr L'nnusrry North 11/ Cuttersny / Norm Grand _/ l Sunor Norm i .zzgjo/Ozg’ggr. ééfaagaa fl '1 T /a" 5 Table 3 Summary of Selected Sites Mile Post Asphalt 1991 1997 1998 Grade Test Test Test District No. Code (Siontrol Route ection PM“ To MSUIZF MSU19F MSUZIF University MSU29F 23092 North MSU35F 16091 37 40ft (12.2m) Is I; la Is a # a 7 Inner Wheel Path 20fi (6.1m) ma & I”; & #,& la #,& & e,& & law; a #,& & s,& 7 7 Outer Wheel Path e 300 ft (91.5m) # : measurement of rut—depth &: measurement of deflection using FWD Figure 6 Description of Typical Test Site 38 macm yearly l . Dis M63511]. 0.05inci for both study. r sections . C to Pat'emei this data . Tra By revie obtained. data for t 0 Dent Nondestrt conductec in Figure deflection inches (en the load 0 conceptual locations . l in a comprehensive database. During the research period, the database was updated on a yearly basis. . Distress (rutting) data Measuring the rut-depth, a six-foot long straight-edge leveling rod with an accuracy of 0.05inch (1.27mm) was used. The rut—depth was measured‘at an interval of 40ft (12.2m) for both inner and outer wheel paths and recorded in inches as shown in Figure 6. In this study, rut-depths of 930 locations were measured on 39 in-service Michigan pavement sections from 1991 to 1998. . Cross sectional properties. Pavement cross-sectional data was obtained from the MDOT PMS database. In the event this data was not available, pavement cores were extracted and measured. Traffic 0 By reviewing MDOT data sufficiency books, a set of traffic data for the test sites was obtained. This traffic data includes average daily traffic (ADT) and percent commercial data for the construction or last rehabilitation year of each test site. . Deflection Data Nondestructive deflection tests (NDT) using a fall weight deflectometer (FWD) were conducted at uniform interval of 20-fi (6.1m) at the beginning of each section as shown in Figure 6. All tests were conducted on the surface along outer wheel path. The 7 deflection sensors (0 (0), 8 (20.3), 12 (30.5), 18 (45.7), 24 (61), 36 (91.5), 60 (152.4) inches (cm) from the center of loading plate) along outer wheel path were installed, and the load of 9000lb (40kN) was applied on the plate with the radius of 5.9lin (15cm). A conceptual drawing is shown in Figure 7. In this study, FWD test was conducted on 930 locations at 39 in-service Michigan pavement sections from 1991 to 1998. PO) Loading Plate 59"” *3 c v v v v 12" 8' 4' 5" 6' 12' 24' Figure 7 Conceptual Configuration of FWD Test . Temperature The air and surface temperature at the test were recorded using a sensor attached to the FWD. In order to obtain comprehensive ambient temperature history of each test site, the database of the department of agriculture was used. From the database, 30 years temperature history data of 27 major cities in Michigan was collected and tabulated in Table 4. 39 Overvie pavemer monitori across tl sections complen (GPS) u second 5 are desig Data is c Perform; e(lllipme Manager Which it DATAP, eaSY‘tO-u Data Ac T mPJM available Overview of Long Term Pavement Performance (LTPP) Database The Long Term Pavement Performance (LTPP) is a 20-year study of in-service pavements. It is the largest and most comprehensive pavement study in the world, monitoring more than 2,400 asphalt and portland cement concrete pavement test sections across the United States and Canada. The LTPP program will collect data on pavement sections in the study during the 20-year period. The LTPP program has two complementary experiments to meet the objectives. The General Pavement Studies (GPS) use in-service pavements as originally constructed or afier the first overlay. The second set of LTPP experiments is the Specific Pavement Studies (SPS.) These studies are designed to meet LTPP objectives that the GPS experiments cannot completely meet. Data is collected on forms found in the Data Collection Guide for Long Term Pavement Performance and other documents, or in machine-readable form from monitoring equipment. Data collected is available from a database known as the LTPP Information Management System (LTPP-[MS or IMS). Most recently, lLTPP is providing the data which it has collected over the past 10 years to the highway community via DATAPAVE, a new software package introduced in 1998 that presents LTPP data on an easy-to-use CD-ROM [22]. Data Acquisition from LTPP Database Twenty-four GPS sections were selected (Table 5). The data regarding rut-depth, cross-sectional properties, material properties, FWD data, and trafi'tc were extracted from LTPPJMS using DATAPAVE. The temperature information that is not currently available in DATAPAVE CD-ROM was obtained from a climatic database provided by 40 Tdfle4' l— Nonl Nonh Soufl Sour / Soufl l VVesu Table 4 Temperature History of Major Cities in Michigan Region City Ambient Ambient Temperature (0F) Temperature (0C) Central Lower Alma 46.91 8.28 Gladwin 43.67 6.48 Eastern Central Lower Badaxe “'05 7'81 Sandusky 46.36 7.98 Chatham 41.60 5.33 Eastern Upper Grandmar 41.47 5.26 Newberry 40.55 4.75 Alpena 42.68 5.93 North Eastern Lower Easttawa 43.01 6.12 Garyling 42.52 5.85 Cheboygan 43.28 6.27 North Western Lower Eastjordan 44.38 6.88 Traverse City 44.64 7.02 South Central Lower Lansing 46.86 8.26 Battle Creek 48.02 8.90 Detroit 48.57 9.21 South Eastern Lower Pontiac 48.37 9.10 Toledo 48.37 9.10 South Western Lower Grandfapid 47'” 8'58 Southbend 49.40 9.67 Western Central Lower Hm “’63 8'13 Muskegon 47. 16 8.42 Herman 28.66 -1 .86 lHoughton 40.01 4.45 Eastern Upper Ironmountain 41.72 5.40 Ironwood 39.85 4.36 Stephenson 39.48 4. 15 41 Table 5 Summary of Selected LTPP-GPS Sections (a)Site Information Interval of . . Section State Climatic 1:231:31: Location of Traffic Tannual (F) [32:23: I.D. Reglon (fi) Fwagl‘est Open Date (centistoke) 33-1001 NH Wet Freeze 500 25 81-1-1 46.1 388.5 42-1599 PA Wet Freeze 500 25 87-7-31 47.8 452 25-1002 MA Wet Freeze 500 25 82-4-30 47.7 425.5 27-1016 MN Wet Freeze 500 25 76-1-1 40.4 304.5 27—1019 MN Wet Freeze 500 25 80-1-1 42.4 461 89-1021 PQ Wet Freeze 500 25 81-6-1 39.2 159 34-1031 NJ Wet Freeze 500 25 73-3-31 52.5 438.5 87-1622 ON Wet Freeze 500 25 76-5-31 41.0 350 84-1684 NB Wet Freeze 500 25 78-8-31 44.3 210 26-1013 MI Wet Freeze 500 25 79-12-31 45.6 305 42-1605 PA Wet Freeze 500 25 71-8-31 50.4 440 8-1053 CO Dry Freeze 500 25 84-2-1 49.1 240 26-1001 MI Wet Freeze 500 25 71-8-3 1 43 .9 3 15 51-1464 VA Wet Freeze 500 25 79-4-30 58.0 424 87-1620 ON Wet Freeze 500 25 81-5-31 41.0 350 34-1011 NJ Wet Freeze 500 25 70-2-28 52.7 356 25-1004 MA Wet Freeze 500 25 74-6-30 51.4 390 30-8129 MT Dry Freeze 500 25 88-6-1 41.4 356 29-1005 MO Wet Freeze 500 25 74-5-1 51.0 389 30-7066 MT Dry Freeze 500 25 81-6-1 46.4 325 32-1021 NV Dry Freeze 500 25 81-3-1 54.9 460 29-1002 MO Wet Freeze 500 25 86-4-1 54.8 381.5 23-1001 ME Wet Freeze 500 25 72-11-1 44.0 367.1 2-1002 AK Wet Freeze 500 25 84-10-1 40.8 140 42 :E2 33. uxauu>< -_c as. 95 E 552% .7224... :5. 2: E 5.57. :. .._ ..CELC 995.22% 925...: ..J ..c antic—Z uni”; < nigh; < omen; < .6390th ‘52:.632 ..c 3:532 ...em22532 “easyf. 92:2: L< . 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Wm. 833.3. 333 .-8 3.3 8&3 . v... 3&3333 8&33... 88. 838 33833. 3.3 333333. .3378 322802 ovflwnsw 3.3m .o 32 .8302on ”WM—“.3“ 033:3 033 $05.23... $05.03... 3< own-5:. owflo>< 328.50 263.3an 2883 23-8.5 38.03 as. 38 3o “.32.... 5:332. .o 88:53 33 43 the Nan from 30 Prelimir o Bac The bad elastic 1H. \WESDE. lowest er reasonab machine. individu; individua individua be noted 1 Accordin‘ usually gr Design C comparab adilmed 1 the backc number is Project [15 the National Oceanic and Atmospheric Administration (N 0AA). The averaged values from 30 years temperature histories at same coordinates of the test sites were used. Preliminary Data Analysis 0 Backcalculation The backcalculation program MICHBACK was used to back-calculate pavement layer elastic moduli [23]. According to a report of LTPP-GPS data analysis, MODCOMP3.6, WESDEF, and MICHBACK produced most reasonable solutions of layer moduli with lowest errors [24]. Thus, the moduli back-calculated by MICHBACK can be considered reasonable. The deflections in the Michigan database measured by KUAB, a FWD machine, were normalized to a 9000lb (40kN) load level and then backcalculated on an individual drop basis, while that of LTPP-GPS database were backclaculated on an individual drop basis without the normalization. The backcalculated moduli on an individual drop basis were, then, filtered and averaged on a per test site basis. It is should be noted that more than 15 individual drops of FWD were conducted at each test section. According to Elliott and Darter et al., the backcalualted or in-situ moduli of subgrade are usually greater than the laboratory moduli that are used as standard values in AASHTO Design Guide [25]. In order for the M-E design procedure to be consistent and comparable with the AASHTO Design Guide, all the backcalulated moduli should be adjusted to values that are consistent with laboratory determined moduli. In this study, the backclaulated moduli by MICHBACK was multiplied by a factor of 0.33. This number is recommended in AASHTO Design Guide and the final report of NCHRP 1-32 project [16,26]. 44 Temper: In an 6ft} adjust [ht mid-dept pans: 1 backcalcx lit by Michi estimatin based on at MSU 5 I11115. in I “fill the I mOdUiuS Temperature Correction Procedure In an effort to obtain effective annual layer moduli of a flexible pavement, the process to adjust the moduli to a reference temperature was applied. This procedure is based on the mid-depth temperature of an asphaltic layer as an effective temperature and has two parts: 1) prediction of the AC mid-depth temperature and 2) adjustment of the backcalculated AC modulus to a reference temperature. In order to calculate the AC mid-depth temperature, a new procedure developed by Michigan State University was used [27]. The procedure suggests two approaches for estimating the AC mid-depth temperature: (1) use a finite difference method (FDM) based on heat transfer theory and (2) use a statistical model. A research study conducted at MSU shows that the two methods produce similar results with the MDOT database. Thus, in this study, the statistical equation was used to avoid the complexity associated with the FDM procedure. The equation is as follows [27]: TM = Tm, + sin(—6.3252Time + 5.0967) * (—0.8767h - 0.2788h2‘ + 0.0321113) (27) where: Tpav = AC pavement temperature at a depth, 0C, Tsurf = AC pavement temperature at surface, 0C, h = pavement depth, in., and Time = Time at the temperature measurement (e.g. 1:30PM _, 13.5/24 = 0.5625) The following equation, developed recently by Park, et al., was used to adjust the AC modulus to a reference temperature of 20 0C [27]: E20 =100.0224(T-20) * E1 (28) 45 where I Table 6 : o Prin mm at] structura was com available and nonli PaVemeni Primary 1 [28]. me ' Estin In general Classifica; 18,000“) ‘ estimating [Elallt'elV 5 l where : E20 = adjusted AC modulus to the reference temperature of 20 0C, ET = backcalculated AC modulus from FWD testing at temperature T (0C), and T = the mid-depth temperature (0C) of the AC layer at the time of FWD testing. Table 6 shows backcalculated and adjusted moduli of pavement layers in the test sites. 0 Primary Pavement Responses With the backcalculated and temperature-adj usted elastic moduli of pavement layers, a structural analysis of the pavement using the mechanistic-based load-deformation model was conducted to calculate the critical pavement responses. There are many models available based on linear layered-elastic, nonlinear layered-elastic, linear finite element, and nonlinear finite element theory. In this study, CHEVRONX, a computer program for pavement analysis based on a linear layered-elastic theory was used to calculate the primary pavement responses because of its relative simplicity and. excellent accuracy [28]. The pavement responses are summarized in Table 7. 0 Estimation of Cumulative Traffic Volume In general, traffic volume is usually represented in terms of particular vehicle classifications and equivalent single axle loads (ESALS). In Michigan, standard EASL is 18,0001b (80kN) as developed at the AASHO Road Test. The current MDOT method for estimating the number of 18-kips ESALS over the design period for the highway is relatively simplistic and easy to use, while the 1993 AASHTO Design Guide adopts a more complex procedure that utilize axle load distributions and vehicle classifications. 46 Table 6 TESTS l Code leinui'r MSLIM MSL 12} MSifiiSl MSL'IGF MEL: 1F Mm ZIP-i MS'L‘IJF-Z .& MSL’ZSF mm; MSL 25F x. MsleF \ Mime; MSL'S'K W [7 HS'L'BZF 56m; 513L351: We 'u\-> SL3 7}: Table 6 Summary of Backcalculated Moduli of Test Sites TESTS IN 1991 Code Correction Factor Base Subbase AC Depth 469419 MSU12F . 580761 822575 60708 652992 830492 14 452136 1067515 11 MSU22F-1 MSU22F-2 820202 2715810 54417 572524 807046 38035 555825 9617 899805 1767789 136776 1 MSU29F . . 564251 734914 665394 396153 702515 25 311297 531344 539247 1 126262 49657 53878 47 Code MS'L‘l il‘ .,_____ MSU 5F __ MSULSI MSL.‘ZZF- HSL'ZZF- 51557; N 313L139} N was; '\ MSLa; Table 6 (cont’d) TESTS IN 1997 Code Subbase MSU18F MSU22F-2 MSU34F MSUSOF MSUS 1 F TESTS IN 1998 Code Subbase MSU22F-2 21 1 8 MSU39F AC 657559 402914 341017 373937 453639 245517 438141 442553 AC 882305 590779 795964 Base Subbase 610202 37895 1202550 364921 36138 1069519 1 619633 61989 Subbase 48 Correction Factor Table Tests ir \ Coc Table 7 Summary of Pavement Responses in Test Sites Tests in 1991 Pavement Responses Vertical Compressive Strain at the Vertical Compressive Strain at the top of Base top of Subgrade Surface Deflection (in) MSU22F-2 49 l - F =L L .L r~l~l TxLl.N.L Table 7 (cont’d) Tests in 1997 Pavement Responses Code Surface Deflection Vertical Compressive Strain Vertical Compressive Strain (in) at the top of Base . at the top of Subgrade MSU22F-2 Tests in 1998 Pavement Responses Code Surface Deflection Vertical Compressive Strain Vertical Compressive Strain (in) at the top of Base at the top of Subgrade MSU22F-2 50 Thee terms . p—a E. _I .5 H. a — U ..a "’1 4;. U) Ix) -—‘ ~—! g: In this lanes II 5) Gro Where: In this W Miching 6) True In Michj Inthisst Gll'en [h | 01’18.kjF The Cum] Table 9 s In this ch; mode] in _‘ The current MDOT technique for estimating traffic volume during a design period in terms of ESALS requires the following inputs [12]; 1) Initial Average Daily Traffic (ADTO) 2) Initial Proportion of Trucks in ADTo (Percent Commercial: PCOM) 3) Directional Distribution Factor (DDF) ' 4) Truck lane Distribution Factor (LDF) In this study, the factor is assumed to be 1.0 for one lane in one direction and 0.9 for two lanes in one direction, as it is in MODT practice. 5) Growth Factor of Trucks (GF): this can be calculated as follows [16]; r where: r = annual growth rate (a proportion), and n = design period, years In this study, annual growth rates for all test sections are assumed to be 1.5% (for local Michigan road) or 2% (for interstate). 6) Truck Equivalency Factor (TEF): In Michigan, the truck equivalency factor of 0.57 (SN=6) or 0.59 (SN=5) has been used. In this study, the mean truck equivalency factor of 0.58 was used for all test sections. Given these inputs, the following equation was used to estimate the cumulative number of 18-kip ESAL for given performance period as follows Cum. ESAL = (ADTO) (PCOM)(LDF)(DDF)(GF)(TEF) (30) The cumulative ESAL estimated by equation 24 for all test sections is shown in Table 8. Table 9 shows the summary of statistics of the variables that were preliminarily analyzed in this chapter. These variables were incorporated in the calibration of the existing rutting model in MICHPAVE, which will be presented in next chapter. 51 --4 CD 2: 9 \n» A V" . lzl M 511 .’ f » ...- (I. I) ' . . ( ...- I) ', } . A 3"; . I. . ‘ z a: '5. (~17 {/3 {/1 ”‘1 r". r”: Table 8 Summary of Traffic in Test Sites Code iilmil‘iiirplif Initial ADT %Commercial 1919:2311. 19:12:“ = = MSUOSF 1965 550 10 366933 MSU06F 1976 700 9 222491 MSUllF 1979 7000 5 MSUIZF 1961 1900 9 1358927 MSUISF 1977 2300 18 1354130 2026646 MSU16F 1966 800 5 254574 MSU18F 1977 2300 18 1354130 2144690 MSU19F 1980 1600 7 281283 MSU21F 1984 700 10 108519 msuzzr 1963 2000 7 1021962 1302089 1351258 MSU23F 1984 600 13 120922 235087 255126 MSU24F 1978 800 12 289338 msuzsr 1966 800 5 254574 MSU26F 1975 2275 10 863654 MSU29F 1980 1500 10 376718 MSU30F 1980 1600 7 281283 MSU32F 1980 1750 6 263703 426817 455448 MSU34F 1977 1000 6 196251 293717 310825 MSU35F 1977 1450 8 379418 . v . MSU36F 1985 3051 12 482838 1010793 MSU37F 1985 3051 12 482838 1010793 _ MSU38F 1980 450 10 113015 . . ‘ MSU39F 1984 1550 11 264322 MSU40F 1980 2150 9 485966 MSU41F 1979 1600 12 530078 MSU42F 1979 5250 19 2753922 MSU45F 1979 3000 11 911072 MSU46F 1980 400 10 100458 MSU47F 1971 400 12 234973 MSU49F 1979 1550 13 MSUSOF 1993 2800 7 MSUSlF 1993 800 8 MSU52F 1985 11 125 3 52 u l v . I ’lfil‘l :..u.E.o._E 2.. 55.3.5ch :76: .53 :2... :c. Est 5...: 2..» WUT~=._..:> UDNA=2~<¥C 20.53.33.73s3 \fihfinQnEZT. 0 0:345 Illlllflqll 1.. 4 . 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'h. :00i .. ll .fi 89% $3 2.3 $3 3..» 83 833 one 9mm 9% a: 833.6 3.3 8% S3: 85.: «~09: 835.; 8.8 8.8 and 882 293.3 33 a? 83 RE: 82:. 5.3». 8.6 52 3a 83 Se.$~.~ 28 3.3. 33.: 863 62.3 34.96 8.2 2.2 3.6 582 EC 93 $3 $3 fie c5 c5 :5 3< EoBE< 3:52 38» a . . n m 68.35 68m 9.. 68.55 68m 9.. 5.88 a 2.3. 68688 2.9.55 868 86o E 54 Vali meek PTOPf total 1 layers Where PD, PD: PD; ‘ “we abb EXisting the tram ”11 pred'f MDOT C] Table 10. CHAPTER IV MODEL DEVLOPEMENT AND SENSITIVITY ANALYSIS Validation of Existing Rut Prediction Model The existing rut model in MICHPAVE predicts rut-depth as a function of various mechanistic and empirical parameters including primary pavement responses, material properties, cross-sectional properties, environmental conditions, and traffic volume. The total rut-depth is calculated by integrating permanent deformations of different pavement layers. The general format of the model is expressed as follows: Total Rut-Depth = PD1+PD2+PD3 (31) where : PD] = permanent deformation of AC surface layer, = f”, (AV,AAT,KV,ESAL,SD,CS,TAC), PDZ = permanent deformation of base and subbase layer, = fro, (MRB,MRSB,SD,ESAL,TB,TSB), and PD3 = permanent deformation of subgrade. = fPD, (ESALMRB, TBaTSB, TAC) The abbreviations PD], PD;, and PD3 have been described previously in equation 25. The existing rut prediction model was evaluated using the field data, as obtained in 1997 and the traffic volume projected up to the testing date. Among the input variables for existing rut prediction model, air void and kinematic viscosity which are not available in the WOT database were assumed based on engineering judgement and are summarized in Table 10. 55 Table 10 Assumptions for Kinematic Viscosity and Air Void MDOT Region Superior North Others Asphalt Grade AC2.5 AC5 AC 1 0 Kinematic Viscosity (Centistoke) 159 212 270 AirVoid (%) 4 4 f 4 56 the of mun exist] Varial Origin. relatioi mOdulu r eamine g “lthout . Strond 5, he regfcs The comparison between predicted rut-depths and observed rut-depth is presented in Figure 8. 32 data points out of 69 test points plotted outside the $0.1 inch (0.25cm) of the deviation. This difference was statistically significant and warrants calibration. Proposed Rut Prediction Model There is an implicit assumption in statistical model development that the variables that predict the dependent variable are mutually independent. When linear combinations of independent variables are highly correlated, multicollinearity exists. Hence, in engineering practice, when building performance models based on statistical regression, mutually less correlated variables should be selected in the process of modeling. The existing rut prediction model includes 12 independent variables to predict a dependent variable of the rut-depth. Some of these variables which have the same mechanistic origins are highly correlated and suspected to result in multicollinearity. For example the relationship between surface deflection and AC thickness, kinematic viscosity and AC modulus or kinematic viscosity and annual ambient temperature. Thus, they must be rearranged to clearly identify their effects and reasonable contributions to the model without introducing multicollinearity. Framework for Calibration and Modification of Rut Prediction Model The first step was to select variables used in the format of the new model and the second step was to develop a conceptual form. Based on these two steps, coefficients of the regression were determined through the calibration procedure described in Figure l. 57 Measured (in) 0. l 0.2 0.3 0.4 0.5 Predicted (in) Figure 8 Measured vs. Predicted Rut-Depth Using Existing Model 58 0.6 pr 1hr ha ad; of : im'c dept Variable Selection With respect to mechanistic responses, two factors must be present in the rutting prediction model in order to characterize the mechanism; vertical permanent strains of the pavement layers and the number of load application's. Typically, these two factors have been key components of all the models that have been developed in the past. In addition, environmental conditions should be considered to explain regional differences of rutting rate with traffic. A correlation matrix was developed using SPSS [29] to investigate the impact of pavement response, environmental condition and traffic on rut- depth based on field data (refer to table 11). Considering mechanistic and statistical relationships between rut-depth and all variables affecting pavement performance, the following variables were selected for building a rutting prediction model; SD : Pavement surface deflection (in.), KV : Kinematic viscosity (centistroke), Tammi : Annual ambient temperature (°F), HAC : Thickness of asphalt concrete (in.), N : Cumulative traffic volume (ESAL), 8w,“ : Vertical compressive strain at the top of base layer (103), smsg : Vertical compressive strain at the top of subgrade (10'3), EAC : Resilient modulus of asphalt concrete (psi), and Egg : Resilient modulus of subgrade (psi). Basic Concept of the Model As outlined previously, the existing multiple regression analysis assumes that the variables have only linear relationships with each other. Theoretical considerations or model formulation may suggest otherwise. A reasonable conceptual model that consists of two categories: non-mechanistic (or empirical) function and mechanistic function was developed: 59 coo. F F.8d ommd god and K3 momd wood. NF Fd Rad NF Fd. mnnd- 3nd 982m doo. F dFNd Bvd mmmd med med 9 F .0. 390 End m F Fd- owed- mmvd €5.51 08. F onwd wand. mmod. «and. vmod- no F .0 wood. mm F d S F d mmmd 058... 08. F vmwd- wand. ddmd. mm F d on F d vmwd owed. and Fde .35..» . . . . - . . . - . - . - 5.8230 08 F ohm d and d nun 0 NF 0. «we 0. 3F 0 mwm o NmF 0 83:5 . . . . - _ - . . - . - 9.8. 59$ 80 F man 0 mwo 0. can 0 an o NmF 0. Nov 0 3F 0 ozmmmano ouflmnaw oooF Fvvd- Food vNFd FFFd- dmmd- «Dd- - Egm . manned—too oooF SFd- RFd- man de Fwdd ed oooF 3nd oFmd. 3nd- Fomd 5mm oooF vad. 8nd- dmmd 3m coo. F 8nd god- ink oooF FmFd 9:. . 358$, 08 F 25595. 32:”. meSK USE... .55.; 8:00:00 83. £95 owmwwww 8m 3m 2m «3:. ofi 3885 83.3 ozmmanoo ozmmdano uszocE 8335/ 608923 .Fo x5e: aoufloboo : 038. 60 Rut Depth = g(x) *fQ’) (32) where: g(x) = non-mechanistic function considering the adjustment of theoretical pavement rutting mechanism to field conditions based on statistically significant variables for pavement rutting, and f(x_’) = mechanistic function reflecting basic mechanism for pavement rutting. The g(x) may be modified with varying regions and is assumed as a deterministic number based on engineering judgement. Nonlinear Regression Approach Using the conceptual model determined above, a nonlinear regression analysis was conducted with data collected from 39 test sections in 1991 and 1997. More than 760 data points from the 39 test sections were analyzed and then were grouped into 51 statistical samples representing every test site. Based on the process of numerical optimization using SYSTAT [30], a statistical computer program, the model is as follows: RD = germ g(x) = a1*HAc+a2*ln(SD)+a3*Tmua.+a4*ln(KV) f(x_’) = a5+a6*(8v,basc)a7+a8*(sv,sg)89+a10*ln(N)-al 1 *ln(EAc/Esg) where : RD = average rut depth along a specified wheel path segment (inch). The results from this nonlinear regression analysis are summarized in Table 12. Finally, the revised rut prediction model is as follows: 61 RD = (— 0.016HAC + 0.0331n(SD)+ 0.011TW, - 0.011n(KV))- 33 [— 2.703 + 0.6570,,” )°'°‘” + 0.2710,,” )0-“3 + O.2581n(N)— 0.034 111(21ij ( ) SC The R2 of 90.5% indicates that the rut prediction of this nonlinear regression equation can be considered relatively useful. From the p-value of 2.044E-18 for the regression relation between predicted rut-depth and independent variables, one can conclude that the regression relation is very significant and useful for making predictions of rut-depths. The comparison between measured versus predicted rut-depth is shown in Figure 9. There is a certain amount of bias associated with the measurement of rut, estimation of trafiic and determination of material and cross-sectional properties. Hence, rut-depth prediction should include a confidence interval. For the purpose of this study, a tolerance level of $0.1 inch was set up. If the difference between the observed and predicted rut-depth is within this tolerance level, it can be considered that the rutting prediction by the model is accurate. As shown in Figure 9, 43 of 51 samples are within this tolerance level indicating that a reasonable fit between the model and the data exists. Sensitivity Analysis There are two objectives associated with the sensitivity analysis 0 Examine the possibility that the rutting prediction model violates physical rules of pavement performance. 0 Determine the effects of major design parameters such as material and cross- sectional properties on the magnitude of pavement rutting. 62 Table 12 Statistical Results of Nonlinear Regression Analysis DEPENDENT VARIABLE IS RD SUM-OF- MEAN- SOURCE SQUARES DF SQUARE F P-value REGRESSION 2.336 9 0.260 43.333 2.044E-18 RESIDUAL 0.188 42 0.004 TOTAL 2.583 51 CORRECTED 0.477 50 RAW R-SQUARED (l-RESIDUAL/TOTAL) = 0.905 CONFIDENCE INTERVAL (95%) PRRAMETER. ESTIMATE A.S.E. LOWER BOUND UPPER BOUND a1 -0.016 0.036 -0.089 0.058 a2 0.033 0.094 -0. 157 0.223 a3 0.01 1 0.023 -0.037 0.058 a4"' -0.010 a5 -2.703 0.181 -3.708 - l .698 a6 0.657 3.300 -6.002 7.317 a7 0.097 0.670 -1.255 1.448 a8 0.271 0.912 -1.569 2.111 a9 0.883 1.601 -2.348 4.114 a10 0.258 0.587 -0.926 1.443 a1 1 0.034 0.1 14 -0. 196 0.264 *A4 is assumed to be a constant value before running statistical analysis due to the difficulty of convergence in the regression model 63 Measured (in) .o m .o .3; P w p N 0.1 0.1 0.2 0.3 0.4 Predicted (in) Figure 9 Measured vs. Predicted Rut-Depth Using Revised Model 64 0.5 For this analysis, an experimental matrix was set up that include low, medium, and high values for AC, base, subgrade modulus and AC thickness. The representative low, medium, and high values for each input were determined based on comments of pavement design engineers of MDOT and the catalog of current state pavement design features of NCHRP 1-32 project [26]. During this sensitivity analysis, other design parameters were held constant. Table 13 shows the experimental matrix and the resulting rut-depths. Figure 10 illustrates the results of the sensitivity analysis. In Figure 10-(a), when the resilient modulus of subgrade soil was changed from low (3,000psi (20,682kPa)) to strong (10,000psi (68,940kPa)) value, the rut—depth decreases by a factor of 10%. In Figure 10-(b), when AC thickness was changed from thin (3in.) to thick (9in.), the rut-depth decreases by a factor of around 48%. These results of the sensitivity analysis indicate that the revised rutting prediction model is more sensitive to AC thickness than other design parameters selected in this analysis. Figure 11 presents the relationship between traffic and rut-depth development based on observed data from the sections of AASHO Road Test and a prediction made by the developed model. In the figure, the rate of pavement rutting development increases rapidly at the beginning of pavement performance and then stabilizes as the pavement age increases. This trend of pavement rutting behavior corresponds well with the results from several field investigations regarding rutting development of in-service pavements [l9,50,51,52]. Since the field data from pavements that had reached the end of their service lives was not collected in this study, the pavement rutting development at the final stage of pavement service life, which is known to increase with highly rapid rate [19,50], is out of the predictive range by the revised model. 65 :3 $2 oFNd m3 FF? 3% 83 80° 22 S . F n S F n 2 F n “8.32.: 9. 2:566: ton—Fan;— Ll 2.1—E Omafl 3382 3. 589.3. 5 8 F «F FF F F ..F F 2 NF _F 2 mm. mw Fe 8 no 8 F 8 S G 8 am wm Fm on m n 3 mm «m S on a. a. FF. 3 S a. 3. 9. a. :. S. mm an FM F 8 mm 3“ mm mm 3 cm am mm m FN 3 2 «N mm mm a on 2 S 2 F_ 2 2 E 2 2 : 2 F a n F o m 4 m N _ m “35.25. 0< man—665 van—Facu— 8 E mu pm Pm 3 elm pm SEE as: E E _ 2: L 3.352 9.. E32 egg 3,228 5 .8“: gen anéaxm 2 23 66 F: :1 6 0.40 ..E H :1. ° 035 . __ , e ' +Eac(100ksi) 7 g i+Eac(300ksi) . 0.30 i—a—Eac (500ksi) J 0.25 . , J , 2 4 6 8 10 12 Subgrade Resilient Modulus (ksi) (b) 065 d —— -— 2 j 0.60 L A 0.55 * 0'40 j l+Ebase (20ksi) I 0.35 ~ i-I-Ebase(50ksi) L ,+Ebase (80ksi) .. 0.30 1 I J 0.25 * 0 2 4 6 8 10 AC Thickcness (in.) Figure 10 Sensitivity of Pavement Rutting to pavement design variables : (a) Rut-Depth vs. Resilient Modulus of Subgrade, (b) Rut-Depth vs. AC Thickness, and (c) Rut-depth vs. Resilient Modulus of Base Layer 67 Rut Depth (in.) __2__22_2222-__#2_ _fl 1 j_ \ l \ '3: Esg (3ksi’)_‘ +Esg (7ksi) ‘ i—.n--I38g(10ksl) J1 0 10 20 30 40 50 60 70 so 90 Base Modulus (ksi) Figure 10 (cont’d) (c) Rut-depth vs. Resilient Modulus of Base Layer 68 9 P P u. 03 F: O Rut-Depth (in) O t.» 3:. .° N 1° — .° o Writ/J: 1 /%3;:’ 1 /"’ / + This Study 3-8-16" // 0 Q/ + AASHO Section 581 5-6-12 + AASHO Section 625 4-6-12 +New AASHO Section 4.5-8.5-23 ‘AC/Base/Suhbase Thickness — 1 ,000 2,000 3,000 4,000 5,000 6,000 7,000 Traffic (KESAL) Figure 11 Rut-Depth Development with Increase of Traffic 69 8,000 In this sensitivity analysis, no violation of mechanistic rules of pavement performance was found implying that the model can successfully explain the relationship between the pavement rutting behavior and material/cross-sectional properties. Validation with Field Data Collected in Michigan 1998 The data collected in 1998 was used to evaluate the accuracy of new rut prediction model and confirm the model’s validity. Figure 12 is a graphical presentation of this evaluation. The observation points are distributed around the 45degree line — an indication of a reasonable fit between the model and the data. The sections on which data collection was conducted sequentially in 1991,1997 and 1998 were selected to compare their rutting development as a fimction of traffic volume, as predicted using the model, to the actual measured rut-depths. The results are shown in Table 14. Figure 13 is a typical presentation of the comparison in a graphical form. Because of little accumulated traffic volume and small changes of material properties between 1997 and 1998, there are no significant changes of rut-depths in the test sections. Validation with LTPP Database Data from twenty-four LTPP-GPS sections were used in order to further validate new rutting prediction model. Figure 14 shows a plot of predicted versus observed rut-depths in LTPP sections. In 19 (79%) of the 24 sites, the differences between measured and predicted rut-depth were less than 0.1in, implying that a new rutting prediction model developed in this study has potential for nation-wide application. 70 r l" "" _ :—:T “t . Measured (in) O 0.2 0.1 - 0 4 - ., . 0 0.1 0.2 0.3 0.4 0.5 0.6 Predicted (in) Figure 12 Measured vs. Predicted Rut-Depth Based on ’98 Michigan Data Set 71 Table 14 Rutting Development at Test Sites with Increase of Traffic 1991 1997 1998 ESAL 35333;: 2332,21: ESAL 5553.21: 3331' ESAL 5.32:: SS .3" ind MSU23F 1 17089 0.16 0.1 1 226268 0.18 0.24 255126 0.18 0.24 MSU34F 196251 0.22 0.17 293717 0.26 0.23 310825 0.26 0.23 MSU39F 264322 0.16 0.11 513876 0.18 0.15 557679 0.19 0.15 MSU18F 1354130 0.24 0.17 2026646 0.26 0.28 2144690 0.25 0.23 MSU45F 911072 0.21 0.15 1431408 0.23 0.24 1 _ m" . _ m_ MSU36F 482838 0.16 0.19 1010793 0.18 0.26 1 103463 0.19 0.28 MSU32F 263703 0.20 0.08 426817 0.21 0.17 455448 0.22 0.18 J MSUlSF 1354130 0.23 0.17 2026646 0.25 0.24 2144690 0.25 0.25 I 72 (125 (120 F’ n— M Rut-Depth (in) F’ '5' (105 (100 100 Figure 13 Typical Rutting Development with Increase of Traffic (MSU39F) + predicted rut—depth + measured rut-depth I kid/Mr,” ///-—l 150 200 250 300 350 400 450 500 550 Cumulative Traffic (KESAL) 73 600 .o as 0.5 0.2 in f/ 1; 0.4 . ° ” e: . “U 2 03 ° ' ° . 5 o O 3 ° . ’ g 0.2 . /' ’ 0.1 0.0 » r _ 1 1 1 o 0.1 0.2 0.3 0.4 Predicted (in) Figure 14 Measured vs. Predicted Rut-Depth Based on Selected LTPP-GPS Data Set 74 CHAPTER V RELIABILITY-BASED APPROACH TO M-E FLEXIBLE PAVEMENT ANALYSIS General As described in Chapter 11, there are still some issues that need to be resolved before implementing M-E flexible pavement design procedure. According to Thompson eta1., following issues exist [2]: o Deterministic nature of design parameters, and 0 Lack of fit of transfer fimctions. In the current M-E design procedures that are analytical in nature, the pavement performance is predicted by deterministic nominal design parameters based on engineering judgement and then compared with established failure criteria. Outputs such as pavement thickness and material properties are derived based on an intended limit state. Limit state is defined as a state of the structure including parameters at which the structure is just on the point of not satisfying its function [31]. In other words, the current M-E design procedures predict average pavement performance using average values of design parameters without considering variability of design parameters and model bias. The reliability theory provides a rational framework for addressing these uncertainties. The objective of reliability analysis is to provide a specific degree of confidence that the pavement will perform satisfactorily while being subjected to traffic and environmental loads during its service life. The following advantages can be derived by the reliability theory if applied to the M-E flexible pavement design procedure [32]. 0 Be able to consider in design construction variability, differences between design and as-built parameters, material variability, and variability associated with traffic prediction during pavement design life. 75 o Simplify the design process by encouraging the use of same design philosophy and procedure to be adopted for all materials of construction. a Overcome the lack of fit of the transfer fimction that is statistical in nature, and the uncertainties of simplified structural analysis algorithms by quantifying model bias factors. ' 0 Provide designed pavement structures with a uniform performance level without which the comparison of life-cycle costs of alternative pavement types would be misleading and could result in the selection of a less cost-effective pavement type. 0 Provide a tool for updating standards in a rational manner, as more data becomes available. Reliability Concepts The pavement design reliability is defined as the probability that the pavement’s traffic load capacity exceeds the cumulative traffic loading on the pavement or the cumulative amount of pavement distress does not exceed a specified level regarded as a failure criterion during a specified design life. Since there are uncertainties in the major parameter values of pavements such as moduli of layers, thickness of layers, traffic volume, etc., it is reasonable to define each parameter as a random variable with its mean and standard deviation or its complete probability distribution. Once the statistical information for each random variable is obtained, one can calculate mean and standard deviation of the pavement performance function, which in this study, is taken as : SMrut : RDmax _ RDpredict (34) where : SMmt = safety margin between maximum allowable and predicted rut-depth, RDm = maximum allowable rut depth in the design period, and RDpredict = predicted rut depth in the design. 76 If a probability distribution function (pdf) of the pavement performance function is assumed and its limit state is taken as SM = 0, the area of pdf below the limit state is the probability of failure, Pr(f). The US. Army Corps of Engineers uses the term probability of unsatisfactory performance, Pr(U) rather than the probability of failure to recognize that the considered cases for rehabilitation projects are not disastrous [33]. Theoretically, the probability of unsatisfactory performance can be determined by constructing a pdf on the performance function (e.g. SM) and calculating the area under the curve that is less than the value of the limit state. However, Pr(U) is not practical because of the incomplete probability information of the design parameters in pavements. Even though the probability information of all parameters can be obtained, the shape of the probability distribution of the performance function that is likely to be non-linear may be difficult to obtain. Practically, approximate statistical moments of the performance function (E[SM] or SD[SM]) are obtained from the estimated statistical moments of parameters from pavements using several reliability analysis techniques which will be described in later sections. Using these approximate moments of the performance function, the reliability can be characterized by a conventional reliability index BC, which is the number of standard deviations by which the expected value of the performance function exceeds the limit state [34]. Figure 15 illustrates the concepts of the probability of unsatisfactory performance and the conventional reliability index, BC. In this study, using the moments of the safety margin (E[SMmt], SD[SMMD and the limit state condition (SM = 0), [5c is: __-E1544nu] fl" SD[SMM] (35) 77 Elxi] ’ HR “x SD[Xi] \ \ Xi Parameter Moments E[Xi+1 Combined ‘I ,/ \SD[Xi+l] . /4— —->\. \\ t . \ g Xi+1 E[SM] Performance Function Moments ,._ fi\ / \ ' ~\ I/ \‘ / / <——> .\ SD[SM] \ I (I l ,/ .' \. 4 I I I a \ x .4: ‘\‘. 1. / f! ‘ / 13c*SD[SMl SM Figure 15 Probability of Unsatisfactory Performance with Specified Variables 22 Safe Region T/ Failure Region Design Point Failure Surface h(zl .z2)=0 BHL 1 Tangent Hyperplane Figure 16 Geometrical Illustration of Haosfer and Lind’s Reliability Index [35] 78 For normal random variables, the probability of unsatisfactory performance, Pr(U), is estimated using following approximate relationship [36]: ,8 Pr(U)=(-fl)= [wgeuz (36) where : ' (I)(— ,6) = area under the pdf of standard normal variate from -oo to -B, and g(z) = pdf of pavement performance. The reliability of pavement performance can now be expressed as: 1-Pr(U). It should be noted that even if no particular distribution was assumed, various designs or trial failure modes could be compared since the lowest value of [3. represents the least safe condition. In other words, engineering system and components with higher 8. values are considered more reliable than those with lower values. The reliability index [3c is a convenient and valid comparative measure of an engineering system that reflects both the mechanics of the problem and uncertainty in the input variables at the same time [37]. However, although the conventional reliability index, [3. is a consistent index of risk measure, it is not invariant to different but mechanically expression of the performance function for non-linear performance functions. To circumvent this problem, Hasofer and Lind proposed an invariant reliability index [35]. In their method, all random variables X are transformed into a standardized parameter space g by means of an orthogonal transformation such that E{Zi} =0; GZi=1 Hasofer and Lind defined the reliability index as the minimum distance between the origin and the surface representing the limit state condition in the standardized parameter space 2 which was taken as SM = 0 in the section above. 79 16m. = where : BHL Z 5 C 5(4) and g0) 8(920 min fie— m.)Tg"(x — m.) or gig 702) (37) = reliability index defined in Hasofer and Lind’s sense, = a vector representing the set of random variables in the 2 space, = a vector representing the set of random variables in x space, = the covariance matrix of the random variables, and = the failure criterion in z and x space. Haosfer and Lind’s invariant reliability index is illustrated in Figure 16. If the performance function is linear, the conventional reliability index (8.) and the Haosfer and Lind reliability index (Bill) will be identical. Sources of Uncertainties in the M-E Flexible Pavement Design Uncertainties affecting pavement performance can be grouped into the following four categories as shown in Table 15: 1. Spatial variability that includes a real difference in the basic properties of materials from one point to another in what are assumed to be homogeneous layers and a fluctuation in the material and cross-sectional properties due to construction quality. 2. The variability due to the imprecision in quantifying the parameters affecting pavement performance (i.e. random measurement error in determining the strength of subgrade soil, and estimation of traffic volume in terms of ADT and mean truck equivalency factor). 3. The model bias due to the assumption and idealization of a complex pavement analysis model with a simple mathematical expression. 4. The statistical error due to the lack of fit of the regression equation. Table 15 Variability Components in M-E Flexible Pavement Design Uncertainties in the Design Uncertainties of Design Parameters Systematic Errors Spatial Variation Imprecision in Quantifying Parameters Model Bias Statistical Error 80 One can combine the first and second sources of uncertainty into uncertainties of design parameters, which represent the variability from site to site and inconsistent estimation of the parameters, and the third and forth sources of uncertainty into systematic errors, which consistently deviate from predicted actual pavement performance. The uncertainties of design parameters cause the variation within the probability distribution of the performance function, whereas systematic errors cause the variation in possible location of the probability distribution of the performance function [38]. Therefore, design parameters describe the scatter of the pavement properties and the variation of traffic estimation and systematic errors are associated with the uncertainty in the location of the trend of predicted pavement performances. This concept is graphically presented in Figure 17 [39]. The methods and procedure to quantify and combine these variations will be described in the subsequent sections. Practical Engineering Reliability Techniques The following numerical reliability techniques are generally used in engineering practices. 0 First Order Second Moment (FOSM) Method F OSM method involves approximation based on Taylor series expansion [40]. The mean value and standard deviation of a performance function can be obtained by linearizing the function at the mean centroid. This method is also referred to as the mean value first order second moment (MVFOSM) method, due to linearizing at mean values. For example, if there is a performance function th) with random vector x’s, its approximate mean value and standard deviation can be mathematically expressed as: 81 abuse. 8083mm 0::on WE 5F? voFemoOmmFx moufietooeb .3 89C. .3 538585 95385 S 035 8.5. ascents 2.58.. 8:58.58: unanFmam 55 8588.4 “cw—am 22868.— mozfificouaD saucepan 53, 33682.2. owcdm coonoE \ 2 ...we/ a i -8? i momusgoofla houogm .23 Bfiuam< owned E5385 82 E [g(£)] e g(mg ) (33) aim = VGTC0V(gc_)VG (39) where : m5 = vector of the mean values of random variables 5 , VG = vector of partial derivatives of the performance function at the mean values of random variables 5 , C0 VQ) = covariance matrix of the random vector g. The partial derivatives may be estimated numerically using the finite difference approach as follows: 580.6) = 800+) - g(xi—) (40) éci x i+ - x i- where xi+ and xi- represent the random variable xi taken at some increment above and below its expected values. Theoretically, an extremely small increment gives the most accurate value of the derivative at the expected value, but in practice, one standard deviation increment for each random variable is adequate [41]. The FOSM method allows the designer to see the contribution of each random variable to the total uncertainty and usually requires fewer computations than the point estimate method. 0 Point Estimate Method (PEM) PEM is the procedure where probability distributions for continuous random variables are considered by discrete equivalent distributions having two or more values [42]. In order to obtain the expected value for the performance function, PEM requires all possible combinations of one low and one high value for each random variable for determining various possible gQ)’s. The results are weighted by the product of their 83 associated probability concentrations Pi. or Pi-, and then summed. The procedure is summarized as: E[g(§)] = 2 (111,111,), -11", IY(x,, , x,, ,...x,,, )] (41) E[g(§)2] = 2011,10,], ...Pm 11120,, ,x,, ,...x,,, )] (42) 2 _ 2 2 a...) — Elgar.) l-(E[g(£)]) (43) When performance functions are significantly nonlinear, the PEM may produce better solutions because of its higher order accuracy in the mean value estimate [3 7]. 0 First Order Reliability Method (FORM) As described in the previous sections, an advanced reliability method was developed by Hasofer and Lind, who introduced an invariant second moment method where the failure surface is approximated to a tangent hyperplane at the failure point [3 5,43]. The shortest distance between the design point on the failure surface and the origin in a standardized normal space is considered as BHL. Rackwitz and Fiessler suggested an alternative iteration method to practically obtain BBL [44]. The method is described as follows: 1. 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Lbl .53. 933.3333 .3 a... = 8383.... .3. .3.. .3.. .3.. .3.. .3553.» 3.83 .855: El... .. flux...”— a.“u.w=_.¢uouz.“.o> u.“ma..nnua.=ho> Buns-“nu...” 33H _zansnm 83am och on”.— oaflba. 73.3839... 3.3— ...38: 2.33.... 83...; 33.8.. 32.... .3338. 3. 3.33.3 Table 20 Summary of the Results of Reliability Analysis for Pavement Performance (a) Section 1 MVFOSM PEM FORM E[SMm] 0.162 0.160 - o[SMm] 0.075 0.076 - COV[SMM] 0.463 0.475 - Reliability Index 2.17 2.11 2.01 Number of Runs 15 128 90 (b) Section 2 MVFOSM PEM FORM E[SMm,] 0.240 0.238 - o[SMm] 0.065 0.066 - COV[SMM] 0.27 1 0.277 - Reliability Index 3.71 3.62 3.07 Number of Runs 15 128 90 99 CHAPTER VI DEVELOPMENT OF PRACTICAL RELIABILITY-BASED M-E FLEXIBLE PAVEMENT DESIGN ALGORITHMS General In Chapter V, engineering reliability techniques that can be applied to pavement structural analysis were presented. In this chapter, illustrative examples will be presented demonstrating the application of reliability algorithms to M-E flexible pavement design. Method 1: Reliability Factor Design (RFD) Approach The basic concept in the reliability-based design is that the reliability associated with an appropriate design equation should equal a target value representing a certain degree of structural safety. Using the rut prediction model, this study suggests a main pavement design equation with a target reliability, R. : RDmax = Somfitarget + RDpredicted ' (51) where : Beige. = target reliability index defined as ¢-‘ (R' ), in which ¢ is the cumulative distribution function of a standard normal variate. Based on equation 51 , the pavement is designed to accommodate a cumulative traffic volume that is expected during its intended service life, there is a probability R. that the pavement will not fail before total rut-depth caused by the cumulative traffic volume reaches a maximum allowable level. In this equation, the product of the overall standard deviation and target reliability index is defined as the reliability factor (RF) to represent a specified level of structural safety. Thus, the pavement design procedure using this equation can be called as the M-E flexible pavement design procedure using the 100 reliability factor design (RFD) approach. Table 21 shows a relationship between the target reliability index and its corresponding reliability. In principle, an optimum target reliability index can be determined by performing a life cycle cost analysis (LCCA) as shown in Figure 19 [16]. It is theoretically possible to reach the most economical target reliability by estimating initial cost and future cost including maintenance and rehabilitation costs, and establishing an optimal strategy. At the present time, however, it is reported by Brown et, al. that such an approach is impractical because the inference space over which a pavement design guide is being applied is much too large that the formulation of LCCA is difficult in practice [47]. This means that for the time being, the most practical way to assign the optimal target reliability of the pavement is to depend on reasonable engineering judgement of experienced pavement designers [48]. The basic objective of the reliability-based design of the pavement is to guarantee that the probability of unsatisfactory performance of a pavement lies below an intended target level. If this probability is located far below the target level, the objective is explicitly achieved. However, that design is uneconomical and the reliability concept in the design is misapplied. Modeling and Analysis of the Uncertainties in RFD Approach As described in the previous sections, the uncertainties associated with predicting the pavement performance can be quantified with five steps by considering their sources and types. 101 Table 21 Relationship between Target Reliability Level and its Corresponding Reliability Index Target Reliability (R‘) Target Reliability Index (pm, = ¢" (R‘ )) 50% 0 60% 0.253 70% 0.524 75% 0.674 80% 0.841 85% 1.037 , 90% 1.232 95% 1.645 99% 2.054 102 C we 0 s W T (5) Initial Cos/ , Optlmum 0 ' ‘ Reliability (%) 50 100 Figure 19 Approach to Identifying the Optimum Reliability Level for a Given Pavement [16] 103 Integrate uncertainties due to spatial variation (V W) and uncertainties due to imprecision in quantifying parameters (V,m ) into parameter precision in Quattijjting Parameter uncertainties (VP ammeter Uncertaint y ) Using FOSM or PEM, quantify in terms of a standard deviation (Sp) of pavement performance predicted by M-E design procedure. VParanteter Uncerta int y Integrate model bias in pavement structural analysis (VW, 8m) and statistical error due to the lack of fit of the transfer function ( VMMM, Em,» into systematic error of the M-E design procedure (VS ystematic Error ) Quantify Vsysmm Em, in terms of a standard deviation (Sm) of pavement performance predicted by M-E design procedure. The technique for quantifying V will be introduced later. Systematic Ermr Determine overall standard deviation (So) of a pavement performance predicted by M-E design procedure as: so = ,/S; + S; (52) These steps are summarized in equation 53. Vs patial where: VParameter Uncertainty + V lm precision in quantijjling parameter VTotal : < rV Model Bias (53) + VSystematic Error< V + Statistical Error . l VM, = total uncertainty in an prediction of the pavement performance, expressed as a variance. 104 Even if the variations of design parameters are adequately quantified and their effects on pavement performance filnction are considered in a reasonable probabilistic manner, a predictive value by the pavement performance function still has a possibility to deviate from the actual value because of systematic error. It is very difficult to estimate the variations of predicted values due to this error [3 8]. The most precise approach to handle this error is to independently treat agents (modeling bias and statistical error) of the error and quantify each of them. However, this approach could yield an excessively sophisticated analysis procedure to pavement engineers and requires elaborate experiments and investigations in order to obtain adequate values. Thus, in this study, an integrated quantification of these agents of the systematic error is used as shown in equation 53. The variance caused'by the systematic error in a prediction of pavement performance was estimated by the following equation [39]: Sf ~MSE+£.s2{g}x. (54) where : MSE = error mean square of the performance function, 1,, = gradient vector of the coefficients of the performance function, which is evaluated at the mean values of the independent variables of the function, and s2 {g} = variance-covariance matrix of the coefficients of the performance function. Using the revised rut prediction model in this study as the performance function, 1,, is derived as follows: r6RD/6al ‘ 6RD 6RD/6a2 _. = — =t : i (55) 6g . [aw/6am 105 where : RD = rutting prediction model developed in this study, and a = vector of the coefficients of the rutting prediction model. 3 2 {g} can be approximately estimated by : s2 {g} = MSE(D'D)" (56) where: D = the matrix of partial derivatives of the coefficients evaluated at all data points as follows: flan @ flfl @ ESE. flflflfl' air. a’lr. aka. afar. 60520 afar. 607;. 608;. (”91.5”ng 6““{1 flifl .229 fly fl aw flflflfl D: air. 6022:. 6‘53. 60452 6"er 641% 607252 Basra abet. 601052 aal'zzm) M-E Flexible Pavement Design Procedure Using RFD Approach In light of the principles mentioned in the above section and using equation 52, a detailed reliability-based M-E flexible pavement design procedure called the Reliability Factor Based Design (RFD), is suggested: Step 1: Prepare input data 0 Input Data : Cross Sectional Data Layers’ Moduli Target Reliability Level Overall Standard Deviation (based on Sp and Sinput) Maximum Allowable Rut-Depth (RDmax) Environmental Information Expected Cumulative Traffic Volume (N) 106 Step 2: Calculate primary structural responses (e.g. deflection, stress, and strain) and predicted rut-depth (Rmedicicd) Step 3: Until the difference between RDmax and Rmedicwd converges to a specified tolerance level, iterate through steps 1 and 2 with changing cross sectional data or layer moduli. Step 4: Produce final cross-section design of the pavement structure. A flowchart illustrating this procedure is shown in Figure 20. In an effort to be compatible with current MDOT design practices that utilizes specified thickness for aggregate base and subbase layers, the pavement designer is asked to consider changing the bituminous layer’s properties. Sample Experimental Design Matrix In order to determine a rational value for the standard deviation (Sp) associated with the uncertainties of design parameters in RFD, a factorial experiment matrix with thirty-six cells was designed and is summarized in Table 22. Each cell represents a specific design feature. The factorial matrix provides a simple but effective way to relate design features to site conditions. Three major design variables of traffic volume, AC thickness, and resilient modulus of subgrade were selected and included in the matrix. High, moderate, and low values for each variable were determined based on the findings reported in NCHRP 1-32 project and MDOT pavement design practice [26]. 107 - Characterization of Surface, Base, and Subbase Materials Properties 0 Characterization of Subgrade Soils —> Structural Analysis of Pavement Section ———N o Cross-Sectional Properties Primary Response of Pavement (stress, strain, and deflection) . Calculation of Rut Traffic Information . . , ' Depth (Rmedimd) with EnVlronmental Condltlon predictive Model 0 Threshold Rut Depth I (RD (RDthreshold) threshold - . Reliability Factors (0%,, EDprlcdicted)+Btarget?o | So) _ To erance Leve Change Cross- + Sectional Properties No Yes Final Design ‘— Figure 20 Flowchart for M-E Flexible Pavement Design Procedure Using RFD Approach 108 a w _e. 3...—52 be: 2m 83% _ Sign _ 3th....— _ 3%”: 2.5.3» ease SEEP use £3352 utmcmnam amend—0E U UQHNMOOmm< mflomumwron Gunfigm MN o—DNH. The eighteen shaded cells in Table 22 were considered and the individual Sp’s were computed by the MVFOSM with 0.5 inches of rut depth as a threshold value. The same statistical conditions as those in the illustrative example of Chapter V were used in the computations. The results are shown in Table 23. 'As can be seen in Table 23, the pavements that are subjected to heavier traffic volume and designed with a thicker AC layer have a larger standard deviation. With this finding, one can explain why the pavement of the interstate or urban freeway that always accommodates heavy traffic volume should be designed with a higher level of design reliability. It is necessary in heavy-duty pavements to reduce the possibility of underestimating traffic volume with higher variance. The design Sp was determined as 0.036 from those in Table 23, while the design Sm was calculated as 0.066 from an analysis of the data collected in this study using equation 54 to 57. Then So for the design was calculated as 0.076. Illustration of RFD Approach Figure 21 shows an example of the design outputs computed by selected design input parameters in the spreadsheet. As mentioned in the above section, the design procedure uses an iterative process to produce an optimal pavement cross-section whose structural resistance allows total permanent deformation to closely reach a threshold amount at the end of design life. A tolerance level of 0.01 inch was used in this study. The explanations of the design steps shown in Figure 21 are as follow: 111 (a) Initial Stage 1.Site Condition and Criterion 4.0.E+06 0.8 0.5 Annual T 45 8000 2.Material and Cross-Sectional Base Subbase Thickness 2.2 8.0 16.0 cm 5.6 20.3 40.6 Moduli 450000 30000 15000 Moduli 3100500 206700 103350 T AC 10 Kinematic 273 3.Degree of Uncertainty Sm 0.066 Sp 0.036 So 0.076 4.1ntermediate Variables from Structural Analysis Surface Strain Base Strain- Deflection ‘ Subgrade 3 .400E-02 1.627E-03 4.255E-04 5.Design Outputs RDpredieted 0.54 Btuget 0.84 6. Decision Tolerance ”Wold" Level (RDpredieted+So*Btnrget) 0.01 0.108 Adjust 2.Material and Cross-section Inputs Figure 21 Illustration of M-E Flexible Pavement Design Using RFD Approach 112 (b) Final Stage (End of the Iteration) 1.Site Condition and Design Criterion Traffic Volume (N) 4.0.E+06 EASL Reliability Level 0.8 - RDMMM 0.5 in Annual Temperature 45 (°F) Subgrade Resilient Moduli 3000 PSi 2.Material and Cross-Sectional Inputs AC Base Subbase Thickness (in) 4.5 8.0 16.0 cm 1 1.4 20.3 40.6 Moduli (psi) 450000 30000 15000 Moduli (kPa) 3100500 206700 103350 Asphalt Type AC 10 I Kinematic Viscosity I 273 centistoke 3.Degree of Uncertainty 7 7 | 8m | 0.066 S 0.036 | So I 0.076 4.1ntermediate Variables from Structural Analysis Surface Strain Base Strain- Deflection ' Subgrade 2.435E-02 8.804E-04 3.1 l7E-04 5.Design Outputs | Rum“... 0.44 | | pm, 0.84 | 6. Decision Tolerance Rpm“- LCVCI (RDpredicted+So* Btu-get) 0.01 | > 0.000 O.K. Figure 21 (cont’d) 113 1. The user is required to input expected traffic volume during pavement service life, a desired reliability level, a threshold rut-depth as failure criterion (RDmmshotd), ambient annual temperature around the site, and effective resilient modulus of the subgrade soil of the site. 2. The user needs to set up initial pavement cross-sectional and material properties. 3. The user needs to determine a certain degree of uncertainty accompanied with the design procedure in terms of an overall standard deviation of the design model (So): The Sm, Sp, and So of 0.066, 0.036 and 0.076 are considered as default values. 4. The pavement analysis computer program computes the surface deflection and compressive vertical strains at the top of the base layer and subgrade. 5. A predictive pavement rut-depth (Rmedicted) is computed using the developed rutting prediction model, and the desired reliability level set up in step 1 is converted to the target reliability index (0), which is a standard normal variate of the desired reliability. 6. If RDumshold - (Rmedict¢d+So*B) > a specified tolerance level, the pavement cross- section should be modified and step 2 through 6 repeated until RDumhold — (RDprcdictcd+So*B) S the tolerance level. When the iteration is stopped, the cross- section at the final iteration becomes the design pavement cross-section. Method 2: Load and Resistance Factor Design (LRFD) Approach In this section, a reliability-based M-E flexible pavement design procedure adopting the LRFD format is presented. The basic concept of the LRFD approach applied to this study can be expressed as follows: 114 Dthreshold Z 7 overallf R (q l a q 2 a ------- qn) (5 8) where: DWeshoId = Threshold amount of pavement distress, 7mm” = Overall safety factor reflecting a specified target reliability, fR = Procedure for predicting pavement performance in terms of pavement distress, and q,- = Parameters in a pavement design procedure. The specific form of the model for this study where pavement rutting is considered as a major pavement distress can be written as follows: RDthreshold Z roverallfR (HAC 9 EAC ’ E303: ’ E88 9 ESG ’ N) (59) where : HM; = AC thickness, EAC = Modulus of AC, EM,c = Modulus of Base, Egg = Modulus of Subbase, Egg = Modulus of Subgrade, and N = Traffic Volume. The 7mm” required to obtain a target reliability index, Bweet can be determined by following partial safety factor approach using FORM, for which an iterative evaluation procedure was described previously. 7 = fR(¢H,¢C HAC’¢EACEAC9¢EMEBmc,¢ESG ,¢ESBESB’ESG97NN) overall fR(TAC’EAC’EBase’Es(;9N) (60) where : (0, or n is a partial safety factor of each variable for reduction or amplification of its amount. For a specified Burger, (15, and )3- can be calculated by the following equations [49]. ¢. =[§i](1+a.fl....con) (61) i 115 m . 7,- = [71%](1 + affirmaCOVy) (62) where: n = Nominal values of design variables, or = Unit vectors associated with the design point, and COV = Coefficients of variations of variables of design variables. The selection of the nominal values of design variables is typically performed on the basis of the judgement of the pavement engineer. In this study, the nominal values of design variables were assumed to be their mean values. If rj is a lognonnally distributed loading variable, then [49] y, = %exp(— 0.51n(C0VJ.2 + l)+ a, am (1n(C0VJ.2 +1))°"); %exp(a,,6,mCOI/j ) (63) J 1 Modeling and Analysis of the Uncertainties in the LRFD Approach In order to successfully implement the LRFD format in a practical pavement design procedure, the uncertainties caused by the systematic errors including model bias and statistical error as well as those of model parameters must be quantified and reflected in the format as they were in the RFD approach. In other words, the quantification of the systematic errors is a prerequisite to computing the overall safety factor in the LRFD format. The most common way to quantify systematic errors is to employ the professional factor, P that is defined as a ratio of the measured to predicted value [46] : RD R D measured ( 6 5) RDpredicted - fR(TA("EAC’EBase’ESB’ESG’N) measured _ P: 116 Enough data is not available to assess the parameters E[P] and COVp in all situations but, where available, comparisons between design predictions and measured results could be used to estimate them. Based on the analysis of observed and predicted rut-depths in the test sites of this study and 24 LTPP-GPS sites, E[P] and COVp of 0.89 and 0.2 were used in this study. M-E Flexible Pavement Design Procedure Using LRFD Approach Incorporating the professional factor, the LRF D format in equation 58 can be rewritten as; RD threshold 2 y'overall [P ' fR(TAC 9EAC 9 Ebase 9ESG 9N )] (64) where: 7' : yPP.fR(¢HACHAC’¢EACEAC’¢EM.E30389¢ESBESB9¢ESGEsasyNN) overall P.fR(HAC,EAC,E ESB,ESG,N) (65) Base ’ A detailed M-E flexible pavement design procedure employing equation 64 is illustrated in Figure 22. In this design procedure, the cross-section of a pavement is optimally determined by an iterative algorithm where the computation is continued until the difference between predicted and threshold rut-depth has converged to a specified tolerance level as it was done in the design procedure adopting the RFD approach. In order to determine reasonable values of overall safety factors corresponding to target reliability indices, a factorial experiment matrix was used as summarized in Table 21. First, the reliability index, failure points of design variables, and unit vectors associated with the design points in each cell were determined by FORM with 0.5 inches of rut depth as the limit state. Then, partial safety factors and overall safety factors corresponding to specified target reliability indices were calculated. 117 0 Characterization of Surface, Base, and Subbase Materials Properties 0 Characterization of Subgrade Soils Structural Analysis of —> Pavement Section Cross-Sectional Properties Primary Response of Pavement (stress, strain, and deflection) l 0 Traffic Information 0 Environmental Condition Calculation of Rut ———H Depth (RDpredieted) With Predictive Model 0 Threshold Rut Depth (RDthreshold) Professional Factor (P) Overall Safety Factor (Yoverall) I RDthreshold - Yoverall*P*RDpredicted l S Tolerance Level Change Cross- No Sectional Properties + Yes ‘__1 Final Design Figure 22 Flowchart for M-E Flexible Pavement Design Procedure Using LRFD Approach 118 As an illustrative example for this procedure, cell No. 35, which is equivalent to pavement section 2 in the illustrative examples of Chapter V, was selected. As can be seen in Table 16, failure points for design variables were evaluated at the end of the iteration in FORM. Using unit vectors at the failure points and the target reliability index of 1.65 for 95% reliability, partial safety factors and overall safety factors were computed using equations 61,62,63, and 65. Table 24 summarizes these computations. From the results of partial and overall safety factors computed in selected 18 cells, the design partial and overall safety factors for various target reliabilities were determined and summarized in Table 25. Illustration of LRFD Approach An illustration of a M-E flexible pavement design procedure using LRFD approach is made in this section. An example of the design outputs computed by selected design input parameters using the spreadsheet is shown in Figure 23. The explanations of the design steps shown in Figure 23 are as follow: 1. The user is required to input expected traffic volume during pavement service life, a desired reliability level, a threshold rut-depth as failure criterion (RDumhotd), ambient annual temperature around the site, and effective resilient modulus of the subgrade soil of the site. 2. The user needs to set up initial pavement cross-sectional and material properties. 119 Table 24 Summary of Com utations for Partial and Overall Safety Factors at Cell No.35 Initial I u t Unit Vector Target Reliability Partial Safety Initial Input up (Alpha) Index Factor "' Partial Safety Factor Eac (psi) 450,000 0135 1.65 0.94 424,999 Tee (in) 10 -0.601 1.65 0.90 9.01 Ebase (psi) 30000 -0.042 1.65 0.99 29,584 Esubbase (psi) 15000 -0.034 1.65 0.99 14,833 Esg (psi) 8000 -0.096 1 .65 0.97 7,745 Traffic Volume (ES AL) 15,000,000 0.257 1 .65 .1 .18 17,676,307 memwm‘ 0.89 0.736 1.65 1.24 1.11 Factor Predicted Rut- Depth 0.29 O .34 0.34 .'.Overall Safety Factor = 124* 0 29 a: 1.454 120 Table 25 Summary of Partial and Overall Safety Factors with Various Target Reliabilities Reliability (%) 75 80 90 95 99 (fidfigiti/aiggfrf) 0.68 0.84 1.28 1.65 2.33 70m, 1.15 1.19 1.30 1.39 1.55 y, 1.12 1.15 1.22 1.29 1.40 7,, 1.08 1.11 1.16 1.21 1.29 45,.“ 0.98 0.98 0.97 0.96 0.94 955,," 0.99 0.99 0.98 0.98 0.97 945...... 0.99 0.99 0.99 0.99 0.98 as,” 0.99 0.99 0.98 0.98 0.97 as,“ 0.98 0.97 0.96 0.95 0.92 121 (a) Initial Stage 1.Site Condition and Design Criterion Traffic Volume (N) 4.0.E+06 Reliability Level 0.8 RDMou 0.5 Annual Temperature 45 Mrade Resilient Moduli 3000 f 2.Material and Cross-Sectional Inputs AC Base Subbase Thickness (in) 5.2 8.0 16.0 cm 13.2 20.3 40.6 Moduli (psi) 450000 30000 15000 Moduli (kPa) 3100500 206700 103350 Asphalt Type AC 10 I Kinematic Viscosity I 273 centistoke 3.Degree of Uncertainty - Professronal 0.890 J Factor 4.1ntermediate Variables from Structural Analysis Surface Strain Base Strain- lDeflection " Subgrade | 2.267E-02 7.620E-04 | 2.871E-04 5.Design Outputs | Rum“... 0.43 | I Yoverall 119 l 6. Decision Tolerance RDWO‘" Level (P*70venfl* RDpredlcted) 0.01 0.049 Adjust 2.Material and Cross-section Inputs Figure 23 Illustration of M-E Flexible Pavement Design Using LRF D Approach 122 (b) Final Stage (End of the Iteration) 1.Site Condition and Design Criterion Traffic Volume (NL 4.0.E+06 EASL Reliability Level 0.8 RDtIrreehold 0.5 in Annual Temperature 45 (°F) . _Slllgrade Resilient Moduli 3000 195i 2.Material and Cross-Sectional Inputs AC Base Subbase Thickness (in) 4.2 8.0 16.0 cm 10.7 20.3 40.6 Moduli (psi) 450000 30000 15000 Moduli (kPa) 3100500 206700 103350 Asphalt Type AC 10 I Kinematic Viscosity I 273 centistoke 3.Degree of Uncertainty Professwnal 0.890 I Factor 4.1ntermediate Variables from Structural Analysis Surface Strain Base Strain- Deflection - Subgrade 2.529E-02 9.494E-04 3.248E-04 5.Design Outputs _ I RDpredicted I 0.47 I I Yoverall I 119 I 6. Decision Tolerance Level 0.01 OK. Figure 23 (cont’d) 123 The user needs to determine a certain degree of uncertainty accompanied with the design procedure in terms of an overall safety factor (7;,m,,) of the design model: From Table 25, select a value in accordance with the desired reliability level set up in step 1. The pavement analysis computer program computes the surface deflection and compressive vertical strains at the top of the base layer and subgrade. A predictive pavement rut-depth (RDprcdictcd) is computed using the developed rutting prediction model. If RDamhold — ( Am,” *P‘RDprcdimd) > a specified tolerance level, the pavement cross-section should be modified and repeat step 2 through 6 until RDumhold — (74mm *P‘Rmedimd) S the tolerance level. When the repetition is stopped, the cross- section at the final iteration becomes the design pavement cross-section. Sensitivity Analysis of' RFD and LRFD Approaches In order to evaluate the effects of the level of reliability, amount of traffic volume, and resilient moduli of subgrade on design pavement thickness with suggested M-E flexible pavement design procedure using the RFD and LRFD approaches, a sensitivity analysis was performed. Table 26 summarizes the set of design parameters held to be constant in the sensitivity analysis. Figures 24 and 25 summarize the results of the sensitivity analysis. Figure 24 shows the relationships between the traffic volume and AC thickness at different reliability levels, while Figure 25 illustrates the relationship between the reliability level or overall safety factor and the AC thickness at different traffic volumes. These illustrations can assist designers in selecting the appropriate 124 pavement cross section based on the expected traffic volume and desired reliability level. The slopes of the curves in the figures correspond to the rate of change of AC thickness corresponding to change of traffic volume or reliability level. The slopes of the curves from RFD and LRF D approaches appear to have similar trends with change of traffic volume and reliability level. This fact can lead to two interpretations: 1. Faced with a specified pavement design situation that is subject to a given traffic volume, two design approaches with a specified failure criterion and reliability level would produce similar results implying that generally, design outputs fiom the two are comparable to each other. 2. The outputs from two design approaches have similar sensitivities to the reliability level. 125 Table 26 Constant Design Parameters in the Sensitivity Analysis Parameter Magnitude Annual Ambient Temperature 45°F Kinematic Viscosity 273 centistroke Thickness of Base 8in Thickness of Subbase 16in Modulus of Bituminous Layer 450ksi Modulus of Base Layer ' 30ksi Modulus of Subbase Layer 15ksi Modulus of Subgrade Soil 8ksi 126 AC Thickness (in) AC Thickness (in) RFD Appraoch 0 5 10 15 20 25 3 0 35 Traffic (million ESAL) LRFD Approach 10 — fr 7 , J iii A 7 9 1 xi 7 L 6 7"” +2 5 i +3 4 l 7:1 3 al 1 . 0 Li- , , - -.-_% . , .71 0 5 10 15 20 25 30 35 Traffic (million ESAL) Figure 24 Variation of AC Thickness with Various Traffic Levels 127 AC Thickness (in.) O '— N u b Ur Os \1 00 \0 AC Thickness (in) RFD Approach +1 +2 ...3 n 50 60 70 80 90 100 l. Target Reliability (%) .134 LRFD Approach 9 8 7 _ 6 >— 5 _ +1 4- :3 3 .. 2 I .. O 4 1 1.1 1.2 1.3 1.4 1.5 1.6 Target Reliability Index T 1 ,000,000 2 9 5, Figure 26 Variation of AC Thickness with Various Target Reliability Levels 128 CHAPTER VII SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS Summary The objectives of this study were to: o Revise a rutting prediction model based on field data and present its application to M-E flexible pavement design. 0 Develop a reliability analysis procedure for the pavement performance 0 Develop a reliability-based M-E flexible pavement design procedure by extending the developed reliability analysis procedure. A comprehensive literature review regarding the state-of-the-art rutting prediction models based on mechanistic and mechanistic-empirical approaches was presented. Based on the field data collected from in-service flexible pavements in Michigan, a M-E rut prediction model was developed. The robustness of this model was tested against the field data collected in 1998 and LTPP data fi'om 24 GPS sites. 80 that the new model systematically combines non-mechanistic factors with primary mechanistic factors, the model was developed through nonlinear regression using SYSTAT [30], a statistical computer program, was developed. The model consists of two parts: one containing observational variables and the other containing mechanistic parameters. This was done in an effort to separately explain the effects of load-related mechanistic and non-mechanistic factors including environmental, asphaltic, and cross- sectional properties on pavement rutting. The attributes of the nonlinear regression model are as it follows: 0 More than 760 data locations from 39 test sections were analyzed and then they were grouped into 51 statistical samples. 129 . «ll-Ilia ._ T... t, . o The R2 of the model was 90.5%. o The p-value of 2.044E-18 for the regression relation between predicted rut-depth and independent variables leads to the conclusion that the regression relation is useful for making predictions of rut-depths. Because of a certain amount of bias associated with the measurement of rut, estimation of traffic and determination of material and cross-sectional properties, this study set up a tolerance level of i0] inch within which the difference between observed and predicted rut-depth was considered not to be significant. The developed model can account for rate-hardening (load applications vs. rut- depth) in the progression of rutting with increased load applications. This model simulated a rapid pavement rutting-rate in the early life of the pavement and a slower rutting development in the middle of the pavement age. This trend of the pavement rutting development corresponds well with the typical field rutting behavior that was reported from several field investigations [19,50,51,52]. The developed model also considers the rut-depth as a performance function and hence can easily handle various threshold rut-depths. This means that pavements can be designed with various terminal service levels using this model. . The developed model characterizes traffic in terms of the ESAL without considering the actual axle load spectrum in light of field practices in pavement engineering. 130 In the sensitivity analysis, no violation of mechanistic rules of pavement performance were found implying that the model can successfully explain the relationship between the pavement rutting behavior and material/cross-sectional properties. The literature review regarding general M-E flexible pavement design procedures suggest that M-E procedures do not accurately address the variabilities associated with design parameters and model bias. This results in a failure to adequately predict pavement performance with a degree of confidence. The performance reliability in a given pavement section can be expressed as the reliability index, BC, the number of standard deviations by which the expected value of the performance function exceeds the limit state or BHL, the invariant minimum distance between the origin and the failure surface [34,3 5]. A reliability analysis model for evaluating uncertainties in the M-E flexible pavement design procedure was developed. This model consists of two subsystems: an analytically derived mechanistic subsystem for predicting pavement performance and a reliability subsystem for analyzing the limit state function that is defined as the difference between maximum allowable (or threshold) and predicted rut-depth in this study. In order to analyze the limit state function and calculate its reliability index, the FOSM, PEM and FORM were used. The results from these methods were compared through illustrative examples. 131 a “H 16.. . .. The probabilistic methodologies applied to the development of the reliability analysis model for pavement performance was also used to improve currently suggested M-E flexible design procedures by providing comprehensive reliability handling tools. Within a framework of the improvement of existing design methods, not intending the replacement of new design method, two practical reliability-based M-E flexible pavement procedures: RFD and LRF D approaches were introduced and explained in detail. In RFD approach, The overall standard deviation of the design procedure is determined by the first order combination of the standard deviations due to uncertainties of design parameters and systematic errors in the design model. Incorporating the reliability factor (RF) that is the product of the overall standard deviation and target reliability index, an iterative process was developed to produce an optimal pavement cross-section whose structural resistance allows its total permanent deformation to closely reach a threshold amount at the end of design life. In LRFD approach, The professional factor, P that can be defined as a ratio of measured rut-depth to predicted rut-depth was employed to quantify systematic errors in the design model [46]. A overall safety factor based on the partial safety factors of all design variables was applied to the limit-state function, which, in this study, was defined as the safety margin reflecting the difference of maximum allowable (threshold) and predicted rut-depth The cross-section of a pavement is optimally computed by an iterative algorithm where the computation is continued until the limit-state function including an overall safety factor converges to zero. 132 Conclusions Revision of Rutting Prediction Model One of the biggest issues in the pavement design is how a transfer/pavement performance function can reasonably combine non-mechanistic factors such as geometric, material, and environmental properties with purely mechanistic factors such as load-related distress mechanisms. The performance functions with only mechanistic factors that were based on laboratory and field testing results have not been successful in getting their applicability to a variety of regional site conditions revealing the lack of consideration of non-mechanistic factors. In the validation study of revised rutting prediction model with field data collected most recently in Michigan and from 24 LTPP-GPS database, the plot of observed versus predicted rut-depth indicates good agreement between them. This fact implies that revised rutting prediction model shows some potential to be nation-wide applied. Development of Reliability Analysis Model for the Pavement Performance Reliability of the pavement performance can be expressed as the probability that the pavement will not exceed distress criterion during its service life. This study showed that the conventional reliability index, BC, is a best representative for the reliability of the pavement performance because it provides a convenient and valid comparative measure for an engineering system not requiring the assumption of any particular distribution for the performance function. However, for design application, BHL should be used to accurately evaluate failure points of design variables and determine exact minimum 133 distance to the failure surface that is approximated to a tangent hyperplane at the failure point. By calculating the reliability index of a given limit state function, the study evaluated both advantages and disadvantages of FOSM, PEM and FORM. Comparisons of the accuracy of calculated reliability indices and the computation time leads to the conclusion that F OSM and PEM are preferred for characterizing the effects of parameter uncertainties on the pavement performance in the pavement reliability analysis, while FORM is the best choice to quantify the uncertainties of design parameters and model bias for establishing reliability-based M-E pavement design procedure. Development of Practical Reliability-Based M-E Flexible Pavement Design Procedures Basically, most of pavement design procedures including AASHTO guide, M-E procedure from NCHRP 1-26, and Corps of Engineers’ method [53] have employed the concept of limit state design that is a logical formalization of the traditional design approach that would help to expedite the explicit recognition and treatment of engineering risks. The reliability methodology can make this limit state design concept robust, accounting for the critical uncertainties around the limit state. It is demonstrated that the two suggested practical reliability-based M-E flexible pavement design procedures, RFD and LRF D approaches, successfully handle design uncertainties and produce design outputs warranting desired reliability level. It should be emphasized again that suggested reliability-based design procedures do not intend to replace existing M-E design procedures but improve on them by providing conventional reliability handling capability. They could partly help the M-E design procedure overcome the obstacles in its more advance implementation. 134 The biggest difference between two approaches is that LRF D approach employs partial safety and overall safety factors whose values are varying with target reliability indices, whereas the RFD directly uses target reliability indices with the overall standard deviation that is independently estimated by a first order probabilistic approach. Despite of this difference, this study showed that the two approaches were likely to produce similar design pavement thickness for a specified design condition (Figures 24 and 25). Recommendations for Future Research In order to achieve higher suitability for various site conditions, the calibration work for the revised rutting prediction model should be continued with updated version of the LTPP database. An attempt needs to be made to apply traffic characterized in terms of actual loading groups rather than ESALS to this rutting prediction model. The proposed reliability analysis model for the pavement performance in this study assumes that all variables are normally or log-normally distributed, which is not entirely accurate. The attempt should be made to enable the reliability analysis model to rationally handle non-normal random variables using advanced probabilistic technique such as normal tail approximation [54]. 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