This rep;:yrt documents the process ofmodel development 83JO the final mod",J.!'; developed fo, t1,,-,:0

prediction of key portland cement concrete (PCC) pavement distress types and rouglv"J.ess, The

models were developed using Long·Tem1 Pavement Performance (LTPP) data Mechanistic·

empirical models were developed for the following distress types: transverse joint f"nJltj;"g,

transverse joint spaHing, transverse cracking, and corner breBJes. The ronghr\ess models

developed were empirical.

The positive outcome ofthis study was the development of mechanistic~basedperfOrEj8nCe

models for use in pavement design and man8,gement This is expected to provide expanded

capabilities for considering the effect of load~, R11d climate~related stresses on PCC p"wement

perfOrm8D.Ce, The development of mechanistic~basedmodels reflects current trends of upgrw:ling

the pavernent design and evaluation process tbrough the use ofmech8JJisti\>basd design

rnethoclso

ThJ.s repo~1: is impOliant to everyone who designs, constrncts, and mm18ges paverrtents,

NOTICE

This docun~lent is disseminated under the sponsorsbip ofthe Departnlent of TraJ1sportBtion ill tb",

interest ofinformation exchange. The United States GovenlJ:nent assumes no liability for its

contents or use thereof. This report does not constitute a standard, specific8tion, or regulation,

The United State Government does not endorse products or manufacturers, Trade Cl-.!-:lQ

manufactmers' Homes appear in this report only because they are essential to the object ofthe:

document
Technical Report Documental on Paae

1. Report No. 2. Government Accession No. 3. Recipient's Catalog No.

FHWA-RD-98-113

4. ntle and Subtitle

DESIGN AND CONSTRUCTION OF PCC PAVEMENTS

Volume III: Improved PCC Performance Models

5. Report Date

January 1999

6. Performing Organization Code

7. Author(s)

L. Titus-Glover, E. B. Owusu-Antwi, and M. I. Darter

8. Performing Organization Report No.

~~~~-------------------------1

9. Performing Organization Name and Address

ERES Consultants, Inc.

505 W. University Avenue

Champaign,IL 61820-3915

10. Work Un" No. (TRAIS)

C6B

11. Contract or Grant No.

D11Pli61-94~-00218

12. Sponsoring Agency Name and Address

Office of Engineering R&D

Federal Highway Administration

6300 Georgetown Pike

McLean, Virginia 22101-2296

14. Sponsoring Agency Code

15. Supplementary Notes

FHWA Contracting Officer's Technical Representative (COTR): Cheryl A. Richter, HNR-30

16. Abstract

This study was conducted to evaluate and analyze portland cement concrete (PCC) pavements in order to develop

recommendations for the design and construction of long-lived concrete pavements. It involved a detailed evaluation

and analysis of the PCC pavement data in the Long-Term Pavement Performance (LTPP) database using a variety of

methods to determine the design features and practices that have beneficial effects on long-term performance.

Emphasis was placed on identifying those specific design features that can be included during design to improve the

performance of PCC pavements under various combinations of environmental and traffic loading conditions, and for

different subgrade support conditions. The study focused on the development of practical recommendations that can

be implemented by highway agencies to increase pavement life.

This volume describes and provides information on improved pavement distress and roughness prediction models

that were developed as part of the study. A key focus was to develop distress and roughness prediction models that

incorporate mechanistic principles but are still practical for use by State highway agencies.

This report is the third in a series of three volumes on the study. The other volumes are as follows:

FHWA No. Vol No. Short Title

FHWA-RD-98-052 I

FHWA-RD-98-127 II

Summary of Design Features and Construction Practices That Influence

Performance of Pavements

Design Features and Practices That Influence Performance of PCC

Pavements

17. Key Words

Concrete pavement, design, construction, faulting,

spalling, transverse cracking, corner breaks,

roughness, mechanistic analysis, pavement evaluation.

18. Distribution Statement

No restrictions. This document is available to

the public through the National Technical

Information Service, Springfield, Virginia

22161.

19. Security Classlf. (of this report) 20. Security Classlf. (of this page) 21. No of Pages 22. Price

Unclassified Unclassified 231

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized
• I •

APPROXIMATE CONVERSIONS TO SI UNITS APPROXIMATE CONVERSIONS 

Symbol When You Know MUltiply By To Find Symbol Symbol When You Know Multiply By 

LENGTH LENGTH

in inches 25.4 millimeters mm mm millimeters 0.039 

ft feet 0.305 meters m m meters 3.28 

yd yards 0.914 meters m m meters 1.09 

mi miles 1.61 kilometers km km kilometers 0.621 

AREA AREA

in2 square inches 645.2 square millimeters mm2 mm2 square millimeters 0.0016 

ft2 square feet 0.093 square meters m2 m2 square meters 10.764 

ydl square yards 0.836 square meters m2 m2 square meters 1.195 

ac acres 0.405 hectares ha ha hectares 2.47 

mi2 square miles 2.59 square kilometers km2 km2 square kilometers 0.386 

VOLUME VOLUME

fI oz fluidounces 29.57 milliliters mL mL milliliters 0.034 

gal gallons 3.785 liters L L liters 0.264 

ttl cubic feet 0.028 cubic meters m3 m3 cubic meters 35.71 

.... III yd3 cubic yards 0.765 cubic meters m3 m3 cubic meters 1.307 

.... NOTE: Volumes greater than 1000 I shall be shown in m3•

MASS MASS

oz ounces 28.35 grams g g grams 0.035 

Ib pounds 0.454 kilograms kg kg kilograms 2.202 

T short tons (2000 Ib) 0.907 megagrams Mg Mg megagrams 1.103 

(or "metric ton") (or Or) (or "to) (or "metric ton")

TEMPERATURE (exact) TEMPERATURE (ex

of Fahrenheit 5(F-32)19 Celcius °C °C Celcius 1.8C + 32 

temperature or (F-32)11.8 temperature temperature 

ILLUMINATION ILLUMINATION

fc foot-candles 10.76 lux Ix Ix lux 0.0929 

fI foot-Lamberts 3.426 candelalm2 cdfm2 cdfm2 candelalm2 0.2919 

FORCE and PRESSURE or STRESS FORCE and PRESSURE o

Ibf poundforce 4.45 newtons N N newtons 0.225 

Ibflin2 poundforce per 6.89 kilopascals kPa kPa kilopascals 0.145 

square inch 

" SI is the symbol for the International System of Units. Appropriate 

rounding should be made to comply with Section 4 of ASTM E380.
TABLE OF CONTENTS

Section

1. INTRODUCTION 1

Background 1

Project Objectives and Scope 1

Research Approach 2

Sequence ofReport 2

2. OVERVIEW OF LTPP DATA USED FOR MODEL

DEVELOPMENT 3

Introduction 3

Overview ofthe LTPP Data 3

Summary 5

3. MODEL DEVELOPMENT METHODS 7

Introduction 7

Model Types 9

Developing Practical Prediction Models 9

4. FAULTING MODEL FOR JOINTED CONCRETE

PAVEMENTS 15

Introduction 15

Faulting Mechanism 15

Evaluation of Existing Faulting Models ; 16

Faulting Model Development Approach 20

Determination of Differential Elastic Deformation Energy 23

Data Preparation and Evaluation 29

Erodibility Scaling Factor 31

Faulting Model Formulation 34

Faulting Model Calibration 36

Final Faulting Prediction Model 37

Sensitivity Analysis 39

Summary 49

Implications and Recommendations 49

iii
TABLE OF CONTENTS (continued)

Section

5. TRANSVERSE JOINT SPALLING 51

Introduction 51

Spalling Mechanism 51

Evaluation of Existing Spalling Models 53

Spalling Model Development Approach 56

Mechanistic-Empirical Spalling Model Formulation 65

Determination of Empirical Scaling Variables 67

Calibration of Mechanistic-Empirical Joint Spalling Models 75

Sensitivity Analysis for Mechanistic-Empirical Spalling Models 84

Summary 92

Implications and Recommendations 93

6. TRANSVERSE CRACKING AND CORNER BREAKS OF JPCP ... 95

Introduction 95

Transverse Cracking and Corner Break Mechanisms 95

Evaluation of Existing Transverse Cracking and Corner Break Models 96

Fatigue Cracking Modeling Approach 98

Application of Fracture Mechanics Principles 99

Development of Empirical Scaling Factors 105

Calibration Procedure for Transverse Cracking and Corner Break Models 105

Final Corner Breaks Model 111

Final Transverse Cracking Model 114

Sensitivity Analysis 117

Summary 126

Implications and Recommendations 127

7. ROUGHNESS MODELS 129

Introduction 129

Roughness Measure 129

Progression ofRoughness 130

Evaluation ofExisting Roughness Models 132

Roughness Model Forms 135

Preliminary Data Analysis 136

Final IRI Prediction Models 146

Sensitivity Analysis 153

Summary 165

Implications and Recommendations 168

IV
TABLE OF CONTENTS (continued)

Section

8. APPLICATION OF DISTRESS PERFORMANCE MODELS 169

Introduction 169

Faulting ofJPCP 169

Transvese Joint Spalling for JPCP and JRCP 172

Transverse Cracking for JPCP 177

Corner Breaks for JPCP 180

Roughness for JPCP, JRCP, and CRCP 181

Suitability of Prediction Models 184

Examples of Application of Performance Models 184

, Checking the Design of New Pavements with Prediction Models 185

Comparing Cost-Effectiveness of Alternative Designs 187

Summary 190

9. CONCLUSIONS AND RECOMMENDATIONS 193

Conclusions 193

Recommendations 193

Recommendations for Future Research 194

APPENDIX A. CALIBRATION OF PREDICTION MODELS 203

Data Preparation and Selection ofIndependent Variables 203

Model Development and Verification 206

Model Evaluation and Verification 212

REFERENCES 215

PROTECTED UNDER INTERNATIONAL COPYRIGHT

ALL RIGHTS RESERVED

NATIONAL TECHNICAL INFORMATION SERVICE

U.S. DEPARTMENT OF COMMERCE

Reproduced from

best available copy.

v
LIST OF FIGURES

Eigure

1 Flow chart for developing distress models for rigid pavements 10

2 Finite element model 26

3 Plot ofmean joint faulting versus significant variables for jointed PCC pavement 33

4 Plot ofpredicted versus measured faulting 39

5 Plot ofresiduals versus predicted faulting 40

6 'Influence of dowel and dowel size on predicted faulting 42

7 Influence ofbase or subbase type on predicted faulting 43

8 Influence ofPCC slab thickness on predicted faulting 44

9 Influence ofmodulus ofsubgrade reaction on predicted faulting 45

10 Influence ofjoint spacing on predicted faulting 46

11 Influence of drainage coefficient on predicted faulting 47

12 Influence of number ofwet days (precipitation >12.7 mm) on predicted faulting 48

13 Schematic diagram ofspalling mechanism for tensile mode offailure in jointed

concrete pavement 58

14 Finite element model for estimating spall stress 60

15 Sensitivity plot oftensile stress versus height ofsealant 62

16 Sensitivity plot oftensile stress versus modulus ofsubgrade reaction 63

17 Sensitivity plot oftensile stress versus sealant modulus 63

18 Sensitivity plot oftensile stress versus PCC slab thickness 64

19 Sensitivity plot oftensile stress versus PCC slab modulus 64

20 Plot ofpercentage ofjoint spalling versus significant variables for JPCP 71

21 Plot ofpercentage ofjoint spalling versus significant variables for JRCP 74

22 Predicted percentage ofspalled joints versus the actual percentage ofspalled

joints for JPCP 79

23 Plot ofresiduals versus the predicted percentage ofspalled joints for JPCP 79

24 Predicted percentage ofspalled joints versus the actual percentage ofspalled

joints for JRCP 83

25 Plot ofresiduals versus the predicted percentage ofspalled joints for JRCP 83

26 Sensitivity plot ofpercentage ofJPCP joint spalling versus average daily

temperature range 85

27 Sensitivity plot ofpercentage ofJPCP spalling versus mean relative humidity during

month of construction ; 85

28 Sensitivity plot of percentage ofJPCP spalling versus number offreeze-thaw cycles .. 87

29 Sensitivity plot ofpercentage ofJPCP spalling versus elongation 87

30 Sensitivity plot ofpercentage ofJPCP spalling versus ESAL's 88

31 Plot of percentage ofjoint spalling versus age 89

32 Effect offreezing index on percentage ofJRCP joints spalled 89

33 Plot ofpercentage ofJRCP joints spalled versus ESAL's 90

34 Influence oftraffic tensile stresses on percentage ofJRCP joints spalled 90

35 Influence ofdifferent ELONG (joint movement) values from temperature

gradients on the percentage ofJRCP joints spalled 91

vi
LIST OF FIGURES (continued)

Figure

36 Influence ofk-value on percentage ofJRCP joints spalled 92

37 Pavement deformation with wheel load placed directly over the plane with the crack. 103

38 Pavement deformation with wheel load placed at the comer ofthe slab 103

39 Plot of percentage ofslabs with comer breaks versus significant variables for JPCP .. 108

40 Plot ofpercentage oftransverse cracking versus significant variables for JPCP 110

41 Measured versus predicted percentage ofslabs with comer breaks 113

42 Plot ofresiduals versus predicted percentage ofslabs with comer breaks 113

43 Measured versus predicted percentage ofslabs with transverse cracking 116

44 Plot ofresiduals versus predicted percentage ofslabs with transverse cracking 116

45 Plot ofpercentage ofslabs with comer breaks versus pavement age 118

46 Plot ofpercentage ofslabs with comer breaks versus cumulative ESAL's 118

47 Plot ofpercentage ofslabs with comer breaks versus cumulative ESAL's

for different slab thicknesses . . . . . . 119

48 Plot ofpercentage ofslabs with comer breaks versus cumulative ESAL's

for different levels ofjoint spacing 120

49 Plot ofpercentage ofslabs with comer breaks versus cumulative ESAL's

for different levels offreeze-thaw cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

50 Plot ofpercentage ofslabs with transverse cracking versus pavement age 122

51 Plot ofpercentage ofslabs with transverse cracking versus cumulative ESAL's 123

52 Plot ofpercentage ofslabs with transverse cracking versus cumulative ESAL's

for different slab thicknesses 124

53 Plot ofpercentage ofslabs with transverse.cracking versus cumulative ESAL's

for different levels offreeze-thaw cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

54 Plot ofpercentage ofslabs with transverse cracking versus cumulative ESAL's

for different annual number ofwet days 125

55 Plot of percentage ofslabs with transverse cracking versus cumulative ESAL's

for different number of days with temperatures above 32°C 125

56 IRI model form A 131

57 IRI model form B 131

58 IRI model form C 132

59 Plots ofIRI versus significant variables for JPCP 140

60 Plots ofIRI versus significant variables for JRCP 141

61 Plots ofIRI versus significant variables for CRCP 142

62 Plot ofpredicted versus actualIRI for JPCP 148

63 Plot ofresidual versus predicted IRI for JPCP 148

64 Plot ofpredicted versus actual IRI for JRCP 150

65 Plot ofresidual versus predicted IRI for JRCP 150

66 Plot of predicted versus actual IRI for CRCP 152

67 Plot ofresidual versus predicted IRI for CRCP 152

68 Influence of annual number ofwet days on IRI ofJPCP 154

69 Influence of climate (freeze or no-freeze) on IRI ofJPCP 154

vii
LIST OF FIGURES (continued)

Figure

70 Influence ofsubgrade type on IRI ofJPCP 156

71 Influence of dowels and dowel diameter on IRI ofJPCP 156

72 Influence of design steel content on JRCP IRI 157

73 Influence ofsubgrade type on JRCP IRI 158

74 Influence of edge drains on JRCP IRI 159

75 Influence ofprecipitation on JRCP IRI 161

76 Influence ofdesign steel content on CRCP IRI 162

77 Influence ofsubgrade support on CRCP IRI 163

78 Influence of climatic region on CRCP IRI 164

79 Influence ofhot weather on CRCP IRI 167

80 Schematic diagram ofpavement design practice with emphasis on cost-effectiveness 189

81 Flow chart for developing distress models 204

82 Typical functional forms used for pavement distress modeling 207

83 Variation in Cp with MSE and R2 ••••••••••••••••••••••••••••••••••••••••• 211

viii
LIST OF TABLES

1 Model and corresponding source of GPS data 5

2 Independent variables significant to the key distress types 8

3 Pavement parameters and range of values used in comer deflection model

development 26

4 Correlation matrix for selected variables for jointed PCC pavement faulting 30

5 Definitions ofselected variables significant to joint faulting ofJCP 31

6 Matrix for selection ofthe overall drainage coefficient, Cd 35

7 Factorial oftraffic and pavement properties used to develop model for predicting

traffic spall stress 61

8 Summary ofinputs and results ofsensitivity analyses oftraffic tensile stress model 62

9 Correlation matrix for variables for JPCP transverse joint spalling model 69

10 Definitions ofselected variables significant to spalling ofJPCP 70

11 Correlation matrix for selected variables for JRCP transverse joint spalling model 72

12 Definition ofselected variables significant to spalling ofJRCP 73

13 Approximate relationship between shrinkage and indirect tensile strength 77

14 Recommended values ofthermal coefficient 77

15 Adjusted sealant modulus for JPCP 77

16 Adjusted sealant modulus for JRCP 81

17 Correlation matrix for selected variables for JPCP comer break model 107

18 Correlation matrix for selected variables for JPCP transverse cracking model 109

19 Variables identified for use in the development ofroughness models 138

20 Summary of correlation analysis for significant variables versus IRI for JPCP 143

21 Summary of correlation analysis for significant variables versus IRI for JRCP 144

22 Summary of correlation analysis for significant variables versus IRI for CRCP 145

23 Summary of variables required for estimating faulting 170

24 Summary ofvariables required for estimating JPCP joint spalling 174

25 Summary of variables required for estimating JRCP joint spalling 175

26 Summary of variables required for estimating JPCP transverse cracking 179

27 Summary of variables required for estimating JPCP comer breaks 182

28 Variables required for predicting IRI for JPCP, JRCP, and CRCP 183

29 Suggested critical values for key performance indicators 186

30 Comparison of cost-effectiveness oftwo alternate pavement designs 191

31 Effect of key pavement design features and site condition factors on transverse

joint faulting 195

32 Effect of key pavement design features and site condition factors on transverse

joint spalling 196

33 Effect of key pavement design features and site condition factors on JRCP

transverse joint spalling 197

34 Effect of key pavement design features and site condition factors on JPCP

comer breaks 198

ix
LIST OF TABLES (continued)

35 Effect ofkey pavement design features and site condition factors on JPCP transverse

cracking 199

36 Effect ofkey pavement design features and site condition factors on JPCP

roughness 200

37 Effect ofkey pavement design features and site condition factors on JRCP

roughness 201

38 Effect ofkey pavement design features and site condition factors on CRCP

roughness 201

39 Diagnostic statistics and corresponding critical values 210

x
AASHO

AASHTO

AC

ANOVA

Cd

CESAL

CRCP

DE

DOWDIA

ESAL

FHWA

FI

FWD

GPS

IMS

IRI

IRRE

JCP

JPCP

JRCP

JTSP

k

LFM

LTE

LTPP

NIMS

PCA

PCC

PMARP

PSI

PSR

R2

SEE

SHA

SHRP

SMP

SPS

LIST OF ACRONYMS AND ABBREVIATIONS

American Association of State Highway Officials

American Association of State Highway and Transportation Officials

asphalt concrete

analysis of variance

drainage coefficient

cumulative equivalent single-axle load

continuously reinforced concrete pavement

differential elastic deformation energy

dowel diameter

equivalent single-axle load

Federal Highway Administration

freezing index

falling weight deflectometer

general pavement studies

information management system

international roughness index

International Road Roughness Experiment

jointed concrete pavements

jointed plain concrete pavement

jointed reinforced concrete pavement

joint spacing or PCC slab length

modulus ofsubgrade reaction

linear fracture mechanics

load transfer efficiency

Long-Term Pavement Performance

National Information Management System

Portland Cement Association

portland cement concrete

Purdue Method for Analysis ofRigid Pavements

present serviceability index

present serviceability rating

coefficient of determination

standard error of estimate

State highway agency

Strategic Highway Research Program

seasonal monitoring program

specific pavement studies

xi

1. INTRODUCTION

Background

The Long-Tenn Pavement Perfonnance (LTPP) study began in 1987 with the goal of

detennining ways ofincreasing pavement life through improvements in design, construction, and

other pavement practices. This is being achieved through the investigation of various designs of

pavement structures that use different materials and experience different loads, environments,

subgrade soils, and maintenance practices. This is emphasized in two ofthe six objectives

established for the LTPP study in 1985, by the Pavement Advisory Committee ofthe Strategic

Highway Research Program (SHRP), which are as follows:

• Detennine the effects ofloading, environment, material properties and variability,

construction quality, and maintenance levels on pavement distress and perfonnance.

• Detennine the effects ofspecific design features on pavement perfonnance.

By investigating the perfonnance ofin-service pavement sections, specific infonnation can be

obtained on the various factors and design features that influence pavement deterioration. In

addition, mathematical prediction models that relate the various factors and specific design

features to pavement perfonnance provide a means for quantifying the effects ofthe specific

design features on long-tenn perfonnance. The results from such investigations and evaluations

can be used to develop recommendations for improving the design and construction of new and

reconstructed pavements.

This study was instituted to evaluate portland cement concrete (PCC) pavements to develop

recommendations to meet the needs ofthe States. It involved an evaluation and analysis ofthe

PCC pavement data in the LTPP database, using a variety ofmeans to detennine the design

features and practices that have beneficial effects on long-tenn perfonnance. Emphasis was

placed on identifying those specific features that can be selected during design to improve the

perfonnance ofPCC pavements under various combinations of environmental and traffic loading

conditions, and for different subgrade support conditions. The study focused on the development

ofpractical recommendations that can be implemented easily by highway agencies to increase

pavement life.

Project Objectives and Scope

The specific objectives ofthis study are as follows:

• Examine and analyze the LTPP data for PCC pavements to detennine the pavement

design features and construction practices that have a beneficial effect on their

perfonnance.

• Develop improved PCC pavement perfonnance models.

• Develop specific recommendations for improving the design and construction ofPCC

pavements.

1
Although all types ofPCC pavement were considered, special emphasis was placed on jointed

plain concrete pavement (JPCP), since it is the pavement type that is constructed most often in

the United States.

Research Approach

To maximize the results obtained from this study, a three-part systematic research approach was

adopted. It involved taking advantage ofthe knowledge from past studies andbuilding on it

using the pavement engineering knowledge obtained from current analysis ofthe LTPP data. The

first part ofthe study consisted of an evaluation ofthe LTPP database using a variety of

techniques to determine the beneficial effects ofvarious pavement design features and practices

on long-term performance.

In the second part ofthe study, improved pavement prediction models were developed, using the

information obtained from a thorough evaluation ofthe database and the results from recent

studies. A key focus was to develop distress prediction models that incorporate mechanistic

principles to the greatest extent possible but that are still practical for use by State highway

agencIes.

The third part ofthe study used the results obtained from this study to develop comprehensive

recommendations for design and construction ofPCC pavements.

Sequence ofReport

This report is the third of a three-volume report on this study and consists of nine chapters.

Chapter 2 provides an overview ofthe LTPP data used for model development and analysis. This

includes information on the data processing and reduction techniques used and the strengths and

weaknesses ofthe data. Chapter 3 provides background information on the different methods and

techniques that were used to develop the prediction models. Chapters 4 through 7 discuss the

background and techniques used to develop models for predicting transverse joint faulting,

transverse joint spalling, transverse cracking, comer breaks, and roughness ofPCC pavements.

Chapter 8 presents examples ofthe application ofthe models developed for design and

construction oflong-lived PCC pavements. It includes comprehensive guidance on use ofthe

models to check new designs and in pavement management systems. Finally, chapter 9

summarizes the results ofthis study and provides recommendations for further research to

improve the models. A detailed description ofthe statistical techniques used in model

development is presented in appendix A.

2
2. OVERVIEW OF LTPP DATA USED FOR MODEL DEVELOPMENT

Introduction

The data used for this study were obtained from the LTPP National Information Management

System (NIMS). The NIMS contains pavement inventory information and performance histories

for over 2,400 in-service and specially constructed pavements. The data include information on

design features, climatic conditions, traffic loads, materials, maintenance, and rehabilitation.<\' 3, 4)

This chapter provides background information on the LTPP data that were used to develop

distress and roughness prediction models for PCC pavements. The data were obtained from the

NIMS at the beginning ofthis study (1993) but were updated frequently to take advantage of

ongoing improvements made to the database. As a result, the study was able to take advantage of

the most comprehensive data on concrete pavements that have ever been available from the

LTPP database. For brevity, the discussion in this chapter is limited to the approximately 300

General Pavement Studies (GPS) concrete pavement sections that were used in this study.

Additional information on the data can be found in volume II.

To guide researchers who use the data in the LTPP database, several sources ofinformation that

describe how to access and use the database were very 'useful to this study.(5) Key sources of

information that are recommended include the Data Collection Guide for Long-Term Pavement

Performance Studies, which provides data collection instructions and data sheets for the LTPP

program.(6) The SHRP Database Structure Reference Manual is also highly recommended for

users ofthe LTPP data.(7) It includes the LTPP IMS schema that defines the various tables and

fields in the NIMS. The schema describes the data structure and also identifies the key fields

(variables) and data types in each table. Other parts ofthe SHRP Database Structure Reference

Manual are a data dictionary that provides a more detailed description of each field in the LTPP

database and tables that define all the codes used in the database.

Overview of the LTPP Data

The LTPP data represent the most comprehensive pavement performance data that have ever

been assembled. Currently, the LTPP database is the world's largest pavement performance

database and has enormous potential for the development ofproducts that will significantly

improve pavement technology. The database includes close to 800 flexible and concrete

pavement sections located across North America as part ofthe GPS. The GPS sections are made

up ofin-service pavement sections, and the data from the concrete pavements in this group offer

an opportunity to refine and improve upon existing PCC pavement performance models.

Advantages

Some ofthe advantages ofthe database include the even distribution of pavement sections across

the four climatic zones in the United States and Canada, defined as wet-freeze, wet-no freeze,

dry-freeze, and dry-no freeze. Also, with the exception ofa few sections, the LTPP experiments

are replicated in all four environmental zones. Extensive design, materials, climatic, traffic,

distress, and roughness information is available on each ofthe sections.

3
The LTPP database also offers some time-series performance data. The time-series data allow

monitoring ofthe rate ofprogression ofthe key distresses for individual pavement sections.

These data also provide a method for evaluating the accuracy and reliability ofthe data on a

section-by-section basis, which is valuable information for developing and validating

performance models.

Clearly, the LTPP database offers enormous potential for the development of performance

prediction models that can be used to address the key issues of concrete pavement analysis,

design, and construction. As a result, a major objective ofthis project was to develop prediction

models for the key PCC pavement distress types and roughness. This follows previous efforts in

the SHRP P-020 LTPP Data Analysis project,(3,4, 11) In that study, prediction models were

developed for several distress types; however, the usefulness ofthese models was limited

because ofthe unavailability ofdata at that time from a majority ofthe pavement sections. Since

then, the database has grown considerably and data are available for many more sections.

Data Available for This Study

The LTPP study consists of nine different experiments. The specific experiments used in this

study were as follows:

• GPS 3 Jointed plain concrete pavement (JPCP).

• GPS 4 Jointed reinforced concrete pavement (JRCP).

• GPS 5 Continuously reinforced concrete pavement (CRCP).

All subsequent discussion ofthe database will focus on the three pavement types listed. Overall,

data from 123 GPS 3, 69 GPS 4, and 85 GPS 5 LTPP pavement sections were available for this

study. For each ofthe pavement types in the LTPP database, data were available for the

following 10 categories:

• Inventory.

• Materials and laboratory testing.

• Traffic.

• Distress.

• Profile.

• Deflection.

• Friction.

• Environment.

• Maintenance.

• Rehabilitation.

Typical LTPP pavement sections evaluated in this study are 150-m sections with 3.65-m-wide

traffic lanes and either asphalt concrete (AC) or tied PCC shoulders.

The data were downloaded from the NIMS and imported into a local Microsoft Access®

database for sorting. Because the LTPP data are provided in several different tables, several

software packages were used for merging and organizing the data. This approach is

recommended because the software also allows exporting ofdifferent combinations ofthe data

4
into spreadsheets for further analysis. For this study, following a thorough checking ofthe data

for consistency and accuracy, spreadsheets were created for development of prediction models

for each ofthe key distress types.

Additional information on the LTPP data used in this study is contained in volume II. Table 1

shows the sources ofthe data that were used for the development ofmodels for four key distress

types and roughness.

Initially, there were plans to include data collected from the LTPP Specific Pavement Studies

(SPS) in this study. The SPS include pavement sections specifically designed and constructed

through a cooperative effort with the State highway agencies (SHA) and that are being observed

over their entire lives. However, although data from the SPS sections are currently available in

the NIMS, they were not available for analysis during this study. It is anticipated that some ofthe

SPS data will be available during the next round ofLTPP data analyses and can be used to check

and improve upon the results obtained in this study. A summary ofthe basic statistics such as

mean, median, and standard deviation ofthe GPS data used in this analysis is presented in

appendix A ofvolume II ofthis report.

Summary

The data used in this study to develop models for predicting key distresses and

roughness of concrete pavements include comprehensive design, materials, traffic loading, and

climatic data from the LTPP database. Specifically, data from the GPS 3,4, and 5 pavement

sections were used to develop models for faulting, spalling, transverse cracking, comer breaks,

and roughness. The data were checked thoroughly and prepared for the subsequent analyses.

Additional information on all the LTPP concrete pavement sections obtained for analyses can be

found in appendix A ofvolume II ofthis report.

Table 1. Model and corresponding source of GPS data.

Model Source of Data

Faulting GPS3

Spalling GPS 3 and 4

Transverse cracking GPS 3

Comer breaks GPS 3

Roughness GPS 3, 4, and 5

5

3. MODEL DEVELOPMENT METHODS

Introduction

In the past, several attempts have been made to develop performance models and

recommendations for concrete pavement design and construction.(3,4,8,9,10,11,12) These have

included studies that have used the LTPP database.(3,4, 11.12) To a large extent, these studies have

all added to the knowledge on the development of predictive models for the key concrete

pavement distress types and roughness. However, it is necessary to improve upon these models

continuously to obtain further insights into the factors that affect the occurrence ofthe key

distress types and roughness, so that further improvements can be made in design and

construction oflong-lived pavements. This chapter reviews the approach used in this study to

develop models for predicting distresses using the LTPP database.

The results from past model development efforts were investigated, including independent and

dependent variables, interaction of variables, mechanistic clusters, and model functional forms

used. This included extensive evaluation ofthe LTPP database to uncover any possible

relationships suggested by the data collected from pavements in service. Table 2 shows the

explanatory variables that were found to be significant to the various PCC distresses in the first

ofthe LTPP concrete pavement data analysis studies and other studies on the performance of

PCC pavementsY)

The best predictive models are those that are first formulated using the principles ofmechanics

and then calibrated using field data. Therefore, a considerable amount oftime was spent

identifying the fundamental mechanisms that cause the distresses being modeled. Once the

underlying principles behind the development ofthe key distress types were understood,

appropriate mechanistic functional forms were selected for investigation and for development of

the most feasible prediction model for each distress type.

Using modem statistical and mathematical techniques, the engineering-based model forms

selected were calibrated using the LTPP database to obtain the best prediction model for each

distress type. This included using the various approaches for optimization, limiting errors, and

maximizing model accuracy. The predictive models were tested in several ways to identify any

weaknesses. The limitations identified were remedied using both statistical techniques and

engineering analysis. Finally, each model was further evaluated by using it to determine the

effect of key design, traffic, and environmental features on performance and for predicting future

pavement deterioration.

7
Table 2. Independent variables significant to the key distress types.(3)

Data Joint Joint Transverse Corner Roughness

Element FaultiDl! SpalIiDl! Crackinl! Breaks

Pavement Age ,/ ,/ ,/ ,/ ,/

Slab Thickness ,/ ,/ ,/ ,/ ,/

Joint Spacing ./ ./ ./ ./ ./

Drainage ./

Base Type ./ ./ ./

Cumulative ESAL's ./ ./ ./ ./ ./

Joint Opening ./ ./

Comer Deflection ./

Freezing Index ,/ ./ ./ ./

Edge Support ./ ./ ./

Subgrade Type ./ ./ ./ ./

Pumping ./ ./ ./ ./

Annual Precipitation ./ ./ ./ ,/ ./

Bearing Stress ,/

Dowel Diameter ./ ,/

Slab Stress ,/ ./

PCC Modulus ofRupture ./ ./ ./ ./

PCC Elastic Modulus ./ ./ ./ ./

PCC Compressive Strength ./

Average Monthly ./ ./ ./ ./ ./ Temperature Range

Thomthwaite Index ./ ./ ./ ./

Static k-value ./ ./ ./ ./

Steel Percentage ./ ,/

Imcompressibles in Joint ./

D-cracking ./ ./

Reactive Aggregate ./ ./

Joint Sealant Type ./

Sealant Damage ./ ,/

Load Transfer Type ./ ./ ./ ./

Freeze-Thaw Cycles ./ ./

8
Model Types

Generally, two types of prediction models can be developed: empirical and mechanisticempirical. Empirical models are developed using statistical regression methods and basic

engineering analysis and judgment; however, they do not explain or model basic mechanisms of

the distress. They are simply the best relationship that allows prediction of an explanatory or

dependent variable from a set ofindependent variables based on the available data. The model

obtained may not necessarily signify a cause-and-effect relationship between the independent

variables and the dependent variable. However, the analyst can use the knowledge available from

past observations and experimental results to improve this empirical aspect ofthe model.

Mechanistic-empirical models, on the other hand, attempt to incorporate mechanistic principles

that account for the cause-and-effect relationship between the explanatory (dependent) variable

and independent variables. Based on the mechanistic principles behind the cause of a particular

distress, a model can be fonnulated that attempts to describe both the occurrence and progression

ofthe distress. The model is then calibrated using field data (e.g., LTPP data) and standard

statistical and optimization techniques. Perhaps the most important benefit of a mechanisticempirical model is its potential to extrapolate beyond the limits ofthe data used in its

development.

For these reasons, the approach adopted in this study was to develop mechanistic-empirical

models for the key distress types. Empirical models were used only in those cases where it was

not possible to develop mechanistic-empirical models, such as for roughness. Roughness is

highly correlated to the development of distress, so there is no single mechanism for modeling

roughness.

A systematic approach was adopted that utilized knowledge accumulated over the years. (4,8,9,10,

12) An essential step in this approach was a thorough investigation to uncover the actual

mechanism responsible for the occurrence and propagation of each distress type. This involved

an evaluation ofprevious studies and an examination ofthe data available for specific sections.

An attempt to model distress was made only after achieving an understanding ofthe engineering

mechanism that causes the distress. Using this approach, it was possible to obtain mechanisticbased prediction models for the distress types analyzed in this study.

Developing Practical Prediction Models

The basic steps that were followed to develop prediction models are summarized in the flow

chart shown in figure 1. This approach, which has been used numerous times in previous studies,

has been continuously improved and provides practical prediction models for implementation as

design checks and for use in pavement managementY' 4,8,9,10,12) Following are the key elements

in the application ofthis approach to develop models for predicting pavement distress and

roughness.

9
Select Distress/IRI Model & Conduct

Literature Review of Previous Models

and Distress Mechanism

Identify and Define Potential Variables

• Dependent Variable (Definition)

• Independent or Explanatory Variables

Identify Missing Data Items for Variables

(Decide which Variables have too Little .-------iJ3L

Data to Keep in Analysis) L~.JAssemble Database ofLTPP Sections

(Determine Specific Subset of Data to Use)

I------I{BExplore Dataset and Clean Data

• Statistics (mean, min., max., etc.)

• 2-Dimensional Bivariate Plots

• Correlation Matrix of all Variables

• Identify Types ofRelationships Between Variables

• Identify Erroneous and Potential Problem Data

• Optional: Create Mechanistic Variable Cluster

I

A

Figure 1. Flow chart for developing distress models for rigid pavements.

10
illModel Building

A • Identify Functional Form of Distress/IRI with Traffic

and Age

• Identify Boundary Conditions

• Select Potential Variables and Transformations for

Initial Evaluation

• Conduct Linear Regression with all

Variables/Clusters (Observe significance Levels,

Collinearity, Residual and Predicted vs. Actual Plots)

• Identify Potential Outliers

• Conduct Further Regression Analyses

• Select Tentative Model

[}-- Sensitivity Analysis

• Set Variables at Their Means

• IncreaselDecrease each Variable by One Standard

Deviation and Compute Distress/IRI for each

• Repeat for all Variables

• Plot Sensitivity Graph

• Evaluate Reasonableness of Direction of Variables on

Distress/IRI

• Evaluate Reasonableness of Sensitivity of each

Exploratory Variable

• Judge Adequacy of Tentative Model

• Revise Model if Deficient

Figure 1. Flow chart for developing distress models for rigid pavements (continued).

11
Step]' Literature Review- Establish Cause ofDistress

This first step involves a comprehensive literature search, review of past studies, and

brainstorming by the research team to establish the cause ofthe distress to be modeled. Past

models for predicting distress and roughness were also evaluated to determine significant

variables.

The goals are to learn as much as possible about the mechanism ofthe distresses, the model

forms previously used to model both distresses and roughness, and the independent variables that

were found to influence the key distress types and roughness in past studies. Also, the form in

which the response variable or distress/roughness was best represented in the models can be

established from a review ofprevious models. The results ofthis review were used to determine

possible shortcomings in the current prediction models and to recommend improvements to the

models.

Step 2: Identify and Define Potential Independent Variables and Clusters

The next important step involves further in-depth investigations to identify and define the

potential independent variables to use in the models for predicting distress or roughness. Of

particular importance are any mechanistic-based independent variables that significantly explain

the cause ofthe distresses. By building on past knowledge, it is possible to identify or develop a

mathematical cluster ofmechanistic parameters relevant to pavement performance prediction,

also called mechanistic clusters, that can be incorporated into models to improve their accuracy

and practicality.

Because such cluster variables are based on mechanistic principles, they offer the advantage of

reducing the data requirements for developing good prediction models. Using these principles, a

systematic process based on both statistical analysis and engineering judgment was used to

determine the independent variables necessary for effective model development. Table 2 shows

the variables that were identified in this study for the development of each prediction model.

Step 3' Assemble Database for Each Model

With the dependent and independent variables for each distress type and roughness established,

the next step is the process of assembling the data required for each model. Table 1 lists the

sources of data that were used to develop the various prediction models in this study. Because of

the structure ofthe LTPP database in the NIMS, a key step in this study was to organize the data

to facilitate its quick retrieval into the unique analysis data sets used for developing the

prediction models. A local Microsoft Access© database proved to be very effective for organizing

the LTPP data.

Step 4' Identify Missing/Erroneous Data Items

Each data set had to be examined thoroughly to identify gaps and erroneous data. In this study,

the LTPP database was examined to determine if data were not available for certain key

variables. In some cases, data were not available because they had not yet been processed into

the NIMS. Some pavements simply did not have data available for certain design features.

12
Therefore, the database was checked closely for anomalies, and appropriate measures were taken

to correct any erroneous data.

Step 5: Explore and Clean Data

For both empirical and mechanistic-empirical models, a very important step in the process is

exploration ofthe data set for each model to examine the general properties ofthe data, clean the

data, and get it ready for further analysis. Basic univariate statistics for the variables are used to

determine ifthe data set is representative ofthe inference space ofthe expected model. Also the

variables are examined using univariate and bivariate analysis methods (e.g., histograms, scatter

plots, and correlations) to identify extreme outliers, erroneous data, and possible transformations,

strong interactions, possible mechanistic clusters, and to determine the relationships between the

distress and explanatory variables. Prior knowledge and expertise should be applied to screen

independent variables and to identify possible transformations, interactions, and specific

mechanistic clusters to consider.

Step 6: Select Model Form

Following the selection of a large pool ofindependent variables, transformed variables,

interactions, and cluster variables to consider, the model building process begins with the

selection ofthe functional form that best describes the path ofprogression ofthe key distresses or

roughness. Various functional forms available for modeling pavement distresses and roughness

are described in appendix A. Several statistical procedures are available for selecting the subset

ofindependent variables, including transformations, interactions, and cluster variable, to include

in the model form for further investigation. They include forward and backward selection

methods, stepwise regression, and other linear regression-based methods that use a variety of

criteria to select the independent variables and the forms ofthe variables to include in a model.

Step 7: Develop and Verify Prediction Model

Following the preliminary investigations to determine the best model form to use, multiple linear

regression analysis is conducted on all ofthe variables and clusters to produce the parameter

estimates and summary statistics for the selected model. Optimization techniques can also be

used to improve this process. The model obtained should then be verified for accuracy ofthe

regression coefficients, reasonableness ofthe regression function, and ability to generalize

inferences drawn from the regression analysis. Appendix A includes some ofthe diagnostic

statistics used in this study to establish the suitability ofthe models developed. Ifthe results

obtained are not satisfactory, remedial measures should be taken and further regression and

optimization analysis conducted as necessary to obtain the best tentative model for predicting the

distress under investigation.

Step 8: Verification ofModel

Following step 7, a robust and reliable model should be available. An extremely important and

final step that should not be neglected is verification ofthe model. This is necessary to check the

13
predictive capability ofthe model outside ofthe data used to develop it. The only reliable

approach is to use data obtained from independent sources to verify the model. However, several

other statistical methods can be used to partially verify models, including the following:

• Sensitivity analyses.

• Statistical diagnostic tests.

• Data splitting (i.e., using part ofthe data that is held back to check the model's predictive

ability).

A sensitivity analysis involves using the model to evaluate the effect ofvarious inputs on the

predicted distress and comparing those results with empirical and theoretical observations. A

comprehensive sensitivity analysis ofthe selected model can be performed as follows:

• Except for the variables ofinterest (the independent and a dependent variable), set all

other variables in the model to their means.

• With all the other variables set at their means, vary the variables ofinterest over their

typical ranges and observe the variation in the response variable or predicted distress. Use

ofplots to observe these variations is highly recommended.

• Compare the results obtained with empirical observations and theoretical results.

14
4. FAULTING MODEL FOR JOINTED CONCRETE PAVEMENTS

Introduction

Faulting is a major distress that occurs in jointed concrete pavements (JCP). It is the difference in

elevation between the adjacent slabs across a transverse joint or crack. Excessive faulting will

greatly reduce the serviceability of a JCP because the increase in roughness caused by the faulted

joints and cracks appreciably increases user discomfort. Therefore, in the design ofjointed

concrete pavements, faulting is one ofthe major distress types that must be prevented. For

existing pavements, forecasting the occurrence ofthe distress is important to ensure a good

riding surface and user safety. Rehabilitation offaulted joints must be performed as soon as

possible in JCP.

Diamond grinding ofthe joints is an effective way to eliminate faulting, provided the faulting is

not excessive. However, unless the fundamental causes offaulting are addressed, it is likely that

the payement will continue to fault. Alternatively, faulting can be remedied with a thick overlay.

In either case, the rehabilitation ofpavements with faulting is costly and time consuming.

Therefore, it is more effective to prevent faulting during design. Some ofthe design features that

can be used to reduce faulting include dowel bars, nonerodible bases, and positive drainage. (3,8,

10,13,14) This chapter describes the development of a model for predicting joint faulting ofJCP.

The model can be used as a design check to ensure that the appropriate measures have been taken

to limit faulting. For pavements already in service, the model also provides a means for

predicting the occurrence offaulting. This information can be used to plan rehabilitation as part

of an overall pavement management system. To provide a model that is most suitable for all

these uses, the model incorporates mechanistic principles that explain the occurrence offaulting.

Faulting Mechanism

Faulting is the result of a combination ofpoor load transfer across a joint or crack, heavy axle

loads, free moisture beneath the pavement, and pumping ofthe supporting base, subbase, or

subgrade material from underneath the slabY' 8,10,13,14) It is primarily caused by erosion ofthe

supporting material from underneath the leave slab and a buildup ofthe loose material under the

approach slab at ajoint or crack. The erosion ofmaterial from underneath the leave slab is

caused by the phenomenon ofpumping. Therefore, it is important to understand pumping in

order to understand the mechanism that leads to faulting.

Pumping is a phenomenon that has been observed on concrete pavements since the advent of

large trucks with heavy axle 10ads.(13, IS, 16, 17, 18, 19,20,21,22) Four elements must be present for

pumping and, therefore, faulting to occur. There must be free water in the pavement, an erodible

underlying or supporting material, heavy truck traffic, and differential deflections due to

inadequate load transfer.

When these elements are present, as a heavy wheel load approaches a joint or crack, the approach

slab deflects and forces water trapped under the slab to transport fine material underneath the

leave slab. As the wheel load crosses the joint or crack, the sudden vertical pressure on the leave

slab causes pumping or ejection ofthe water and loose material from beneath the slab through

the joint or crack. A large part ofthe fine material that is eroded from beneath the leave slab is

15
deposited under the approach slab. Repeated cycles ofthis phenomenon, which occurs with each

wheel load application, can be in the millions. Eventually, this leads to measurable faulting at the

joint or crack because of a lift up ofthe approach slab and a depression ofthe leave slab.

Although this is the basic mechanism ofpumping that leads to faulting, several other factors can

exacerbate the distress and need to be taken into account. Field results show that the reduced

support from upward curling or warping ofthe slab at the joint or crack will increase pumping

pressures because ofthe higher deflections experienced.(24) The potential for faulting of a

pavement is at a minimum in the summer months when the joints are closed due to thermal

expansion.(24) Also, faulting increases in the other seasons when the joint width is widest and the

underlying materials typically have a higher moisture content,(24,25)

The impact of a heavy wheel load as it crosses the joint or crack is far more pronounced ifthere

is inadequate load transfer. The higher differential deflections that occur at the joint or crack will

lead to more pumping and faulting. However, it is important to note that, even for a pavement

with 100 percent load transfer, deflections at the joint or crack can be abnormally high and result

in horizontal pumping.(13) This was observed at the American Association of State Highway

Officials (AASHO) Road Test, where the joints with dowels used for load transfer showed

extensive pumping but no faulting in the 2-year period ofthe study.(19) Laboratory and empirical

evidence show that the loss ofsupport caused by horizontal pumping will eventually lead to

more pumping.(12, 23) This will increase corner deflections and lead to faulting as the magnitude of

the deflections increases. In addition, the loss ofsupport at the joints and slab edge caused by

pumping will also increase the stress in the slab and can eventually lead to corner cracking.

Based on the mechanism described, it is clear that the following conditions must exist for

pumping and faulting to occur:

• Significant joint differential deflections brought on by several factors, including heavy

whee1loads, inadequate load transfer, and loss ofsupport.

• A high percentage offines in the underlying base, subbase, or subgrade material that is

erodible.

• Saturation or a high moisture content ofthe underlying base, subbase, or subgrade

material.

These factors must be considered in the development of a model for predicting joint faulting.

Evaluation ofExisting Faulting Models

To determine the factors that should be considered in the development of a model for predicting

faulting, several existing doweled and nondoweled faulting models were reviewed. These models

included empirical and mechanistic-empirical models.

16
Empirical Models

An early empirical faulting model based on distress surveys from six States is shown below.(8)

The m'odel predicts faulting for both doweled and nondoweled pavements.

FAULT = ESALo.144 [-0.298 + 0.2671/(THICK°.3184) - 0.0285*BTYF

+ 0.00406(FI + 1)°·3598 _0.0462*EDSUP + 0.2384*(PUMP+1)°·0109

- 0.0340*DOW2

.

0587 ]

(1)

where

FAULT =

ESAL =

THICK

BTYF =

FI =

EDSUP =

PUMP

DOW

mean transverse joint faulting, in

accumulated 18-kip single-axle loads, millions

slab thickness, in

ofor granular and 1 iftreated

freezing index

ofor AC shoulders and 1 for tied PCC shoulder

oifno pumping and 1, 2, or 3 for low, medium, or high severity

diameter of dowel bar in inches and 0 ifno dowel bars present

The unique aspect ofthis model is the inclusion ofshoulder type and a pumping factor. The

pumping factor is similar to an erosion factor, which recognizes the effect pumping has on

faulting. The pumping factor is calculated from traffic, soil type, slab thickness, precipitation,

and freezing index. It was realized from this study that tied shoulders reduce faulting by about 50

percent. It was also one ofthe first models to relate dowel diameter to faulting.

In the first attempt to develop prediction models using the LTPP data, the following faulting

models were also developed for doweled and nondoweled pavements:(3, 4)

FAULTD 0 CESAL 0". [0.0238 + 0.0006.( ITS~~CE)'

where

FAULTD

CESAL

JTSPACE

KSTATIC

+ 0.0037*( 100 )2 + 0.0039*( AGE)2

KSTATIC 10

,

- 0.0037 *EDGESUP - 2.18 *DOWDIA 1

100

mean transverse doweled joint faulting, in

cumulative 18,000-lb ESAL's in traffic lane, millions

mean transverse joint spacing, ft

mean backcalculated static k-value, psi/in

17

(2)
AGE = EDGESUP =

DOWDIA

age since construction, yr

edge support (1 for tied concrete shoulder and 0 for other

shoulder types)

diameter of dowels in transverse joints, in

FAULTND = CESALo.2S *[- 0.0757 + 0.0251 *VAGE

+ 0.0000012 FI*PRECIP - 0.0378 DRAIN + 0.000013 PRECIp2 (3)

where

FAULTND =

CESAL =

AGE =

PRECIP =

FI =

DRAIN -

mean transverse nondoweled joint faulting, in

cumulative 18,000-lb ESALs in traffic lane, millions

age since construction, yr

mean annual precipitation, in

mean freeze index, degree-days

drainage type, 1=longitudinal subdrainage exists; O=otherwise

For the nondoweled pavement, the significant variables include traffic loading, dowel diameter,

edge support, joint spacing, and subgrade support. Environmental factors that influence the

erodibility ofthe underlying materials and joint width were significant.

Faulting models were also developed recently in the Federal Highway Administration (FHWA)

jointed concrete pavement study, commonly referred to as RIPPER, for both doweled and

nondoweled concrete pavements.(IO)

FAULTND =

FAULTD =

where

FAULTND =

CESALS =

Cd =

Slabthick =

Jtspace =

Basetype =

FI =

CESALSO.25*[0.2347 - O.l516*Cd- 0.00025*Slabthick2/Jtspaceo.25

- 0.0115*Basetype + 0.7784*1O·7*FI1.5*Precipo.25

- 0.002478 *Days90 - 0.0415*Widenlane]

CESALSO.25[0.0628 - 0.0628*Cd+ 0.3673 *10·8*Bstress2

+ 0.4116* 10-5*Jtspace2+ 0.7466* 1O-9*FI2*Precipo.5

- 0.009503*Basetype - 0.01917*Widenlane + 0.0009217*Age]

mean transverse nondoweled joint faulting, in

cumulative 18-kip ESAL's, millions

drainage coefficient

slab thickness, in

joint spacing, ft

stabilized or unstabilized base

freezing index

18

(4)

(5)
Precip

Days90

Widenlane

FAULTD

Bstress

Age

=

=

annual precipitation, in

days temperature is above 90 of

presence of a widenlane or not

mean transverse doweled joint faulting, in

maximum dowel/concrete bearing stress, psi

pavement age, yr

Much like the previous faulting models, these models show that a combination of variables that

influence the level of differential deflection at the joint, erodibility ofthe underlying material,

and the availability offree water have a significant effect on faulting.

Mechanistic-Empirical Models

In 1993, a mechanistic-empirical faulting model developed by the Portland Cement Association

(PCA) introduced the concept of erodibility as one ofthe important parameters to consider

directly in a model for predicting faulting.(26) The PCA model defines the rate ofwork or power

of each axle pass at the comer of a slab as follows:

where

P

P

t

k

=

=

power (rate ofwork)

pressure at slab-foundation interface, psi

slab thickness, in

modulus ofsubgrade reaction, psi/in

(6)

For each axle, the number of allowable axle load applications for the pavement was calculated as

follows:

log N = 14.524 - 6.777 * (Cl * P - 9.0)°·103

where

(7)

allowable axle load repetitions to end of design period

1 - (k/2000*4/t)2

power

Using Miner's damage equation, erosion damage at the slab comer was calculated with the

following equation:

EROSION = 1OO*nl *(C/N)

where

(8)

EROSION percent erosion damage

expected number of axle load repetitions for each axle group

19
0.06 for pavements without a shoulder and 0.94 for pavements with a tied

concrete shoulder

allowable number ofrepetitions for each axle group

The erosion damage calculated in this fashion was used as a cluster variable to develop the

following models for predicting faulting of doweled and nondoweled jointed concrete

pavements:

FAULTND =

FAULTD =

where

FAULTND = EROSION

Precip

JS =

DRAIN

FAULTD

EROSIOW·25 [9.75873xlO-4*(Precip)0.91907 + 0.0060291 *JS°.54428

- 0.016799*DRAIN]

EROSIOW·25 [0.0038332*(Precip/1 0)1.84121

+ 0.0057763*JSO.38274 ]

mean faulting at nondoweled transverse pavement joints, in

calculated accumulated erosion

annual precipitation, in

joint spacing, ft

dummy variable for the presence of edge drains

mean faulting at doweled transverse pavement joints, in

(9)

(10)

Other mechanistic-empirical faulting models have been developed based on the concept of

damage estimated from the pavement's corner deflection. Equations 11 and 12 are examples of

some ofthe models developed to estimate the allowable number ofload repetitions:(27)

(11)

(12)

where

Nd

Df =

w

h =

k

number ofload repetitions before critical damage

damage index

corner deflection

pavement thickness

subgrade reaction modulus

Faulting Model Development Approach

Based on the review ofliterature and previous models, an approach similar to the peA procedure

was adopted for development of a mechanistic-empirical model for predicting faulting.(26,27) It

involved the identification of a mechanistic parameter that could be related to the damage that

causes faulting. The mechanistic parameter that was selected is the differential elastic

deformation energy (DE) imposed on the underlying base, subbase, or subgrade at the slab

corner.(22, 28, 29, 30)

20
The differential elastic deformation energy imposed on the underlying material by traffic loads is

related to the differential deflection at the joint. The pore water pressure generated by the

differential energy imposed on the slabs is responsible for the erosion and ejection offine

material from underneath the slab. The differential elastic deformation energy was used as a

mechanistic response parameter for predicting the allowable number of cycles of 80-kN

equivalent single axle load (ESAL) applications to failure. This approach was used successfully

to develop similar models for predicting faulting for cost allocation purposes.(12)

Preliminary Model Form

With DE selected as the mechanistic parameter to relate to faulting, it is possible to use Miner's

linear damage hypothesis to determine the total damage that is accumulated by a pavement from

repeated 80-kN ESAL load applications. However, in recognition ofthe effect ofother non-load

factors such as the pumping potential ofthe underlying material and the environment, the

following general model form was selected for consideration as a faulting model:

where

FAULT = (FDAMAGE)PC (13)

P

FDAMAGE =

FAULT ,

C

n

Nf

=

=

mean joint faulting, mm

erodibility scaling factor related to the pumping potential ofthe underlying

material and the environment

regression coefficient

accumulated faulting damage = L nlNf

actual number of 80-kN ESAL's

allowable number of 80-kN ESAL's to failure related to the differential

elastic deformation energy, DE

Although this model assumes that the faulting damage (FDAMAGE= LnlNf

) due to load

applications accumulates linearly with the number of 80-kN ESALs, there is a non-linear

relationship between the total damage and predicted faulting. The scaling factor, C, accounts for

the interaction between the load causes offaulting and the other non-load-related factors

described previously that contribute to faulting. This model form meets the boundary conditions

for faulting; faulting is equal to zero when there are no load applications, and faulting increases

early in the life ofthe pavement and levels off after early load applications.

Mechanistic Response Parameter

A procedure for calculating DE for pavements was developed for use in the development ofthe

faulting model. The concept of a deflection-based deformation energy criterion has been used

several times in the past for pavement research.(22,28,29,30) The Purdue Method for Analysis of

Rigid Pavements (PMARP) to compute the volume ofmaterials pumped from beneath a loaded

slab was developed in 1984.(22) The volume of pumped materials was defined as a function ofthe

deformation energy imposed on the pavement by a load, which was defined as follows:

21
where

DE

~i

=

=

D

DE = L kjAjLl: j=1

defonnation energy imposed by an axle load, kN mm

modulus ofsubgrade reaction, kN/mm3

area associated with node i, mm2

deflection at node i, mm

(14)

In this model, only those nodes within the finite element mesh with deflections over 0.5 mm are

considered significant to pumping. However, there is ample empirical and laboratory evidence to

suggest that even lesser deflections can lead to pumping and faulting.(13, 23, 25)

As a wheel load crosses a joint, the difference in the elastic defonnation energy between the

loaded (leave) slab and the unloaded (approach) slab is directly related to the pore water pressure

generated and the resultant volume ofmaterial that is pumped from beneath the load slab.

Therefore, a response parameter that can be related to pumping and faulting is the difference

between the elastic defonnation energy per unit area imposed on the loaded and unloaded slabs,

defined as follows:

where

DE

=

differential elastic defonnation energy per unit area between the loaded and

unloaded slab, kN/mm

elastic defonnation energy per unit area imposed on the loaded slab, kN/mm

elastic defonnation energy imposed on the unloaded slab, kN/mm

(15)

The elastic defonnation energy in equation 15 is defined as follows:

E = ~wp

where

(16)

E

w

p

= elastic defonnation energy per unit area, kN/mm

slab's deflection at the joint, mm

pressure at the slab-foundation interface at the joint, kN/mm2

Ifthe underlying material is modeled as a Winkler foundation, the pressure at the slab-foundation

interface can be detennined from the following equation:

p = kw

22

(17)
where

P

k

=

=

pressure at the slab-foundation interface, kN/mm2

modulus ofsubgrade reaction, kN/mm3

Substituting equation 17 into equation 16 results in the following relationship:

(18)

Therefore, DE can be defined as follows:

(19)

The validity ofrelating DE to faulting can be checked by examining the following form of

equation 19:

(20)

The term (wL - W UL) is the differential comer deflection between the loaded and unloaded slabs. It

represents the relative movement between the loaded and unloaded slabs and is an indication of

the amount ofload transfer present at the joint. The higher the difference (i.e., inadequate load

transfer), the higher the joint faulting will be. Without any differential deflections at the comer

(perfect load transfer), there will be no faulting. The term (wL + W UL) is equivalent to the freeedge comer deflection wfe and is defined as follows:

(21)

It represents the total flexibility ofthe slab at the joint. The higher the slab's flexibility, the

higher the potential for joint deterioration and faulting. This increases the resulting differential

comer deflections. These observations support use ofthe differential elastic deformation energy

as a response parameter to model faulting.

Determination of Differential Elastic Deformation Energy

The comer deflections ofthe loaded and unloaded slabs at the joint are required to calculate the

differential elastic deformation energy. These comer deflections are dependent on pavement

design features such as the load transfer at the joint, material strength properties, saturation level

ofthe underlying materials, and the applied loads. Finite element analysis presents the best

approach for calculating these required deflections. However, since it is impractical to use finite

element analysis every time the model is used, simple deflection prediction equations were

developed for use in calculating the deflections.

Loaded and Unloaded Comer Deflections

Following is a general equation for calculating the free-edge comer deflection for a load placed

along the joint based on Westergaard's free comer deflection equation:(31)

23
where

Wfe

a

p

k

Q

=

=

=

=

free comer deflection, mm

nondimensional scale factor

applied load, kN

modulus ofsubgrade reaction, kN/mm3

radius ofrelative stiffness, mm

(22)

This equation takes the applied load, modulus ofsubgrade reaction, and radius ofrelative

stiffness into consideration for calculation ofthe comer deflection. The nondimensional scale

factor takes into account factors such as the distance ofthe load from the comer and the type and

configuration ofthe load.

Another parameter critical to faulting is the load transfer at the comer, which is defined as

follows:

where

LTE =

=

comer load transfer efficiency

unloaded slab comer deflection

loaded slab comer deflection

(23)

For any pavement, ifthe free-edge comer deflection and the load transfer across the joint of a

pavement at the comer are known, the unloaded comer deflection can be calculated as follows:

WUL = wfe *(LTE)/(l + LTE) (24)

The loaded comer deflection can then be calculated from the comer LTE and the unloaded comer

deflection in the following manner:

(25)

Therefore, if equations are available for calculating the free-edge comer deflection and the comer

load transfer, both the unloaded and loaded comer deflections can be calculated. This was

accomplished by developing prediction equations for calculating the free-edge comer deflection

and the comer load transfer efficiency. The results from finite element runs for a factorial of

pavement design features that cover a wide range offield conditions were used to develop the

models.

Finite Element Analysis

The finite element analysis program ILLI-SLAB was used in the analysis of a factorial of

pavement design features to develop the regression equations for calculating the free-edge comer

deflection and comer load transfer efficiency. The factorial was designed to cover the range of

24
pavement parameters covered by the GPS 3 sections, as well as those expected to be encountered

in the field. Additionally, two nondimensional parameters, L/Q and AGG/kQ, were used to

minimize the number of cases that had to be analyzed. The L/Q ratio gives an indication ofthe

effect ofslab size on the comer deflection, where L is the joint spacing and Qis the radius of

relative stiffness. AGG/kQ and Qare defined as follows:

AGG/kQ = AGGoexp[l + ana -b(L/Q)]

Q4 = E*h3 / [12*k(1-,u2)]

where

(26)

(27)

AGG

D = L =

Q

AGGo, a, b, a =

E

h = k =

Jl

load transfer factor, kPa

dowel diameter, rom

joint spacing, m

radius ofrelative thickness, rom

regression coefficients

modulus ofPCC slab, kPa

slab thickness, rom

modulus ofsubgrade reaction, kPa/rom

Poisson's ratio

AGG/kQ is essentially a nondimensionalload transfer factor that is directly related to the joint

load transfer efficiency. Following a review ofthe LTPP database, the pavement parameters and

ranges given in table 3 were selected for use in the factorial analysis. The basic model used for

the finite element analysis is shown in figure 2 and consisted offour adjacent slabs in the

longitudinal direction. Slabs in the transverse direction were used in the analysis because the

finite element analysis showed that, even when loaded, they did not significantly affect the

pavement's comer deflections. However, the analysis showed that all the wheels on an axle

influenced comer deflection; therefore, the entire axle was considered in the analysis.

25
Table 3. Pavement parameters and range of values used in comer

deflection model development.

Variable Range of Values

Load, kN 80-kNESAL

Load transfer factor, kPa 185 to 400

Outer wheel distance from comer, mm oto 915

Slab length, mm 4600

Slab width, mm 3600

AGG/kQ 0.0171 to 3701

L/Q 3.1 to 6.7

Modulus of concrete, kPa 34.5*106

Modulus ofsubgrade reaction, kPa/mm 27

Poisson's ratio 0.15

2160

1400

3600

3175

00

lA:

oc

0 1800 2850 3860 4600 5280 6300 92

760

460

305

152

o

4270 4870

Figure 2. Finite element model.

26
Free-Edge Corner Deflection Model

The highest deflection at the comer of a slab occurs when the load is placed at the outside edge

of a pavement without edge support or tied shoulders. As the load is placed at increasing

distances inward from the unsupported pavement edge, the magnitude ofstress and deflection at

the comer decreases.

Studies on pavement encroachment show that most trucks are driven with the outside wheels

placed about 460 to 610 mm from the edge, and only approximately 6 percent oftrucks run with

their wheels placed at the edge.(32) To take this distribution into account, it was decided to

develop models for predicting deflections for loads placed along the joint anywhere between 0

and 915 mm from the edge.

From the results obtained, the following equations were developed for calculating the free-edge

comer deflection for an 80-kN ESAL placed at the comer (i.e., 0 mm from the comer) and 915

mm from the comer, respectively:

where

=

=

Wfe x=O = (0.1051 2 + 87.18 + 231473)/ke

Wfe x=915 = (0.078 2 + 123.6 - 19993)/ke

free-edge comer deflection, mm

modulus ofsubgrade reaction, kPalmm

radius ofrelative stiffness, mm

(28)

(29)

Regression analysis ofthe results obtained from these models and those from finite element

analysis runs showed that the models estimated deflections with reasonable accuracy.

Load Transfer Efficiency Models

As noted, equations 28 and 29 calculate the free-edge comer deflections for pavements with no

load transfer. However, for most pavements, there is some load transfer across adjacent slabs,

either through aggregate interlock or by the provision of dowels. The free-edge comer

deflections calculated should therefore be corrected for the effect ofload transfer. This requires

knowledge ofthe load transfer across the pavement slabs.

Several studies have developed models from finite element analysis for calculating load transfer

for wheel loads placed close to the comer of a pavement slab. Two such equations are provided

as equations 30 and 31. Equation 30 was developed for calculating load transfer efficiency (LTE)

for a load placed at the comer of a slab, and equation 31 was developed for calculating the LTE

for a load placed 915 mm from the slab comer.<2,3)

27
where

LTEx=o = 1/[1 + 1.2*(AGG/K~yO.849]

LTEx=9IS = 1/[1 + 0.3483*(AGG/K~rI.l3677]

(30)

(31)

LTE

x

AGG/k~

=

=

load transfer efficiency, percent

distance ofload from comer, mm

nondimensionalload transfer factor

A linear relationship exists between the load transfer calculated for loads placed between 0 and

915 mm from the comer ofa slab. Therefore, equations 30 and 31 can be used to calculate the

comer LTE for any load placed between 0 and 915 mm from the slab comer by linear

interpolation between LTEx=o and LTEx=9IS'

Calculation ofComer Deflections for Loaded and I Inloaded Slabs

Using equations 28 through 31, the unloaded comer deflection for an 80-kN ESAL placed at a

distance of 0 or 915 mm from the comer can be calculated as follows:

WUL = wfe,x=Oor9ISmm *(LTEx=oor91Smm)/(l + LTEx=oor9ISmm) (32)

The unloaded comer deflection for an axle load placed at any distance between 0 and 915 mm

from the comer can be determined by interpolating between the results obtained for x = 0 and x =

915 mm. This result was verified using the results obtained from finite element analysis. The

loaded comer deflection can then be calculated from the unloaded comer deflection and the

comer LTE as follows:

(33)

Calculation ofDifferential Elastic Deformation Energy

On the basis of equations developed in the preceding section, following is a procedure that was

used to obtain estimates ofthe differential elastic deformation energy for the LTPP sections for

use in the model development. In this study, an axle load with the outer wheel placed 305 mm

from the comer was considered. This procedure is also required for calculating the differential

elastic deformation energy, DE, for use in the final model that was developed.

1. Calculate the nondimensionalload transfer factor, AGG/ld, using equation 26 (use its

final form, equation 39, for the final model).

2. Using equations 28 and 29, calculate the deflections, wfe ' using the values of and k for

the pavement and with the load, P, placed at x = 0 and x = 915 mm.

3. Calculate LTE at x = 0 and x = 915 mm using equations 30 and 31 and the value of

AGG/k~ from step 1.

28
4. Correct the free-edge deflections, wfe ' for comer LTE at x = 0 and 915 mm to obtain the

unloaded slab comer deflections, wuu at x = 0 and x = 915 mm using equation 32.

5. Calculate W UL at x = 305 mm by interpolating between the unloaded slab deflections at x

= 0 and 915 rom.

6. Calculate the loaded comer deflection, WL , at x = 305 rom using equation 33.

7. With W UL and wL at 305 mm, calculate the differential elastic deformation energy, DE, for

an 80-kN axle placed 305 rom from the comer using equation 19.

Data Preparation and Evaluation

The next step in the model development was preparation and evaluation ofthe data available

from the GPS 3 sections in order to determine the plausibility ofthe preliminary model form and

to gain further insight about the variables that influence faulting. The database ofGPS 3

pavement sections that was created was checked thoroughly for gross errors, cleaned, and

prepared for analysis. A comprehensive statistical analysis ofthe cleaned data was conducted to

evaluate the preliminary relationships between the measured faulting and several explanatory

variables.

Table 4 is a correlation table that shows the strength ofthe relationships between the explanatory

variables and faulting, as well as the relationship between the variables themselves. The

definitions ofthe variables in table 4 are provided in table 5. Although the results do not show

very strong relationships between the independent variables and faulting, several interesting

trends are evident. The"variables with the highest positive correlations to faulting are cumulative

ESAL's and age.

29
o

Table 4. Correlation matrix for selected variables for jointed PCC pavement faulting.*

HPCC k-value JTSP DOWDIA DT FI PRECIP WTDYS MEANT AGE ESAL EPeC LTC Cd H

HPCC 1 0.20058 0.04567 0.16603 0.04809 -0.14939 -0.04082 -0.18801 0.03885 -0.09302 0.0706 0.02911 -0.24665 -0.04158 

k-value 0.20058 1 0.02185 -0.01931 0.10616 -0.32218 0.07737 0.05085 0.34421 -0.23584 0.04577 -0.05402 -0.08062 0.33438 

TSP 0.04567 0.02185 1 0.30383 0.20279 -0.37042 0.5018 0.28681 0.34266 0.3585 0.43957 -0.26813 -0.22995 -0.02778 

DOWDIA 0.16603 -0.01931 0.30383 1 0.10763 -0.12995 0.40269 0.26912 0.08382 -0.16885 -0.04356 -0.16687 -0.90703 -0.37105 

DT 0.04809 0.10616 0.20279 0.10763 1 -0.05898 0.13129 0.21816 0.0227 -0.08369 0.24234 -0.19285 -0.0931 0.17399 

FI -0.14939 -0.32218 -0.37042 -0.12995 -0.05898 1 -0.40791 -0.06858 -0.86655 -0.23369 -0.26391 -0.06718 0.21947 -0.30104 

PRECIP -0.04082 0.07737 0.5018 0.40269 0.13129 -0.40791 1 0.7998 0.53686 0.20402 0.30838 -0.1409 -0.32447 -0.13718 

WTDYS -0.18801 0.05085 0.28681 0.26912 0.21816 -0.06858 0.7998 1 0.25122 0.16788 0.25769 -0.00947 -0.19399 -0.22116 

MEANT 0.03885 0.34421 0.34266 0.08382 0.0227 -0.86655 0.53686 0.25122 1 0.12936 0.29552 0.07864 -0.12578 0.39311 

AGE -0.09302 -0.23584 0.3585 -0.16885 -0.08369 -0.23369 0.20402 0.16788 0.12936 1 0.4926 -0.07957 0.21124 -0.18921 

ESAL 0.0706 0.04577 0.43957 -0.04356 0.24234 -0.26391 0.30838 0.25769 0.29552 0.4926 1 -0.17086 0.05907 -0.01568 

EPeC 0.02911 -0.05402 -0.26813 -0.16687 -0.19285 -0.06718 -0.1409 -0.00947 0.07864 -0.07957 -0.17086 1 0.21413 0.1227 

LTC -0.24665 -0.08062 -0.22995 -0.90703 -0.0931 0.21947 -0.32447 -0.19399 -0.12578 0.21124 0.05907 0.21413 1 0.295 

Cd -0.04158 0.33438 -0.02778 -0.37105 0.17399 -0.30104 -0.13718 -0.22116 0.39311 -0.18921 -0.01568 0.1227 0.295 1 

BT 0.0478 0.18896 0.10025 -0.02979 0.07708 -0.40403 -0.0112 -0.21582 0.3522 -0.2184 -0.12794 -0.02004 -0.03455 0.54272 

T -0.19419 0.24932 -0.09234 -0.28474 -0.03085 -0.0306 -0.00776 0.08471 0.15304 -0.1231 -0.04847 0.17256 0.28067 0.69938 

FAULT -0.18126 0.04164 0.12074 -0.27488 0.0149 -0.16442 0.1984 0.26939 0.22041 0.23186 0.1522 0.03083 0.27485 0.15073 

*See table 5 for defmitions.
Table 5. Definitions ofselected variables significant to joint faulting ofJCP.

I Symbol I Potential Independent Variable I

Hpcc PCC slab thickness, mm

k-value Static backcalculated k-value, kPa/mm

JTSP Mean transverse joint spacing, m

DOWDIA Dowel diameter, mm

DT Presence of edge drain, O=no edge drain, 1=edge drain present

FI Freezing index, degree-days eC) below freezing

PRECIP Average annual precipitation, mm

WTDYS Number of days precipitation> 12.7 mm in a year

MEANT Average mean daily temperature, °c

AGE Time since pavement construction, yr

ESAL Cumulative equivalent 80-kN single axle load

Epcc PCC slab modulus of elasticity, kPa

LTC AASHTO load transfer coefficient, J-Factor

Cd Time since pavement construction, yr

BT Base type, O=erodible and 1=nonerodible

ST Subbase type, O=fine and 1=coarse

FAULT Mean edge joint faulting, mm

Faulting is, of course, strongly related to the number of heavy axle loads passing over a joint that

cause differential deflections. The number ofwet days and precipitation level are also positively

correlated to faulting, supporting the empirical evidence that higher levels ofmoisture in the

pavement will result in more faulting. There is also an indication that base type and dowel

diameter are negatively correlated to faulting; that is, a nonerodible base and larger dowel

diameter will result in less faulting. A pictorial representation ofsome ofthese trends is shown in

the bivariate plots in figure 3.

Erodibility Scaling Factor

The scaling factor, C, in equation 13 accounts for important factors that interact with the

differential elastic deformation energy at the joint to cause pumping and faulting, but that cannot

yet be fully described with mechanistic response parameters. The factors include the type and

31
erodibility ofthe underlying pavement layers, the environment, drainage, and other pavement

features. Mainly, these factors influence the pumping potential ofthe base, subbase, or subgrade

beneath the PCC slab and are collectively represented by the erodibility factor.

The degree to which the underlying materials pump or erode when subjected to heavy wheel

loads depends on the material type, physical properties, and level ofsaturation. The level of

saturation ofthe pavement materials depends on the environment and the drainage provided.

Therefore, the challenge is to select the components ofthe scaling factor that account for these

effects as much as possible. Several model forms and variables were selected to be used for

defining the erodibility factor. Based on the results ofpast studies and evaluation ofthe data for

the GPS 3 concrete pavements from the correlation analysis and stepwise regression, the

following model form and variables were selected as the most promising for defining the

erodibility factor: '

where

(34)

C

WETDAYS

DOWDIA

Cd

BASE

Po, PI' P2' P3' P4 =

erodibility scaling factor

number of days with precipitation greater than 12.7 mm

dowel diameter, mm

drainage coefficient

base or subbase type, O=erodible, 1=nonerodible

regression constants

For all types of pavement materials, pumping and faulting can be magnified by environmental

factors such as the amount of precipitation, freeze-thaw damage, depth offrost penetration,

thermal expansion ofthe slab, and daytime slab curling.

Evaluation ofthe GPS 3 data showed that the number ofdays with precipitation greater that 12.7

mm was relatively highly correlated with faulting, and was therefore selected to account for the

general effect ofthe environment in the scaling factor. Past results show a similar significant

effect ofprecipitation on faulting.<3, 10) Another variable included in the scaling factor is dowel

diameter. Although dowel diameter is considered in the calculation ofthe load transfer parameter

i!1,%\uation 26, there is strong evidence from past models that dowels are significant to faultingY'

32
5 5 5

E 4 ••• • E 4 E 4 •

E E E • tii 3 • •• tii 3 tii 3 c • .-.. c c B 2 • B2 :2 2

{!." 1 " " .-. • {!. 1 {!. 1

• 0 • 0 10 20 30 40 500 1000 1500 50 100 150 200

Age, yr Freezing Index,·C Days Annual no. of freeze·thaw

cycles, days

5 5 5

E 4 • E 4 • E 4 E

•

• E

• E tii 3 tii 3 tii c c 3 • c B 2 B 2 • B 2

" " .. " co co II. 1 II. 1 {!. 1

0 0 •

• • 0

0 0.5 1.5 2 0 100 200 300 0 10 20 30 40

Precipitation, m Annual no. of Annual maximum

wet days, days temperature, ·C

5 5 5

E 4 • •

E. 3 • E 4 • E 4 • • E E Ol tii 3 • tii 3

B

c 2 c c • co" B 2 B 2 • II. 1 {!." 1 {!." 1

10 20 30 10 20 30 40 50 100 150

Annual average minimum temperature, Annual mean temperature, Annual no. of days

·C ·C above 32·C

5 5 5

E 4 • E 4 • • E 4

E • E • E

tii 3 tii 3 • • • tii 3

c c c B 2 E 2 B 2

{!." 1 " " co

II. 1 {!. 1

0 0

50 100 150 200 0.7 0.9 1.1 1.3 0

Annual no. of days Drainage coefflclen~ C. Base type

below 0 ·C, days

Figure 3. Plot ofmean joint faulting versus significant variables for jointed PCC pavement.

The results from the correlation studies also show that dowel diameter is very significant to

faulting. Consequently, dowel diameter was also included.

The drainage coefficient, Cd' used in the scaling factor is a modified version ofthe American

Association of State Highway and Transportation Officials (AASHTO) drainage coefficient

introduced in the AASHTO rigid pavement design procedure in 1986.(33) It accounts for the

pavement's ability to drain excessive moisture from within the structure, as well as the

pavement's potential to be exposed to near-saturated conditions. It considers precipitation, base

and underlying soil type, permeability ofthe underlying material, and the presence of edge

drains. This makes it possible for factors that are not included directly in the faulting model to be

accounted for. For this study, the drainage coefficients for the GPS 3 pavement sections were

determined from the simplified matrix presented in table 6.(10) This matrix is based on the

33
original AASHTO drainage coefficients and several additional recommendations that account for

the base type and other material properties.

The type ofbase or subbase has a strong influence on faulting. A nonerodible base increases the

resistance ofthe pavement structure to erosion. In unbound granular materials such as densegraded aggregates, pore water pressure buildup is the main factor that causes horizontal and

vertical movement ofmaterials.(34,35,36,37) In stabilized materials such as lean concrete, cementtreated base (CTB), or soil-cement subbases, surface erosion ofthe material is ofmain concern.

For all base types, degradation, aggregate abrasion and fracture resistance, and stability under

repeated loads are some ofthe other factors that influence pumping and faulting. Therefore, a

variable was also included in the scaling factor to account for the type of base. Because ofthe

strong interaction between the drainage coefficient and base type, it was considered important to

model the interaction between those two variables in the scaling factor.

It is recognized that the factors selected for inclusion in equation 34 are not exhaustive. For

eXample, it was found that vehicle speed affects the pore water pressure under a slab.(23, 38)

Similar analysis and results showed that the use ofskewed joints and an increase in joint opening

decrease the water expulsion velocity under the slab and, therefore, reduce pumping and

faulting.(39) Paradoxically, a larger joint opening will increase joint deterioration and increase the

potential for faulting. Such additional factors can be considered in future improvements ofthe

faulting model.

Faulting Model Formulation

From the results ofthe analysis conducted, the final model form for predicting joint faulting that

was selected for calibration consisted ofthe following key parts:

• A model for calculating the allowable number ofload applications to reach a critical level

offaulting as a function ofDE.

• A model for predicting faulting.

34
Table 6. Matrix for selection ofthe overall drainage coefficient, Cd.(IO)

Edge Precipitation Fine-Grained Soils Coarse-Grained Soils

Drains Level

Nonpermeable Permeable Nonpermeable Permeable

Base Base Base Base

Wet 0.70-0.90 0.85-0.95 0.75-0.95 0.90-1.00

No

Dry 0.90-1.10 0.95-1.10 0.90-1.15 1.00-1.15

Wet 0.75-0.95 1.00-1.10 0.90-1.10 1.05-1.15

Yes

Dry 0.95-1.15 1.10-1.20 1.10-1.20 1.15-1.20

Notes: 1. Fine-grained = A-I through A-3 classes

2. Coarse-grained = A-I through A-3 classes

3. Permeable base = k = 300 m/day or Cu 0::::: 6

4. Wet climate = Precipitation> 635 mm/yr

5. Dry climate = Precipitation 0::::: 635 mm/yr

6. Select midpoint ofrange and use other drainage features to adjust upward or

downward.

Allowable Number ofLoad Repetitions

The allowable number ofload repetitions to failure, Nj) is a function ofthe differential elastic

deformation energy, DE. DE is calculated from equation 19 and requires the determination ofthe

comer deflections and the load transfer efficiency using equations 28 through 33. This, in tum,

requires calculation ofthe nondimensionalload transfer factor, given as follows:

AGG/kQ = AGGoexp[l + aDa - b(L/Q)]

where

(35)

AGG = D

L =

Q

AGGo' a, (x, b

load transfer factor, kPa

dowel diameter, mm

joint spacing, m

radius ofrelative thickness, rom

regression coefficients

To determine the model form to use for estimating Nr

, several model forms were obtained from

the literature and were tested for their suitability for fitting the available data.(40) The model form

with the best fit for estimating the number of allowable axle passes a slab can endure before

reaching critical faulting that was selected is as follows:(3)

Log N = (Xl - (X2 *Log(DE + 1)

35

(36)
where

N

DE =

allowable number of 80-kN axle loads

differential elastic deformation energy calculated from equation 19

regression coefficients

According to the functional form, as DE increases, the allowable number ofrepetitions

decreases. Furthermore, ifDE is zero, the allowable number ofrepetitions practically approaches

an infinite number of 80-kN load applications and faulting damage will not occur. Although this

model is not unique, on the basis ofthe mechanistic understanding offaulting, it provides a

logical equation for calculating N.

Faulting Prediction Model

From the results ofthe analysis presented, the final model form selected for predicting joint

faulting is as follows:

where

FAULT

FDAM

n

Nf

WETDAYS

DOWDIA

Cd

BASE

P, Po, PI' P2' P3' P4

=

=

=

=

mean joint faulting, mm

accumulated faulting damage = L nIN

actual number of80-kN ESAL's

allowable number of 80-kN ESAL's calculated from equation 35

number ofdays with precipitation greater than 0.254 mm

dowel diameter, mm

drainage coefficient

base or subbase type, O=erodible, 1=nonerodible

regression constants

Faulting Model Calibration

Calibration of equations 35 through 37 using the LTPP data for GPS 3 was the final step in

development ofthe prediction model for JPCP faulting. A combination of optimization

techniques and nonlinear regression analysis was used to determine the values ofthe parameters

in those equations that provide the best fit for the LTPP data. The criterion used was

minimization ofthe error between the actual field faulting and the predicted faulting. The

procedure that was used is as follows:

1. For nonlinear regression analysis, initial values were assigned to the load transfer factor

parameters (AGGo' a, b, and a in equation 35) to calculate the nondimensionalload

transfer factor, AGGlkQ.

2. With the calculated AGGlke, the LTE, WL , WUL> and DE were calculated for each section.

36
3. For nonlinear regression analysis, initial values were assigned to "I and "2 in equation 36

and the number ofload applications to failure, Nt) was calculated for every section.

4. From the actual traffic load level and the corresponding number ofload applications to

failure, Nt) the accumulated damage, n/Nt) corresponding to the faulting level measured

on each section was calculated.

5. For the assigned values ofthe aggregate interlock (equation 35) and damage model

(equation 36) parameters AGGo, a, b, ", "I and "2' nonlinear regression analysis was

performed to find the values ofthe faulting model (equation 37) parameters P, Po, PI' P2'

P3' and P4 that minimize the following objective function:

Minimize = 1: (Measuredpault - PredictedpauIJ2 (38)

6. For different assigned values ofthe aggregate interlock parameters (AGGo' a, b, and")

and damage model parameters ("I and (2)' steps 1 through 5 were repeated until the

corresponding faulting model regression parameters P, Po, PI' P2' P3' and P4 were found

thatdid not,change the minimum value of equation 38. Step 6 is essential to ensure that

the final regression constants obtained are not those for a local minima.

Final Faulting Prediction Model

The final faulting model obtained consists ofthe following models:

Load Transfer Factor Model

where

AGG/ke =

D =

L =

e

AGG (I + O.0992D O

•

I

-99.93!.)

= 0.25 e I

kQ

nondimensionalload transfer factor

dowel diameter, mm (D=O ifnondoweled pavement)

slab length, m

radius ofrelative stiffness, mm

(39)

Allowable Number ofLoad Repetitions

Loge Nr = 5.5 Loglo (0.005706 DE + 1)

where

(40)

k

=

allowable number ofload repetitions

differential elastic deformation energy

O.5*k*(WL+WUL)(WL-WUL)

modulus ofsubgrade reaction, kPa/mm

37
WL deflection ofloaded slab, mm

WUL deflection of unloaded slab, mm

Faulting Prediction Model

Fault =

where

FDAM°.3 [1.25 + 0.00102WETDAYS - 2.5*1O-3DOWDIA

- 0.625ClO.5 + BASE)] (41)

FDAM

n

Nf

WETDAYS

DOWDIA

Cd

BASE

Statistics:

N

R2

SEE

p-value

=

=

=

=

=

<

nlNf

number of 80-kN ESAL applications, in thousands

allowable number of 80-kN ESAL applications, in thousands

number ofwet days in the year

dowel diameter, mm

drainage coefficient

base or subbase type, O=erodible 1=nonerodible

120

0.56

0.762mm

0.0001 (level ofsignificance ofmodel)

A plot ofthe predicted and measured faulting is shown in figure 4. A plot ofthe residuals

(predicted - actual faulting) against the predicted faulting is shown in figure 5. The overall

accuracy ofthe faulting model is reflected by the R2 of 0.56, which is the proportion ofvariation

offaulting explained by the variables included in the model. A test ofhypothesis was performed

to determine the significance ofthe variables used in the model for predicting faulting. The null

and alternate hypotheses were as follows:

Ho: all model parameters are zero (variables are not significant)

HA : all model parameters are not zero

The F-test statistic used for the hypothesis test was calculated as the ratio ofthe mean square for

the model divided by the mean square ofthe error. For this study the null hypothesis will be

rejected ifthe level ofsignificance is less than 5 percent (0.05). A level ofsignificance (p-value)

ofless than 0.0001 implies a rejection ofthe null hypothesis. This shows that the variables in the

model are highly significant. Also, individual t-tests were conducted to test ifthe individual

parameter estimates are equal to zero.

The p-values for this test ranged from 0.0001 to 0.01. The results show that all the parameter

estimates had values other than zero; therefore, the variables in the model were significant.

Prediction accuracy offaulting in absolute units is reflected by the standard error of estimate

(SEE = 0.762 mm). The overall effectiveness ofthe model should be judged on all ofthe

diagnostic statistics, the residual plots, and the results from the sensitivity analysis to follow. The

38
diagnostic statistics obtained for the faulting model show that the model can predict transverse

faulting with reasonable accuracy for the LTPP database utilized.

Sensitivity Analysis

The final step in the model-building process is the verification ofthe selected regression model.

For the faulting model developed, model verification was limited to a comprehensive sensitivity

analysis that involved the comparison ofresults with theoretical expectations, earlier empirical

results, and simulated results reported in previously published literature. The sensitivity analysis

involved using the model to determine the effect of each variable on faulting when the other

variables were held at their mean values.

Plots were prepared to show these results. The plots were examined and the results compared

with theoretical expectations and empirical results from earlier research studies. There were

relatively limited data for model development, so a comprehensive validation ofthe model was

not possible. However, with more data being collected as part ofthe LTPP GPS and SPS, data

should be available soon for additional model validation. The plots and discussions on the results

from the sensitivity analysis are discussed in the following sections.

6-,---------------------------,

5 6

,

• • •

,

4

\

•

• •

3

,

•

..

••

.....

•

• •••

\ ••••

2

,

••

•

•

o 1

S 5

S

~4

r:: .....

.....

........

3 '+-l •

""d • • • 2 • • . 2 .' I "., ,.

..

1 1-+4···-'.., ..•• •

,- ... , .

r..... • • 0·· ·

,

Measured faulting, mm

Figure 4. Plot of predicted versus measured faulting.

39
5 •

••

3

S

S

.... 1

-m

"'0

'!""'4 -1 • +. CJ)

OJ •

-3

-5

Predicted faulting, mm

Figure 5. Plot ofresiduals versus predicted faulting.

Effect ofTraffic Loading

Figures 6 through 12 illustrate the effect oftraffic loading on the predicted joint faulting for

different conditions. Clearly, in all cases, the predicted faulting increases rapidly in the beginning

with increasing traffic loading and then levels off. This agrees with previous observations of

faulting ofjointed concrete pavements in the field. It shows that the model form selected and

approach used to develop the model are both plausible from an engineering sense.

Effect ofPavement Design Features

For further verification ofthe models, the effect ofkey pavement design features on the faulting

predicted by the model was checked against empirical and theoretical observations. Figure 6

shows a plot ofthe predicted faulting for different dowel diameters. It clearly shows that dowels

ofa minimum size of25.4 mm greatly decrease faulting ofjointed concrete pavements.

Increasing the dowel diameter further reduces faulting. However, the small difference in faulting

predicted for pavements using 25.4- and 38.1-mm-diameter dowels does not agree with the

results ofprevious research studies.

The influence ofthe type ofbase (or subbase) used underneath the PCC slab is shown in figure 7.

The results confirm that there is a tremendous reduction in faulting from the use of a nonerodible

base such as lean concrete. The rate of progression and magnitude offaulting is far less for

pavements with a nonerodible base in comparison to those with erodible bases. The effects of

PCC slab thickness and subgrade support on the predicted faulting are shown in figures 8 and 9,

respectively. According to the model, an increase in stiffness provided by either an increase in

slab thickness or an increase in subgrade support results in less faulting. Increased slab thickness

reduces joint deflection regardless ofload transfer. The increase in subgrade stiffness, by

40
contributing to a reduction in deflections at the joints, is believed to be responsible for the

reduction in faulting. Figure 10 shows the effect ofjoint spacing on faulting and shows that

shorterjoint spacing results in less faulting. Longerjoint spacing results in more expansion and

contraction, and wider joint widths, which lead to an increase in differential deflections.

Effect ofthe Environment

Two important variables in the model that deal with the effect of environmental factors on the

predicted faulting are Cd and number ofwet days. Figures 11 and 12 show the effect of drainage

coefficient and annual number ofwet days on faulting. The plots clearly show that a higher Cd

will reduce faulting. Fewer rainfall events, which will generally cause an increase in Cd' will also

result in less faulting.

41
4 Iii I

30 25 10 15 20

ESAL's (millions)

5

o • I I I I I

o

-+-No dowel

___ Dowel diameter=25.4 rom

.........- Dowel diameter=38.1 rom

3

1

s

S

~2 .....

...

'3

..j::o.

N

Figure 6. Influence of dowel and dowel size on predicted faulting.
4

Erodible base

- Nonerodible base

30 25 20 15 10 5

o • I I I I

o

3

gf2

'.0

.....

::s

4>-

t\l

1

ESAL's (millions)

Figure 7. Influence of base or subbase type on predicted faulting.
4>-

4>-

4

pce thickness =300 mm

- pce thickness = 200 mm

3

§

gf>2

'.0

.....

ca

1

o • I I I I

o 5 10 15 20 25 30

ESAL's (millions)

Figure 8. Influence of PCC slab thickness on predicted faulting.
-l:>-

U1

4

~k = 27kPajmm

_ k =81.5 kPajmm

3

E

E

~2 '.0

.......

;:::l

ro

1

o • I I I

o 5 10 15

ESAVs (millions)

20 25 30

Figure 9. Influence of modulus of subgrade reaction on predicted faulting.
0'

-4

-+-JTSP = 4.6 m

- JTSP = 9.15 m

3

s

S

~2 '.0

"3

CI:l

1

o • I I I I I

o 5 10 15

ESAL's (millions)

20 25 30

Figure 10. Influence of joint spacing on predicted faulting.
4 "----~~-------------------,

-+-Drainage coefficient =1.2

- Drainage coefficient =0.8

3

00

..§ 2 .....

::s

...j:o..

ca

'I

1

o • I I I I

o 5 10 15

ESAL's (millions)

20 25 30

Figure 11. Influence of drainage coefficient on predicted faulting.
4 .,,-------------------~---------,

..j:>..

00

--.-WTDYS=80

--WTDYS=130

-.-WTDYS=180

3

s

S

@2 .....

.......

::s

m

1

30 25 20 15 10 5

o • I " " " " I

o

ESAL's (millions)

Figure 12. Influence of number of wet days (precipitation > 12.7 mm)

on predicted faulting.
Summary

The following can be summarized about the faulting model:

• Fifty-six percent ofthe total variation offaulting can be explained by the included

variables.

• Some ofthe unexplained variation may be due to errors in the independent variables used

to develop the model, such as the traffic estimates.

• The "average" residual in predicting faulting is 0.762 mm.

• There are no discernible patterns in the residuals. This means that there was little or no

serial correlation in the data used for model development.

• Data from a large number of pavement sections from all over the United States were used

•to develop the model (N = 120).

• Each independent variable was significant at the p < 0.05 level, and the overall model

was highly significant with a p-value ofless than 0.0001.

• The sensitivity analysis shows that all ofthe explanatory variables have a plausible effect

on faulting that agrees with theoretical expectations and previous empirical field results.

Implications and Recommendations

The model developed for predicting faulting uses the differential elastic deformation energy

concept. The differential elastic deformation imposed by traffic loading is postulated to be

directly related to the pore water pressure that is generated underneath a PCC slab and that leads

to faulting. The model obtained clearly indicates that the incorporation of pavement design

features that reduce the differential deflections at the joints ofPCC pavements will decrease

faulting. For example, the use of dowels that are at least 25.4 mm in diameter will decrease

faulting appreciably.

According to the model, a stiffer pavement obtained by increasing the PCC slab thickness, higher

subgrade support, use of a nonerodible base such as lean concrete, and shorter joint spacing will

all combine to decrease the average faulting. From the results ofsensitivity analyses conducted,

each ofthese features by itself has an influence on faulting. Therefore, they will together have a

tremendous influence on the progression offaulting.

The model obtained also shows that measures taken to reduce moisture in the pavement will

reduce faulting. Higher drainage coefficients, which imply le1;ls saturation ofthe underlying

material and shorter periods of exposure to moisture, cause a reduction in faulting. Similarly, less

faulting was predicted for pavements in locations with a lower frequency of days during which

the precipitation is in excess of 12.7 mm.

49
An important finding is the interacting effect of Cd with a nonerodible base. According to the

model, a nonerodible base will increase the effect ofthe drainage coefficient on faulting about

threefold. Therefore, a nonerodible base used in conjunction with other measures taken to

increase the drainage coefficient will reduce faulting significantly.

50
5. TRANSVERSE JOINT SPALLING

Introduction

The SHRP Distress Identification Manual/or the Long-Term Pavement Performance Studies

describes spalling as the breakdown or disintegration of a PCC slab's edges at joints or cracks or

directly over the reinforcement steel, usually resulting in the removal ofsound concrete.(41) Spalls

are generally categorized by their length and depth. The same manual classifies spalling into

three levels ofseverity: low, medium, and high. Spalling is measured both numerically (number

ofspalled cracks/joints and length of cracks/joints spalled) and qualitatively (low-, medium-, or

high-severity).

Several field studies have observed that joint spalling may be due to infiltration of

incompressib1es into pavement joints, the deterioration ofthe concrete material from

environmental factors, or the exposure ofthe slab's joint to a sudden and massive tensile stress.

Spalling caused by a sudden force is usually oflow severity and does not progress or deteriorate

with time. However, spalling caused by incompressib1es, repeated high tensile stress at the slab

edges (fatigue), or concrete deterioration is more significant. It increases in severity with time

and eventually causes pavement joint deterioration. It also results in the deterioration ofload

transfer devices such as dowels through corrosion and the loss of cover. Spalling eventually

causes an increase in the roughness ofthe pavement, resulting in a decrease in serviceability of

the pavement and costly rehabilitation.

Therefore, spalling is an important distress to PCC pavements. Monitoring and predicting the

occurrence ofspalling is important for pavement design and management. The development of

sound prediction models for use in pavement design and management will provide engineers

with an efficient tool for budgeting and planning, resulting in savings for State highway agencies

throughout the United States. This chapter describes the development ofmechanistic-empirical

models for predicting joint spalling. The concepts used have been applied successfully to develop

mechanistic-empirical models for spalling.(12)

Spalling Mechanism

Research into spalling of concrete pavements has been ongoing since the early 1960s. The

mechanism ofspalling is yet to be fully understood. However, spalling is believed to be caused

by several interacting mechanisms, including stresses imposed on the pavement ,by both traffic

and environmental forces and inadequate quality control during construction.

Some primary causes ofspalling identified from past research are as follows:(42)

• Entrapment ofincompressib1es in cracks, which causes a buildup ofstress at the pec

slab joint when the pavement is subjected to temperature stresses and a combination of

shear and tensile stress under the whee110ad.

• Poor concrete at the slab surface due to poor construction practices.

51
The findings summarize the interacting forces that result in spalling and have been confirmed by

other researchers.(42) Finite element analyses also showed that spalling results from

incompressible material lodged in the pavement's joints or cracks.(43) They indicated that stiffer

materials in a pavement's joint or crack restrain the pavement slab from volumetric changes

when subjected to temperature gradients. This results in high stress concentrations at the slab

joints and, hence, spalling. Some researchers have suggested that the use ofjoint filler would

retard the development of crack orjoint spalling by inhibiting edge raveling, admission of

incompressible material, and corrosion ofreinforcement.(44)

A study oftwo projects in Minnesota noted that spalls generally occurred in the wheel path.(45) It

was also realized that a majority of deep spalls were caused by the corrosion ofthe reinforcement

in the PCC slab by the chloride in the concrete. Studies at the University ofIllinois also reported

that the loss ofbending stiffness at the transverse crack is related to spalling in CRCP. The

analysis indicated that considerable stresses, both shear and normal, are created at the face ofthe

transverse crack and result in a high potential for spalls to develop. The study also reported that

loss ofpavement support significantly increases stresses at the pavement joints and, hence,

spalling.(46)

Researchers at the Texas Transportation Institute and Texas A&M University reported that poor

construction practices can result in spalling later in the pavement's life. They reported that

several planes ofweakness develop during the early age ofthe pavement from differential

shrinkage in the concrete and an inadequate aggregate cement paste bond. The addition oftraffic

and temperature stresses, shrinkage, and incompressible materials in the joints later in the

pavement's life increases tensile stresses around the joint. These stresses acting on the already

weakened planes from construction and environmental effects at the time of construction result

in spalling.(47)

It can therefore be concluded that factors that cause an increase in tensile stresses at the edge of

joints and cracks significantly influence the occurrence ofspalling. Only recently has

mechanistic modeling ofspalling been investigated. CRCP spalling models based on traffic and

environmental loading conditions have been developed by several researchers.(46,47) The

mechanistic analysis considered the following:

• The development ofmicrocracks at or near the joint in the early age ofthe concrete.

• Microcracks develop primarily at the aggregate-cement paste interface.

• Microcracks grow into delaminations as a result of early age shrinkage, temperature

curling, or excessive tensile stresses at or near the joint due to the infiltration of

incompressibles in the pavement joint.

• The composition ofthe concrete mix is very important in determining the amount of

microcracking and eventual delamination in the concrete.

• Delamination near the joint eventually spalls off as a result of continuing cyclic

temperature, shrinkage, and traffic stresses.

52
On the basis ofthe preceding infonnation, the mechanism ofspalling can be summarized as

follows:

• It is caused by a stress concentration at the edge of a slab joint or crack.

• The stress concentration can be attributed to any combination ofthe following:

Traffic stress imposed on the pavement.

Environmental stress imposed on the pavement by temperature variations and

shrinkage.

The stiffness ofthe material in the pavement joint, which ranges from moderately

soft materials such as regular joint sealing material (e.g., asphalt concrete, low

modulus silicone, and prefonned sealants) to very stiffincompressibles such as

aggregates that fill up the joint with no joint sealant.

Current empirical models do not address all these variables; therefore, they cannot predict the

percentage ofjoints spalled with precision and accuracy. The introduction of a mechanisticempirical spalling model will allow better representation ofthe phenomenon ofspalling in

concrete pavements. Such a model should include mechanistic clusters that take into

consideration these causes ofspalling.

Evaluation ofExisting Spalling Models

A lot of empirical knowledge has been accumulated from past development of empirical models.

These models were reviewed as a means of bringing expert knowledge into the model

development process at an early stage. The review was used to select potential variables to

consider in calibrating a final mechanistic spalling model. A lot of attention was paid to the

engineering significance ofthe variables. The models reviewed were from the SHRP P-020 and

RIPPER studies.(4, 10)

SHRP P-020

The following is a model developed using the LTPP data available in 1992 for predicting joint

spalling in JPCp:(4)

where

SPALLJP 9.79 + 10.09[ -1.227 + O.0022*(O.985AGE + O.1709FT)2] (42)

SPALLJP

AGE

FT

predicted percentage ofjoints spalled (all severities) expressed as a

percentage ofthe total number ofjoints

pavement age, yr

mean annual number of air freeze-thaw cycles

53
The model relates spalling to the pavement age and the mean annual number of air freeze-thaw

cycles. This model suggests that joint spalling increases with age, and that stress cycles generated

within the pavement while undergoing freezing and thawing contribute to spalling. Freezing and

thawing of concrete also result in the expansion ofwater in the pores ofthe concrete, creating

additional stresses that weaken the concrete.

The following similar model was developed for predicting spalling for JRCP:

SPALLJR = -79.0 + 0.604*AGE1.5 + 0.129*TRANGE1.5

where

(43)

SPALLJR

AGE

TRANGE

predicted percentage oftransverse joint spalling (all severities)

pavement age, yr

mean monthly temperature range, OF

For this model, the rate ofincrease in spalling is also dependent on the age ofthe pavement. The

magnitude ofspalling depends on the temperature range (i.e., the difference between the mean

maximum and minimum annual temperatures) at the location ofthe pavement. This model, like

the previous one, is based on environmental factors. Also, the age variable in both models

represents several factors. These include factors such as slab curling, warping, and temperature

cycles due to daily and seasonal temperature variations that result in joint movements. The joint

movements increase joint openings and allow for the infiltration ofincompressibles into the

joints. Traffic loading is also represented, since older pavements are expected to have carried

more traffic.

The models indicate that spalling generally increases slowly during the first few years ofthe

pavement's life and then increases more rapidly after several years. This is logical because it

takes some time for incompressibles in the pavement's joints or cracks to accumulate and

increase the stress concentrations at the pavement joint. It also takes time for damage to the

pavement to accumulate. However, both models include only two ofthe variables that are known

to cause spalling. Therefore, it can be expected that the addition of other variables and clusters

that account directly for the effect oftraffic and construction practices will improve the model's

accuracy.

RIPPER Study

The RIPPER study undertook a detailed examination ofseveral past models.(IO) It resulted in a

comprehensive list of explanatory variables that can be used in exploratory analysis for model

development. The explanatory variables are as follows:

AGE:

CESAL:

JTSP:

THICK:

Cd:

JTOPEN:

time since pavement was constructed

cumulative 18-kip (80-kN) ESAL's in the traffic lane

mean transverse joint spacing

PCC slab thickness

AASHTO drainage coefficient

joint opening

54
JTWIDTH:

Epcc:

Kvalue:

MI:

JTSEAL:

mean joint width

elastic modulus ofthe PCC slab

mean backcalculated modulus ofsubgrade reaction

Thomthwaite moisture index

joint sealant type

These explanatory variables were used to develop two models for JPCP and JRCP pavements

using the RIPPER database:

SPALLJP = AGE2

*10-6*JTSP*(551.6 - 847.3*[LIQSEAL +PREFSEAL]

+ 0.936*Days903 * 10-3 + 364*DOWELCOR + [2.783 - 1.400* (44)

LIQSEAL - 2.368*PREFSEAL - 0.676*SILSEAL]*FI)

SPALLJR = AGE3

*JTSP*(1.94*DOWELCOR + 8.819BASE*(1-

PREFSEAL) + 0.00701 FI)*10-s

where

(45)

SPALLJP

SPALLJR

AGE

JTSP =

LIQSEAL

PREFSEAL =

Days90

DOWELCOR=

SILSEAL =

FI =

BASE

percentage medium- and high-severity spalled joints in JPCP

percentage medium- and high-severity spalled joints in JRCP

pavement age, yr

mean joint spacing, ft

0, if no liquid sealant exists

1, ifliquid sealant exists

0, if no preformed sealant exists

1, if preformed sealant exists

mean number of days in the year with temperature above 32 DC

0, if no dowels exist, or dowels are protected from corrosion

1, if dowels are not protected from corrosion

0, if no silicone sealant exists

1, ifsilicone sealant exists

mean annual freezing index, DF days

0, if nonstabilized base

1, ifstabilized base

The models are more comprehensive because they take into account more variables related to

spalling. Also, the variables can be divided into two distinct groups- environmental and designrelated variables.

The environment-related variables include age (cycles of climate changes such as opening and

closing ofjoints), annual number of days with temperature above 32 DC, and freezing index. The

annual number of days with temperature above 32 DC is indicative ofthe magnitude of expansion

or contraction to which the PCC slab is subjected. Since pavements located in areas with a high

annual number of days with temperature above 32 DC generally undergo a lot of expansion, this

can result in the generation of high stresses in the PCC slab and joint that result in more spalling.

Older pavements and those subjected to a higher freezing index are subjected to prolonged cycles

55
offrozen water within the pores ofthe PCC slab and deterioration ofthe concrete material. This

generally results in the disintegration ofthe concrete slab material at the slab surfaces and joints

and, hence, spalling.

The design-related variables include joint spacing, liquid sealant, preformed sealant, silicone

sealant, coated or uncoated dowels, and base type. The joint spacing is highly correlated to the

degree ofjoint movement. Longer slabs expand more when subjected to cyclic temperature

variations and create higher stresses at the joint when restrained by the presence of

incompressibles. The base type is an indication ofthe support condition ofthe pavement.

Pavements on firm supports are likely to experience smaller deflections and, hence, less stresses.

Spalling can also be caused by the corrosion ofthe dowel bar by the chlorides and other

chemicals in PCe. Protecting the dowels from corrosion therefore reduces spalling. The final

design variable considered in the models is the joint sealant type. The role ofjoint sealants in

minimizing spalling is to prevent the intrusion ofincompressibles into the joint. Incompressibles

restrain the slab joints from moving and, in the process, increase stresses around the pavement

joint, increasing spalling. The RIPPER study suggests that the use ofpreformed sealants in both

JPCP and JRCP resulted in the lowest level ofspalling for all sealed and unsealed joints.

Preformed sealants are particularly effective in minimizing the intrusion ofincompressibles into

pavement joints.

Spalling Model Development Approach

Most ofthe models developed in the past, like the SHRP P-020 and RIPPER models, have been

empirical models that did not attempt to account directly for the mechanism ofspalling

described. This is because previous attempts to use mechanistic principles to describe spalling

have not been very successful. However, these empirical models have been used successfully to

identify the environmental and design factors that have an effect on spalling (see table 2). Recent

research work has resulted in considerable progress in the application ofmechanistic principles

for modeling spalling, and this made it possible to develop mechanistic-based models for

predicting spalling for both JPCP and JRCp.(47)

Application ofMecbanistic Principles to Spalling

To determine the mechanistic-based response to use in modeling spalling, the mechanism of

spalling previously described was evaluated in detail. The key concepts investigated concerned

the mechanism that causes tensile stresses across the face ofjoints and cracks in PCC pavements.

Spalling initially begins as microcracks and delaminations that exist at the joint interface early in

the life of a pavement because ofstresses from temperature variations and shrinkage from bad

construction practices.(47) These delaminations are continuous flaws parallel to the pavement

surface and usually occur at a depth of not more than 25.4 mm.

Traffic load and additional temperature and shrinkage tensile stresses will tend to enlarge and

propagate the microcracks and delaminations within the concrete slab. Even though the

occurrence oftensile stresses in this part ofthe PCC slab will eventually transform the

delaminations into spalls, not all ofthe delaminated portion ofthe slab edge will necessarily spall

off. However, tensile stresses of higher magnitude can create new cracks within the pavement

and at the joint interface. With the initiation of new cracks or the transformation of existing

56
construction defects into cracks, the tensile stresses propagate these cracks from the joint

interface to the slab surface and result in spalling.

This mode ofspall initiation and propagation is known as the tensile mode ofspalling ofPCC

pavements.(47) The tensile stress within the slab at the joint interface and along the path of crack

growth is the mechanistic parameter that was used to model spalling. It is called the tensile or

spall stress, at' and can be used to estimate the allowable number ofstress cycles the pavement

slab will withstand before spalling occurs.

Determining the Tensile Spall Stress

Figure 13 is a free body diagram that illustrates the stresses that occur at the joint interface of a

j~inted concrete pavement because ofboth traffic and environmental loads.(47) An analysis ofthe

free body diagram showed that the tensile spall stresses are dependent on the normal and shear

stresses caused by traffic and environmental loading and the properties ofthe joint sealant.

Resolving all forces for equilibrium in the horizontal direction and solving provides the

following equation for estimating the spall stress:(47)

where

1" =

1"f

I =

t

q

I! =

e =

ajs

at = (1" - 1")! + - a.

f t tanS JS

vehicle tire shear stress, kPa

friction stress = ql!, kPa

tire pressure load length, mm

depth ofspall delamination, mm

normal tire pressure, kPa

concrete friction coefficient

orientation angle ofprincipal stresses, degrees

joint sealant or incompressibles stress, kPa

57

(46)
Tire Normal Pressure

Joint

Filler~~

•

~~~~~~

Deleminatlon

• •

(Spall) Plane

• •t •

1

---- 1-_--L T_I_e_S_he_a_rS_t_re....Jss

Prestressed ---------~ t

Com pression

Seal Stre ss (K f'U) Friction Stress

Con c re te P a v em en t

Figure 13. Schematic diagram ofspalling mechanism for tensile mode offailure in jointed

concrete pavement.(47)

The last part of equation 46, 0js, represents the stress exerted by the joint sealant or

incompressibles, ifpresent. It can be determined using the following equation:

(47)

where

kjs =

u =

t =

C =

L =

ex =

aT =

e =

spring coefficient ofjoint sealant or incompressibles in the joint, kPa

displacement ofspalled concrete, mm

depth ofspall delamination, mm

subbase friction factor

joint spacing, mm

concrete thermal expansion

thermal gradient in the slab

concrete drying shrinkage strain

Equation 47 represents the spall stress caused by environmental loading. An assumption of a unit

value for the depth ofspall delamination, t, is reasonable for most cases. Additionally, 0js can be

used to represent the stress caused by incompressibles that have infiltrated into the joint if an

equivalent kjs is used. If a sealant is used, the stress 0js can be positive ifthe joint sealant

maintains a compressive stress (e.g., preformed compression seals) across the whole face ofthe

joint. This will decrease the spall stress given by equation 46. For other sealants and

incompressibles, 0js may be negative or zero and will increase or not change the spall stress.

The remaining portions of equation 46 represent the stresses due to traffic loads. This part ofthe

equation may be difficult to implement for everyday use because some ofthe inputs are not

58
readily available. Therefore, a series offinite element runs were conducted to develop a

regression model for estimating the traffic spall stress, atr' defined as follows:

(48)

Traffic Load Tensile Stress Model

Since calculation ofthe tensile stress using equation 48 requires inputs that may not be readily

available, a simple equation for determining the traffic spall stress was developed. This was

accomplished by modeling the tensile stresses that occur at a PCC slab joint using the threedimensional finite element program ABAQUS.(48) A two-dimensional model (assuming plane

strain conditions) was used in ABAQUS to analyze a PCC slab over a subgrade subjected to

traffic loads, to determine and examine the tensile stress distribution within the PCC slab and to

identify the occurrence of peak stresses at the joint surface. The finite element configuration

consisted of450 nodes and 200 elements. The finite element model and boundary conditions

used in the analysis are shown in figure 14.

Joint sealants and incompressibles were modeled as an elastic material with different moduli

corresponding to the different joint sealant types and incompressibles in the joint. Preliminary

analysis showed that the end conditions (fixed or simply supported) ofthe PCC slab joint had

little or no influence on the analysis. The foundation was modeled as a Winkler foundation, with

the elastic-spring constant ofthe foundation corresponding to the modulus ofsubgrade reaction,

k, ofthe subgrade. The PCC slab was assumed to be a homogeneous elastic material, and the

aggregate interlock and load transfer across the joint were modeled using vertical springs of

varying spring constants to refle.ct different levels ofload transfer.

59
Wheel Load

!!!!!!!!! .....-.....- .....- .....- Friction

mm

/

.........

:$.

>

'/

.........

>

/'

........

.;>

/

........

:$.

>

Joint---. Sealant

Springs

Stimulating

Load---.

Transfer

III III III lilli' II11I1111 III III III III

111111111 111 111 III III III III 111 111 III

Subgrade Modeled as Winkler Foundation

Figure 14. Finite element model for estimating spall stress.(14)

A factorial of different material properties and design features was used to obtain the maximum

tensile stress that occurs at the face ofthe joint or crack for different pavement conditions. The

variables and the range ofvalues used in the factorial are shown in table 7. An 80-kN axle load

was used in this instance, but it IS important to note that a regression equation can be obtained

that can be used for different load levels by varying the load level. The results from the

ABAQUS factorial runs were used to develop the following regression model for predicting the

maximum traffic load tensile stress:(3)

atr

where

air =

hs

ks =

Ep

305.5 + 48.563hs- 23.62~ + 0.000757 ks- 0.17728~hs

+ 0.0888~~ - 1.89*10-6~ks - 1.889*1O-7hsEp

+ 1.98*10-6hsks- 1.32*1O-6~s

maximum tensile stress at crack orjoint surface from traffic loading, kPa

depth ofsealant, mm

modulus ofsubgrade reaction, kPa/mm

modulus ofsealant material, kPa

PCC slab thickness, mm

modulus ofPCC slab, kPa

(49)

60
Statistics:

N =

R2

SEE =

340

0.74

250 kPa

Sensitivity Analysis ofTraffic Load Tensile Stress Model

Sensitivity analyses were conducted to verify whether equation 49 was in agreement with results

from mechanistic and finite element analysis. Other checks, such as analyzing the diagnostic

statistics results and plots ofthe predicted tensile stress versus the independent variables, were

also made to test the suitability ofthe model. The primary input parameters ofinterest were the

PCC slab thickness, sealant depth, sealant or incompressible modulus, and PCC elastic modulus.

The ranges ofvalues used and the results obtained are presented in table 8.

The effects ofthe different design features on the estimated traffic tensile stress for an 80-kN

axle load are illustrated in figures 15 through 19. The sensitivity analysis indicates that, in all

cases, the model provides results in line with engineering expectations.

Table 7. Factorial oftraffic and pavement properties used to develop model for predicting traffic

spall stress.(3)

Pavement/Traffic Variable Range of Values Used in Finite

Element Analysis

PCC slab modulus, kPa 27.6*106 to 55.2*106

Modulus ofjoint sealant or incompressible, kPa 1.4*106 to 5.5*106

Modulus ofsubgrade reaction, kPa/mm 27 to 136

PCC slab thickness, mm 100 to 300

Single axle load, kN 80

Sealant depth, mm 12.7 to 115

61
Table 8. Summary ofinputs and results ofsensitivity analyses oftraffic tensile

stress modelY) .

Variable Inputs Spall Stress, kPa

Mean Min. Max. Min. Max.

Slab thickness, mm 300 100 300 2350 380

Sealant depth, mm 64 12.7 115 830 1070

PCC slab modulus, kPa 31 *106 14*106 62*106 1240 790

Modulus ofsubgrade 95 27 163 1240 450

reaction, kPa/mm

Sealant/incompressibles 3.45*106 1.38*106 5.52*106 276 1450

modulus, kPa

Calculating Total Tensile Spa]] Stress

The total tensile spall stress can be calculated using equations 47 and 49 to account for the tensile

stress due to environmental loading and traffic loads, respectively. These models are simple to

use and were used to estimate the total spall stress for each ofthe GPS 3 and 4 sections. This was

the mechanistic parameter used for developing a model for predicting spalling in this study.

1200 -,-----------------------,

1100 .-

0:

--[J)

[J)

lj 1000 [J)

Q)

':';:l

] 900

800 -1------1-----+----1------1-------1

a 20 40 60 80 100

Depth of sealant material (mm)

Figure 15. Sensitivity plot of tensile stress versus height of sealant.(3)

62
1600 ,..--.----------------------,

1400

l1200

';; 1000 Ct:J

b 800 Ct:J

600 Ct:J

Q) 400

25 50 75 100 125 150 175 200

200

O+---t------f---+---l----t---+----Ii------l

o

Effective k-value (kPa/mm)

Figure 16. Sensitivity plot of tensile stress versus modulus of

subgrade reaction.

1600 .,-----------------------,

600

400

1400

(;' 1200

1000 Ct:J

t 800 Ct:J

Q)

......

.....

2 3 4 5 6

200

O-+-----+-------+-----+-----t--------i

1

(millions)

Modulus of sealant material (kPa)

Figure 17. Sensitivity plot of tensile stress versus sealant modulus.(3)

63
240 280 320 360 400

0-+------1:------+-----+------1-----\

200

1600 -,-------------------------,

-..

ctl 1200 p..

--- C/)

C/)

(J)

l:l 800 C/)

(J)

-.....

C/)

r::

400 (J)

PCC slab thickness (mm)

Figure 18. Sensitivity plot of tensile stress versus PCC slab thickness.(3)

1300

1200 -..

1100

---C/)

C/) 1000 (J)

l:l

C/)

(J) 900

-..... C/)

r::

(J) 800

700

600

0 10 20 30 40 50 60 70

pce slab modulus (kPa)

Figure 19. Sensitivity plot of tensile stress versus PCC slab modulusY)

64
Mechanistic-Empirical Spalling Model Formulation

Using the equations developed for calculating the total spall stress, it is possible to develop

mechanistic-empirical models for predicting joint spalling ofJPCP and JRCP using Miner's

damage accumulation approach.(49) The three key parts ofthe model are as follows:

• A damage accumulation model that is used to accumulate the damage caused by

individual traffic and environmental load applications.

• A model for calculating the allowable number oftraffic and environmental spall stress

applications to failure.

• A model for predicting the percentage ofjoints spalled from the damageaccumulation.

Spalling Damage Accumulation

Ifthe spalling damage caused by traffic and environmental loading is assumed to be additive, the

following equation based on Miner's hypothesis can be used to calculate the total damage:(49)

where

=

number of cycles oftraffic loads

number of environmental stress cycles

allowable number of cycles for traffic loading

allowable number of cycles for environmental stresses

regression constants

(50)

The number of cycles oftraffic loads is essentially equal to the cumulative number of 80-kN

ESAL applications. Since the number of cycles of environmental stresses is also a function ofthe

pavement age, equation 50 can be rewritten as follows:

where

KESAL

AGE =

KESAL AGE Damage = (Xl --- + (X --

N 2 N

T E

cumulative number of80-kN ESAL's, ~housands

pavement age, yr

65

(51)
Allowable Number ofTraffic and Environmental Stress Repetitions

The estimated allowable number oftraffic load spall stress repetitions to failure, NT' and the

allowable number of environmental spall stress repetitions to failure, NE , are required to use

equation 51. To develop models for predicting NT and NE, several model forms were evaluated

for their suitability for predicting the number ofload cycles to failure. A typical model form that

relates the allowable number ofload repetitions, N, to the calculated tensile stress in concrete

pavements is as follows:(50)

where

= tensile stress that causes spalling, kPa

regression constants

(52)

This model form, which is used in fatigue analysis of concrete pavements, is in accordance with

basic engineering principles and was selected for use. According to the model, an increase in

tensile stress decreases the allowable number of cycles to failure, and a decrease in tensile stress

increases the allowable number of cycles to failure.

For spalling caused by the traffic load stress, at can be replaced with atr from equation 49 to

obtain the following appropriate model form:

(

1 1k

2

N = k -

T 1 a

tr

Replacing at in equation 52 with the joint sealant stress from equation 47, ajs' the following

model can be used to estimate the number of environmental spall stress cycles to failure,

assuming a unit thickness ofdepth ofspall delamination:

where

(53)

(54)

~s

ELONG

L

~T

=

=

=

modulus ofthe sealant material or incompressibles, kPa/mm

a factor estimating the horizontal movement ofthe slab, m

CL(a~T +e)

slab length or jointspacing, m

thermal gradient in the slab, °C

66
= concrete drying shrinkage strain

concrete thermal expansion, / DC

subbase friction factor

regression constants

Mechanistic-Empirical Spalling Prediction Model Form

Using the damage calculated from equation 51 and based on an examination ofthe progression

ofspalling with traffic loading and pavement age for the LTPP pavements, the following form

was selected for the development ofmodels for predicting transverse joint spalling for JPCP and

JRCP:

where

%Spall Damage m

---=--- (Scaling Factor)

(1 + Damage)n (55)

~Spall

Damage

Scaling Factor

m,n

the percentage ofjoints with low-, medium-, or high-severity spalls

the total damage due to traffic and environmental stresses

scaling factor used to calibrate the model to field conditions

regression parameters

This model form assumes that the percentage ofjoints with spalls is a function ofthe interaction

between the damage caused by traffic and environmental stresses and a scaling factor. The

scaling factor accounts for all the other factors that are not directly considered in the mechanistic

portion ofthe model.

Determination ofEmpirical Scaling Variables

An essential part of equation 55 is the scaling factor that is applied to calibrate the model to field

conditions. An exhaustive evaluation ofthe LTPP GPS 3 and 4 data was conducted to determine

the best scaling factor to use. This included using the knowledge obtained from the review of

past models and statistical analyses ofthe GPS 3 and 4 data. The objective was to use the results

to identify potential variables for inclusion in the model.

Jointed Plain Concrete Pavement

Table 9 presents a summary ofthe correlation analysis results for the potential variables selected

for development of a JPCP spalling model. It shows the strength ofthe relationships between

several significant variables and spalling. The definitions ofthe variables are presented in table

10. Figure 20 shows a plot ofthose independent variables against the percentage ofJPCP joints

with low-, medium-, or high-severity spalling in the LTPP database. These results were analyzed

to evaluate the independent variables that show an influence on spalling for possible use in

developing the model. The results confirm that an increase in traffic loading and age (which are

related) results in more spalling and that these are important variables to consider in a spalling

67
model for JPCP. Also, ofthe variables selected for evaluation, several environmental variables

were comparatively more correlated to spalling. The number ofwet days, the average relative

humidity during the month of construction, and annual precipitation are all negatively correlated

to spalling, with increasing values ofthose factors resulting in less spalling. Conversely, higher

values ofthe mean monthly temperature range and number of air freeze-thaw cycles result in

more spalling. The design features that were relatively highly correlated to spalling were the

mean joint spacing and the type ofjoint sealant.

68
0'

'"

Table 9. Correlation matrix for variables for JPCP transverse joint spalling model.*

RH TRANGE HPCC BTHICK K JTSP ST FI FTCYC PRECIP WTDYS AGE E

RH 1 -0.39738 -0.00177 -0.24465 -0.08145 0.40414 -0.11217 -0.19846 -0.38549 0.53343 0.45624 0.08518 

TRANGE -0.39738 1 0.08987 -0.02222 0.02256 -0.2113 0.11469 -0.04922 0.39865 -0.53464 -0.56232 0.02027 

HPCC -0.00177 0.08987 1 -0.09364 0.14486 0.13208 0.03054 0.00229 0.11117 -0.00142 -0.05859 -0.10402 

BTHICK -0.24465 -0.02222 -0.09364 1 0.00075 -0.22472 0.24054 -0.09388 -0.12418 0.09575 0.23869 -0.34868 

k-value -0.08145 0.02256 0.14486 0.00075 1 -0.09458 0.17845 -0.37952 -0.14078 0.01048 -0.00819 -0.11041 

JTSP 0.40414 -0.2113 0.13208 -0.22472 -0.09458 1 -0.25111 -0.23863 -0.14154 0.53154 0.32552 0.2899 

ST -0.11217 0.11469 0.03054 0.24054 0.17845 -0.25111 1 -0.41399 -0.18469 -0.02482 -0.16453 -0.06583 

FI -0.19846 -0.04922 0.00229 -0.09388 -0.37952 -0.23863 -0.41399 1 0.48967 -0.34727 -0.10239 -0.19996 

FTCYC -0.38549 0.39865 0.11117 -0.12418 -0.14078 -0.14154 -0.18469 0.48967 1 -0.41372 -0.29057 -0.04611 

PRECIP 0.53343 -0.53464 -0.00142 0.09575 0.01048 0.53154 -0.02482 -0.34727 -0.41372 1 0.82875 0.14309 

IwTDYS 0.45624 -0.56232 -0.05859 0.23869 -0.00819 0.32552 -0.16453 -0.10239 -0.29057 0.82875 1 0.08088 

AGE 0.08518 0.02027 -0.10402 -0.34868 -0.11041 0.2899 -0.06583 -0.19996 -0.04611 0.14309 0.08088 1 

ESAL -0.19678 0.11601 0.05562 -0.16771 -0.00504 0.1594 0.04793 -0.24355 -0.0275 0.02319 -0.04418 0.39556 

PSPALL -0.312 0.29578 -0.15785 0.045 -0.01219 -0.21851 0.20583 -0.04915 0.15023 -0.28214 -0.36436 0.1742 

* See table 10 for definitions.
Table 10. Definitions ofselected variables significant to spalling ofJPCP.

Symbol Potential Independent Variable

RH Mean relative humidity during month of construction, percent

TRANGE Mean monthly temperature range, °C

HPCC PCC slab thickness, mm

BTHICK Base thickness, mm

K Static backcalculated k-value, kPa/mm

JTSP Mean transverse joint spacing, mm

ST Sealant type

FI Freezing index, degree-days eC) below freezing

FTCYC Yearly number of air freeze-thaw cycles

PRECIP Average annual precipitation, mm

WTDYS Number ofwet days in a year, days

AGE Time since pavement construction, yr

ESAL Cumulative equivalent 80-kN single axle load

PSPALL Percentage ofioints with low-, medium-, or high-severity spalling

70
100 100 100 ." , ." • 90 ,§ • ,§ ."

Oi 80 •• Oi 80 i • :E 80 a. a. Oi •• Ul • Ul a. 70 •

=

60 ••

=

60 • Ul 60 ..

'j; • 'j; • ='j; 50

J!l 40 •

• J!l 40

c • 40 •

.' c

• • J!l

'0 '0 c 30 • .... 20 • .... 20 • '0 ••

• •• • .... 20

· • . ';!.

0 0 10 • •

0 50 100 0 10 20 30 0

0 100 200 300 400

Relative humidity, % Temperature range, DC

PCC thickness, mm

100 100 ." •• ." 90 100

,§ ,§ ."

Oi 80 80 :E •

•• • Oi • Oi 80 I a. a. 70 Ul I/) a.

• 60 Ul

=

60 • ..c 60 j 50 'j; • = • 'j;

J!l • 40 J!l 40 40 c c 30 J!l

'0 • c '0 20 '0 .... 20 .... • .... 20

';!. 10 .. ';!. · 0 0 0 I

0 100 200 300 0 50 100 150 0 5 10

Base thickness, mm k-value, kPalmm Joint spacing, m

100 100 100 ." 90 ,§ • ." '." • •

80 • 80 ,§ 80 Oi

a. 70 • Oi Oi • • • a. a. Ul 60

• • Ul Ul •

=

•

=

60

=

60

'j; 50

•

• • 'j; 'j;

J!l 40 •• • J!l 40 J!l 40 c 30 • '0 '0

c c • .... '0 20 .... 20 .... 20 10 ';!. .~ · . 0 •

0 2 4 6 500 1000 1500 2000

50 100 150 200

Sealant type Freezing index, DC Days Annual freeze-thaw cycles

100 100 100 90 • • • ." ." 90 • ."

80

• •

•• ,§

Oi 80 80

70 Oi • • a. Oi • • a. 70 • a. Ul # 60 Ul Ul 60 ••

= = =

60

'j; 50 'j; 50 • 'j;

J!l 40 J!l 40 • •

• J!l 40 c 30 c '0 30 c '0 '0 .... 20 .... 20 .... 20

';/!. 10 10 ';!. • . 0 0 •

0 0.5 1.5 0 10 20 30 5 10 15 20

Precipitation, m Age,yr ESAL's (millions)

Figure 20. Plot ofpercentage ofjoint spalling versus significant variables for JPCP.

71
'J

N

Table 11. Correlation matrix for selected variables for JRCP transverse joint spalling model

FI FTCYC PRECIP WTDYS MAXT MINT MEANT D90 JTSP HPCC EPCC ESAL AGE BTHICK BTYPE Cd 

FI 1 0.57991 -0.74212 -0.03719 -0.89006 -0.8824 -0.89017 -0.77309 -0.46041 -0.41858 -0.01902 0.02284 0.00474 -0.09942 -0.5767 -0.46

FTCYC 0.57991 1 -0.81893 -0.00997 -0.80147 -0.8538 -0.83184 -0.79381 -0.18328 -0.46474 -0.16779 0.13122 -0.18318 -0.13859 -0.4015 -0.42

PRECIP -0.74212 -0.81893 1 0.19078 0.80481 0.83679 0.8248 0.7104 0.35478 0.41184 0.09325 0.04284 0.24926 0.23176 0.37458 0.32

WTDYS -0.03719 -0.00997 0.19078 1 -0.16577 -0.0768 -0.12104 -0.35508 0.15484 0.29129 0.01827 0.22645 0.1207 0.27547 -0.3514 -0.39

MAXT -0.89006 -0.80147 0.80481 -0.16577 1 0.98212 0.99535 0.9545 0.3693 0.40402 0.02191 -0.05428 0.08585 0.08135 0.64368 0.56

MINT -0.88242 -0.85376 0.83679 -0.07676 0.98212 1 0.99569 0.91242 0.36377 0.49067 0.07765 -0.07447 0.08379 0.13627 0.60155 0.5

MEANT -0.89017 -0.83184 0.8248 -0.12104 0.99535 0.99569 1 0.93725 0.36809 0.45021 0.05055 -0.0649 0.08518 0.10982 0.62504 0.55

D90 -0.77309 -0.79381 0.7104 -0.35508 0.9545 0.91242 0.93725 1 0.27871 0.28123 -0.01334 -0.11472 0.0649 0.00147 0.62835 0.57

JTSP -0.46041 -0.18328 0.35478 0.15484 0.3693 0.36377 0.36809 0.27871 1 0.04951 -0.17453 0.37116 0.35035 -0.09127 0.00282 0.00

HPCC -0.41858 -0.46474 0.41184 0.29129 0.40402 0.49067 0.45021 0.28123 0.04951 1 0.3628 0.03391 -0.07105 0.1667 0.15603 0.13

EPCC -0.01902 -0.16779 0.09325 0.01827 0.02191 0.07765 0.05055 -0.01334 -0.17453 0.3628 1 0.14583 -0.05375 -0.03553 0.00829 0.17

ESAL 0.02284 0.13122 0.04284 0.22645 -0.05428 -0.0745 -0.0649 -0.11472 0.37116 0.03391 0.14583 1 0.47839 0.1062 -0.2121 -0.14

lA.GE 0.00474 -0.18318 0.24926 0.1207 0.08585 0.08379 0.08518 0.0649 0.35035 -0.07105 -0.05375 0.47839 1 -0.07076 -0.1657 -0.09

BTHICK -0.09942 -0.13859 0.23176 0.27547 0.08135 0.13627 0.10982 0.00147 -0.09127 0.1667 -0.03553 0.1062 -0.07076 1 -0.0575 -0.27

BTYPE -0.57668 -0.40147 0.37458 -0.35139 0.64368 0.60155 0.62504 0.62835 0.00282 0.15603 0.00829 -0.21214 -0.16574 -0.05748 1 0.79

Cd -0.46159 -0.42369 0.32675 -0.39467 0.56878 0.5463 0.55984 0.57072 0.00807 0.13792 0.17392 -0.14971 -0.09605 -0.27232 0.79679 

k-value -0.37244 -0.17988 0.25818 -0.06923 0.36552 0.32641 0.34715 0.34526 -0.07957 0.01732 -0.13616 -0.14787 0.0071 0.1944 0.56174 0.38

PSPALL -0.24593 -0.05075 -0.0394 -0.00579 0.16011 0.1741 0.16798 0.13082 -0.00827 0.31903 -0.12035 -0.09871 -0.25296 0.24687 0.07514 -0.12

* See table 12 for definitions.
Table 12. Definition ofselected variables significant to spalling ofJRCP.

Symbol Potential Independent Variable

FI Freezing index, degree-days caC) below freezing

FTCYC Yearly number of air freeze-thaw cycles

PRECIP Average annual precipitation, mm

WTDYS Number ofwet days in a year, days

MAXT Average maximum daily temperature, DC

MINT Average minimum daily temperature, DC

MEANT Average mean daily temperature, DC

D90 Number of days maximum temperature is greater than 32DC

JTSP Mean transverse joint spacing, mm

HPCC PCC slab thickness, mm

EPCC Elastic modulus, kPa

ESAL Cumulative equivalent 80-kN single axle load, thousands

AGE Time since pavement construction, yr

BTHICK Base thickness, mm

BTYPE Type of base, O=erodible and l=nonerodible

Cd Drainage coefficient

k-value Backcalculated static k-value, kPa/mm

PSPALL Percentage ofjoints with low-, medium-, or high-severity spalling

73
"CI 100 "CI 1oo • 100

.!! .!! • "CI

.!! iii 80 iii 80 I • iii 80 Q, Q, •• Ul 60 Ul 60 • Q,

Ul 60 •••

J!l 40 J!l 40 • J!l c c • • • c 40 '0 '0 ... 20 '0 •

I ... 20 • ... 0

20 ••••

0 · 0 ;1.

0 • •

20 40 60 80 100 0 10 20 30 150 200 250 300 350

Relative humidity, percent Temperature range, ·C PeC thickness, mm

100 "CI "CI 1oo "CI 100 • .!! 80 .!! .!! iii • iii 80 I iii 80 • Q,

Ul 60 • Q, Q,

Ul 60 Ul 60 .. J!l

• • J!l

'0

'E 40 c 40 c 40 • ... '0 '0 20 • ... 20 ... 20 . •• ;1. 0 . 0

40 60 80 100 120 2 4 6 8 10 0 2 3 4 5

k-value, kPalmm Joint spacing, m Sealant type

100 100

"CI • • "CI • • "CI 100

.!! 80 ., .!! 80 • .!! 80 iii iii iii Q, Q, l:l.

Ul 60 •• Ul 60 Ul 60

J!l • J!l • .. • .. c 40 40 c 40 c

'0 • '0 '0 ... ... 20 ... 20

20 ;1. • 0

· •

500 1000 1500 2000

10 20 30 10 20

ESAL's (millions) Freezing index, ·C Days

Age,yr

100 "CI 100 "CI 100 • "CI • • • .!! .!! .!! 80

iii 80 iii •• • • iii 80 l:l. l:l. # • • • l:l. Ul 60 Ul 60 • Ul 60 J!l J!l ••

40 • J!l 40 c 40 • c c '0 '0 • '0 ... ... 20 ... 20 20

;1. ;1. 0 · 0

20 22 24 26 28 30 0 100 200 300 0.5 1.5 2

PCC modulus, (mil/Ions) kPa Base thickness, mm Precipitation, mm

Figure 21. Plot of percentage ofjoint spalling versus significant variables for JRCP.

74
Jointed Reinforced Concrete Pavement

The results of correlation analysis that show the strength ofthe relationships between selected

variables and JRCP spalling are shown in table 11. The definitions ofthe variables in table 11 are

presented in table 12. Figure 21 is a plot ofthose independent variables versus the percentage of

joints with low-, medium-, or high-severity spalling in the LTPP database for JRCP. These

results were analyzed to evaluate the independent variables that show a strong influence on JRCP

spalling.

From the results, the variables that were relatively highly correlated to JRCP joint spalling were

the thicknesses ofthe PCC slab and base, pavement age, and freezing index. Unlike the results

obtained for JPCP spalling, however, the results ofthe correlation analysis showed some

unexpected trends. Traffic loading and age both turned out to be negatively correlated with

spalling, with the younger and less trafficked GPS 4 sections showing more spalling than the

older sections. Other variables that were relatively significantly correlated to spalling included

environmental variables such as the average maximum, minimum, and mean monthly

temperatures and the number ofdays with temperature greater than 32°C.

Calibration of Mechanistic-Empirical Joint Spalling Models

The final step in the development ofthe prediction models was calibration ofthe models

formulated with the LTPP data for the GPS 3 and 4 pavement sections. Mechanistic-empirical

models were developed for joint spalling ofJPCP and JRCP. This was accomplished using

optimization and regression analysis techniques similar to those described previously for the

other models developed in this study. The procedure involved determining the best-fit parameters

(a), az, K), Kz, K3, K4, m, and n) in equations 51,53,54, and 55.

JPCP Spalling Model

The mechanistic-empirical model for predicting JPCP spalling developed using the LTPP GPS 3

database consists ofthree parts. They include equations for estimating the allowable number of

traffic and environmental load applications to failure, a spalling damage accumulation model,

and a model for calculating the percentage ofjoints with spalling of all severities. Following are

the models that were developed.

Allowable Number ofTraffic (NT) and Environment (NrJ Load Applications

The equations for calculating NT and NE for JPCP are as follows:

where

=

(

1) 0.15

NT = 199252 at

tensile stress, kPa (calculated from equation 49)

75

(56)
~s

ELONG =

L =

~T =

e

ex = C

t

( )

0.85

N E = 650162 t

kjsELONG

modulus ofthe sealant material or incompressibles, kPa

a factor estimating the horizontal movement ofthe slab, m

3.28CL(3.24ex~T + e)

slab length or joint spacing, m

thermal gradient in the slab, DC

concrete drying shrinkage strain

concrete thermal expansion, per DC

subbase friction factor

Imm

(57)

Tables 13 through 15 provide estimates for shrinkage, e, concrete thermal coefficient, ex, and the

sealant and incompressible modulus ifthey cannot be obtained from field or laboratory tests. The

type of aggregates used in the PCC, the indirect tensile strength, and the sealanttype are

available in most databases, including the LTPP database.

Damage Accumulation Model

The final model for calculating the total damage from traffic and environmental loading for JPCP

is as follows:

where

(

KESALJ ( AGE 0.145J Damage = +

NT N E

80-kN ESAL's in thousands

pavement age in years

allowable number of cycles due to traffic stresses

allowable number of cycles due to environmental stresses

76

(58)
Table 13. Approximate relationship between shrinkage and indirect tensile strength.(33)

Indirect Tensile Strength Shrinkage mm/mm

300 or less 0.0008

400 0.0006

500 0.00045

600 0.0003

700 or greater 0.0002

Table 14. Recommended values ofthermal coefficient,(33)

Type of Coarse Aggregate Concrete Thermal Coefficient (10-6

/

o

C)

Quartz 3.66

Sandstone 3.61

Gravel 3.33

Granite 2.94

Basalt 2.66

Limestone 2.11

Table 15. Adjusted sealant modulus for JPCP.

Sealant Type Adjusted Sealant Modulus (106 kPa)

Preformed 1.405

Low modulus asphalt 1.396

Silicone 2.529

Others 2.300

Incompressibles 5.290

77
JPCP Spalling Model

The final model for predicting the percentage of spalled joints for JPCP is as follows:

SpallJPCp

where

= 100Damage 2.1 (o.344TRANGE _ O.042RH + O.0318FTCYC)

1 + Damage 2.5

(59)

SpallJPcp

TRANGE

RH

FTCYC

Damage

Statistics:

N

R2

SEE

p-value

=

=

=

=

=

=

=

=

<

percentage ofJPCP joints with spalling of all severities

average daily temperature range, °C

average daily range ofrelative humidity during the month of construction

that can be obtained from the National Oceanic and Atmospheric

Adminstration (NOAA) tables, percent

number offreeze-thaw cycles

damage from traffic and environmental stresses (equation 58)

52

0.61

12 percent

0.0001 (significance ofmodel)

A plot ofthe predicted and measured percentage ofspalled joints is shown in figure 22. A plot of

the residuals (predicted - actual percentage ofjoints spalled) against the predicted percentage of

joints spalled is shown in figure 23. Figure 22 does not show very good fit ofthe LTPP data with

the model. However, the overall accuracy ofthe spalling model is reflected by the R2 of 0.61,

which is the proportion ofvariation ofspalling explained by the variables included in the model.

A test of hypothesis was performed to determine the significance ofthe variables used in the

model for predicting spalling. The null and alternate hypothesis were as follows:

Ho: all model parameters are zero (variables are not significant)

HA: all model parameters are not zero

The F-test statistic used for the hypothesis test was calculated as the ratio ofthe mean square for

the model divided by the mean square ofthe error. For this study the null hypothesis will be

rejected ifthe level ofsignificance is less than 5 percent (0.05). A level ofsignificance (p-value)

ofless than 0.0001 implies a rejection ofthe null hypothesis. This shows that the variables in the

model are highly significant.

78
•

•

100

--

"- 80

"'0

Q)

.......

.......

co

0..

rJ) 60 rJ)

.S

0

'''-' 40 "'0

Q)

....

u.....

"'0

Q) 20 •

d::

a

a 20 40

•

60 80

•

100

Observed joints spalled (%)

Figure 22. Predicted percentage of spalled joints versus the actual

percentage of spalled joints for JPCP.

40 -,---+-------------------------,

•

20 f- • .......

ctl .

•

;:::l 4

"'0

..... 0 IP•• • f/)

Q)

(

, iO 40 60 80 ·11 0 •

•

-20 •

-40 ...L- ----'

Predicted joints spalled (%)

Figure 23. Plot of the residuals versus the predicted percentage of

spalled joints for JPCP.

79
Also, individual t-tests were conducted to test ifthe individual parameter estimates are equal to

zero. The p-values for this test ranged from 0.0002 to 0.016. The results show that all the

parameter estimates had values other than zero; therefore, the variables in the model were

significant. Prediction accuracy ofthe percentage ofspalled joints in absolute units is reflected

by the standard error of estimate (SEE = 12 percent). The overall effectiveness ofthe model

should be judged on all ofthe diagnostic statistics, the residual plots, and the results from the

sensitivity analysis to follow. The diagnostic statistics obtained for the JPCP spalling model

show that the model can predict transverse joint spalling with reasonable accuracy for the LTPP

database utilized.

JRCP Spalljng Model

The mechanistic-empirical model for predicting JRCP spalling developed using the LTPP GPS 4

database also consists ofthree parts. Following are the different parts ofthe model.

Allowable Number ofTraffic (NT) and Environment (NJ LoadApplications

The equations for calculating NT and NE for JRCP obtained are as follows:

(60)

(61)

where

at

~s =

ELONG =

k

~cc =

tensile stress, kPa (calculated from equation 49)

modulus ofthe sealant material or incompressibles, kPa

an estimate ofthe horizontal movement defined for equation 57, m

modulus ofsubgrade reaction, kPa/mm

PCC thickness, mm

The recommended values for elastic moduli ofthe sealants or incompressible, ~s, for JRCP are

given in table 16.

80
Table 16. Adjusted sealant modulus for JRCP.

Sealant Type Adjusted Sealant Modulus (106 kPa)

Preformed 9.00

Rubberized asphalt 17.78

Silicone 0.069

Asphalt 0.069

Incompressibles 22.84

Damage Accumulation Model

The final model for JRCP for calculating the total damage from traffic and environmental

loading is as follows:

where

Damage 0.0667 *KESAL

NT + (62)

=

=

number of80-kN ESAL's in thousands

pavement age in years

allowable number of cycles due to traffic stresses

allowable number of cycles due to environmental stresses

JRCP Spalling Model

The final model for predicting the percentage ofspalled joints for JRCP is as follows:

SpallJRCp = 100 DAMo.ss (1.764*10-sFI + 6.348*10-sEpcc - 0.02714 k)

where

(63)

SpallJRCp

FI

Epcc

k

DAM

=

=

=

=

percentage ofjoints with spalling of all severities

mean annual freezing index, °C days

PCC elastic modulus, kPa

modulus ofsubgrade reaction, kPa/mm

damage due to traffic and environmental stresses I

81
Statistics:

N

R2

SEE

p-value <

68

0.43

5.06 percent

0.002 (significance ofmodel)

A plot ofthe predicted and measured percentage ofspalled joints is shown in figure 24. A plot of

the residuals (predicted - actual percentage ofspalled joints) against the predicted percentage of

spalled joints is shown in figure 25. The overall accuracy ofthe JRCP spalling model is reflected

by the R2 of 0.43, which is the proportion ofvariation ofJRCP spalling explained by the

variables included in the model. A test of hypothesis was performed to determine the

significance ofthe variables used in the model for predicting spalling. The null and alternate

hypothesis were as follows:

Ho: all model parameters are zero (variables are not significant)

HA : all model parameters are not zero

The F-test statistic used for the hypothesis test was calculated as the ratio ofthe mean square for

the model divided by the mean square ofthe error. For this study the null hypothesis will be

rejected ifthe level ofsignificance is less than 5 percent (0.05). A level ofsignificance (p-value)

ofless than 0.002 implies a rejection ofthe null hypothesis. This shows that the variables in the

model are significant. Also, individual t-tests were conducted to test ifthe individual parameter

estimates are equal to zero. The p-values for this test ranged from 0.001 to 0.03.

The results show that all the parameter estimates had values other than zero; therefore, the

variables in the model were significant. Prediction accuracy ofpercentage ofspalled joints in

absolute units is reflected by the standard error of estimate (SEE = 5.06 percent). The overall

effectiveness ofthe model should be judged on all ofthe diagnostic statistics, the residual plots,

and the results from the sensitivity analysis to follow. The diagnostic statistics obtained for the

JRCP spalling model show that the model can predict transverse joint spalling for JRCP with

reasonable accuracy for the LTPP database utilized.

82
40 -,----------------------,

•

•

• •

• • • •

•

• • • • • • •

10 20 30 40

Observed joints spalled (%)

o+-1~-+__--+__--+_-____1

o

] 30 ......

......

ctl

0..

en

en

20 .....

o'''-'

"'0

OJ

;ati 10 ~..*

OJ

!-<

Figure 24. Predicted percentage of spalled joints versus the actual

percentage of spalled joints for JRCP.

30

•

20 • •••

•

10 • ...... •

ctl •

"'0 0 ... • • ..... •• I I

en

'. ~1~. OJ ( 20 .30 40 50

-10

-20

-30 -'-- ---.J

Predicted joints spalled (%)

Figure 25. Plot of residuals versus the predicted percentage of

spalled joints for JRCP.

83
Sensitivity Analysis for Mechanistic-Empirical Spalling Models

The final step in the model-building process is the verification ofthe selected regression model.

For the JPCP and JRCP spalling models developed, model verification was limited to a

comprehensive sensitivity analysis that involved the comparison ofresults with theoretical

expectations, earlier empirical results, and simulated results reported in previously published

literature. The sensitivity analysis involved using the model to determine the effect of each

variable on percentage ofjoints spalled when the other variables in the model were held at their

mean values. Plots were prepared to show these results. The plots were examined and the results

compared with theoretical expectations and emipirical results from earlier research studies. There

were relatively limited data for model development, so a comprehensive validation ofthe model

was not possible. The plots and results from the sensitivity analysis are discussed in the

following sections.

.IPCP Mechanistic-Empirical Model

The effects ofthree key groups offactors on JPCP spalling were checked using the mechanisticempirical model. The factors investigated included environmental effects, traffic loading, and

sealants and incompressibles.

Effect ofEnvironmental Factors

The key environmental variables that were found to have an influence on joint spalling ofJPCP

were the average daily temperature range, the mean monthly relative humidity during the month

of construction, and the number of annual freeze-thaw cycles. The model also shows the

influence ofthe type ofsealant, or lack thereof, in relation to all these factors.

Figure 26 shows the significance ofthe daily temperature range and type ofjoint sealant on

spalling. A high daily temperature range results in more spalling regardless ofthe type ofsealant

used. It is believed that the higher temperature range may result in higher restrained thermal

stresses. Early in the life ofthe pavement, this may result in more microcracks and delaminations

that contribute to more spalling. Preformed sealants seem to decrease these stresses and cause

less spalling, whereas joints without any sealants and that are probably filled with

incompressibles experience more spalling. As shown in figure 27, a high relative humidity

during the month of construction reduces the occurrence ofspalling. A possible explanation is

that, by aiding the curing process because ofthe reduced rate at which moisture leaves the PCC

slab, a high relative humidity may increase strength gain and reduce shrinkage. This

can reduce the magnitude of early age stresses and the occurrence of delaminations and

microcracks that lead to spalling.

84
100

~Asphalt

80 _Preformed

---- -6-Silicone

Others

"'d-- 60 .-

.-

OJ ~NoneorN/A

ro

0..

rJ)

rJ)

..... 40

I=: .....

0

-.

20

0 ".~-

0 5 10 15 20 25

Daily air temperature range tC)

Figure 26. Sensitivity plot of percentage ofJPCP joint spalling versus average

daily temperature range.

80 100

~Asphalt'

_Preformed

-6-Silicone

--+E- 0 thers

~NoneorN/A

40 60

Relative humidity (%)

Figure 27. Sensitivity plot of percentage ofJPCP spalling versus mean relative

humidity during month of construction.

60

50

---- 40

"'d--

OJ .-

.-

ro 30 0..

rJ)

rJ)

.....

I=: ..... 20 0

-.

10

0

20

85
The influence offreeze-thaw cycles is shown in figure 28. The higher the number offreeze-thaw

cycles, the greater the chance for durability damage ofthe concrete. This will lead to more

spalling. Finally, figure 29 shows the effect ofthe horizontal movement or elongation ofthe PCC

slab on joint spa11ing. As expected, such movement increases spalling because this causes an

increase in the pressure or reaction to the joint surface to sealants and incompressibles, as well as

from actual contact ofthe two concrete slab surfaces.

Effect ofTraffic Loads

The influence oftraffic loading on joint spalling ofJPCP as depicted by the model is shown in

figure 30. An increase in traffic load applications increases spalling, as expected. The rate of

increase ofspalling is quite rapid and is greatest for joints with no sealants. Joints with

preformed sealant perform the best in terms ofjoint spalling.

Effect ofJoint Sealant and Incompressibles

The tremendous influence ofsealants on joint spalling is illustrated by the sensitivity plots shown

in figures 26 through 30. In all cases, the greatest spalling was for joints without any sealants

(presumably filled up with incompressibles). For those pavements with sealed joints, there is also

an appreciable effect ofthe type ofsealant used and the amount ofspalling that occurs.

Preformed sealants are far better at reducing joint spalling than the other types ofsealants.

Because ofthe relatively uniform compression on the surface ofthe joint provided by preformed

sealants or because they keep out incompressibles, it seems that they somewhat reduce the tensile

stresses that cause microcracks and delaminations at the joint to spall off. The performance ofthe

other types ofsealants is comparable.

JRCP Mechanistic-Empirical Model

A similar sensitivity analysis was conducted for the mechanistic-empirical model for predicting

joint spalling ofJRCP. Following are the results that were obtained that show the significance of

the environment, traffic loading, joint sealant, and other factors on the predicted percentage of

joints spalled.

Effect ofEnvironmental Factors

The influence ofthe environment was less prominent for the mechanistic-empirical model

developed for predicting joint spalling ofJRCP. The only environmental variable that was found

to be mildly significant was freezing index. However, the pavement age, which is related to the

cyclic effect ofthe environment, has a significant effect on joint spalling ofJRCP, according to

the model. Figure 31 is a plot ofpercentage ofjoints spalled versus age. The influence ofthe type

ofsealant used is also shown by the plot. The clear trend ofthe percentage ofspalled joints

increasing with age confirms the validity ofthe model. The plot also shows that the different

sealant types influence spalling appreciably.

86
100 ..,------------------------------;

-+-Asphalt

__ Preformed

--..- Silicone

Others

____ None or N/ A

40

80

60

O-t--------I-------+------t--------j

o 50 100 150

Annual No. of freeze-thaw cycles (days)

200

Figure 28. Sensitivity plot of percentage ofJPCP spalling versus

number of freeze-thaw cycles.

-+-Asphalt

__ Preformed

--..- Silicone

Others

--.-None or N/A

100

80 --

"'t'l --

Q) 60

::::

0..

CI:J

CI:J 40

.5

0

....... 20

a

a 1 2 3 4 5 6 7

Elongation (mm)

Figure 29. Sensitivity plot of percentage ofJPCP spalling versus elongation.

87
100

~Asphalt

__ Preformed

80 -.-Silicone -. --*-Others

* ___ None or N/A

"'0--

OJ 60

-

ca

0.-

rJ:J

....

rJ:J 40 .S

0

-.

20

0

0 10 20 30

ESAL's (millions)

Figure 30. Sensitivity plot of percentage ofJPCP spalling versus ESAL's.

Figure 32 shows the effect offreezing index on spalling. The higher the freezing index, the

higher the percentage ofspalled joints predicted by the model. This is reasonable, because

concrete material will deteriorate more in the colder regions ofthe country since they experience

prolonged freezing and freeze-thaw cycles that result in the disintegration ofthe concrete

material and increase spalling.

Effect ofTraffic Loading

An increase in the number ofload applications shows the same trend as that for age and increases

the percentage ofJRCP joints spalled, as shown in figure 33. Figures 34 and 35 are plots ofthe

percentage ofjoints spalled versus age for a pavement with a preformed sealant and different

traffic stress values and elongation due to temperature gradients within the pavement. The figures

show that there is more spalling as the traffic and temperature stresses increase. This is in

agreement with the mechanistic causes ofspalling outlined in earlier sections ofthis chapter. An

increase in tensile stresses around the PCC slab joint helps to propagate existing cracks or

develop new ones.

88
50 -,----------------------------,

--+- Preformed

--Rubberized asphalt

........-Silicone

-e-Asphalt

No joint sealant

O-F'---+------\-----+----+----+-----I

10

40

30

0..

[/)

$ 20

.S

o-.

o 5 10 15

Age (yr)

20 25 30

Figure 31. Plot of percentage of joint spalling versus age.

50 ,-------------------------------,

5 10 15 20 25

--+- FI =833 deg. C Days

--FI =333 deg. C Days

........- FI =83 deg. C Days

0..",,=------+-------+-----+-----+------1

o

40

10

30

:::::l

C1i

0..

[/)

[/) 20

.....

"E

o

-.

Age (yr)

Figure 32. Effect of freezing index on percentage ofJRCP joints spalled.

89
50 -,----------------------------,

10 20 30

-+- Preformed

___ Rubberized asphalt

.......-Silicone

--*- Asphalt

-.-No joint sealant

0-=--------t---------I--------1

o

40

10

30

::::

ro

0..

Cf)

Cf) 20

1:: .....

ESAL's (millions)

Figure 33. Plot of percentage ofJRCP joints spalled versus ESAL's.

30 -,----------------------------,

5 10 15 20 25

-+-Traffic tensile stress = 4000 kPa

---Traffic tensile stress = 1725 kPa

--.- Traffic tensile stress = 345 kPa

O-w"'-----+------t------t------t-------l

o

5

25

Age (yr)

Figure 34. Influence of traffic tensile stresses on percentage ofJRCP joints spalled.

90
100

-+- ELONG = 61 mm

80 ___ ELONG = 6.1 mm

......- ELONG = 0.61 mm .......

'--'

"0 60 C1J

--t1i

0-

<rJ

<rJ

-oJ 40 .....

0

......

20

a 5 10

Age (yr)

15 20 25

Figure 35. Influence of different ELONG Goint movement) values from temperature

gradients on the percentage ofJRCP joints spalled.

Effect ofJoint Sealant

The effect ofthe different types ofsealants on joint spalling ofJRCP was not very different from

that observed for the JPCP model. Figures 29 and 32 both illustrate the influence ofthe different

joint sealant conditions. For JRCP, unsealed joints were also found to spall more, and the type of

sealant used has an influence on spalling. However, silicone sealants seem to provide the best

protection against spalling, followed by preformed sealants. Joints with rubberized asphalt

sealants do not perform as well and seem not to be much better than unsealed joints.

Effect ofModulus ofSubgrade Reaction

Figure 36 is a plot of percentage ofjoints spalled versus age for a pavement with a preformed

sealant and different subgrade k-values. The figure shows that there is less spalling as the k-value

ofsubgrade strength increases. This is reasonable because stronger subgrades reduce deflections

at the pavement joints, thus reducing spalling stresses.

91
-+-k = 54 kPa/mm

--k =41 kPa/mm

---.- k = 27 kPa/mm

70

60

.-.. 50

""d-- 40 Q)

......

......

co

0..

C/)

C/) 30

.....

-..

0 20

10

0

0 5 10

Age, yr

15 20 25

Figure 36. Influence of k-value on percentage ofJRCP joints spalled.

Summary

JPCP Spalling

The following can be summarized about the JPCP spalling model:

• Sixty-one percent ofthe total variation ofspalling can be explained by the included

variables.

• Some ofthe unexplained variation may be due to errors in the independent variables used

to develop the model, such as the traffic estimates.

• The "average" error in predicting JPCP spalling is 12 percent.

• There are no discernible patterns in the residuals. This means that the data used in model

development had little or no serial correlation.

• Data from 52 pavement sections from all over the United States were used to develop the

model (N = 52).

• Each independent variable and the overall model was found to be significant.

• The sensitivity analysis shows that all ofthe explanatory variables have a plausible effect

on spalling that agrees with theoretical expectations and previous empirical field results.

92
JRCP Spalling

The following can be summarized about the JRCP spalling model:

• Forty-three percent ofthe total variation ofspalling can be explained by the included

variables.

• Some ofthe unexplained variation may be due to errors in the independent variables used

to develop the model, such as the traffic estimates.

• The "average" error in predicting JRCP spalling is 5 percent.

• There are no discernible patterns in the residuals.

• Data from 68 pavement sections from all over the United States were used to develop the

model (N = 68).

• Each ofthe independent variables and the overall model was significant at a level of

significance of 5 percent.

• The sensitivity analysis shows that all ofthe explanatory variables have a plausible effect

on spalling that agrees with theoretical expectations and previous empirical field results.

Implications and Recommendations

The mechanistic-empirical models presented were successfully developed through a combination

of applying the knowledge available about the mechanism ofspalling and analytical methods

currently available. The models show that this approach can be used to develop models that

reasonably predict joint spalling ofJPCP and JRCP. The mechanistic analysis for both types of

jointed concrete pavements shows that spalling is a function oftensile stresses generated from

both traffic and environmentally imposed stresses.

Although both models show that the environment has a strong influence on joint spalling, for the

data set used, the influence was more significant for JPCP. The models indicate that the

environmental factors that influence the durability ofthe concrete and the restrained thermal

stresses within the pavement influence spalling. These results are in line with empirical evidence

from the field. Also, the model for JPCP indicates that the conditions that exist during

construction ofthe pavement influence the amount ofspalling, possibly because oftheir effect on

the occurrence of early microcracks and de1aminations.

Both models show the influence ofjoint sealing on spalling, probably through differences in

incompressib1es infiltrating into the joints. There is strong evidence that sealing ofjoints will

greatly decrease the occurrence ofspalling. The models predict that the most spalling will occur

ifjoints are not sealed and incompressib1es get into the joint. Preformed sealants and silicone

sealants were found to be most effective for JPCP and JRCP, respectively.

93

6. TRANSVERSE CRACKING AND CORNER BREAKS OF JPCP

Introduction

Transverse cracks can occur at the midslab ofJPCP slabs parallel to the joint. Typically, midslab

cracks initiate as a single crack at the edge ofthe slab that propagate through the entire slab and

across the slab. Transverse cracks can also occur close to the joint, and they can propagate across

the slab or cut diagonally from the edge to the transverse joint and become comer breaks. Both

transverse cracks and comer breaks in JPCP can be measured by counting the number of cracks

and comer breaks that exist in the original PCC pavement.

Transverse cracks and comer breaks will increase the roughness ofthe pavement as the cracks

fault and spall and there is a general breakup ofthe pavement. This decreases serviceability and

results in costly rehabilitation. Transverse cracks, especially when they are badly spalled, also

cause surface runoff from rainfall to infiltrate the pavement structure. This normally results in the

weakening and erosion ofthe base course, increasing deflections and resulting in increased

cracking and faulting. Transverse cracks and comer breaks must be avoided as much as possible.

Models developed for predicting transverse cracks and comer breaks can be used as design

checks to avoid their occurrence. These models are also useful in pavement management for

predicting the occurrence oftransverse cracks and comer breaks so that needed rehabilitation can

be scheduled properly.

Transverse Cracking and Corner Break Mechanisms

The mechanisms for transverse cracking and comer breaks are similar, and for this study a

similar mechanism for crack initiation and propagation was used to model both transverse

cracking and comer breaks. The occurrence of cracking in concrete pavements can be attributed

to early age cracking, fatigue failure ofthe concrete, or both. Early age cracking is usually

material- and construction-related. Fatigue cracking, however, is caused by the repeated

application oftraffic and environmental stresses to the pavement at both the midsection and

comer. These stresses are typically less than the ultimate failure stress ofthe PCC slab; they do

not result in the sudden breakup ofthe concrete, but rather open up new or existing microcracks

that develop into the main cracks that propagate through the PCC slab.

Transverse Cracking Mechanism

There are two modes of crack development for transverse fatigue cracking: top down cracking

and bottom up cracking. Top down cracking occurs from the application oftraffic loads on a slab

that is in a severely curled-Up position due to a negative temperature differential and drying

shrinkage at the slab surface. These cracks typically occur close to the joint. Bottom up cracking

occurs from the application ofloads on a pavement that is in a curled-down position as a result of

a positive temperature differential that causes the slab to lose support at the midslab. The crack

typically occurs at the midslab location, starts from the edge ofthe outer lane, and propagates

transversely through the slab.

The first model described in this chapter was based on the assumption that most transverse

cracks observed on JPCP are the result offatigue failure initiated at the slab bottom (bottom up

95
failure). This assumption is reasonable if nighttime temperature curling combined with shrinkage

and moisture warping are not significant and dowel bars are used at the joints. This is a typical

mode offailure that has been observed in the field for JPCP in most parts ofthe United States.

The goal was to develop a fatigue cracking model based on the repeated maximum stress due to

both traffic and temperature loading at the critical location ofthe PCC slab.

Corner Breaks

Corner breaks are initiated from the top ofthe PCC slab (i.e., top down cracking). Top down

crack initiation and progression occur in situations where the pavement support is weak or

erosion has occurred, load transfer across the joint is poor, the slab is curled up at the corner, and

the pavement corners are subjected to heavy wheel loads. This results in excessive deflection of

the slab corners and a corresponding increase in the tensile stresses at the top ofthe PCC slab

corner. The tensile stresses cause the initiation ofmicrocracks. Repeated loading propagates

these cracks through the pec slab and results in corner breaks. Corner breaks start at the edge of

the PCC slab joint but do not propagate transversely across the slab. Rather, they cut across

diagonally to the joint.

Evaluation ofExisting Transverse Cracking and Corner Break Models

A lot of empirical and mechanistic knowledge has been accumulated over the years in modeling

cracking ofPCC pavements. Several existing models were reviewed to evaluate the potential

variables for model development.

SHRP P-020 Study

The following is a mechanistic model developed for predicting transverse cracking in JPCP using

the LTPP data available in 1992:(4)

where

peRK 1 (64)

PCRK

FD

n

N

Ratio

Stress

Strength =

percentage ofslabs cracked

fatigue damage = nIN

expected number of applied edge stress

allowable number of applied edge stress = 1Q[2.13*(1/Ratio)1.2j

stress/strength

f(Epee, Thick, Poisson's ratio, Kstatic), psi

mean 28-day flexural strength, psi

Sensitivity analysis ofthis model showed that, by far, slab thickness had the greatest effect on

transverse cracking. This was followed by the flexural strength ofthe concrete at 28 days.

Although the model was developed using limited data, it provides useful insights into the

potential variables that can be used to develop a model for transverse cracking ofJPCP.

96
RIPPER Study

Following is a similar model that was developed in the FHWA research study commonly referred

to as RIPPER, using data from concrete pavement sections surveyed as part ofthe study:(IO)

PCRK 100

1 + 1.41 FD -1.66

(65)

where

PCRK

FD =

n

N =

Ratio =

Stress = Strength =

percentage ofslabs cracked

accumulated fatigue damage = nIN

expected number of applied edge stress

allowable number of applied edge stress = IO[2.13*(I/Ratio)1.2]

stress/strength

f(Epcc ' Thick, Poisson's ratio, Kstatic), edge support, psi

mean 28-day flexural strength, psi

Sensitivity analysis ofthis model showed that increasing the thickness ofthe PCC slab decreases

cracking. According to the model, shorter joint spacing will reduce transverse cracking, as will a

tied PCC shoulder in comparison to an AC shoulder. Bonding between the PCC slab and an

underlying stabilized base and stronger support in terms of a higher k-value were also found to

decrease cracking. As expected, the effect ofmodulus ofrupture was very significant, with a

higher modulus ofrupture resulting in an appreciable decrease in cracking.

NAPCOM Cost Allocation Model

Following is another model developed recently for cost allocation purposes using concepts

similar to the previous models:(3)

where

Percent Cracking

100 FD 1.52

1 + FD 1.52

(66)

FD

n

N

accumulated fatigue damage = nIN

expected number of applied edge stress

allowable number of applied edge stress

The allowable number ofthe combined traffic and temperature edge stress repetitions to failure is

calculated using the following equation:

N

0.531 + 2.13 ( 0 .... ) -1.2

__1_ 10 M R

1 - R

97

(67)
where

R <Jtem/<Jmax

<Jtemp curling stress (stress in the slab when no axle loading is applied), psi

A unique feature about this model is that equations were developed for calculating the maximum

edge stress, 0max' for different axle loads and types as follows:

where

(68)

TANDEM

TRIDEM

S

Q

°combined

=

=

code for tandem axle type, 1= tandem, O=otherwise

code for tridem axle type, 1= tridem, O=otherwise

axle spacing, in

radius ofrelative stiffness, in

bending stress induced in the pavement from combined axle loading and

temperature curling stress, psi

Sensitivity analyses ofthe model provided similar results as for the previous model. However, it

was also possible to use this model to determine the effect of axle load level and configuration.

Fatigue Cracking Modeling Approach

The approach used to develop the cracking model in this study is similar to that used to develop

the previous models. It is based on the fatigue damage approach and requires determination of

the allowable number ofload applications to failure. In the models presented, the number of

allowable load repetitions to failure, N, is determined as the ratio ofthe maximum bending stress

to the modulus ofrupture. In this study, it was decided to investigate the use oflinear fracture

mechanics (LFM) principles to estimate the number ofload applications to failure.

The approach used is based on extensive investigation ofthe mechanism of crack propagation

using LFM principles. These studies confirmed that stress intensity factor at the crack tip as the

crack propagates through the PCC slab can be used effectively to estimate fatigue damage to

JPCP. The stress concentration at the crack tip is induced by the traffic and environmental loads

applied to the pavement. Ifthe stress intensity factor can be determined, it can be used to

estimate the allowable number ofload repetitions using Paris's law.(51)

Consequently, a major need ofthis approach was calculating accurately the stress intensity factor

caused by traffic load and temperature stresses. It was important to account for the effect ofthe

interaction between traffic loading factors, temperature curling, and design factors (i.e., joint

spacing, slab thickness, concrete and foundation elastic properties) on the calculated stress

intensity factor. The stress intensity factor obtained was used to calculate the allowable number

ofload applications to failure and, consequently, the accumulated fatigue damage. The procedure

for calculating stress intensity factor is presented in later sections ofthis chapter. Using

information from the LTPP database, accumulated damage for pavements from both traffic- and

98
environmental-related stresses was calculated. The distress observed in the field was used to

calibrate the following model form for predicting fatigue transverse cracking:

(69)

where

FDT , = FDE =

aI' a2, m, n =

CI , C2 =

accumulated fatigue damage from traffic-related stress

accumulated fatigue damage from temperature-related stress

regression constant

scaling variables that account for unexplained effects

The fatigue damage in equation 66 is based on Miners law and is defined as follows:

k

FD = L~i=l Ni

where

(70)

n

N

=

=

actual number ofload cycles

allowable number ofload cycles to fracture

Application of Fracture Mechanics Principles

Current mechanistic-empirical design procedures for JPCP estimate fatigue life of uncracked

pavements as a function ofthe ratio ofthe maximum bending stress to the modulus ofrupture of

the concrete. The equations to describe the fatigue life of concrete slabs are derived empirically

from laboratory and field performance data. Fatigue cracking (transverse cracking or comer

breaks) can also be analyzed using the principles of crack propagation and fracture mechanics.

Several researchers have used such fracture mechanics principles and beam-on-elastic foundation

theory to develop theoretical mechanistic models for crack growth analysis.

In general, the fracture mechanics approach is applicable to homogeneous materials with

continuous crack growth. Crack growth in most materials, including concrete, is not continuous.

Also, because concrete is not homogeneous, the accurate application offracture mechanics

principles requires complicated three-dimensional finite element analysis that can take this into

account. However, in spite ofthese limitations, linear fracture mechanics principles can be used

to develop practical models for predicting cracking in pavements.(3) Following is a description of

the approach that was used in this study.

Application of Stress Intensity Factor in Damage Analysis

Several studies have shown that Paris's crack growth law can be used to model crack propagation

in pavement materials such as PCC. It is stated mathematically as follows:<3. 51)

99
where

dc/dN

K =

A,n =

dN

rate of crack propagation through pavement material

stress intensity factor

fracture properties ofthe pavement material

(71)

Integrating equation 71 yields equation 72, which can be used to estimate the number ofrepeated

stress applications it will take for the crack to propagate through the PCC slab. The number of

repeated stress applications is also called the allowable number ofload applications to failure,

that is, the number of cycles it will take for a crack to propagate through the PCC slab.

(72)

where

Nj number ofload cycles to failure

Co initial crack length, 0 mm

Cr final crack length, slab thickness, mm

K stress intensity factor, kPa/mm2

A, n fracture properties ofthe materials

The stress intensity factor is required to use equation 72. It can be determined using a modified

version ofthe ILLISLAB finite element analysis program.(52) However, since this modified

ILLISLAB program is not yet readily available, it was necessary to develop mathematical

expressions for calculating the integral ofthe stress intensity factors.

Determination of Stress Intensity Factor

Figures 37 and 38 show a PCC slab subjected to wheel and temperature stresses at the

midsection and comers ofthe slab, respectively. The mode of crack propagation ofinterest at

these locations is bending, or mode I crack propagation. A modified version ofILLISLAB, a

two-dimensional finite element program, was used to model the stresses and cracks at the

midsection and the comers of a PCC slab.(52)

The finite element analysis approach used is as follows:

• The PCC slab was modeled as a plain strain elastic material.

• The pavement foundation was modeled as a Winkler foundation with k-values

represented by equivalent spring constants.

100
• The JPCP slab was assumed to have no load transfer.

• An 80-kN axle load placed at the PCC slab comer and midsection was used to model

stress applied by traffic loading.

• A temperature gradient from 3 to 11 DC was used to model the effects oftemperature

differentials through the pavement, depending on the PCC slab thickness.

Following is the procedure used to analyze the ILLISLAB output to obtain the stress intensity

factor:(52)

1. A finite element model was developed to calculate stresses, strains, and moments with a

given PCC pavement structure with a partial crack. The elements at the zone around the

crack tip were modified to take the effect ofsingularity into account when estimating the

stress intensity factor at the crack tip.

2. Calculate the moment, stress, rotation, and displacement for the nodes ofthe finite

element model around the crack tip. This will be done for different crack positions, or

crack length to PCC slab thickness ratios (a/h). Note that for a/h = 0, the PCC slab has no

crack present; for a/h = 1, the slab is fully cracked.

3. The stress intensity factor at the tip ofthe crack can then be determined using the

equation shown below:

where

=

mode I stress intensity factor from the crack tip, kPa/mm2

PCC slab thickness, mm

stress due to restraint at the slab edges, kPa

geometric functions that are a function of a/h

crack depth, mm

bending moment in the slab from imposed stresses, kN-m

(73)

The geometric functions,J; and./;" are defined as follows:

(74)

101
(75)

where

a/h =

1t =

h =

ratio of crack length to slab thickness

3.142

PCC slab thickness, mm

Using this approach, the stress intensity factor was calculated for each pavement section in the

LTPP database. The finite element model accounted for both traffic-imposed stresses and

positive and negative (daytime and nighttime) temperature gradient curling. The variables used

in calculating stresses at the edge and midsections ofthe PCC slab include slab thickness,

modulus of elasticity, Poisson's ratio, slab length, coefficient of expansion of concrete, and

subgrade k-value.

102
Wheel Load

t Crack

PCC

I - _ _ - ==111

III = =111==1 ==1 ==~ =111_111 1JI=III= - 111I11111 III 111 = III = III _ III = =111 ==

SUbgrade -

Figure 37. Pavement deformation with wheel load placed directly over the plane with the crack.

Wheel Load

Crack

I I I I I I I-II I I I II I I II I-II I I 11-1II I I II I

Subgrade

PCC

111== 111= = II 111-1 --

Figure 38. Pavement deformation with wheel load placed at the comer ofthe slab.

103
Development of Stress Intensity Factor Models

This section describes the method used to obtain a database ofstress intensity factors, crack tip

locations, and other pavement properties that were then used to develop models for predicting the

stress intensity factors at both the midsections and corners ofPCC slabs. The model development

and integration procedure is summarized as follows:

1. Use the database ofpavement properties and stress intensity factor from the ILLISLAB

runs to develop models for determining stress intensity factor ofthe following form:

f (aJh, pavement properties) (76)

2. Numerically integrate the stress intensity factor equation in the form (dc/KD=AN) for aJh

= 0 to 1 to obtain values for the factorial ofpavements. In this study, n values ranging

from 1 to 3 were used to obtain the integral ofthe stress intensity factor for the factorial.

3. Using the results obtained, develop an empirical model that can be used to determine the

integral ofstress intensity factor for the database ofpavement properties in the LTPP

database.

Note that from Paris's law the integral of(dc/KD) is related to the number of allowable load

repetitions as follows:

Cf

AN. = f de = f(pavement properties) 1 K n

Co (77)

Therefore, ANi can be related to the model for determining the integral ofstress intensity factor

as follows:

ANi = f (pavement properties) (78)

The model for estimating the allowable number ofload repetitions can therefore be determined

as follows:

Nj = Po f(pavement properties)

where

(79)

N·I

Po

allowable number ofload repetitions

VA

Allowable Load Repetitions Models

Using the approach outlined above, models for estimating the allowable number ofload

repetitions, which is the product ofP = VA, the fracture properties ofthe material, and the

integral of dc/KD, were developed for corner breaks and transverse cracking. Following are the

equations that were developed:

104
Corner Breaks

PE(-0.02 + 5.507*10-9

Epcc + 1.5063*10·4hpcc - 4.564*1O-12Epcchpcc

+ 1.0082*10·sEpcc2

)

Transverse Cracking

(80)

elastic modulus ofPCC pavement, kPa

PCC slab thickness, mm

1/A

Ni

where

Epcc

hpcc

Pi =

= PTc(0.0056 + 8.7*10-IIEpcc - 4.724*1O-S

hpcc - 1.7117*10-I3Epcchpcc

+ 1.056*1O-6hpcc2) (81)

Development of Empirical Scaling Factors

The empirical scaling factors to be used in model calibration were selected from the LTPP

database on the basis of a review of existing cracking models. The data for development of

comer breaks and transverse cracking models for JPCP were obtained from the GPS 3 sections.

The database was evaluated thoroughly to check for gross errors, cleaned, and prepared for

analysis. A comprehensive statistical analysis ofthe cleaned data was conducted to evaluate the

preliminary relationships between the measured transverse cracking and the explanatory

variables, including cluster variables. Tables 17 and 18 are correlation tables that show the

strength ofthe relationships between the independent variables and comer breaks for JPCP, the

relationships between the independent variables and transverse cracks for JPCP, and the

relationship between the variables themselves. Figures 39 and 40 are bivariate plots ofthe

distress versus the potential independent variables for transverse cracking and comer breaks,

respectively.

Calibration Procedure for Transverse Cracking and Corner Break Models

In the previous sections, the model forms for estimating the allowable number of 80-kN

equivalent axle load repetitions and the final cracking model form were selected. Calibration was

accomplished using the LTPP database and optimization techniques to find values for the

regression parameters that best match field data. The calibration procedure is summarized as

follows:

1. Select initial starting values and variables for the parameters, ai' a2, P, m, n, and C =

, f(climate variables).

2. For the 80-kN ESAL load, calculate the number ofload applications to failure.

3. Estimate total damage using the model based on Miner's damage equation (equation 70).

105
4. For the given set ofthe cracking and damage data, perfonn nonlinear regression or

optimization analysis to detennine the values ofthe cracking model parameters aI' a2, p,

n, and C that minimize the error function given below:

ERR(al' a2, A, n, C) = L (PredictedDistress - MeasuredDistresi (82)

5. Repeat steps 2,3, and 4 until the regression parameters that minimize the error function

are obtained.

106
o-........

Table 17. Correlation matrix for selected variables for JPCP comer break model.

FI FTCYC PRECIP WTOYS MAXT MINT MTEMP 090 032 EPCC lTSP HPCC HB EB Cd KvaIue KESAL 

FI 1 0.12891 -0.30987 -0.10834 -0.61918 -0.55818 -0.59389 -0.44905 0.50446 0.12714 -0.19632 -0.00485 -0.0809 -0.27989 -0.30367 -0.40043 -0.1536

FTCYC 0.12891 1 -0.61932 -0.57251 -0.75339 -0.84469 -0.80856 -0.69399 0.88922 0.13766 -0.35459 0.12129 -0.32083 -0.00551 -0.24247 -0.19671 -0.1081

PRECIP -0.30987 -0.61932 1 0.80856 0.63192 0.74007 0.69456 0.41471 -0.68036 0.00719 0.58853 -0.09631 0.16193 0.07879 -0.00319 0.11511 -0.0818

WTOYS -0.10834 -0.57251 0.80856 1 0.40854 0.58877 0.5062 0.16329 -0.5032 0.09215 0.37037 -0.20513 0.23031 -0.17289 -0.04768 0.0849 -0.2066

~AXT -0.61918 -0.75339 0.63192 0.40854 1 0.95913 0.98919 0.89573 -0.95294 -0.34259 0.45366 -0.02888 0.23518 0.26349 0.44367 0.39097 0.1725

MINT -0.55818 -0.84469 0.74007 0.58877 0.95913 1 0.99025 0.82878 -0.97037 -0.21722 0.44025 -0.01777 0.28268 0.18187 0.32812 0.37175 0.0934

MEANT -0.59389 -0.80856 0.69456 0.5062 0.98919 0.99025 1 0.87033 -0.97188 -0.28124 0.45148 -0.02344 0.26226 0.22392 0.3884 0.38503 0.1334

090 -0.44905 -0.69399 0.41471 0.16329 0.89573 0.82878 0.87033 1 -0.83644 -0.3656 0.34464 0.08135 0.16168 0.34147 0.47126 0.49402 0.1350

032 0.50446 0.88922 -0.68036 -0.5032 -0.95294 -0.97037 -0.97188 -0.83644 1 0.23447 -0.43953 0.04592 -0.29883 -0.19396 -0.34258 -0.34619 -0.2128

EPCC 0.12714 0.13766 0.00719 0.09215 -0.34259 -0.21722 -0.28124 -0.3656 0.23447 1 -0.22497 0.12909 -0.00314 -0.14677 -0.50245 -0.16991 -0.2113

TSP -0.19632 -0.35459 0.58853 0.37037 0.45366 0.44025 0.45148 0.34464 -0.43953 -0.22497 1 0.02662 -0.06332 0.0201 0.1123 0.13188 0.0163

HPCC -0.00485 0.12129 -0.09631 -0.20513 -0.02888 -0.01777 -0.02344 0.08135 0.04592 0.12909 0.02662 1 0.06334 0.37325 -0.16222 0.03189 0.1665

HB -0.0809 -0.32083 0.16193 0.23031 0.23518 0.28268 0.26226 0.16168 -0.29883 -0.00314 -0.06332 0.06334 1 -0.1128 -0.0719 0.04313 -0.1165

IEB -0.27989 -0.00551 0.07879 -0.17289 0.26349 0.18187 0.22392 0.34147 -0.19396 -0.14677 0.0201 0.37325 -0.1128 1 0.22586 0.17771 0.2010

K:d -0.30367 -0.24247 -0.00319 -0.04768 0.44367 0.32812 0.3884 0.47126 -0.34258 -0.50245 0.1123 -0.16222 -0.0719 0.22586 1 0.40539 0.0604

Ir<vaIue -0.40043 -0.19671 0.11511 0.0849 0.39097 0.37175 0.38503 0.49402 -0.34619 -0.16991 0.13188 0.03189 0.04313 0.17771 0.40539 1 -0.1223

KESAL -0.15367 -0.10811 -0.08188 -0.20666 0.17258 0.09347 0.13341 0.13503 -0.21288 -0.21131 0.01631 0.16657 -0.11654 0.20109 0.06043 -0.12238 

AGE -0.10516 -0.08101 -0.00806 -0.15485 0.11283 0.0704 0.09205 0.07687 -0.16009 -0.0259 0.18986 0.13369 -0.00607 -0.07446 -0.23663 -0.10809 0.5637

rB 0.06936 -0.02442 0.10098 0.00916 0.08185 0.02299 0.0522 -0.01756 -0.05403 -0.35674 0.23111 -0.26215 -0.09276 -0.02849 0.03059 -0.0851 0.3245
.. .. .. 20 -: 20 ...

.. 20

i!! i!! i!! lXl lXl • lXl

.. 15 • li; 15 li; 15 • c .. E .. E • :; 0 0

U 10 ,. U 10

•• U 10

:; .c • E ••

j

•

• • • i .. 5 5 •• • • • •

, ... .. _.. t. .. 5

• .Q • .Q • • .Q

.!l! .!l! .!l! • til 0 til 0 til 0 >!1 'if. 30 40 'if. 0 10 20 30 40 0 10 20 0 50 100 150

Age,yr ESAL's (millions) k-value, kPa/mm

.. .= 20 20 ... .. .= 20 .. i!! .. i!! lXl i!! lXl 15 • 15 • lXl

.. .. 15 •

E .. c

• :; 0 E

u 10 u 10 0 •

•• • U 10

E • • E • • .c .. •• • .. i .. 5 .. 5 • •

• .Q • .. 5 .Q

... .!l! • .... • • • .Q • • .!l! .!l! til til til

'if. 0 'if. 0 'if. 0

4 6 8 10 0 500 1000 1500 20000 30000 40000 50000

Joint spacing, m Freezing Index, DC Days PCC slab modulus, MPa

.. .= 20 .. 20 .. 20 i!! i!!

lXl i!! lXl 15 • lXl 15 • .. .. E .. 15 •

E • 0 0 • E u 10 u 10 0 •

: .c • • U 10 .c • i • •• i • • • :; • 5 • .. 5 j .. • •• ..t .Q • * t. .. 5

•• • .Q

.!l! • • • .!l! .Q

til 0 til .!l! • >!1 0 til 0 'if. 100 150 200 250 300 0.7 0.9 1.1 1.3 'if. 0 50 100 150 200

PCC slab thickness, mm Drainage coefficient, Cd Annual freeze-thaw

cycles, days

.= 20 .. .= 20 .= 20 i!! .. .. lXl i!! i!! 15 • lXl 15 • lXl ..

c .. 15 •

is • E .. • E u 10 •• 0

.c U 10 0 •

t u 10 i • .c • •

• • • i :; .. 5 • • • •• j

• .Q •• • • •• .. .. 5

t. • .. 5 .!l! .Q

•• • • .Q .!l! ... •••• • til 0 til .!l! .... til 'if. 0 0 0 0.5 1.5 'if. 60 120 180 0 20 40 60 80 100 Precipitation, m Annual number of Annual number of days with wet days temperature above 32 DC

Figure 39. Plot ofpercentage ofslabs with comer breaks versus significant

variables for ]PCP.

108
......

o

....0

Table 18. Correlation matrix for selected variables for JPCP transverse cracking model.

FI FTCYC PRECIP WTOYS MAXT MINT MEANT 090 032 JTSP HPCC EPCC HB KESAL AGE CO 

FI 1 0.13982 -0.3171 -0.0845 -0.6175 -0.5546 -0.5912 -0.4442 0.50483 -0.2522 0.03989 0.2136 0.08901 -0.1206 -0.1173 -0.2631 

FTCYC 0.13982 1 -0.6559 -0.5476 -0.751 -0.8556 -0.8129 -0.6912 0.88802 -0.3357 -2E-05 0.2062 -0.4112 -0.0583 -0.0099 -0.2297 

PRECIP -0.3171 -0.6559 1 0.78913 0.63895 0.74183 0.69882 0.40997 -0.6962 0.66681 -0.1141 -0.1808 0.22045 -0.1185 -0.1468 0.05191 

IwTOYS -0.0845 -0.5476 0.78913 1 0.34869 0.52063 0.44133 0.07311 -0.4591 0.37199 -0.2757 -0.1995 0.26624 -0.2378 -0.3033 0.09892 

MAXT -0.6175 -0.751 0.63895 0.34869 1 0.95938 0.98928 0.89062 -0.9559 0.43065 0.03074 -0.2957 0.34519 0.2214 0.08244 0.36674 

MINT -0.5546 -0.8556 0.74183 0.52063 0.95938 1 0.9903 0.83233 -0.9793 0.43034 0.02075 -0.2727 0.34644 0.13077 0.03578 0.28808 

MEANT -0.5912 -0.8129 0.69882 0.44133 0.98928 0.9903 1 0.86963 -0.9779 0.43499 0.02588 -0.2869 0.34948 0.17681 0.05913 0.32981 

090 -0.4442 -0.6912 0.40997 0.07311 0.89062 0.83233 0.86963 1 -0.8349 0.2667 0.1708 -0.1776 0.34627 0.22488 0.12826 0.31901 

032 0.50483 0.88802 -0.6962 -0.4591 -0.9559 -0.9793 -0.9779 -0.8349 1 -0.4332 -0.0396 0.29169 -0.3662 -0.1749 -0.0904 -0.3074 

JTSP -0.2522 -0.3357 0.66681 0.37199 0.43065 0.43034 0.43499 0.2667 -0.4332 1 0.01526 -0.3945 -0.0943 0.07407 0.09979 0.04123 

HPCC 0.03989 -2E-05 -0.1141 -0.2757 0.03074 0.02075 0.02588 0.1708 -0.0396 0.01526 1 0.21021 -0.0885 0.32944 0.14587 -0.1444 

EPCC 0.2136 0.2062 -0.1808 -0.1995 -0.2957 -0.2727 -0.2869 -0.1776 0.29169 -0.3945 0.21021 1 0.01797 -0.1786 -0.1061 -0.2202 

HB 0.08901 -0.4112 0.22045 0.26624 0.34519 0.34644 0.34948 0.34627 -0.3662 -0.0943 -0.0885 0.01797 1 0.15259 -0.1066 0.11341 

KESAL -0.1206 -0.0583 -0.1185 -0.2378 0.2214 0.13077 0.17681 0.22488 -0.1749 0.07407 0.32944 -0.1786 0.15259 1 0.60192 0.04439 

AGE -0.1173 -0.0099 -0.1468 -0.3033 0.08244 0.03578 0.05913 0.12826 -0.0904 0.09979 0.14587 -0.1061 -0.1066 0.60192 1 -0.2625 

CO -0.2631 -0.2297 0.05191 0.09892 0.36674 0.28808 0.32981 0.31901 -0.3074 0.04123 -0.1444 -0.2202 0.11341 0.04439 -0.2625 1 

Kvalue -0.3778 -0.1425 0.1538 0.10001 0.41848 0.34587 0.38518 0.43481 -0.334 0.19848 0.06101 -0.0952 0.14518 -0.0756 -0.1585 0.5457 

TC -0.1181 -0.0656 0.07909 0.06874 0.1962 0.17338 0.18645 0.18221 -0.1311 0.1756 0.29021 -0.3424 -0.0532 0.57422 0.09209 0.19523 
., ., .. .. 70 ., eo .. eo > 60 -. > > .. • .. • •• .. ..

c ... 50 :i Of 60 :; C) 60 • • • c c • c • ~:;;: 40 • ~- ~-

30 • =- .. 40 • • E 40 • •

: 0 20 • .- .. ° 20 • • • .. ° 20

.!!

Ul

'" ,10

0 .!! '"

Ul 0 ....... iii '".. 0 --~ • 0 40 80 120 ..... 0 0.5 1.5 2 ..... 0 20 40

k-value, kPa/mm Precipitation, m Age, yr

.. eo ., • • >.. 60 c

.....c • ~-E 40 • • .. 0

* '".. 20 .. iii

..... 0 • 150 200 250 300 350

PCC slab thickness, mm

., 80 .. • •• >.. 60 c

.. ...

c • ~-

:5 40 - .. •• .. 0

'" • 20 ..

iii • • ..... ... : 0

* .6_·

20000 30000 40000

PCC slab modulus, kPa

50 100

• •

•

., eo ., • >..

c 60 • .. '"c • ~-

:: 40 - .. • • .. 0

20 '" • • ..

iii

.....

100 200

Annual number of air

freeze-thaw cycles

Annual number of days with

temperature above 32 ·c

., 80 ,.----------,

.,

> 60 .. ... ~.5

E 40 :0

'".. 20

iii

.....

., 80

.. • >.. 60 # c

l! ... • ~.:

:: 40 -

.. 0

.. • 20 '" • • ..

iii

..... 0 .- • 2 4 6 8

Joint spacing, m

.. 80 .,

> • • • ..

c 60 • .. ...

c ~-

:5 ti 40 • - .. • .. 0 20 '" • •• ..

iii • • t ..... 0 •• • 0.7 0.9 1.1 1.3

Drainage coefficient

Figure 40. Plot ofpercentage oftransverse cracking versus significant

variables for JPCP.

110
Final Corner Breaks Model

Estimatinll Damaf:e Due to Temperature and Traffic Loadinf:

Damage to the pavement from the imposed stresses was calculated using Miner's cumulative

damage equation (equation 70). The damage for both traffic and temperature stresses was

calculated as follows:

= [ KESAL] 0.75 DAMTRCB NTRCB

_ [ AGE ]0.25 DAMTECB - --

NTECB

where

(83)

(84)

KESAL

AGE

Nj

=

=

=

cumulative number ofESAL's/l 000

pavement age in years

allowable number ofload repetitions

Allowable Number ofLoad Repetitions Model

The final model for estimating Nj for traffic was as follows:

(5.6 + 8.7*1O-s

Epcc - 4.724*1O-2hpcc - 1.7*10-10 Epcchpcc

+ 1.056*10-3hpcc2)2.93 (85)

The final model for estimating Nj for temperature was as follows:

where

NTECB = (5.6 + 8.7*1O-s

Epcc - 4.724*10-2hpcc - 1.7*10-10 Epcchpcc

+ 1.056*10-3hpcc2)s.s (86)

Epcc = hpcc =

PCC slab modulus, kPa

PCC slab thickness, mm

Final Form ofComer Breaks Model

The final model for predicting the occurrence of comer breaks is as follows:

SWCB = 100*(24.26JTSP + 2.236AGE - 9.95*1O-7Epcd DAMTEcB

+ 100*(3.08*1O-3

FTCYC - 3.78*1O-3

Cd) DAMTRcB

111

(87)
where

SWCB

JTSP

AGE

Epcc

DAMTECB

FTCYC

Cd

DAMTRCB

Statistics:

R2

N

SEE

p-value

=

=

=

=

<

percentage ofslabs with comer breaks

pavement joint spacing, m

pavement age, yr

elastic modulus ofPCC, kPa

damage due to temperature stresses

annual number offreeze-thaw cycles

drainage coefficient

damage due to traffic stresses

0.69

92

9 percent

0.0001 (significance ofmodel)

A plot ofthe predicted and measured percentage ofjoints with comer breaks is shown in figure

41. A plot ofthe residuals (predicted - actual percentage ofjoints with comer breaks) against the

predicted percentage ofjoints with comer breaks is shown in figure 42. The overall accuracy of

the comer breaks model is reflected by the R2 of 0.69, which is the proportion of variation of

comer breaks explained by the variables included in the model. A test of hypothesis was

performed to determine the significance ofthe variables used in the model for predicting comer

breaks. The null and alternate hypotheses were as follows:

Ho: all model parameters are zero (variables are not significant)

HA: all model parameters are not zero

The F-test statistic used for the hypothesis test was calculated as the ratio ofthe mean square for

the model divided by the mean square ofthe error. For this study, the null hypothesis will be

rejected ifthe level ofsignificance is less than 5 percent (0.05). A level ofsignificance (p-value)

ofless than 0.0001 implies a rejection ofthe null hypothesis. This shows that the variables in the

model are highly significant. Also, individual t-tests were conducted to test ifthe individual

parameter estimates are equal to zero. The p-values for this test ranged from 0.0001 to 0.001. The

results shows that all the parameter estimates had values other than zero; therefore, the variables

in the model were significant. Prediction accuracy of comer breaks in absolute units is reflected

by the standard error of estimate (SEE = 9 percent). This value was found to be reasonable. The

overall effectiveness ofthe model should be judged on all the diagnostic statistics, the residual

plots, and the results from the sensitivity analysis to follow. The diagnostic statistics obtained for

the comer breaks model show that the model can predict comer breaks with reasonable accuracy

for the LTPP data utilized.

112
30

•

•

•

• •

•• •

4. t •

•

• I

o 10 20

0+--------+--------+-----------1

10

en 30 .,-----------------------,

Cl:l

OJ

,.Q

o 20

u

-:S-

.....

en

~-­

.......

en

"'0

2

u.....

"'0

OJ

&::

Measured slabs with corner breaks (%)

Figure 41. Measured versus predicted percentage of slabs with corner breaks.

12 --.----------------------------,

25

•

15 20

•

•

•

•

4 /_.:.

o +-----:;;~---'..~.t______4r'.~--_t_----_+---------lI__---___j , ..

8

(~

-4

-8

-12 -L- --'

Predicted slabs with corner breaks (%)

Figure 42. Plot of residuals versus predicted percentage of slabs with corner breaks.

113
Final Transverse Cracking Model

Estimatin2 Dama2e Due to Temperature and Traffic Loading

The damage to the pavement from the imposed stresses can be calculated using a modified form

ofMiner's cumulative damage equation.The modified damage equations for estimating both

traffic and temperature stresses are as follows:

where

KESAL = AGE = NfRTC = NTETC =

DAM = ( KESAL1o.S . TRTC N

TRTC

_ ( AGE ]0.7S DAMTETC - --

N TETC

cumulative number ofESAL's, thousands

pavement age, yr

allowable number ofload repetitions for traffic loads

allowable number ofload repetitions for climate-related loads

(88)

(89)

Allowable Number ofLoad Repetitions Model

The final model for estimating Nj for traffic is as follows:

(-2.0*104 + 5.507*10-3Epcc + 150.63hpcc + 4.564*1O-6Epcchpcc

+ 0.744hpcc

2

)1.33 (90)

The final model for estimating Nj for temperature is as follows:

where

NTETC = (-2.0*104 + 5.507*1O-3

Epcc + 150.63hpcc + 4.564*10-6Epcchpcc

+ 0.744hpcc

2)2 (91)

PCC slab modulus, kPa

PCC slab thickness, mm

Final Form ofTransverse Crackinll Model

The final model for predicting transverse cracking is given as follows:

TC = 100*(50.8FTCYC - 3.2* lO-s

Epcd DAMTETc

+ 100*(0.274WTDYS + 0.432D32) DAMTRTc

114

(92)
where

TC

FTCYC

Epcc

DAMTETC

WTDYS

D32

DAMTRTC

Statistics:

R2

N

SEE

p-value

=

=

=

=

=

=

=

<

percentage ofslabs with transverse cracks

annual number offreeze-thaw cycles

elastic modulus ofPCC, kPa

damage caused by temperature stresses

annual number ofwet days

annual number of days with temperature above 32 °C

damage caused by traffic stresses

0.64

92

12

0.0001 (significance ofmodel)

A plot ofthe predicted and measured percentage ofslabs with transverse cracking is shown in

figure 43. A plot ofthe residuals (predicted - actual percentage ofslabs with transverse cracking)

against the predicted percentage ofslabs with transverse cracking is shown in figure 44. The

overall accuracy ofthe transverse cracking model is reflected by the R2 of 0.64, which is the

proportion of variation oftransverse cracking explained by the variables included in the model.

A test ofhypothesis was performed to determine the significance ofthe variables used in the

model for predicting transverse cracking. The null and alternate hypotheses were as follows:

Ho : all model parameters are zero (variables are not significant)

HA : all model parameters are not zero

The F-test statistic used for the hypothesis test was calculated as the ratio ofthe mean square for

the model divided by the mean square ofthe error. For this study the null hypothesis will be

rejected ifthe level ofsignificance is less than 5 percent (0.05). A level ofsignificance (p-value)

ofless than 0.0001 implies a rejection ofthe null hypothesis. This shows that the variables in the

model are highly significant. Also, individual t-tests were conducted to test ifthe individual

parameter estimates are equal to zero. The p-values for this test ranged from 0.001 to 0.035.

115
0) 100 CfJ

!i:l

> --* CfJ

l:: en

ro 0) 75

t: .,l:l

..... -:S I-<

0)

..... 0)>

CIJ

CIJ ...... 50 ...... ro ...... CIJ

"- •

b.O •

'1j .s 25 0)

I-< U •

;:l ro :.. •• CIJ l-l

•

ro u ••

o I 0) •I' • :;s •

a 25 50 75 100

Predicted slabs with transverse cracking (all severities, %)

Figure 43. Measured versus predicted percentage of slabs with transverse cracking.

50

•

•

25 • • • • CfJ ......

ro •

;:l •

""d 0 .....

CfJ i \\*1 20 0) 30 40 5

-25

-50 --'-------------------------------'

Predicted slabs with transverse cracking (all severities, %)

Figure 44. Plot of residuals versus predicted percentage of slabs with transverse

cracking.

116
The results show that all the parameter estimates had values other than zero; therefore, the

variables in the model were significant. Prediction accuracy oftransverse cracking in absolute

units is reflected by the standard error of estimate (SEE = 12 percent). The overall effectiveness

ofthe model should be judged on all the diagnostic statistics, the residual plots, and the results

from the sensitivity analysis to follow. The diagnostic statistics obtained for the transverse

cracking model show that the model can predict transverse cracking with reasonable accuracy for

the LTPP data utilized.

Sensitivity Analysis

The mechanistic-empirical models developed for predicting comer breaks and transverse

cracking were evaluated to determine trends predicted by the models and engineering plausibility

ofthe results obtained. The models were also checked against previous empirical and theoretical

observations.

Comer Breaks Model

The effects ofthe significant variables that influence the occurrence of comer breaks according

to the mechanistic-empirical model developed are discussed in the next few sections.

Effect ofAge and Traffic

The number oftemperature stress cycles the pavement is subjected to directly relates to the age

ofthe pavement. Also, the number of 80-kN ESAL's applied to the pavement gives an estimate

ofthe traffic stress cycles the pavement has undergone. An increase in both ofthese stress cycles,

which can occur separately or simultaneously, increases both damage to the pavement and the

amount of distress on the pavement. Figures 45 and 46 confirm this trend.

Effect ofPCC Thickness

Figure 47 is a plot of percentage ofslabs with comer breaks versus cumulative ESAL's for

different slab thicknesses. The plot shows a rapid increase in the amount of comer breaks in a

pavement as the slab thickness decreases. This is in agreement with the fact that it will take

longer for a microcrack to propagate from the bottom to the top of a PCC slab as the slab

thickness increases.

117
20

--ra

"-"

rJJ

,...l4

ra 15

Cl) ...-... !-<

..0

!-< .. Cl) rJJ

l::: Cl)

'+:l !-< ..... 10 0 !-< U Cl)

.£ Cl) > ,.... rJJ

rJJ 5

..0

co

-

Cf)

O..---------t----------+------------l

o 10

Age (yr)

20 30

Figure 45. Plot of percentage of slabs with corner breaks versus pavement age.

20 -,--------------------------,

rJJ

co

Cl) ...-... 15 !-<

..0

!-< .. Cl) rJJ

l::: Cl)

..... !-< ... 0 ..... U !-<

Cl) 10

...c: > ... Cl) ..... rJJ

rJJ --co

..0 "-" 5 co

-

Cf)

0..--------+--------+--------1

o 10 20 30

ESAL's (millions)

Figure 46. Plot of percentage of slabs with corner breaks versus cumulative ESAL's.

118
80

--+- PCC thickness = 150 mm

C/) - PCC thickness = 225 mm

lIS 60

OJ -.. -.-PCC thickness = 300 mm l-<

,.0

l-< .. OJ C/)

r:: OJ .... l-< .... 0 .... U OJ

l-< 40

.£.... C/)

.-

.- C/) lIS

{l "-"

.- 20

Cf)

o 10

ESAL's (millions)

20 30

Figure 47. Plot of percentage of slabs with corner breaks versus cumulative ESAL's for

different slab thicknesses.

Effect ofFreeze-Thaw Cycles

Figure 48 is a plot ofpercentage ofslabs with comer breaks versus cumulative ESAL's for

different levels offreeze-thaw cycles. The plot shows that there is a rapid increase in the amount

of comer breaks in a pavement as the level offreeze-thaw cycles increases. This is in agreement

with empirical data that show that subjecting concrete to freezing and thawing weakens the

concrete material and makes it susceptible to distress.

Effect ofJoint Spacing

Figure 49 is a plot ofpercentage ofslabs with comer breaks versus cumulative ESAL's for

different pee joint spacing. The plot shows that there is an increase in the amount of comer

breaks in a pavement as the joint spacing increases. This is in agreement with engineering

principles.

119
20

-+-JTSP = 3 m C/)

ca -JTSP=6m

Q) ...- 15

,.a ---.-JTSP = 9 m ... Q) C/)

l:: Q)

',c

0 ..... u Q) 10

o£l Q) > ..... C/)

C/) --ca

,.a -- 5

ca

-

Cf)

0

0 10 20 30

ESAL's (millions)

Figure 48. Plot of percentage of slabs with corner breaks versus cumulative ESAL's

for different levels of joint spacing.

30

-.-FTCYC = 2 C/)

--FTCYC= 70 ca

Q) ...- ,.a ---.- FTCYC = 170

20

Q) en

l:: Q)

.....

.... 0 ..... u Q)

...c: > .... Q) ..... C/)

10 C/) --ca

,.a

ca -- -

Cf)

0

0 10 20 30

ESAL's (millions)

Figure 49. Plot of percentage of slabs with corner breaks versus cumulative ESAL's for

different levels of freeze-thaw cycles.

120
Transyerse Cracking Model

The significant variables that influence the occurrence oftransverse cracks, according to the

mechanistic-empirical model developed, are discussed in the next few sections.

Effect ofAge and Traffic

This is similar to the trends obtained for the transverse cracking model. The number of

temperature stress cycles to which the pavement is subjected directly relates to the age ofthe

pavement. Also, the number of 80-kN ESAL's applied to the pavement gives an estimate ofthe

traffic stress cycles the pavement has undergone. An increase in both ofthese stress cycles,

which can occur separately or simultaneously, increases damage to the pavement and therefore

increases the amount of distress on the pavement. Figures 50 and 51 confirm this trend.

Effect ofPCC Thickness

Figure 52 is a plot of percentage ofslabs with transverse cracks versus cumulative ESAL's for

different slab thicknesses. The plot shows a rapid increase in the amount oftransverse cracking

in a pavement as the slab thickness decreases. This is in agreement with the fact that it takes

longer for a microcrack to propagate from the bottom to the top of a PCC slab as the slab

thickness increases.

Effect ofFreeze-Thaw Cycles

Figure 53 is a plot of percentage ofslabs with transverse cracking versus cumulative ESAL's for

different levels offreeze-thaw cycles. The plot shows that there is a rapid increase in the number

of comer breaks in a pavement as the level offreeze-thaw cycles increases. This is in agreement

with empirical data that show that subjecting concrete to freezing and thawing weakens the

concrete material and makes it susceptible to distress.

Effect ofthe Number ofWet Days and Days with Temperature Above 32°C

Figures 54 and 55 are plots of percentage ofslabs with transverse cracking versus cumulative

ESAL's for different levels ofwet days and days with temperature above 32°C. Both plots

indicate that with more wet days and higher temperatures there are corresponding higher levels

oftransverse cracking. This is in agreement with empirical data because pavements in wet

environments tend to have weaker and eroded foundations as the pavement structure ages, and

higher temperatures generate higher stresses in the pavement slab.

121
60

.-

50 rn

0

.-.....

.-

1-1

0

40

--

--gp

:.g 30

1-1

...... U

tv 0

tv rn

1-1

20 0

>rn

oS 10 .-

rn

Cf) - 0 ... 

0 10 20 

Age (yr)

Figure 50. Plot of percentage of slabs with transverse cracking versus pavement age.
60 ..........

*... C1J

Q)

:-E 50

l::

Q)

;;-

Q)

C1J

40 '-'"

00

]

30 l-l

U

Q)

C1J

l-l

Q)

20

..... b N

\j.)

.£i

..... 10 C1J

en

0

0 10 20 

ESAL's (millions)

Figure 51. Plot of percentage of slabs with transverse cracking versus

cumulative ESAL's.
-

--t/)

u

ctl

I-<

U

Q) -- t/)

I-<

Q) ul

> Q)

..... t/) .... I:: .....

I-< eli Q)

....

I-< >(1)

-:S t/)

.....

t/)

,.0

ctl

-rJ)

80 --,------,r=============,------------,

-+- PCC thickness = 150 mm

- PCC thickness = 225 mm

60 ---...- PCC thickness = 300 mm

40

20

O ----------t-------------t-------------j

o 10

ESAL's (millions)

20 30

Figure 52. Plot of percentage of slabs with transverse cracking versus cumulative ESAL's for

different slab thicknesses.

100 Tr=======::::;--------------~

--ctl

--00

I::

:.l2u

eli

I-<

U -- Q)

ul t/)

I-< Q) Q) ..... > .... ..... t/) I-< I:: Q)

ctl > .t:i Q)

t/)

.£j

.....

t/)

,.0

ctl

-rJ)

75

50

25

o

o

-+-FTCYC = 0

-FTCYC = 70

---...-FTCYC = 170

10 20 30 40

ESAL IS (millions)

Figure 53. Plot of percentage of slabs with transverse cracking versus cumulative

ESAL's for different levels of freeze-thaw cycles.

124
- 100 -etl --+- WTDYS = 50 --bl)

..... l=: -ll-WTDYS = 120

u 75 etl -.-WTDYS = 180 l-< .- U

OJ .. rJ:J rJ:J l-< OJ OJ ..... > .....

4-' 50 rJ:J l-< l=: OJ

l-<

etl >

OJ 4-' rJ:J

...c: 25 4-'

.....

rJ:J

..0

etl

-

cJ) 0

0 10 20 30 40

ESAL's (millions)

Figure 54. Plot of percentage of slabs with transverse cracking versus cumulative ESAL's for

different annual number of wet days.

100

--<1i --+-D32 = a ---- bO -ll-D32 = 50 s:: ..... 75 u -.-D32 = 100 <1i

I-< ---. U

OJ

00 00'0 I-< OJ OJ ..... > .....

.... 50 00 I-<

s:: OJ

I-<

<1i >

OJ .... 00

..c:

.-;::

~, 25. 00

..a

<1i

-

CJ)

0iF----------+----------f---------I

a 10

ESAL's (millions)

20 30

Figure 55. Plot of percentage of slabs with transverse cracking versus cumulative ESAL's for

different number of days with temperatures above 32°C.

125
Summary

Corner Breaks

The following can be summarized about the JPCP comer breaks model:

• Sixty-nine percent ofthe total variation of comer breaks can be explained by the included

variables.

• Some ofthe unexplained variation is caused by errors in the independent variables used

to develop the model, such as the traffic estimates.

• The "average" error in predicting comer breaks is 9 percent.

• There are no discernible patterns in the residuals.

• Data from 92 pavement sections from all over the United States were used to develop the

model (N = 92).

• Each independent variable and the overall model was significant at a level ofsignificance

of 5 percent.

• The sensitivity analysis shows that all ofthe explanatory variables have a plausible effect

on comer breaks that agrees with theoretical expectations and previous empirical field

results.

Transverse Cracking

The following can be summarized about the JPCP transverse cracking model:·

• Sixty-four percent ofthe total variation oftransverse cracking can be explained by the

included variables.

• Some ofthe unexplained variation is caused by errors in the independent variables used

to develop the model, such as the traffic estimates.

• The "average" error in predicting transverse cracking is 12 percent.

• There are no discernible patterns in the residuals.

• Data from 92 pavement sections from all over the United States were used to develop the

model (N = 92).

• Each independent variable and the overall model was significant at a level ofsignificance

of 5 percent.

126
• The sensitivity analysis shows that all ofthe explanatory variables have a plausible effect

on transverse cracking that agrees with theoretical expectations and previous empirical

field results.

Implications and Recommendations

The procedure used to develop the models used fracture mechanics principles for analysis of

crack propagation within a PCC slab at both the center and edge positions. Using a modified

version ofILLISLAB, a two-dimensional finite element model was used to analyze crack

propagation in PCC slabs. Several mathematical expressions were developed for calculating the

integral ofthe stress intensity factor across the thickness ofthe PCC slab. The equations can be

used to estimate the allowable number of applications oftemperature and traffic stresses that it

takes for the crack to propagate across the slab thickness using Paris's crack growth law.

Using the LTPP database, the number ofload applications to failure and the total damage caused

by traffic and temperature loading were determined. Damage to the pavement was determined

using Miner's cumulative damage hypothesis. Statistical and optimization techniques were then

used to obtain mechanistic-empirical models that can be used to predict the percentage ofslabs

with tr,ansverse cracks or comer breaks in JPCP. The models were partially verified by

conducting comprehensive sensitivity analyses. The fracture mechanics approach resulted in

models that reasonably predict transverse cracks and comer breaks.

127

7. ROUGHNESS MODELS

Introduction

Roughness is the irregularity ofthe surface of a pavement. Road users, in general, consider

roughness the most important criterion when evaluating the condition of a road. Rough roads

lead to user discomfort, increased travel times, and higher vehicle operating costs that can lead to

millions of dollars in losses to the general economy. Although the structural performance of a

pavement is most important to highway designers, the complaints generated by rough roads often

contribute to a large part ofthe rehabilitation decisions that are made by State highway agencies.

The importance ofroughness dates back many decades. The AASHO Road Test introduced the

concept ofserviceability as a measure of a pavement's ability to serve the traveling public,

essentially the primary purpose ofroadways.(18) The present serviceability rating (PSR) concept

was adopted as a subjective measure ofthe ability of a pavement to serve the traveling public on

the basis of panel ratings. The history ofthe serviceability ofthe pavement in relation to the

loads appplied was also used to represent the performance ofthe pavement.

For practical purposes, an objective measure ofperformance based on the serviceability concept,

called the present serviceability index (PSI), was developed as a means of determining

performance from physical measurements on the pavement.(53) Although the physical

measurements used in computing PSI included distresses such as cracking and patching, it was

the longitudinal profile or roughness ofthe pavement that provided the major correlation

variable. Several studies since the AASHO Road Test have confirmed roughness as a strong

indicator ofthe serviceability of a pavement, and most State highway agencies rely on roughness

to estimate serviceability.(54, 55, 56, 57) Therefore, models for predicting roughness of pavements are

very important as design checks and in pavement management systems. This chapter describes

the development ofsuch models for predicting the roughness of concrete pavements using the

LTPP database.

Roughness Measure

Road roughness can be defined as "the variation in surface elevation that induces vibrations in

traversing vehicles."(58) Although there are various methods for measuring the roughness of

pavements, one ofthe most common indices used is the International Roughness Index (IRI).(57)

In 1982, the World Bank initiated the International Road Roughness Experiment (IRRE) in

Brazil to study and serve as a reference for all profilic and response type systems that are used to

measure roughness.(59, 60, 61) The experiment resulted in the evolution ofthe IRI.

IRI is a mathematical summary ofthe longitudinal surface profile ofthe road in the wheel path

and is representative ofthe typical vibrations induced in a passenger car by the roughness ofthe

road. IRI was adopted as a standard measure ofroughness for the following reasons:

• It is time stable and can be reproduced easily from elevation data, since it is just a

summary ofthe road profile.

129
• It gives consistently high correlations with the outputs of other roughness measuring

devices at different speeds.

Following the World Bank study, the FHWA adopted IRI as a standard for measuring roughness

and, since 1989, has been requiring all States to report pavement roughness in terms ofIRI units

for paved rural arterials and urban freeways, including Interstates.(57) As a result, IRI, computed

from roughness measurements using the K. 1. Law profilometer, is also used in the LTPP

database as a measure ofroughness. This profilometer uses a noncontact light sensor system to

measure the distance between the vehicle frame and the road surface. It also measures the vertical

motion ofthe vehicle. The difference between the displacement and vehicle motion is computed

and is the raw road profile output stored in the database.

Progression ofRoughness

No one fundamental mechanism can be attributed to the development ofroughness on

pavements. A key factor is the initial smoothness (or roughness) ofthe pavement when it is

constructed. Results from a recent extensive evaluation ofseveral projects showed that initial

smoothness is significantly related to future smoothness for all pavement types.(57) For PCC

pavements, the study found that the initial smoothness was significant to the future smoothness

for over 80 percent ofthe projects evaluated.

An evaluation ofthe LTPP IRI data for GPS 3, 4, and 5 pavement sections also found similar

results.(62) Plots ofthe IRI over time for different pavement designs for the different pavement

types are illustrated in figures 56, 57, and 58. In general, a comparison ofthe plots shows a

remarkable stability in the development ofroughness for the individual pavements. This suggests

that pavements that are constructed smoother will typically stay smoother, and pavements that

are rougher initially will tend to get rougher with time. Therefore, the initial smoothness of a

pavement is very important to the prediction ofthe future progression ofroughness for all

pavements.

For a given pavement with a particular initial smoothness, several factors combine to contribute

to the progression ofroughness. Chief among them are the occurrence and progression of distress

on the pavement. Increasing distress on the pavement will contribute to an increase in the

roughness.

130
J

......................................... In itial IR I

ESAL's or Age-----....-

Figure 56. IRI model form A.

................................................. Initial IRI

ESAL's or Age-----II..•

Figure 57. IRI model form B.(62)

131
InitiallRI

ESAL's or Age------t...

Figure 58. IRI model form C.OI)

The occurrence and progression ofthe distresses are directly related to the deterioration caused

by the application oftraffic loads, the environment, the support provided by the foundation, and

the effects of aging ofthe pavement materials. Therefore, these factors also play an important

part in the progression ofroughness. The ability ofthe design features incorporated into the

pavement to mitigate the deterioration ofthe pavement also has an important effect on the

progression ofroughness.

Evaluation ofExisting Roughness Models

To determine the significant variables associated with the various factors that contribute to the

progression ofroughness, previous models developed for predicting roughness were evaluated.

The models evaluated were mainly empirical models that related IRI to pavement and

environmental variables.

SHRP P-020 Study

In the SHRP P-020 study, models were developed for predicting the IRI of doweled JPCP,

nondoweled JPCP, JRCP, and CRCP.(4)

132
1RIModel for Doweled JPCP

The model developed for doweled JPCP is as follows:

IRI = 105.9 +159.1[ AGE ]+ 2.16JTSP

KSTATIC

where

AGE =

KSTATIC

JTSP

hpcc

EDGESUP

+ 7. 13hpcc + 13.5EDGESUP

pavement age, yr

modulus ofsubgrade reaction, psi/in

joint spacing, ft

PCC slab thickness, in

edge support; 1= tied PCC shoulder, 0= other shoulder type

(93)

In this model, IRI is related to the age ofthe pavement and basic pavement design factors.

According to the model, IRI is positively correlated to age and increases with age. This is

reasonable because pavement distresses that increase the roughness ofthe pavement generally

tend to increase with age. The pavement design features that were found to be significant to IRI

were the modulus ofsubgrade reaction, joint spacing, PCC slab thickness, and the type of edge

support.

1RIModel for Nondoweled JPCP

The SHRP P-020 model developed for nondoweled JPCP is as follows:

IRI = 38.85 + 12.89CESAL + 0.2217FT + 1.5PRECIP - 10.96BASE - 13.7SUBG (94)

where

CESAL

FT

PRECIP

BASE

SG

cumulative number ofESAL's

number offreeze-thaw cycles

precipitation, in

base type; 1=treated (asphalt treated or lean concrete), O=untreated

subgrade type; 1= coarse-grained, O=fine-grained

The most significant variables in this model were the cumulative number ofESAL's and amount

of precipitation. Traffic loading, high number offreeze-thaw cycles, and increased precipitation

were all found to increase roughness. The type of base and subgrade were also found to influence

roughness, with treated bases and coarse-grained soils decreasing roughness. All these trends

indicate a reasonable model.

133
IRI ModeljorJRCP

The model developed for JRCP is as follows:

where

AGE

KSTATIC

hpcc

EDGESUP

PRECIP

IRI O.85AGE + 0.347PRECIP +1390/KSTATIC

+ 21.2hpcc +15.1 EDGESUP - 141

pavement age, yr

modulus ofsubgrade reaction, psi/in

PCC slab thickness, in

edge support; 1 = tied PCC, 0 = other

precipitation, in

(95)

The model predicts IRI as a function ofbasic pavement properties, climatic data, and age. Age is

positively correlated to lRI with an increase in age increasing the predicted 00. This is similar to

the trend observed for JPCP pavements. The other pavement material and design features that

influenced the predicted lRI include the modulus ofsubgrade reaction, the PCC slab thickness,

precipitation, and the PCC slab edge support condition.

1MModelfor CRCP

The SHRP P020 model developed for CRCP is as follows:

00 = 262 + 1.47CESAL - 2.94hpcc - 232.2PSTEEL -29.8WIDENED - 16.8SUBG (96)

where

hpcc

CESAL =

SUBG

PSTEEL

WIDENED

PCC slab thickness, in

cumulative number ofESAL's

subgrade type; 1= coarse-grained, O=fine-grained

percentage ofsteel in PCC slab

presence ofwidened lanes

The CRCP model also predicts lRI as a function ofbasic pavement properties and climatic data.

CESAL is positively correlated to lRI; that is, an increase in the number of 80-kN ESAL

applications increases IRI. The pavement subgrade type and design features such as widened

lanes, percentage ofsteel in PCC slab, and PCC slab thickness were all shown to have an

influence on the predicted IRI.

RIPPER Study

In the FHWA jointed concrete pavement research study commonly referred to as the RIPPER

study, a model for predicting lRI ofJPCP was developed that is based on pavement distresses

such as faulting, spalling, and cracking.(lO) The final model developed for predicting lRI is as

follows:

134
where

99.6 + 2.6098FaultT + 1.84Spall + 2.28*10-6T-crack3

) (97)

FaultT

T-crack

Spall

=

=

total joint faulting per mile, in

total number oftransverse cracks

percentage ofspalled joints

This model presents another approach to developing roughness models. It is based on the

philosophy that IRI should be directly correlated to the pavement distresses that lead to

roughness.

Other LTPP-Based IRI Models

There have been two recent efforts to develop models for predicting IRI on concrete pavements

using the LTPP data.(1I·62) Both ofthese efforts resulted in the development ofmodels for

predicting IRI for JPCP, JRCP, and CRCP. This followed an extensive evaluation ofthe LTPP

data, and they showed that IRI is correlated to a host of pavement design and climatic

variables.(11.62)

Roughness Model Forms

The models reviewed show that a variety ofmethods can be used to develop models for

predicting IRI. They include models that relate IRI to pavement design features and climatic

variables, as well as those that predict IRI directly from distresses. However, the most common

IRI models are those that include a wide range ofpavement design and climatic variables that

potentially, through their influence on the occurrence and progression of distress, influence

roughness. Another important observation common to most ofthe models is that they include an

estimate of an average initial IRI. In spite ofthe difficulty in determining the actual initial IRI

values for the pavements in the databases used, the results obtained are quite consistent when the

estimated average initial IRI values are compared. An examination ofthe models shows that

three main forms have been used in past studies to model roughness.(4. 10. 11.62) The model forms

are shown in figures 56, 57, and 58, and the mathematical expressions for the models are given

by equations 98, 99, and 100, respectively:

Model Form A:

IRI (98)

where

IRI International Roughness Index, mIkm

DET age or cumulative ESAL's

IRIo initial IRI, mIkm

Xi various pavement and climatic variables

aj regression constants

135
Model Fonn B:(62)

[

IRI * IRI ] IRI (t) = e 'ot max 0

IRIo{e 'ot - 1) + IRImax

where

(99)

IRI (t) =

000

~ax =

r (t)

t

IRI at time t, m/km

estimated initial IRI, m/km

estimated long-tenn 00, m/km

growth rate constant

time in years

Model Fonn C:(ll)

where

(100)

initial IRI, m/km

pavement age or cumulative ESAL's at failure

pavement age or cumulative ESAL's

regression parameters that are correlated to pavement structural and climatic

properties

All three models are similar at the initial stages ofthe pavement's life, in the sense that they

agree on the existence of an initial 00 value at the traffic opening date ofthe pavement that

influences the future IRI. However, the progression ofroughness over time is different for each

ofthe model fonns.

Model A assumes a rapid increase in roughness in the initial stages of aging or deterioration of

the pavement. The rate ofincrease decreases appreciably thereafter and approaches a maximum

value asymptotically. Conversely, model fonn B assumes that in the initial stages ofthe

pavement's life the increase in roughness is slow. However, later in life the rate increases

appreciably and IRI continues to increase as the pavement gets rougher. Model C is a

combination ofthe previous two model fonns. It assumes that, for the most part, 00 follows the

trend similar to that described for model fonn A; however, instead ofthe 00 approaching a

maximum value asymptotically, after some point in time the rate ofincrease in roughness once

again increases rapidly with no maximum IRI value.

Preliminary Data Analysis

The procedure outlined previously for developing prediction models was followed to detennine

the explanatory variables and model fonns for the development of00 prediction models.

136
Data Assembly, Cleaning, and Exploration

This included the assembly ofthe data required for the development ofthe models for predicting

IRI ofJPCP, JRCP, and CRCP; the data were obtained from the GPS 3, 4, and 5 experiments, .

respectively. The variables included in the databases were those identified from the review of

literature and existing models for predicting roughness. Table 19 shows the variables that were

included in the investigation. The databases were evaluated thoroughly to check for missing and

erroneous data, cleaned, and prepared for analysis.

The databases were then explored to learn more about their suitability for model development.

This included a comprehensive statistical analysis ofthe cleaned data to evaluate the preliminary

relationships between the measured roughness and the explanatory variables. Univariate

statistical analyses were conducted to learn about the distribution ofthe IRI for each ofthe

pavement types and the explanatory variables. In addition, the data exploration consisted of

evaluation of bivariate plots ofIRI for the different pavement types versus potential independent

variables and correlation studies.

137
Table 19. Variables identified for use in the development ofroughness models.

Symbol Explanatory Variable

FI Freezing index

FTCYC Mean annual number offreeze-thaw cycles

PRECIP Mean annual precipitation, mm

WTDYS Mean annual number ofwet days

TEMP Mean annual temperature, °C

JTSP Joint spacing, m

Cd Drainage coefficient

k value Modulus ofsubgrade reaction, kPa/mm

D90 Mean annual days with temperature above 90°C

BASE Base type, 0 =erodible, 1 =nonerodible

DTYPE Presence of edge drains, 0 =not present, 1 =present

PSTEEL Percentage ofsteel reinforcement in PCC slab

BTHICK Base thickness, mm

BTYPE Base material type, 0 fine, 1 =coarse

PCCthick PCC layer thickness, mm

MAXTEMP Average daily maximum temperature, °C

MINTEMP Average daily minimum temperature, °C

TRANGE Difference in daily maximum and minimum temperatures, °C

SGTYPE Subgrade type, 0 = fine, 1 =coarse

AGE Pavement age since construction, yr

KESAL Cumulative number of 80-kN axle loads, thousands

IRI International RouQ:hness Index m/km

A key part ofthe data evaluation was examination ofthe trends between the various independent

variables and IRI. Figures 59, 60, and 61 show bivariate plots that relate the IRI ofJPCP, JRCP,

and CRCP, respectively, to several individual variables. In all cases, an increase in age and traffic

loading results in an increase in IRI. Increases in most ofthe climatic variables, such as

precipitation, number offreeze-thaw cycles, and freezing index, also tend to increase IRI.

Stronger base and subgrade materials, such as nonerodible bases and granular subbases, tend to

decrease IRI. Other pavement design variables, such as the thickness ofthe PCC concrete layer,

138
increase or decrease roughness depending on pavement type. The correlation tables that show the

strength ofthe relationships between the potential independent variables and lRI for JPCP,

JRCP, and CRCP, as well as the relationships between the independent variables themselves, are

shown in tables 20 through 22.

Selection ofModel Form

On the basis ofresults obtained from the preliminary evaluation ofthe databases assembled for

development ofthe lRI models, and an evaluation ofseveral model forms, the final model form

that was selected for consideration is as follows:

where

lRI =

lRIo =

ESAL =

Xj,Zj =

~,bi' a, p =

International Roughness Index, m/km

initial 00, m/km

cumulative ESAL's

various pavement design and climatic variables

regression constants

The basic philosophy behind this model form is that the future lRI is dependent on the initial IRI

after construction. The model then assumes that the progression ofroughness is dependent on

two major factors, namely, the effect oftraffic loading on the pavement and the effect of aging

on the pavement. These effects are accounted for by including the interactions between traffic

loading and pavement and climatic variables that influence roughness, and the interactions

between age and pavement and climatic variables that influence roughness in the model. The

model agrees with the results ofseveral earlier studies on the effect ofinitial lRI.(4, 10, 11,62) In

addition, it is reasonable to assume that the progression ofroughness is a function ofthe

interaction between traffic loading and age on one side and pavement and climatic variables on

the other. However, because ofthe errors associated with estimating the initial lRI for all the

pavements in the LTPP database used for this analysis, it was decided to obtain an average lRIo

for each ofthe pavement types from regression analysis, included in the model as an intercept.

139
200

4 ,---__~---_,

.*

{:(.. ;; gl ....

0+-----+----1

o 100

4-.---_,,-----__----,

•

3 ••

{2 .J~. g I ~~4.

O+----+----t------j

o 500 1000 1500 20 40

o+---__-+-__-j

o

Age,yr Annual freezing index,

°Cdays

Annual no. offreeze-thaw cycles, days

30 40 50

O+-----t----t------i

20

4-.----,---;- --,

!; lli(i~ 100 200

4-,-- --:----,

.* II 3 ...,

8 2 ••:J~-

gi ~.

O+-----t-------j

o

o+----+---1-----1----1

o 0.4 0.8 1.2 1.6

4 -.---__----:-__,

..

•• • .~ :!(:ia;

Precipitation, m Annual number ofwet days Mean temperature,OC

Subdrainage type

4.---- ----,

3

2 •

§f I

O+- ----j

o

4 -,-- ---,

3

2

~i I ......

Rtsetype

0+----------1

o

40 80 120

•

••

.~t ...

•

0+---+---+-----1

o

Anual no ofdays with temperature

below 32°C

4-.-----------,

3

2

iiI ......

200 400

4-.----------,

3

2 a

gi

0+-- ---1

o

4 -,-- -----,

3 ·1 ; ~. 2l.; •i..

g It. • :••

O+--t---t------j

0.7 0.9 l.l 1.3

4 -.---_-,---;- --,

3 •• •

:,.

g: .~:.l O-j-----t--------j

o

Subgrade type Drainage coefficient, Cd k-value, kPai mm

Figure 59. Plots ofIRI versus significant variables for JPCP.

140
4 4 4

3

•

3

•

3

•

2

~, 2

'-.!s': gl g ef

2

.'.~~ •• •

0

• ••

0

•

0

0 10 20 30 0 300 600 900 0 40 80 120

Age, yr

Annual freezing index, Annual no. offreeze-thaw cycles,

°Cdays days

4 4

• • 4

3

",. 3 • ~. 3

.,:~"i 2 2

. 2

g el • • g 0

0 0.5 1.5 2

0 0

•

50 100 150 200 0 6 12 18 24

Precipitation, m Annual no. ofwet days Mean temperature, °C

4

• 4 4

3 • • :11,. a

3

tel"

3

2

2

ItI' 2

g

• gl el"

0 0 0

0 10 20 30 40 200 250 300 150 200 250 300

Joint spacing, m PCC thickness, mm Base thickness, mm

4 4 4

3 3

•

3

•

W-. 2 .. 2

-III 2

g gl el" 1 •

0

•

0

•

10000 20000 0.7 0.9 1.1 1.3 0 25 50 75 100

ESAL's (thousands) Drainage coefficient, Cd k-value, kPal mm

Figure 60. Plots ofIRI versus significant variables for JRCP.

141
3.,-- ---,

0.5 1.0 1.5 2.0

3 ,-- --,

2

el" 1

o-I---+-----+--+------j

0.0 50 100 ISO 200

•.....•

.

... .,.~. ·:tt..~!. •

3 ,-- -,

o-I--+---t---+---1

o

2

el" 1

500 1000 1500

0-1---+---+--....--1

o

2

el" 1

Freezing index,oC days Annual no. offreeze-thaw

cycles, days

Precipitation, m

3.,----------,

• a·

• • ••I..

•• ~l • :\t;:' •

3.,-- -,

•••••

.. .. • t./t~# •1...... • •

3.,------------,

• •

...-. t f •• •• ,~. , ..

•

50 100 ISO

0-1---+----1------1

10 20 30 o

0+------1---+---1

100 200 o

0-1- -1-__--1

o

Annual no. ofwet days Mean temperature, °C Annual no. ofdays with temperature

above 32°C

3.,----------, 3.,----------------,

2

gl

0-1---------------1

o

3-,----- ----,

2

g" I

0+-- --1

o 20000

•

..

10000

1...

..~.

.....

.....

••

0-1- +--__--1

o

ESAL's (thousands) Base type Subdrainage type

• . .... ~.

....

. ~.;:'.

.... ... . ..,

3.,--------------,

• ..t.· wi··· ,..-...

3.,-- -----.

• •

.I· I •

3,- ----,

10 20 30

0-1-----+----+----1

50 100 ISO o

o+----1----+------1

0.8 1.0 13 o

0+----+---1------1

0.5

Drainage coeffient, Cd k-value, kPa/ mm Age,yr

Figure 61. Plots ofIRI versus significant variables for CRCP.

142
.......

,j::>.

c.v

Table 20. Summary of correlation analysis for significant variables versus IRI for JPCP.

AGE FI FTCYC PRECIP WTOYS TEMP 032 BTYPE OTYPE Cd k-value KESAL 

!AGE 1 -0.031 -0.163 0.215 0.166 0.057 -0.038 -0.179 0.001 -0.204 -0.114 0.4

FI -0.031 1 0.096 -0.038 0.206 -0.549 -0.399 -0.282 -0.028 -0.290 -0.350 -0.2

FTCYC -0.163 0.096 1 -0.516 -0.396 -0.738 -0.540 -0.114 -0.045 -0.169 -0.047 -0.1

PRECIP 0.215 -0.038 -0.516 1 0.803 0.461 0.106 0.123 0.231 -0.137 -0.081 0.0

WTOYS 0.166 0.206 -0.396 0.803 1 0.134 -0.232 -0.037 0.283 -0.256 -0.153 -0.0

TEMP 0.057 -0.549 -0.738 0.461 0.134 1 0.837 0.405 0.072 0.407 0.322 0.2

032 -0.038 -0.399 -0.540 0.106 -0.232 0.837 1 0.451 0.002 0.548 0.418 0.2

BTYPE -0.179 -0.282 -0.114 0.123 -0.037 0.405 0.451 1 0.230 0.594 0.452 0.0

OTYPE 0.001 -0.028 -0.045 0.231 0.283 0.072 0.002 0.230 1 0.171 0.137 0.2

Cd -0.204 -0.290 -0.169 -0.137 -0.256 0.407 0.548 0.594 0.171 1 0.499 0.0

k-value -0.114 -0.350 -0.047 -0.081 -0.153 0.322 0.418 0.452 0.137 0.499 1 -0.0

KESAL 0.438 -0.204 -0.139 0.095 -0.091 0.254 0.216 0.070 0.223 0.083 -0.004 

IRI 0.340 0.269 0.050 0.169 0.229 -0.148 -0.181 -0.173 0.022 -0.224 -0.215 0.
......

Table 21. Summary of correlation analysis for significant variables versus IRI for JRCP.

FI FTCYC PRECIP WTDYS TEMP JTSP HPCC BTHICK KESAL AGE Cd k-value 

FI 1 0.09345 -0.45447 -0.04821 -0.25457 -0.32615 -0.34355 -0.13245 -0.11539 0.30547 -0.01839 0.01

FTCYC 0.09345 1 -0.7146 0.20345 -0.22403 -0.05634 -0.26593 0.06205 -0.03748 -0.17301 -0.19912 0.08

PRECIP -0.45447 -0.7146 1 0.13559 0.12159 0.32848 0.34467 0.30223 0.11636 0.17202 0.20329 -0.09

WTDYS -0.04821 0.20345 0.13559 1 -0.11206 0.25538 0.28804 0.44631 0.11165 0.06847 -0.22195 0.16

IrEMP -0.25457 -0.22403 0.12159 -0.11206 1 0.09631 0.07509 0.00394 0.00728 -0.13732 0.26433 -0.05

JTSP -0.32615 -0.05634 0.32848 0.25538 0.09631 1 0.26412 0.28814 0.35098 0.28078 -0.22819 -0.22

HPCC -0.34355 -0.26593 0.34467 0.28804 0.07509 0.26412 1 0.07091 0.10401 -0.16212 -0.12534 0.23

BTHICK -0.13245 0.06205 0.30223 0.44631 0.00394 0.28814 0.07091 1 0.21768 0.18112 -0.06467 0.22

KESAL -0.11539 -0.03748 0.11636 0.11165 0.00728 0.35098 0.10401 0.21768 1 0.42592 -0.22965 -0.1

AGE 0.30547 -0.17301 0.17202 0.06847 -0.13732 0.28078 -0.16212 0.18112 0.42592 1 -0.0225 -0.30

Cd -0.01839 -0.19912 0.20329 -0.22195 0.26433 -0.22819 -0.12534 -0.06467 -0.22965 -0.0225 1 -0.02

k-value 0.01059 0.08984 -0.09988 0.16088 -0.05527 -0.22984 0.23021 0.22079 -0.1783 -0.30201 -0.02382 

IRI -0.28991 -0.30063 0.44008 0.2318 0.16051 0.34608 0.40374 0.09112 0.21929 0.24155 -0.15156 -0.25
......

-/::>.

V1

Table 22. Summary of correlation analysis for significant variables versus IRI for CRCP.

FI FTCYC PRECIP WTOYS TEMP 032 KESAL BTYPE OTYPE Cd k-value AGE 

FI 1 0.63806 -0.53522 -0.10866 -0.83279 -0.57413 0.05743 -0.43926 0.16635 -0.17619 -0.21588 0.32

FTCYC 0.63806 1 -0.51159 0.0611 -0.89745 -0.74752 0.16812 -0.3434 0.17454 -0.1757 -0.1082 0.24

PRECIP -0.53522 -0.51159 1 0.46404 0.53244 0.11391 -0.03543 0.09119 0.08404 -0.18431 -0.03479 -0.16

WTOYS -0.10866 0.0611 0.46404 1 -0.14247 -0.54119 0.22258 -0.12269 0.46103 -0.22013 0.00223 -0.15

h"EMP -0.83279 -0.89745 0.53244 -0.14247 1 0.84365 -0.15855 0.4299 -0.3025 0.12834 0.0971 -0.21

032 -0.57413 -0.74752 0.11391 -0.54119 0.84365 1 -0.22817 0.41421 -0.45313 0.26423 0.11748 -0.15

KESAL 0.05743 0.16812 -0.03543 0.22258 -0.15855 -0.22817 1 0.07539 0.26156 0.23042 0.05881 0.24

BTYPE -0.43926 -0.3434 0.09119 -0.12269 0.4299 0.41421 0.07539 1 -0.24196 0.50606 0.14997 -0.27

OTYPE 0.16635 0.17454 0.08404 0.46103 -0.3025 -0.45313 0.26156 -0.24196 1 -0.04748 -0.18992 -0.13

Cd -0.17619 -0.1757 -0.18431 -0.22013 0.12834 0.26423 0.23042 0.50606 -0.04748 1 0.01158 -0.05

k-value -0.21588 -0.1082 -0.03479 0.00223 0.0971 0.11748 0.05881 0.14997 -0.18992 0.01158 1 -0.22

AGE 0.32686 0.24905 -0.16405 -0.15962 -0.21393 -0.15332 0.24008 -0.27279 -0.13788 -0.05897 -0.22884 

IRI -0.06188 -0.11489 -0.07238 -0.0417 0.1826 0.25191 0.1521 -0.05728 -0.07511 -0.15216 0.02666 -0.09
Development ofFinal Models

The final step was to perfonn multiple linear regression analysis using the most suitable

variables and interactions to obtain the final model parameter estimates for the model fonn

selected. The relevant diagnostic statistics to be used to verify the suitability and stability ofthe

model were also obtained. In each case, several models were developed and evaluated for each

pavement type. The most suitable model was selected based on both engineering judgment and

diagnostic statistics. The diagnostic statistics used included the coefficient of detennination, R2

,

and standard error of estimate (SEE). The relevance ofthese statistics is discussed in appendix A.

For each pavement type, the model that was in accordance with engineering principles and also

had the best combination ofdiagnostic statistics was selected as the final model for predicting

IRI. A primary goal was to select the model that best describes the progression ofIRI but

includes just the appropriate number of explanatory variables and parameters. Including too

many variables in the model will not necessarily improve its predictive capability. A model's R2

will always increase with an increasing number ofindependent variables, but the standard error

of estimate may also increase and compromise the accuracy ofthe model.

Final IRI Prediction Models

The final models developed for predicting IRI ofJPCP, JRCP, and CRCP are presented in this

section.

JPCP IRI Prediction Model

The model developed for predicting IRI ofJPCP pavements is as follows:

IRI = 1.3033 + KESAL°.4(1.578WETDAYS + 113.6FREEZE)

* 10-4 + AGE°.4(1.4437FI + 3.6*1O-5

Epee - 552 SUGTYP

- 19.08DOWDIA) * 10-4 (102)

where

IRI

KESAL

WETDAYS

FREEZE =

AGE =

FI

Epee

SUGTYP

DOWDIA =

International Roughness Index, mJkm

cumulative 80-kN equivalent single axle loads, thousands

number ofdays precipitation is greater than 12.7 mm

LTPP climatic zone, I=freezing climate, O=nonfreezing climate

pavement age, yr

freezing index, °C days

PCC elastic modulus, kPa

subgrade type, 1=coarse-grained, O=fine-grained

Dowel diameter, mm

146
Statistics:

N

R2

SEE

p-value

=

<

155

0.50

0.328 m/km

0.005 (significance ofmodel)

A plot ofthe predicted and measured JPCP IRI is shown in figure 62. A plot ofthe residuals

(predicted - actual IRI) against the predicted IRI is shown in figure 63. The overall accuracy of

the JPCP IRI model is reflected by the R2 of 0.50, which is the proportion ofvariation ofIRI

explained by the variables included in the model. A test of hypothesis was performed to

determine the significance ofthe variables used in the model for predicting IRI. The null and

alternate hypotheses were as follows:

Ho : all model parameters are zero (variables are not significant)

HA: all model parameters are not zero

The F-test statistic used for the hypothesis test was calculated as the ratio ofthe mean square for

the model divided by the mean square ofthe error. For this study the null hypothesis will be

rejected ifthe level ofsignificance is less than 5 percent (0.05). A level ofsignificance (p-value)

ofless than 0.005 implies a rejection ofthe null hypothesis. This shows that the variables in the

model are highly significant. Also, individual t-tests were conducted to test ifthe individual

parameter estimates are equal to zero. The p-values for this test ranged from 0.0001 to 0.004. The

results show that all the parameter estimates had values other than zero; therefore, the variables

in the model were significant. Prediction accuracy ofIRI in absolute units is reflected by the

standard error of estimate (SEE = 0.328 m/km). The overall effectiveness ofthe model should be

judged on all the diagnostic statistics, the residual plots, and the results from the sensitivity

analysis to follow. The diagnostic statistics obtained for the JPCP IRI model show that the model

can predict JPCP IRI with reasonable accuracy for the current LTPP database utilized.

JRCP IRI Prediction Model

The model developed for predicting IRI ofJRCP pavements is as follows:

IRI = 1.272 + 0.00866*PSTEEL*KESALoA + 0.00742*AGEo.7

(5.78

+ 0.0106PRECIP - 1.95DRAIN - 3.73SUGTYP)

147

(103)
3

•

s •

2.5 • .......... •

••

S •

•••••• •

• •

P::: """" . .". ,.. .. •• """" 2

"'lj • * ••.. • t • .....

OJ . •

• • *:1. • ..... u • ••

"'lj

OJ •

..

,_. .,; ·l~""~· ~·*t • . . lo-< 1.5

4... .. ....

. ...

•••

•

1-+------1------1-------+--------1

1 1.5 2

Measured IRI m/km

2.5 3

Figure 62. Plot of predicted versus actual IRI for JPCP.

1

•

• • •

• ••

• . •

0.5 • .. : .

•

• • • ....... ..~. • •

t\l

;:l

"'lj

.....

(1)

0 ..

OJ

-... .~~ ... 2.5

•

-0.5 •

• •

•• •

• •

• •

-1

Predicted IRI m/km

Figure 63. Plot of residual versus predicted IRI for JPCP.

148
where

IRI

KESAL

PSTEEL

AGE

PRECIP

DRAIN

SUGTYP

Statistics:

N

R2

SEE

p-value

=

=

=

=

=

<

International Roughness Index, mlkm

cumulative 80-kN equivalent single axle loads, thousands

percentage ofsteel

pavement age, yr

average annual precipitation, mm

presence of edge drain, 1 = edge drain 0 = no edge drains

subgrade type, I =coarse-grained, O=fine-grained

93

0.50

0.246m1km

0.0001 (significance ofmodel)

A plot ofthe predicted and measured JRCP IRI is shown in figure 64. A plot ofthe residuals

(predicted - actual IRI) against the predicted IRI is shown in figure 65. The overall accuracy of

the JRCP IRI model is reflected by the R2 of 0.50, which is the proportion of variation ofIRI

explained by the variables included in the model. A test of hypothesis was performed to

determine the significance ofthe variables used in the model for predicting IRI. The null and

alternate hypotheses were as follows:

Ho : all model parameters are zero (variables are not significant)

HA : all model parameters are not zero

The F-test statistic used for the hypothesis test was calculated as the ratio ofthe mean square for

the model divided by the mean square ofthe error. For this study the null hypothesis will be

rejected ifthe level ofsignificance is less than 5 percent (0.05). A level ofsignificance (p-value)

ofless than 0.0001 implies a rejection ofthe null hypothesis. This shows that the variables in the

model are highly significant. Also, individual t-tests were conducted to test ifthe individual

parameter estimates are equal to zero. The p-values for this test ranged from 0.0001 to 0.01. The

results show that all the parameter estimates had values other than zero; therefore, the variables

in the model were significant. Prediction accuracy ofIRI in absolute units is reflected by the

standard error of estimate (SEE = 0.246 mIkm). The overall effectiveness ofthe model should be

judged on all the diagnostic statistics, the residual plots, and the results from the sensitivity

analysis to follow. The diagnostic statistics obtained for the JRCP IRI model show that the model

can predict JRCP IRI with reasonable accuracy for the current LTPP database utilized.

149
3

•

••

•

] 2.5 •

e.. .. ...# ••• • • •• - 2 f- ~\:4. "'0 .,: ., .. ••

.2:/

u ••,.,~.. ~.# ..... • • ••# • "'0

OJ ;.~.....~',.. 1.5 • 1':,.. •

1+------+-------+------+--------1

1 1.5 2

Measured IRI, m/km

2.5 3

Figure 64. Plot of predicted versus actual IRI for JRCP.

1

•

0.5 • •

••

..... • ...... .,:·~t·· C'd ..J • ~." ..

::l

• • •

"'0 0 • T..

..... (/)

OJ ~..... . ·1.~ .~ •••• 2.5

.......# ••:..

-0.5 .. ..

-1 ...L- --'

Predicted IRI, m/km

Figure 65. Plot of residual versus predicted IRI for JRCP.

150
CRCP IRI Prediction Model

The model developed for predicting IRI for CRCP pavements is as follows:

IRI =

where

1.118 + KESALo.3(0.0142 - 9.787*10-3PSTEEL) + AGE°.4(3. 157*1O-3D32

- 0.054DRY + 0.293FREEZE - 4.65*1O-4KVAL + 0.1203) (104)

IRI

KESAL

PSTEEL

EPCC

AGE

D32

DRY

FREEZE

KVAL

Statistics:

N

R2

SEE

p-value

=

=

=

=

=

=

=

=

=

=

<

International Roughness Index, m/km

cumulative 80-kN equivalent single axle loads, thousands

percentage ofsteel

PCC elastic modulus, kPa

pavement age, yr

average annual number of days with temperatures above 32 °C

LTPP climatic zone, 1 = dry climate, 0 = wet climate

LTPP climatic zone, 1 = freezing climate, 0 = nonfreezing climate

modulus ofsubgrade reaction, kPalmm

156

0.51

0.277 m/km

0.0007 (significance ofmodel)

A plot ofthe predicted and measured CRCP IRI is shown in figure 66. A plot ofthe residuals

(predicted - actual IRI) against the predicted IRI is shown in figure 67. The overall accuracy of

the CRCP IRI model is reflected by the R2 of 0.51, which is the proportion of variation ofIRI

explained by the variables included in the model. A test ofhypothesis was performed to

determine the significance ofthe variables used in the model for predicting 00. The null and

alternate hypotheses were as follows:

Ho: all model parameters are zero (variables are not significant)

HA: all model parameters are not zero

The F-test statistic used for the hypothesis test was calculated as the ratio ofthe mean square for

the model divided by the mean square ofthe error. For this study the null hypothesis will be

rejected ifthe level ofsignificance is less than 5 percent (0.05). A level ofsignificance (p-value)

ofless than 0.0007 implies a rejection ofthe null hypothesis. This shows that the variables in the

model are highly significant. Also, individual t-tests were conducted to test ifthe individual

parameter estimates are equal to zero. The p-values for this test ranged from 0.0001 to 0.012. The

results show that all the parameter estimates had values other than zero, so the variables in the

151
2.5--.----------------------------,

1 -

... -

- 1.5 "0

2

u.....

"0

Q)

P-!

• # ••

< •••

. .. ...

.....,.•••••* •••

....

,...... ..

... , .,(+••

•

...,...

,

1 1.5 2 2.5

0.5+------+------+-------+--------1

0.5

Measured IRI, m/ km

Figure 66. Plot of predicted versus actual IRI for CRCP.

0.6 -,-------------------------,

0.3 -

-0.3

\

•

'.

•

•

t.

• •

....

25

••

-0.6 --'---------------.11_--.--------'

Predicted IRI

Figure 67. Plot of residual versus predicted IRI for CRCP.

152
model were significant. Prediction accuracy ofCRCP IRI in absolute units is reflected by the

standard error of estimate (SEE = 0.276 m/km). The overall effectiveness ofthe model should be

judged on all ofthe diagnostic statistics, the residual plots, and the results from the sensitivity

analysis to follow. The diagnostic statistics obtained for the CRCP IRI model show that the

model can predict CRCP IRI with reasonable accuracy for the current LTPP database.

Sensitivity Analysis

A final and important step in the development ofthe models for predicting IRI was sensitivity

analysis to check the engineering plausibility ofthe models. This was accomplished by studying

the effects ofthe various input parameters on the output generated by the roughness models and

comparing the results to theoretical and empirical observations. By virtue ofthe model form

selected, traffic loading and pavement age automatically have a significant influence on the

progression ofIRI.

JPCP IRI Model

In addition to traffic loading and age, the variables that were found to be significant in the model

developed for predicting IRI ofJPCP include several climatic and pavement design variables.

The climatic variables include the number ofwet days, whether the pavement is in the LTPP

freeze or no-freeze zone, and the freezing index. ,

The pavement design variables that were significant include the modulus of elasticity ofthe PCC

slab, dowel diameter, and the type ofsubgrade. The influence ofthese factors on the progression

ofthe IRI predicted with the model are discussed below.

Effect ofClimate

Figure 68 is a plot of cumulative ESAL's versus IRI for different number ofwet days (i.e., days

with precipitation greater than 12.7 mm), and figure 69 is a plot ofIRI versus cumulative

ESAL's for pavements in different climatic zones. Both plots and the parameter estimate

associated with freezing index in the model show that harsher climatic conditions will cause an

increase in IRI. This is reasonable, since harsher climatic conditions in general increase the rate

of progression ofmost ofthe distresses associated with JPCP pavements. The precipitation

associated with the number ofwet days will tend to saturate, weaken, and erode the pavement

support layers. This weakens the pavement structure as a whole and reduces its ability to

withstand traffic and environmental loads. For pavements that experience freezing conditions,

freezing and thawing cycles will lead to further weakening ofthe pavement structure and

increase roughness.

153
3

-+- Wet days = 70

_Wet days =120

2.5 -.-Wet days =170

S

...........

S 2

1.5

l+-----+-----f------+------+--------l

o 5 10 ' 15 20 25

ESAL's (millions)

Figure 68. Influence of annual number of wet days on IRI ofJPCP.

3

-+- No-freeze

2.5 -Freeze

S

.........

S 2

P:::

1.5

1+-----+-----f-----t------+-------i

o 5 10 15 20 25

ESAL's (millions)

Figure 69. Influence of climate (freeze or no-freeze) on IRI ofJPCP.

154
Effect ofPavement Design Features

Figure 70 shows the influence ofsubgrade type on the predicted IRI. The influence of dowel

diameter on IRI is illustrated in figure 71. According to figure 70, pavements with fine-grained

subgrades will be more prone to an increased progression ofroughness. Fine-grained soils

provide less support because they are more sensitive to moisture effects. An interesting

observation about the model is the influence of dowel diameter on roughness.· According to the

model, increasing dowel diameter will reduce the progression ofroughness. This can be

explained by the influence of dowels on faulting. The model clearly shows the importance of

using dowels and also shows that, the larger the dowel diameter, the more it reduces the

progression of distress. The model also confirmed. that increasing traffic loading and age will

increase the progression ofroughness.

JRCP IRI Model

The model for predicting IRI on JRCP confirmed that increasing traffic loading and age will

increase the progression ofroughness. The other variables that were found to be significant to the

progression ofroughness ofJRCP included the design steel content, amount ofprecipitation, the

presence of edge drains, and the subgrade type. The effects ofthe factors for increasing traffic

load applications were examined by comparing the results predicted by the model to empirical

and theoretical observations.

Effect ofPavement Design Features

The design features that were found to be significant to roughness ofJRCP are the design steel

content, the presence of edge drains, and subgrade type. Figure 72 shows the effect ofthe design

steel content on the progression of distress. According to the model, the higher the design steel

content, the higher the predicted IRI. There is no obvious explanation for this trend. The

influence ofsubgrade type is shown in figure 73. Because coarse-grained subgrades are less

susceptible to moisture, they provide better support to the PCC slab. Therefore, pavements with

coarse-grained soils can be expected to experience less distress and less roughness. Figure 74

shows that the provision of an edge drain will reduce the progression ofroughness. This is a

reasonable trend, since the positive drainage will improve the overall performance ofJRCP.

Effect ofthe Climate

The only climatic variable that turned out to be significant to roughness was the amount of

precipitation. According to the model, more precipitation will result in increased progression of

roughness, as illustrated in figure 75. Again, this is a reasonable trend, as more precipitation

generally results in more pavement distress because ofthe higher chance ofmoisture-related

distress, such as faulting.

155
3--,;=========::;-----------------;;\

--+- Coarse Subgrade

_ Fine Subgrade 2.5 -L'-----------==------'

s

S 2

-

- 1.5

1+-----f-----+-----f----f--------j

o 5 10 15 20 25

ESAL's (millions)

Figure 70. Influence of subgrade type on IRI ofJPCP.

3-,-------------------------.

--+- Dowel = 0

_ Dowel =25.4 mm

---A- Dowel =38.1 mm

1+------+---------1----+------+---------1

o 5 10 15 20 25

ESAL's (millions)

Figure 71. Influence of dowels and dowel diameter on IRI ofJPCP.

156
3

-+-Design steel content =0.05%

_ Design steel content = 0.25%

-+-Design steel content = 0.6%

2.5

s

............

S 2

- .......

VI

- "l

1.5

1 -+1--------1------+--------+-------+---------1

o 5 10 15

ESAL's (millions)

20 25

Figure 72. Influence of design steel content on JRCP IRI.
2.5 -,-------------------

--+- Fine subgrade

--Coarse subgrade

2

S

.........

S

-

- 1.5 \Jl

00

1 I I I I I I

o 5 10 15 20 25

ESAL's (millions)

Figure 73. Influence ofsubgrade type on JRCP IRI.
2.5

2

S

...........

S

-

- .......

VI

1.5 \,()

~Drain

__ No drain

1 I I I I I I

o 5 10 15 20 25

Cumulative ESAL's (millions)

Figure 74. Influence of edge drains on JRCP IRI.
CRCP 1&1 Model

As with the other IRI models, an increase in traffic loading and age was found to increase the

progression ofroughness. In addition, several other variables were found to be significant to

roughness. They include pavement design variables such as the design steel content, the modulus

of elasticity ofthe PCC slab, and the modulus ofsubgrade reaction. The climatic variables that

were found to be significant to roughness include the climatic region in which the pavement is

located and the number of days with the highest temperature exceeding 32°C.

Effect ofPavement Design Features

Figures 76 and 77 are plots ofIRI versus the CRCP design steel content and the modulus of

subgrade reaction, respectively. According to the model, the predicted IRI decreases with

increasing steel content, as illustrated in figure 76. This result is reasonable and is in agreement

with recent observations in Illinois and Belgium that indicate that higher steel contents for CRCP

are beneficial, as they keep the cracks that form tight and reduce punchouts.(63, 64) Although the

higher steel contents induce more closely spaced cracks in CRCP, this does not appear to cause a

problem as long as they are kept tight.

Another design variable that was found to influence roughness is the modulus ofsubgrade

reaction. As shown in figure 77, the better the support provided by the subgrade, the less the

roughness predicted by the model. The greater support will mean that the pavement can

withstand more traffic loading before experiencing the typical distresses that are associated with

CRCP and the increase in pavement roughness.

Effect ofthe Climate

The climatic variables found to be significant to the roughness ofCRCP all show reasonable

trends. The model obtained shows an interesting influence ofthe climatic region of a pavement

on the progression ofroughness. According to the model, pavements located in freezing regions

will experience more roughness than those in the no freeze region. Less roughness will be

experienced by pavements located in a drier region. Therefore, as illustrated in figure 78, in

terms ofreducing the progression ofroughness, the best location for CRCP pavements is in the

dry-no freeze region. This is not unexpected, since that is the region within which a pavement

will experience the least distress (all things being equal). The influence ofthe number of days

when the maximum temperature exceeds 32°C, as illustrated in figure 79, is interesting. CRCP

slabs that experience a higher number of days when the temperature exceeds 32°C are more

prone to expansive forces that can lead to more spalling and blowups.

160
3

-+-Precip = 0.63 m

____ Precip = 1.0 m

-.-Precip = 1.65 m.

.....

.....

'"

2.5

2

-

1.5

1

------ ------ ------ /-/-

~./. ~.~ ....---.-- ~.~ ---~- _/ --.--- / --.

: /- .........-.........-. :/.------

o 5 10 15 20 25

ESAL's (millions)

Figure 75. Influence of precipitation on JRCP 00.
3.5 I

0-

-

N

fg

3

2.5

2

1.5

-+-Design steel content = 0.4%

_ Design steel content = 0.7%

-.-Design steel content = 1.0%

1 I I I I I

o 5 10 15

ESAL's (millions)

20 25 30

Figure 76. Influence of design steel content on CRCP 00.
2 -.,-,-------------------------------,

-+--k = 27.1 kPa/mm

_ k = 81.5 kPa/mm

1.75

s

........... 1.5 S

.......

0'

1.25

Vol

30 25 20 15 10 5

1 I I I I I I

o

ESAL's (millions)

Figure 77. Influence of subgrade support on CRCP 00.
3.5 '1---------------------------------,

3

2.5

E

...........

E

- 0'

- - 2

-J>.

1.5

Dry-no freeze

- Dry-freeze

.........- Wet-no freeze

-*-Wet-freeze

1 I I I I

o 5 10 15

ESAL's (millions)

20 25 3

Figure 78. Influence of climatic region on CRCP IRI.
Summary

JPCP lRI

The following can be summarized about the JPCP lRI model:

• Fifty percent ofthe total variation ofroughness can be explained by the included

variables.

• Some ofthe unexplained variation may be due to errors in the independent variables used

to develop the model, such as the traffic estimates.

• The "average" error in predicting JPCP lRI is 0.328 m/km.

• There are no discernible patterns in the residuals.

• Data from a large number of pavement sections from all over the United States were used

to develop the model (N = 155).

• Each independent variable and the overall model were significant at a level of

significance of 5 percent.

• The sensitivity analysis shows that all ofthe explanatory variables have a plausible effect

on roughness that agrees with theoretical expectations and previous empirical field

results.

JRCP lRI

The following can be summarized about the JRCP lRI model:

• Fifty percent ofthe total variation ofroughness can be explained by the included

variables.

• Some ofthe unexplained variation may be due to errors in the independent variables used

to develop the model, such as the traffic estimates.

• The "average" error in predicting JRCP lRI is 0.246 m/km.

• There are no discernible patterns in the residuals.

• Data from a large number of pavement sections from all over the United States were used

to develop the model (N = 93).

• Each independent variable and the overall model was significant at a level ofsignificance

of 5 percent.

165
• The sensitivity analysis shows that all ofthe explanatory variables have a plausible effect

on roughness that agrees with theoretical expectations and previous empirical field

results.

166
3.5 --,----------------------------.

3

--+-D32 = 0

_D32=40

--.- D32 = 110

I-'

C1'

'J

S 2.5

...........

S

-

- 2

1.5 If' • • • • • • • • • • • • • • •

1 I I I I I I

o 5 10 15 20 25 30

ESALIS (millions) _

Figure 79. Influence of hot weather on CRCP IRI.
CRCP IRI

The following can be summarized about the CRCP IRI model:

• Fifty-one percent ofthe total variation ofroughness can be explained by the included

variables.

• Some ofthe unexplained variation may be due to errors in the independent variables used

to develop the model, such as the traffic estimates.

• The "average" error in predicting CRCP IRI is 0.277 m/km.

• There are no discernible patterns in the residuals.

• Data from a large number ofpavement sections from all over the United States were used

to develop the model (N = 93).

• Each independent variable and the overall model was significant at a level ofsignificance

of5 percent.

• The sensitivity analysis shows that all ofthe explanatory variables have a plausible effect

on roughness that agrees with theoretical expectations and previous empirical field

results.

Implications and Recommendations

The models developed for predicting IRI ofJPCP, JRCP, and CRCP were based on basic

principles. The model forms selected are backed by results that have been obtained from an

extensive evaluation ofthe LTPP data and recent studies on IRI.(57,62) Although reasonable

results were obtained, the models had some limitations. The major limitation was the inability to

include the initial IRI for a majority ofthe pavement sections in the LTPP database. Thus, the

effect ofinitial IRI on the future roughness was not considered.

In spite ofthese limitations, the models obtained provide reasonable predictions and show the

influence ofseveral significant pavement design and climatic variables on roughness. An

interesting result from these studies, confirmed and reported by other LTPP studies, is the values

ofthe estimated initial IRI for JPCP, JRCP, and CRCp.(62) According to the models developed,

the average initial IRI for the JPCP, JRCP, and CRCP sections from the GPS studies were

approximately 1.3, 1.2, and 1.1 m/km. Recent LTPP studies investigating the development of

pavement roughness, which involved the evaluation of data from newly constructed pavement

sections, have reported similar initial IRI results, with the actual and estimated initial IRI ranging

from about 0.63 to more than 1.6 m/km.(62)

168
8. APPLICATION OF DISTRESS PERFORMANCE MODELS

Introduction

The performance prediction models developed in this study can be used to determine whether a

given pavement design will meet certain performance criteria. Mechanistic-empirical models are

recommended because they more realistically consider the mechanism of distress formation. The

critical checks recommended for concrete pavements include the following:

• Faulting for doweled and nondoweled JPCP.

• Transverse joint spalling for JPCP and JRCP.

• Transverse cracking ofJPCP.

• Comer breaks for JPCP.

• Roughness for JPCP, JRCP, CRCP.

Each ofthe models should be used to predict distress over the design period for the applicable

PCC pavement design, and the results should be checked against the performance criteria ofthe

agency. The models can also be used for analysis ofthe cost effectiveness of design alternatives.

This chapter presents a summary ofthe variables required as inputs and examples ofthe models'

applications. The methods ofmodel formulation, calibration, and limitations identified in the

model development process are discussed in previous chapters ofthis report.

Faulting of JPCP

Faulting is the most critical distress related to JPCP ride quality. The faulting model developed

as part ofthis study using data from the GPS 3 pavement sections in the LTPP database is

recommended for checking design. A summary ofthe input variables required for use in the

model is presented in table 23, and the procedure to determine faulting follows. The actual

faulting model and procedure for calculating faulting are given in chapter 4.

1. Calculate Load Transfer Factor (Chapter 4, equation 39).

AGG (1 + O.0992Do.1 - 99.93 !:.) = 0.25 e I

kQ

where

AGG/k~

D

L

nondimensional load transfer factor

dowel diameter, mm (D = 0, ifnondoweled pavement)

slab length, m

radius ofrelative stiffness, mm

169
Table 23. Summary of variables required for estimating faulting.

Dependent Variable Independent Variables Effect on Joint Faulting*

Cumulative number of 80-kN +

ESAL applications

PCC elastic modulus, kPa -

PCC thickness, mm - Transverse joint

faulting, mm Modulus ofsubgrade reaction, -

kPa/mm

Dowel diameter, mm -

Drainage coefficient -

Annual number ofwet days +

BASE, Base, or subbase type, -

O=erodible, 1=nonerodible

* Positive indicates that an increase in this variable results in an increase in faulting.

2. . Calculate Load Transfer Efficiency (Chapter 4, equations 30 and 3] ).

where

LTEx=915

=

=

1 / [1 + 1.2*(AGGIKQ)-o.849]

1 / [1 + 0.3483*(AGGIK~y1.13677]

LTE

x

AGG/k~

=

=

=

load transfer efficiency

distance ofload from corner, mm

nondimensionalload transfer factor

Interpolate to obtain the load transfer efficiency for wheel loads placed between 0 and 915 mm

from the slab corner.

3. Calculate Free Edge Corner Deflection, assuming no load transfer, (Chapter 4,

equations 28 and 29).

wfe,x=O = (0.10514~ 2+ 87.18~ + 231473)/k~2

wfe, x=915 = (O.0784e + 123.6~ - 19993)/ke

170
where

=

=

free edge comer deflection, rom

modulus ofsubgrade reaction, kPa/rom

radius ofrelative stiffness, rom

Interpolate to obtain the free edge comer deflection for wheel loads placed between 0 and 915

rom from the slab comer.

4. Calculate Loaded and Unloaded Comer Deflection, assuming load transfer, (Chapter 4,

equations 32 and 33).

where

wL,x = WUL,x / LTEx

Wfe

X

LTE

=

=

free edge comer deflection, rom

distance between wheel load and slab comer (less tan 915 rom)

load transfer efficiency

5. Calculate Differential Elastic Deformation Energy (Chapter 4, equation 20).

where

DE =

k =

=

=

modulus ofsubgrade reaction, kPa/rom

deflection ofloaded slab, rom

deflection ofunloaded slab, rom

6. Calculate Allowable Number ofESAL Repetitions (Chapter 4, equation 40).

where

= 5.50 - Log\O (0.005706 DE + 1)

=

=

allowable number of80-kN ESAL's to failure, in thousands

differential elastic deformation energy

7. Calculate Faulting Damage.

EDAM =

171
where

= actual number of 80-kN ESAL's, in thousands

allowable number of 80-kN ESAL's to failure, in thousands

8. Cakulate Transverse Joint Faulting (Chapter 4, equation 41).

where

Fault = FDAMo,3 [1.25 + 0.00102WETDAYS - 2.5*10-3

DOWDIA

- 0.625Cd (0.5 + BASE)]

FDAM

n

Nf

WETDAYS

DOWDIA

Cd

BASE

=

faulting damage = nlNf

number of 80-kN ESAL applications, in thousands

allowable number of 80-kN ESAL applications, in thousands

number ofwet days in the year

dowel diameter, mm

drainage coefficient

base or subbase type, O=erodible, 1=nonerodible

Transverse Joint Spalling for JPCP and JRCP

The mechanism ofspalling is yet to be fully understood; however, it is believed to be caused by

several interacting mechanisms, including stresses imposed by traffic and environmental forces,

as well as inadequate quality control during construction. Although traffic may have some effect

on spalling, environmental factors constitute the largest contributor to development ofthe

distress.

Two models were developed for estimating the percentage oftransverse joints with spalling (all

severities) for JPCP and JRCP, and they are recommended for design checking. A summary of

the input variables required for use in the models is presented in tables 24 and 25, and the

procedure for calculating spalling is presented below. The actual spalling models are given in

chapter 5.

1. Calculate Traffic Load Tensile Stress (Chapter 5, equation 49).

305.5 + 48.563hs- 23.62~ + 0.000757 ks- 0.17728~hs

+ 0.0888a~ - 1.89*1O-6~ks - 1.889*1O·7hsEp+ 1.98*1O-6hs

ks - 1.32*1O-Ii~ks

where

=

maximum tensile stress at crack orjoint surface from traffic loading, kPa

depth ofsealant, mm

modulus ofsubgrade reaction, kPa/mm

modulus ofsealant material, kPa

PCC slab thickness, mm

172
Ep modulus ofPCC slab, kPa

2. Calculate Thermal Load Tensile Stress (Chapter 5, equation 47).

0js = ~s CL(a.AT + e)/2t

where

kjs

u

t

C

L

a.

AT

e

=

=

=

=

=

=

spring coefficient ofjoint sealant or incompressibles in the joint, kPa

displacement ofspalled concrete, m

depth ofspall delamination (= 1)

subbase friction factor

joint spacing, m

concrete thermal expansion, per °C

thermal gradient in the slab, °C

concrete drying shrinkage strain

3. Calculate Allowable Number ofTraffic (NT) and Environment (NE) Load Applications

for }PCP (Chapter 5, equations 56 and 57).

The equations for calculating NT and NE are as follows:

(

1) 0.15

NT =199252 at

where

= tensile stress, kPa (calculated from chapter 5, equation 49)

173
Table 24. Summary ofvariables required for predicting JPCP joint spalling.

Predicted Variable Dependent Variables Effect on Joint Spalling

Cumulative number of 80-kN +

ESAL applications

Joint spacing, m +

PCC coefficient ofthennal +

JPCP transverse joint expanSIOn

spalling (percentage Thennal gradient within the +

ofjoints spalled) PCC slab

PCC drying shrinkage strain +

Subbase friction factor +

Depth ofsealant, mm +

Modulus ofsealant or +

incompressibles, kPa/mm

PCC elastic modulus, kPa -

PCC thickness, mm -

Modulus ofsubgrade reaction, - kPa/mm

Pavement age in years +

Average daily temperature +

range,OC

Average daily relative humidity -

range for the month of

construction

Average annual freeze-thaw +

cycles

* Positive indicates that an increase in this variable results in an increase in joint spalling.

174
Table 25. Summary of variables required for estimating JRCP joint spalling.

Predicted Variable Dependent Variables Effect on Joint Spalling

Cumulative number of 80-kN ESAL +

applications

Joint spacing, m +

PCC coefficient ofthermal expansion +

JRCP transverse Thermal gradient within the PCC slab +

joint spalling PCC drying shrinkage strain + (percentage ofjoints

spalled) Subbase friction factor +

Depth ofsealant, mm +

Modulus ofsealant or incompressibles, +

kPa/mm

PCC elastic modulus, kPa -

PCC thickness, mm -

Modulus ofsubgrade reaction, kPa/mm -

Pavement age in years +

Average annual freezing index, DC days +

* Positive indicates that an increase in this variable results in an increase in joint spalling.

( )

0,85

N E =650162 t

kjsELONG

where

~s =

ELONG

=

L =

AT

e =

ct =

C

t =

modulus ofthe sealant material or incompressibles, kPa

a factor estimating the horizontal movement ofthe slab, m

3.28CL(3.24ctAT + e)

slab length orjoint spacing, m

thermal gradient in the slab, DC

concrete drying shrinkage strain

concrete thermal expansion, per DC

subbase friction factor

Imm

175
4. Calculate Damage Accumulation for JPCP (Chapter 5. equation 58).

The model for calculating the total damage from traffic and environmental loading for

JPCP is as follows:

Damage

KESAL AGE 0.145

---+---

NT N E

where,

KESAL

AGE =

NT =

NE =

80-leN ESAL's, in thousands

pavement age in years

allowable number of cycles due to traffic stresses

allowable number of cycles due to environmental stresses

5. Calculate JPCP Transverse Joint Spalling (Chapter 5. equation 59).

The final model for predicting the percentage ofspalled joints for JPCP is as follows:

SpallJPCp

where

SpallJPcp =

TRANGE

RH =

FTCYC =

Damage =

= 100Damage 2.1 (O.344TRANGE _ O.042RH + O.0318FTCYC)

1 + Damage 2.5

percentage ofJPCP joints with spalling of all severities

average daily temperature range, °C

average daily range ofrelative humidity during the month of construction

(can be obtained from NOAA tables), percent

annual number offreeze-thaw cycles

total damage (chapter 5, equation 58)

6. Calculate Allowable Number ofTraffic (NT) and Environment (NE) Load Applications

for JRCP (Chapter 5. equations 60 and 61).

The equations for calculating NT and NEfor JRCP obtained are as follows:

26841k 2 + 28.9khpcc NT = -------=-=-=- at

,

868hpcc2 + 83800khpcc

kjsELONG

176
where

at

~s

ELONG

k

~cc

tensile stress, kPa (calculated from chapter 5, equation 49)

modulus ofthe sealant material or incompressibles, kPa

an estimate ofthe horizontal movement, mm

modulus ofsubgrade reaction, kPalmm

PCC thickness, mm

The recommended values for elastic moduli ofthe sealants or incompressibles, ~s' for JRCP are

given in chapter 5, table 16.

7. Calculate Damage Accumulation for JRCP (Chapter 5, equation 62).

The model for calculating the total damage to JRCP from traffic and environmental

loading is as follows:

0.0667 *KESAL 5.667 *AGE Damage = + ----

NT NE

where

=

number of 80-kN ESAL's, in thousands

pavement age in years

allowable number of cycles due to traffic stresses

allowable number of cycles due to environmental stresses

8. Calculate JRCP Transverse Joint Spalling (Chapter 5, equation 63).

The final model for predicting the percentage ofspalled joints for JRCP is as follows:

SpallJRCp = 100DAMo.8s (1.764*1O-s FI + 6.3478*10-8 Epcc - O.0271k)

where

SpallJRCp

DAM

FI

Epcc

k

percentage ofjoints with spalling of all severities

damage due to traffic and environmental stresses

mean annual freezing index, °C days

PCC elastic modulus, kPa

modulus ofsubgrade reaction, kPalmm

Transverse Cracking for JPCP

Transverse cracks are a major cause ofstructural failure ofJPCP. They develop from the

repeated application of heavy axle loads and as the slab responds to drying shrinkage, thermal

curling, and thermal contractions. Medium- and high-severity transverse cracks in JPCP cause

increased roughness and user discomfort and trigger the need for rehabilitation. A model was

developed as part ofthis study for estimating the percentage ofslabs with transverse cracks (all

severities), and it is recommended for design checking. A summary ofthe input variables

177
required for use in the model developed is presented in table 26. The actual transverse cracking

model and the procedure for calculating the percentage ofslabs with transverse cracking for a

given pavement section are given in chapter 6.

1. Calculate Allowable Number ofLoad Repetitions (Chapter 6, equations 90 and 91).

The final model for estimating Nj for traffic and temperature stresses are as follows:

NTRTC =

NTETC =

(-2.0*104 + 5.507*10-3Epcc + 150.63hpcc + 4.564*1Q-6Epcchpcc

+ 0.744hpcc2)1.33

(-2.0*104 + 5.507*10-3Epcc + 150.63hpcc + 4.564*1Q·6Epcchpcc

+ 0.744hpcc

2

f

where

NTRTC =

NTETC =

Epcc =

hpcc

allowable number of 80-kN ESAL applications

allowable number oftemperature stress applications

PCC slab modulus, kPa

PCC slab thickness, mm

2. Calculate Damage Due to Temperature and Traffic (Chapter 6, equations 88 and 89).

The damage to the pavement from the imposed stresses can be calculated using a

modified form ofMiner's cumulative damage equation. The modified damage equations

for estimating both traffic and temperature stresses are as follows:

178
Table 26. Summary of variables required for estimating JPCP transverse cracking.

Dependent Effect on Transverse

Variable Independent Variables Cracking*

Cumulative number of 80-kN +

ESAL applications

Transverse PCC elastic modulus, kPa -

cracking PCC thickness, mm - (percentage of

slabs cracked) Pavement age in years +

Average annual number offreeze- +

thaw cycles

Annual number of wet days +

Average annual number of days +

with temperature above 32°C

* Positive IndIcates that an Increase In thIS varIable results In an increase in transverse

cracking.

DAMTRTC

= ( KESAL) 0.5

NTRTC

where

KESAL

AGE

Nj

=

=

=

_ ( AGE )0,75 DAMTETC - --

NTETC

cumulative number ofESAL's, thousands

pavement age, years

allowable number ofload repetitions

3. Calculate Percentage of Slabs with Transverse Cracking (Chapter 6. equation 92).

The model for predicting transverse cracking is given as follows:

where

TC = lOO*(50.8FTCYC - 3.2*1O-sEpcd DAMTETC +

lOO*(O.274WTDYS + 0.432D32) DAMTRTC

TC = percentage ofslabs with transverse cracks

179
FTCYC

Epcc

DAMTETc

WTDYS

D32

DAMTRTc

=

=

=

annual number offreeze-thaw cycles

elastic modulus of PCC, kPa

damage caused by temperature stresses

annual number of wet days

annual number of days with temperature above 32°C

damage caused by traffic stresses

Corner Breaks for JPCP

Comer breaks also are a major cause ofstructural failure in JPCP with inadequate load transfer

or weak underlying material. They develop as the slab comers are subjected to repeated

application of heavy axle loads. Comer breaks in JPCP cause increased roughness and user

discomfort, and they trigger the need for rehabilitation. A model was developed as part ofthis

study for estimating the percentage ofslabs with comer breaks (all severities), and it is

recommended for design checking. A summary ofthe input variables required for use in the

model developed is presented in table 27. The actual comer breaks model and the procedure for

calculating the percentage ofslabs with comer breaks for a given pavement secti0n are given in

chapter 6.

1. Calculate Allowable Number ofTraffic and Temperature Load Repetitions Model

(Chapter 6, equations 85 and 86).

The final model for estimating Nj for traffic was as follows:

(5.6 + 8.7*lO,sEpcc - 4.724*1O-2hpcc - 1.7*10'10 Epcchpcc

+ 1.056* lO,3hpcc2)2.93

The final model for estimating Nj for temperature was as follows:

(5.6 + 8.7*10,sEpcc - 4.724*lO'2hpcc - 1.7*10'10 Epcchpcc

+ 1.056* 10,3hpcc

2)s.s

where

PCC slab modulus, kPa

PCC slab thickness, mm

2. Calculate Damage Due to Temperature and Traffic Loading (Chapter 6, equations 83 and

M).

Damage for traffic and temperature stresses was calculated as follows:

- ( KESAL10.75 DAMTRCB -

NTRCB

180
_ ( AGE )0,25 DAMTECB - --

N TECB

where

KESAL

AGE

Nj

=

=

=

cumulative number ofESAL's, thousands

pavement age in years

allowable number ofload repetitions

3. Calculate Percentage of Slabs With Comer Breaks (Chapter 6. equation 87).

The model for predicting the occurrence of comer breaks is as follows:

SWCB

where

= lOO*(24.26JTSP + 2.236AGE- 9.9S*lO-7Epcc) DAMTECB

+ lOO*(3.08*lO-3FTCYC - 3.78*1O-3

Cd) DAMTRCB

SWCB

JTSP

AGE

Epcc

DAMTECB

FTCYC

Cd

DAMTRCB

=

=

=

=

=

=

percentage ofslabs with comer breaks

pavement joint spacing, m

pavement age, yr

elastic modulus of PCC, kPa

damage due to temperature stresses

annual number offreeze-thaw cycles

drainage coefficient

damage due to traffic stresses

Roughness for JPCP, JRCP, and CRCP

Roughness is the irregularity ofthe pavement surface. In general, road users consider roughness

the most important criterion when deciding on the state or condition of a road. Rough roads lead

to user discomfort, increased travel times, and higher vehicle operating costs that can lead to

millions of dollars in losses to the general economy. Although the structural performance of a

pavement is most important to highway designers, the complaints generated by rough roads often

contribute to a large part ofthe rehabilitation decisions made by State highway agencies. Three

models were developed as part ofthis study for estimating roughness for JPCP, JRCP, and

CRCP, and they are recommended for design checking. A summary ofthe input variables

required for use in the roughness models developed is presented in table 28. The actual

roughness models are given in chapter 7.

181
Table 27. Summary of variables required for estimating JPCP comer breaks.

Dependent Variable Independent Variables Effect on Corner Breaks*

Cumulative number of 80- +

kN ESAL applications

PCC elastic modulus, kPa -

PCC thickness, mm - Comer breaks

(percentage ofslabs Drainage coefficient, Cd -

cracked) Joint spacing, m +

Pavement age in years +

Average annual number of +

freeze-thaw cycles

* Positive indicates that an increase in this variable results in an increase in comer breaks.

1. Calc.ula~CP~ghness (Chapter 7, equation 102).

IRI

where

IRI

KESAL

WETDAYS

FREEZE

AGE

FI

Epcc

SUGTYP

DOWDIA

1.3033 + KESAL°.4(1.578WETDAYS + 113.6FREEZE)

* 10-4 + AGE°.4(1.4437FI + 3.6* 10-5Epcc - 552 SUGTYP

- 19.08DOWDIA) * 10-4

International Roughness Index, m1km

cumulative 80-kN equivalent single axle loads, thousands

number of days precipitation is greater than 12.7 mm

LTPP climatic zone, 1=freezing climate, O=nonfreezing climate

pavement age, yr

freezing index, DC days

PCC elastic modulus, kPa

subgrade type, 1=coarse-grained, O=fine-grained

dowel diameter, mm

182
Table 28. Variables required for predicting IRI for JPCP, JRCP, and CRCP.

* Posltlve mdlcates that an mcrease m this vanab1e results in an mcrease in roughness.

Predicted Dependent Variables Effect on

Variable Roughness*

Cumulative number of 80-kN ESAL applications +

Dowel diameter, mm -

Elastic modulus of PCC slab, kPa +

Pavement age since construction, yr +

JPCP IRI

Freezing index in degree days caC days) (m/km) +

FREEZE (pavements located in climates with average mean +

temperature less than 12.75 DC)

Subgrade type, 1=coarse-grained, O=fine-grained -

Average annual number ofwet days +

Cumulative number of 80-kN ESAL applications +

Percentage ofsteel per area for PCC slab +

JRCP IRI Presence of edge drain, 1 = edge drain, 0 = no edge drains - (m/km)

Pavement age since construction, yr +

Average annual precipitation, mm +

Subgrade type, 1=coarse-grained, O=fine-grained -

Cumulative number of 80-kN ESAL applications +

Percentage ofsteel per area for PCC slab -

Pavement age since construction, yr +

CRCP IRI

(m/km) Average annual number of days with temperature above 32 DC +

DRY (pavements located in climates with average precipitation less - than 0.6 m)

FREEZE (pavements located in climates with average mean +

temperature less than 12.75 DC)

Modulus ofsubgrade reaction, kPa/mm - ..

183
2. Calculate JRCP Roughness (Chapter 7, equatioalillJ.

where

IRI

KESAL

PSTEEL

AGE

PRECIP

DRAIN

SUGTYP

IRI

=

1.272 + O.00866*PSTEEL*KESAL°.4 + O.00742*AGEo.7(5.78

+ O.Ol06PRECIP - 1.95DRAIN - 3.73SUGTYP)

International Roughness Index, milan

cumulative 80-kN equivalent single axle loads, thousands

percent steel, percent

pavement age, yr

average annual precipitation, mm

presence of edge drain, I = edge drain 0 = no edge drains

subgrade type, 1 = coarse-grained, 0 = fine-grained

3. . Calculate CRCP Roughness (Chapter 7, equation 104).

The model developed for predicting IRI for CRCP is as follows:

IRI

where

IRI

KESAL

PSTEEL

AGE =

D32

DRY =

FREEZE

KVAL =

1.118 + KESALo.3(0.0142 - 9.787*10-3PSTEEL) + AGE°.4

(3.157*10-3D32 - 0.054DRY + 0.293FREEZE - 4.65*1O-4KVAL

+ 0.1203)

International Roughness Index, m/km

cumulative 80-kN equivalent single axle loads, thousands

percent steel

pavement age, yr

annual number of days with temperature below 32°C

LTPP climatic zone, 1 = dry climate, 0 = wet climate

LTPP climatic zone, 1 = freezing climate, 0 = nonfreezing climate

modulus ofsubgrade reaction, kPa/mm

Suitability of Prediction Models

The models presented in this report have all been checked using both diagnostic statistics and

sensitivity analyses. In all cases, the models were found to be in agreement with sound

engineering principles and judgment. These models can therefore be used for checking new

pavement design. Detailed procedures for using these models and discussions on their limitations

are presented in chapters 4 through 7.

Examples of Application of Performance Models

The assessment ofPCC pavement performance and failure is based on critical levels ofthe

common distresses that occur. The distress and roughness prediction equations developed under

this study may be used for a variety of applications, including:

184
• Evaluation of a pavement design obtained through a standard procedure.

• Evaluation ofthe cost-effectiveness of designs.

The application ofthese models can be best explained by use of examples. Example 1 uses

prediction models to check and evaluate a new pavement design. Example 2 uses prediction

models to evaluate the cost-effectiveness of alternative pavement designs.

Checking the Design of New Pavements with Prediction Models

The inputs to each ofthe prediction models must be obtained first. Ifthe predicted distress at the

end ofthe initial performance period exceeds some defined critical level, the pavement design

will be considered inadequate, and modifications to certain design inputs may be appropriate.

Table 29 provides suggested critical distress levels. An example of using the models for checking

concrete pavement design is as follows:

Example 1

Pavement Design Features

Pavement type

Modulus ofsubgrade

reaction, k

Joint spacing

Standard lane slab width

Joint sealant type

Drainage coefficient

PCC elastic modulus

PCC thickness

Dowel diameter

Base type

Sealant depth

Climatic Variables

=

=

=

=

JPCP without dowels

20.4 kPa/mm

6.1 m

3.65m

Silicone joint sealant (modulus = 2,520,000 kPa)

0.7 (poor)

24,150,000 kPa

200mm

omm (no dowels)

erodible (untreated aggregate)

50.8mm

Wet climate, annual precipitation

Freezing Index, FI

Annual air freeze-thaw cycles

Temperature range

Annual number ofwet days

Relative humidity =

Days with temperature above 32°C

1.016 m

278°C days (cold climate)

70

11°C

50 (precipitation> 12.7 mm)

30 percent

40

185
Table 29. Suggested critical values for key perfonnance indicators.

Performance Indicator JPCP JRCP

Joint faulting 3.05 mm 6.1 mm

Transverse cracking 40 percent 30 deteriorated transverse

cracks/km

Comer breaks 10 percent 10 percent

Joint spalling 40 percent ofjoints 25 percent ofjoints

IRI 2.7 m/km 2.7 m/km

Design Period

Design age

Design ESAL applications

Eyaluation ofDesign

20yr

20 million

Iteration No.1 - Initial pavement design

Predicted mean transverse joint faulting =

Predicted mean transverse joint spalling

Percentage ofslabs with transverse cracking =

Percentage ofslabs with comer breaks

Predicted IRI

4.06 mm (high)

41 percent (high)

43 percent (high)

11 percent (high)

2.64 m/km (rough)

The design is not adequate because the levels of all five distresses are above acceptable or too

close to the acceptable values to ensure an adequate safety factor. Some design features should

be modified to obtain more acceptable levels of distress.

Iteration No.2

The following inputs are used in the next iteration:

Drainage coefficient Cd

Base type

Dowel diameter

Depth ofsealant

Elastic modulus ofPCC

PCC thickness

=

=

=

=

1.2 (penneable treated base with edge drain)

Nonerodible

25.4mm

12.7 mm

31,000,000 kPa

300mm

The revised design results in the following projected distress levels after 20 yr and with 20

million ESAL applications:

186
Predicted faulting

Predicted spalling

Slabs with transverse cracking

Slabs with comer breaks

Predicted IRI

Summary

=

=

0.42mm

31 percent

28.5 percent

1.8 percent

2.56mm/km

The distress levels are reduced considerably in all cases (refer to iteration 1) and, based on the

results ofthis final iteration, the revised design is reasonable. The acceptability ofthe distress

levels is based on the values in table 17, which presents recommendations for critical levels of

pavement distress at which some form ofrehabilitation is required. The critical distress levels are

subjective and depend on an agency's performance standards or the local experience ofthe

design and maintenance engineer. The evaluation ofthis design illustrates the use of distress and

roughness equations and shows that distress and roughness models are very important tools in

pavement design and evaluation.

Comparing Cost-Effectiveness of Alternative Designs

Good management ofpavements can provide several benefits for highway agencies at both the

network and project levels. Foremost among these benefits is the selection of cost-effective

design alternatives. Whether new construction, rehabilitation, or maintenance is concerned, an

evaluation of cost-effectiveness can help management achieve the best possible performance

value for the public dollar.

At the project level, detailed consideration is given to alternative designs, construction,

maintenance, or rehabilitation activities for a particular roadway section or project within the

overall program. By comparing the costs and benefits among alternative designs, an optimum

strategy is identified that will provide the desired benefits and service levels at the least total cost

over the analysis period. Figure 80 presents a flow chart of a procedure for selecting alternative

designs based on performance models. The process is further explained with the following

example.

Exampk2

Design Featuresfor Design Alternative 1

Pavement type

Modulus ofsubgrade reaction, k-value

Joint spacing

Joint sealant type

Depth ofsealant

Drainage coefficient

PCC elastic modulus

PCC thickness

Base type

Dowel diameter

187

JPCP

54.33 kPa/mm

4.6m

preformed joint sealant

50.8mm

1.1

31,000,000 kPa

300mm

nonerodible

25.4mm
Climatic Variablesfor Design Alternative 1

Annual precipitation

Annual number ofwet days

Freezing Index

Annual number of air freeze-thaw cycles

Annual number of days with temperature

above 32°C =

Climate =

Relative humidity =

Design Featuresfor Design Alternative 2

1.1 m

50

555°C days

75

45

freeze

40 percent

Pavement type

Granular base, k

Joint spacing

Joint sealant type

Drainage coefficient

PCC elastic modulus

PCC thickness

Base type

Dowel diameter

JPCP

20.4 kPa/mm

9.15 m

silicone joint sealant

0.7

24,150,000 kPa

200mm

erodible

Omm

188
Matenals

Time

(Agel

'-----NO

I INPUTS Environment

Traffic and Loading

MODELS OF DESIGN PAVEMENT STRUCTURE

INCL. ENGR. FACTORS CONSTRAINTS

I BEHAVIOR 1

r

I DISTRESS I

I PERFORMANCE I

LIFE CYCLE

I RELIABILITY I (Meets Constraints])

I

YES

- -

I LIFE CYCLE COSTS 1

I COST

DIRECT

INDIRECT

ECONOMIC

EVALUATION

OPTIMIZATlON

(List by minimum cost at specified level of reliability)

SELECT FINAL DESIGN I I BUDGET I

I CONSTRUCT I

I MONITOR l

PERFORMANCE

f DATAl

PMS

BANK [ -- INFORMATION

SYSTEM

FEEDBACK 1 J

Figure 80. Schematic diagram of pavement design practice with

emphasis on cost-effectiveness.(33)

189
Climatic Variablesfor Design Alternative 2

All the climate variables remain the same as those for alternative 1.

Performance Criteria

Performance period

MaximumIRI

Maximum faulting =

Maximum spalling

Transverse cracking =

Comer breaks

determined based on critical distress values in table 28

2.7 m/km

3.05mm

40 percent ofjoints with low, medium, and high severity

40 percent

10 percent

A comparison ofthe two design alternatives is given in table 29. The percent cost and life are

calculated as follows:

P C t 100 Cost of Alternative 1 - 1

ercent os = *--------

Cost of Alternative 2

Percent Life = 100 *ESAL IS 1 - 1

ESAL IS 2

(105)

(106)

Ifthe percent increase in life is greater than the percent increase in cost, then Alternative 1 is

more cost-effective. However, ifthe percent increase in life is less than the percent increase in

cost, then this design alternative is not more cost-effective. It is obvious from the analysis

presented in table 30 that Alternative 1 is more cost-effective. Performance equations are used in

this manner by design engineers to evaluate different pavement design alternatives and strategies.

Summary

This chapter has presented two different ways performance models are used. The models were

used in the evaluation ofpavements designed using standard design procedures and in selecting

between alternative pavement designs. These are just a couple ofthe wide variety ofways in

which performance models can be used. However, these models must be used with care and

should not extend beyond the inference space for which they were developed.

190
Table 30. Comparison of cost-effectiveness oftwo alternate pavement designs.

Alternate Design 1 Alternate Design 2

Faulting (ESAL's/millions to reach 30+ 8

critical)

Spalling (ESAL's/millions to reach 28.5 21

critical)

Transverse cracking (ESAL's/millions to

reach critical) 28 16

Comer breaks (ESAL's/millions to reach

critical) 30+ 6

IRI (ESAL's/millions to reach critical) 23 20.5

Cost of design $2.0 million $1.6 million

Lifespan of design (ESAL's) 20*106 7*106

Percent cost 124 percent

Percent life 380 percent

More cost-effective design ./

191

9. CONCLUSIONS AND RECOMMENDATIONS

Conclusions

Models that are used to predict the occurrence and amount of distress and roughness are

important tools in pavement engineering. They can be used to check the adequacy of new designs

or to predict the distress of existing pavements for use in pavement management systems.

Prediction models also provide information on the design features and practices that influence

the long-term performance ofpavements.

A major objective ofthis study was to use the LTPP database to develop improved prediction

models for PCC pavements. An important goal was to use innovative analytical techniques and

mechanistic principles to develop state-of-the-art prediction models that are practical for

application by State highway agencies.

This report presents several mechanistic-empirical and empirical models that have been

developed for predicting the following key types of distress and roughness ofPCC pavements:

• Transverse joint faulting.

• Transverse joint spalling.

• Transverse cracking and comer breaks.

• Roughness.

The models for transverse joint faulting, transverse spalling, transverse cracking, and comer

breaks are based on mechanistic clusters derived from mechanistic analysis. For each distress

type, this required the identification of a primary mechanistic response parameter that could be

related to the damage accumulation in the pavement that leads to distress. Using a combination

ofpavement analysis techniques, this was successfully accomplished, and several mechanistic

clusters were developed for the key distress types. Distress model forms including the

mechanistic clusters were then calibrated with LTPP data to obtain the models presented.

Because ofthis approach, the models obtained take into consideration many ofthe significant

factors that have an influence on pavement performance.

Each ofthe models was evaluated and verified using statistical techniques and by performing

comprehensive sensitivity analyses. This was to ensure the ability of each model to predict

distress within reasonable accuracy and within the limits ofthe LTPP database. The sensitivity

analyses also confirmed that the pavement distress models are in agreement with sound

engineering principles and judgment. The roughness models developed in this study were also

checked in a similar manner. As an illustration, examples ofthe application ofthe models are

presented in chapter 8 ofthis report. Recommendations on the design and construction ofPCC

pavements developed using the models presented in chapters 4 through 7 are presented in volume

I ofthis report.

Recommendations

The main products developed in this study are the improved mechanistic-empirical and empirical

models for predicting PCC pavement distress and roughness. Extensive checks ofthe models i

193
indicate that they provide reasonably accurate results and can be used in pavement design and

management. The innovative techniques used also provide evidence that mechanistic principles

can be applied successfully to develop mechanistic-based models that provide more accurate

predictions. This report presents an example that future analysts can follow to improve on the

results obtained. Examination ofthe models provides several insights and recommendations that

are immediately useful to State highway agencies for improving the long-term performance of

PCC pavement. As indicated previously, recommendations that include specific information on

the design features and practices for the design and construction oflong-lived PCC pavements

are presented in volume I. Tables 18 through 25 in the present volume provide a summary ofthe

effects ofsignificant pavement design and climatic variables on the distress types and roughness,

based on the models developed. The tables present useful information for designers and analysts

on the design and construction ofPCC pavements.

Tables 31 through 38 confirm the importance ofthe interacting effect of climate, traffic, and

pavement design features on pavement performance. In most instances, the climate cannot be

controlled and traffic can only be controlled to a certain extent; therefore, designers need to pay

attention to those design features that affect the occurrence and progression ofdistress. The most

practical way to minimize the onset and severity ofdistress is to take these effects into account

during the design process.

Recommendations for Future Research

The results presented in this report are based on a comprehensive analysis ofthe LTPP data and

the use ofinnovative analytical techniques to develop improved models for predicting key PCC

distress and roughness. To a large extent, the attempt to use mechanistic principles to develop

mechanistic-empirical models was successful. However, because of a variety oflimitations, a

number ofimprovements are warranted in future efforts. Future research is necessary to address

some ofthe limitations that were faced in this effort. For example, the traffic loading data used in

this research were historical ESAL estimates. For most ofthe pavements in the LTPP database,

ESAL data were not available for several years. Therefore, projections were necessary to obtain

the cumulative and yearly ESAL's used in the analysis. Improved traffic loading data that

include load spectra data for investigating the effect ofdifferent load levels, type, and

configuration on distresses will greatly improve the accuracy ofthe models

presented.(12)

The lack ofpavement-specific environmental data (e.g., thermal gradients in the PCC slab) made

it difficult to estimate accurately the effect of environmental stresses within the scope ofthis

study. Environmental data from the LTPP Seasonal Monitoring Program (SMP) should be

obtained in future studies for the development ofmodels that can be used to estimate such data.

Finally, the techniques applied in this study provided an opportunity for application of

mechanistic principles to the development ofprediction models for pavement distress. However,

in several cases, because ofthe current scope ofthe project and limitations in the data available

(in particular, traffic loading and materials data), an in-depth application ofmechanistic

principles was not possible. These innovative analytical techniques should be explored further in

future research to improve on the models.

194
\,Q

-\J1

Table 31. Effect ofkey pavement design features and site condition factors on transverse joint faul

Key Design Feature or Site

I Effect on JPCP Joint Faulting

Condition Factor

Traffic loading Significantly increases the progression offaulting.

Load transfer or dowels Dowels of at least 25.4 mm diameter reduce faulting by at least half. The la

diameter, the more the reduction in faulting. Thus, dowel diameter can be d

given pavement design.

PCC slab thickness Thicker PCC slabs reduce the progression offaulting.

Base type A nonerodible base (e.g., lean concrete) appreciably decreases faulting in c

erodible bases, such as untreated materials. There is a strong interaction bet

and the drainage coefficient. Coarse, permeable, and nonerodible bases incr

coefficient ofthe pavement and reduce faulting.

Modulus ofsubgrade reaction, k- A stiffer support reduces faulting, but not as effectively as a nonerodible ba

value subgrade.

Joint spacing Pavements with shorter slabs fault less than those with longer joint spacing

Drainage coefficient, Cd Increasing the drainage coefficient by improving drainage reduces the prop

pavement to be saturated for long periods. This results in reduced faulting.

Number ofwet days (i.e., A high frequency ofprecipitation will result in more faulting.

frequency ofprecipitation)
.....

'!)

0'

Table 32. Effect ofkey pavement design features and site condition factors on transverse joint spal

Key Design Feature or Effect on JPCP Joint Spalling

Site Condition Factor

Traffic loading/age Both traffic loading and aging increase spalling ofJPCP.

Climatic conditions during The relative humidity and temperature range during construction influenc

construction A high relative humidity, probably caused by improving the curing proces

reducing the formation of early microcracks, reduces spalling in later year

other hand, a high daily temperature range, probably caused by an increas

restrained temperature stresses, increases microcrack formation and spallin

Annual freeze-thaw cycles Pavements located in areas with a high number offreeze-thaw cycles will

experience more spalling.

Average daily temperature The higher the average daily temperature range during the life of a pavem

range higher the chance ofspalling.

Joint sealant characteristics In general, pavements with sealants experience less spalling than those wi

Among the different sealants, preformed sealants perform best in terms of

reduction in joint spalling. Stiffer sealants cause more spalling.

PCC slab thickness Pavements with thicker PCC slabs experience less spalling in general.

PCC slab elastic modulus Stiffer PCC slabs (i.e., higher elastic modulus) experience less spalling. M

and material properties properties that cause less horizontal expansion or elongation ofthe PCC s

also reduce spalling.

Modulus ofsubgrade Pavements with higher subgrade and, therefore, better support experience 

reaction spalling.
......

'-0

'.J

Table 33. Effect ofkey pavement design features and site condition factors on JRCP transverse joint s

Key Design Feature or Effect on JRCP Joint Spalling

Site Condition Factor

Traffic loading/age Traffic loading and aging both increase spalling ofJRCP.

Freezing index A higher freezing index will cause more spalling in JRCP.

Annual freeze-thaw cycles Pavements located in areas with a high number offreeze-thaw cycles will

experience more spalling.

Joint sealant characteristics In general, JRCP pavements with sealants will experience less spalling th

without. Among the different sealants, silicone and asphalt sealant perform 

terms ofreduction in joint spalling. Stiffer sealants cause more spalling.

PCC slab thickness Pavements with thicker PCC slabs experience less spalling in general.

PCC slab elastic modulus For JRCP, stiffer PCC slabs (i.e., higher elastic modulus) will cause more 

and material properties Material properties that cause less horizontal expansion or elongation oft

slab will reduce spalling.

Modulus ofsubgrade Pavements with higher subgrade modulus and, therefore, better support w

reaction experience less spalling.
--0 -

00

Table 34. Effect ofkey pavement design features and site condition factors on JPCP comer brea

Key Design Feature or Effect on JPCP Corner Breaks

Site Condition Factor

Traffic loading/age Traffic loading and aging increase the occurrence of comer breaks.

Joint spacing Longerjoint spacing will increase the occurrence of comer breaks. This may b

to the higher levels of curling that occur over longerjoint spacing and the loss 

the comer that is associated with it.

PCC slab thickness Thicker slabs will experience less comer breaks.

PCC elastic modulus Stiffer PCC slabs will experience less comer breaks.

Number offreeze-thaw More freeze-thaw cycles will increase comer breaking.

cycles

Drainage coefficient A higher drainage coefficient will reduce the occurrence of comer breaks.
......

-..0

-..0

Table 35. Effect ofkey pavement design features and site condition factors on JPCP transverse crac

Key Design Feature or Site Effect on JPCP Transverse Cracking

Condition Factor

Traffic loading/age Traffic loading and aging will increase transverse cracking ofJPCP.

PCC slab thickness JPCP with thicker PCC slabs will experience less transverse cracking.

PCC slab elastic modulus A stiffer PCC slab will reduce the occurrence oftransverse cracking.

Number offreeze-thaw More freeze-thaw cycles will increase the occurrence oftransverse cracks.

cycles

Frequency ofprecipitation A higher frequency ofprecipitation will increase the occurrence oftransverse 

Number ofdays temperature A higher number of days during which the temperature exceeds 32°C will ca

exceeds 32 °C transverse cracking.
N

a

a

Table 36. Effect ofkey pavement design features and site condition factors on JPCP roughness

Key Design Feature or Effect on JPCP Roughness

Site Condition Factor

Traffic loading/age Both traffic loading and aging will increase roughness.

Climatic conditions Harsher climatic conditions, probably because ofthe higher levels of distr

associated with them, increase roughness. Specifically, a higher frequency 

precipitation and the location of a pavement in a freezing climate (i.e., hig

freezing index) will cause more roughness.

PCC slab elastic modulus Pavements with higher PCC elastic moduli seem to get rougher with time

Dowel diameter Use ofdowels in JPCP pavements reduces roughness. Increasing the dow

diameter, probably by reducing joint distress such as faulting, further redu

roughness.

Subgrade type Coarse-grained subgrade types will cause less roughness.
N

a

.......

Table 37. Effect ofkey pavement design features and site condition factors on JRCP roughne

Key Design Feature or Effect on JRCP Roughness

Site Condition Factor

Traffic loading/age Traffic loading and aging increase the roughness of all pavements.

Steel content JRCP with a higher steel content exhibited more roughness.

Precipitation JRCP pavements that experience more rainfall will get rougher with tim

Drainage An edge drain will reduce the progression ofroughness on a JRCP by pr

positive drainage.

Subgrade type Coarse-grained subgrades will cause less roughness ofJRCP.

Table 38. Effect ofkey pavement design features and site condition factors on CRCP roughn

Key Design Feature or Effect on CRCP Roughness

Site Condition Factor

Traffic loading/age Traffic loading and aging increase the roughness of all pavements.

Steel content A higher steel content in CRCP will reduce roughness.

Climatic conditions A freezing climate will cause more roughness. Pavements located in dri

will experience less roughness, but a large number of days during which 

maximum temperature exceeds 32°C will increase roughness.

Modulus ofsubgrade CRCP pavement with better support (i.e., higher modulus ofsubgrade r

reaction will experience less roughness.

APPENDIX A. CALIBRATION OF PREDICTION MODELS

This appendix provides information on the process that was used to calibrate the prediction

models presented in this study. The process is the culmination ofthe research team's many years

or'experience. It involves application ofmodem statistical techniques, combined with a large

dose of engineering theory, to obtain models for predicting the distress and performance of

pavements. Figure 81 is a flow chart that provides an overview ofthe process, which can be

divided into the following:

• Data preparation and selection ofindependent variables.

• Tentative model development and verification.

• Model evaluation, verification, and validation.

Data Preparation and Selection ofIndependent Variables

An important part ofthe process for calibrating or developing regression models is the collection

and preparation ofthe data needed and selection ofthe independent variables that should be

considered. The following are the steps taken to accomplish this:

Literature Review

A comprehensive literature search and review is required to determine the most appropriate

variables, clusters, and mechanistic equations that could be used to develop the model. In model

development efforts that use observational data, the information from past studies and the

experience ofthe researcher are necessary for selecting the independent variables that should be

considered. For studies with observational data, this step is more important than is often

recognized. Theory can often provide guidance on the variables that should be selected, as well

as the model form that will provide good models. Accordingly, in this study, considerable effort

was spent to review past studies.

Identify and Define Potential Variables and Clusters

This is an important follow-up to the literature review process. The goal is to identify which

variables are relevant to the model and need to be included in the final analysis data set. Not all

the variables identified in the literature search may be relevant; however, it provides a starting

point for identifying potential variables and clusters to look at more closely.

203
Select Distress/IRI Model & Conduct

Literature Review of Previous Models

and Distress Mechanism ----10- Identify and Define Potential Variables

• Dependent Variable (Definition)

• Independent or Explanatory Variables

Identify Missing Data Items for Variables

(Decide which Variables have too Little .-------iJ3lData to Keep in Analysis)

Assemble Database ofLTPP Sections

(Determine Specific Subset of Data to Use)

I------I_@}__

Explore Dataset and Clean Data

• Statistics (mean, min., max., etc.)

• 2-Dimensional Bivariate Plots

• Correlation Matrix of all Variables

• Identify Types of Relationships Between Variables

• Identify Erroneous and Potential Problem Data

• Optional: Create Mechanistic Variable Cluster

I

A

Figure 81. Flow chart for developing distress models.

204
®-

Model Building

A • Identify Functional Form of Distress/lRI with Traffic

and Age

• Identify Boundary Conditions

• Select Potential Variables and Transformations for

Initial Evaluation

• Conduct Linear Regression with all

Variables/Clusters (Observe significance Levels,

Collinearity, Residual and Predicted vs. Actual Plots)

• Identify Potential Outliers

• Conduct Further Regression Analyses

• Select Tentative Model

[]-- Sensitivity Analysis

• Set Variables at Their Means

• Increase/Decrease each Variable by One Standard

Deviation and Compute Distress/lRI for each

• Repeat for all Variables

• Plot Sensitivity Graph

• Evaluate Reasonableness of Direction of Variables on

Distress/IRI

• Evaluate Reasonableness of Sensitivity of each

Exploratory Variable

• Judge Adequacy of Tentative Model

• Revise Model if Deficient

Figure 81. Flow chart for developing distress models (continued).

205
Assemble Analysis Database

This involves assembly ofthe data set to be used for model development on the basis ofthe

information on potential variables and clusters obtained from literature review and preliminary

statistical analysis. In this study, the LTPP database was the source ofdata used for developing

all models.

Explore Data Set and Clean Data

A thorough evaluation ofthe analysis data set is always necessary to identify any missing data

elements and possible problem spots in the database. Attempts should be made to obtain

replacements for missing data where possible. The analysis data set should also be checked

closely for anomalies and gross data error. Data determined to be outliers were cleaned out ofthe

data set used in the analysis.

Basic univariate analyses are required to provide information on the distribution of each variable

being considered, as well as the dependent variable. Bivariate analyses should be conducted to

identify relationships between independent variables and between the independent variables and

the dependent variable. Exploration ofthe data set will also provide insights into possible model

forms. Univariate and bivariate analyses are also good methods for determining whether the data

include outliers, errors, potential problem sources, and the possibility of creating interactions and

mechanistic clusters. These analyses should provide useful information for further reducing the

number ofindependent variables to subsets that contain only those that are known to be essential

to the model.

Model Development and Verification

Development ofTentative Model

The first step in model building is the identification ofsuitable mathematical model forms for

evaluation. For pavements, deterioration or distress progression varies for different pavement

types and distresses. Figure 82 shows common mathematical models that have been used

successfully to develop models for the progression ofpavement distress.

Selecting the most suitable model form is the key to developing a sound and stable model. Most

statistical packages available provide the capability ofusing multiple regression analyses to

identify the model forms that fit the data well. The procedures are also very useful for narrowing

down the variables that should be included in the final models. However, for observational data

(such as pavement performance data), it is very important to conduct such analyses with care to

ensure than essential independent variables are not eliminated.

206
y

y = a +~ x

y

y = ax~x

x

(a) Linear

x

(b) Exponential

X

1

Y = -Logx

a+a

(f) S-shaped

Y

n

Y = E~.Xi i=O I

(e) Polynomial X

y y 1

Y=a+~x Y = a+ax~

for >1, a>O

0 X X

(c) Power (d) Hyperbolic

Y

Figure 82. Typical functional forms used for pavement distress modeling.

207
Standard mathematical model fonns, such as linear, quadratic, log-transfonned, and other

nonlinear model fonns, can be used to fit the independent data to the dependent variable once the

final list ofvariables has been selected. Model fonns that work well for pavement distresses are

given in Figure 82. The following are the mathematical equations that describe these model

fonns:

Linear Model

y

Exponential Model

=

(figure 82(a))

(figure 82(b))

y = 80 + at

PX

Power Model (figure 82(c))

y = 80 + atXP

Hyperbolic Model (figure 82(d))

1

y = aO+a1X

Polynomial Model

S-Shaped Model

" Y = Lat X t

t=O

1 Y = ------,...

C -LogX/

ao+ at t

(figure 82(e))

(figure 82(f))

The advantage ofthe linear regression model is its simplicity in development and use, as well as

its relative insensitivity to the "noise" in the database. The main drawback is that the

deterioration ofpavements and the progression ofdistresses exhibit a more complex relationship

with other independent pavement properties or parameters. The polynomial functional fonn

pennits the most flexibility in modeling; however, polynomial regression does not guarantee that

the resulting model will decrease or increase in the entire interval ofthe inference space, as could

be required by engineering judgment.

208
The diagnostic statistics listed in table 39, which are part ofthe output for multiple regression,

must be analyzed to establish the suitability and stability ofthe model under consideration. The

critical values ofthe diagnostic statistics are also given in table 39 and are explained in greater

detail in the subsequent section.

Coefficient ofDetermination (R2

)

The coefficient of determination is an indication of how much variation is explained by the

model. It is defined as follows:

= 1- SSE/TSS (107)

where

R2 =

SSE =

TSS =

coefficient of determination

sum ofsquares for error

corrected sum ofsquares error

A good model that fits the data should have the maximum possible coefficient ofdetermination.

Variance Inflation Factor

Variance inflation factors measure the strength ofinterrelationships among regressor or

independent variables in the model. If all variables are independent of each other, the variance

inflation factor is equal to 1.0. If a variable is closely related to other variables, its tolerance goes

to zero as the variance inflation factor gets very large. Tolerance (TOL) and variance inflation

factor (VIE) are defined as follows:

where

=

TOL =

coefficient of determination

(l08)

VIF = lITOL

209

(109)
Table 39. Diagnostic statistics and corresponding critical values.

Diagnostic Statistic Diagnostic Objective Critical Values

Coefficient ofdetermination (R2) Goodness offit Maximize

Variance inflation factor (VIF) Multicollinearity < 10

Durbin-Watson test statistic (d) Serial correlation and 1.5 < d <2.5

independence of variables

Mallow's Cp Optimum number of Approximately equal to number

independent variables ofindependent variables

Mean square error (MSE) Goodness offit Minimize

Press statistic (PresSp) Ability to predict outside Minimize

of current data set

Test ofsignificance (Prob>F- Significance of parameter <0.05

statistic) estimate

For model development, the effect of correlations between independent variables or

multicollinearity should be minimized to obtain a model that will be adequate and robust for

different databases. A tolerance level of 0.1 or a maximum VIF value of 10 should ensure this.

Durbin-Watson Test Statistic (d)

The Durbin-Watson test statistic (d) is a measure ofthe independence of errors in time-series

data used in the model. As noted in earlier sections ofthis report, one ofthe key assumptions

made in model development is the independence ofthe variables. With most data, especially

time-series data, the errors are autocorrelated, that is, ej is correlated with ei-l just before it.

Autocorrelation is a symptom ofsystematic lack offit. The Durbin-Watson test statistic is

defined as follows:

where

d

n

E (ei - ej-l)

i=2 (108)

= error (ymeasured - Ypredicted) for data i

The value of d is close to 2.0 ifthe errors are uncorrelated. A value of d ranging from 1.5 to 2.5

is reasonable for most models.

210
Mallow's Cp

To choose a model that provides the best prediction using the sample estimates, there is the need

to guard against the use ofmore independent variables than can be reliably used with the given

sample size. Cp is a criterion for selecting the optimum number ofindependent variables in a

model. Cp is defined as:

SSE

C

p = --p - (N - 2p)

S2 (111)

where

SSEp = s = N =

P =

sum ofsquares error for a model with p number ofindependent variables

mean square error for the full model

total number ofindependent variables in the full model

number of parameters in a given model, including the intercept

14 -r;=========================:::;-----i _ • _Mean square error

___Coefficient of determ ination (RA 2)

12 -1-- -'-- ____1

\

8 -I-----I-----'lO-------------=.--""----------1

,;

--...... ......... --." 6+-_~_+_---+_---+_---+_--____I

8-i 10 -I----\----~'-----------------I

o 2 4 6 8 10

Number of variables in the mod el

Figure 83. Variation in Cp with MSE and R2

•

211
Mallow suggests that the model where Cp first approaches p is the optimum model with

parameter estimates unbiased. Figure 83 shows the variation ofCp with the mean square error

(MSE) and the coefficient ofdetermination (R2

) of a model. .

Mean Square Error and Test for Significance

The mean square error is an estimate ofthe absolute difference between the actual and predicted

dependent variable. It is calculated as follows:

where

MSE = SSE/en - p) (112)

SSE =

n = p

sum ofsquares error

number ofdata points in database

number of variables in the model

MSE should be minimized for all models. The test ofsignificance or p-values do not necessarily

measure the importance of a variable. They do, however, give an indication ofthe contribution

the variable makes to predicting the dependent variable. This test statistic is used to eliminate

variables that contribute little to the model. A significance level ofless than 5 percent is

satisfactory.

PRESS Statistic p

The predicted residual for observationj is defined as the residual for the kth observation that

results from dropping the jth observation from the parameter estimates. The sum ofsquares of

the predicted residual errors is called the PRESSp statistic. The PRESSp statistic gives an

indication ofthe ability ofthe model to be used outside the database that was used in model

development. PRESSp should be minimized.

Model Evaluation and Verification

Each model was verified to check its predictive accuracy and whether it made engineering sense.

Model validation is the process of checking the ability ofthe model to predict distress when used

with independent data. Attempts were made to validate the models with independent data, but

this was not possible. However, a variety ofstatistical approaches were used to evaluate the

predictive capability ofthe models, including the following:

• Sensitivity analyses.

• Statistical diagnostic tests.

The sensitivity analyses involved using the model to evaluate the effect ofvarious inputs on the

predictyd distress and comparing the results with empirical and theoretical observations. It

involved setting all other variables at their means and varying the inputs ofinterest. Plots ofthe

results obtained were evaluated to check the engineering plausibility ofthe models and whether

212
the models provided predictions that made sense. The tentative model was selected on the basis

ofthe results ofthis process and the acceptable diagnostic statistic results.

213

REFERENCES

1. Rowshan, S. and S. Harris. Long Term Pavement Performance Information Management

System. Report No. FHWA-RD-93-094. Federal Highway Administration, Washington,

DC, July 1993.

2. Crovetti, J.A. Evaluation ofJointed Concrete Pavement Systems Incorporating OpenGraded Permeable Bases. Ph.D. dissertation. University ofIllinois at UrbanaChampaign, 1994.

3. Owusu-Antwi, E.B. and M.1. Darter. "Early Results ofthe LTPP Concrete Pavement Data

Analysis." Third International Workshop on the Design and Evaluation ofConcrete

Roads, Vienna, Austria, 1994.

4. Simpson, AL., IB. Rauhut, P.R Jordahl, E.B. Owusu-Antwi, M.1. Darter, and R

Ahmad. Early Analysis ofLTPP General Pavement Studies Data, Volume 3: Sensitivity

Analysesfor Selected Pavement Distresses. Report No. SHRP-P-393. Strategic Highway

Research Program, Washington, DC, 1994.

5. Federal Highway Administration. Program Reference Guide-Version 1.0. Federal

Highway Administration, LTPP Division, Washington, DC, March 1996.

6. Federal Highway Administration. Data Collection Guide for Long-Term Pavement

Performance Studies. Operational Guide No. SHRP-LTPP-OG-OO1. Strategic Highway

Research Program, Washington, DC, January 1990 (Revised October 1993, FHWALTPP Division).

7. Strategic Highway Research Program. SHRP Database Structure Reference Manual.

Washington, DC, April 1992.

8. Darter M.I., J.M. Beck, M.B. Snyder, and RE. Smith, Portland Cement Concrete

Pavement Evaluation System-COPES. National Cooperative Highway Research Program

Report No. 277. Transportation Research Board, Washington, DC, 1985.

9. Smith, KD., D.G. Peshkin, M.1. Darter, and AL. Mueller, Performance ofJointed

Concrete Pavements, Volume III: Summary ofResearch Findings. Report No. FHWARD-89-138. Federal Highway Administration, Washington, DC, November 1990.

10. Yu, H.T., M.1. Darter, KD. Smith, I Jiang, and L. Khazanovich. Performance of

Concrete Pavements, Volume III - Improving Concrete Pavement Performance, Final

Report. Contract No. DTFH61-91-C-00053. Federal Highway Administration, McLean,

VA, 1996.

11. Wilde, W.J., D.G. Zollinger, E.D. Moody, RO. Rasmussen, and D.K Rozycki. Long

Term Pavement Performance Data Analysis: Model Developmentfor Prediction of

Distress and Roughness in PCC Pavements, Draft Final Report. Contract No. DTFH61-

94-C-00208. Federal Highway Administration, McLean, VA, 1996.

215
12. Owusu-Antwi, RB., L. Titus-Glover, L. Khazanovich, and J.R. Roesler. Development

and Calibration ofMechanistic-Empirical Distress Modelsfor Cost Allocation.

Preliminary Draft Final Report. Federal Highway Administration, Washington, DC,

March 1997.

13. Permanent International Association ofRoad Congresses. Combating Concrete Pavement

Slab Pumping by Interface Drainage and Use ofLow-Erodibility Materials: State ofthe

Art and Recommendations, Paris, France, 1987.

14. Christory, J.P. "Assessment ofPIARC Recommendations on the Combatting ofPumping

in Concrete Pavements." Sixth International Symposium on Concrete Roads. Madrid,

Spain, 1990.

15. Highway Research Board. Research Reports No. lD, Special Papers on the Pumping

Action ofConcrete Pavements, 1945.

16. Highway Research Board. Research Reports No. 1D, Special Papers on the Pumping

Action ofConcrete Pavements, Supplement,. 1946.

17. Highway Research Board. Current Road Problems No. 4R, Maintenance Methodsfor

Preventing and Correcting the Pumping Action ofConcrete Pavement Slabs, 1947.

18. Highway Research Board. Research Reports No. lD, A Survey ofPumping in Illinois,

1948.

19. Highway Research Board. The AASHO Road Test-Report 5, Pavement Research.

Special Report 61R Highway Research Board, Washington, DC, 1962.

20. Phu, N.C., J.P. Christory, and J. Ray, "The Hydromechanics ofPumping in Concrete

Pavements: Modeling and Prevention, Appendix I, Combating Concrete Pavement

Pumping: State-of-the-Art and Recommendations," PIARC Technical Committee on

Pavements, 1986.

21. Gulden, W. "Experience with Drainage ofJointed Concrete Pavements." Permanent

International Association ofRoad Congresses, International Seminar on Drainage and

Erodibility at the Concrete Slab-Subbase-Shoulder Interface, March 1983.

22. Larralde, J. "Structural Analysis ofRigid Pavements With Pumping." Ph.D. dissertation.

Purdue University, West Lafayette, IN, 1984.

23. Hansen, R, R. Johannesen, and J.M. Armaghani. "Field Effects ofWater Pumping

Beneath Concrete Pavement Slabs," ASCE, Journal ofTransportation Engineering, Vol.

117, No.6, Nov-Dec 1991.

24. Poblete, M. "Informe Anual 1986," Control y Seguimiento de Pavimentos de Hormigon,

IDIEM-Direccion de Vialidad, Universidad de Chile, 1986.

216
25. Neal, B.F. Evaluation ofDesign Changes and Experimental pce Construction Features.

Report No. FHWAICAlTL-85/07. Caltrans, Sacramento, CA, 1987.

26. Wu, C.L., lW. Mack, P.A. Okamoto, and R.G. Packard. "Prediction ofFaulting ofJoints

in Concrete Pavements," Proceedings, Fifth International Conference on Concrete

Pavement Design and Rehabilitation, Vol. 2., Purdue University, West Lafayette, IN,

April 1993.

27. Yao, Z. "Design Theory and Procedure ofConcrete Pavements in China," Second

International Workshop on the Theoretical Design ofConcrete Pavements, Siguenza,

Spain, 1990.

28. Yoder, EJ., and M.W. Witczak. Principles ofPavement Design. John Wiley & Sons,

Inc., New York, NY, 1975.

29. Van Wijk, AJ., l Larralde, C.W. Lovell, and W.F. Chen. "Pumping Prediction Model for

Highway Concrete Pavements," ASCE, Journal ofTransportation Engineering, Vol. 115,

No.2, 1989, pp. 161-175.

30. Bhatti, M.A., J.A. Barlow, and J.W. Stoner. "Modeling Damage to Rigid Pavements

Caused by Subgrade Pumping," ASCE, Journal ofTransportation Engineering, Vol. 122,

No.1, Jan.-Feb. 1996, pp. 12-21.

31. Westergaard, H.M. "Analysis of Stresses in Concrete Pavements Due to Variations of

Temperature," Proceedings, Sixth Annual Meeting, Highway Research Board,

Washington, DC, 1926.

32. Benekohal, R.F., K.T. Hall, and H.W. Miller "Effects ofLane Widening on Lateral

Distribution ofTruck Wheels," Transportation Research Record 1286, Transportation

Research Board, Washington, DC, 1990.

33. American Association of State Highway and Transportation Officials. AASHTO Guide

for Design ofPavement Structures -1993. Washington, DC, 1993.

34. Dempsey, B.J., S.H. Carpenter, and M.1. Darter. Improving Subdrainage and Shoulders

ofExisting Pavements, Final Report. Federal Highway Administration, Washington, DC,

1980.

35. Dempsey, BJ. "Laboratory and Field Studies ofChanneling and Pumping,"

Transportation Research Board, Transportation Research Record 849, 1982, pp. 1-12.

36. Raad, L. "Pumping Mechanisms ofFoundation Soils Under Rigid Pavements,"

Transportation Research Board, Transportation Research Record 849, 1982, pp. 29-37.

37. Raad, L., G.H. Miniassian, and lL. Hulsey. "Mechanistic Evaluation of Saturated Bases

Under Concrete Pavements," ASCE, Journal o/Transportation Engineering, Vol. 121,

No.6, Nov.-Dec. 1995, pp. 495-501.

217
38. Van Wijk, A.J. "Rigid Pavement Pumping: (1) Subbase Erosion and (2) Economic

Modeling." Ph.D. dissertation. Purdue University, West Lafayette, IN, 1985.

39. Phu, N.C. "Hydraulique du pompage des chaussees en beton et erodabilite des materiaux

de couche de fondation et de couche de forme." Ph.D. dissertation. Univesite Paris VI,

LCPC, March 1979.

40. Huang, Y.H. Pavement Design and Analysis. Prentice Hall, Englewood Cliffs, NJ, 1993.

41. Distress Identification Manualfor the Long-Term Pavement Performance Project. Report

No. SHRP-P-338. Strategic Highway Research ProgramlNational Research Council,

Washington, DC, 1993.

42. McCullough, B.F. and G.B. Elkins. eRC Pavement Design Manual, Austin Research

Engineers, 1979.

43. Tayabji, S.D. and B.B. Colley. Improved Rigid Pavement Joints. Report No. FHWA-RD86-040. Federal Highway Administration, Washington, DC, 1986.

44. Darter, M.l. and E.J. Barenberg. Design ofZero-Maintenance Plain Jointed Concrete

Pavements, Vol. 1. Report No. FHWA-RD-77-111. Federal Highway Administration,

Washington, DC, January 1993.

45. Guiterriz de Veiasco, M. and RF. McCullough. Summary Reportfor 1978 CRCP

Condition Survey in Texas. Research Report 177-20. Center for Transportation Research,

University ofTexas, Austin, Texas, 1981.

46. Zollinger, D.G. and E.J. Barenberg. Continuously Reinforced Pavements: Punchouts and

Other Distresses and Implicationsfor Design. Report No. FHWA/IL/UI/227. Illinois

Department ofTransportation, Springfield, IL, 1990.

47. Sanadheera, S.P. and D.G. Zollinger. Influence ofCoarse Aggregate in Portland Cement

Concrete on Spalling ofConcrete Pavements. Research Report 1244-11. Texas

Transportation Institute, College Station, TX, 1995.

48. Hibbit, Karlson, and Sorenson, Inc. ABAQUS/Standard Example Problems Manual,

1996.

49. Miner, M.A. "Cumulative Damage in Fatigue," ASME, Transactions, Volume 67, 1945.

50. Pell, P.S. "Characterization ofFatigue Behavior." In Special Report 140: Structural

Design ofAsphalt Concrete Pavement Systems to Prevent Fatigue Cracking, Highway

Research Board, National Research Council, Washington, DC, 1973.

51. Anderson, T.L. Fracture Mechanics Fundamentals and Applications. CRC Press, Inc.,

Boca Raton, FL, 1991.

218
52. Roesler, lR. and L. Khazanovich. "Finite-Element Analysis ofPortland Cement

Concrete Pavements With Cracks," Transportation Research Record 1568,

Transportation Research Board, Washington, DC, 1997.

53. Carey, W.N. and P.E. Irick. "The Pavement Serviceability-Performance Concept."

Highway Research Bulletin 250. Highway Research Board, Washington, DC, 1990.

54. American Association of State Highway and Transportation Officials. Summary Results

of1987 AASHTO Rideability Survey. Washington, DC, 1987.

55. Janoff, M.S. Pavement Smoothness. Information Series 111. National Asphalt Pavement

Association, Lanham, MD, 1991.

56. AI-Omari, B. and M.l. Darter. Relationships Between IRI and PSR. Report No. UILUENG-92-2013. Illinois Department ofTransportation, Springfield, IL, 1992.

57. Smith, K.L., K.D. Smith, L.D. Evans, T.E. Hoerner, and M.l. Darter. Smoothness

Specificationsfor Pavements. Final Report. National Cooperative Highway Research

Program, Washington, DC, March 1997.

58. Sayers, M.W. and T.D. Gillespie. "The International Road Roughness Experiment: A

Basis for Establishing a Standard Scale for Road Roughness Measurements."

Transportation Research Record 1084. Transportation Research Board, Washington, DC,

1986.

59. Queiroz, c.A.V. and W.R. Hudson."A Stable, Consistent, and Transferable Roughness

Scale for Worldwide Standardization." Transportation Research Record 997.

Transportation Research Board, Washington, DC, 1984.

60. Sayers, M.W., T.D. Gillespie, and W.D.O. Paterson. Guidelinesfor Conducting and

Calibrating Road Roughness Measurements. Technical Paper 46. The World Bank,

Washington, DC, 1986.

61. Sayers, M.W., T.D. Gillespie, and c.A.V. Queiroz. The International Road Roughness

Experiment: Establishing Correlation and a Calibration Standardfor Measurements.

Technical Paper 45. The World Bank,Washington, DC, 1986.

62. Perera, M. Long Term Pavement Performance Data Analysis: Study to Investigate the

Development ofPavement Roughness. Draft Final Report. Contract No. DTFH61-95-C00124. Federal Highway Administration, McLean, VA, 1996.

63. Larson, R.M., S. Vanikar, and S. Forster. Summary Report-Us. Tour ofEuropean

Concrete Highways (US. TECH)-Follow-Up Tour ofGermany and Austria, Report No.

FHWA-SA-93-080. Federal Highway Administration, Washington, DC, October 1993.

64. Darter, M.l. Report on the 1992 US. Tour ofEuropean Concrete Highways. Report No.

FHWA-SA-93-012., Federal Highway Administration, Washington, DC, January 1993.

219