Improved Prediction Models for PCC 

Pavement Performance-Related 

Specifications, Volume I: Final Report

PUBLICATION NO. FHWA-RD-00-130 SEPTEMBER 2000

Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

Technical Report Documentation Page

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

FHWA-RD-00-130

 4. Title and Subtitle 5. Report Date

September 2000

 6. Performing Organization Code

 8. Performing Organization Report No.

 7. Author(s)

 9. Performing Organization Name and Address 10. Work Unit No. (TRAIS)

 ERES Consultants (A Division of Applied Research Associates, Inc.) xxxx

 505 W. University Avenue 11. Contract or Grant No.

 Champaign, IL 61820-3915 DTFH61-97-C-00071

 13. Type of Report and Period Covered

 12. Sponsoring Agency Name and Address Final Report

 Office of Engineering R&D November 1997–April 2000

 Federal Highway Administration

 6300 Georgetown Pike 14. Sponsoring Agency Code

 McLean, Virginia 22101-2296

 15. Supplementary Notes

 FHWA Contracting Officer's Technical Representative (COTR): Peter A. Kopac, HRDI–12

 16. Abstract

 17. Key Words 18. Distribution Statement

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

Unclassified Unclassified 220

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

No restrictions. This document is available to the public 

through the National Technical Information Service, 

Springfield, Virginia 22161.

T.E. Hoerner, M.I. Darter, L. Khazanovich, L. Titus-Glover,

 and K.L. Smith

The current performance-related specifications (PRS) methodology has been under development by the Federal Highway Administration (FHWA)

for several years and has now reached a level at which it can be implemented by State highway agencies. PRS for highway pavements depend

heavily on performance prediction models to determine the impact of varying levels of construction quality. This study focused on the improvement

of the key distress and smoothness prediction models used in the PRS for jointed plain concrete pavement (JPCP). Performance models for

transverse joint faulting, transverse slab cracking, transverse joint spalling, and smoothness (International Roughness Index [IRI]) were evaluated

and then improved substantially. This was accomplished using a comprehensive national database of JPCP performance data, along with sound

statistical and engineering techniques. Performance model calibration guidelines were also developed so that a State can calibrate any of these

models specifically to its pavement performance data. 

The PaveSpec PRS demonstration software was upgraded to Version 3.0 under this study. Some of the specific improvements incorporated in

PaveSpec 3.0 include: 1) incorporation of the improved distress indicator models, as well as the ability to calibrate or modify the default models, 2)

sensitivity analysis capibilities, 3) expected pay charts, and 4) online help. Appendix A of this report contains a complete updated PaveSpec User's

Guide.

This volume is the first of two volumes. The other volume is:

FHWA-RD-00-131 Volume II: Appendix A—PaveSpec 3.0 User's Guide

performance-related specifications, performance prediction, 

pavement distress, smoothness, concrete pavement, quality 

assurance, specifications, life-cycle costing, and pavement 

construction

IMPROVED PREDICTION MODELS FOR PCC PAVEMENT PERFORMANCE-RELATED 

SPECIFICATIONS, Volume I: Final Report
iv

TABLE OF CONTENTS

CHAPTER 1: INTRODUCTION....................................................................................1

RECENT PROGRESS IN PRS DEVELOPMENT............................................................1

PROJECT OBJECTIVES AND SCOPE..............................................................................4

RESEARCH APPROACH.....................................................................................................4

SEQUENCE OF REPORT.....................................................................................................6

CHAPTER 2: EVALUATION OF DISTRESS INDICATOR MODELS

AND POTENTIAL DATA SOURCES............................................7

INTRODUCTION..................................................................................................................7

STEP 1—IDENTIFICATION OF AVAILABLE JPCP DISTRESS INDICATOR

MODELS..................................................................................................................................8

STEP 2—IDENTIFICATION AND EVALUATION OF POTENTIAL DATA

SOURCES..............................................................................................................................10

Identification of Required Data Types for Inclusion in the National PRS

Database...........................................................................................................................10

Specific Data Elements Required by the Available Distress Indicator

Models..............................................................................................................................11

Identification and Evaluation of Potential Data Sources.......................................11

Availability of Required Data Elements in the Identified Potential Data

Sources .............................................................................................................................20

STEP 3—SELECTION OF BEST-AVAILABLE DISTRESS INDICATOR

MODELS................................................................................................................................21

Transverse Joint Faulting Model ................................................................................29

Transverse Fatigue Cracking Model ..........................................................................29

Transverse Joint Spalling Model................................................................................29

IRI Model.........................................................................................................................29

STEP 4—IDENTIFICATION OF SPECIFIC DATA SOURCES TO BE INCLUDED

IN THE NATIONAL PRS DATABASE...........................................................................30

CHAPTER 3: PROCEDURES USED TO VALIDATE/IMPROVE

DISTRESS INDICATOR MODELS..............................................31

INTRODUCTION................................................................................................................31

PREPARATION OF MODEL TYPE SPECIFIC DATA SETS .....................................31

TECHNIQUES OF THE MODEL VALIDATION/IMPROVEMENT PROCESS....31

Engineering Assessment...............................................................................................32

Statistical Analyses ........................................................................................................32

ACCEPTABILITY OF MODELS.......................................................................................37
v

TABLE OF CONTENTS (continued)

CHAPTER 4: TRANSVERSE JOINT FAULTING MODEL.............................39

INTRODUCTION................................................................................................................39

CURRENT PRS JPCP TRANSVERSE JOINT FAULTING MODEL.........................39

JPCP Transverse Joint Faulting (Not Including Percent Consolidation

Around Dowels).............................................................................................................40

JPCP Transverse Joint Faulting (Including Percent Consolidation Around

Dowels) ............................................................................................................................41

LIMITATIONS OF THE CURRENT PRS TRANSVERSE JOINT FAULTING

MODEL..................................................................................................................................42

EXISTING JPCP TRANSVERSE JOINT FAULTING MODELS ...............................43

SHRP P-020 JPCP Transverse Joint Faulting Model...............................................43

FHWA RPPR 1997 JPCP Transverse Joint Faulting Model....................................46

ACPA JPCP Transverse Joint Faulting Model .........................................................48

FHWA NAPCOM JPCP Transverse Joint Faulting Model ....................................49

LTPP Data Analysis Study JPCP Transverse Joint Faulting Model.....................50

Overview of Existing JPCP Transverse Joint Faulting Models.............................51

RECALIBRATION OF THE CURRENT JPCP TRANSVERSE JOINT

FAULTING MODEL ...........................................................................................................51

Data Preparation.............................................................................................................53

Statistical Tools for Regression and Optimization .................................................55

Final JPCP Transverse Joint Faulting Model............................................................55

MODEL VERIFICATION (SENSITIVITY ANALYSIS)..............................................60

Effect of Material- and Design-Related Factors .......................................................60

Effect of Climatic Variables .........................................................................................66

SUMMARY ...........................................................................................................................68

CHAPTER 5: JPCP TRANSVERSE FATIGUE CRACKING MODEL........71

INTRODUCTION................................................................................................................71

CURRENT PRS JPCP TRANSVERSE SLAB CRACKING MODEL .........................72

ATTEMPTED VALIDATION OF THE CURRENT PRS TRANSVERSE SLAB

CRACKING MODEL..........................................................................................................74

EXISTING JPCP TRANSVERSE SLAB CRACKING MODELS................................75

NCHRP Project 1-26 JPCP Transverse Cracking Model.........................................75

FHWA RPPR 1997 JPCP Transverse Cracking Model ............................................79

Overview of Existing JPCP Transverse Cracking Models .....................................82

IMPROVEMENT OF THE RPPR 1997 JPCP TRANSVERSE CRACKING

MODEL..................................................................................................................................83

Data Preparation.............................................................................................................85

Statistical Tools for Regression and Optimization .................................................85
vi

TABLE OF CONTENTS (continued)

Final JPCP Transverse Cracking Model ....................................................................85

Procedure Used to Predict Fatigue Damage..............................................................88

MODEL VERIFICATION (SENSITIVITY ANALYSIS)............................................105

Effect of Material- and Design-Related Factors .....................................................105

Effect of Site-Related Factors.....................................................................................108

SUMMARY .........................................................................................................................112

CHAPTER 6: TRANSVERSE JOINT SPALLING MODEL............................113

INTRODUCTION..............................................................................................................113

CURRENT PRS JPCP TRANSVERSE JOINT SPALLING MODEL .......................113

Transverse Joint Spalling Baseline Model (Not Including Air Content) .........114

Transverse Joint Spalling Model and Procedure (Including Air Content).......114

ATTEMPTED VALIDATION OF THE CURRENT PRS TRANSVERSE JOINT

SPALLING MODEL..........................................................................................................118

EXISTING JPCP TRANSVERSE JOINT SPALLING MODELS..............................121

SHRP P-020 JPCP Transverse Joint Spalling Model.............................................121

LTPP Data Analysis JPCP Transverse Joint Spalling Model..............................122

CTL JPCP Transverse Joint Spalling Model...........................................................124

FHWA RPPR JPCP Transverse Joint Spalling Model ..........................................124

Overview of JPCP Transverse Joint Spalling Models ..........................................126

DEVELOPMENT OF A NEW JPCP TRANSVERSE JOINT SPALLING

MODEL................................................................................................................................127

Data Preparation...........................................................................................................128

Selection of a Suitable JPCP Transverse Joint Spalling Prediction Model

Form................................................................................................................................130

Statistical Tools for Regression and Optimization ...............................................130

Final JPCP Transverse Joint Spalling Model .........................................................131

MODEL VERIFICATION (SENSITIVITY ANALYSIS)............................................132

Effect of Air Content ...................................................................................................132

Effect of PCC Compressive Strength .......................................................................134

Effect of Joint Sealant Type .......................................................................................134

Effect of PCC Slab Thickness ....................................................................................136

Effect of Total Air Freeze-Thaw Cycles ...................................................................136

Effect of Water/Cement Ratio....................................................................................137

SUMMARY .........................................................................................................................137

CHAPTER 7: IRI MODEL ..............................................................................................139

INTRODUCTION..............................................................................................................139

CURRENT PRS IRI MODEL...........................................................................................139
vii

TABLE OF CONTENTS (continued)

ATTEMPTED VALIDATION OF THE CURRENT PRS IRI MODEL....................140

EXISTING JPCP IRI MODELS .......................................................................................142

SHRP P-020 JPCP IRI Models....................................................................................142

LTPP Data Analysis JPCP IRI Model.......................................................................144

FHWA RPPR JPCP IRI Model...................................................................................145

Overview of JPCP IRI Models...................................................................................145

DEVELOPMENT OF A NEW JPCP IRI MODEL ........................................................146

Data Preparation...........................................................................................................147

Selection of a Suitable JPCP IRI Prediction Model Form....................................152

Statistical Tools for Regression and Optimization ...............................................154

Final JPCP IRI Model..................................................................................................154

MODEL VERIFICATION (SENSITIVITY ANALYSIS)............................................155

Effect of Initial IRI.......................................................................................................155

Effect of Transverse Slab Cracking ..........................................................................157

Effect of Transverse Joint Spalling...........................................................................158

Effect of Transverse Joint Faulting...........................................................................159

Effect of Pavement Site Conditions..........................................................................159

SUMMARY .........................................................................................................................160

CHAPTER 8: DEVELOPMENT OF INITIAL SMOOTHNESS

RELATIONSHIPS................................................................................163

INTRODUCTION..............................................................................................................163

BACKGROUND ................................................................................................................164

Initial Smoothness Testing ........................................................................................164

Smoothness Monitoring .............................................................................................166

PRELIMINARY INVESTIGATION—PAST STUDIES ON SMOOTHNESS

RELATIONSHIPS..............................................................................................................167

Pennsylvania Transportation Institute Profilograph Calibration Study..........167

Arizona DOT Initial Smoothness Study .................................................................169

University of Texas Smoothness Specification Study..........................................169

Florida DOT Ride Quality Equipment Comparison Study.................................170

Texas Transportation Institute Smoothness Testing Equipment

Comparison Study .......................................................................................................172

Summary of IRI–PI Relationships............................................................................173

DETAILED INVESTIGATION—LTPP CORRELATION ANALYSIS...................174

LTPP Profile and Smoothness Data .........................................................................176

Development and Application of Simulation Software ......................................177

Data Analysis................................................................................................................178

SUMMARY AND RECOMMENDATIONS ................................................................186
viii

TABLE OF CONTENTS (continued)

CHAPTER 9: GUIDELINES FOR MODEL CALIBRATION AND

DEVELOPMENT..................................................................................189

INTRODUCTION..............................................................................................................189

GUIDELINES FOR CALIBRATING AN EXISTING DISTRESS INDICATOR

MODEL................................................................................................................................189

Step 1—Compile the Calibration Data Set..............................................................190

Step 2—Compute Corresponding Predicted Values .............................................191

Step 3—Plot Predicted vs. Measured Distress Values ..........................................191

Step 4—Statistical Analysis of Predicted vs. Measured Distress Values..........192

Step 5—Determine Calibration Coefficients A and B..........................................192

Step 6—Determine Calibrated Distress Values .....................................................192

Step 7—Plot Calibrated vs. Measured Distress Values ........................................193

Step 8—Statistical Analysis of Calibrated vs. Measured Distress Values........193

GUIDELINES FOR DEVELOPING NEW DISTRESS INDICATOR MODELS...194

Distress Indicator Prediction Model Types ............................................................194

Basic Principles to Developing Improved Distress Indicator Prediction

Models............................................................................................................................195

CHAPTER 10: SUMMARY AND RECOMMENDATIONS..........................199

SUMMARY .........................................................................................................................199

Improved Performance Prediction Models.............................................................200

Investigation of Initial Smoothness Relationships...............................................201

Distress Indicator Model Calibration Guidelines.................................................201

Development of PaveSpec 3.0....................................................................................202

RECOMMENDATIONS FOR FUTURE RESEARCH ................................................202

REFERENCES.......................................................................................................................205
ix

LIST OF FIGURES

Figure No.

1 Example of a plot of predicted versus actual data...................................................... 33

2 Conceptual illustration of the difference between bias and precision..................... 34

3 Example of the sensitivity of a JPCP cracking model to slab thickness................... 37

4 Predicted versus measured transverse joint faulting (using the compiled

validation data set). ......................................................................................................... 44

5 Residual versus predicted transverse joint faulting (using the compiled

validation data set) .......................................................................................................... 44

6 Predicted versus measured faulting for the validated JPCP faulting model.......... 60

7 Residual versus predicted faulting for the validated JPCP faulting model............ 61

8 Sensitivity of the final JPCP transverse joint faulting model to changes in dowel

diameter............................................................................................................................. 62

9 Sensitivity of the final JPCP transverse joint faulting model to changes in

transverse joint spacing................................................................................................... 63

10 Sensitivity of the final JPCP transverse joint faulting model to changes in base

erodibility factor............................................................................................................... 63

11 Sensitivity of the final JPCP transverse joint faulting model to changes in

dynamic modulus of subgrade reaction....................................................................... 64

12 Sensitivity of final validated JPCP joint faulting model to changes in base

permeability...................................................................................................................... 65

13 Sensitivity of the final JPCP transverse joint faulting model to changes in PCC

slab thickness.................................................................................................................... 65

14 Sensitivity of the final JPCP transverse joint faulting model to changes in PCC

modulus of elasticity ....................................................................................................... 66

15 Sensitivity of the final JPCP transverse joint faulting model to changes in

percent consolidation of PCC around 25.4-mm (1-in) dowels .................................. 67

16 Sensitivity of the final JPCP transverse joint faulting model to changes in

percent consolidation of PCC around 38.1-mm (1.5-in) dowels ............................... 67

17 Sensitivity of the final JPCP transverse joint faulting model to changes in

precipitation...................................................................................................................... 68

18 Sensitivity of the final JPCP transverse joint faulting model to changes in

number of hot days.......................................................................................................... 69

19 Predicted (equation 36) versus measured JPCP transverse slab cracking (using

the compiled validation data set) .................................................................................. 76

20 Residual versus predicted (equation 36) transverse JPCP slab cracking (using

the compiled validation data set) .................................................................................. 76

21 Predicted (RPPR 97 model) versus actual slab cracking (using the section-bysection temperature shift factors and gradient distributions)................................... 84
x

LIST OF FIGURES (continued)

22 Predicted (RPPR 97 model) versus actual slab cracking (using regional

temperature shift factors with section-by-section temperature gradient

distributions) .................................................................................................................... 84

23 Predicted (equation 55) versus measured JPCP transverse cracking....................... 87

24 Residual versus predicted (equation 55) JPCP transverse cracking......................... 87

25 Sensitivity of the final JPCP transverse slab cracking model to changes in PCC

slab thickness....................................................................................................................106

26 Sensitivity of the final JPCP transverse slab cracking model to changes in PCC

flexural strength ...............................................................................................................106

27 Sensitivity of the final JPCP transverse cracking model to changes in modulus

of elasticity ........................................................................................................................107

28 Sensitivity of the final JPCP transverse cracking model to changes in modulus

of elasticity and corresponding changes in PCC flexural stiffness...........................107

29 Sensitivity of the final JPCP transverse slab cracking model to changes in PCC

slab joint spacing..............................................................................................................109

30 Sensitivity of the final JPCP transverse slab cracking model to changes in edge

support ..............................................................................................................................109

31 Sensitivity of the final JPCP transverse slab cracking model to changes in base

type and bond condition.................................................................................................110

32 Sensitivity of the final JPCP transverse slab cracking model to changes in

climate................................................................................................................................111

33 Sensitivity of the final JPCP transverse slab cracking model to changes in

dynamic k-value...............................................................................................................111

34 Predicted (equation 83) versus measured JPCP transverse joint spalling (using

the LTPP validation data set) .........................................................................................120

35 Residual versus predicted (equation 83) transverse joint spalling (using the

LTPP validation data set)................................................................................................121

36 Predicted (equation 97) versus measured spalling for the final JPCP transverse

joint spalling model .........................................................................................................133

37 Residual versus predicted (equation 97) spalling for the final JPCP transverse

joint spalling model .........................................................................................................133

38 Sensitivity of final JPCP joint spalling model to changes in PCC concrete air

content (measured with air pressure meter)................................................................134

39 Sensitivity of final JPCP joint spalling model to changes in PCC 28-day

compressive strength.......................................................................................................135

40 Sensitivity of final JPCP joint spalling model to changes in joint sealant type.......135

41 Sensitivity of final JPCP joint spalling model to changes in PCC slab thickness ...136

42 Sensitivity of final JPCP joint spalling model to changes in cumulative air

freeze-thaw cycles............................................................................................................137

43 Sensitivity of final JPCP joint spalling model to changes in water-cement ratio ...138
xi

LIST OF FIGURES (continued)

44 Predicted (equation 99) versus measured JPCP IRI (using the LTPP validation

data set) .............................................................................................................................141

45 Residual versus predicted (equation 99) JPCP IRI (using the LTPP validation

data set) .............................................................................................................................142

46 Example of the linear model method used to backcast an initial IRI from timeseries data..........................................................................................................................150

47 Initial IRI distribution for measured (SPS) and backcasted JPCP (GPS-3) data .....151

48 Plot of estimated initial backcasted IRI versus section age for JPCP .......................152

49 Predicted (equation 108) versus measured IRI for the final JPCP IRI model..........156

50 Residuals versus predicted (equation 108) IRI for the final JPCP IRI model..........156

51 Sensitivity of the final JPCP IRI model to changes in initial IRI and percent

cracked slabs.....................................................................................................................157

52 Sensitivity of the final JPCP IRI model to changes in percent joints spalled and

initial IRI............................................................................................................................158

53 Sensitivity of the final JPCP IRI model to changes in total joint faulting per km

and initial IRI....................................................................................................................159

54 Effect of freezing index on JPCP IRI after 30 years.....................................................160

55 Effect of subgrade percent passing 0.075-mm sieve on JPCP IRI after 30 years.....161

56 Relationship between IRI and manually generated PI in PTI profilograph

calibration study ..............................................................................................................168

57 Relationship between IRI and computer-generated PI in PTI profilograph

calibration study ..............................................................................................................168

58 Correlation of IRI and PI in Arizona pavement smoothness study .........................170

59 IRI–PI5-mm (PI0.2-in) correlations established in Florida’s ride quality equipment

study ..................................................................................................................................171

60 IRI–PI2.5-mm (PI0.1-in) and IRI–PI0.0 correlations established in Florida’s ride quality

equipment study ..............................................................................................................172

61 Relationship between IRI and computer-simulated PI values in TTI equipment

comparison study ............................................................................................................173

62 Graphical illustration of documented IRI–PI5-mm (PI0.2-in) smoothness

relationships .....................................................................................................................175

63 Graphical illustration of documented IRI–PI2.5-mm (PI0.1-in) smoothness

relationships .....................................................................................................................175

64 Graphical illustration of documented IRI–PI0.0 smoothness relationships..............176

65 Graphical illustration of LTPP IRI–PI5-mm (PI0.2-in) smoothness relationship ..........179

66 Graphical illustration of LTPP IRI–PI2.5-mm (PI0.1-mm) smoothness relationship......180

67 Graphical illustration of LTPP IRI–PI0.0 smoothness relationship............................180

68 Graphical comparison of IRI–PI5-mm (PI0.2-in) smoothness relationships..................181

69 Graphical comparison of IRI–PI2.5-mm (PI0.1-in) smoothness relationships................181

70 Graphical comparison of IRI–PI0.0 smoothness relationships ...................................182
xii

LIST OF FIGURES (continued)

71 Comparison of IRI–PI5-mm (PI0.2-in) relationships for different filter types and

settings...............................................................................................................................184

72 Comparison of IRI–PI2.5-mm (PI0.1-in) relationships for different filter types and

settings...............................................................................................................................185

73 Comparison of IRI–PI0.0 relationships for different filter types and settings..........185

74 Illustration of predicted vs. actual CRS both before calibration and after

calibration with new data ...............................................................................................190

75 Flow chart for developing pavement distress models for rigid pavements ...........197
xiii

LIST OF TABLES

Table No.

1 Summary of recently developed distress indicator models considered relevant

to the PRS methodology.................................................................................................. 9

2 Summary of required data elements included in the short list of best-available

JPCP transverse joint faulting models .......................................................................... 12

3 Summary of required data elements included in the short list of best-available

JPCP transverse fatigue cracking models..................................................................... 13

4 Summary of required data elements included in the short list of best-available

JPCP transverse joint spalling models .......................................................................... 14

5 Summary of required data elements included in the short list of best-available

JPCP IRI models ............................................................................................................... 15

6 Availability of data required by the short-listed JPCP transverse joint faulting

models ............................................................................................................................... 22

7 Availability of data required by short-listed JPCP transverse cracking models .... 23

8 Availability of data required by the short-listed JPCP transverse joint spalling

models ............................................................................................................................... 24

9 Availability of data required by the short-listed JPCP IRI models .......................... 25

10 Assessment of best-available JPCP transverse joint faulting models....................... 26

11 Assessment of best-available JPCP transverse cracking models .............................. 27

12 Assessment of best-available JPCP transverse joint spalling models ...................... 27

13 Assessment of best-available JPCP IRI models ........................................................... 28

14 Specific databases that will be used to validate/improve chosen best available

distress indicator models ................................................................................................ 30

15 Example of paired t-test analysis results (from an investigation of the AASHTO

rigid pavement design model using LTPP data)......................................................... 35

16 Results of the components of variance example ......................................................... 36

17 Summary of JPCP data used in the initial validation of the current transverse

joint faulting model ......................................................................................................... 42

18 Summary of variables found to significantly affect JPCP transverse joint

faulting .............................................................................................................................. 52

19 PIARC recommendations for erosion potential of base/subbase materials

(based on base type and base cement and asphalt content) ...................................... 54

20 Supplemental recommendations for erosion potential of CTB (based on

long-term compressive strength)................................................................................... 54

21 Recommendations for assigning of erodibility factor based on PIARC

erodibility class................................................................................................................. 55

22 Range of values of data used in the sensitivity analysis for the final validated

JPCP transverse joint faulting model ............................................................................ 61

23 Average daytime thermal gradients (based on slab thickness and climatic zone),

°F/in................................................................................................................................... 73
xiv

LIST OF TABLES (continued)

24 JPCP data used in the initial validation of the current transverse slab cracking

model ................................................................................................................................. 74

25 Temperature shift factor coefficients by climatic zone............................................... 86

26 Frequency distributions of temperature gradients for the wet-freeze region

(based on rounded effective thickness) ........................................................................ 97

27 Frequency distributions of temperature gradients for the wet-nonfreeze region

(based on rounded effective thickness) ........................................................................ 99

28 Frequency distributions of temperature gradients for the dry-freeze region

(based on rounded effective thickness) ........................................................................101

29 Frequency distributions of temperature gradients for the dry-nonfreeze region

(based on rounded effective thickness) ........................................................................103

30 Summary of LTPP data used in the initial validation of the PaveSpec 2.0 JPCP

transverse joint spalling model......................................................................................119

31 Summary of variables found to significantly affect JPCP transverse joint

spalling ..............................................................................................................................128

32 Summary of GPS-3 JPCP data and CTL laboratory data used in model

development and calibration .........................................................................................129

33 Range of values of data used in sensitivity analysis...................................................132

34 Summary of JPCP LTPP data used in the initial validation of the current IRI

model .................................................................................................................................140

35 Summary of distresses and variables identified in previous research as

significantly affecting JPCP IRI......................................................................................146

36 Summary of t-test results for the comparison of measured and backcasted

initial IRI for JPCP............................................................................................................151

37 Summary of GPS-3 JPCP data considered in the IRI model development and

calibration procedures.....................................................................................................153

38 Diagnostic statistics for JPCP IRI model.......................................................................155

39 Summary of documented IRI–PI relationships ...........................................................174

40 Summary of JPCP test sections included in LTPP correlation analysis ...................177

41 Summary of IRI–PI relationships based on different filter types and settings.......184

42 Effects of alternative filter types and settings on IRI–PI relationships ....................186

43 Format for a calibration data set....................................................................................191

44 Example calibration data set table with predicted values included.........................191
xv

LIST OF ACRONYMS AND

ABBREVIATIONS

AASHTO American Association of State Highway and Transportation Officials

AC Asphalt concrete

AC-AD RATIO As-constructed to as-designed CTL spalling ratio

ACPA American Concrete Pavement Association

ANOVA Analysis of variance

AQC Acceptance quality characteristic

ATB Asphalt treated base

BPR Bureau of Public Roads

COPES Concrete Pavement Evaluation System (NCHRP Project 1-19)

CRCP Continuously reinforced concrete pavement

CRS Condition rating survey

CTB Cement treated base

CTL Construction Technology Laboratories, Inc.

DMI Distance measuring instrument

DOT Department of transportation

EP Expected pay

ERD Engineering Research Division

ESAL Equivalent single axle-load

FHWA Federal Highway Administration

FWD Falling-weight deflectometer

GPS LTPP general pavement studies

HPMS Highway Performance Monitoring System

ICC International Cybernetics Corporation

ICM Integrated Climate and Materials

IMS LTPP Information Management System

IRI International Roughness Index

JPCP Jointed plain concrete pavement

JRCP Jointed reinforced concrete pavement

LCB Lean concrete base

LCC Life-cycle cost

LTPP Long Term Pavement Performance

M&R Maintenance and rehabilitation

Mn/ROAD Minnesota Test Road

MRN Mays ride number

NAPCOM Nationwide Pavement Cost Model (FHWA project)

NCHRP National Cooperative Highway Research Program
xvi

LIST OF ACRONYMS AND

ABBREVIATIONS (continued)

NCRCO LTPP North Central Regional Contracting Office

NLIN SAS nonlinear procedure

NOAA National Oceanic and Atmospheric Administration

PCA Portland Cement Association

PCC Portland cement concrete

PI Profile index

PIARC Permanent International Association of Road Congresses

PMS Pavement management system

PRS Performance-related specifications

PSR Present serviceability rating

PTI Pennsylvania Transportation Institute

PW Present worth

PW$ Present worth dollars

R2 Coefficient of determination

RMSVA Root Mean Square Vertical Acceleration

RPPR FHWA Rigid Pavement Performance and Rehabilitation study

SEE Standard error of the estimate

SHA State highway agency

SHRP Strategic Highway Research Program

SPS Specific pavement studies

TTI Texas Transportation Institute

UMTRI University of Michigan Transportation Research Institute
1

CHAPTER 1: INTRODUCTION

Over the past decade, significant progress has been made in the development of

performance-related specifications (PRS) for the acceptance of newly constructed

jointed plain concrete pavements (JPCP). A PRS is a construction specification that

describes the desired levels of key materials and construction acceptance quality

characteristics (AQC's) that have been found to correlate with fundamental engineering

properties that predict performance. These AQC's (e.g., smoothness, thickness,

strength, air content, and percent consolidation around dowels) are amenable to

acceptance testing at the time of construction. A true PRS not only describes the desired

levels of the selected AQC's, but also employs the quantified relationships to predict

subsequent pavement performance and associated life-cycle costs (LCC's) for a given

project. This ability to relate AQC's (measured during construction) to the level of

expected performance and future LCC provides the basis for rational acceptance and

price adjustment decisions.(1)

Because price adjustments are directly dependent on the future pavement

performance predicted through selected mathematical distress indicator prediction

models (e.g., transverse joint faulting and spalling, transverse fatigue cracking,

International Roughness Index [IRI]), it is important to have confidence in the validity

or accuracy of these models. In recent years, State highway agencies (SHA's) have

expressed concern over whether the distress indicator prediction models used in the

current PRS approach would accurately predict the pavement performance associated

with their agency’s specific designs, materials, subgrades, traffic, and climatic

conditions. This important question must be adequately addressed, or it will inhibit the

implementation of the PRS in many States. Therefore, the focus of this study was to

validate or improve the default performance models used in the current PRS approach

(included in the PaveSpec 2.0 software) and to provide guidelines for SHA's that allow

them to calibrate the default models, or develop new models that reflect their local

conditions.

RECENT PROGRESS IN PRS DEVELOPMENT

The advancement of PRS research has been a high-priority research area within the

Federal Highway Administration (FHWA) since 1987. Some of the more notable early

efforts include the pioneering PRS work done in New Jersey by Weed, a National

Cooperative Highway Research Program (NCHRP)-sponsored study on PRS for asphalt

concrete (AC) pavements, and the initial FHWA study on developing PRS for portland

cement concrete (PCC) pavements.(2,3,4)

Based on the promising results of these early projects, FHWA sponsored additional

research in the early 1990's that focused on the development of a more practical (and

easily implementable) prototype PRS for PCC pavements. The first of these studies
2

considerably advanced the PCC PRS research by developing a prototype PRS approach

driven by LCC's.(5,6,7) Using this approach, the estimated total future (after initial

construction) LCC of a pavement lot is directly related to the AQC quality (means and

standard deviations) and is used as the overall measure of quality for the lot.

The approach requires the agency to define the desired as-designed AQC quality

target values (means and standard deviations) for a pavement lot. The quality of the asconstructed pavement is determined by taking samples directly from the constructed

pavement lot. A difference in AQC quality between the as-designed and as-constructed

lots, therefore, results in a difference in predicted future LCC's. The lot pay factor is

determined, as a function of these two estimated LCC's, using the following equation:

PFLOT = 100 * (BID + [LCCDES – LCCCON])/BID (1)

where:

PFLOT = Pay factor, percentage of original bid price.

BID = Contractor's unit bid price for the lot, present worth dollars per km

(PW$/km).

LCCDES = As-designed life-cycle unit cost for the lot (computed using target

AQC's), PW$/km.

LCCCON = As-constructed life-cycle unit cost for the lot (computed using AQC

test results from the as-constructed lot), PW$/km.

As can be seen from this equation, both positive and negative pay adjustments are

possible. The approach is in accordance with the legal principle of liquidated damages,

which are computed at the time of construction on the basis of the projected increase or

decrease in estimated future costs.

The first version of the PRS demonstration software, PaveSpec, was developed

under this 1990–1993 FHWA research study and was used to simulate the construction

of the lot, predict future performance and costs, and generate pay adjustments for a

given project.

Also as part of this 1990–1993 FHWA research study, an extensive laboratory testing

program was conducted to fill several gaps in the materials area. Among the major

laboratory studies that were conducted were:

• An evaluation of the factors that affect concrete strength and modulus of

elasticity (many PCC mixes were evaluated over a range of materials).

• An investigation into inter-strength (e.g., flexural to compressive) relationships.

• A comparison of the compressive strengths of cores to the compressive strengths

of cylinders having the same maturity.
3

• A demonstration of the use of maturity and pulse velocity for monitoring the insitu slab strength for potential use in determining early strength.

• An investigation of the effect of air void system parameters on joint spalling.

A final part of the FHWA research study was the development of test plans for the

evaluation of various construction variables. These studies were needed so that the

effect of other AQC's that are under the control of the contractor could be quantified

and eventually included in the PRS.

A second FHWA research study was therefore conducted, from 1994 to 1998,

involving field and laboratory investigations of several performance-related PCC

pavement construction variables.(8,9,10,11) Under this study, the researchers:

• Determined typical variability of key AQC's (air voids, slab thickness, initial

smoothness, concrete strength, and others) and provided recommendations for

default variabilities of each AQC.

• Revised the prototype PRS developed under the first contract by adding new

and improved construction AQC's (consolidation near dowels, air void

validations) and by defining three levels of PRS implementation.

• Fully developed the first level of PRS implementation, which is practical and

immediately implementable by SHA's (with the exception of verified

performance prediction models).

• Developed version 2.0 of the PaveSpec computer program to give it many

additional PRS capabilities, including the ability to automatically simulate and

generate pay factors based on user-defined inputs for a given highway

construction project and the ability to input testing results directly from a lot to

compute the corresponding pay factors.

• Replaced most of the existing performance prediction models with improved

models from recent FHWA and Long Term Pavement Performance (LTPP)

studies.

• Conducted several field trials of the prototype PRS and used the findings to

improve the prototype PRS.

It is clear that these studies on the development of PRS for PCC pavements made

significant advancements in several areas:

• Extension of the underlying theory governing PRS.

• Development of a first level (Level 1) implementable PRS.
4

• Laboratory demonstrations of the development of concrete strength/stiffness

relationships, the application of nondestructive testing, the effect of concrete

durability on spalling/scaling, and cylinder versus core strength.

• The consideration of several key AQC's (concrete strength, slab thickness, initial

smoothness, PCC air content, percent consolidation around dowels) and the

variability of these characteristics.

• Several successful field trials of PRS implementation.

PROJECT OBJECTIVES AND SCOPE

The focus of this study was to conduct research that will continue the advancement

toward the development of a fully practical and implementable PRS for JPCP

construction. Specifically, the contract objectives were to:

1. Validate and, where appropriate, make improvements or adjustments to the

distress indicator prediction models currently used in the prototype PRS (and

PaveSpec 2.0) for JPCP paving.

2. Develop guidelines to assist those SHA's that may want to 1) calibrate national

distress-prediction models to reflect local conditions or 2) develop new distress

indicator models using a separate data set.

3. Conduct a study to investigate relationships between different methods of

measuring initial smoothness (e.g., IRI versus profile index [PI] using different

blanking bands) so that smoothness could be more adequately predicted over

time.

4. Update the PaveSpec 2.0 software.

RESEARCH APPROACH

The research team began by evaluating the distress indicator models used in the

current prototype PRS (those used in PaveSpec 2.0). Specifically, the distress indicator

models considered were limited to the following:

• Transverse joint faulting.

• Transverse fatigue cracking.

• Transverse joint spalling.

• IRI.

The research team assessed the practicality, completeness, and accuracy of each of the

models and compiled a plan to validate or improve each model independently.
5

Next, data sources that could potentially be used to validate/improve the models

were identified and evaluated for content and accuracy. Specifically, each potential

database was assessed by evaluating the following types of data:

• Time-series distress indicators.

• Design feature characteristics.

• Traffic.

• Construction AQC's.

• Climatic variables.

Those data sources that were found to be adequate were compiled into a national PRS

database.

Each distress indicator model was then validated or improved using a series of

statistical methods. The sensitivity of each of the validated/improved models was

assessed. Improvements were made to the models until they were considered adequate

for use in the current PRS methodology.

During the evaluation of the IRI model, it was determined that more guidance was

needed in the area of initial smoothness relationships. The PRS approach allows the

user to predict smoothness over time in terms of IRI; however, an initial IRI value is not

typically measured directly by a SHA. While a few SHA's are now starting to measure

initial IRI with a lightweight profiler, the majority of SHA's continue to assess the initial

smoothness of a new pavement by measuring a PI using a California profilograph.

Because of this situation, a study was conducted to determine the best relationships

between the initially measured PI values (using different blanking bands) and the initial

IRI values required by the smoothness-over-time models.

In addition to the model validation and improvement procedures, the research team

also compiled a set of model calibration guidelines. The model calibration procedure

allows a SHA to calibrate any of the national distress indicator models with a data set

that better reflects the local conditions of a project. If the SHA would rather develop

new or additional distress indicator models for use in a PRS, some general model

development guidelines are also provided.

The previous version of the PRS demonstration software (PaveSpec 2.0) was also

greatly improved under the current contract. Specific improvements included in

PaveSpec 3.0 include:

• Incorporation of validated or improved distress indicator models.

• The capability to calibrate or modify a national distress indicator model to better

reflect a project's local conditions.

• Inclusion of sensitivity analysis capabilities.
6

• The ability to assess risks to both the contractor and agency through the

development of project-specific expected pay (EP) charts.

• An online user's guide.

SEQUENCE OF REPORT

This volume summarizes the results of this research. Specifically, the chapters of

this report discuss the following:

• Chapter 2 describes the preliminary work conducted by the research team

during the development of the PRS national database (required for model

validation/improvement). This preliminary work consisted of a simultaneous

evaluation of existing distress indicator models and potential data sources.

• Chapter 3 outlines the different evaluation methods and tools used in the

procedures followed to validate or improve the distress indicator models.

• Chapters 4 through 7 present the validated/improved models for JPCP

transverse joint faulting, transverse fatigue cracking, transverse joint spalling,

and IRI.

• Chapter 8 summarizes the approach and results of the study conducted to

identify best-available initial smoothness relationships.

• Chapter 9 provides guidelines that a SHA can use to calibrate an existing

national distress indicator model to reflect local conditions. A basic procedure

for developing new distress indicator models is also included as part of this

chapter.

• Chapter 10 provides a summary of the research conducted under this study, as

well as recommendations for future research.

Appendix A contains the complete user's guide for the PaveSpec 3.0 computer software.

As a result of this work, a complete PRS for JPCP is now available for

implementation. A user-friendly software package, PaveSpec 3.0, is available to

demonstrate the PRS approach and assist in the implementation procedures.
7

CHAPTER 2: EVALUATION OF DISTRESS INDICATOR MODELS

AND POTENTIAL DATA SOURCES

INTRODUCTION

One of the most important components of the current PRS approach is the set of

pavement distress indicator models used to predict pavement performance. Such

models predict the development of joint spalling and faulting, slab cracking, and

pavement smoothness over time, and are based on carefully controlled and welldocumented pavement research studies conducted at the national level. Although these

national models are of generally high merit, many SHA's are concerned about the

models' abilities to adequately predict performance representative of their specific

designs, materials, subgrades, traffic, and climatic conditions. Given that the data

supporting each model fall well short of covering the limitless combinations of these

factors, this concern is a legitimate one. If not properly addressed, this issue could

inhibit the advancement toward implementation of PRS in many States.

This project addressed the validation or improvement of the distress indicator

models included as part of the current PRS approach. These validations/improvements

were based on the best available data that represented as many different North

American site conditions as possible. As a result of completing the following steps, a

new nationwide PRS database was compiled to serve as the basis for

validating/improving a chosen set of best-available models:

1. Identification of available JPCP distress indicator models—The most recently

published JPCP distress indicator models of the same types as those included in

the current PRS methodology were identified and evaluated. Only those models

deemed applicable to the current PRS methodology are discussed in this report.

2. Identification and evaluation of potential data sources—All data sources

believed to be potentially useful in the validation/improvement of JPCP-related

distress indicator models were identified and evaluated.

3. Selection of best-available distress indicator models—Based on a comparative

analysis of the available distress indicator models (identified in step 1) and the

data sources deemed relevant to the model validation/improvement process

(identified under step 2), a set of best-available models was selected for

validation/improvement under this study.

4. Identification of specific data sources to be included in the nationwide PRS

database—The initial list of potential data sources (identified in step 2) was

refined to include only those data sources that were directly applicable to the

validation/improvement of the chosen best-available distress indicator models.

Useful data from all applicable sources were compiled into a nationwide PRS
8

database, representative of as many North American geographical locations as

possible.

The details of each step in this database compilation process are discussed separately in

the sections below.

STEP 1—IDENTIFICATION OF AVAILABLE JPCP DISTRESS INDICATOR

MODELS

The distress indicator models included in the 1993 original prototype PRS (PaveSpec

1.0) were largely empirical, and thus related the material test result (or construction

process test) to a distress through correlation, not necessarily causation. The models

incorporated into PaveSpec 2.0 in 1998 were considered to be significant improvements

over the original PaveSpec models, but were still lacking in many ways.

The ideal distress prediction models for PRS are those that explain the cause and

effect mechanism involved. Hence, they relate the material test value to the resulting

development of distress through the mechanisms that occur between the

pavement/subgrade structure, traffic loadings, and climate. Such models are referred

to as mechanistic-empirical models, and they incorporate fundamental engineering

properties and relationships.

Since 1993, many studies have been conducted that have produced improved

distress indicator models for JPCP. The initial list of distress indicator models

investigated in this project was limited to mechanistic-empirical models that meet all of

the following criteria:

• Model type—Only prediction models for transverse joint faulting, transverse

fatigue cracking, transverse joint spalling, and IRI were chosen for investigation

under this project.

• Recently developed models—The initial list of models was limited to those included

in research reports published in 1993 or after.

• Functions of PRS-related AQC's—Only existing models that were functions of one

or more of the currently identified PRS-related AQC's (concrete strength, slab

thickness, air content, initial smoothness, or percent consolidation around

dowels) were included in the initial list of distress indicator models to be

investigated.

The initial models and the associated research studies that were identified for

consideration are summarized in table 1.
Table 1. Summary of recently developed distress indicator models considered relevant to the PRS 

Distress Indicator Model Pavement Type

Model Source (see list

below)

Doweled JPCP Simpson et al., 1994

Yu et al., 1997

Non-doweled JPCP Simpson et al., 1994

Yu et al., 1997

Owusu-Antwi et al., 1997Titus-Glover et al., 1999

Transverse joint faulting

Doweled and Non-doweled JPCP

Yu et al., 1998

Simpson et al., 1994Owusu-Antwi et al., 1997Titus-Glover et al., 1999

Transverse fatigue cracking Doweled and Non-doweled JPCP

Yu et al., 1997

Simpson et al., 1994Titus-Glover et al., 1999

Transverse joint spalling Doweled and Non-doweled JPCP

Yu et al., 1997

IRI Doweled and Non-doweled JPCP Byrum et al., 1997

Titus-Glover et al., 1999Yu et al., 1997Hoerner et al., 1999

Doweled JPCP Simpson et al., 1994

Non-doweled JPCP Simpson et al., 1994

* The transverse cracking model used in PaveSpec 2.0 was a modified version of the 1990 transverse cracking model by Smith et al.(18)

Model Source Reference List

Byrum et al., 1997. The Effect of PCC Strength and Other Parameters on the Performance of PCC Pavements.(12)Hoerner et al., 1999. Guide to Developing Performance-Related Specifications for PCC Pavements, Volume III: Appendixes C Through F.(10)Owusu-Antwi et al., 1997. Development and Calibration of Mechanistic-Empirical Distress Models for Cost Allocation.(13)Simpson et al., 1994. Early Analysis of LTPP General Pavement Studies Data, Volume III: Sensitivity Analyses for Selected Pavement Distresses.(14)Titus-Glover et al., 1999. Design and Construction of PCC Pavements, Volume III: Improved PCC Performance.(15)Yu et al., 1997. Performance of Concrete Pavements, Volume III: Improving Concrete Pavement Performance.(16)Yu et al., 1998. Final Report, NCHRP Project 1-34—Guidelines for Subsurface Drainage.(17)

9
10

STEP 2—IDENTIFICATION AND EVALUATION OF POTENTIAL DATA

SOURCES

This section contains a complete summary of the procedures used to identify and

evaluate the potential data sources included in the national PRS model

validation/improvement database. The evaluation includes an assessment of the

accuracy, applicability, advantages, and limitations of the data included in each data

source.

Identification of Required Data Types for Inclusion in the National PRS Database

To successfully validate/improve the distress indicator models, it was imperative

that the national PRS database be as comprehensive and complete as possible. To be

included in the database, pavement sections were required to have some form of each of

the following five data types:

• Traffic data—Most of the existing PRS distress indicator models require

cumulative or annual 80-kN (18-kip) equivalent single-axle loads (ESAL's) as an

input. (Note: the only model exceptions to this traffic requirement are some

transverse joint spalling and pavement smoothness-related models, which are a

function of age rather than traffic.) Because of this large dependency on traffic

information, only data sources with adequate time-series traffic data were

targeted for inclusion in the national database. Although the American

Association of State Highway Transportation Officials (AASHTO)-based load

equivalency factors have certain limitations, the limited resources of this project

did not allow for a more thorough consideration of traffic loads.

• Design feature characteristic data—Each useful data source must contain adequate

pavement design feature data to relate design characteristics to the measured

performance (time-series distress data). For clarification, design features can be

divided into materials-, PCC slab support-, drainage-, and joint-related variables.

Examples of variables included in each of these design-related categories include

the following:

- Materials—PCC strength and coefficient of thermal expansion, joint

sealant type, and base material strength.

- PCC slab support—base type, modulus of subgrade reaction (k-value),

subgrade type, and shoulder type.

- Drainage—AASHTO drainage coefficient (Cd), base permeability,

presence of longitudinal edge drains, and subgrade soil type.

- Joints—presence of dowel bars, dowel bar diameter, and transverse joint

spacing.
11

The usefulness of each potential database was assessed by comparing the types

of design inputs available in a given database to those design inputs specifically

required by the available models.

• Climatic data—It was desired that each data source chosen for inclusion in the

PRS database have climatic data characterizing the included sections. Examples

of climate-related variables include average annual total precipitation, average

annual number of wet days, mean freezing index, and number of days above

32 °C (90 °F). Such climatic information was very important to this study, since a

major focus of the model validation/improvement process was to develop

models that more accurately represent the local geographical conditions of a

project.

• AQC construction data—The current PRS methodology is driven by the

comparison of the as-designed AQC values with as-constructed AQC values

measured in the field. The AQC values are used in the distress indicator models

to predict the expected performance and corresponding LCC's of both the asdesigned and as-constructed pavements. It was therefore critical that each useful

data source included in the national PRS database have construction data

directly or indirectly representing at least one of the five AQC's available in the

current PRS approach (i.e., concrete strength, slab thickness, air content, initial

smoothness, and percent consolidation around dowels).

• Time-series distress indicator data—Adequate time-series distress data were

required to quantify the long-term performance of JPCP sections. Data sources

containing time-series data for transverse joint faulting, transverse cracking,

transverse joint spalling, and IRI were targeted. The performance data within

each data source were evaluated based on many different characteristics,

including the number of independent sections, the number of years of time-series

data, and the measurement units used to define each distress type.

Specific Data Elements Required by the Available Distress Indicator Models

In preparation for the search for potential data sources, it was important to

summarize all of the specific data elements required by the short list of best-available

distress indicator models identified under step 1. Tables 2 through 5 summarize the

data elements (cross-referenced by model type and source) required by the best

available JPCP transverse joint faulting, transverse fatigue cracking, transverse joint

spalling, and IRI models. This model information was used to identify specific data

sources that could be included in the national PRS database.

Identification and Evaluation of Potential Data Sources

Since the overall objective of the study was to validate or improve the best available

existing models, it was important that some or all of the required model inputs and

outputs be compatible with the data available from the data sources. Based on the
Table 2. Summary of required data elements included in the short list of best-available JPCP transv

models.

Model Inputs (in English units)

Pavement

Type Model Source

Used in PaveSpec 2.0

Cumulative ESAL's

Age, years

Avg. Joint Spacing/Slab Length, ft

Presence of Dowel Bars

Dowel Bar Diameter, in

PCC Modulus of Elasticity, psi

Avg. Annual Freezing Index, °F-days

Avg. Annual Precipitation, in

Avg. Annual Number of Wet Days

Avg. Annual No. of Days Above 90 °F

Avg. Temperature Range, °F

Base Type

Erodibility of Base (erodible vs. non-erodible)

Presence of Lean Concrete Base

Mod. of Subgrade Reaction (k-value), psi/in

Presence of Widened Lane

Widened Lane Amount, in

Shoulder Type/Edge Support

AASHTO Drainage Coefficient, Cd

Base Permeability

Presence of Long. Edge Drains

Simpson et al., 1994.(14) Doweled √√√ √ √ √

Yu et al., 1997.(16) √√√ √√√√ √√ √√ √ 

Simpson et al., 1994.(14) Non- √√ √√ √

doweled Yu et al., 1997.(16) √ √ √√ √ √ √ √ 

Owusu-Antwi et al., 1997.(13) √ √ √√√ √ √ √ √ Titus-Glover et al., 1999.(15) √ √ √√ √ √ √ √ √ Yu et al., 1998.(17) √ √√√√ √√ √ √√ √ √ 

Doweled

and Nondoweled

Hoerner et al., 1999.(10) √∗ √ √ √ √ √ √ √ √ √ √ √ √ 

* The transverse joint faulting model used in PaveSpec 2.0 is a modified version of the 1998 faulting model by Yu et al.

12
Table 3. Summary of required data elements included in the short list of best-available JPCP transver

models.

Model Inputs (in English units)

Model Source

Used in PaveSpec 2.0*

Cumulative ESAL's

Age, years

Avg. Joint Spacing/Slab Length, ft

PCC Coefficient of Thermal Expansion

PCC Modulus of Elasticity, psi

Avg. Annual Number of Wet Days

Avg. Annual Freeze-Thaw Cycles (air)

Avg. Annual No. of Days Above 90 °F

Thermal Gradient in Slab

Base Type (stabilized/non-stabilized)

Base Thickness, in.

Base Modulus of Elasticity, psi

Mod. of Subgrade Reaction (k-value), psi/in

Presence of Widened Lane

Presence of Tied PCC Shoulder

PCC 28-day Flexural Strength, psi

PCC Slab Thickness, in Model O

Owusu-Antwi et al., 1997.(13) √ √√√ √√ √ √ √ √Titus-Glover et al., 1999.(15) √√ √√√√ √Yu et al., 1997.(16) √ √√√ √√√√√√√ √ √

% Sl

Cracke

severi

* The transverse cracking model used in PaveSpec 2.0 is a modified version of the 1990 model by Smith et al.(18)

13
Table 4. Summary of required data elements included in the short list of best-available JPCP transv

models.

Model Inputs (in English units)

Model Source

Used in PaveSpec 2.0

Cumulative ESAL's

Age, years

Avg. Joint Spacing/Slab Length, ft

PCC Coefficient of Thermal Expansion

PCC Modulus of Elasticity, psi

Average Daily Temperature Range, °F

Avg. Annual Freezing Index, °F-days

Avg. Annual Freeze-Thaw Cycles (air)

Avg. Ann. Freeze-Thaw Cycles (in-pavement)

Avg. Annual No. of Days Above 90 °F

Thermal Gradient in Slab

Avg. Daily Range of Relative Humidity

During the Month of Construction

Presence of Salt

Subbase Friction Factor

Joint Sealant Type

Joint Sealant Modulus, psi/in

Joint Sealant Depth, in

Mod. of Subgrade Reaction (k-value), psi/in

Presence of Dowel Bar Corrosion

PCC Slab Thickness, in

Indirect Tensile Strength, psi

28-day Compressive Strength, psi

PCC Air Content, % 

Simpson et al., 1994.(14) √ √Titus-Glover et al., 1999.(15) √√√√√√ √ √ √ √ √√√ √√

% 

Yu et al., 1997.(16) √√ √ √ √ √Hoerner et al., 1999.(10) √ √√ √ √√ √ √ √ √√

% 

(

14
Table 5. Summary of required data elements included in the short list of best-available JPCP 

Model Inputs (in English units)

Pavement

Type Model Source

Used in PaveSpec 2.0

Cumulative ESAL's

Annual ESAL's

Age, years

Avg. Joint Spacing/Slab Length, ft

Avg. Annual Freezing Index, °F-days

Avg. Annual Precipitation, in.

LTPP Climatic Zone (freeze/non-freeze)

Avg. Annual Number of Wet Days

Avg. Annual Freeze-Thaw Cycles (air)

Avg. Annual No. of Days Below 32 °F

Base Type (stabilized/non-stabilized)

Mod. of Subgrade Reaction (k-value), psi/in

Subgrade AASHTO Soil Classification

Subgrade Type (fine/coarse)

Subgrade Percent Passing #200

Subgrade Moisture Content, %

Subgrade Overburden Pressure, psf

Presence of Tied PCC Shoulder

Dowel Diameter, in.

PCC Modulus of Elasticity, psi

PCC Split-Tensile Strength, psi

PCC Water/Cement (w/c) Ratio

PCC Slab Thickness, in

Initial IRI

Initial PSR

Total Trans. Joint Faulting Per Mile, in/mile

Avg. Trans. Faulting Per Joint, in

Doweled Simpson et al., 1994.(14) √√ √ √ √

Nondoweled Simpson et al., 1994.(14) √ √ √√√

Byrumet al., 1997.(12) √√√√ √ √ √√√ √√√√Titus-Glover etal., 1999.(15) √ √ √ √√ √ √√Yu et al.,1997.(16) √ 

Doweled

and Nondoweled

Hoerner et al.,1999.(10) √ √ √ √

15
16

identification of available distress indicator models and their required data elements,

the following initial list of five data sources identified for potential inclusion in the

national PRS database was created:

• FHWA Rigid Pavement Performance and Rehabilitation (RPPR) database.(16,18)

• Strategic Highway Research Program (SHRP)/FHWA LTPP program database—

includes Ohio Test Road sections.

• NCHRP Project 1-19 database—includes sections from six States plus the

extended AASHTO Road Test.(19)

• NCHRP Project 1-34 database.(17)

• Minnesota Test Road (Mn/ROAD) database.

To determine if the data included in each of these five data sources were suitable for

use in the model validation/development task of this study, each database was

evaluated in terms of the applicability, completeness, advantages, and limitations of the

data. Some examples of specific data source characteristics that were assessed include

the following:

• Number of independent sections.

• Geographic coverage (national, regional, State, other).

• Availability of time-series distress data (types of distress data, number of years of

data, units of measured distress data).

• Availability of site condition data (traffic, climate, subgrade type).

• Availability of design feature data (design slab thickness, joint spacing, joint load

transfer, subdrainage, shoulders, widened slab, base-related variables).

• Availability of construction AQC data (concrete strength, slab thickness, air

content, initial smoothness, and percent consolidation around dowels).

• Assessments of the consistency and accuracy of the data.

The results of each evaluation are summarized in the following sections.

FHWA RPPR(16,18)

The FHWA RPPR database contains data on 303 concrete pavement sections located

throughout 15 U.S. States and 1 Canadian Province. Of these 303 sections, 161 are JPCP

with or without dowels. The JPCP sections cover all 16 States/Provinces and all 4
17

SHRP climatic zones. Of the 161 JPCP sections, 53 were evaluated for field performance

(i.e., distresses, roughness) during two separate years: 1987 and 1992. The remaining

108 sections were evaluated only in 1992. Hence, initial performance data (actual or

assumed) aside, true time-series performance data (i.e., 2 or more performance data

points over time following an immediate post-construction testing period) are available

for 53 sections.

In general, the RPPR database was found to be fairly complete with regard to site

condition data (e.g., traffic, climate, subgrade) and design feature data (e.g., PCC

thickness, joint spacing, base, drainage, load transfer, shoulder). Traffic loading values

are estimated values based on traffic data provided by participating highway agencies,

and many climatic variables are available and complete. AQC data include PCC core

thickness values for approximately one-third of the sections and PCC core modulus of

rupture (MR) values (converted from split-tensile strength tests) for approximately onefourth of the sections (falling-weight deflectometer [FWD] backcalculated slab modulus

of elasticity values are available for all sections). Initial smoothness measurements and

PCC air content measurements are not available for any sections.

The RPPR performance data of primary interest in this study included transverse

joint edge faulting (average faulting expressed in inches per joint), transverse fatigue

cracking (percent cracked slabs), transverse joint spalling (percent spalled joints), and

surface smoothness (present serviceability rating [PSR], expressed as a rating between 0

and 5; IRI, expressed in inches/mile; and Mays ride number [MRN], expressed in

inches/mile). Faulting, cracking, spalling, and PSR values were obtained through the

on-site surveys in 1987 and 1992. IRI values were obtained in the 1992 surveys through

profile measurements using a South Dakota-type inertial profiler. MRN values were

obtained in the 1987 surveys through Mays Ride Meter testing. It is important to note

that the LTPP distress identification definitions were used in all field surveys.

SHRP/FHWA Long Term Pavement Performance Program

The SHRP/FHWA LTPP program database was the most comprehensive and

detailed database considered in this study. It contains information on 916 general

pavement studies (GPS) sections and approximately 2,500 specific pavement studies

(SPS) sections located throughout 50 U.S. States, 10 Canadian Provinces, the District of

Columbia, and Puerto Rico. Of the 916 GPS sections, 134 are designated as GPS-3

sections, which are doweled or non-doweled JPCP. The GPS-3 sections cover 33 States,

3 Canadian Provinces, and Puerto Rico, and all 4 SHRP climatic zones.

 The latest official release of the LTPP database was made in 1999 through the

release of DataPave 2.0. This software facilitates the exploration and retrieval of all

available GPS and SPS pavement section data (inventory, material testing, monitoring,

climatic, traffic, maintenance, rehabilitation, and seasonal testing) collected and

reviewed to the highest quality assurance level (level E). In general, the current LTPP
18

database is fairly complete with regard to site condition and design feature data for

GPS-3 sections. Traffic loading data, based on traffic counts and weigh-in-motion

devices, are available for nearly all sections; however, for several sections, the data only

represent 1 or 2 years or are not very recent (i.e., before 1995). Climate and subgrade

data are largely complete, as are pavement design data, such as PCC thickness, joint

spacing, load transfer, and shoulder data.

AQC data available in the LTPP database include PCC thickness, concrete strength

(various strength types and PCC elastic modulus), air content, and historical

smoothness data (which can be used to backcast the initial smoothness). Though

average PCC thickness values are largely available from the construction records (i.e.,

inventory data) kept by participating highway agencies, most sections include multiple

thickness measurements made on cores extracted under the LTPP testing program.

Although the database includes PCC strength (flexural, compressive, split-tensile) and

modulus data (based on different test methods and core/beam specimen ages) derived

from highway agency construction testing records, those data are often not complete

and typically include only average values. Strength and modulus data on cores

extracted under the LTPP testing program are also available and are quite complete;

however, these data represent long-term measurements rather than initial construction

measurements. Initial smoothness data, in the form of profilograph PI values and K.J.

Law Profilometer IRI values, are available for several SPS-2 (PCC pavement) sections.

Lastly, inventory PCC air content values are available for a limited number of sections.

LTPP performance data are fairly abundant and generally span 3 to 5 years from the

year of the first field survey. Both automated and manual distress survey data are

available, with the manual survey data believed to be more reliable. Though many

forms of performance data exist within the LTPP database, those of primary interest in

this study were largely complete and available for use. They included transverse joint

edge faulting (average joint faulting in millimeters), transverse fatigue cracking

(number of cracked slabs), transverse joint spalling (number of medium and high

severity spalled joints), and surface smoothness (expressed in various forms, including

average IRI).

NCHRP Project 1-19(19)

The NCHRP 1-19 Concrete Pavement Evaluation System (COPES) database contains

data on 425 JPCP and jointed reinforced concrete pavement (JRCP) sections located

throughout 8 U.S. States. Of these 425 sections, 152 are JPCP with and without dowel

bars. The JPCP sections represent five States and all four SHRP climatic zones. For

some sections, time-series performance data are available. However, the long-term

performance measurements of most sections are depicted by one point in time.

In general, site condition data in the COPES database were found to be available and

complete. Subgrade reaction moduli reflect estimated values based on the AASHTO
19

soil classification. Traffic loading data are derived from traffic counts provided by

participating agencies.

AQC data are essentially not available. Thickness measurements contained in the

database represent the design thickness. Moreover, although flexural strength values

(based on beam tests) are available, only the average value for each section is listed and

different test methods and test ages were used. Data for PCC air content, initial surface

smoothness, and percent consolidation around dowels were not available.

The following types of long-term performance data are available on the COPES

evaluation sections:

• Average transverse joint edge faulting.

• Percentage of spalled transverse joints.

• Length of transverse fatigue cracking.

• Length of longitudinal cracking.

• PSR.

For each of these performance variables, no more than one-third of the JPCP sections

have true time-series performance data available. The definitions of these distresses are

generally similar to the LTPP definitions.

NCHRP Project 1-34(17)

The NCHRP Project 1-34 database consists of pavement sections from three recent

pavement research studies: FHWA RPPR, SHRP/FHWA LTPP, and the NCHRP Project

1-34 drainage surveys. It contains data on 483 flexible, rigid, and composite pavement

sections located throughout the United States and Canada. The 1-34 database was

developed with the specific objectives of quantifying the benefits of subsurface drainage

and identifying criteria and conditions for which subsurface drainage is appropriate.

The FHWA RPPR and LTPP databases were discussed earlier. The NCHRP 1-34

drainage survey contains a total of 26 doweled or non-doweled JPCP sections. These

sections are located in five U.S. States and one Canadian Province, and they represent

the wet-freeze and wet-nonfreeze SHRP climatic zones. The sections were constructed

between 1980 and 1990, and each section was manually surveyed once in the fall of

1996. Hence, true time-series performance data are not available for any of the 26 JPCP

sections.

With the exception of modulus of subgrade reaction (k-value) data, the 1-34

drainage database was found to be quite complete with respect to site condition data.

Estimated cumulative ESAL's at the time of field surveys are available for each section,

as are several key climatic variables and subgrade soil classifications. Since FWD

testing was not part of the drainage surveys, backcalculated subgrade k-values and

PCC elastic modulus values are not available. It should be noted that in the
20

development of the NCHRP 1-34 JPCP faulting model, k-values for these sections were

estimated based on AASHTO soil classification. Design feature data, such as layer

types and thicknesses, joint and load transfer information, and drainage system data,

are available and complete.

AQC data on the 1-34 drainage survey sections are nonexistent. PCC thickness

values contained in the database represent the design thickness, not as-constructed

thickness. There are no PCC strength, air content, percent consolidation around

dowels, or initial smoothness measurements available.

Though the performance data contained in the database represent only one point in

time, they are complete. Each JPCP section has measured values of transverse joint

faulting (average joint edge faulting), transverse fatigue cracking (percent cracked

slabs), transverse joint spalling (percent spalled joints), and surface smoothness (PSR).

Mn/ROAD Test Sections

The Mn/ROAD database contains comprehensive information on 40 pavement

sections constructed in the early 1990s along I-94 near Otsego, Minnesota. The sections,

which are denoted as test cells, include 23 flexible and rigid pavement designs that are

part of the I-94 mainline roadway and 17 flexible and rigid designs that are part of a

low-volume, controlled traffic test loop lying parallel to I-94.

The Mn/ROAD test sections represent only one State (Minnesota) and one SHRP

climatic zone (wet-freeze). There are nine doweled JPCP sections on the I-94 mainline

and five doweled and non-doweled JPCP sections on the low-volume test loop.

Climatic, traffic, and subgrade data in the Mn/ROAD database were found to be

comprehensive and complete. Climatic data are available for various time frames (i.e.,

hourly, daily, monthly), and accurate traffic loading data have been produced from

weigh-in-motion devices. Subgrade reaction moduli and layer elastic moduli are

available as a result of FWD testing and analysis. Design feature data are also

comprehensive and complete.

True time-series performance data are available for all 14 JPCP sections. Key

pavement distress data, such as transverse joint spalling (percent joints spalled),

transverse fatigue cracking (number of cracked slabs), and longitudinal cracking (length

of cracking) have been measured manually every year since about 1994. IRI

measurements made with a PaveTech inertial profiler are available on a quarterly basis

for the years 1994 through 1996, and average transverse joint faulting data using the

Georgia fault meter are available on a quarterly basis for the years 1994 through 1998.
21

Availability of Required Data Elements in the Identified Potential Data Sources

As a first step in assessing the usefulness of the identified potential data sources to

the validation or improvement of the available distress indicator models, the data

inputs required by the short-listed best-available models (those variables shown in

tables 2 through 5) were cross referenced with each of the five potential databases.

Tables 6 through 9 contain model-type specific tables that illustrate the availability of

specific data elements required by the transverse joint faulting, transverse slab cracking,

transverse joint spalling, and IRI models.

STEP 3—SELECTION OF BEST-AVAILABLE DISTRESS INDICATOR MODELS

After completing an initial review of both the available distress indicator models

and potential data sources, the most suitable models of each type were selected for use

within the PRS methodology. This model selection procedure consisted of a multi-part

process that assessed the general quality of each model, evaluated each model's

applicability for use within the current PRS methodology, and finally reviewed the

availability of data required to validate/improve each model. For this comparative

study, the following characteristics were appraised for each model:

• Mechanistic/empirical—Is the model based on mechanistic or empirical concepts?

• Development database—What data sources were used in the development of the

model?

• Data quality—What is the quality of the data used in the model development

process?

• AQC's included in model—What PRS AQC's are included as inputs to the model?

• Model statistics—What are the model statistics (i.e., number of data points,

coefficient of determination [R2], standard error estimate [SEE]) associated with

each model?

• Availability of required model inputs—Are there sufficient data available (in the

collective potential data sources) to sufficiently validate or improve the model?

If specific data elements are not available, can values for these required data

elements be estimated or interpreted from other data in the data sources (e.g.,

flexural strength estimated from compressive strength)?

Based on significant past experience in developing distress indicator models for

JPCP, the most suitable models for the validation/improvement portion of the study

were selected. Tables 10 through 13 summarize the evaluations of each model's

characteristics as they relate to the questions outlined above. Brief discussions of the

processes used to select the best available model for each model type are presented in

the following sections.
Table 6. Availability of data required by the short-listed JPCP transverse joint faulting m

Database

Data Element RPPR LTPP

NCHRP

1-19

NCHRP

1-34 

Traffic loads (ESAL's) Estimated ESAL's Estimated ESAL's and WIM data Estimated ESAL's Estimated ESAL's Pavement age Yes Yes Yes Yes Avg. transverse joint spacing Yes Yes Yes Yes Presence of dowel bars Yes Yes Yes Yes Dowel bar diameter Yes Yes Yes Yes PCC modulus of elasticity Backcalculated Field testing data (cores and cylinders) No No Avg. annual freezing index Yes Yes Yes Yes Avg. annual precipitation Yes Yes Yes Yes Avg. annual no. of wet days Yes Yes No Yes Avg. annual no. of hot days Yes Yes No No Avg. temperature range Yes Yes Yes Yes Base type information Yes Yes Yes Yes Modulus of subgrade reaction (k-value) Backcalculated from deflection data Backcalculated from deflection data Estimated Estimated Widened lane information Yes Yes No Yes Shoulder type Yes Yes Yes Yes AASHTO drainage coefficient, C

d Yes No No No 

Base permeability (yes/no) Yes Yes No Yes Drainage type Yes Yes Yes Yes PCC slab thickness Design and from cores Design and from cores Yes (design) Yes (design) Percent consolidation around dowels No No No No Transverse joint edge faulting time-series data Yes Yes Yes No 

22
Table 7. Availability of data required by short-listed JPCP transverse cracking mode

Database

Data Element RPPR LTPP

NCHRP

1-19

NCHRP

1-34 

Traffic loads (ESAL's) Estimated ESAL's Estimated ESAL's and WIM data Estimated ESAL's Estimated ESAL's Pavement age Yes Yes Yes Yes Avg. transverse joint spacing Yes Yes Yes Yes PCC coefficient of thermal expansion No Yes No No PCC modulus of elasticity Backcalculated from deflection data Field testing data (cores and cylinders) No No Avg. annual no. of wet days Yes Yes No Yes Avg. annual freeze-thaw cycles (air) Yes Yes No Yes Avg. annual no. of hot days Yes Yes No No Temperature gradient in slab Estimated Measured for some sections No No Base type information Yes Yes Yes Yes Base thickness Design and from cores Yes Yes Yes Base modulus of elasticity No From cores and cylinders No No Modulus of subgrade reaction (k-value) Backcalculated from deflection data Backcalculated from deflection data Estimated Estimated Widened lane information Yes Yes No Yes Shoulder type Yes Yes Yes Yes PCC flexural strength Estimated from elastic modulus and cores Yes Yes No PCC thickness Design and from cores Design and from cores Yes (design) Yes (design) Transverse fatigue cracking time-series data Yes Yes Yes No 

23
Table 8. Availability of data required by the short-listed JPCP transverse joint spalling m

Database

Data Element RPPR LTPP

NCHRP

1-19

NCHRP

1-34 

Traffic loads (ESAL's) Estimated ESAL's Estimated ESAL's and WIM data Estimated ESAL's Estimated ESAL's Pavement age Yes Yes Yes Yes Avg. transverse joint spacing Yes Yes Yes Yes PCC coefficient of thermal expansion No Yes No No PCC modulus of elasticity Backcalculated from deflection data Field testing data (cores and cylinders) No No Average daily temperature range Yes Yes Yes Yes Avg. annual freezing index Yes Yes Yes Yes Avg. annual freeze-thaw cycles (air) Yes Yes No Yes Avg. annual freeze-thaw cycles (in-pavement) No No No No Avg. annual no. of hot days Yes Yes No No Thermal gradient in slab Estimated Measured for some sections No No Average daily range of relative humidity during themonth of construction No Yes No No Presence of salt No No No No Subbase friction factor No No No No Joint sealant type Yes Yes Yes No Joint sealant modulus No No No No Joint sealant depth No No No No Modulus of subgrade reaction (k-value) Backcalculated from deflection data Backcalculated from deflection data Estimated Estimated Presence of dowel bars Yes Yes Yes Yes Presence of dowel bar corrosion No No No No PCC slab thickness Design and from

cores Design and from cores Yes (design) Yes (design) 

PCC indirect tensile strength Estimated Lab and field testing data No No PCC Compressive strength Estimated Lab and field testing data No No PCC air content No Some design, fresh, and hardened air data No No Transverse joint spalling time-series data Yes Yes Yes No 

24
Table 9. Availability of data required by the short-listed JPCP IRI models.

Database

Data Element RPPR LTPP

NCHRP

1-19

NCHRP

1-34 

Traffic loads (ESAL's) Estimated ESAL's Estimated ESAL's and WIM data Estimated ESAL's Estimated ESAL's Pavement age Yes Yes Yes Yes Avg. transverse joint spacing Yes Yes Yes Yes Avg. annual freezing index Yes Yes Yes Yes Avg. annual precipitation Yes Yes Yes Yes LTPP climatic zone Yes Yes Yes Yes Avg. annual no. of wet days Yes Yes No Yes Avg. annual freeze-thaw cycles (air) Yes Yes No Yes Avg. annual no. of freezing days Yes Yes No No Base type information Yes Yes Yes Yes Modulus of subgrade reaction (k-value) Backcalculated from deflection data Backcalculated from deflection data Estimated Estimated Subgrade AASHTO soil classification Yes Yes No No Subgrade type Yes Yes Yes Yes Subgrade % passing 200 No Yes Yes No Subgrade moisture content No Yes No No Subgrade overburden pressure No No No No Shoulder type Yes Yes Yes Yes Dowel bar diameter Yes Yes Yes Yes PCC modulus of elasticity Backcalculated from deflection data Field testing data (cores and cylinders) No No PCC tensile strength Estimated Lab and field testing data No No PCC water/cement (w/c) ratio No Yes No No PCC slab thickness Design and from

cores Design and from cores Yes (design) Yes (design) 

Initial IRI No Estimated from time- series data No No Transverse joint edge faulting time-series data Yes Yes Yes No Transverse joint spalling time-series data Yes Yes Yes No Transverse fatigue cracking time-series data Yes Yes Yes No IRI time-series data Yes Yes No No 

25
Table 10. Assessment of best-available JPCP transverse joint faulting models.

Pavement

Type Model Source Model Type

Development

Database

Quality of Data

Used in Model

Development

Current PRS AQC's

Included in Model

Model

Statistics

Availabili

Doweled

JPCP

Simpson et al.,1994.(14)

Empirical LTPP Good None N=59 sections

R2=0.53

SEE=0.028 in

All 6 inputs apotential dat

Yu et al.,1997.(16)

MechanisticEmpirical RPPR Good Thickness N= 146 sections

R2=0.60

SEE=0.022 in

Sufficient dainputs. Limidrainage coe

Nondoweled

JPCP

Simpson et al.,1994.(14)

Empirical LTPP Good None N=25 sections

R2=0.55

SEE=0.047 in

All 5 inputs apotential dat

Yu et al.,1997.(16)

MechanisticEmpirical RPPR Good Thickness N= 131 sections

R2=0.45

SEE=0.034 in

Sufficient dainputs. Limidrainage coe

Doweled

and Nondoweled

JPCP

Owusu-Antwiet al., 1997.(13)

MechanisticEmpirical RPPR Good Thickness N=101 sections

R2=0.52

SEE=0.03 in

Sufficient dainputs. Limidrainage coe

Titus-Glover etal., 1999.(15)

MechanisticEmpirical LTPP Good Thickness N=120 sections

R2=0.56

SEE=0.03 in

Sufficient dainputs. Limidrainage coe

Yu et al.,1998.(17)

MechanisticEmpirical RPPR LTPP Good Thickness N= 351 sections

R2=0.50

SEE=0.035 in

Sufficient dainputs.

Hoerner et al.,1999.(10)

MechanisticEmpirical RPPR LTPP Good Thickness % Consolidation1 N= 351 sections

R2=0.50

SEE=0.035 in

Sufficient dainputs. No dconsolidation 

1 The faulting model used in PaveSpec 2.0 is the 1998 faulting model (developed by Yu) modified to include percent consolidation around dowels.

26
Table 11. Assessment of best-available JPCP transverse cracking models.

Model Source Model Type

Development

Database

Quality of Data

Used in Model

Development

Current PRS

AQC's

Included in

Model Model Statistics

Availability 

Owusu-Antwi etal., 1997.(13)

MechanisticEmpirical RPPR Good Strength Thickness N= 302 sections

R2=0.88

SEE=9.8% cracked slabs

Sufficient data ainputs. Limited coefficient of th

Titus-Glover etal., 1999.(15)

MechanisticEmpirical LTPP Good Thickness N=92 sections

R2=0.64

d = 1.816

VIF=0 to 2.32

Sufficient data ainputs.

Yu et al.,1997.(16)

MechanisticEmpirical RPPR Good Strength Thickness N=465 sections

R2=0.91

SEE=6.8% cracked slabs

Sufficient data ainputs. Limited coefficient of th

Table 12. Assessment of best-available JPCP transverse joint spalling models.

Model Source Model Type

Development

Database

Quality of Data

Used in Model

Development

Current PRS

AQC's

Included in

Model Model Statistics Availability of R

Simpson et al.,1994.(14)

Empirical LTPP Good None N= 56 sections

R2=0.36

SEE=11.05% spalled

joints

Sufficient data ava

Titus-Glover etal., 1999.(15)

MechanisticEmpirical LTPP Good Thickness Strength N=52 sections

R2=0.61

SEE=12.0% spalled joints

Sufficient data avainputs. Limited daof thermal expansisubbase friction famodulus, and join

Yu et al.,1997.(16)

MechanisticEmpirical RPPR Good None N= 164 sections

R2=0.76

SEE=5.4% spalled joints

Sufficient data avaNo data for presencorrosion.

Hoerner et al.,1999.(10)

MechanisticEmpirical RPPR Good Strength Air Content1 N= 164 sections

R2=0.76

SEE=5.4% spalled joints

Sufficient data avaLimited data for Ppresence of salt, anannual in pavemenand presence of do

1 The spalling model used in PaveSpec 2.0 is the 1997 joint spalling model (developed by Yu) modified to include PCC 28-day compressive streng

27
Table 13. Assessment of best-available JPCP IRI models.

Pavement

Type Model Source Model Type

Development

Database

Quality of Data

Used in Model

Development

Current PRS

AQC's

Included in

Model Model Statistics

Availabili

Doweled

JPCP

Simpson et al.,1994.(14)

Empirical LTPP Good Thickness N=21 sections

R2=0.55

SEE=19.06 in/mi

All 5 inputs apotential dat

Nondoweled

JPCP

Simpson et al.,1994.(14)

Empirical LTPP Good None N=28 sections

R2=0.644

SEE=31.29 in/mi

Sufficient dainputs.

Doweled and

Nondoweled

JPCP

Byrum et al.,1997.(12)

MechanisticEmpirical LTPP Good Strength Thickness N=104 sections

R2=0.79

SEE=21.8 in/mi

Sufficient dainputs. Limimoisture conwater/cemensubgrade ove

Titus-Glover etal., 1999.(15)

Empirical LTPP Good Function of

other distresses

N=155 sections

R2=0.50

SEE=22.0 in/mi

Sufficient dainputs.

Yu et al.,1997.(16)

Empirical RPPR Good Function of

other distresses

N=144 sections

R2=0.61

SEE=64.11 in/mi

Sufficient dainputs.

Hoerner et al.,1999.(10)

Empirical LTPP Good Function of

initial IRI and

other distresses

N=122 sections

R2=0.51

SEE=28.35 in/mi

Sufficient dainputs. Limi

28
29

Transverse Joint Faulting Model

The faulting model developed by Yu et al. in 1998 (under the NCHRP 1-34 project)

and modified by Hoerner et al. in 1999 was identified as the most suitable for inclusion

in the current PRS methodology.(10,17) The original model was developed using 351 data

points from two reliable databases (RPPR and LTPP) and included one PRS AQC (slab

thickness) as an input. In 1999, this NCHRP 1-34 faulting model was modified to

include percent consolidation around dowels as an input.(10) This modified version of

the model was used in the PaveSpec 2.0 software. Based on its many merits, including a

strong basis on mechanistic principles, the modified NCHRP 1-34 faulting model was

chosen as the most appropriate faulting model for validation/improvement under this

project.

Transverse Fatigue Cracking Model

A comparison of the three short-listed transverse cracking models resulted in the

identification of the model developed by Yu et al. in 1997 (under the RPPR project) as

the most suitable for this project.(16) The 1997 model by Yu is a largely mechanistic

transverse cracking model that includes two PRS AQC's as inputs (thickness and

strength). A significant number of reliable data points (465 from the RPPR database)

were used to develop the original model, with very good associated model statistics

(R2=0.91, SEE=6.8% cracked slabs). This model was selected because of its strong

mechanistic characteristics and the extensive data used for calibration.

Transverse Joint Spalling Model

The transverse joint spalling model developed by Yu et al. in 1997 (under the RPPR

project) and modified by Hoerner et al. in 1999 was identified as the most suitable for

inclusion in the current PRS methodology.(10,16) The original model was developed

using 164 data points from the reliable 1997 RPPR database, with very good associated

model statistics (R2=0.76, SEE=5.4% spalled joints). One drawback of Yu's original

model, from a PRS standpoint, is that it is not a direct function of any PRS AQC's. In an

attempt to remedy this problem, Hoerner et. al. used Yu's 1997 model in a modified

procedure that incorporated concrete strength and PCC air content (based on a major

laboratory study of PCC freeze-thaw).(7,10) This modified version of the 1997 Yu

spalling model was used in the PaveSpec 2.0 software.

IRI Model

The original list of six IRI models was first reduced to the three models in which IRI

is a function of other predicted distresses—those developed by Titus-Glover et al.

(1999), Yu et al. (1997), and Hoerner et al. (1999).(10,15,16) An IRI model directly based on

other distress is a very desirable characteristic for the model chosen for use in the PRS

procedure, since the other distresses directly identify predicted performance. Of the

three IRI models identified, the model developed by Hoerner et al. in 1999 was chosen
30

as the most appropriate for use in the PRS methodology because of its inclusion of

initial IRI, key distresses, and a good model development database (i.e., LTPP).(10)

STEP 4—IDENTIFICATION OF SPECIFIC DATA SOURCES TO BE INCLUDED IN

THE NATIONAL PRS DATABASE

After identifying the most suitable distress indicator models for use within this

study, the five identified potential data sources were investigated for their applicability

to the validation/improvement of each specific model. Table 14 summarizes the

specific databases deemed useful to the validation/improvement of each model. Data

from these data sources were imported into Microsoft Access (database software) and

organized into a national PRS database in preparation for the validation/improvement

portion of this study.

Table 14. Specific databases that will be used to validate/improve chosen bestavailable distress indicator models.

Distress

Indicator Model

Type

Source of Chosen BestAvailable Model

Databases Deemed Appropriate

for Use in the

Validation/Improvement Effort

Transverse joint

faulting

Yu et al., 1998 (modified by

Hoerner et al. in 1999).(10,17)

RPPR

LTPP (including Mn/ROAD data)

NCHRP 1-19

Transverse

fatigue cracking

Yu et al., 1997.(16) RPPR

LTPP (including Mn/ROAD data)

Transverse joint

spalling

Yu et al., 1997 (modified by

Hoerner et al. in 1999).(10,16)

LTPP (including Mn/ROAD data)

IRI Hoerner et al., 1999.(10) LTPP (including Mn/ROAD data)
31

CHAPTER 3: PROCEDURES USED TO VALIDATE/IMPROVE

DISTRESS INDICATOR MODELS

INTRODUCTION

After choosing the models that were most promising for use within the current PRS

methodology, the next step was to determine how to validate the models and, if

necessary, improve them. First, a more detailed evaluation of each model was

conducted to determine which models (if any) could simply be validated (confirmed)

using the compiled national PRS database. If a given model could be adequately

validated with the new data set, then no model improvement efforts would be

attempted. If it was determined that a model needed to be improved (i.e., re-regressed

with the possible addition or removal of variables), then a number of statistical tools

were identified that could be used to achieve that goal.

This chapter includes discussions of the following:

• Compilation of the national PRS database and specific model type data sets.

• The techniques used in the model validation/improvement process (engineering

assessment, statistical analyses, and sensitivity analyses).

• The criteria used to determine when a model was acceptable for use within the

PRS methodology.

PREPARATION OF MODEL TYPE-SPECIFIC DATA SETS

In preparation for the initial model evaluation procedures, the data compiled in the

national database were organized into subsets associated with each distress indicator

model. Each of these model-specific data sets contained all potential data elements

(design, climatic, traffic, time-series distress, AQC quality) associated with the

particular distress model being validated/improved. Specific data sets were organized

using Microsoft Access and exported to Microsoft Excel or the SAS statistical

software for further data manipulation and analysis.

TECHNIQUES OF THE MODEL VALIDATION/IMPROVEMENT PROCESS

After the specific data sets were organized, each distress indicator model was

evaluated in more detail to assess its adequacy and sensitivity to key variables. The

evaluations were not only based on an engineering assessment of the models

(documenting observed model capabilities and limitations), but the results of statistical

and sensitivity analyses as well. Each of the methods used in the model evaluation

methods is discussed briefly in the following sections.
32

Engineering Assessment

The capabilities and limitations of each distress indicator model were identified and

documented as a first step in the evaluation process. Under this general assessment, the

models were evaluated on the basis of such items as:

• Specific variables (inputs) included in the model (especially the inclusion of the

PRS AQC's).

• Specific variables obviously missing from the model.

• Applicable ranges for input variables.

• Ability of a SHA to estimate the model inputs.

• Errors associated with estimating model inputs (especially the sampling and

testing of AQC's).

• Consideration of materials- or mix-related problems.

• Appropriateness of the model output units.

• Geographic scope—inference space of the development database.

• Relative effects (reasonableness) of each input variable.

Much of this general assessment work was completed during the initial model review

presented in chapter 2.

Statistical Analyses

Many different statistical analysis tools were used to evaluate the initial model and

assess the quality of the model after any validation or improvements were made. All of

the utilized statistical analysis tools focused on a comparison of predicted and actual

distress indicator data. The actual distress indicator data are represented by those timeseries distress data collected for each pavement section. The predictive distress

indicator models are used to generate the predicted values. Each predicted value is

based on a specific cumulative traffic (ESAL) value or age, as well as project-specific site

and design-related inputs extracted from the national PRS database. Note that

comparisons between predicted and actual values (for a pavement section) are only

valid if the predicted value is calculated using the same cumulative ESAL's (or age for

spalling models) as observed for the actual value. The four different statistical analysis

procedures used in this study are described separately below.
33

Plots of Predicted versus Actual Data

Plots of predicted versus actual data provide visual evidence of how well a model

predicts, by comparing the general location of the data points to a one-to-one line

(representing predicted = actual). A general understanding of the bias in a prediction

model is determined by how well the plotted data are centered around this one-to-one

line. A model is said to have an overprediction bias if most of the data points lie above

this line; conversely, an underprediction bias is said to be observed when most of the

data points lie below the line. A general understanding of the precision of a model is

determined by the amount of scatter of the data points around the one-to-one line.

Figure 1 shows an example of such a plot from a former evaluation of the NCHRP 1-19

JPCP faulting model as it is applied to the data in the wet-freeze climatic region only.(19)

Figure 2 shows a more conceptual diagram that illustrates the difference between bias

and precision in a model.(20)

Figure 1. Example of a plot of predicted versus actual data.(19)

Plots of Residuals versus Actual Data

A residual is defined as the difference between the predicted and actual data values

(predicted – actual) for a given pavement section. A plot of residuals versus predicted

data is used to examine how well a model predicts over the range of the predicted data.

If a trend is observed in the plot, it generally means that one or more significant

variables are missing from the model. Under this project, plots of residuals versus

predicted data were used to provide insight into the type, trend, and possibly the

source of any observed bias.
34

Exactness of Measurement

Bias

Good Precision

Poor Accuracy

(Biased)

(Average off Center)

Exactness of Measurement

Poor Precision

Good Accuracy

(Unbiased)

(Average on Center)

Exactness of Measurement

Good Precision

Good Accuracy

(Unbiased)

(Average on Center)

Figure 2. Conceptual illustration of the difference between bias and precision.(20)

Paired t-tests

Although the plots of predicted versus actual data provide visual feedback into the

bias of a model, a statistical test is required to quantify the amount of bias and determine

its significance. The research team used a two-tailed t-test (or other appropriate test) to

investigate the bias of each model. Specifically, the t-test was used to determine if the

mean difference between the sets of predicted and actual values is significantly different

from zero. The following demonstrates this statistical method.

A recent study by Hoerner et al. evaluated the 1986 AASHTO rigid pavement

design model by comparing the predicted ESAL's with the actual ESAL's (to a given

level of roughness) using LTPP data.(21) Table 15 contains results of the paired t-test

analysis conducted on the JPCP section data.

The paired t-test was used to evaluate these results for bias. The null hypothesis is

that the mean difference between predicted log ESAL and actual log ESAL is equal to

zero, and the alternate hypothesis is that it is not equal to zero (the model could over- or

underpredict log ESAL). The results show that the absolute value of the computed t
35

Table 15. Example of paired t-test analysis results (from an investigation of the

AASHTO rigid pavement design model using LTPP data).(21)

Pavement

Type

No. of

Sections

Pred.

Log

ESAL's

Actual

Log

ESAL's t-calc

t-crit

(0.05

level)

Reject

Null

Hypoth.?

Ratio of

Pred. to

Actual

ESAL's

Standard

Error of

the

Estimate*

JPCP 94 6.80 6.45 -5.19 1.99 Yes 2.25 0.66

* Standard deviation of the differences between predicted and actual log ESAL's.

(5.19) is greater than the critical t (1.99) at the 0.05 level of significance; therefore, the

null hypothesis is rejected at the 0.05 level of significance. Thus, in engineering terms,

the mean difference between predicted log ESAL and actual log ESAL values for JPCP

sections is not zero for these conditions. The mean actual and predicted ESAL values

are 2.8 million and 6.3 million, respectively, showing that the model overpredicts

ESAL's by a ratio of 2.25 (on average) for JPCP. Similar analyses were conducted on the

predicted versus actual data sets compiled under this project.

Investigation of Components of Variability

The final statistical investigation evaluated the magnitude of variation in predicting

the distress indicator values for individual sections. This investigation attempted to

explain, and quantify, the overall scatter of points about the one-to-one line between the

predicted and actual data.

This procedure is also best illustrated by an example. Under a recent study by Hall

et al., many plots of predicted log ESAL's versus actual log ESAL's were used to

evaluate an improved AASHTO rigid pavement design model.(22) In an attempt to

explain the scatter of the plotted data points, an investigation of the components of

variation was conducted. It was first determined that there were four primary

components of variation adding to the scatter observed on these plots:

• Errors associated with the estimation of actual traffic (VT).

• Errors associated with estimating each design input for each LTPP section (VI).

• Random or normal variation between the performance of supposedly identical

replicate sections (similar to the variation of strength between two replicate

concrete specimens) (VR).

• Inability of the model to predict actual pavement performance (serviceability, in

this case) due to deficiencies in the model (VM). This is the real model associated

error in prediction. The relatively simple function form of the model does not, of

course, completely represent the real pavement behavior under load and climate.

These components of variance were mathematically expressed as follows (base 10 logs):
36

Prediction Error = Log[Actual ESAL's] – Log[Predicted ESAL's] (2)

Variance [Prediction Error] = Variance Log[Actual ESAL's] + (3)

Variance Log[Predicted ESAL's] –

Covariance [Log(Actual ESAL's), Log(Predicted ESAL's)]

Thus, the total scatter of data in any of the actual versus predicted ESAL plots

consisted of several components of variation, including:

• Estimation of the historical ESAL's (horizontal axis).

• Estimation of true inputs to the model for each section (vertical axis).

• Random differences in performance between sections due to unknown

replication error (vertical axis).

• True lack of ability of the model to represent pavement performance (vertical

axis).

These components of variance were divided into percentages of the total variation (VE),

as shown in table 16. Similar analyses were conducted on the predicted versus actual

data sets compiled under this project. However, the analyses are in terms of distress

rather than traffic.

Table 16. Results of the components of variance example.(22)

Variance Component Estimated Variance Percent of Total

ESAL Estimation, VT 0.09 28

Input Estimation, VI 0.07 22

Random Variation, VR 0.06 19

Model Error, VM 0.10 31

Total, VE 0.32 100

Sensitivity Analyses

The sensitivity of each model output (distress) to its corresponding inputs was

investigated as part of the model validation/improvement process. Such an analysis

will quantify the significance of each input relative to changes in output. Plots showing

the sensitivity of the individual inputs are included. A reasonable sensitivity of each

input variable is critical to a successful prediction model. Figure 3 contains an example

of such a plot showing the sensitivity of JPCP cracking with respect to slab thickness

and cumulative ESAL's. Under this project, similar two-dimensional plots were

developed to illustrate the sensitivity of the distress indicator models to specific inputs.
37

Figure 3. Example of the sensitivity of a JPCP cracking model to slab thickness.(16)

ACCEPTABILITY OF MODELS

The acceptability of each validated/improved model was judged based on the

results of the engineering assessment, statistical analysis, and sensitivity analysis.

Specifically, the validation/improvement process focused on achieving the following

for each model:

• Eliminating model bias (improving accuracy)—The research team attempted to

remove (or minimize) any observed bias in the plot of predicted versus actual

data points.

• Improving model precision (reducing scatter)—Model improvements (variable

changes, model form changes, or model re-regressions) were conducted to

improve accuracy. The accuracy of the model can be assessed by observing how

close the data points fall to the one-to-one line in the predicted versus actual plot.

The closer the data points are to the line, the more precise the model.

• Including PRS-related AQC's as inputs—An acceptable model under this study

must be a function of one or more PRS-related AQC's.

• Obtaining reasonable model sensitivity—The output sensitivity of the prediction

model to changes in model inputs was assessed for each model. Engineering
38

judgment based on extensive previous experience was used to determine if the

created sensitivity plots were reasonable.

• Expanding the inference space of the model—The focus of this study was to base all

validation/improvement efforts on a much more comprehensive database (the

national PRS database). The intention is to make each validated/improved

model much more applicable and accurate over a larger range of geographical

and site conditions.

Using these criteria as a guide, each best-available model (identified in chapter 2)

was investigated separately to determine if it could be simply validated, or if it needed

to be improved. The specific procedures used in the validation/improvement of the

transverse joint faulting, transverse fatigue cracking, transverse joint spalling, and IRI

models are presented in chapters 4 through 7.
39

CHAPTER 4: TRANSVERSE JOINT FAULTING MODEL

INTRODUCTION

Transverse joint faulting is defined as the difference in elevation between adjacent

joints at a transverse joint. The development of faulting is often attributed to a

combination of repeated heavy axle loads, insufficient load transfer between the

adjacent slabs, free moisture in the pavement structure, and erodible base or subgrade

material.

(17) When excess moisture exists in a pavement with an erodible base or

underlying fine-grained subgrade material, repeated vehicle loadings typically cause

the mixture of water and fine material (fines) to be removed from beneath the leave slab

corner and ejected to the surface through the transverse joint or along the shoulder.

This process, commonly referred to as pumping, will eventually result in a void below

the leave slab corner. In addition, some of the fines that are not ejected will be

deposited under the approach slab corner, causing the approach slab to rise. This

combination of a buildup of material beneath the approach corner and the loss of

support resulting from a void under the leave corner can lead to significant faulting at

the joint (especially for JPCP without dowels). Significant joint faulting has a major

impact on the LCC of the pavement in terms of early rehabilitation and vehicle

operating costs.

(17)

This chapter describes the attempted validation of the chosen best-available JPCP

transverse joint faulting model (that used in PaveSpec 2.0) and the subsequent

development of a new, improved faulting model for use in PaveSpec 3.0.

CURRENT PRS JPCP TRANSVERSE JOINT FAULTING MODEL

The selected best-available transverse joint faulting model was that incorporated

into the PaveSpec 2.0 software by Hoerner et al. in 1999.

(10) The procedure is based on

the faulting model developed in 1998 by Yu et al. (17) In 1999, this model was adjusted

(specifically for use in PaveSpec 2.0) to incorporate the effects of percent consolidation

of PCC around dowel bars.

Within the PaveSpec 2.0 software, two different procedures were used to estimate

transverse joint faulting, depending on whether percent consolidation around dowels

is considered. Regardless of the procedure chosen, the baseline transverse joint

faulting model is that developed by Yu et al. in 1998.

(17) If percent consolidation

around dowels (percent of consolidation at other locations away from joint) is not

considered, transverse joint faulting is predicted directly using the baseline model. If

percent consolidation around dowels is considered, the transverse joint faulting values

(predicted using the baseline model) are then altered by adjusting the non-dimensional

aggregate interlock stiffness (AGG*) term of the model. The procedures making up

both situations are summarized in the following sections. (Note: The model outputs

and inputs are presented in English units.)
40

JPCP Transverse Joint Faulting (Not Including Percent Consolidation Around

Dowels)

When percent consolidation around dowels is not considered, transverse joint

faulting is computed using the following (baseline) equation:(17)

FAULT = DAMAGE0.2475 * [0.2405 – 0.00118 * DAYS90 + 0.001216 * (4)

WETDAYS – 0.04336 * BASETYPE – (0.004336 + 0.007059 *

(1 – DOWEL)) * LCB]

where:

FAULT = Average transverse joint faulting per joint, in.

BASETYPE = Base type (0 if nonstabilized; 1 if asphalt stabilized [ATB], cement

stabilized [CTB], or lean concrete base [LCB]).

LCB = Presence of lean concrete base (1 if LCB is present, 0 if LCB is not

present).

WETDAYS = Average number of wet days per year.

DAYS90 = Number of days per year with the maximum temperature greater than

32 °C (90 °F).

DOWEL = Presence of dowels (1 if dowels are present, 0 if dowels are not

present).

DAMAGE = n/N.

n = Actual number of applied cumulative ESAL’s.

N = Allowable number of applied cumulative ESAL’s.

Statistics:

N = 391.

R2 = 0.50.

SEE = 0.035 in (0.89 mm).

Equation 5 is used to compute allowable ESAL's (N):

Log(N) = 0.785983 – 0.92991 * (1 + 0.40 * PERM * (1 – DOWEL)) (5)

* Log (DE)

where:

PERM = Base permeability (0 = not permeable, 1 = permeable).

DE = Differential energy density at a corner.

The DE at a corner is defined as the energy difference in the elastic subgrade

deformation under the loaded slab (leave) and the unloaded slab (approach). The

computation of DE involves completing a multi-step process in which maximum corner
41

deflections are computed for loaded and unloaded conditions. The details of this

calculation are presented later in this chapter (in the section describing the final joint

faulting model developed under this study).

One important equation used in the computation of DE concerns the nondimensional aggregate interlock stiffness (AGG*) factor. When percent consolidation

around dowels is not considered, AGG* is computed using equation 6.

AGG* = (AGG/kL) (6)

= 2.3 Exp(1 – 1.987 * JTSPACE / L + 3.48 * DOWELDIA3.56)

where:

AGG* = Nondimensional aggregate interlock stiffness.

AGG = Aggregate load transfer stiffness, psi.

k = Dynamic modulus of subgrade reaction (dynamic k-value), psi/in.

L = Slab’s radius of relative stiffness, in.

= [(EPCC * hPCC3) / (12 * (1 – μ2) * k)]

0.25

EPCC = PCC modulus of elasticity, psi.

hPCC = Slab thickness, in.

μ = PCC Poisson's ratio (assumed to be equal to 0.15).

JTSPACE = Slab length (joint spacing), ft.

DOWELDIA = Dowel diameter, in.

JPCP Transverse Joint Faulting (Including Percent Consolidation Around Dowels)

The only difference between computing transverse joint faulting with or without

considering percent consolidation around dowels (percent of consolidation at other

locations away from joint) is a change in the equation used to compute AGG*. When

percent consolidation is considered, the AGG* (computed using equation 6) is adjusted

to incorporate the effects of percent consolidation. This adjusted AGG* is termed

AGG*NEW and is computed using the following equation:

AGG*NEW = 10[Log(AGG*) + 0.27 * (%CON – 100)] (7)

where:

AGG*NEW = Nondimensional aggregate interlock stiffness (adjusted to incorporate

the effects of percent consolidation around dowels).

AGG* = Nondimensional aggregate interlock stiffness computed using

equation 6.

%CON = Percent consolidation around dowels.

The DE is then computed by substituting AGG*NEW for AGG* in the equations making

up the multi-step DE procedure.
42

LIMITATIONS OF THE CURRENT PRS TRANSVERSE JOINT FAULTING

MODEL

The first step in the process of validating/improving the current PRS transverse

joint faulting model involved identifying any weaknesses in the model. Specifically,

weaknesses were first identified by:

• Reviewing plots of predicted versus measured faulting.

• Reviewing plots of residuals versus predicted faulting.

• Analyzing diagnostic statistics such as the R2 and SEE to determine the

goodness-of-fit of the models when used with independent data.

In addition, the models were checked to determine whether they made engineering

sense and agreed with trends and observations from previous research.

The independent data used in the initial model validation process consisted of JPCP

data from the RPPR, LTPP (GPS-3 data only), and NCHRP-19 (COPES) databases.

(16,18,19)

The final validation data set consisted of 338 pavement test sections located in 34 States

and Provinces. A summary of the validation data is presented in table 17.

Table 17. Summary of JPCP data used in the initial validation of the current transverse

joint faulting model.

Range

Variable Min. Max. Mean

Standard

Deviation

Cumulative ESAL's, millions 0.15 56.0 6.5 6.4

Joint spacing, ft 7.0 30.0 17.4 4.8

Presence of dowel bars 150 data points used dowels and 361 aggregate interlock as

the load transfer mechanism

Dowel bar diameter, in 1.0 1.5 1.2 0.2

PCC modulus of elasticity, psi 3,050,000 14,492,739 5,948,588 1,880,322

Avg. annual number of wet days 34.0 180.0 92.2 40.7

Avg. total precipitation, in 4.9 60.7 30.6 15.5

Number of hot days (days with

temperature above 32 °C (90 °F) 0.2 150.0 40.9 32.2

Base type 79 data points had ATB, 201 had CTB, 46 had LCB, 166 had

granular bases, and 19 had no base

Dynamic modulus of subgrade

reaction (k-value), psi [backcalculated

from FWD data]

45 1,800 468 384

Base permeability 43 data points had permeable bases while 470 did not

PCC slab thickness, in 7.0 15.0 9.4 1.3

Percent consolidation around dowels,

%

No data were available

ATB = asphalt treated base; CTB = cement treated base; LCB = lean concrete base.
43

Unfortunately, no percent consolidation around dowel data were available for the

validation process. Therefore, a validation attempt could only be made on the baseline

model, which does not consider consolidation.

The validation data set was used in the current transverse joint faulting model to

obtain predicted faulting values for each section. Associated measured faulting values

were obtained directly from the selected databases. Figures 4 and 5 show plots of

predicted versus measured faulting, and residuals versus predicted faulting,

respectively. The diagnostic statistics and both plots indicate that the predicted

transverse joint faulting has a reasonable correlation with the measured transverse joint

faulting. However, additional calibration of the existing model may significantly

improve the model’s prediction ability.

The key model limitations identified in the initial validation process were:

• The model significantly overestimates load transfer efficiency of transverse joints

(an average estimate of LTE was 69 percent for non-doweled pavements and 99

percent for doweled pavements).

• The base layer erodibility potential needs to be incorporated in a more rational

manner.

• The empirical portion in equation 4 is a function of climate and design-related

variables (i.e., DAYS 90, Wet days, base type, presence of lean concrete base, and

presence of dowels), but it is more desirable for this factor to be dependent on

site condition factors only.

Based on the results of this initial validation process, it was decided to recalibrate the

existing faulting model using the data available in the newly compiled PRS national

database. The recalibration effort focused on addressing the identified limitations of

the model and improving its overall predictability.

EXISTING JPCP TRANSVERSE JOINT FAULTING MODELS

In preparation for the development of a new JPCP transverse joint faulting model,

many of the faulting models developed under previous research were reviewed.

During the review process, specific attention was paid to the variables chosen for

inclusion in the models. The details of each of the faulting models reviewed under this

study are described separately in the following sections.

SHRP P-020 JPCP Transverse Joint Faulting Model(14)

In a SHRP study conducted by Simpson et al. in 1994, titled Early Analysis of LTPP

General Pavement Studies Data, separate JPCP faulting models were developed for

doweled and non-doweled JPCP.

(14) Each of these models are presented as follows:
44

0.00

0.05

0.10

0.15

0.20

0.00 0.05 0.10 0.15 0.20

Measured Faulting, in.

Predicted Faulting, in.

N = 511

R

2

 = 0.47

SEE = 0.031 in

Figure 4. Predicted versus measured transverse joint faulting (using the compiled

validation data set).

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.00 0.05 0.10 0.15 0.20

Predicted Faulting, in.

Residual Faulting, in.

Figure 5. Residual versus predicted transverse joint faulting (using the compiled

validation data set).
45

SHRP P-020 Faulting Model for JPCP With Dowels

2

0.25

10

JTSPACE FAULTD CESAL *[0.0238 0.0006* 











= + (8)

2 2

10

AGE 0.0039*

KSTATIC

100 0.0037 * 











 +











+

− 0.0037* EDGESUP − 0.0218*DOWELDIA ]

where:

FAULTD = Mean transverse doweled joint faulting, in.

CESAL = Cumulative 80-kN (18-kip) ESAL's in traffic lane, millions.

JTSPACE = Mean transverse joint spacing, ft.

KSTATIC = Mean backcalculated static k-value, psi/in.

AGE = Age since construction, years.

EDGESUP = Edge support (1=tied PCC shoulder, 0=any other shoulder type).

DOWELDIA = Diameter of dowels in transverse joints, in.

Statistics:

N = 59.

R2 = 0.534.

SEE = 0.028 in (0.7 mm).

SHRP P-020 Faulting Model for JPCP Without Dowels

The faulting model developed for non-doweled JPCP was the following:

2

0.25

10

PRECIP FAULTND CESAL *[ 0.07575 0.0251* AGE 0.0013* 











= − + + (9)

0.0378* DRAIN]

1000

PRECIP 0.0012* FI*  −











+

where:

FAULTND = Mean transverse non-doweled joint faulting, in.

CESAL = Cumulative 80-kN (18-kip) ESAL's in traffic lane, millions.

PRECIP = Mean annual precipitation, in.

FI = Mean freezing index, °F-days.

AGE = Age since construction, years.

DRAIN = Drainage type (1=longitudinal subdrainage, 0=otherwise).
46

Statistics:

N = 25.

R2 = 0.550.

SEE = 0.047 in (1.2 mm).

Both of these models predict faulting as a function of traffic, age, and various site

conditions and pavement design features. A review of the output of these models

indicates a trend that non-doweled pavements develop more faulting than doweled

pavements. In addition, for doweled pavements, faulting decreases as dowel diameter

increases. As expected, both models were positively correlated with cumulative

ESAL's (i.e., faulting increases with an increase in cumulative ESAL's). Pavement

design features that were found to be significant in the models included drainage type,

joint spacing, base type, and presence of a tied PCC shoulder. Two climatic variables

(precipitation and freezing index) were found to significantly affect the development of

faulting for non-doweled pavements; however, it is interesting to note that no climaterelated variables were included in the model for doweled JPCP.

In the final SHRP P-020 report, the research team that developed these models

acknowledged that both models were developed with limited data, which most likely

led to relatively low coefficients of correlation and fairly high SEE. Because of these

model statistics, the research team stated that improvements could most likely be made

to both models.

FHWA RPPR 1997 JPCP Transverse Joint Faulting Model(16)

In 1997, Yu et al. also developed separate JPCP faulting models for doweled and

non-doweled pavements as part of the FHWA RPPR project.

(16) The development of

these models identified several pavement design features and site conditions that

significantly affect transverse joint faulting. Each of these models is discussed

separately below:

RPPR Faulting Model for JPCP With Dowels

FAULTD = CESAL0.25 * [0.0628 – 0.0628 * Cd + 0.3673*10–8 * BSTRESS2(10)

+ 0.4116 * 10–5 * JTSPACE2 + 0.7466 * 10–9 * FI2 * PRECIP0.5

– 0.009503 * BASE – 0.01917 *WIDENLANE + 0.0009217 * AGE]

where:

FAULTD = Mean transverse doweled joint faulting, in.

CESAL = Cumulative 80-kN (18-kip) ESAL's in traffic lane, millions.

Cd = Modified AASHTO drainage coefficient, calculated from database

information.

BSTRESS = Maximum dowel/concrete bearing stress, psi.
47

JTSPACE = Mean transverse joint spacing, ft.

FI = Mean freezing index, °F-days.

PRECIP = Mean annual precipitation, in.

BASE = Base type (0 = nonstabilized base; 1 = stabilized base).

WIDENLANE = Widened lane (0 = not widened, 1 = widened).

AGE = Age since construction, years.

Statistics:

N = 146.

R2 = 0.60.

SEE = 0.022 in (0.56 mm).

RPPR Faulting Model for JPCP Without Dowels

FAULTND = CESAL 0.25 * [0.2347 – 0.1516*Cd – 0.000250 * Hpcc2/JTSPACE0.25 (11)

– 0.0115 * BASE + 0.7784 * 10-7 * FI1.5 * PRECIP0.25

– 0.002478 * DAYS900.5 – 0.0415 * WIDENLANE]

where:

FAULTND = Mean transverse non-doweled joint faulting, in.

CESAL = Cumulative 80-kN (18-kip) ESAL's in traffic lane, millions.

Cd = Modified AASHTO drainage coefficient, calculated from database

information.

hPCC = PCC slab thickness, in.

JTSPACE = Mean transverse joint spacing, ft.

BASE = Base type (0 = nonstabilized base; 1 = stabilized base).

FI = Mean freezing index, °F-days.

PRECIP = Mean annual precipitation, in.

DAYS90 = Mean annual number of hot days (days with maximum

temperature greater than 32 °C [90°F]).

WIDENLANE = Widened lane (0 = not widened, 1 = widened).

Statistics:

N = 131.

R2 = 0.45.

SEE = 0.034 in (0.86 mm).

The results of these models were found to generally agree with the results from the

models developed under the LTPP Early Analysis (SHRP P-020) study.

(14,16) One

important characteristic of both RPPR models that was not addressed in the SHRP

P-020 models is the inclusion of presence of a widened traffic lane as an independent

variable. The presence of a widened traffic lane was found to be negatively correlated

with faulting in both RPPR models (i.e., predicted faulting for pavements with a
48

widened lane will be less than that predicted for a similar pavement without a widened

lane).

ACPA JPCP Transverse Joint Faulting Model(23)

In 1994, Wu et al. developed separate mechanistic-empirical JPCP faulting models

for doweled and non-doweled pavements for the American Concrete Paving

Association (ACPA).

(23) These models were extensions of faulting models originally

developed for the Portland Cement Association (PCA) in 1977.(24) These models are

unique in that they include erodibility of the base/subgrade material as the main factor

influencing faulting. Using the concept of Miner s linear damage, the percent of

erosion damage occurring at the slab corner was computed using the following

equation:(23)

∑

i i

2

i

N

C EROSION =100 n * (12)

where:

EROSION = Percent erosion damage.

ni = Expected number of axle load repetitions for each axle group i.

Ni = Allowable number of repetitions for axle group i.

C2 = 0.06 for pavements without a tied PCC shoulder and 0.94 for

pavements with a tied PCC shoulder.

Next, the allowable number of load applications (N) was computed as a function of

the power, or rate of work, of each axle pass at the corner of the slab. This equation is

shown as the following:(23)

log N = 14.524 – 6.777 * (C1 * P – 9.0)0.103 (13)

where:

N = Allowable load repetitions to end of design period.

P = Power (rate of work) of each axle pass at the corner of the slab.

C1 = 1 – (KSTATIC / 2000 * [4/Hpcc])

2

.

KSTATIC = Modulus of subgrade reaction, psi/in.

hPCC = Slab thickness, in.

The power of each axle pass at the corner of the slab is computed using equation

14:(23)

P = 268.7 * p2/ hPCC/KSTATIC0.73 (14)
49

where:

P = Power (rate of work) of each axle pass at the corner of the slab.

p = Pressure at slab-foundation interface, psi.

The final JPCP faulting models developed under this ACPA study are included as

equations 15 and 16, respectively.

(23)

FAULTD = EROSION0.25 * [0.0038332 * (PRECIP/10)

1.84121 (15)

+ 0.0057763 * JTSPACE0.38274 ]

FAULTND = EROSION0.25 * [9.75873 * 10–4 * (PRECIP)

0.91907 (16)

+ 0.0060291 * JTSPACE0.54428 – 0.016799 * DRAIN]

where:

FAULTD = Mean transverse doweled joint faulting, in.

FAULTND = Mean transverse non-doweled joint faulting, in.

EROSION = Calculated accumulated erosion (using equation 12).

PRECIP = Annual precipitation, in.

JTSPACE = Transverse joint spacing, ft.

DRAIN = Dummy variable for the presence of edge drains (1 = edge drains are

present, 0 = edge drains are not present).

An evaluation of these models by Yu et al. in 1998 found that they generally agreed

with the JPCP faulting models developed under the RPPR and SHRP P-020 studies.

(17)

In addition, it was noted that PCC slab thickness was found to be a significant

parameter that is negatively correlated with faulting (i.e., an increase in slab thickness

results in a decrease in transverse joint faulting).(23) It is also important to note that the

presence of edge drains was included in the non-doweled faulting model, whereas no

drainage-related variables were used in the doweled model.

FHWA NAPCOM JPCP Transverse Joint Faulting Model(13)

Under the FHWA Nationwide Pavement Cost Model (NAPCOM) study completed

in 1997, Owusu-Antwi et al. developed the following mechanistic-empirical faulting

model for doweled and non-doweled JPCP:(13)

FAULT = DAMAGE0.23 * (0.35 – 0.0277 * BASE – 0.25 * Cd + 2.17 * 10–5 * FI) (17)

where:

FAULT = Mean transverse joint faulting, in.

DAMAGE = n/N.
50

n = Cumulative number of actual axle load applications, in thousands.

N = Number of allowable axle load applications, in thousands.

Cd = AASHTO drainage coefficient.

BASE = Base type (0 = erodible base; 1 = nonerodible base).

FI = Freezing index, °F-days.

Statistics:

N = 101.

R2 = 0.52.

SEE = 0.03 in (0.8 mm).

The allowable number of load applications (N) is defined as follows:

Log(N) = 4.27 – 1.6 * Log(DE – 0.002) (18)

where:

N = Number of allowable axle load applications, in thousands.

DE = Differential of subgrade elastic energy density.

The NAPCOM model (equation 17) illustrates that the presence of dowels

significantly reduces faulting by reducing the differential of subgrade elastic energy

density. In addition, the output of the model illustrates trends showing that a

stabilized base, stiff subgrade, and improved drainage are negatively correlated with

faulting.

(13)

LTPP Data Analysis Study JPCP Transverse Joint Faulting Model(15)

In 1999, Titus-Glover et al. recalibrated the 1997 NAPCOM JPCP transverse joint

faulting model under a FHWA LTPP data analysis contract.

(15) This model, recalibrated

using LTPP data only, is as follows:

FAULT = DAMAGE0.3 * [0.05 + 0.00004 * WETDAYS (19)

– 0.0024 * DOWDIA – 0.025 * Cd * (0.5 + BASE)]

where:

FAULT = Mean transverse joint faulting, in.

DAMAGE = n/N.

n = Cumulative number of actual 90-kN (18-kip) ESAL applications, in

thousands.

N = Number of allowable 90-kN (18-kip) ESAL applications, in thousands.

WETDAYS = Annual average number of wet days.

DOWDIA = Dowel diameter, in.

Cd = AASHTO drainage coefficient.

BASE = Base or subbase type (0 = erodible base; 1 = nonerodible base).

Statistics:

N = 120.
51

R2 = 0.56.

SEE = 0.03 in (0.8 mm).

The main difference between the recalibrated model and the original NAPCOM

model is that the recalibrated model expresses traffic in terms of ESAL's, whereas the

original NAPCOM model uses actual axle loads. In addition, the effects of climate are

characterized with different variables in the two models. In the original NAPCOM

model, the influence of climate is considered by freezing index, whereas the average

annual number of wet days was used as the important climatic parameter in the

calibrated LTPP model.

(13)

Overview of Existing JPCP Transverse Joint Faulting Models

A review of recently developed JPCP faulting models identified a number of

distinct relationships between faulting and traffic, age, and various climatic, site, and

pavement design variables. All of the models showed trends of faulting increasing

rapidly and then slowly leveling off over time. Several of the models indicate that

shoulder type has a significant effect on faulting. While the SHRP P-020 doweled

faulting model calculates less faulting if a tied PCC shoulder is used, the more recent

RPPR study showed that tied PCC shoulders do not have a significant effect in

reducing faulting.

(14,16) This finding is attributed to the observation that the sections

included in the RPPR database did not supply significant load transfer efficiency at the

slab corner to reduce deflections and affect faulting. The RPPR study did, however,

find that the presence of a widened lane significantly reduced faulting.

(16)

Most of the models discussed in this section indicate that an improved pavement

drainage system will generally reduce the potential of faulting, particularly for nondoweled joints. In the RPPR, LTPP, and NAPCOM models, drainage quality was

characterized by using the modified AASHTO drainage coefficient, Cd. This coefficient

is based on several parameters, such as presence of a permeable base and edgedrains,

precipitation level, and subgrade type. Although this coefficient provides a reasonable

estimate of the pavement's ability to drain excessive moisture from the structure, it can

confound the effect of different design features and site conditions on faulting.

(17)

The review of the recently developed transverse joint faulting models identified a

number of variables that have been consistently found to significantly influence

faulting. A summary of the significant variables used in past model development (for

those models reviewed in this section) is summarized in table 18. This collective list of

variables (or variables related to these) will be considered in the transverse faulting

model validation/development procedures conducted under this project.

RECALIBRATION OF THE CURRENT JPCP TRANSVERSE JOINT FAULTING

MODEL

An analysis of the data parameters included in table 18 shows that the current PRS

JPCP transverse joint faulting model (that used in PaveSpec 2.0) accounts for the most

significant design parameters and site conditions. As was stated earlier, the
Table 18. Summary of variables found to significantly affect JPCP transverse joint faulting.

Variable

SHRP P020

(1984)(14)

RPPR

(1997)(16)

ACPA

(1994)(23)

NAPCOM

(1997)(13)

LTPP

Data

Analysis

(1997)(15)

PaveSpec

2.0(10)

Age 3 3

80-kN (18-kip) ESAL's 3 3 3 3

Axle load repetitions 3 3

Annual temperature range 3

Average annual number of wet days 3 3

Freezing index 3 3 3

Mean annual precipitation 3 3 3

Average annual number of days with

maximum temperature > 32°C (90 °F)

3

Drainage type 3 3 31

AASHTO drainage coefficient, Cd

3 3 3

PCC slab thickness 3 3 3 3 3

PCC modulus of elasticity 3 3 3 3

Modulus of subgrade reaction (k-value) 3 3 3 3 3 3

Base type 3 3 3 3

Shoulder type 3 3 32 32 32

Transverse joint spacing 3 3 3 3 3 3

Dowel diameter 3 3 3 3

Notes:

1 Includes the effects of base permeability.

2 Includes the effects of presence of widened lane.

52
53

model was found to predict faulting with reasonable accuracy. Nevertheless, it was

believed that the current model could be greatly improved under this study by:

1. Accounting for base erodibility potential in a more rational manner.

2. Estimating load transfer efficiency of transverse joints using a more realistic

procedure.

3. Incorporating all design variables into the damage calculation portion of the

model, making the empirical adjustment factor portion of the model a function

of site condition variables only.

The recalibration procedures used to address these limitations are described in detail

below.

Data Preparation

In preparation for the recalibration of the PaveSpec 2.0 faulting model, all pertinent

data from the database used for verification of the current faulting model (see table 17)

was compiled into a faulting model development database. As mentioned previously,

the independent data used in the initial model validation process consisted of JPCP

data from the RPPR, LTPP (GPS-3 data only), and NCHRP-19 (COPES) databases. The

final validation data set consisted of 338 pavement test sections located in 34 States and

Provinces. This database not only consisted of all variables used in the validation

process, but contained additional climate- and design-related variables as well.

One of the key variables added to the database is a base erodibility factor. This

factor is a subjective classification that characterizes the potential for base erosion

beneath the PCC slab. Accounting for erodibility is important because it was shown in

several previous studies that JPCP constructed over base/subbase materials with a

high potential for erosion generally experience significantly higher levels of pumping

and faulting.

(16,17,19)

Several field and laboratory analyses have been performed to determine the most

suitable procedure for characterizing paving materials erodibility. The most rational

and widely accepted procedure is that developed by the Permanent International

Association of Road Congresses (PIARC). This procedure was developed using data

collected from more than 100 concrete pavement sections in an international survey of

26 countries, including the United States.

(25,26,27,28) The PIARC recommendations

(modified to include a permeable drainage base layer) for the erosion potential of

base/subbase materials (based on base type and material characteristics) are presented

in table 19. Moving from A to E, each class has approximately 10 times as much

erodibility potential as the class before it (e.g., class C material is approximately 10

times as erodible as class B material). These guidelines have been used extensively in

Europe with success.
54

Table 19. PIARC recommendations for erosion potential of base/subbase materials

(based on base type and base cement and asphalt content).

(25)

Erodibility Class Material Description

A

Lean concrete with 8 percent cement; bituminous concrete

with 6 percent asphalt cement, or a permeable drainage

layer.

B

Cement treated granular material with 5 percent cement

manufactured in plant; bitumen treated granular material

with 4 percent asphalt cement.

C

Cement-treated granular material with 3.5 percent cement

manufactured in plant; bitumen treated granular material

with 3 percent asphalt cement.

D

Granular material treated in place with 2.5 percent cement,

treated soils.

E Untreated granular material.

While the PIARC recommendations are based on the stabilizer content (asphalt or

portland cement) of the base/subbase materials, this information was not available or

reliable for many pavement sections in the compiled PRS database. However, recent

research conducted in Germany demonstrated that the long-term compressive strength

(strength measured at a time much later than 28 days) of cement treated bases is

another reliable indicator of their erodibility.

(29) Since compressive strength information

was available for the majority of the pavement sections with CTB in the model

development database, PIARC classifications were estimated based on ranges of

cement stabilized base long term compressive strength. The chosen correlations are

shown in table 20. (Note: the development of table 20 was based on general

relationships observed in the LTPP database.) Long-term compressive strength was

used to estimate base erodibility class for those sections in which cement content

information was not available.

Table 20. Supplemental recommendations for erosion potential of CTB (based on longterm compressive strength).

Base Erodibility Class Material Description

A

Cement treated granular material with long-term

compressive strength > 2,500 psi.

B

Cement treated granular material with long-term

compressive strength <= 2,500 and > 2,000 psi.

C

Cement treated granular material with long-term

compressive strength <= 2,000 and > 1000 psi.

D

Cement treated granular material with long-term

compressive strength <= 1000 psi.
55

Based on these recommendations, an erodibility class was estimated for each

section. This erodibility class was then converted into a numerical base erodibility

factor, EROD. It was assumed that if two sections have the same design parameters

and site conditions except different erodibility of base layers, then to exhibit the same

level of faulting they have to receive an amount of traffic in reverse proportion of their

base erodibility factors, i.e.

1

2

2

1

EROD

EROD

n

n

= (20)

where:

n1, n2 = Number of applied cumulative ESAL’s to achieve a certain

level of faulting for sections 1 and 2, respectively.

EROD1,EROD2 = Base erodibility factors for sections 1 and 2, respectively.

Table 21 presents the final base erodibility factors associated with each PIARC

erodibility class.

Table 21. Recommendations for assigning erodibility factor based on

PIARC erodibility class.

PIARC Erodibility

Class

Recommended Ranges for

Base Erodibility Factor

A 0.5–1.5

B 1.5–2.5

C 2.5–3.5

D 3.5–4.5

E 4.5–5.5

No base 5.5–7.5

The entire model development database was thoroughly evaluated to identify any

missing data elements and possible problem spots in the database (e.g., time series

data with a significant decrease in faulting over time). Attempts were made to obtain

replacements for missing data where possible. The data set was also checked and

cleaned for anomalies and gross data error.

Statistical Tools for Regression and Optimization

The SAS nonlinear procedure (NLIN) was selected as the appropriate nonlinear

regression tool to be used in model development and calibration.

(30) Other SAS

procedures, such as STEPWISE, REG, RSQUARE, and RSREG, were used in selecting

the most suitable variables for incorporation into the model.

Final JPCP Transverse Joint Faulting Model

The final recalibration procedure consisted of solving for the various constants in

the conceptual faulting model using the nonlinear regression approach. Optimization
56

techniques and regression analysis were used to determine regression coefficients that

minimized the error between the predicted and measured faulting values. The specific

procedure used is the following:

1. Assign initial values to the variables and parameters in the conceptual model.

2. For those assigned values, perform nonlinear regression analysis to find the

values of the faulting prediction model parameters that minimize the error

vector, ,.

3. Repeat step 2 for different values of $ until the error vector is minimized and the

conversion criteria are met (i.e., error is within acceptable limits).

Based on the successful completion of the iterative optimization process, the final

models making up the final JPCP transverse joint faulting procedure were determined.

As with the faulting procedure used in PaveSpec 2.0, two different processes are

used to estimate transverse joint faulting, depending on whether percent consolidation

around dowels is considered. The specific multi-step procedures used to compute

transverse joint faulting for both situations are summarized in the following sections.

(Note: The model outputs and inputs are presented in English units.)

JPCP Transverse Joint Faulting (Not Including Percent Consolidation Around Dowels)

FAULT = DAMAGE0.275 * [0.1741 – 0.0009911 * DAYS90 + 0.001082 * PRECIP] (21)

where:

FAULT = Average transverse joint faulting per joint, in.

DAMAGE = n/N.

n = Actual number of applied cumulative ESAL’s.

N = Allowable number of applied cumulative ESAL’s.

DAYS90 = Number of days per year with the maximum temperature greater than

32 °C (90 °F).

PRECIP = Average annual precipitation, in.

Statistics:

No. of data = 511.

R2 = 56 percent.

SEE = 0.029 in (0.74 mm).

Equation 22 is used to compute allowable ESAL's (N):
57

Log(N) = 0.785983 – Log(EROD) – 0.92991 * (1 + 0.40 * PERM (22)

* (1 – DOWEL)) * Log (DE*(1 – 1.432*DOWELDIA

+0.513*DOWELDIA2.))

where:

N = Allowable number of applied cumulative million ESAL’s.

EROD = Base erodibility factor for the base (value between 0.5 and 7.5).

PERM = Base permeability (0 = not permeable, 1 = permeable).

DOWEL = Presence of dowels (1 if dowels are present, 0 if dowels are not

present).

DOWELDIA = Dowel diameter, in. (maximum allowed is 1.50 in)

DE = Differential energy density at a corner.

As stated previously in this chapter, the DE at a corner is defined as the energy

difference in the elastic base/subgrade deformation under the loaded slab (leave) and

the unloaded slab (approach). One important equation used in the computation of DE

is that for the nondimensional aggregate interlock stiffness (AGG*) factor. When

percent consolidation around dowels is not considered, AGG* is computed using

equation 23.

AGG* = (AGG/kL) (23)

= 2.3 * Exp(– 1.987 * JTSPACE / L + DOWELDIA2.2)

where:

AGG* = Nondimensional aggregate interlock stiffness.

AGG = Aggregate load transfer stiffness, psi.

k = Dynamic modulus of subgrade reaction (dynamic k-value), psi/in.

L = Slab’s radius of relative stiffness, in.

= [(EPCC * hPCC3) / (12 * (1 – μ2) * k)]

0.25

EPCC = PCC modulus of elasticity, psi.

hPCC = Slab thickness, in.

μ = PCC Poisson's ratio (assumed to be equal to 0.15).

JTSPACE = Slab length (joint spacing), ft.

DOWELDIA = Dowel diameter, in. (maximum allowed is 1.50 in)

The computation of DE involves completing a multi-step process in which

maximum corner deflections are computed for loaded and unloaded conditions. The

detailed step-by-step procedure used to compute DE is described below.

1. Calculate the radius of relative stiffness (L) using equation 24.

L = [(EPCC * hPCC3) / (12 * (1 – μ

2

) * k)]

0.25 (24)
58

2. Calculate AGG* using equation 23.

3. Calculate the maximum corner deflections of the loaded and unloaded slabs

assuming that the 80-kN ESAL is located 305 mm from the corner (914 mm from

the corner if widened slab is used). The following steps are used:

a. Use equation 25 to calculate the free-edge corner deflection (no load transfer

to the adjacent slab) assuming that the load is placed at the slab corner.

wfe,0 = (0.0000864 * L2 + 0.002824 * L + 0.2953) * 18000/kL2(25)

b. Use equation 26 to calculate the free-edge corner deflection (no load transfer

to the adjacent slab) assuming that the load is placed at the transverse joint

914 mm away from the slab corner.

wfe,914 = (0.0000648 * L2 + 0.003934 * L – 0.02548) * 18000/kL2(26)

c. Use equation 27 to calculate the corresponding load transfer efficiency (LTE)

for a load placed at the slab corner.

LTEx=0(%) = 1 / [0.01 + 0.012 * (AGG*)-0.849] (27)

d. Use equation 28 to calculate the corresponding LTE at the slab corner for a

load placed 914 mm away from the slab corner.

LTEx=914(%) = 1 / [0.01 + 0.003483 * (AGG*)-1.13677] (28)

e. Calculate the corner deflection of the unloaded slab for a load placed at 0 and

914 mm from the slab corner using equations 29 and 30, respectively.

wUL,0 = wfe,0 * (LTEx=0)/(1 + LTEx=0) (29)

wUL,91.4 = wfe,91.4 * (LTEx=91.4)/(1 + LTEx=91.4) (30)

f. Use equation 31 to calculate the corner deflection of the unloaded slab for an

axle load located at a transverse joint in the wheelpath (305 mm from the slab

corner for a non-widened slab).

wUL = wUL,0 + (wUL,914 – wUL,0) * x/914 (31)

This equation interpolates between the unloaded slab deflections at x = 0 and

914 mm, where "x" is the distance from the wheelpath to the slab corner. The

variable “x” is calculated as the additional width provided by the widened
59

lane plus 305 mm (this sum is limited to 914 mm). For example, if the chosen

widened lane width is 4.3 m, and the regular lane width is 3.7 m, the added

width is 609 mm. The variable “x” is then calculated as 609 mm + 305 mm, or

914 mm.

g. Use equation 32 to calculate the LTE at the slab corner for an axle load

located at the transverse joint in the wheelpath (305 mm from the slab corner

for a non-widened slab).

LTE = LTE0 +(LTE914 – LTE0) * x/914 (32)

This equation interpolates between the LTE’s computed for x = 0 and 914

mm.

h. Use equation 33 to calculate the loaded corner deflection for the load located

in the wheelpath.

wL = wUL / LTE (33)

i. Use equation 34 to calculate the differential energy density, DE.

DE = 0.5 * k * (wL

2

 – wUL2) (34)

4. Calculate the allowable number of ESAL applications (N) using equation 22.

5. Calculate predicted faulting using equation 21.

JPCP Transverse Joint Faulting (Including Percent Consolidation Around Dowels)

The only difference between computing transverse joint faulting with or without

considering percent consolidation around dowels is a change in the equation used to

compute AGG*. When percent consolidation is considered, AGG* (computed using

equation 23) is adjusted to incorporate the effects of percent consolidation. This

adjusted AGG* is termed AGG*NEW and is computed using the following equation:

AGG*NEW = 10[Log(AGG*) + 0.27 * (%CON – 100)] (35)

where

AGG*NEW = Nondimensional aggregate interlock stiffness (adjusted to incorporate

the effects of percent consolidation around dowels).

AGG* = Nondimensional aggregate interlock stiffness computed using

equation 23.

%CON = Percent consolidation around dowels.
60

The DE is then computed by substituting AGG*NEW for AGG* in the equations making

up the multi-step DE procedure.

Final Faulting Model Summary

Plots of the predicted versus measured faulting, and residuals versus predicted

faulting, are shown in figures 6 and 7, respectively. The diagnostic statistics and both

plots verify that the model is effective for predicting transverse joint faulting. The R2 of

56 percent and SEE of 0.7 mm (0.029 in) are very reasonable given the large number of

data points (N = 511) used in model development.

0.00

0.05

0.10

0.15

0.20

0.00 0.05 0.10 0.15 0.20

Measured Faulting, in.

Predicted Faulting, in.

N = 511

R

2

 = 0.56

SEE = 0.029 in

Figure 6. Predicted versus measured faulting for the validated JPCP faulting model.

MODEL VERIFICATION (SENSITIVITY ANALYSIS)

A sensitivity analysis was conducted on the final faulting model to determine its

reliability for predicting faulting within and outside of the inference space of the

development database. This was accomplished by studying the effects of the various

input parameters on the output generated by the faulting model. The ranges of the

input values used in the sensitivity analysis are presented in table 22. Note that the

sensitivity analyses were accomplished by investigating the effects of changing one

variable at a time, while holding all other variables at their mean values.
61

Effect of Material- and Design-Related Factors

Various material-, site-, and pavement design-related variables were included in the

final validated faulting model. These variables consist of dowel diameter, transverse

joint spacing, base erodibility factor, dynamic modulus of subgrade reaction,

-0.10

-0.05

0.00

0.05

0.10

0.00 0.05 0.10 0.15 0.20

Predicted Faulting, in.

Residual Faulting, in.

Figure 7. Residual versus predicted faulting for the validated JPCP faulting model.

Table 22. Range of values of data used in the sensitivity analysis for the final validated

JPCP transverse joint faulting model.

Range

Variable Min. Max. Default

Cumulative ESAL's 0 20,000,000

Presence of dowels 1 = dowels are present, 0 = dowels are not present

Dowel diameter, in 1.0 1.5 -

Transverse joint spacing, ft 13 30 15

Average annual hot days (number of days

with maximum temperature > 32 °C (90 °F) 10 90 30

Average annual precipitation, in 5.0 60.0 30.0

Erodibility factor, EROD 1.0 5.0 4.0

Dynamic modulus of subgrade reaction

(dynamic k-value), psi/in

[backcalculated from FWD data]

100 500 200

Base permeability 1 = permeable, 0 = not permeable

PCC modulus of elasticity, psi 3,000,000 8,000,000 4,000,000

PCC slab thickness, in 8.0 12.0 9.0
62

Percent consolidation around dowels, % 90 102 100

permeability of the base, PCC modulus of elasticity, PCC slab thickness, and percent

consolidation around dowels. The sensitivity of the final faulting model to each of

these variables is discussed separately in the following sections.

Dowel Diameter

Figure 8 provides a sensitivity plot of the joint faulting with ESAL and dowel

diameter. It is clearly shown that dowels decrease faulting and that faulting decreases

with an increase in dowel diameter.

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0 4,000,000 8,000,000 12,000,000 16,000,000 20,000,000

Cumulative Traffic, ESAL's

Average Transverse Joint Faulting, in

No dowels

D=1.0 in

D=1.25 in

D=1.5 in

Joint spacing = 15 ft

Hpcc = 9 in

PCC elastic modulus = 4 Mpsi

Consolidation at dowels = 100%

Dynamic k-value = 200 psi/in

Non-permeable base

Aggregate base (EROD = 5)

Number of hot days = 20

Average annual precip. = 30 in

Figure 8. Sensitivity of the final JPCP transverse joint faulting model to changes in

dowel diameter.

Transverse Joint Spacing

Figure 9 demonstrates that the model predicts higher faulting for pavements with

longer PCC slabs. This is reasonable since an increase in joint spacing increases slab

movements due to temperature contraction, which increases joint opening and reduces

load transfer efficiency at the joint. The latter causes higher corner and differential

deflections and, therefore, higher faulting.
63

Base Erodibility Factor

Figure 10 shows that the model predicts a significant reduction in faulting level if a

less erodible base layer is used (for example, changing from an unbound granular base

where EROD = 5.0 to a high quality lean concrete or hot-mixed asphalt treated base

where EROD = 1.0). This agrees with the findings of the previous studies that

pavements with stabilized bases exhibit less faulting than pavements with granular

bases. Pavements with lean concrete bases (with higher cement content and

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0 4,000,000 8,000,000 12,000,000 16,000,000 20,000,000

Cumulative Traffic, ESAL's

Average Transverse Joint Faulting, in

L=30 ft

L=20 ft

L=15 ft

L=13 ft

No dowels

Hpcc = 9 in

PCC elastic modulus = 4 Mpsi

Consolidation at dowels = 100%

Dynamic k-value = 200 psi/in

Non-permeable base

Aggregate base (EROD = 5)

Number of hot days = 20

Average annual precip. = 30 in

Figure 9. Sensitivity of the final JPCP transverse joint faulting model to changes in

transverse joint spacing.
64

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0 4,000,000 8,000,000 12,000,000 16,000,000 20,000,000

Cumulative Traffic, ESAL's

Average Transverse Joint Faulting, in

EROD=5.0

EROD=4.0

EROD=3.0

EROD=2.0

EROD=1.0

No dowels

Joint spacing = 15 ft

Hpcc = 9 in

PCC elastic modulus = 4 Mpsi

Consolidation at dowels = 100%

Dynamic k-value = 200 psi/in

Non-permeable base

Number of hot days = 20

Average annual precip. = 30 in

Figure 10. Sensitivity of the final JPCP transverse joint faulting model to changes in

base erodibility factor.

compressive strength) exhibited less faulting than pavements with lower strength

stabilized bases (assuming all other factors remain the same).

Dynamic Modulus of Subgrade Reaction (dynamic k-value)

Figure 11 shows that pavements built on softer subgrades (with lower k-values) are

more likely to develop higher faulting than pavements built on a stronger subgrade

(with higher k-values), assuming that all other parameters are the same. This highlights

the importance of using positive design features (dowels and/or less erodible bases)

for pavements built on softer subgrade.
65

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0 4,000,000 8,000,000 12,000,000 16,000,000 20,000,000

Cumulative Traffic, ESAL's

Average Transverse Joint Faulting, in

Dynamic k=100 psi/in

Dynamic k=200 psi/in

Dynamic k=300 psi/in

Dynamic k=500 psi/in

No dowels

Joint spacing = 15 ft

Hpcc = 9 in

PCC elastic modulus = 4 Mpsi

Consolidation at dowels = 100%

Non-permeable base

Aggregate base (EROD = 5)

Number of hot days = 20

Average annual precip. = 30 in

Figure 11. Sensitivity of the final JPCP transverse joint faulting model to changes in

dynamic modulus of subgrade reaction.

Base Permeability

Figure 12 demonstrates that a permeable base significantly reduces faulting of nondoweled pavements. However, this reduction is less than what could be achieved if

dowels were installed.

PCC Thickness and Modulus of Elasticity

Figures 13 and 14 show an increase in PCC thickness and elastic modulus reduces

faulting. This is reasonable since more rigid PCC slabs experience lower deflections

that reduce faulting potential.
66

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0 4,000,000 8,000,000 12,000,000 16,000,000 20,000,000

Cumulative Traffic, ESAL's

Average Transverse Joint Faulting, in

Dense graded base

Permable base

No dowels

Joint spacing = 15 ft

Hpcc = 9 in

PCC elastic modulus = 4 Mpsi

Consolidation at dowels = 100%

Dynamic k-value = 200 psi/in

Aggregate base (EROD = 5)

Number of hot days = 20

Average annual precip. = 30 in

Figure 12. Sensitivity of final validated JPCP joint faulting model to changes in base

permeability.

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0 4,000,000 8,000,000 12,000,000 16,000,000 20,000,000

Cumulative Traffic, ESAL's

Average Transverse Joint Faulting, in

Hpcc = 8 in

Hpcc = 9 in

Hpcc = 10 in

Hpcc = 12 in

No dowels

Joint spacing = 15 ft

PCC elastic modulus = 4 Mpsi

Consolidation at dowels = 100%

Dynamic k-value = 200 psi/in

Non-permeable base

Aggregate base (EROD = 5)

Number of hot days = 20

Average annual precip. = 30 in

Figure 13. Sensitivity of the final JPCP transverse joint faulting model to changes in

PCC slab thickness.
67

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0 4,000,000 8,000,000 12,000,000 16,000,000 20,000,000

Cumulative Traffic, ESAL's

Average Transverse Joint Faulting, in

Epcc=3 Mpsi

Epcc=4 Mpsi

Epcc = 6 Mpsi

Epcc=8 Mpsi

No dowels

Joint spacing = 15 ft

Hpcc = 9 in

Consolidation at dowels = 100%

Dynamic k-value = 200 psi/in

Non-permeable base

Aggregate base (EROD = 5)

Number of hot days = 20

Average annual precip. = 30 in

Figure 14. Sensitivity of the final JPCP transverse joint faulting model to changes in

PCC modulus of elasticity.

Percent Consolidation of PCC Around Dowels

Figures 15 and 16 show the importance of proper consolidation of PCC around 25.4-

and 38.1-mm (1- and 1.5-in) dowels. Poor consolidation may significantly reduce the

effectiveness of dowels. Note that the trend in figure 15 demonstrates that 90 percent

consolidation around a 25.4-mm (1-in) dowel reduces its effectiveness almost to the

level of a non-doweled joint.

Effect of Climatic Variables

Two climatic variables were included in the final validated JPCP transverse joint

faulting model—average annual precipitation and average annual number of hot days

(days above 32 °C [90 °F]). The sensitivity of the final faulting model to each of these

climatic variables is discussed below.

Average Annual Precipitation

Figure 17 shows that transverse joint faulting is positively correlated with average

annual precipitation (i.e., an increase in precipitation causes an increase in faulting

while holding all other variables constant). This trend is explained by the fact that JPCP
68

subjected to greater total precipitation (or days with precipitation) will have more free

water beneath the slab to cause erosion (all other design features being equal).

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0 4,000,000 8,000,000 12,000,000 16,000,000 20,000,000

Cumulative Traffic, ESAL's

Average Transverse Joint Faulting, in

No dowels

% cons=90%

% cons=98%

% cons=102%

% cons=100%

Joint spacing = 15 ft

Hpcc = 9 in

PCC elastic modulus = 4 Mpsi

Dynamic k-value = 200 psi/in

Non-permeable base

Aggregate base (EROD = 5)

Number of hot days = 20

Average annual precip. = 30 in

Dowel diameter = 1.0 in

Figure 15. Sensitivity of the final JPCP transverse joint faulting model to changes in

percent consolidation of PCC around 25.4-mm (1-in) dowels.

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0 4,000,000 8,000,000 12,000,000 16,000,000 20,000,000

Cumulative Traffic, ESAL's

Average Transverse Joint Faulting, in

No dowels

% cons=90%

% cons=98%

% cons=100%

% cons=102%

Joint spacing = 15 ft

Hpcc = 9 in

PCC elastic modulus = 4 Mpsi

Dynamic k-value = 200 psi/in

Non-permeable base

Aggregate base (EROD = 5)

Number of hot days = 20

Average annual precip. = 30 in

Dowel diameter = 1.5 in
69

Figure 16. Sensitivity of the final JPCP transverse joint faulting model to changes in

percent consolidation of PCC around 38.1-mm (1.5-in) dowels.

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0 4,000,000 8,000,000 12,000,000 16,000,000 20,000,000

Cumulative Traffic, ESAL's

Average Transverse Joint Faulting, in

Precip=5 in

Precip=30 in

Precip=60 in

No dowels

Joint spacing = 15 ft

Hpcc = 9 in

PCC elastic modulus = 4 Mpsi

Consolidation at dowels = 100%

Dynamic k-value = 200 psi/in

Non-permeable base

Aggregate base (EROD = 5)

No. of hot days. = 20

Figure 17. Sensitivity of the final JPCP transverse joint faulting model to changes in

precipitation.

Average Annual Number of Hot Days

Figure 18 demonstrates the importance of air temperature on the development of

transverse joint faulting. The observed trends show that faulting typically decreases as

the number of hot days increases. This trend is due to the fact that pavements in

warmer climates experience less damage associated with the spring thawing period.

Another possible explanation of this effect is that greater use of deicing salts and

increased moisture level accelerate corrosion of the dowel bars.

SUMMARY

The previous PRS faulting model was improved under this study by validating the

model with a larger, more comprehensive data set, and also by directly considering the

effect of base erosion. This validated model is deemed suitable for use with the current

PRS procedure because it incorporates PRS-related AQC's (slab thickness and percent

consolidation around dowel bars) as well as other site-, design-, material-, and climaterelated variables that significantly influence faulting. Base erosion was considered in a

realistic way in the calibrated model and proved to be highly significant. The final
70

calibrated model has a reasonable correlation (R2 = 0.56) and a low SEE (0.029 in per

joint) for a large number of data points (N = 511).

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0 4,000,000 8,000,000 12,000,000 16,000,000 20,000,000

Cumulative Traffic, ESAL's

Average Transverse Joint Faulting, in

Days90=10

Days90=40

Days90=90

No dowels

Joint spacing = 15 ft

Hpcc = 9 in

PCC elastic modulus = 4 Mpsi

Consolidation at dowels = 100%

Dynamic k-value = 200 psi/in

Non-permeable base

Aggregate base (EROD = 5)

Average annual precip. = 30 in

Figure 18. Sensitivity of the final JPCP transverse joint faulting model to changes in

number of hot days.
71

CHAPTER 5: JPCP TRANSVERSE FATIGUE CRACKING MODEL

INTRODUCTION

Fatigue cracking is a key measure of concrete pavement performance for JPCP. The

deterioration of a transverse crack in JPCP often leads to roughness and additional

cracks in the slab, eventually becoming a shattered slab that requires replacement. Slab

replacement is costly and can lead to early rehabilitation of the pavement as more and

more cracking occurs. Fatigue cracking is caused by the repeated application of traffic

and environmental loading at stress levels less than ultimate. As the loadings are

repeated over time, cracking can occur in the slab. The keys to accurately predicting

the development of such cracking include:

• The accurate determination of stresses in the slab (both traffic and

environmentally induced stresses).

• The identification of the critical location in the slab where both traffic and

environmentally induced stresses are greatest.

• The accurate prediction of fatigue damage using a reliable fatigue damage

algorithm.

Previously developed transverse cracking models have typically only considered

bottom-up cracking since the critical bending stress considered is at the bottom of the

slab along the longitudinal edge. Recently, the phenomenon of top-down cracking

(consisting of transverse, longitudinal, and corner cracking) has been observed on

several in-service JPCP projects. These projects were constructed during hot sunny

days and thus had significant built-in construction curling. These construction

conditions result in a slab that is concave upward when the temperature gradient is

zero through the slab. Drying shrinkage of the slab surface also significantly

contributes to an upward curling of a slab. Slabs that are built with built-in curl plus

significant drying shrinkage of the surface have an increased probability of

experiencing top-down cracking when the load is near the joint, and a decreased

probability of bottom-up cracking at the longitudinal edge. Although procedures for

predicting top-down cracking are under development at this time, they are out of the

scope of this PRS study and will not be included in the PRS model development

procedures discussed in this chapter. The full consideration of top-down cracking

would be a very beneficial addition to PRS as it would add an appropriate AQC

representing the curling process.

This chapter describes the attempted validation of the chosen best-available

transverse fatigue cracking model (that used in PaveSpec 2.0), as well as the

development of a new, improved fatigue cracking model for use in PaveSpec 3.0.
72

CURRENT PRS JPCP TRANSVERSE SLAB CRACKING MODEL

The current PRS 2.0 transverse slab cracking model is based on a fatigue cracking

model developed by Smith et al. in 1990.

(18) Specifically, the model is based on a

fatigue-consumption approach that assumes a concrete pavement has a finite life and

can only withstand a maximum allowable number of 80-kN (18-kip) ESAL repetitions.

The transverse slab cracking model included in PaveSpec 2.0 consists of a multistep procedure that gives the expected amount of slab cracking as a function of the

accumulated fatigue damage at the critical point in the slab. The accumulated fatigue

damage is determined considering load stress, slab curling from thermal gradients, and

lateral distribution of traffic. The details of this transverse slab cracking model are

presented in this section as they were presented in a 1999 report by Hoerner et al.

(10)

Note that the model was developed using English units.

%CRACKED = 1 / [0.01 + 0.03 * (20–log(n/N))] (36)

where:

%CRACKED = Slabs cracked (transverse cracking), %.

n = Actual number of 80-kN (18-kip) ESAL applications at slab edge.

= (0.05 * TotESAL’s) for pavements without widened slabs.

= (0.001 * TotESAL’s) for pavements with widened slabs.

TotESAL’s = Cumulative total number of measured 80-kN (18-kip) ESAL

applications.

N = Allowable 80-kN (18-kip) ESAL applications.

= 10[2.13*(1/Ratio)^1.2] (37)

Ratio = The ratio of computed edge stress (σEDGE) to 28-day modulus of

rupture (MR28).

σEDGE = Total resultant stress in the longitudinal direction at the bottom of the

PCC slab edge when the wheel load is located at the slab edge, psi.

= σTRAFFIC + (R) * σCURLING (38)

σTRAFFIC = Stress at bottom of PCC slab edge when load is located at slab edge

(no thermal curling stress), psi.

= [P/18.0 * h2] * [17.35783 + (0.07801 * ES) – (0.05388 * h3/k) + (39)

7.41722 * log10(h3/k)]
73

σCURLING = Stress at bottom of PCC slab edge caused by curling of slab due to

thermal gradient (no traffic load), psi.

= [(G * ET) / (5 x 10–6)] * [(0.06712 * k) + (79.07391 * log10(k)) + (40)

(11.72690 * L) – (0.00720 * k * L) – (3.22139 * L * log10(k)) –

(0.06883 * L * ES) – (0.59539 * ES * log10(k)) – (204.39477 * h/k) –

(38.08854 * L/h) – (8.36842 * h * log10(k)) + (0.07151 * ES * h) +

(0.05691 * L * ES * log10(k)) + (0.20845 * L * h * log10(k)) +

(0.00058 * L * h * k) – (0.00201 * L * ES * log10(k))]

R = Adjustment factor for σCURLING so that it can be combined with

σTRAFFIC to give correct σEDGE.

= 0.48039 + (0.01401 * h) – (0.00427 * ES) – (0.27278 * G) – (41)

(0.00403 * L) + (0.19508 * log10(k)) + (0.45187 * G * log10(h)) –

(0.00532 * G2) + (0.01246 * G * L) – (0.00622 * G * L * log10(k)) +

(8.7872 * log10(h3/k)/h2) + (0.00104 * G * ES) – (0.11846 * G *

log10(h3/k)) + (0.07001 * log10(ES + 1.0)) – (0.01331 * G *

log10(ES + 1.0))

P = Total applied load, lb (assumed to be 9,000 lb).

hPCC = Slab thickness, in.

ES = Erodibility of support along slab edge, in (assumed to be zero).

k = Modulus of subgrade reaction, psi/in.

ET = PCC coefficient of thermal expansion (assumed to be 0.0000055).

L = Slab length (joint spacing), ft.

MR28 = 28-day modulus of rupture (third-point loading flexural strength), psi.

G = Thermal gradient through slab (estimated from table 23), °F/in.

Table 23. Average daytime thermal gradients (based on slab thickness and climatic

zone), °F/in.

(18)

Slab

Thickness, mm

Wet-Nonfreeze

Climatic Zone

Dry/Wet-Freeze

Climatic Zones

Dry-Nonfreeze

Climatic Zone

203 1.40 1.13 1.41

229 1.30 1.05 1.31

254 1.21 0.96 1.21

279 1.11 0.87 1.10

305 1.01 0.79 1.00
74

ATTEMPTED VALIDATION OF THE CURRENT PRS TRANSVERSE SLAB

CRACKING MODEL

Before any new model development or calibration techniques were pursued, the

research team attempted to validate the current PRS JPCP transverse fatigue cracking

model with an expanded data set. The validity of the current cracking model was

assessed by:

• Reviewing plots of predicted (equation 36) versus measured cracking.

• Reviewing plots of residuals versus predicted (equation 36) cracking.

• Analyzing diagnostic statistics such as R2 and SEE to determine the goodness-offit of the model when the expanded data set is used.

• Identifying any general observed weaknesses in the model.

The data used in the initial model validation process consisted of JPCP data from

the RPPR and LTPP (GPS-3) experiment databases. The final data set consisted of a

total of 815 observations for pavement test sections located in 28 States and 3 Canadian

Provinces. A summary of the validation data is presented in table 24.

Table 24. JPCP data used in the initial validation of the current transverse slab cracking

model.

Range

Variable Min. Max. Mean

Standard

Deviation

Cumulative ESAL's, millions 0.003 56.0 5.6 7.0

PCC thickness, in 7.0 15.0 9.3 1.2

Joint spacing, ft 3.0 30.0 17.0 3.9

PCC modulus of elasticity, ksi 3,050 12,200 5,750 1,540

Dynamic modulus of

subgrade reaction (k-value),

psi/in

35 1,298 258 147

PCC modulus of rupture, psi 621 1,018 739 67

Base thickness, in 0.0 23.2 4.9 2.2

Base modulus of elasticity, ksi 0 3,386 440 478

Shoulder type 337 data points with AC shoulder

331 data points with tied PCC shoulder

147 data points with widened lane

Climate 346 data points in wet-freeze region

170 data points in wet-nonfreeze region

111 data points in dry-freeze region

188 data points in dry-nonfreeze region
75

 The validation data set was used in the current transverse slab cracking model to

obtain predicted percentages of cracked slabs for each section. The actual measured

percentages of cracked slabs were obtained directly from the database. A comparison

of the measured and predicted slab cracking (using the expanded database) showed a

low R2 value of 0.18 percent and an SEE of 35.8 percent.

Figures 19 and 20 show plots of predicted versus measured slab cracking, and

residuals versus predicted slab cracking, respectively. The diagnostic statistics and

both plots indicate that the predicted transverse slab cracking is much higher than

measured cracking. The most likely explanation of this phenomenon is that the current

PRS model does not adequately address the effect of base layer properties or the effects

of PCC shrinkage, construction curling, and moisture warping. Recent research has

indicated that accounting for these effects is imperative to accurately predic the

development of transverse cracking.

(16)

Because of the limitations of the cracking model currently included in PaveSpec 2.0,

it was decided that the current model could not be simply validated. Instead, a new

transverse cracking model was developed under this study using the compiled

validation data set. The details of this model development procedure are discussed in

the remaining sections of this chapter.

EXISTING JPCP TRANSVERSE SLAB CRACKING MODELS

In preparation for the development of a new JPCP transverse cracking model, many

of the cracking models developed under previous research were reviewed. A review

of previous models not only provided guidance as to what variables should be

considered for inclusion in the new model, but also added expert knowledge into the

model development process at an early stage. During the review process, specific

attention was paid to the engineering significance of the variables.

JPCP transverse cracking has been the focus of numerous field and laboratory

investigations over the past 25 years. The FHWA-sponsored Design of Zero-Maintenance

Plain Jointed Concrete Pavement study was the first mechanistic-based study to show a

direct correlation between fatigue damage accumulation and measured transverse

cracking in the field.

(31) This approach was later expanded under the FHWA-sponsored

Rigid Pavement Performance Study (RPPR) and the NCHRP Project 1-26 study.(16,18,32,33) A

summary of some of the past JPCP cracking models, other than the 1990 model by

Smith et al. (presented above), are summarized in the following sections.

NCHRP Project 1-26 JPCP Transverse Cracking Model(32,33)

Under the NCHRP 1-26 study, the following JPCP transverse cracking model was

developed:
76

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100

Predicted Percent Cracked Slabs, %

N = 817 

R

2

 = 0.18

SEE = 35.8 percent

Figure 19. Predicted (equation 36) versus measured JPCP transverse slab cracking

(using the compiled validation data set).

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 10 20 30 40 50 60 70 80 90 100

Predicted Percent Cracked Slabs, %

Residual, Percent Cracked Slabs

Figure 20. Residual versus predicted (equation 36) transverse JPCP slab cracking

(using the compiled validation data set).
77

0.01 0.0713*( 2.5949 )

1

%CRACKED -logFD += (42)

where:

%CRACKED = Slabs cracked (transverse cracking), %.

FD = Total accumulated fatigue damage occurring at the critical fatigue

location in the slab, defined as follows:

= ∑ ∑ ∑

= = =

p

k 1

2

j 1

m

i 1 ijk

ijk

N

n

nijk = Number of edge stress repetitions of the i-th magnitude over day or

night for the k-th month.

Nijk = Number of edge stress repetitions of i-th magnitude over day or night

for the k-th month.

i = Counter for the magnitude of the axle load.

j = Counter for day or night.

k = Counter for months over the design period.

m = Total number of axle load groups.

p = Total number of months in the design period.

The allowable number of 80-kN (18-kip) ESAL applications (N) is defined from the

following equations:

4.394

1

5.367

28

0.0032

log(1 )

ó

MR

N 10





















































− −

−

=

EDGE P

(43)

where:

σ EDGE = Total resultant stress in the longitudinal direction at the bottom of the

PCC slab edge when the wheel load is located at the slab edge, psi.

MR28 = PCC modulus of rupture at 28-days, psi.

P = Probability level.

The equation for total resultant stress in the longitudinal direction is defined as

follows:

ó EDGE = ó TRAFFIC + R *ó CURLING (44)

where:

σ TRAFFIC = Edge stress due to traffic load, psi.
78

σCURLING = Curling stress due to temperature gradient, psi.

R = Curling stress reduction factor.

The traffic load edge stresses are obtained using Westergaard's equation for an

infinite slab under a circular load with a free edge loading condition. The computed

Westergaard free edge stress (σFE) is then corrected for slab size, presence of stabilized

base, and edge support. (Note: the correction factors were applied in an attempt to

reproduce the results obtained from the ILLI-SLAB finite element program.) The final

equation used to compute the corrected traffic load edge stress is the following:

TRAFFIC LTE SLAB BASE FE σ = f f f σ (45)

where fLTE, fSLAB, and fBASE are edge support, slab size, and base correction factors, and

the equation for Westergaard’s free edge stress is defined as:

















+ + μ

−μ

+ − μ +

















π + μ

+ μ

σ =

l

e

PCC

PCC

4 PCC

e

3

PCC PCC

2

PCC PCC

PCC

FE

a

1.18*(1 2 ) *

2

1

184 0.75

100ka

E h

Ln

(3 )h

2

P

3(1 )

(46)

where:

P = Total axle load, lb.

hPCC = PCC slab thickness, in.

EPCC = PCC modulus of elasticity, psi.

:PCC = Poisson’s ratio.

k = Coefficient of subgrade reaction, psi/in.

aeq = Equivalent radius, in. (An equivalent radius [aeq] of a multiple-wheel

assembly is used as the load radius of the Westergaard equation,

resulting in the same stress as the one obtained from finite element

method with the real wheel configuration.)

l = Radius of relative stiffness, in.

= 4

2

PCC

3

PCC PCC

12(1 )k

E h

− μ

(47)

The stress caused by the temperature differential only is defined using the

following Westergaard’s expression:

2

CEPCCET T

CURLING

Δ

σ = (48)

where:
79

σCURLING = Curling stress due to temperature differential in slab, psi.

C = Coefficient that depends on the ratio of the slab length to the radius of

relative stiffness.

EPCC = PCC modulus of elasticity, psi.

ET = PCC coefficient of thermal expansion.

ΔT = Temperature differential throughout the slab thickness, °F (defined as

the difference between the temperature at the top and that at the

bottom of the slab). It was recommended to predict distribution of

temperature differentials using a calibrated model like the Integrated

Climate and Materials (ICM) model.

(34)

FHWA RPPR 1997 JPCP Transverse Cracking Model(16)

In 1997, Yu et al. developed another JPCP transverse cracking model under a second

RPPR contract.

(16) Although this model uses the same approach as the RPPR 1990 and

the NCHRP Project 1-26 models, it included a number of improvements, such as:(18,32,33)

• The model was calibrated with a more widespread database.

• The effect of construction curling and differential shrinkage was incorporated.

• A more rigorous procedure for traffic wander was introduced.

• The critical stress calculation procedure was corrected.

The RPPR 1997 model used the following relationship between cumulative fatigue

damage (FD) and percentage of cracked slabs (%CRACKED):

1+ 4.15* FD

100

%CRACKED = -1.52 (49)

Statistics:

N = 465.

R2 = 0.91.

SEE = 7.1.

Under this study, accumulated fatigue damage is defined as follows:

∑

Δ

σ Δ

=

i

i

EDGE i

N( T )

pc( ) n( T )

FD (50)

where:

FD = Fatigue damage.

n(ΔT) = Actual number of 80-kN (18-kip) ESAL applications acting together

with the temperature gradient ΔT.
80

σEDGE = Total resultant stress in the longitudinal direction at the bottom of the

PCC slab edge when the wheel load is located at the slab edge, psi.

pc = Pass-to-coverage ratio (based on σedge).

N = Allowable number of 80-kN (18-kip) ESAL applications.

= 10

1.2

MR 2.13*

















EDGE

s

(51)

MR = PCC modulus of rupture

The total resultant stress in the longitudinal direction is defined using the same

equation as the NCHRP Project 1-26 model (equation 44). In the NCHRP Project 1-26

procedure, the stress due to traffic loading is determined by applying various

adjustment factors to the free edge stress calculated using Westergaard's equation

(equation 45).

(32,33) However, in the RPPR 1997, model the adjustment factor for the slab

size effect was not used because the ILLI-SLAB analysis performed to validate the

stress calculation procedure showed that the use of this factor could result in

overcompensation for the slab size effect. The analysis showed that the response of a

multiple slab system, with even a moderate load transfer efficiency at the transverse

joints, closely approximates that of an infinitely long slab.

One of the main differences between the RPPR 1997 and NCHRP Project 1-26

models is the method used to calculate curling stress. Although the same

Westergaard’s equation is applied (equation 48), the actual ΔT is reduced by a

determined shift factor (TS), as follows:

2

CE ET ( T T )

PCC S

CURLING

Δ −

σ = (52)

where:

σCURLING = Curling stress due to temperature differential in slab, psi.

C = Coefficient that depends on the ratio of the slab length to the radius of

relative stiffness.

EPCC = PCC modulus of elasticity, psi.

ET = PCC coefficient of thermal expansion.

ΔT = Temperature differential throughout the slab thickness, °F (defined as

the difference between the temperature at the top and that at the

bottom of the slab).

TS = Temperature shift factor, °F (defined as the effective temperature

gradient that would produce the total built-in construction curling in a

pavement).

The total built-in construction curling present in a pavement is caused by a number

of factors, including the following:
81

• Moisture gradient—The top of the slab is usually drier than the bottom

throughout most of the year; therefore, moisture gradients generally tend to

cause lifting of the slab corners. The moisture gradients could be treated as

equivalent negative temperature gradients, but insufficient information is

available to adequately quantify this effect.

• Differential drying shrinkage—Field moisture measurements have shown that

surface shrinkage of PCC occurs only to a depth of about 51 mm (2 in).

(35) The

net effect of this phenomenon is an equivalent temperature gradient

(temperature difference between top and bottom) of about –1.4 °C (–2.5 °F ) for a

250-mm- (10-in-) thick slab.

• Built-in temperature gradient (residual temperature gradient)—At the time when an asconstructed slab hardens, the temperature difference between the top and

bottom of the slab (temperature differential) will greatly influence the amount of

curling that develops in the slab. When a positive temperature differential

(temperature at the top > temperature at bottom) is present at the time of

hardening, the hardened slab will permanently experience what appears to be a

negative built-in temperature gradient. This built-in negative gradient is

explained by realizing that the slab was flat when it hardened with a positive

temperature differential. Therefore, when this temperature differential becomes

zero (i.e., temperature at top = temperature at bottom) the slab will be curled

upward (due to the combination of contraction of the upper portion and

expansion of the lower portion of the slab). A slab hardened under such a

condition will only become flat when it is subjected to a positive temperature

gradient of the same magnitude that was present at the time of hardening.

Daytime construction with sunshine generally causes positive temperature

gradients through the PCC at hardening, resulting in built-in negative

temperature gradients in the slabs. Since pavement slabs are exposed to daily

cycling of temperature gradients (from large positive gradient at midday to

negative gradients at night), any relaxing of the residual gradients through creep

effects are not likely. Studies have shown that the magnitude of this residual

temperature gradient in some highway pavements is –0.055 °C/mm (–2.5 °F/in)

or more, which translates to a –14 °C (–25 °F) gradient in a 250-mm- (10-in-) thick

slab.

(36)

Moisture gradients, differential drying shrinkage, and built-in temperature

gradients all cause upward curling of the pavement slabs, and the effects of the last two

are permanent. According to these factors, the magnitude of negative residual

temperature gradient could be very significant in many pavement sections. The

combined net effects of all factors that cause curling or warping of pavement slabs can

be expressed in terms of an effective temperature gradient. The magnitude of curling

stress depends on the net result of all factors at work. Hence, the initial upward curling
82

has the effect of shifting the actual temperature gradients in the negative direction by

the amount corresponding to the degree of initial curling. The initial upward curling,

therefore, reduces the combined stress at the longitudinal edge but increases the critical

tensile stresses at the surface under corner loading conditions.

In the RPPR 1997 model calibration, the cumulative effects of curling (or warping)

caused by all factors other than temperature gradients were addressed by shifting the

temperature gradients determined for each pavement section individually. The actual

magnitude of the effective residual curling is unknown; however, the consistency

within the data set was used as the guide to make relative adjustments. Random joint

sections typically included a wide range of slab sizes (e.g., 3.7 to 5.8 m [12 to 19 ft]).

Since the edge stress is very sensitive to temperature gradient and slab length, any

changes in the temperature gradient had a significant effect on fatigue damage. Since

the temperature gradient was required to be assigned consistently to slabs of different

sizes within a given pavement section, the calculated fatigue damage had to be

reasonable for all slab sizes in order for the assignment to be made.

Overview of Existing JPCP Transverse Cracking Models

The review of past JPCP transverse fatigue cracking model development efforts

indicates that significant progress has been achieved in the past 20 years. Of those

models reviewed, that developed by Yu et al. under the 1997 FHWA RPPR study was

selected as the best-available JPCP transverse cracking model for the following

reasons:

(16)

• The model development utilized experience gained in the development of

models developed under previous research (i.e., the Zero-Maintenance, NCHRP

Project 1-26, and RPPR 1990 models).(18,31,32,33)

• The model has the most advanced stress calculation procedure of all reviewed

JPCP transverse cracking models.

• The model is the only existing JPCP transverse cracking model that accounts for

such factors as PCC shrinkage, moisture warping, and construction curling.

• The model was calibrated using a very comprehensive database.

Even though the RPPR 1997 model was selected as the best available, the following

drawbacks make it difficult for immediate incorporation into the current PRS

methodology:

• The model requires that the ICM program be used to determine the distribution

of hourly temperature gradients (through concrete slabs for an average year) for

each pavement section. Running the ICM program may be time-consuming, as
83

the program requires the input of a substantial number of climatic and material

parameters.

• The procedure for estimation of construction curling differential requires

simplification for use in the current PRS methodology.

It should be noted that an attempt was made in the RPPR 1997 study to develop a

more objective way to determine appropriate temperature shift factors. This attempt

resulted in the suggestion to use the following mean shift factors specific to climatic

regions: (16)

• Dry-Freeze: 6.1 °C (11.0 °F)

• Dry-Nonfreeze: 6.4 °C (11.5 °F)

• Wet-Freeze: 4.4 °C (8 °F)

• Wet-Nonfreeze: 4.7 °C (8.5 °F)

However, the use of these average shift factors (instead of individual section shift

factors) resulted in a much worse predictive ability, even for the same RPPR 1997

database.

Figure 21 illustrates that the RPPR 1997 model predicts very well (R2 = 0.93) when

individual section temperature shift factors and individual temperature gradient

distributions (i.e., temperature shift factors and gradient distributions determined

specifically for each section independently) were applied. Figure 22 shows that the

accuracy of the model decreases substantially (R2 = 0.52) when individual section

temperature shift factors are replaced with the suggested overall climatic zone means

(note that for this case, the section specific temperature gradient distributions are still

used). Finally, when climatic zone mean values were used for both temperature shift

factors and gradient distributions, the model's predictive ability decreased even farther

(R2 = 0.44).

IMPROVEMENT OF THE RPPR 1997 JPCP TRANSVERSE CRACKING MODEL

Based on the results of the validation process, and the review of previously

developed models, the transverse slab cracking model validation/improvement effort

focused on improving the RPPR 1997 model so that it would be more applicable for

use within the current PRS methodology. The specific procedure used in the

improvement of the RPPR 1997 model includes:

• Preparation of the model improvement data set.

• Selection of appropriate statistical tools for regression and optimization.

• Recalibration of the final JPCP transverse cracking model.

These tasks are described in greater detail in the following sections.
84

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100

Model

Field

DF

DN

WF

WN

R

2

 = 0.93

Figure 21. Actual (field) versus predicted (RPPR 97 model) slab cracking (using the

section-by-section temperature shift factors and gradient distributions).

(16)

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100

Model

Field

DF

DN

WF

WN

R

2

 = 0.52

Figure 22. Actual (field) versus predicted (RPPR 97 model) slab cracking (regional

temperature shift factors with section-by-section temperature gradient distributions).

(16)
85

Data Preparation

The same data used in the validation of the current PaveSpec 2.0 model were used

in the recalibration of the RPPR 1997 model. As discussed above, data from the RPPR

database were combined with JPCP data from the LTPP study (GPS-3 data only) to

develop a comprehensive model validation/development data set. This final data set

consisted of a total of 815 observations for pavement test sections in 28 States and 3

Canadian Provinces. A detailed summary of this data was presented previously in

table 24.

Statistical Tools for Regression and Optimization

The SAS nonlinear procedure (NLIN) was selected as the appropriate regression

tool to be used in final model calibration because the procedure is versatile and allows

for constraining model coefficients where required.

(30) Other SAS procedures, such as

STEPWISE, REG, RSQUARE, and RSREG, were used in preliminary model

development for determining and selecting the most suitable variables for

incorporation into the final model. The SAS NLIN Marquardt algorithm was used in

the optimization of the transverse cracking model.

Final JPCP Transverse Cracking Model

The first step in the final calibration of the RPPR 1997 cracking model involved

incorporating a simplified method for determining frequency distributions of

temperature differentials between the PCC top and bottom surfaces. Specifically, the

following approach was used:

1. The ICM model was used to generate the frequencies of temperature

differentials between the PCC top and bottom surfaces for typical conditions

associated with the four climatic regions (wet-freeze, wet-nonfreeze, dry-freeze,

and dry-nonfreeze).

(34) Within each climatic region, frequency distributions were

generated for different PCC slab thicknesses (varied from 127 to 381 mm [5 to 15

in] at 6-mm [0.25-in] increments). Frequencies for other slab thicknesses were

determined by linearly interpolating between these generated frequency

distributions.

2. It was proposed to estimate construction temperature gradients based on the

PCC slab thickness and the climatic region using the following equation:

+ ψ

−

= ξ s 3

h

(h 2)

T (53)

where:
86

h = Slab thickness, in.

ξ,Ψ = Climatic region specific parameters determined during the model

calibration.

The same S-shaped functional form used in the RPPR 1997 model for the

relationship between the cumulative damage and the percentage of cracked slabs was

used in the recalibration procedures. Specifically, this model form is as follows:

b

1 a *FD

100 %CRACKED −

+

= (54)

where %CRACKED is the percentage of cracked slabs, and a and b are regression

coefficients that will be determined during the calibration.

A nonlinear regression was performed using performance data for 815 observations.

The regression resulted in the temperature shift factor coefficients presented in table 25.

Table 25. Temperature shift factor coefficients by climatic zone.

Climatic Zone > R

Wet-Freeze 327.27 5.73

Wet-Nonfreeze 218.18 6.26

Dry-Freeze 436.36 6.78

Dry-Nonfreeze 436.36 7.37

Using these temperature shift coefficients in the regression analysis, the following

equation was developed for the relationship between fatigue damage, FD, and

percentage of cracked slabs, %CRACKED:

1.3

1 1.16 FD

100 %CRACKED −

+

= (55)

The diagnostic statistics for this calibrated slab cracking model are as follows:

N = 815.

R2 = 0.56.

SEE = 9.3 percent of slabs.

Plots of the predicted versus measured transverse cracking, and residuals versus

predicted transverse cracking, are shown in figures 23 and 24, respectively. Figure 23

shows that crack prediction is low for higher amounts of measured cracking. However,

it is important to note that this trend should have little effect when used within the PRS

methodology since the actual percentage of cracked slabs on an in-service highway

pavement is rarely allowed to reach such high levels. The diagnostic statistics and both
87

plots verify that the model is effective for predicting transverse cracking. The R2 of 0.56

and SEE of 9.3 percent are very reasonable given the large number of RPPR and LTPP

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100 

Measured Percent Slabs Cracked

Predicted Percent Slabs Cracked

N = 815

R

2

 = 0.56

SEE = 9.3 percent

Figure 23. Predicted (equation 55) versus measured JPCP transverse cracking.

-100.0

-80.0

-60.0

-40.0

-20.0

0.0

20.0

40.0

60.0

80.0

100.0

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0

Predicted Percent Slabs Cracked

Residual Percent Slabs Cracked

Figure 24. Residual versus predicted (equation 55) JPCP transverse cracking.
88

field data observations (N=815) and the likelihood that some transverse cracking was

caused by other factors (such as late joint sawing).

Procedure Used to Predict Fatigue Damage

The detailed step-by-step procedure used to compute fatigue damage is presented

in this section. This procedure is very similar to that used in the original RPPR 1997

model.

Step 1—Find the Effective Slab Thickness

If the pavement has a base layer, the structural contribution of the base is accounted

for by replacing the original two-layered slab (PCC and base layer) with an equivalent

slab that has the same deflection profile as the original two-layered slab. The

maximum stresses in the PCC layer and the equivalent slab are related to each other.

Depending on the interface condition between the slab and the PCC layer, the thickness

of the equivalent slab, he, is defined using the following equations:

If an unbonded interface is chosen:

3

3

base

PCC

3 base

e PCC h

E

E

h = h + (56)

If a bonded interface is chosen:

3

base

2

base

PCC

PCC

base

2

PCC

PCC

3

base

PCC

3 base

e PCC h

2

h

h x

E

E

2

h

h 12 h x

E

E

h h

































+ − +

















= + + − (57)

where x is a distance from the top surface of the PCC layer to the neutral axis:

base

PCC

base

PCC

base

base PCC

PCC

base

2

PCC

h

E

E

h

)

2

h

h (h

E

E

2

h

x

+

+ +

= (58)

where:

hPCC = PCC slab thickness, in.

hbase = Base thickness, in.

EPCC = Elastic modulus of PCC, psi.

Ebase = Elastic modulus of base material, psi.
89

Step 2—Calculate Load Stresses

To calculate maximum bending stresses in the effective slab, load and curling

stresses should be determined. Calculation of load stresses involves the following

steps:

Step 2.1. Calculate the radius of relative stiffness (l) (currently used for the faulting

model):

4

2

PCC

3

PCC e

12(1 )k

E h

− μ

l = (59)

where:

EPCC = Elastic modulus of PCC, psi.

he = Effective thickness computed in step 1.

μPCC = Poisson's ratio for PCC (assumed to be 0.15).

k = Modulus of subgrade reaction (k-value), psi/in.

Step 2.2. Calculate the effective wheel radius (aeff) using the following equation:

































































 +











+

























 −











 +























−













 −











 +











+

=

l

a

a

s

0.001

l

s

0.034664

l

a

a

s

0.301805

a

s

0.000436

a

s

l

a

0.045229

a

s

0.017881

l

a

0.103946

a

s

0.909 0.339485

a a *

2 3

2 3 3

2

eff (60)

where:

aeff = Computed effective wheel radius, in.

a =

4* *95

18,000

p

= 3.883019 in.

s = Assumed tire spacing of 12 in.

l = Radius of relative stiffness computed in step 2.1.

Step 2.3. Compute the nondimensional wheel radius, aR.

l

l

eff a

a = (61)

Step 2.4. Calculate free edge stress, σfe.
90





















+ + μ

− μ

+

μ

+ −

















π + μ

+ μ

σ =

l 1.18*(1 2 )*a

2

1

3

4

1.84

100ka

E h

Ln

(3 )h

2

P

3(1 )

PCC

PCC PCC

4

e

3

PCC e

2

PCC e

PCC

fe (62)

Step 2.5. Calculate edge support reduction factor, fLTE.

This calculation is dependent on the type of edge support present. The

following apply:

If No Edge Support, then:

f LTE = 1 (63)

If Tied PCC Shoulder, then:

+ σ

=

1 LTE

1

f LTE (64)

where:

LTEσ = A chosen stress load transfer efficiency (value between 0.05 and

0.30).

If Widened Lane, then:

3

2

LTE

D

a

0.053891

D

a

0.24565

D

a

0.386201

D

0.013211 f 0.454147

















+

















= + + −

l

l

l

l

l

l

l

(65)

where:

al = Nondimensional wheel radius (computed in step 2.3).

Dl = 42/l.

l = Radius of relative stiffness computed in step 2.1.

Step 2.6. Compute the stress due to load, σLOAD.

LOAD LTE fe σ = f σ (66)

where:

σLOAD = Computed stress due to load, psi.

fLTE = Edge support reduction factor (computed in step 2.5).

σfe = Free edge stress (computed in step 2.4).
91

Step 3—Compute Array of Temperature Stresses

Step 3.1. Compute the curling stress coefficient, C:

(tan tanh )

sin 2 2sinh *cosh

2cos *cosh 1 l l

l l l

l l

+

+

C = − (67)

where:

8

L

l

λ = (68)

L = Joint spacing expressed in inches.

l = Radius of relative stiffness computed in step 2.1.

Step 3.2. Compute the temperature shift factor, TS.

+ ψ

−

= ξ

3

e

e

s

h

(h 2)

T (69)

where:

he = Effective thickness computed in step 1.

>, R = Temperature shift factor coefficients presented in table 25.

Step 3.3. Compute an array of temperature stresses.

For each temperature gradient (ΔT) throughout the slab thickness (from

ΔT = –8 °F to 34 °F in increments of 2 °F), calculate corresponding curling stress due

to temperature, (FTEMPERATURE)i.

2

CE ( T T )

( )

PCC PCC S i

TEMPERATURE i

α Δ −

σ = (70)

where:

(FTEMPERATURE)I = Computed curling stress (due to temperature) associated with

the ith entry in the array of ΔT – TS values.

i = Array index number equal to 1 to 22; the original ΔT array has

22 values (–8 °F to 34 °F in increments of 2 °F).

ΔT – TS = Temperature difference.

ΔT = Temperature gradient through the slab.

TS = Temperature shift factor computed in step 3.2, °F.

C = Curling stress coefficient computed in step 3.1.

EPCC = Elastic modulus of PCC, psi.
92

αPCC = PCC coefficient of thermal expansion, 1/oF (assumed to be 5.5

E-06).

Step 4—Compute Array of Combined Temperature and Load Stresses

Step 4.1. Compute a curling stress reduction factor (R) associated with each value

in the temperature difference (ΔT – TS) array (for i = 1 to 22 values).

( )

( )

( )

( )

2

PCC S i

3

3 5

PCC S i

10

PCC S i

2

2

PCC PCC S i

3

2

PCC PCC S i

8

2

PCC PCC S i

PCC PCC S i

6

PCC S i

i S i

( T T )

L

816396

L

3.4351*10 ( T T ) 8.697*10

( T T )

L

17.487 L1.84 *10 E k ( T T )

)

L

1.051*10 E k ( T T ) (

0.0181E k ( T T )

1.17*10 E k ( T T )

L

387.317 ( T T )

L

R 1.062 1575.68 ( T T ) 0.0000876k 0.01068

 α Δ −











−













+ α Δ − +

 α Δ −











+ α Δ − −

− α Δ −

− α Δ −

+ α Δ − + α Δ −

= − α Δ − − −

−

−

−

−

l

l

l l

l

l

l

(71)

where:

Ri = Computed curling stress reduction factor associated with the ith entry

in the array of ΔT – TS values.

i = Array index number equal to 1 to 22; the original ΔT array has 22

values (–8 °F to 34 °F in increments of 2 °F).

ΔT – TS = Each value in the temperature difference array (determined in step 3).

ΔT = Temperature gradient through the slab. As stated above, there is an

array of these values that goes from –8 °F to 34 °F in increments of 2 °F.

TS = Temperature shift factor computed in step 3.2, oF.

k = Modulus of subgrade reaction (k-value), psi/in.

L = Joint spacing expressed in inches.

l = Radius of relative stiffness computed in step 2.1.

αPCC = PCC coefficient of thermal expansion, 1/oF (assumed to be 5.5 E-06).

EPCC = Elastic modulus of PCC, psi.

If R < 0.42 then R = 0.42 should be used.

Step 4.2. Calculate an array of combined stresses (not adjusted for presence of a

base layer).
93

Using the arrays of temperature stresses (σTEMPERATURE computed in step 3.3) and

curling stress reduction factors (R determined in step 4.1), compute an array of

associated combined stresses using the following equation (note: these combined

stresses are not adjusted for the presence of the base layer):

COMB NOADJUST i LOAD i TEMPERATURE i

(σ ) = σ + R (σ )

−

(72)

where:

(FCOMB-NOADJUST)i = Computed combined load and temperature stresses (not

adjusted for the presence of the base layer) associated with the

ith entry in the array of ΔT – TS values.

σLOAD = Stress due to load, psi (computed in step 2.6).

(FTEMPERATURE)i = Curling stress (due to temperature) associated with the ith entry

in the array of ΔT – TS values (computed in step 3.3).

Ri = Computed curling stress reduction factor associated with the ith

entry in the array of ΔT – TS values.

i = Array index number equal to 1 to 22; the original ΔT array has

22 values (–8 °F to 34 °F in increments of 2 °F).

ΔT – TS = Each value in the temperature difference array (determined in

step 3).

ΔT = Temperature gradient through the slab. As stated above, there

is an array of these values that goes from –8 °F to 34 °F in

increments of 2 °F.

TS = Temperature shift factor computed in step 3.2, oF.

Step 4.3. Adjust the combined stresses (computed in step 5.2) for the presence of a

base layer). The maximum PCC bending stresses should be calculated using the

following relationship between the PCC and effective slab stresses:(37)

For the unbonded case,

COMB NOADJUST i

e

pcc

COMB i

( )

h

h

( ) σ = σ −(73)

For the bonded case,

COMB NOADJUST i

e

pcc

COMB i

( )

h

h x

( ) σ −

−

σ = (74)

where:

(FCOMB)i = Combined load and temperature stresses (adjusted for the

presence of the base layer) associated with the ith entry in the

array of ΔT – TS values.
94

(FCOMB-NOADJUST)i = Combined load and temperature stresses (not adjusted for the

presence of the base layer) associated with the ith entry in the

array of ΔT – TS values.

i = Array index number equal to 1 to 22; the original ΔT array has

22 values (–8 °F to 34 °F in increments of 2 °F).

ΔT – TS = Each value in the temperature difference array (determined in

step 3).

ΔT = Temperature gradient through the slab. As stated above, there

is an array of these values that goes from –8 °F to 34 °F in

increments of 2 °F.

TS = Temperature shift factor computed in step 3.2, oF.

x = Distance from the top surface of the PCC layer to the neutral

axis (computed in step 1).

hPCC = PCC slab thickness, in.

he = Effective slab thickness, in (computed in step 1).

Step 5—Compute an Array of Allowable Load Repetitions

For i = 1 to 22, the following equation is used to get an array of allowable load

repetitions (expressed as Log10(N)):

1.2

28

( )

( ) 2.13

−

















=

MR

Log N

COMB i

i

s

(75)

where:

(Log N)i = Allowable load repetitions (expressed as a base 10 log value)

associated with the ith entry in the array of ΔT – TS values.

(FCOMB)i = Combined load and temperature stresses (adjusted for the

presence of the base layer) associated with the ith entry in the

array of ΔT – TS values (computed in step 4.3).

i = Array index number equal to 1 to 22; the original ΔT array has

22 values (–8 °F to 34 °F in increments of 2 °F).

MR28 = PCC modulus of rupture at 28 days, psi.

Step 6—Compute Array of Pass-to-Coverage Ratios

For i = 1 to 22, the following equations are used to get an array of pass-to-coverage

(pc) ratios. The particular equation used to compute pc ratios is dependent on a

computed stress ratio, SR.

Step 6.1. Compute the stress ratio, SR.

SR = MR28/(FCOMB)I (76)
95

where:

SR = Stress ratio.

MR28 = PCC modulus of rupture, psi.

(FCOMB)i = Combined load and temperature stresses (adjusted for the presence of

the base layer) associated with the ith entry in the array of ΔT – TS

values (computed in step 4.3).

Step 6.2. Compute the pass-to-coverage ratios using one of the following equations:

Case 1: If SRi < 0, then:

pci = 10,000. (77)

Case 2: If SRi > 1, then:

(1 ) 2.6

( )

491.55

( )

1259.9

( )

416.3 1148.6

3

28

2

28 28

− +













































−

















− +

= WL

MR

MR MR

pc

COMB i

COMB i COMB i

i

s

s s

(78)

 Case 3: If 0 <= SRi <= 1, then:

(1 ) 2.6

( )

12.04

( )

77.94

( )

140.2 172.3

3

28

2

28 28

− +













































−

















− +

= WL

MR

MR MR

pc

COMB i

COMB i COMB i

i

s

s s

(79)

where:

pci = Computed pc ratio associated with the ith entry in the array of ΔT – TS

values.

(FCOMB)i = Combined load and temperature stresses (adjusted for the presence of

the base layer) associated with the ith entry in the array of ΔT – TS

values (computed in step 4.3).

MR28 = PCC modulus of rupture at 28 days, psi.

WL = Presence of widened lane. If widened lanes are present, WL = 1;

otherwise WL = 0.

i = Array index number equal to 1 to 22; the original ΔT array has 22

values (–8 °F to 34 °F in increments of 2 °F).
96

Step 7—Select the Appropriate Frequency Distribution

Step 7.1. Round the effective thickness (he, computed in step 1) to the nearest 0.25

in.

Step 7.2. Based on climatic region and rounded effective thickness, select the

appropriate frequency distribution of temperature gradients from tables 26 through

29. Note, the selected array contains i = 1 to 22 entries that are associated with the

other previously computed arrays.

Step 8—Compute Array of Actual Traffic Coverage Values

The traffic coverage of 80-kN (18-kip) ESAL load application is determined from the

following equation:

i

i

i

pc

f *CESAL

n = (80)

where:

ni = Actual traffic value associated with the ith entry in the array of ΔT – TS

values.

pci = Computed pc ratio associated with the ith entry in the array of ΔT – TS

values.

CESAL = Cumulative ESAL's.

i = Array index number equal to 1 to 22; the original ΔT array has 22

values (–8 °F to 34 °F in increments of 2 °F).

Step 9—Compute Cumulative Damage

Finally, cumulative damage is determined using the following equation:

= ∑

i=1to22 i

i

N

n

FD (81)

where:

FD = Cumulative fatigue damage.

ni = Actual traffic value associated with the ith entry in the array of ΔT – TS

values (computed in step 9).

Ni = Allowable load repetitions (computed as 10^[Log N]i where [Log N]i

was computed in step 6) associated with the ith entry in the array of

ΔT – TS values.

This computed fatigue damage is then used in the final model (equation 55) for

predicting slab cracking.
97

Table 26. Frequency distributions of temperature gradients for the wet-freeze region (based on rounded effective thickness).

Rounded Effective Thickness, in

DT 5.00 5.25 5.50 5.75 6.00 6.25 6.50 6.75 7.00 7.25 7.50 7.75 8.00 8.25 8.50 8.75 9.00 9.25 9.50 9.75

-8 0.211 0.189 0.168 0.146 0.125 0.123 0.121 0.120 0.118 0.117 0.115 0.114 0.112 0.109 0.105 0.101 0.098 0.096 0.094 0.093

-6 0.159 0.146 0.132 0.118 0.104 0.103 0.101 0.100 0.098 0.097 0.095 0.094 0.092 0.094 0.095 0.096 0.098 0.095 0.093 0.091

-4 0.103 0.104 0.105 0.107 0.108 0.106 0.103 0.100 0.098 0.095 0.093 0.090 0.087 0.083 0.079 0.075 0.071 0.073 0.076 0.078

-2 0.085 0.079 0.073 0.067 0.061 0.061 0.061 0.062 0.062 0.062 0.062 0.062 0.062 0.063 0.064 0.065 0.067 0.067 0.067 0.068

0 0.064 0.064 0.065 0.066 0.066 0.065 0.064 0.063 0.063 0.062 0.061 0.060 0.059 0.058 0.058 0.058 0.057 0.056 0.054 0.052

2 0.053 0.050 0.047 0.044 0.041 0.040 0.040 0.039 0.038 0.037 0.037 0.036 0.035 0.035 0.035 0.035 0.035 0.036 0.036 0.036

4 0.046 0.045 0.045 0.044 0.043 0.043 0.043 0.043 0.043 0.043 0.043 0.043 0.043 0.042 0.040 0.039 0.037 0.038 0.039 0.040

6 0.064 0.060 0.057 0.053 0.050 0.048 0.046 0.045 0.043 0.041 0.040 0.038 0.036 0.037 0.038 0.038 0.039 0.037 0.034 0.032

8 0.041 0.039 0.037 0.035 0.033 0.033 0.033 0.033 0.033 0.033 0.033 0.034 0.034 0.033 0.033 0.032 0.032 0.033 0.035 0.036

10 0.056 0.053 0.049 0.045 0.041 0.041 0.040 0.039 0.039 0.038 0.038 0.037 0.036 0.036 0.035 0.035 0.034 0.033 0.032 0.031

12 0.079 0.068 0.058 0.047 0.036 0.035 0.034 0.033 0.032 0.031 0.029 0.028 0.027 0.028 0.028 0.028 0.029 0.028 0.028 0.028

14 0.010 0.021 0.032 0.043 0.054 0.052 0.051 0.049 0.048 0.046 0.045 0.043 0.042 0.039 0.037 0.035 0.033 0.033 0.033 0.034

16 0.000 0.013 0.026 0.038 0.051 0.049 0.047 0.045 0.042 0.040 0.038 0.036 0.033 0.034 0.034 0.034 0.035 0.032 0.030 0.028

18 0.000 0.001 0.002 0.002 0.003 0.008 0.013 0.018 0.023 0.028 0.033 0.038 0.043 0.042 0.041 0.040 0.039 0.039 0.039 0.039

20 0.000 0.000 0.000 0.000 0.000 0.003 0.006 0.009 0.012 0.016 0.019 0.022 0.025 0.028 0.031 0.035 0.038 0.038 0.038 0.037

22 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.003 0.004 0.005 0.009 0.013 0.017

24 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

26 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

28 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

30 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

32 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

34 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
98

Table 26. Frequency distributions of temperature gradients for the wet-freeze region (based on rounded effective thickness) (continued).

Rounded Effective Thickness, in D

T 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75 12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00

-8 0.091 0.090 0.088 0.086 0.084 0.083 0.081 0.079 0.077 0.077 0.076 0.075 0.075 0.074 0.073 0.072 0.072 0.072 0.072 0.073 0.073

-6 0.088 0.089 0.090 0.091 0.092 0.093 0.094 0.095 0.096 0.096 0.096 0.097 0.097 0.098 0.098 0.098 0.099 0.099 0.099 0.099 0.100

-4 0.081 0.081 0.081 0.081 0.081 0.081 0.081 0.081 0.081 0.081 0.081 0.080 0.080 0.080 0.079 0.079 0.079 0.079 0.079 0.079 0.079

-2 0.068 0.068 0.068 0.068 0.068 0.067 0.067 0.067 0.067 0.068 0.069 0.069 0.070 0.071 0.072 0.073 0.074 0.073 0.073 0.073 0.073

0 0.051 0.050 0.050 0.050 0.049 0.049 0.049 0.048 0.048 0.048 0.048 0.048 0.048 0.047 0.047 0.047 0.047 0.047 0.047 0.048 0.048

2 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.038 0.038 0.038 0.038 0.038 0.038 0.039 0.039 0.039 0.039 0.040

4 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.039 0.038 0.038 0.037 0.036 0.036 0.035 0.034 0.034 0.033 0.033 0.033

6 0.030 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.030 0.030 0.031 0.031 0.032 0.032 0.033 0.034 0.035 0.035 0.036

8 0.038 0.037 0.036 0.036 0.035 0.034 0.034 0.033 0.033 0.032 0.032 0.031 0.031 0.031 0.030 0.030 0.030 0.030 0.029 0.029 0.029

10 0.029 0.030 0.030 0.031 0.031 0.032 0.032 0.033 0.033 0.032 0.032 0.031 0.030 0.029 0.028 0.028 0.027 0.026 0.025 0.024 0.022

12 0.027 0.027 0.026 0.025 0.024 0.024 0.023 0.022 0.022 0.022 0.023 0.024 0.024 0.025 0.026 0.027 0.027 0.028 0.028 0.029 0.029

14 0.034 0.034 0.034 0.034 0.033 0.033 0.033 0.033 0.033 0.032 0.032 0.031 0.030 0.030 0.029 0.028 0.028 0.027 0.027 0.027 0.027

16 0.026 0.026 0.026 0.025 0.025 0.025 0.024 0.024 0.024 0.024 0.025 0.026 0.026 0.027 0.028 0.028 0.029 0.028 0.027 0.026 0.026

18 0.039 0.038 0.037 0.037 0.036 0.036 0.035 0.035 0.034 0.033 0.032 0.031 0.030 0.029 0.028 0.027 0.027 0.028 0.029 0.030 0.031

20 0.037 0.037 0.036 0.036 0.035 0.035 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.035 0.034 0.033 0.032 0.031

22 0.021 0.022 0.024 0.025 0.026 0.027 0.029 0.030 0.031 0.031 0.030 0.030 0.029 0.028 0.028 0.027 0.027 0.027 0.027 0.027 0.027

24 0.000 0.001 0.003 0.004 0.005 0.007 0.008 0.009 0.010 0.012 0.014 0.015 0.017 0.018 0.020 0.021 0.023 0.023 0.023 0.024 0.024

26 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.001 0.001 0.001 0.001

28 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

30 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

32 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

34 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
99

Table 27. Frequency distributions of temperature gradients for the wet-nonfreeze region (based on rounded effective thickness).

Rounded Effective Thickness, in

DT 5.00 5.25 5.50 5.75 6.00 6.25 6.50 6.75 7.00 7.25 7.50 7.75 8.00 8.25 8.50 8.75 9.00 9.25 9.50 9.75

-8 0.211 0.188 0.164 0.141 0.118 0.116 0.114 0.112 0.110 0.107 0.105 0.103 0.101 0.098 0.095 0.092 0.089 0.086 0.083 0.079

-6 0.145 0.134 0.123 0.113 0.102 0.099 0.096 0.093 0.090 0.087 0.084 0.081 0.078 0.077 0.075 0.073 0.071 0.072 0.073 0.075

-4 0.106 0.095 0.083 0.071 0.059 0.059 0.059 0.058 0.058 0.057 0.057 0.056 0.056 0.055 0.054 0.053 0.053 0.052 0.052 0.051

-2 0.041 0.039 0.037 0.035 0.034 0.034 0.034 0.034 0.034 0.034 0.033 0.033 0.033 0.035 0.036 0.037 0.038 0.040 0.041 0.043

0 0.037 0.039 0.040 0.042 0.043 0.041 0.039 0.037 0.035 0.033 0.031 0.029 0.027 0.026 0.026 0.026 0.026 0.026 0.025 0.025

2 0.051 0.046 0.040 0.035 0.029 0.029 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.031 0.031 0.031

4 0.029 0.029 0.028 0.028 0.028 0.029 0.030 0.031 0.032 0.034 0.035 0.036 0.037 0.038 0.038 0.038 0.039 0.037 0.035 0.033

6 0.047 0.046 0.044 0.043 0.042 0.039 0.037 0.035 0.032 0.030 0.027 0.025 0.023 0.022 0.022 0.021 0.020 0.022 0.023 0.024

8 0.048 0.041 0.034 0.028 0.021 0.021 0.020 0.020 0.020 0.020 0.020 0.019 0.019 0.019 0.019 0.019 0.018 0.019 0.019 0.020

10 0.069 0.062 0.054 0.047 0.040 0.040 0.041 0.041 0.042 0.042 0.042 0.043 0.043 0.041 0.039 0.037 0.035 0.034 0.033 0.031

12 0.064 0.060 0.056 0.052 0.048 0.045 0.042 0.039 0.037 0.034 0.031 0.028 0.026 0.027 0.028 0.029 0.031 0.030 0.030 0.029

14 0.071 0.066 0.061 0.056 0.052 0.050 0.049 0.048 0.046 0.045 0.044 0.042 0.041 0.039 0.037 0.035 0.033 0.034 0.035 0.036

16 0.000 0.012 0.025 0.037 0.050 0.049 0.049 0.048 0.048 0.047 0.046 0.046 0.045 0.045 0.044 0.044 0.044 0.041 0.039 0.036

18 0.000 0.016 0.032 0.047 0.063 0.060 0.057 0.055 0.052 0.049 0.046 0.044 0.041 0.041 0.041 0.040 0.040 0.041 0.043 0.044

20 0.000 0.002 0.004 0.007 0.009 0.013 0.018 0.022 0.027 0.031 0.036 0.040 0.045 0.043 0.042 0.040 0.039 0.038 0.036 0.035

22 0.000 0.000 0.000 0.000 0.000 0.006 0.011 0.017 0.022 0.028 0.033 0.039 0.044 0.045 0.046 0.046 0.047 0.046 0.045 0.044

24 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.005 0.011 0.016 0.021 0.025 0.029 0.033

26 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.001 0.002

28 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

30 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

32 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

34 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
100

Table 27. Frequency distributions of temperature gradients for the wet-nonfreeze region (based on rounded effective thickness) (continued).

Rounded Effective Thickness, in D

T 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75 12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00

-8 0.076 0.076 0.076 0.077 0.077 0.077 0.078 0.078 0.078 0.079 0.080 0.081 0.082 0.083 0.084 0.085 0.085 0.085 0.085 0.085 0.084

-6 0.076 0.075 0.074 0.073 0.072 0.071 0.070 0.069 0.069 0.068 0.067 0.066 0.066 0.065 0.064 0.064 0.063 0.064 0.065 0.066 0.067

-4 0.051 0.051 0.051 0.051 0.051 0.052 0.052 0.052 0.052 0.052 0.051 0.050 0.050 0.049 0.048 0.048 0.047 0.046 0.045 0.044 0.043

-2 0.045 0.043 0.042 0.041 0.040 0.039 0.038 0.037 0.036 0.038 0.039 0.041 0.042 0.044 0.045 0.047 0.048 0.049 0.051 0.052 0.053

0 0.024 0.027 0.029 0.031 0.034 0.036 0.038 0.041 0.043 0.043 0.042 0.042 0.042 0.042 0.041 0.041 0.041 0.039 0.037 0.035 0.033

2 0.031 0.031 0.031 0.030 0.030 0.030 0.029 0.029 0.029 0.030 0.030 0.031 0.032 0.033 0.034 0.034 0.035 0.037 0.039 0.041 0.043

4 0.031 0.031 0.030 0.030 0.029 0.028 0.028 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.028 0.028 0.028 0.029

6 0.026 0.025 0.023 0.022 0.021 0.020 0.019 0.018 0.017 0.017 0.017 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.017 0.017 0.017

8 0.020 0.022 0.023 0.025 0.027 0.029 0.030 0.032 0.034 0.033 0.033 0.032 0.031 0.031 0.030 0.029 0.029 0.028 0.028 0.027 0.027

10 0.030 0.029 0.028 0.028 0.027 0.026 0.026 0.025 0.024 0.025 0.026 0.027 0.028 0.029 0.030 0.030 0.031 0.030 0.029 0.029 0.028

12 0.029 0.028 0.027 0.025 0.024 0.023 0.022 0.021 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.021 0.022 0.023 0.024

14 0.037 0.037 0.038 0.038 0.039 0.039 0.039 0.040 0.040 0.040 0.039 0.039 0.038 0.038 0.037 0.037 0.036 0.036 0.036 0.036 0.036

16 0.034 0.034 0.034 0.034 0.034 0.033 0.033 0.033 0.033 0.033 0.033 0.032 0.032 0.032 0.031 0.031 0.031 0.030 0.030 0.030 0.029

18 0.045 0.044 0.042 0.040 0.038 0.037 0.035 0.033 0.032 0.032 0.032 0.032 0.033 0.033 0.033 0.034 0.034 0.034 0.035 0.035 0.036

20 0.034 0.035 0.036 0.038 0.039 0.040 0.041 0.042 0.044 0.043 0.042 0.041 0.041 0.040 0.039 0.039 0.038 0.037 0.037 0.037 0.036

22 0.043 0.041 0.040 0.038 0.037 0.035 0.034 0.032 0.031 0.031 0.032 0.033 0.033 0.034 0.035 0.035 0.036 0.036 0.035 0.035 0.035

24 0.036 0.037 0.038 0.039 0.040 0.040 0.041 0.042 0.043 0.041 0.040 0.039 0.037 0.036 0.035 0.034 0.032 0.033 0.033 0.033 0.034

26 0.003 0.005 0.007 0.010 0.012 0.015 0.017 0.020 0.022 0.024 0.025 0.026 0.027 0.028 0.029 0.031 0.032 0.032 0.033 0.033 0.033

28 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.006 0.007 0.008 0.008 0.008 0.009

30 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

32 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

34 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
101

Table 28. Frequency distributions of temperature gradients for the dry-freeze region (based on rounded effective thickness).

Rounded Effective Thickness, in

DT 5.00 5.25 5.50 5.75 6.00 6.25 6.50 6.75 7.00 7.25 7.50 7.75 8.00 8.25 8.50 8.75 9.00 9.25 9.50 9.75

-8 0.205 0.188 0.172 0.156 0.140 0.135 0.130 0.125 0.121 0.116 0.111 0.106 0.101 0.098 0.095 0.092 0.088 0.088 0.088 0.088

-6 0.170 0.150 0.130 0.110 0.090 0.089 0.089 0.089 0.089 0.088 0.088 0.088 0.088 0.089 0.090 0.091 0.092 0.091 0.090 0.090

-4 0.124 0.121 0.118 0.116 0.113 0.109 0.105 0.102 0.098 0.095 0.091 0.087 0.084 0.081 0.079 0.077 0.074 0.074 0.075 0.075

-2 0.073 0.067 0.061 0.055 0.048 0.049 0.050 0.051 0.052 0.053 0.054 0.055 0.056 0.056 0.056 0.057 0.057 0.056 0.055 0.054

0 0.070 0.068 0.066 0.064 0.062 0.062 0.062 0.062 0.061 0.061 0.061 0.061 0.061 0.061 0.061 0.061 0.061 0.060 0.059 0.058

2 0.051 0.050 0.049 0.047 0.046 0.045 0.043 0.042 0.040 0.039 0.038 0.036 0.035 0.034 0.033 0.032 0.031 0.032 0.033 0.034

4 0.053 0.048 0.043 0.038 0.033 0.033 0.034 0.034 0.034 0.034 0.034 0.034 0.035 0.035 0.035 0.035 0.036 0.036 0.037 0.037

6 0.061 0.060 0.059 0.058 0.057 0.055 0.053 0.052 0.050 0.048 0.046 0.045 0.043 0.043 0.043 0.043 0.043 0.040 0.037 0.035

8 0.043 0.040 0.037 0.034 0.031 0.031 0.031 0.031 0.032 0.032 0.032 0.032 0.032 0.032 0.031 0.030 0.029 0.031 0.033 0.034

10 0.055 0.052 0.048 0.045 0.041 0.041 0.042 0.042 0.042 0.042 0.043 0.043 0.043 0.042 0.040 0.039 0.037 0.036 0.035 0.034

12 0.080 0.070 0.060 0.049 0.039 0.037 0.034 0.032 0.029 0.026 0.024 0.021 0.019 0.020 0.022 0.024 0.026 0.025 0.024 0.023

14 0.003 0.013 0.023 0.034 0.044 0.045 0.045 0.045 0.045 0.046 0.046 0.046 0.047 0.044 0.041 0.039 0.036 0.036 0.037 0.037

16 0.000 0.016 0.032 0.048 0.064 0.060 0.055 0.051 0.046 0.042 0.037 0.033 0.028 0.029 0.029 0.029 0.030 0.028 0.026 0.024

18 0.000 0.001 0.001 0.002 0.003 0.008 0.013 0.017 0.022 0.027 0.032 0.037 0.042 0.039 0.037 0.034 0.032 0.032 0.033 0.033

20 0.000 0.000 0.000 0.000 0.000 0.004 0.009 0.013 0.017 0.022 0.026 0.030 0.034 0.039 0.043 0.047 0.051 0.049 0.046 0.044

22 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.004 0.005 0.007 0.013 0.018 0.024

24 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

26 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

28 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

30 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

32 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

34 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
102

Table 28. Frequency distributions of temperature gradients for the dry-freeze region (based on rounded effective thickness) (continued).

Rounded Effective Thickness, in D

T 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75 12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00

-8 0.088 0.086 0.085 0.083 0.081 0.080 0.078 0.077 0.075 0.075 0.074 0.074 0.074 0.074 0.073 0.073 0.073 0.073 0.074 0.075 0.076

-6 0.089 0.090 0.091 0.092 0.093 0.094 0.095 0.096 0.097 0.096 0.096 0.096 0.095 0.095 0.094 0.094 0.094 0.093 0.092 0.091 0.090

-4 0.076 0.075 0.074 0.073 0.073 0.072 0.071 0.071 0.070 0.070 0.071 0.071 0.071 0.072 0.072 0.073 0.073 0.073 0.073 0.073 0.073

-2 0.053 0.054 0.056 0.057 0.058 0.060 0.061 0.062 0.064 0.063 0.063 0.063 0.063 0.062 0.062 0.062 0.061 0.062 0.063 0.064 0.065

0 0.058 0.057 0.056 0.055 0.054 0.053 0.052 0.051 0.051 0.052 0.053 0.054 0.055 0.056 0.057 0.058 0.059 0.059 0.059 0.059 0.058

2 0.035 0.035 0.036 0.036 0.036 0.036 0.036 0.036 0.037 0.036 0.035 0.034 0.034 0.033 0.032 0.032 0.031 0.031 0.030 0.030 0.030

4 0.038 0.038 0.038 0.037 0.037 0.037 0.037 0.037 0.037 0.036 0.036 0.036 0.036 0.036 0.036 0.036 0.036 0.037 0.037 0.037 0.038

6 0.032 0.032 0.032 0.032 0.032 0.033 0.033 0.033 0.033 0.033 0.033 0.033 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.033 0.033

8 0.036 0.035 0.035 0.034 0.033 0.032 0.031 0.030 0.030 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.030 0.032 0.034 0.035

10 0.033 0.034 0.034 0.034 0.035 0.035 0.035 0.036 0.036 0.035 0.035 0.034 0.033 0.032 0.031 0.031 0.030 0.028 0.026 0.023 0.021

12 0.022 0.022 0.021 0.021 0.020 0.020 0.019 0.019 0.018 0.019 0.020 0.021 0.021 0.022 0.023 0.024 0.024 0.025 0.026 0.027 0.028

14 0.037 0.037 0.036 0.036 0.036 0.035 0.035 0.035 0.034 0.034 0.033 0.033 0.033 0.032 0.032 0.032 0.031 0.030 0.030 0.029 0.028

16 0.023 0.023 0.023 0.023 0.023 0.023 0.023 0.023 0.023 0.022 0.022 0.022 0.022 0.022 0.022 0.021 0.021 0.021 0.021 0.020 0.020

18 0.033 0.033 0.033 0.033 0.032 0.032 0.032 0.032 0.032 0.031 0.031 0.031 0.031 0.031 0.031 0.030 0.030 0.031 0.031 0.031 0.032

20 0.042 0.040 0.039 0.037 0.036 0.034 0.032 0.031 0.029 0.029 0.028 0.027 0.027 0.026 0.025 0.025 0.024 0.023 0.022 0.021 0.021

22 0.030 0.031 0.032 0.034 0.035 0.037 0.038 0.040 0.041 0.040 0.038 0.037 0.036 0.034 0.033 0.032 0.030 0.031 0.032 0.033 0.034

24 0.000 0.002 0.004 0.005 0.007 0.009 0.011 0.013 0.014 0.017 0.020 0.023 0.026 0.028 0.031 0.034 0.037 0.037 0.036 0.036 0.036

26 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.001 0.001 0.001

28 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

30 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

32 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

34 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
103

Table 29. Frequency distributions of temperature gradients for the dry-nonfreeze region (based on rounded effective thickness).

Rounded Effective Thickness, in

DT 5.00 5.25 5.50 5.75 6.00 6.25 6.50 6.75 7.00 7.25 7.50 7.75 8.00 8.25 8.50 8.75 9.00 9.25 9.50 9.75

-8 0.128 0.121 0.113 0.105 0.098 0.095 0.093 0.090 0.088 0.085 0.083 0.080 0.078 0.079 0.081 0.083 0.085 0.083 0.080 0.078

-6 0.125 0.116 0.108 0.099 0.091 0.088 0.085 0.082 0.079 0.075 0.072 0.069 0.066 0.065 0.064 0.063 0.062 0.062 0.063 0.063

-4 0.092 0.086 0.080 0.073 0.067 0.067 0.067 0.067 0.067 0.067 0.067 0.067 0.067 0.064 0.061 0.058 0.055 0.056 0.057 0.058

-2 0.057 0.051 0.044 0.038 0.032 0.033 0.034 0.035 0.036 0.037 0.038 0.039 0.040 0.041 0.042 0.043 0.045 0.043 0.042 0.041

0 0.035 0.035 0.036 0.037 0.038 0.037 0.036 0.035 0.033 0.032 0.031 0.030 0.028 0.029 0.029 0.029 0.030 0.030 0.031 0.031

2 0.044 0.041 0.039 0.037 0.034 0.033 0.032 0.030 0.029 0.028 0.026 0.025 0.024 0.024 0.024 0.024 0.024 0.024 0.024 0.025

4 0.031 0.028 0.025 0.022 0.019 0.021 0.022 0.023 0.024 0.025 0.026 0.028 0.029 0.028 0.027 0.026 0.025 0.025 0.026 0.026

6 0.039 0.037 0.036 0.035 0.033 0.032 0.031 0.031 0.030 0.029 0.028 0.027 0.026 0.027 0.028 0.028 0.029 0.026 0.024 0.021

8 0.044 0.040 0.036 0.032 0.028 0.026 0.024 0.023 0.021 0.019 0.018 0.016 0.014 0.014 0.014 0.014 0.014 0.017 0.020 0.022

10 0.050 0.044 0.038 0.032 0.026 0.027 0.027 0.028 0.028 0.028 0.029 0.029 0.030 0.029 0.027 0.026 0.025 0.024 0.024 0.023

12 0.064 0.060 0.056 0.052 0.047 0.046 0.045 0.044 0.043 0.041 0.040 0.039 0.038 0.037 0.036 0.035 0.035 0.033 0.031 0.029

14 0.069 0.061 0.053 0.045 0.037 0.036 0.034 0.033 0.031 0.030 0.028 0.027 0.025 0.026 0.027 0.028 0.028 0.030 0.032 0.034

16 0.035 0.037 0.039 0.042 0.044 0.044 0.044 0.044 0.044 0.044 0.044 0.045 0.045 0.043 0.041 0.039 0.038 0.037 0.036 0.035

18 0.000 0.013 0.026 0.039 0.052 0.049 0.047 0.045 0.042 0.040 0.038 0.035 0.033 0.034 0.036 0.037 0.039 0.035 0.032 0.028

20 0.000 0.015 0.030 0.045 0.060 0.057 0.055 0.052 0.050 0.047 0.044 0.042 0.039 0.038 0.036 0.035 0.033 0.035 0.037 0.039

22 0.000 0.000 0.000 0.000 0.000 0.005 0.011 0.016 0.022 0.027 0.033 0.038 0.044 0.040 0.036 0.032 0.028 0.028 0.028 0.028

24 0.000 0.000 0.000 0.000 0.000 0.005 0.010 0.015 0.019 0.024 0.029 0.034 0.039 0.040 0.040 0.041 0.042 0.043 0.044 0.045

26 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.007 0.014 0.021 0.028 0.030 0.032 0.034

28 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

30 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

32 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

34 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
104

Table 29. Frequency distributions of temperature gradients for the dry-nonfreeze region (based on rounded effective thickness) (continued).

Rounded Effective Thickness, in

DT 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75 12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00

-8 0.076 0.075 0.074 0.072 0.071 0.070 0.069 0.068 0.066 0.066 0.065 0.064 0.063 0.062 0.062 0.061 0.060 0.061 0.063 0.064 0.065

-6 0.063 0.064 0.064 0.065 0.066 0.066 0.067 0.067 0.068 0.069 0.070 0.071 0.072 0.073 0.074 0.075 0.076 0.074 0.072 0.071 0.069

-4 0.059 0.059 0.059 0.059 0.059 0.058 0.058 0.058 0.058 0.057 0.055 0.054 0.052 0.051 0.049 0.048 0.046 0.046 0.046 0.045 0.045

-2 0.039 0.039 0.039 0.038 0.038 0.038 0.038 0.038 0.037 0.038 0.038 0.039 0.040 0.040 0.041 0.041 0.042 0.044 0.046 0.048 0.051

0 0.032 0.032 0.032 0.032 0.032 0.032 0.032 0.032 0.032 0.032 0.033 0.033 0.034 0.034 0.034 0.035 0.035 0.034 0.034 0.033 0.032

2 0.025 0.026 0.028 0.029 0.030 0.032 0.033 0.034 0.036 0.036 0.036 0.036 0.036 0.035 0.035 0.035 0.035 0.036 0.037 0.037 0.038

4 0.026 0.025 0.025 0.024 0.023 0.023 0.022 0.021 0.021 0.021 0.022 0.022 0.023 0.023 0.024 0.024 0.025 0.025 0.026 0.026 0.026

6 0.018 0.017 0.017 0.016 0.015 0.014 0.014 0.013 0.012 0.012 0.013 0.013 0.013 0.013 0.013 0.014 0.014 0.014 0.014 0.014 0.014

8 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.024 0.024 0.024 0.024 0.023 0.023 0.023 0.023 0.023 0.023 0.023 0.023

10 0.022 0.024 0.026 0.027 0.029 0.030 0.032 0.034 0.035 0.034 0.033 0.032 0.031 0.030 0.029 0.028 0.027 0.027 0.026 0.026 0.026

12 0.027 0.025 0.024 0.022 0.021 0.019 0.018 0.016 0.015 0.016 0.017 0.019 0.020 0.021 0.022 0.024 0.025 0.024 0.024 0.023 0.023

14 0.036 0.035 0.034 0.033 0.032 0.031 0.030 0.029 0.028 0.028 0.028 0.028 0.027 0.027 0.027 0.027 0.026 0.027 0.028 0.029 0.030

16 0.034 0.034 0.034 0.034 0.034 0.035 0.035 0.035 0.035 0.034 0.034 0.033 0.032 0.032 0.031 0.031 0.030 0.030 0.030 0.030 0.030

18 0.025 0.025 0.025 0.026 0.026 0.026 0.027 0.027 0.027 0.027 0.027 0.027 0.026 0.026 0.026 0.026 0.026 0.025 0.024 0.024 0.023

20 0.041 0.040 0.039 0.038 0.036 0.035 0.034 0.033 0.031 0.032 0.033 0.034 0.035 0.036 0.037 0.038 0.039 0.039 0.040 0.041 0.041

22 0.027 0.029 0.031 0.032 0.034 0.036 0.037 0.039 0.041 0.039 0.037 0.035 0.033 0.032 0.030 0.028 0.026 0.026 0.025 0.025 0.024

24 0.046 0.044 0.042 0.040 0.038 0.035 0.033 0.031 0.029 0.030 0.031 0.032 0.033 0.034 0.036 0.037 0.038 0.037 0.037 0.037 0.036

26 0.036 0.036 0.035 0.035 0.035 0.034 0.034 0.033 0.033 0.032 0.031 0.029 0.028 0.027 0.026 0.024 0.023 0.023 0.024 0.024 0.024

28 0.000 0.004 0.007 0.011 0.015 0.018 0.022 0.025 0.029 0.030 0.031 0.032 0.033 0.034 0.035 0.036 0.037 0.037 0.036 0.036 0.036

30 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.002 0.003 0.005 0.006 0.007 0.008 0.009 0.010 0.011 0.011 0.012

32 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

34 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
105

MODEL VERIFICATION (SENSITIVITY ANALYSIS)

A sensitivity analysis was conducted on the final transverse cracking model to determine its

reliability for predicting cracking within and outside of the inference space of the development

database. This was accomplished by studying the effects of the various input parameters on the

output generated by the cracking model. Note that the sensitivity analyses were accomplished by

investigating the effects of changing one variable at a time, while holding all other variables constant.

Effect of Material- and Design-Related Factors

The material- and design-related factors that were incorporated into the final slab cracking model

included PCC slab thickness, PCC flexural strength, PCC modulus of elasticity, PCC joint spacing,

base type and thickness, and PCC slab edge support (shoulder type and presence of a widened lane).

The sensitivity of the final cracking model to each of these variables is discussed separately in the

following sections.

Effect of PCC Slab Thickness

Figure 25 shows that transverse slab cracking increases as slab thickness decreases. This trend is

expected because a thicker slab exhibits much lower stresses than a thinner slab under the same site

conditions assuming that all other design parameters are the same. This sensitivity indicates that

PCC slab thickness is one of the most important parameters that should be controlled during

construction.

Effect of PCC Flexural Strength

Figure 26 illustrates the sensitivity of the final JPCP transverse slab cracking model to changes in

PCC compressive strength. The figure clearly shows that an increase in PCC flexural strength

represented by the modulus of rupture results in a reduction in slab cracking. This trend is in

agreement with the mechanistic principle that a concrete slab with higher flexural strength has lower

fatigue damage than a corresponding slab with lower strength under the same level of bending

stresses. However, it should be noted that in some cases, increased slab cracking has been associated

with increased concrete strength due to an increase in drying shrinkage from additional cement in

the mix. Mix design must be done properly to avoid high shrinkage for higher strengths.

Effect of PCC Modulus of Elasticity

Figure 27 shows that transverse slab cracking increases as PCC modulus of elasticity increases.

Although this trend is expected because an increase in PCC modulus leads to an increase in

maximum PCC bending stresses, this figure is somewhat misleading. An increase in PCC modulus

will also increase PCC flexural strength. Figure 28 presents a comparison of predicted slab cracking

for different values of PCC modulus
106

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

100

0 5 1 0 1 5 2 0

Cumulative Traffic, ESAL's

Percent Slabs Cracked

Hpcc = 9 in

Hpcc= 10 in

Hpcc= 11 in

Wet-freeze climate 

Joint spacing = 20 ft

MR = 700 psi

PCC elastic modulus = 5 Mpsi

Dynamic k-value = 200 psi/in

AC shoulder

Aggregate base

Figure 25. Sensitivity of the final JPCP transverse slab cracking model to changes in PCC slab

thickness.

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

100

0 5 1 0 1 5 2 0

Cumulative Traffic, ESAL's

Percent Slabs Cracked

MR = 600 psi

MR = 700 psi

MR = 800 psi

Wet-freeze climate 

Joint spacing = 15 ft

Hpcc = 10 in

PCC elastic modulus = 5 Mpsi

Dynamic k-value = 200 psi/in

AC shoulder

Aggregate base

Figure 26. Sensitivity of the final JPCP transverse slab cracking model to changes in PCC flexural

strength.
107

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

100

0 5 1 0 1 5 2 0

Cumulative Traffic, ESAL's

Percent Slabs Cracked

Epcc = 6 Mpsi

Epcc = 5 Mpsi

Epcc = 4 Mpsi

Wet-freeze climate 

Joint spacing = 15 ft

Hpcc = 9 in

MR = 700 psi

Dynamic k-value = 200 psi/in

AC shoulder

Aggregate base

Figure 27. Sensitivity of the final JPCP transverse cracking model to changes in modulus of

elasticity.

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

100

0 5 1 0 1 5 2 0

Cumulative Traffic, ESAL's

Percent Slabs Cracked

Epcc = 6 Mpsi

Epcc = 5 Mpsi

Epcc = 4 Mpsi

Wet-freeze climate 

Joint spacing = 15 ft

Hpcc = 9 in

MR varies with Epcc

Dynamic k-value = 200 psi/in

AC shoulder

Aggregate base

Figure 28. Sensitivity of the final JPCP transverse cracking model to changes in modulus of elasticity

and corresponding changes in PCC flexural stiffness.
108

of elasticity assuming that the PCC flexural strength is related to PCC modulus of elasticity as

predicted by Foxworthy’s equation:

488.5

10

MR 43.5 6= +

E

(82)

where MR is the PCC modulus of rupture, (psi) and E is the PCC modulus of elasticity (psi).(38) An

analysis of figure 28 shows that PCC slab cracking decreases slightly when the PCC modulus of

elasticity and modulus of rupture increase together.

Effect of PCC Transverse Joint Spacing

Figure 29 illustrates the sensitivity of the final JPCP transverse slab cracking model to changes in

PCC transverse joint spacing. The figure clearly shows that an increase in joint spacing results in a

dramatic increase in slab cracking. This trend agrees with numerous field observations that longer

slabs crack much earlier than shorter slabs in pavements with variable joint spacing. This trend also

means that if joint sawing is not done on time and proper joints are not formed, large "effective" joint

spacing will be developed, which can cause random slab cracking.

Effect of PCC Slab Edge Support

Figure 30 shows that a tied PCC shoulder and widened slabs can significantly reduce the amount

of slab cracking compared with an asphalt shoulder. The tied PCC shoulders improve cracking

performance by reducing stresses at the pavement edge. The effectiveness of the tied PCC shoulder

depends on the load transfer efficiency across the lane-shoulder joint. Widened slabs effectively

move the traffic away from the pavement edges, thus allowing the interior stresses (rather than much

higher edge stresses) to control fatigue cracking.

Effect of Base Type

The presence of a stabilized base can have a significant effect on slab cracking if the base is

bonded to the pavement slab; however, the effect is negligible if the bonded response cannot be

obtained. These trends are illustrated in figure 31. In reality, there is most often a partial bond with

some slippage.

Effect of Site-Related Factors

In addition to being sensitive to the numerous material- and design-related factors discussed

above, the final slab cracking model is also very sensitive to site-related factors. Two site condition

factors that affect the development of JPCP cracking include climate (climatic zone) and subgrade

support (dynamic k-value). The effects of these factors are described separately below.
109

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20

Cumulative Traffic, ESAL's

Percent Slabs Cracked

JT Space= 20 ft

JT Space= 18 ft

JT Space= 15 ft

Wet-freeze climate 

Hpcc = 10 in

MR = 700 psi

PCC elastic modulus = 5 Mpsi

Dynamic k-value = 200 psi/in

AC shoulder

Aggregate base

Figure 29. Sensitivity of the final JPCP transverse slab cracking model to changes in PCC slab joint

spacing.

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

100

0 5 1 0 1 5 2 0

Cumulative Traffic, ESAL's

Percent Slabs Cracked

A C

PCC

Widened

Wet-freeze climate 

Joint spacing = 15 ft

Hpcc = 9 in

MR = 700 psi

PCC elastic modulus = 5 Mpsi

Dynamic k-value = 200 psi/in

Aggregate base

Figure 30. Sensitivity of the final JPCP transverse slab cracking model to changes in edge support.
110

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

100

0 5 1 0 1 5 2 0

Cumulative Traffic, ESAL's

Percent Slabs Cracked

Aggregate base

CTB base (unbonded with PCC)

CTB base (bonded with PCC)

Wet-freeze climate 

Joint spacing = 15 ft

Hpcc = 9 in

MR = 700 psi

PCC elastic modulus = 5 Mpsi

Dynamic k-value = 200 psi/in

AC shoulder

Figure 31. Sensitivity of the final JPCP transverse slab cracking model to changes in base type and

bond condition.

Effect of Climate

Figure 32 illustrates that climatic conditions can have a significant effect on slab cracking. The

conditions in the hotter climates generally lead to more slab cracking because of the higher

temperature differentials. For top-down cracking, moisture conditions may also be important; drier

conditions cause greater amounts of cracking because of the greater differential shrinkage.

Effect of Subgrade Support

Figure 33 contains a plot that illustrates the sensitivity of the final JPCP transverse cracking model

to changes in subgrade support conditions (dynamic k-value backcalculated from FWD tests). This

plot shows that the subgrade modulus of reaction has a relatively minor effect at lower levels, but

the difference between the extreme conditions can be significant. For reference, the mean dynamic kvalue of all LTPP GPS-3 sections has been found to be approximately 54 kPa/mm (200 psi/in). The

static k-value, which is the traditional k-value used in pavement design for the past 75 years, is

approximately one-half of the dynamic k-value. To avoid confusion since most engineers are

familiar with the static k-value, the PaveSpec 3.0 software requires the input of a static k-value.
111

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

100

0 5 1 0 1 5 2 0

Cumulative Traffic, ESAL's

Percent Slabs Cracked

Wet Nonfreeze

Dry Nonfreeze

Wet Freeze

Dry Freeze

Joint spacing = 20 ft

Hpcc = 10 in

MR = 700 psi

PCC elastic modulus = 5 Mpsi

Dynamic k-value = 200 psi/in

AC shoulder

Aggregate base

Figure 32. Sensitivity of the final JPCP transverse slab cracking model to changes in climate.

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

100

0 5 1 0 1 5 2 0

Cumulative Traffic, ESAL's

Percent Slabs Cracked

Dynamic k-value = 100 psi/in

Dynamic k-value = 200 psi/in

Dynamic k-value = 300 psi/in

Wet-freeze climate 

Joint spacing = 20 ft

Hpcc = 9 in

MR = 700 psi

PCC elastic modulus = 5 Mpsi

AC shoulder

Aggregate base

Figure 33. Sensitivity of the final JPCP transverse slab cracking model to changes in dynamic kvalue.
112

SUMMARY

The RPPR 1997 JPCP transverse cracking model was recalibrated under this study. The

recalibrated model is deemed suitable for use with the current PRS procedure because it

incorporates PRS-related AQC's (PCC concrete strength and slab thickness) as well as other design-,

material-, and site-related variables that significantly influence slab cracking. The model has

reasonable statistics for being calibrated with such a large number of data points. Specific

improvements to the new model include the following:

• Direct consideration of the characteristics of the base layer.

• Direct consideration of the effects of a tied PCC shoulder.

• Incorporation of improved procedures for computing load and thermal curling stresses.

• Incorporation of the influence of built-in construction curling on slab cracking.

• Recalibration of the model was accomplished using a much improved database (in both

quality and quantity).

As mentioned previously, this model only considers the development of bottom-up cracking.

However, both slab thickness and PCC strength will affect top-down cracking and bottom-up

cracking similarly. Thus, the two AQC's important to the prediction of transverse cracking in PRS

will have a significant effect on both bottom-up and top-down cracking. Once procedures for

predicting top-down cracking are developed (they are under development at this time under other

research), it is strongly recommended that they be incorporated into the transverse cracking

prediction procedures used in the PRS.
113

CHAPTER 6: TRANSVERSE JOINT SPALLING MODEL

INTRODUCTION

Spalling is defined as the breakdown or disintegration of a PCC slab’s edges at

transverse joints and is generally categorized by its quantity (number of spalled joints

or total length of joint spalled) and severity (low, medium, or high).

(13,39) Joint spalling

may be caused by infiltration of incompressibles into pavement joints, deterioration of

the concrete material because of environmental factors, problems with load transfer

devices, or the exposure of the slab’s joint to a sudden and massive tensile stress.

Spalling caused by a sudden force is usually of low severity and does not progress or

deteriorate with time. However, spalling caused by incompressibles, repeated high

tensile stress at the slab edges (fatigue), load transfer devices, or concrete deterioration

is more significant. Spalling generally increases in amount and severity over time and

eventually causes significant pavement joint deterioration and a need for associated

repairs. An increase in pavement roughness, associated with developing spalling,

typically results in a decrease in pavement serviceability and the need for costly

rehabilitation.

(10,13,39,40,41)

This chapter describes the researchers' initial attempt to validate the chosen bestavailable transverse joint spalling model (that used in PaveSpec 2.0), as well as the

development of a new, improved spalling model for use in PaveSpec 3.0.

CURRENT PRS JPCP TRANSVERSE JOINT SPALLING MODEL

The transverse joint spalling model selected as the best available was that used in

the PaveSpec 2.0 software. It is a combination of a spalling model developed by Yu et

al. for the 1997 FHWA RPPR project and an adjustment ratio developed in 1993 by

ERES and CTL.

(10,16) The adjustment ratio was included in the process to incorporate

the effects of two PRS-related AQC's (concrete strength and air content). Currently, no

single model predicts transverse joint spalling based on both the AQC variables

essential for PRS analysis and other significant climate, site, and design variables.

The transverse joint spalling model included in PaveSpec 2.0 consists of a multistep procedure that adjusts a predicted baseline spalling (spalling predicted only as a

function of various site, design, and climatic inputs) to account for changes in PRSrelated AQC's. The following paragraphs summarize the details of this spalling model

as they were presented in a 1999 report by Hoerner et al.

(10)

Two different procedures are used to estimate transverse joint spalling, depending

on whether air content is considered. If air content is not considered, transverse joint

spalling is predicted directly using the baseline model. If air content is considered, the

transverse joint spalling (predicted using the baseline model) is then adjusted based on
114

a comparison of as-constructed to as-designed mean air content and compressive

strength. Both model procedures are presented separately below. (Note: The model

outputs and inputs are presented in English units.)

Transverse Joint Spalling Baseline Model (Not Including Air Content)

%SPALL = AGE2 *10–6 * JTSPACE * [551.6 – 847.3 * (LIQSEAL + (83)

PREFSEAL) + (0.936 * (DAYS90)3 * 10–3) + (364 *

DOWELCOR) + (2.783 – 1.40 * LIQSEAL – 2.368 *

PREFSEAL – 0.676 * SILSEAL) *FI]

where:

%SPALL = Percentage of medium- and high-severity spalled joints where air

content is not considered (LTPP definition).

AGE = Number of years since original construction.

DOWELCOR = Dowel corrosion potential.

= 0, if no dowels exist or dowels are protected from corrosion.

= 1, if dowels are not protected from corrosion.

JTSPACE = Mean transverse joint spacing, ft.

LIQSEAL = 1, if liquid sealant exists in joint; otherwise, 0.

PREFSEAL = 1, if preformed sealant exists in joint; otherwise, 0.

SILSEAL = 1, if silicone sealant exists in joint; otherwise, 0.

FI = Mean annual freezing index, °F-days.

DAYS90 = Number of days with temperature greater than 90 °F.

Statistics:

N = 164.

R2 = 0.76.

SEE = 5.4 percent of joints.

Transverse Joint Spalling Model and Procedure (Including Air Content)

If air content is included, a four-phased procedure is used to predict transverse joint

spalling. The details of each phase are defined below.

Phase 1—Calculate the As-Designed Transverse Joint Spalling

The first step in computing the estimated yearly as-constructed transverse joint

spalling is to determine the yearly as-designed transverse joint spalling values. The asdesigned transverse joint spalling is assumed to be equal to the baseline spalling

computed using equation 83.
115

Phase 2—Calculate the Relative Difference Between the As-Designed and AsConstructed Spalling (due to the effects of air content and compressive strength)

This relative difference between as-constructed and as-designed spalling is

computed based on the differences between as-constructed and as-designed air content

and concrete strength. This as-constructed to as-designed ratio (AC-AD RATIO) is

computed based on equations that are functions of air content, compressive strength,

freeze-thaw cycles (in the pavement), and age. Different equations are used depending

on whether deicing salt is present. Each of these scenarios is described separately

below.

Case 1—Salt is Present

If salt is present, an AC-AD RATIO is computed using the results of equations 84

and 85.

AC-SPALL = 115 – (9.29 * AIRAS-CON) – (0.0114 * f’cAS-CON) + (0.118 * FTC3) (84)

AD-SPALL = 115 – (9.29 * AIRAS-DES) – (0.0114 * f’cAS-DES) + (0.118 * FTC3) (85)

where:

AC-SPALL = As-constructed joint spalling (function of as-constructed air content

and compressive strength), percentage of joint length.

AD-SPALL = As-designed joint spalling (function of as-designed air content and

compressive strength), percentage of joint length.

FTC3 = Cumulative number of estimated in-pavement freeze-thaw cycles (at

76 mm [3 in] below the pavement surface).

AIRAS-CON = Measured as-constructed air content, percent.

AIRAS-DES = As-designed air content, percent.

f’cAS-CON = Measured as-constructed 28-day compressive strength, psi.

f’cAS-DES = As-designed 28-day compressive strength, psi.

Finally, the AC-AD RATIO is computed as a function of AC-SPALL and AD-SPALL

using equation 86.

AC-AD RATIO =

AD - SPALL

AC -SPALL (86)

Case 2—Salt is Not Present

If salt is not present, equation 87 (developed under a previous PRS project) is

used.

(5,6,7)

SPALL = 22.6 + 75.1 * SALT * log(FTC3) – 78.0 * SALT – (87)
116

11.7 * AIR * SALT – 0.00478 * f’c

where:

SPALL = Joint spalling, percentage of joint length.

SALT = 0 if no calcium chloride is present, 1 if calcium chloride is present.

FTC3 = Cumulative number of estimated freeze-thaw cycles in the pavement

(at 76 mm [3 in] below the pavement surface).

AIR = Measured air content of the fully consolidated specimen, percent.

f’c = Measured 28-day compressive strength mean, psi.

Without the presence of salt, equation 87 simplifies to be a function of compressive

strength only. Therefore, the effects of air content are no longer considered directly, but

instead are considered indirectly through compressive strength. The equation is

calculated for both the as-constructed and as-designed pavements (using representative

as-constructed and as-designed compressive strength means), as shown in equations 88

and 89, respectively.

AC-SPALL = 22.6 – 0.00478 * f’cAS-CON (88)

AD-SPALL = 22.6 – 0.00478 * f’cAS-DES (89)

where:

AC-SPALL = As-constructed joint spalling (function of as-constructed compressive

strength only), percentage of joint length.

AD-SPALL = As-designed joint spalling (function of as-designed compressive

strength only), percentage of joint length.

f’cAS-CON = Measured as-constructed 28-day compressive strength, psi.

f’cAS-DES = As-designed 28-day compressive strength, psi.

Finally, the AC-AD RATIO is again computed using equation 86.

Phase 3—Determine the As-Constructed Spalling Values Using the Phase 2 AC-AD

RATIO

The phase 3 as-constructed yearly spalling values are calculated by multiplying the

phase 1 as-designed spalling values by the computed phase 2 AC-AD yearly ratios.
117

Phase 4—Adjustment of Phase 3 Spalling Values to the Assumed Boundary Conditions

Finally, the phase 3 as-constructed spalling values are adjusted to comply with the

set of assumed boundary conditions presented in this section. The following general

assumptions are used to define the boundary conditions:

• The as-designed and as-constructed curves are never allowed to cross.

• As-designed and as-constructed transverse joint spalling values are both equal

to zero at an age equal to zero (i.e., at time of construction).

• The predicted transverse joint spalling value must increase (or stay constant) as

time increases.

• If the as-constructed curve is above the as-designed curve (poorer quality than

the as-designed), the as-constructed curve is assumed to go through the origin at

an age of zero.

The following step-by-step procedure is used to determine the as-constructed

spalling curve values required to match the boundary conditions. The values in

question are near an age of zero. The procedure differs depending on whether the asconstructed values are greater than or less than the as-designed values. The asdesigned and as-constructed values at the end of the analysis period are used to

determine which scenario is used. Each scenario is explained in detail below.

Scenario 1: The as-constructed value is less than the as-designed value at the end of the analysis

period.

Scenario 1 represents the case where the as-constructed pavement is constructed

with better quality than specified for the as-designed pavement. When this occurs, the

following procedure is used to ensure boundary conditions:

1. Calculate the yearly slope changes starting at the last year of the analysis period.

2. Compare year-to-year slopes starting at the last year of the analysis period and

working backwards (i.e., moving toward an age of zero).

3. Identify the first yearly interval (trigger interval) where the slope stops

decreasing and begins increasing (Trigger Interval = SLOPE(n) = SPALLYEAR(n) –

SPALLYEAR(n-1)).

4. If the slopes begin increasing, use the last decreasing slope in the series

(SLOPE(n+1)) as the assumed slope for the early age slopes (SLOPE = 0 to n).
118

5. One final check is to make sure that the as-constructed values are less than or

equal to the as-designed values.

Scenario 2: The as-constructed value is greater than the as-designed value at the end of the

analysis period.

Scenario 2 represents the case where the as-constructed pavement is constructed

with poorer quality than that specified for the as-designed pavement. When this

occurs, the following procedure is used to ensure boundary conditions:

1. Calculate the yearly slope changes starting at the last year of the analysis period.

2. Determine the projected y-intercept associated with each calculated slope.

3. Compare year-to-year projected y-intercepts starting at the last year of the

analysis period and working backwards (i.e., moving toward an age of zero).

4. Identify the first yearly interval (trigger interval) where the y-intercept becomes

greater than or equal to zero (Trigger Interval = SLOPE(n) = SPALLYEAR(n) –

SPALLYEAR(n-1)).

5. Determine the difference between the as-constructed and as-designed values at

year n (DIFFERENCE(n) = AC-SPALL(n) – AD-SPALL(n)).

6. As (n) moves toward zero, the difference between the spalling values decreases

linearly. For example, if the difference is determined to be 6 (100 percent of the

observed difference) at a time of n=10 years, 50 percent of the observed

difference will be applied at a time of n/2 (therefore, difference = 3 at 5 years).

This difference progresses until a difference of zero is applied at a time equal to

zero.

ATTEMPTED VALIDATION OF THE CURRENT PRS TRANSVERSE JOINT

SPALLING MODEL

Before any new model development or calibration techniques were undertaken, the

research team attempted to validate the current PRS transverse joint spalling model

with a new independent data set. The validity of the current spalling model was

assessed by:

• Reviewing plots of predicted versus measured spalling.

• Reviewing plots of residuals versus predicted spalling.

• Analyzing diagnostic statistics such as the R2 and the SEE to determine the

goodness-of-fit of the models when the independent data set is used.

• Identifying any general observed weaknesses in the model.
119

The independent data used in the initial model validation process consisted of JPCP

data from the LTPP experiment database (GPS-3 data only). It consisted of 61

pavement test sections located in 17 States. A summary of the validation data is

presented in table 30.

Table 30. Summary of LTPP data used in the initial validation of the PaveSpec 2.0 JPCP

transverse joint spalling model.

Climatic Range

Region Variable Min. Max. Mean

Standard

Deviation

Age, years 2 24 11.6 5.6

Joint spacing, ft 14 30 19 4

Liquid sealant 0 data points - -

Preformed sealant 11 data points - -

Silicone sealant 36 data points - -

Other sealant 12 data points - -

Days with temperature

above 90 °F

15 99 60 24

Load transfer mechanism 42 data points used dowels and 16

used aggregate interlock as the load

transfer mechanism

Freezing index, °F days 0 147 60 56

Air content, percent 3.8 9.8 5.4 1.8

Core 28-day compressive

strength, psi

3,700 6,000 4,800 884

Nonfreeze

Air freeze-thaw cycles 2 80 42 28

Age, years 0 25 10 5.6

Joint spacing, ft 12.5 20 15.7 0

Liquid sealant 30 data points - -

Preformed sealant 26 data points - -

Silicone sealant 50 data points - -

Other sealant 3 data points - -

Days with temperature

above 90 °F

3 56 24 17.2

Load transfer mechanism 21 data points used dowels and 87

used aggregate interlock as the load

transfer mechanism

Freezing index, °F days 160 2,815 1,087 604

Air content, percent 2.1 7 5.7 0.76

Core 28-day compressive

strength, psi

3,110 6,780 5,000 704

Freeze

Air freeze-thaw cycles 63 172 110 26.6
120

• The models used for estimating AD-AC RATIO were developed with laboratorygenerated data with a limited inference space.

• A key input variable, freeze-thaw cycles at 76 mm (3 in) below the pavement

surface, is a subjective variable that is difficult to estimate and is not present in

national databases.

• A comparison of the measured and predicted spalling (using the independent

LTPP data) showed a low R2 value of 0.37 percent and an SEE of 3.2 percent.

Figures 34 and 35 show plots of predicted versus measured spalling, and residuals

versus predicted spalling, respectively. The diagnostic statistics and both plots

indicate that the predicted transverse joint spalling is random in nature and does not

have a very strong correlation with the measured transverse joint spalling. Because of

the lack of a strong correlation between the predicted and measured spalling values, it

was decided that a simple calibration of the existing model would not significantly

improve the model’s prediction ability. Therefore, it was decided that the only way to

obtain a transverse joint spalling model that would be truly suitable for use within the

current PRS methodology was to develop a new model based on the data available in

the newly compiled PRS national database.

0

5

10

15

20

25

0 5 10 15 20 25

Measured percent spalled joints

Predicted percent spalled joints

N = 166

R

2

 = 0.37

SEE = 3.2 percent

Figure 34. Predicted (equation 83) versus measured JPCP transverse joint spalling

(using the LTPP validation data set).
121

-25

-20

-15

-10

-5

0

5

10

15

20

25

0 5 10 15 20 25

Predicted percent spalled joints

Residual, percent

Figure 35. Residual versus predicted (equation 83) transverse joint spalling (using the

LTPP validation data set).

EXISTING JPCP TRANSVERSE JOINT SPALLING MODELS

The first step in the model development process was to review transverse spalling

models developed under previous research efforts. Reviewing previous studies not

only provided guidance as to what variables should be considered for inclusion in the

new model, but also added expert knowledge into the model development process at

an early stage. During the review process, specific attention was paid to the

engineering significance of the variables. The specific models reviewed were from the

SHRP P-020, LTPP Data Analysis, CTL, and RPPR studies.

(5,14,15, 16) The details of each

of these models are described separately in the following sections.

SHRP P-020 JPCP Transverse Joint Spalling Model(14)

In a SHRP study conducted by Simpson et al. in 1994, titled Early Analysis of LTPP

General Pavement Studies Data, the following JPCP joint spalling model was developed

using LTPP data:(14)

%SPALL = 9.79 + 10.09 * [–1.227 + 0.0022 * (0.9853 * AGE + 0.1709 * FTCYC)

2

] (90)

where:
122

%SPALL = Predicted mean percentage of transverse joint spalling (all severities),

percentage of the total number of joints.

AGE = Age since construction, years.

FTCYC = Mean annual air freeze-thaw cycles.

Statistics:

N = 56.

R2 = 0.335.

SEE = 11.05 percent of joints.

This 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 of

water in the pores of the concrete, creating additional stresses that weaken the concrete.

The age variable in this model could represent several factors, such as cyclic slab

curling and warping, and temperature cycles due to daily and seasonal temperature

variations that result in joint movements and the generation of stresses within the PCC

slab concrete. Cyclic joint movements ultimately increase joint openings and damage

the joint sealant, allowing for the infiltration of incompressibles into the joints. Age

also represents the amount of repeated traffic loading, since older pavements are

expected to have carried more traffic.

The SHRP P-020 model indicates that spalling generally increases slowly during the

first few years of the 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 joint. It also

takes time for pavement damage to accumulate.

LTPP Data Analysis JPCP Transverse Joint Spalling Model(15)

In 1999, Titus-Glover et al. developed a JPCP transverse joint spalling model under

a FHWA LTPP data analysis contract.

(15) This model, based solely on LTPP data, is as

follows:

(0.34*TRANGE 0.42*RH 0.0318*FTCYC)

Damage

100*Damage %SPALL 2.5

2.1

= − + (91)

where:

%SPALL = Percentage of JPCP joints with spalling (all severities).

TRANGE = Average daily temperature range, °C.
123

RH = Average daily range of relative humidity during the month of

construction (can be obtained from the National Oceanic and

Atmospheric Administration [NOAA] tables, percent.

 FTCYC = Number of air freeze-thaw cycles.

 Damage = Damage from traffic and environmental stresses.

Statistics:

N = 52.

R2 = 0.61.

SEE = 12 percent of joints.

Damage is calculated as follows: (15)

0.145

T NE

AGE

N

KESAL

Damage 















= + (92)

where:

KESAL = Number of 80-kN (18-kip) ESAL’s, in thousands.

AGE = Pavement age in years.

NT = Allowable number of cycles due to traffic stresses.

NE = Allowable number of cycles due to environmental stresses.

The allowable numbers of cycles, NT and NE, used to calculate damage are obtained

from tensile stresses generated at the slab joint from traffic and environmental stress

cycles. The specific variables of which NT and NE are functions are defined as follows:

NT = f(height of sealant, modulus of subgrade reaction [k-value], transverse

joint sealant type, PCC slab thickness, elastic modulus of PCC slab).

NE = f(transverse joint sealant type, transverse joint spacing, thermal

gradient in the slab, indirect tensile strength, concrete coefficient of

thermal expansion, subbase friction factor).

The LTPP data analysis model identified three key groups of factors that influence

JPCP spalling: environmental effects, traffic loading, and sealants and incompressibles.

The key environmental variables that were found to influence joint spalling 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 of the type of sealant, or lack thereof, in relation to all these factors.

A large daily temperature range results in more spalling regardless of the type of

sealant used. It is believed that a larger temperature range may result in higher

restrained thermal stresses at the slab joint. Preformed sealants seem to decrease these

stresses and cause less spalling, whereas joints without any sealants (most likely filled
124

with incompressibles) experience more spalling. A high relative humidity during the

period of construction reduces the occurrence of spalling. A possible explanation of

this trend is that, by aiding the curing process because of the reduced rate at which

moisture leaves the PCC slab, a high relative humidity may increase strength gain and

concrete durability and reduce shrinkage, causing early age delaminations and

microcracks that lead to spalling.

CTL JPCP Transverse Joint Spalling Model(5)

Under a previous PRS study, CTL conducted a laboratory materials study that

evaluated the effects of presence of salt, freeze-thaw cycles in the pavement, PCC air

content, and 28-day compressive strength on transverse joint spalling.

(5) The detailed

CTL model is as follows:

SPALL_LEN = 22.6 + 75.1 * SALT * log(FTC3) – 78.0 * SALT – 11.7 * AIR * (93)

SALT – 0.00478 * f’c

where:

SPALL_LEN = Joint spalling, percentage of joint length.

SALT = 0 if no calcium chloride is present, 1 if calcium chloride is present.

FTC3 = Cumulative number of estimated freeze-thaw cycles at 76 mm (3 in)

below the pavement surface.

AIR = Air content of the fully consolidated specimen, percent.

f’c = 28-day compressive strength mean, psi.

Statistics:

R2 = 0.855.

SEE = 9.0 percent of joint length.

This model shows a decrease in predicted spalling with an increase in air content

and PCC compressive strength. However, there was a significant increase in spalling as

the total number of in-pavement freeze-thaw cycles increased (especially when deicing

salt was present).

Equation 93 was calibrated using field data obtained from in-service pavements in a

subsequent PRS study.

(7) This calibrated model was the basis of the spalling

adjustment factor (AC-AD RATIO) used in the transverse spalling prediction procedure

currently used in PaveSpec 2.0. In general, a good correlation was observed between

the field data and the calibrated model, indicating that the variables in the CTL models

significantly influence spalling.

FHWA RPPR JPCP Transverse Joint Spalling Model(16)

The FHWA RPPR study (completed by Yu et al. in 1997) undertook a detailed

examination of several past models.

(16)

 It resulted in the following comprehensive list
125

of explanatory variables that can be used in the exploratory analysis for model

development:

• Pavement age (time since construction).

• Cumulative 80-kN (18-kip) ESAL’s in the traffic lane.

• Mean transverse joint spacing.

• PCC slab thickness.

• AASHTO drainage coefficient (Cd).

• Transverse joint opening.

• Mean transverse joint width.

• Transverse joint sealant type.

• Elastic modulus of the PCC slab.

• Mean backcalculated modulus of subgrade reaction (k-value).

• Thornthwaite moisture index.

• Number of days in which temperature was greater than 90 °F.

• Mean monthly temperature range.

• Mean annual freezing index.

• Mean annual air freeze-thaw cycles.

• Potential of dowel corrosion.

Under the RPPR study, Yu et al. considered all of these potential variables in the

development of the following JPCP transverse joint spalling model:(16)

%SPALL = AGE2 *10–6 * JTSPACE * [551.6 – 847.3 * (LIQSEAL + (94)

PREFSEAL) + (0.936 * (DAYS90)3 * 10–3) + (364 * DOWELCOR) +

(2.783 – 1.40 * LIQSEAL – 2.368 * PREFSEAL – 0.676 * SILSEAL) *FI]

where:

%SPALL = Percentage of medium- and high-severity spalled joints where air

content is not considered.

AGE = Number of years since original construction.

DOWELCOR = Dowel potential corrosion (assumed to be equal to 0).

= 0, if no dowels exist or dowels are protected from corrosion.

= 1, if dowels are not protected from corrosion.

JTSPACE = Mean transverse joint spacing, ft.

LIQSEAL = 1, if liquid sealant exists in joint; otherwise, 0.

PREFSEAL = 1, if preformed sealant exists in joint; otherwise, 0.

SILSEAL = 1, if silicone sealant exists in joint; otherwise, 0.

FI = Mean annual freezing index, °F-days.

DAYS90 = Number of days with temperature greater than 90 °F.

Statistics:

N = 164.

R2 = 0.76.
126

SEE = 5.4 percent of joints.

This RPPR spalling model is the baseline model used in the transverse spalling

prediction procedure currently included in PaveSpec 2.0.

The variables in this model can be divided into two groups—environment-related

and design-related variables. The environment-related variables include age (cycles of

climate changes, such as opening and closing of joints), annual number of days with

temperature above 32 °C (90 °F) (Days 90), and freezing index. DAYS90 is indicative of

the magnitude of repeated high compressive stresses to which the joint is subjected in

the summer. Since pavements located in areas with high DAYS90 values generally

undergo a great amount of compression, this can result in the generation of high

stresses in the PCC slab and joint that lead to a greater amount of spalling, especially if

incompressibles are present in the joints.

Pavements located in areas with a high freezing index are subjected to prolonged

cycles of frozen water within the pores of the PCC slab and deterioration of the concrete

material. This situation generally results in the disintegration of the concrete slab

material at the slab surfaces and joints and, hence, leads to the development of spalling.

The design-related variables in the model include transverse joint spacing, sealant

type, and dowel corrosion potential. The joint spacing is highly correlated to the

degree of joint 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. Spalling can be caused by dowel corrosion produced as a

result of the dowel's exposure to chlorides and other chemicals that infiltrate the joint;

therefore, applying a protective coating (epoxy, plastic, stainless steel) to the dowels

will typically reduce the amount of spalling.

The role of joint sealants in minimizing spalling is to prevent the intrusion of

incompressible material into the joint. Incompressibles restrain the slab joints from

moving which, therefore, causes an increase in the stresses around the pavement joint.

This increase in stresses around the joint generally leads to an increase in the spalling

at the joint. The results of the RPPR study suggested that the use of preformed sealants

in JPCP resulted in the lowest level of spalling for all sealed and unsealed joints.

Preformed sealants are particularly effective in minimizing the intrusion of

incompressibles into pavement joints.

Overview of JPCP Transverse Joint Spalling Models

The review of past spalling model development efforts indicates that, even though

research has been ongoing since the early 1960's, the mechanism of spalling is yet to be

fully understood. This is mainly due to the fact that most of the previously developed

models are empirical. Empirical models typically have no mechanistic structural
127

inputs and draw entirely on statistical analysis of measured real-life data to arrive at

models that predict distress or damage.

Although the new transverse spalling model developed under this project will be

strongly based on empirical data, it is nonetheless important to identify the mechanistic

relationships that influence transverse joint spalling. Spalling can be attributed to

several interacting mechanisms caused by tensile stresses imposed on the pavement by

environmental forces and inadequate quality control during construction. Some

mechanistic-based causes of spalling identified in previous research include the

following:

• The combination of repeated temperature cycles and entrapped incompressibles

in a joint. A buildup of compressive stress is created when a joint with

incompressibles is subjected to high temperatures.

• Poor consolidation of the concrete at the joint resulting from poor construction

practices.

• The use of poor quality construction materials (e.g., reactive aggregates, Dcracking aggregates, and non-coated dowels).

• PCC with low entrained air content.

• Severe climatic conditions that cause frequent freezing and thawing and wetting

and drying of the PCC slab, along with use of deicing salts.

• Inaccurate placement of load transfer devices, resulting in breakup of the joint.

The review of the recently developed transverse joint spalling models also

identified a number of variables that significantly influence spalling. A summary of the

significant variables used in past model development (for those models reviewed in

this section) is summarized in table 31. This collective list of variables (or variables

related to these) will be considered in the transverse spalling model development

procedures conducted under this project.

DEVELOPMENT OF A NEW JPCP TRANSVERSE JOINT SPALLING MODEL

Based on the results of the validation process, the transverse joint spalling

validation/improvement effort focused on replacing the current spalling model with a

new empirical model that was not only a function of significant site, design, and
128

Table 31. Summary of variables found to significantly affect JPCP transverse joint

spalling.

Variable

SHRP

P-020(14)

LTPP Data

Analysis(15) CTL(5) RPPR(16)

Age 3 3 3 3

80-kN (18-kip) ESAL's 3 3

Annual temperature range 3

Mean annual air freeze-thaw cycles 3 3 3*

Thermal gradient in PCC slab 3

Relative humidity 3

Freezing index 3

Presence of salt 3

Average annual number of days with

maximum temperature > 32°C (90 °F)

3

Transverse joint spacing 3 3

Transverse joint sealant type 3 3

Height of sealant material 3

PCC slab thickness 3

PCC slab elastic modulus 3

PCC air content 3

PCC compressive strength 3

PCC indirect tensile strength 3

PCC coefficient of thermal expansion 3

Modulus of subgrade reaction (k-value) 3

Subbase friction factor 3

Dowel corrosion potential 3

* The CTL model was based on in-pavement (76 mm [3 in] below the surface) freeze-thaw cycles rather than air

freeze-thaw cycles.

climatic variables, but a function of PRS-related AQC's as well. The specific procedures

used in the development and calibration of a new JPCP transverse joint spalling model

suitable for use within the current PRS methodology included the following:

• Preparation of the model development data set.

• Selection of a suitable model form.

• Selection of appropriate statistical tools for regression and optimization.

• Development of the final IRI model.

The tasks are described in greater detail in the following sections.

Data Preparation

In preparation for the calibration steps of the model development process, all

pertinent GPS-3 data from the LTPP database were compiled into a spalling model

development database. This compiled database was used to link LTPP time-series

spalling data with all climatic- and design-related variables that were believed to

influencing transverse joint spalling. In addition to the linked LTPP data, CTL
129

laboratory data (used in the development of the CTL model discussed previously in

this chapter) were included in the database to ensure that the data for model

development had a wide range of design properties, climatic properties, and distress.

Data assembly was accomplished using Microsoft Access, Microsoft Excel, and the

SAS statistical software.

The LTPP data consisted of 88 pavement sections in 28 States and 2 Canadian

Provinces. A summary of the data making up the final data set, its inference space, and

other statistical characteristics are presented in table 32. The assembled data were

thoroughly evaluated to identify any missing data elements and possible problem

spots in the database (e.g., time-series data with a significant decrease in spalling over

time). Attempts were made to obtain replacements for missing data where possible.

The data set was also checked for anomalies and gross data errors.

Table 32. Summary of GPS-3 JPCP data and CTL laboratory data used in model

development and calibration.

Range

Data Source Variable Min. Max. Mean

Standard

Deviation

Medium- and high-severity

spalling, percent joints 0.0 26.1 1.3 3.8

Age, years 2.0 27.4 13.7 5.2

PCC thickness, in 7.0 14.3 9.8 1.3

Water cement ratio 0.27 0.72 0.45 0.09

Air content, percent 3.8 9.8 5.7 1.1

Compressive strength, psi 3,840 12,488 6,335 1,937

Air freeze-thaw cycles 15 3102 1101 653

LTPP

(146 records)

Sealant type 33 records had preformed sealants

Medium- and high-severity

spalling, percent joints1

0.0 84.0 28.7 27.5

Age, years2 3.3 28.1 11.7 8.1

PCC thickness, in 6.0 6.0 6.0 0

Water cement ratio 0.42 0.50 0.45 0.04

Air content, percent 2.5 4.8 3.7 0.9

Compressive strength, psi 2,720 7,150 4,984 1,595

Total air freeze-thaw cycles3 262 2,250 942 653

CTL

(33 records)

Sealant type No records had a preformed sealant

Notes:

1. CTL data were measured as average length of spalling per joint, percent. This was converted to percent joint

spalled using the assumption that average length of spalling per joint (in percent) is approximately equal to

percentage of spalled joints.

2. An average air freeze-thaw cycle of 80 per year was assumed and used to estimate age for the CTL data.

3. The CTL laboratory study measured the total in-pavement freeze-thaw cycles at a depth of 76 mm (3 in) from

the slab surface. The cumulative number of in-pavement freeze-thaw cycles was converted to total air freeze-
130

thaw cycles by multiplying the measured in-pavement cycles by a factor of 7.5. The 7.5 multiplying factor was

obtained by determining the ratio of air and pavement base freeze-thaw cycles in Illinois.(42)

Selection of a Suitable JPCP Transverse Joint Spalling Prediction Model Form

An S-shaped curve was selected to be the characteristic model form for the new

JPCP transverse joint spalling model because it is representative of the development

and progression of spalling observed when plotting field observations versus time.

The S-shaped curve is constrained to ensure that the predicted percentage of joints

spalled ranges between 0 and 100. The specific chosen model form is the following:

(á*AGE SF) C2 C3

C1

AGE 0.01

AGE %SPALL +

+













+

= (95)

where:

 %SPALL = Percentage joints spalled (medium and high severities).

 ", C1, C2, C3 = Regression constants.

 AGE = Time since construction, years.

 SF = A scaling factor based on site-, design-, and climate-related

 variables that significantly influence spalling.

The scaling factor, SF, in equation 95 accounts for the effect of variables that

significantly influence the development of spalling, including sealant type, PCC mix

properties, PCC air content, air freeze-thaw cycles, precipitation, and PCC slab

thickness. The following model form was selected for defining the scaling factor:

SF = C0 + 81A1 + 82A2 + ... + 8nAn + :1D1 + :2D2 + ... + :nDn (96)

where:

SF = Scaling factor.

Ai = Climate-related variable.

Di = Design- and material- related variable.

C0, 8i, :i = Regression constants.

Statistical Tools for Regression and Optimization

Equation 95 is nonlinear; therefore, nonlinear statistical techniques were utilized for

calibration. The SAS NLIN procedure was selected as the appropriate regression tool

to be used in model development and calibration.

(30) Other SAS procedures, such as

STEPWISE, REG, RSQUARE, and RSREG, were used in selecting the most suitable

variables for incorporation into the model. The SAS NLIN procedure utilized the

Marquardt iterative method to optimize the developed spalling model. Further details

on the Marquardt procedure can be obtained from the SAS/STAT User’s Guide.

(30)
131

Final JPCP Transverse Joint Spalling Model

The final step in the development of the JPCP transverse joint spalling model was

the calibration of equations 95 and 96 (using the nonlinear optimization procedure) to

obtain specific values for the required regression coefficients. Optimization techniques

and regression analysis were used to determine regression coefficients that minimized

the error between the predicting and measured spalling values. The specific procedure

used was as follows:

1. Assign initial values to the variables and parameters in equations 95 and 96.

2. For those assigned values, perform nonlinear regression analysis to find the

values of the spalling prediction model parameters that minimize the error

vector, ,.

3. Repeat step 2 for different values of $ until the error vector is minimized and the

conversion criteria are met (i.e., error is within acceptable limits).

Based on the successful completion of the iterative optimization process, the final

spalling model was determined to be the following:













+













+

= (-12*AGE +SF) 1 1.005

100

AGE 0.01

AGE %SPALL (97)

where:

 %SPALL = Percentage joints spalled (medium and high severities).

 AGE = Time since construction, years.

 SF = Scaling factor based on site-, design-, and climate-related variables.

The scaling factor is defined as the following:

SF = –1400 + 350 * AIR% * (0.5 + PREFORM) + 43.4 * f'c0.4 (98)

– 0.2 * (FTCYC * AGE) + 43 * hPCC – 536 * WC_Ratio

where:

AIR% = PCC air content, percent.

 AGE = Time since construction, years.

PREFORM = 1 if preformed sealant is present, 0 if other sealant types or no sealant.

f'c = PCC slab compressive strength, psi.

FTCYC = average annual number of air freeze-thaw cycles.

hPCC = PCC slab thickness, in.

WC_Ratio = PCC water/cement ratio.

The diagnostic statistics for the spalling model are as follows:
132

N = 179.

R2 = 0.78.

SEE = 6.8 percent of joints.

Plots of the predicted versus measured spalling, and residuals versus predicted

spalling, are shown in figures 36 and 37, respectively. The diagnostic statistics and

both plots verify that the model is effective for predicting JPCP transverse joint

spalling. The R2 of 78 percent and SEE of 6.8 percent are very reasonable given the

large number of LTPP GPS-3 field data (N=146) and CTL laboratory data (N= 33) used

in model development.

MODEL VERIFICATION (SENSITIVITY ANALYSIS)

A sensitivity analysis was conducted on the final spalling model to determine its

reliability for predicting spalling within and outside of the inference space of the

development database. This was accomplished by studying the effects of the various

input parameters on the output generated by the spalling model. The ranges of the

input values used are presented in table 33. Note that the sensitivity analyses were

accomplished by investigating the effects of changing one variable at a time, while

holding all other variables at their mean values. The results obtained were compared

with past empirical data and theoretical observations.

Table 33. Range of values of data used in sensitivity analysis.

Range

Variable Min. Max. Mean

Age, years 0 30 —

PCC thickness, in 8 12 10

Water/cement ratio 0.38 0.50 0.44

Air content, percent 2 7 5.5

Compressive strength, psi 2,500 7,500 5,000

Avg. annual air freeze-thaw cycles 0 160 80

Sealant type Preformed = 1, No sealant or other type = 0

Effect of Air Content

Figure 38 shows a significant reduction in predicted joint spalling corresponding to

an increase in air content from 2 to 7 percent. This trend clearly agrees with past

laboratory observations and other studies that show that increased air content (up to <

12 percent) increases concrete durability and, therefore, reduces durability-related

distresses such as spalling.

(5)
133

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

100

0 2 0 4 0 6 0 8 0 100

Measured Percent Spalled Joints

Predicted Percent Spalled Joints

N = 179

R

2

 = 0.78

SEE = 6.8 percent

Figure 36. Predicted (equation 97) versus measured spalling for the final JPCP

transverse joint spalling model.

-30

-20

-10

0

1 0

2 0

3 0

0 2 0 4 0 6 0 8 0 100

Predicted Percent Spalled Joints

Residual, Percent

Figure 37. Residual versus predicted (equation 97) spalling for the final JPCP

transverse joint spalling model.
134

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

100

0 5 1 0 1 5 2 0 2 5 3 0

Age, yrs

Percent Joints Spalled

2 percent

4 percent

6 percent

8 percent

Sealant = Non-preformed

28-day f'c = 5000 psi

Annual Freeze-Thaw Cycles = 80/year

PCC Thickness = 10 in

Water/Cement Ratio = 0.44

Figure 38. Sensitivity of final JPCP joint spalling model to changes in PCC concrete air

content (measured with air pressure meter).

Effect of PCC Compressive Strength

Figure 39 illustrates the sensitivity of the final spalling model to changes in PCC

compressive strength. The figure clearly shows that an increase in PCC compressive

strength results in a reduction in spalling. This trend is in agreement with observations

from the CTL materials study and the trends of the CTL joint spalling model. This also

agrees with the mechanistic principle that concrete slabs with high compressive

strength have a correspondingly high tensile strength and a reduced potential for

spalling.

(5)

Effect of Joint Sealant Type

Examination of figure 40 shows the influence of preformed sealants on joint

spalling. The figure shows that preformed sealants were better at reducing joint

spalling than other types of sealants (or no sealant). The most likely explanation for

this benefit is the fact that preformed sealants are effective at preventing

incompressibles from infiltrating into the slab joints.

(15,16) This effect has been found in

several previous studies.
135

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

100

0 5 1 0 1 5 2 0 2 5 3 0

Age, yrs

Percent Joints Spalled

2500 psi

5000 psi

7500 psi

Sealant = Non-preformed

Air Content = 6 percent

Annual Freeze-Thaw Cycles = 80/year

PCC Thickness = 10 in

Water/Cement Ratio = 0.44

Figure 39. Sensitivity of final JPCP joint spalling model to changes in PCC 28-day

compressive strength.

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30

Age, yrs

Percent Joints Spalled

Non-preformed

Preformed

Air Content = 6 percent

28-day f'c = 5000 psi

Annual Freeze-Thaw Cycles = 80/year

PCC Thickness = 10 in

Water/Cement Ratio = 0.44

Figure 40. Sensitivity of final JPCP joint spalling model to changes in joint sealant type.
136

Effect of PCC Slab Thickness

Figure 41 shows that transverse joint spalling increases as slab thickness decreases.

This trend is most likely explained by the fact that thicker slabs generally result in

stiffer pavements that are less susceptible to excessive deflections and strains under

loads.

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

100

0 5 1 0 1 5 2 0 2 5 3 0

Age, yrs

Percent Joints Spalled

8 in

10 in

12 in

Sealant = Non-preformed

Air Content = 6 percent

28-day f'c = 5000 psi

Annual Freeze-Thaw Cycles = 80/year

Water/Cement Ratio = 0.44

Figure 41. Sensitivity of final JPCP joint spalling model to changes in PCC slab

thickness.

Effect of Total Air Freeze-Thaw Cycles

The climate-related variable found to have a significant effect on the prediction of

joint spalling for JPCP was the cumulative number of air freeze-thaw cycles. Figure 42

shows the effect of air freeze-thaw cycles on predicted transverse joint spalling.

Pavements in the freeze regions exhibited more spalling than those in the nonfreeze

regions. Explanations for this trend include the fact that pavements in freeze regions

are subjected to repeated freezing and thawing conditions. When water is present in

the pores of the concrete, this repeated freezing and thawing typically causes the

concrete slab to deteriorate, especially for concrete with lower entrained air contents. In

addition, the typical presence of deicing salts on pavements in freeze regions has been

found to accelerate the concrete scaling and the subsequent development of

spalling.

(10,13,15,16)
137

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

100

0 5 1 0 1 5 2 0 2 5 3 0

Age, yrs

Percent Joints Spalled

0 per year

40 per year

80 per year

120 per year

160 per year

Sealant = Non-preformed

Air Content = 6 percent

28-day f'c = 5000 psi

PCC Thickness = 10 in

Water/Cement Ratio = 0.44

Figure 42. Sensitivity of final JPCP joint spalling model to changes in cumulative air

freeze-thaw cycles.

Effect of Water/Cement Ratio

The effect of water/cement ratio on JPCP joint spalling is shown in figure 43. The

trends illustrate that as water/cement ratio increases, so does spalling. However, in

comparison with other input variables, the sensitivity of the spalling model to changes

in water/cement ratio is relatively small.

SUMMARY

A new nonlinear empirical JPCP transverse joint spalling model was developed

under this study for use within the current PRS procedure. The model is deemed

suitable for use with the current PRS procedure because it incorporates PRS-related

AQC's (PCC concrete strength, slab thickness, and air content) and other design-,

materials-, and climatic-related variables that were found to significantly influence

spalling. The model has a good correlation (R2 = 0.78) and a low SEE (6.8 percent) for a

large number of data points (N = 179).
138

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

100

0 5 1 0 1 5 2 0 2 5 3 0

Age, yrs

Percent Joints Spalled

0.38 w/c ratio

0.44 w/c ratio

0.50 w/c ratio

Sealant = Non-preformed

Air Content = 6 percent

28-day f'c = 5000 psi

Annual Freeze-Thaw Cycles = 80/year

PCC Thickness = 10 in

Figure 43. Sensitivity of final JPCP joint spalling model to changes in water-cement

ratio.
139

CHAPTER 7: IRI MODEL

INTRODUCTION

Road roughness has been defined as “the variation in surface elevation that induces

vibrations in traversing vehicles.”(43) Previous studies have shown that 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, users'

complaints about rough roads are often a key factor in the rehabilitation decisions that

are made by State highway agencies.

Although many objective methods for measuring pavement smoothness have been

developed since the AASHO Road Test, the most widely accepted index used today is

IRI.

(44) IRI is defined as the accumulated suspension vertical motion divided by the

distance traveled as obtained from a mathematical model of a simulated quarter-car

traversing a measured profile at 80 km/h.(44) Since the World Bank first published

guidelines for conducting and calibrating pavement smoothness measurements, IRI has

been adopted as a standard for the FHWA Highway Performance Monitoring System

(HPMS).(45)

Because of the widespread usage and acceptance of IRI as the smoothness

measurement standard for construction and pavement management, the IRI was

incorporated into the current PRS methodology (both as a measurement of initial

smoothness and for prediction over time). This chapter describes the attempted

validation of the chosen best-available IRI model (identified in chapter 2), as well as the

specific procedures used in the development of a new IRI model suitable for use within

the current PRS methodology (and inclusion into PaveSpec 3.0).

CURRENT PRS IRI MODEL

The selected best-available IRI model was that developed in 1999 by Hoerner et al.

and used in the previously developed PaveSpec 2.0 software.

(10) This particular model

was selected for validation/improvement as it was a function of both initial IRI and key

distress indicators. The model was developed using distress data and backcasted

initial IRI's (backcasted from time-series IRI data) from the LTPP database. (Note: The

model outputs and inputs are presented in English units.)

IRI = INITIRI + (4.8389 * Age) – (0.047 * Age * INITIRI) + (0.7165 * (99)

%CRACKED) + (359.956 * FAULT) + (0.3828 * %SPALL)

where:
140

IRI = International roughness indicator, in/mi.

INITIRI = Initial IRI, in/mi.

Age = Number of years since construction, years.

%CRACKED = Percentage of slabs cracked due to transverse fatigue cracking

(expressed as a number between 0 and 100).

FAULT = Average joint faulting per joint, in.

%SPALL = Percentage of medium- and high-severity spalled joints (expressed as

a number between 0 and 100).

Statistics:

N = 122.

R2 = 0.51.

SEE = 28.35 in/mi.

ATTEMPTED VALIDATION OF THE CURRENT PRS IRI MODEL

Before any new model development or calibration techniques were tried, the

research team attempted to validate the current PRS IRI model with a new independent

data set. The validity of the current IRI model was assessed by:

• Reviewing plots of predicted versus measured IRI.

• Reviewing plots of residuals versus predicted IRI.

• Analyzing diagnostic statistics such as the R2 and the SEE to determine the

goodness-of-fit of the model when the independent data set is used.

• Identifying any general observed weaknesses in the model.

The independent data used in the initial model validation process consisted of JPCP

data from the LTPP experiment database (GPS-3 data only). It consisted of 184 timeseries points from 81 pavement test sections located in 26 States and 3 Canadian

Provinces. A summary of the validation data is presented in table 34.

Table 34. Summary of JPCP LTPP data used in the initial validation of the current IRI

model.

Range

Variable Min. Max. Mean

Standard

Deviation

Initial IRI, in/mi 27.2 164.1 74.9 27.6

Pavement age, years 2.4 33.7 14.1 6.0

Cracked slabs, percent 0.0 65.1 5.3 11.9

Average joint faulting per joint, in 0.00 0.35 0.05 0.07

Spalled joints, percent 0.0 100.0 19.6 30.3
141

The validation data set was used in the current IRI model to obtain predicted IRI

values for each section, while associated measured IRI values were obtained directly

from the LTPP database. Figures 44 and 45 show plots of predicted versus measured

IRI, and residuals versus predicted IRI, respectively. The key results obtained from the

initial validation process were as follows:

• The model form is suitable for inclusion in the PRS methodology as it is a

function of both initial IRI and other predicted distress indicators.

• A comparison of the measured and predicted spalling (using the independent

LTPP data) showed a low R2 value of 0.40 percent and a SEE of 27.5 in/mi.

• The plot of residuals versus predicted IRI shows a definite trend, indicating that

one or more significant variables are not being considered in the current model.

0

50

100

150

200

250

300

0 50 100 150 200 250 300

Measured IRI, in/mi

Predicted IRI, in/mi

N = 184

R

2

 = 0.40

SEE = 27.5 in/mi

Figure 44. Predicted (equation 99) versus measured JPCP IRI (using the LTPP

validation data set).

Given the relatively poor diagnostic statistics and the observed trend in the plot of

residuals versus predicted IRI, it was concluded that a simple calibration of the existing

model would not significantly improve the model’s prediction ability. Therefore, the

IRI model improvement effort focused on developing a new IRI model that is a

function of initial IRI, other key pavement distress indicators, and additional site and

climatic variables. The model was developed using the data available in the newly
142

compiled PRS national database. The details of the IRI model development effort are

described in the following sections.

-150

-100

-50

0

50

100

150

0 50 100 150 200 250 300

Predicted IRI, in/mi

Residual, in/mi

Figure 45. Residual versus predicted (equation 99) JPCP IRI (using the LTPP

validation data set).

EXISTING JPCP IRI MODELS

In preparation for the model development process, a number of similar IRI models,

developed under previous research studies, were reviewed. A review of previous

models not only provided guidance as to what variables should be considered for

inclusion in the new model, but also added expert knowledge into the model

development process at an early stage. During the review process, specific attention

was paid to the engineering significance of the variables. The details of each of these

reviewed models are described separately in the following sections.

SHRP P-020 JPCP IRI Models(14)

In a SHRP study conducted by Simpson et al. in 1994, titled Early Analysis of LTPP

General Pavement Studies Data, two different IRI models were developed—one for

doweled JPCP and one for non-doweled JPCP.

(14) Each of these models is presented

below:
143

SHRP P-020 IRI Model for JPCP With Dowels

IRI = 105.9 + 159.1 * 











KSTATIC

AGE + 2.167 * JTSPACE (100)

– 7.127 * THICK +13.49 * EDGESUP

where:

IRI = International roughness index, in/mi.

AGE = Age since construction, years.

KSTATIC = Mean backcalculated static k-value, psi/in.

JTSPACE = Mean transverse joint spacing, ft.

THICK = Concrete slab thickness, in.

EDGESUP = Edge support (1 = tied PCC shoulder, 0 = any other shoulder type).

Statistics:

N = 21.

R2 = 0.55.

SEE = 19.06 in/mi.

An analysis of the P-020 doweled IRI model showed that increases in AGE and

JTSPACE caused an increase in IRI, whereas increases in KSTATIC and THICK resulted

in a decrease in IRI. The only variable that appeared to have a trend that was opposite

of what was expected is EDEGSUP. The model indicates that a pavement with a tied

PCC shoulder will exhibit higher IRI than a similar pavement with no edge support.

No climatic variables were found to be significant enough for inclusion in the model.

SHRP P-020 IRI Model for JPCP Without Dowels

IRI = 38.85 + 12.89 * CESAL + 0.2217 * FTCYC + 1.498 * PRECIP (101)

– 10.96 * BASE – 13.69 * SUBGRADE

where:

IRI = International roughness index, in/mi.

CESAL = Cumulative 80-kN (18-kip) ESAL's in traffic lane, millions.

FTCYC = Mean annual air freeze-thaw cycles.

PRECIP = Mean annual precipitation, in.

BASE = Base type (1 = treated granular material [with asphalt cement] or lean

concrete, 0 = untreated granular material).

SUBGRADE = AASHTO subgrade classification (0 = coarse grained [A-1, A-2, A-3],

1 = fine grained [A-4, A-5, A-6, A-7]).

Statistics:
144

N = 28.

R2 = 0.64.

SEE = 31.29 in/mi.

The non-doweled IRI model indirectly relates IRI to other distress indicators by

making use of the CESAL's variable (other distress indicators typically increase with

age or ESAL applications). The model indicates that IRI increases linearly with an

increase in CESAL's. The climatic influence on IRI is addressed with the inclusion of

FTCYC and PRECIP. Specifically, IRI increases with increases in both FTCYC and

PRECIP. The effect of slab support conditions on IRI is accounted for with the

inclusion of the BASE and SUBGRADE variables into the model. An investigation of

the model shows that pavements with treated base materials will have lower IRI values

than pavements with untreated bases, when all other variables are held constant. In

addition, the model indicates that pavements constructed on fine-grained subgrades

will develop higher IRI values over time than similar pavements constructed on coarsegrained subgrades.

As evidenced by the diagnostic statistics, there is "considerable room for

improvement of this model."(14) In addition, several other variables (e.g., transverse

joint spacing) that had been identified in previous research studies as having a

significant influence on IRI were absent from this model.

LTPP Data Analysis JPCP IRI Model(15)

In 1999, Titus-Glover et al. developed an IRI model for JPCP under an FHWA LTPP

data analysis contract.

(15) This model is the following:

IRI = 82.56 + KESAL0.4 * (0.01 * WETDAYS + 0.72 * ZONE) + AGE0.4 * (102)

(0.00506 * FI + 1.57 * 10–6 * EPCC – 3.5 * SUBGRADE

– 3.07 * DOWELDIA)

where:

IRI = International roughness index, in/mi.

KESAL = Cumulative 80-kN (18-kip) ESAL's in traffic lane, thousands.

WETDAYS = Number of days precipitation is greater than 0.5 in.

ZONE = LTPP climatic zone (1 = freezing climate, 0 = nonfreezing climate).

AGE = Age since construction, years.

FI = Freezing index, °F-days.

EPCC = PCC elastic modulus, psi.

SUBGRADE = Subgrade type (1 = coarse grained, 0 = fine grained).

DOWELDIA = Dowel diameter, in.

Statistics:
145

N = 155.

R2 = 0.50.

SEE = 22.0 in/mi.

The review of this IRI model showed that it was a function of traffic and age, as well

as many climatic, site, and support condition variables. For the continuous variables,

the model showed that increases in KESAL, WETDAYS, AGE, FI, and EPCC caused an

increase in IRI, whereas an increase in DOWELDIA resulted in a decrease in IRI. For

the ZONE variable, the model indicated that pavements experiencing a freezing

climate showed higher IRI values than similar pavements in nonfreeze climates.

Similarly, pavements constructed on a fine-grained subgrade had higher IRI values

than pavements with coarse-grained subgrades.

FHWA RPPR JPCP IRI Model(16)

The FHWA RPPR study investigated the direct effects of distress on IRI.

(16) This

model, based on data in the RPPR database, is as follows:

IRI = 99.59 + 2.6098 * TFAULT + 2.2802 * TCRACK3 + 1.8407 * %SPALL (103)

where:

IRI = International Roughness Index, in/mile.

TFAULT = Total cumulated joint faulting per mile, in/mile.

TCRACK = Total number of transverse cracks, number of cracks per mile.

%SPALL = Percentage of joints spalled (medium and high severity), expressed as

a number between 0 and 100.

Statistics:

N = 144.

R2 = 0.61.

SEE = 64.11 in/mile.

A model such as this one is ideal for inclusion in a PRS because of its direct

dependence on other developed distress indicators. However, one very serious

limitation of the RPPR IRI model is that initial IRI is not included as a direct variable.

Overview of JPCP IRI Models

A review of past JPCP IRI models indicated that increasing quantities and severities

of JPCP distress such as faulting, transverse cracking, and joint spalling will greatly

contribute to a loss of pavement smoothness (increase in IRI) over time. Each of the

reviewed models considers the influence of these distresses directly or indirectly
146

through the inclusion of many design, site, and climatic variables that influence the

development of these other distresses.

One key factor that is especially significant in the prediction of IRI over time is the

initial IRI measured at the time of construction.

(41,45) Results from the NCHRP 1-31

project showed that future smoothness is significantly related to initial smoothness for

all pavement types and AC overlays.(41,45) For PCC pavements, the study found that the

initial smoothness significantly affected future smoothness on more than 80 percent of

the projects evaluated. This finding suggests that pavements that are constructed

smoother will typically stay smoother over time. Other more recent studies have

confirmed these results.

(46,47)

The review of the previously developed IRI models identified many different

variables that influence the occurrence and progression of JPCP distress, and therefore

IRI. A summary of those distresses and variables used in past model development

efforts (for those models reviewed in this section) is included in table 35. This

collective list of variables (or variables related to these) will be considered in the IRI

model validation/development procedures.

Table 35. Summary of distresses and variables identified in previous research as

significantly affecting JPCP IRI.

Distress/Variable

SHRP P020(14)LTPP Data

Analysis(15) RPPR(16)

DISTRESS

Transverse joint faulting 3

Transverse slab cracking 3

Transverse joint spalling 3

DISTRESS-RELATED VARIABLES

Age 3

Cumulative 80-kN (18-kip) ESAL's 3 3

Mean annual air freeze-thaw cycles 3

Mean annual precipitation 3

Average annual number of wetdays 3

LTPP climatic zone 3

Freezing index 3

Transverse joint spacing 3

PCC slab thickness 3

PCC slab elastic modulus 3

Base type 3

Mean backcalculated modulus of

subgrade reaction (k-value)

3

Subgrade type 3 3

Presence of tied PCC shoulder 3

Dowel diameter 3
147

DEVELOPMENT OF A NEW JPCP IRI MODEL

The specific procedure used in the development and calibration of a new IRI model

suitable for use within the current PRS methodology involved the following:

• Preparation of the model development data set.

• Selection of a suitable model form.

• Selection of appropriate statistical tools for regression and optimization.

• Development of the final IRI model.

The tasks are described in greater detail in the following sections.

Data Preparation

The first step in the IRI model development process was the creation of the required

model development database. Data preparation and assembly procedures for the

development of the IRI model consisted of the following tasks:

1. Identify and retrieve all variables potentially related to the development of JPCP

IRI.

2. Identify missing/erroneous data elements and merge LTPP design, climatic, and

profile data sets.

3. Backcast initial IRI values from existing IRI time-series data.

4. Explore and clean data.

The details of these steps are described in the following sections.

Database Assembly

In preparation for the calibration steps of the model development process, all

pertinent GPS-3 data from the LTPP database were compiled into an IRI model

development database. The GPS pavements are existing JPCP sections nominated by

State and provincial departments of transportation (DOT) and selected by SHRP and

the FHWA's Pavement Performance Division for inclusion into the LTPP data collection

program. To meet the experimental criteria, pavement section materials and structural

designs must reflect standard engineering practices in the United States and

Canada.

(48,49,50)

For the data collected and recorded in the LTPP Information Management System

(IMS), clear procedures and standards were established and are observed. These

procedures help guarantee the consistency and the quality of the data collected.

Information is also available showing the data reliability for a set of data. Throughout
148

the selection, gathering, and recording process, the basic philosophy of the LTPP

program has been to provide high-quality data collected in a statistically correct and

consistent manner.

(48,49,50)

The data sets from the LTPP IMS used in model development are

automated/manual distress and longitudinal profile. Automated and manual distress

data provide a measure of pavement condition, primarily on the surface. The data

include the frequency and severity of distresses such as cracking (longitudinal,

transverse, durability), pumping, faulting, joint damage, surface deformation, and

surface defects. Maintenance activities such as patching are also recorded.

( 48,49,50) The

primary means used to obtain the surface distress data stored in the LTPP IMS is visual

inspection of the pavement surface or visual interpretation of high-resolution 35-mm

photographic images of the pavement surface.(48,50) The guidelines for distress data

collection are contained in the Distress Identification Manual for the Long-Term Pavement

Performance Project.

(51) The surface distress data are collected every 1 to 2 years.(50)

Longitudinal profile data show the relative elevation of the pavement along the

wheel path. The IRI, Mays Index, Root Mean Square Vertical Acceleration (RMSVA),

and an approximation of slope variance are also computed from the data. The raw data

include the X-Y profile data for at least five repeat runs for each wheelpath. It is stored

separately from the statistics.

(48,49,50) LTPP regional offices are responsible for collecting

longitudinal profile data using profilometers or dipsticks.(51) The longitudinal profile

of each LTPP test section is measured approximately once per year. Sections for the

detailed study of seasonal effects are tested quarterly every other year.

(50)

Data assembly was accomplished using Microsoft Access©, Microsoft Excel©, and the

SAS/STAT statistical software.

Identification of Missing/Erroneous Data Elements and Merging of LTPP Data Sets

The second step of the data preparation procedure involved merging the LTPP

section design and climatic data with corresponding profile and distress values. Prior

to merging, the individual data sets were examined thoroughly to identify missing or

erroneous data. As a result of this data review effort, the following were observed:

• The majority of distress and profile survey dates did not coincide (i.e., distress

surveys were not conducted on the same days as profile surveys).

• The LTPP profile database contained no initial IRI information.

• The profile data had only minimal errors since they had recently been cleaned as

part of the ongoing LTPP data analysis project.

• The faulting data had minimal errors since they had recently been cleaned as

part of the ongoing LTPP data analysis project.
149

• Distress data had some errors, depending on which data set was used (manual

or automated). The most reliable distress data for JPCP distress were in the

MON_DIS_JPCC_REV table, so this information was used for model

development.

Based on these observed results, it was determined that two issues needed to be

resolved before a successful merger of the data sets could be accomplished. First,

reasonable estimates of initial IRI needed to be determined, and second, discrepancies

between survey and profile dates had to be resolved. Two methods were proposed for

resolving these issues:

• Assuming that there are no significant changes in measured profile or distress

within 120 days of data collection, profile and distress data collected during this

period can be merged with minimal error.

• Models could be developed based on the pavement age and measured IRI for

each pavement section with time-series IRI data, then used to estimate IRI

corresponding to distress survey dates by interpolation or extrapolation. The

models developed may also be used for obtaining estimates of initial IRI by

extrapolating to age = 0 years.

The second method was adopted for use in estimating initial IRI, as well as IRI at the

time of distress surveys.

Backcasting of Initial IRI Values

As noted, the LTPP database did not contain initial IRI values. Therefore, initial IRI

had to be backcasted from IRI time-series data. The specific process chosen to backcast

initial IRI values was as follows:

1. Determine a suitable model form for backcasting initial IRI.

2. Backcast initial IRI values for each pavement section using available time-series

IRI data.

3. Evaluate the reasonableness of backcasted initial IRI values by reviewing trends

and slopes of time-series data, comparing backcasted values with measured

initial IRI from LTPP SPS pavement sections, and reviewing diagnostic statistics

from the fitted model.

4. Compare the distribution (mean and variance) of backcasted initial IRI to typical

initial IRI values measured from newly constructed LTPP SPS pavement

sections.
150

Various model forms (e.g., linear, exponential, logarithmic, and polynomial) were

evaluated for backcasting initial IRI with pavement age as the independent variable

and measured IRI as the dependent variable. The functional form was thus:

IRI = f(age) (104)

Initial IRI was therefore the IRI at age = 0 years. The typical pavement section used in

the analysis was more than 10 years old and had three or more time-series data points.

Using a linear model for backcasting initial smoothness was found to be the most

practical since there were no available data close to the construction date (less than 3

years). The linear model form used for interpolating and extrapolating smoothness

values was as follows:

IRI = "AGE + $ (105)

where:

" = Slope.

AGE = Pavement age, in years.

$ = Regression constant equivalent to initial smoothness.

Figure 46 shows an example of a linear model fitted to IRI time-series data for the

purpose of backcasting an initial IRI value.

Smoothness (IRI, m/km)

X

X

X

X

X

X

IRI 0

0 Age, y r

Linear model (IRI = IRI

0

 + β * Age) used in backcasting

Figure 46. Example of the linear model method used to backcast an initial IRI from

time-series data.

The reasonableness of the backcasted initial IRI values was evaluated by

determining:

• If there was a significant difference in mean initial IRI values for the backcasted

JPCP data and reference-measured initial IRI data.
151

• If there was a significant difference in variance in the backcasted and measured data

sets.

• If the diagnostic statistics of the linear models used in interpolating or extrapolating

IRI values are reasonable.

The reference-measured initial IRI values used for comparison were obtained from the

LTPP SPS database. IRI values measured within the first 12 months of pavement

construction were used. Analysis of variance (ANOVA) and t-test comparisons were used in

determining if there were significant differences in the means and variance from the

reference-measured and backcasted initial IRI values. The results are presented in table 36.

The t-test results for comparison of the mean initial IRI and variance values show that there

are no significant differences between measured initial IRI (from SPS pavements) and

backcasted initial IRI for JPCP. Backcasted initial IRI for JPCP showed a higher variance than

that of the measured SPS data; however, the variance was not excessive (as shown in figure

47).

Table 36. Summary of t-test results for the comparison of measured and backcasted initial

IRI for JPCP.

Data Set N Mean IRI

Std. Dev.

IRI

Std. Error

IRI Min. IRI Max. IRI

Backcasted (GPS-3) 73 1.227 0.39 0.0465 0.389 2.246

Measured (SPS) 97 1.252 0.28 0.0288 0.758 2.094

Variances T DF Prob>|T|

Unequal -0.4608 124.2 0.6457

Equal -0.4826 168.0 0.6300

For H0: variances are equal, F' = 1.96 DF = (72,96) Prob>F' = 0.0021

0

0.4

0.8

1.2

1.6

0.0 0.5 1.0 1.5 2.0 2.5

Initial IRI, m/km

Frequency

GPS-3

SPS

Figure 47. Initial IRI distribution for measured (SPS) and backcasted JPCP (GPS-3) data.
152

Measured initial IRI for SPS sections generally ranged from 0.5 to 2.0 m/km. This

range of values was adopted as the reasonable range for backcasted values, and values

out of this range were assumed to be outliers.

The final step in evaluating the quality of the backcasted initial smoothness values

was to determine if there was any correlation between the backcasted initial IRI values

and the current age of pavement sections. Bivariate plots of initial smoothness versus

age were developed for the LTPP GPS-3 data to determine if there was any correlation.

Figure 48 shows no significant trends between initial IRI and age for JPCP. The

backcasted data were therefore determined to be suitable for model development.

0.5

1.0

1.5

5

2.0

0 5 1 0 1 5 2 0 2 5 3 0

Age, yrs

Estimated Initial IRI, m/km

Figure 48. Plot of estimated initial backcasted IRI versus section age for JPCP.

After the data were merged, the assembled database was evaluated to identify

possible problem spots (such as time-series data with a significant decrease in IRI with

time). Attempts were made to obtain replacements for missing data where possible.

The data set was also checked and cleaned for anomalies and gross data error. A

summary of the variables initially considered for inclusion into the new IRI model, and

their statistical characteristics, is presented in table 37.

Selection of a Suitable JPCP IRI Prediction Model Form

Clearly, several pavement distresses have a significant effect on IRI and should be

used in modeling and predicting IRI over time. The general hypothesis to be used in

the proposed IRI model is that the various distresses resulting in significant changes in

IRI should be represented by separate components within the model. The chosen

structure for the IRI model is the following:
153

Table 37. Summary of GPS-3 JPCP data considered in the IRI model development and

calibration procedures.

Range

Distress/Variable Min. Max. Mean

Transverse cracking,1 percent slabs 0 42 3

Corner cracks,1 percent slabs 0 20 1

Transverse joint spalling,2 percent joints 0 100 16

Total transverse joint faulting, mm/km 0 1367 230

Annual mean temperature, °C 5.1 21.8 10.2

Freezing index, °C days 0 1862 301

Percent subgrade passing 0.075-mm sieve 1 98 39.5

Annual mean precipitation, mm 142 1542 897

IRI (estimated initial), m/km 0.4 1.8 1.2

IRI (measured overtime), m/km 0.8 3.6 1.7

1

 Transverse cracking and corner cracks (all severities) were combined to estimate total cracking.

2

 Only medium- and high-severity spalling were considered.

IRI(t) = IRI0 + a1D(t)1 + a2 D(t)2 + ............ + an D(t)n + bn SITE(t) (106)

where:

IRI(t) = Pavement IRI over time, in m/km.

IRI0 = Initial IRI, in m/km.

ai, bj = Regression constants.

D(t)I = i

th distress at a given time.

SITE(t) = Site factor at a given time.

The general model form proposed was based on existing smoothness models that

show an additive combination of initial smoothness and the development of distresses

over time.

Empirical studies have identified several pavement site conditions (climate,

subgrade, and traffic) that affect smoothness. Such identified variables can be used as

the basis for developing mechanistic clusters for improving smoothness predicted from

distress alone. Some of the site condition variables that affect smoothness are as

follows:

• Traffic.

• Age.

• Freezing index.

• Subgrade soil type.

• Annual mean temperature.

• Number of air freeze-thaw cycles.
154

• Mean annual precipitation.

• Number of wet days.

The general hypothesis to be used in the proposed smoothness models is that a site

factor (SITE) defined by the properties of the pavement location (e.g., age, freezing

index, subgrade soil type) will significantly improve on the prediction capability of the

models. The proposed structure of the site factor is as follows:

SITE = $ * AGE * (A1* A2 * ... An) (107)

where:

SITE = Site factor.

AGE = Pavement age, years.

Ai = Variables representing the temperature, moisture, and subgrade

properties at the pavement location.

Statistical Tools for Regression and Optimization

The SAS NLIN was selected as the appropriate regression tool to be used in final

model calibration because the procedure is versatile and allows for constraining model

coefficients where required (e.g., initial IRI should always have a coefficient of 1.0).

(30)

Other SAS procedures, such as STEPWISE, REG, RSQUARE, and RSREG, were used in

preliminary model development for determining and selecting the most suitable

variables for incorporation into the final model. The SAS NLIN Marquardt algorithm

was used in the optimization of the IRI model.

Final JPCP IRI Model

The assembled JPCP data were explored to learn more about the suitability of

individual distresses (at different levels of severity) for model development. The final

model form was determined by conducting a comprehensive stepwise regression

analysis of the cleaned data in order to evaluate the preliminary relationships between

the measured smoothness, backcasted initial smoothness, and distress. A site factor

(SITE) was included in the model as a method of incorporating the effects of age,

freezing index, and percent subgrade passing 0.075-mm (#200) sieve. The final JPCP

IRI model is as follows (Note: the final IRI model is expressed in metric units):

IRI = IRI0 + 0.013 * %CRACKED + 0.007 * %SPALL + (108)

0.001 * TFAULT + 0.03 * SITE

where:

IRI0 = Initial smoothness measured as IRI, m/km.
155

%CRACKED = Percentage of slabs with transverse cracking and corner cracks (all

severities) (expressed as a number between 0 and 100).

%SPALL = Percentage of joints with spalling (medium and high severities)

(expressed as a number between 0 and 100).

TFAULT = Total joint faulting cumulated per km, mm.

SITE = Site factor = AGE * (1 + FI)

1.5 * (1+P0.075) * 10–6

.

AGE = Pavement age since construction, years.

FI = Freezing index, °C-days.

P0.075 = Percentage of subgrade material passing the 0.075-mm (#200) sieve

(expressed as a number between 0 and 100).

Statistics:

N = 183.

R2 = 0.70.

SEE = 0.35 m/km.

Additional model development statistics are presented in table 38. Plots of

predicted versus actual IRI and residuals versus predicted IRI are presented in figures

49 and 50, respectively. The R2 and other diagnostic statistics for the model are

reasonable and verify that the model provides reasonable predictions of IRI for JPCP.

Table 38. Diagnostic statistics for JPCP IRI model.

Distress Variable Severities

tcalc for H0:

Parameter = 0

Probability

tcalc > t0.05

Is Distress/Site

Variable

Significant?*

Initial IRI — 9.569 0.0001 Yes

Cracking (L, M, H) 1.99 0.0481 Yes

Transverse joint spalling (M, H) 2.955 0.0036 Yes

Faulting — 13.836 0.0001 Yes

Site factor — 10.735 0.0001 Yes

* Significance level = 5 percent.

MODEL VERIFICATION (SENSITIVITY ANALYSIS)

A sensitivity analysis was conducted on the final IRI model to determine its

reliability for predicting IRI within and outside of the inference space of the database

used in model development. This was accomplished by studying the effects of the

various input parameters on the output generated by the final IRI model.

Effect of Initial IRI

Initial IRI is not only an indicator of overall quality of construction, but all other

things being equal, new pavements constructed with a lower IRI (smoother profile) will

last longer than those constructed with a higher IRI. An analysis of the JPCP data
156

contained in the LTPP database shows that initial IRI typically ranges from 0.5 to 2.0

m/km.

(47) Figure 51 illustrates the sensitivity of the final IRI model to changes in initial

IRI and percent cracked slabs.

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Measured IRI, m/km

Predicted IRI, m/km

N = 184

R2 = 0.72

SEE = 0.40 m/km

Figure 49. Predicted (equation 108) versus measured IRI for the final JPCP IRI model.

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Predicted IRI, m/km

Residual, m/km
157

Figure 50. Residuals versus predicted (equation 108) IRI for the final JPCP IRI model.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 100

Percent Slabs Cracked (L, M, H-severity), Percent

IRI, m/km

IRI0 = 0.5 m/km

IRI0 = 0.9 m/km

IRI0 = 1.5 m/km

IRI0 = 2.0 m/km

Percent joint spalled = 0 percent

Total joint faulting = 0 mm

FI = 300 

o

C days

Percent passing 0.075-mm sieve = 40

Age = 10 yrs

Figure 51. Sensitivity of the final JPCP IRI model to changes in initial IRI and percent

cracked slabs.

Effect of Transverse Slab Cracking

Transverse cracks can occur at the midslab of JPCP slabs parallel to the joint.

Typically, midslab cracks begin as a single crack at the edge of the slab that propagates

through the entire slab as traffic is applied to the pavement.

(15,52) Transverse cracks

increase pavement roughness as the cracks fault and spall and there is a general

breakup of the pavement.(15,52) 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, which normally results

in erosion of the base and faulting, increasing deflections and resulting in an additional

increase in IRI.

(52)

Cracks are not always perpendicular to the centerline of the pavement but can occur

close to the joint, diagonally from the slab shoulder edge of the pavement to the joint.

This form of cracking is called corner cracks.

(51) Corner cracks normally are initiated

from the top of the PCC slab and progress downward (i.e., top-down cracking) as the

pavement foundation erodes, 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.(13) This

results in excessive deflection of the slab corners and a corresponding increase in the
158

tensile stresses at the top of the PCC slab. The tensile stresses cause the initiation of

micro-cracks, and repeated loading propagates these cracks through the PCC slab.

The occurrence of corner cracks results in an increase in IRI because the developed

cracks typically fault and spall, leading to a general breakup and deterioration of the

pavement. This decreases serviceability and user comfort and results in costly

rehabilitation. Once corner cracks become badly spalled, they contribute to joint

deterioration, resulting in joint seal damage, infiltration of water into the pavement

foundation, pumping, and faulting.

The effect of percent slabs cracked (transverse and corner) on IRI over time was

shown previously in figure 51. Specifically, this plot shows that IRI increases as the

percentage of slabs with cracking increases for any given age. This plot confirms the

trends observed in previous research.

(16)

Effect of Transverse Joint Spalling

As was stated in chapter 6, spalling is the breakdown or disintegration of a PCC

slab's edges at transverse joints, usually resulting in the removal of sound concrete.

(15,41)

Several field studies have observed that joint spalling may be due to the deterioration

of the concrete material from environmental factors and from infiltration of

incompressibles.(16,19)

Spalling (medium and high severity) eventually causes a decrease in the

smoothness of the pavement, resulting in a need for costly rehabilitation. Figure 52

shows the effect of the percentage of joints spalled (and initial IRI) on the development

of IRI over time.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 10 20 30 40 50 60 70 80 90 100

Percent Joints Spalled, Percent

IRI,

m/

km

IRI0 = 0.5 m/km

IRI0 = 0.9 m/km

IRI0 = 1.5 m/km

IRI0 = 2.0 m/km

Percent slabs cracked = 0 percent

Total joint faulting = 0 mm

FI = 300 oC days

Percent passing 0.075-mm sieve = 40

Age = 10 yrs

Figure 52. Sensitivity of the final JPCP IRI model to changes in percent joints spalled and

initial IRI.
159

Effect of Transverse Joint Faulting

As was discussed in chapter 4, faulting is the result of a combination of poor load

transfer across a joint or crack, heavy axle loads, free moisture beneath the pavement,

and pumping of the supporting base, subbase, or subgrade material from underneath

the slab.

(15,53) It is primarily caused by the erosion of the supporting material from

underneath the leave slab or treated base and a buildup of the loose material under the

approach slab at a joint or crack. It is the difference in elevation between the adjacent

slabs across a transverse joint or crack. Excessive faulting will greatly reduce the

smoothness of a JPCP and will appreciably increase user discomfort. The influence of

pavement joint faulting on smoothness of JPCP, as depicted by the model, is shown in

figure 53.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 150 300 450 600 750 900 1050 1200

Total Transverse Joint Faulting per km, mm

IRI, m/km

IRI0 = 0.5 m/km

IRI0 = 0.9 m/km

IRI0 = 1.5 m/km

IRI0 = 2.0 m/km

Percent slabs cracked = 0 percent

Percent joints spalled = 0 percent

FI = 300 

o

C days

Percent passing 0.075-mm sieve = 40

Age = 10 yrs

Figure 53. Sensitivity of the final JPCP IRI model to changes in total joint faulting per

km and initial IRI.

Effect of Pavement Site Conditions

The influence of pavement site conditions on JPCP IRI is depicted by including a

cluster of site-related variables in the IRI prediction model. Freezing index and percent

subgrade material passing the 0.075-mm (#200) sieve were found to be two site-related

variables that significantly influence IRI.

Freezing index was multiplied by pavement age to provide a cumulative freezing

index experienced by the pavement. Age can also be assumed to account for the
160

presence of distresses such as settlement, frost heave, swelling soils, scaling, and

durability problems that are not included in the smoothness model. Pavement age is

therefore an alias variable accounting for the effects of hidden factors that influence

pavement smoothness.

Figures 54 and 55 show that IRI increases with increases in freezing index and

amount of subgrade fines (percent passing the 0.075-mm sieve), respectively.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Nonfreeze, FI = 0 Freeze, FI = 600

Freezing Index, °C- days

IRI, m/km

Initial IRI = 0.9 m/km

Percent slab cracking = 30

Percent joints spalled = 30

Total joint faulting = 600 mm

Percent passing 0.075-mm sieve = 40

Age = 30 yr

Figure 54. Effect of freezing index on JPCP IRI after 30 years.

SUMMARY

A new distress-based empirical JPCP IRI model was developed under this study for

use within the current PRS procedure. The model is deemed suitable for use because it

directly incorporates initial smoothness (a PRS AQC) and other JPCP distresses and

variables that were found to significantly influence the development of IRI over time.

The JPCP model was evaluated and verified using statistical techniques and by

performing comprehensive sensitivity analyses. The sensitivity analyses confirm that

the final IRI model is in agreement with sound engineering principles and judgment.

The model has a good fit (R2 = 0.72) and a low SEE of 0.40 m/km for a large number of

data points (N=184).

One aspect of this new IRI model is that initial smoothness is expressed as an initial

IRI. Many SHA's are currently in the process of adopting the use of lightweight
161

profilers that measure initial IRI directly on newly constructed PCC pavements;

however, the majority of SHA's continue to use other types of more traditional

equipment (e.g., California profilograph) to accomplish this task. The research team

recognizes this potential difficulty and, therefore, has included information on

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

10 percent 40 percent 75 percent

Percent Subgrade Material Passing the 0.075-mm (#200) Sieve

IRI, m/km

Initial IRI = 0.9 m/km

Percent slab cracking = 30

Percent joints spalled = 30

Total joint faulting = 600 mm

Freezing index = 600 °C-days

Age = 30 yr

Figure 55. Effect of subgrade percent passing 0.075-mm sieve on JPCP IRI after 30

years.

relationships that can be used to estimate initial IRI based on some of the more

common construction smoothness indices (see chapter 8, Development of Initial

Smoothness Relationships).
163

CHAPTER 8: DEVELOPMENT OF INITIAL SMOOTHNESS

RELATIONSHIPS

INTRODUCTION

The pavement smoothness model to be incorporated into the PRS process is based

upon IRI. The model asserts that the IRI at any given time in a pavement’s life is a

function of its as-constructed or initial IRI, age and predicted key distresses at that time,

and certain site factors.

Some SHA's are now using IRI directly to measure the smoothness of newly built

PCC pavements, due to the introduction of inertial profilers, particularly lightweight

systems, into the construction acceptance arena. However, many agencies still use

profilographs to measure initial smoothness and assess compliance with profile index

(PI)-based smoothness specifications. For these agencies, there is a real need to include

in the updated PRS a reliable set of PI-to-IRI conversion equations. Such equations will

enable the PaveSpec program user to quickly transform sublot PI values collected in

the field to closely approximated IRI values, which will then be used to predict service

lives and subsequently influence pay factors.

The relationship between PI and IRI can be somewhat clouded because the

equipment and processes used to produce the two values are quite different. As will

be discussed later, the most significant differences relate to 1) the reference profiles

from which the two indexes are computed, 2) the type of sensors used, and 3) the

degree and type of wavelength filtering done to produce PI and IRI values.

Although both indexes relate fairly well to user response to roughness, their

correlation to each other is not as strong because different roughness components (i.e.,

short bumps, long dips) are amplified or attenuated in computing each index.

(54) As

various studies have indicated, the correlation of PI and IRI becomes progressively

higher with the application of smaller and smaller blanking band widths (i.e., from 5-

mm [0.2-in] blanking band to 0-mm [0.0-in] blanking band).(55,56,57) The larger blanking

band widths have the obvious effect of masking more roughness.

In recognition of the problems described above, a concerted effort was made to

establish practical relationships that link the commonly used initial smoothness

statistic PI with the IRI statistic used in the PRS pavement smoothness-over-time

model. Specifically, the following relationships were sought in this work effort:

• IRI as a function of PI determined using a 5-mm (0.2-in) blanking band (herein

denoted as PI5-mm (PI0.2-in).
164

• IRI as a function of PI determined using a 2.5-mm (0.1-in) blanking band (herein

denoted as PI2.5-mm (PI0.1-in).

• IRI as a function of PI determined using a zero blanking band (herein denoted as

PI0.0).

The approach toward accomplishing these objectives was twofold. First, a

preliminary investigation was staged, consisting of a detailed literature search/review

and the collection and correlation analysis of actual smoothness data. Next, a

comprehensive analysis of LTPP smoothness data was performed, whereby profile

data on many GPS-3, SPS-2, and SPS-4 test sections were transformed into PI values

using commercial profilograph simulation software. The resulting PI values were then

compared with the IRI values previously computed and recorded in the LTPP

database.

The details of each IRI–PI investigation are presented in this chapter, following a

short discussion of the current state of the practice for initial smoothness testing and

subsequent smoothness monitoring. Based on the overall results of both

investigations, recommended PI-to-IRI conversion equations are offered that can be

used in the absence of more reliable agency-derived formulas.

BACKGROUND

Initial Smoothness Testing

For four decades, the profilograph has served as a construction quality control tool

for highway pavements.

(56) First developed by Francis Hveem in 1940 and first

implemented into a specification by the California Department of Highways in 1960, it

became one of the benchmark pieces of pavement smoothness testing equipment in the

1970's, and remains so to this day. Though predominantly used by highway agencies

to test the initial smoothness of concrete pavements, many agencies have also used the

profilograph for new asphalt pavements and asphalt overlays.

Past national surveys on the practice of measuring initial pavement smoothness

indicated a significant trend toward the use of profilographs. While a 1987 AASHTO

survey showed that 11 and 69 percent of all States used a profilograph to test asphalt

and concrete pavements, respectively, a similar 1994 NCHRP survey showed these

percentages increased to 36 and 75 percent.

(45,58) Both surveys also showed

overwhelming use of the California-type profilograph and the calculation of PI5-mm.

The widespread use of the profilograph over the years is living testimony to its

success, and its success is due in large part to the following factors:

• Relatively inexpensive to purchase and operate.
165

• Portability.

• Accuracy in identifying localized bumps.

• Ability to reasonably assess ride quality.

• Computerized profile measurement and trace reduction and analysis (beginning

in the mid-1980's).

In essence, the profilograph has provided agencies with a tool to quantify and specify

pavement smoothness. This, in turn, has helped fuel the drive for smoother and

smoother pavements.

In recent years, new demands from the pavement community have perhaps begun

to foreshadow the use of profilographs as construction quality control devices. Key

among these demands are the following:

(45)

• Accuracy—More restrictive smoothness specifications and specifications

containing incentive/disincentive payment provisions have resulted in a need

for greater accuracy (i.e., precision and bias) in the measurement of the

pavement profile. Because profilographs have a short, fixed baselength

(typically 7.6 m [25 ft]), the profile traces they generate represent somewhat

skewed versions of the true profile.

• Speed—The need for quicker assessment of initial smoothness is making the

slow operating speed (3 to 5 km/hr [2 to 3 mi/hr]) of the profilograph less

tolerable. This is helping open the door to high-speed profilers capable of

operating at speeds in excess of 50 km/hr (30 mi/hr).

• Relation to user response—Greater emphasis has been placed on correlating

smoothness measurements with user response to roughness (i.e., the highway

user’s perception of ride quality). Because profilographs amplify and attenuate

certain critical wavelengths in the pavement profile, there is concern about how

well the profilograph output relates to the wavelengths that are felt by highway

users.

• Compatibility with smoothness monitoring indexes—With thousands of lanekilometers of pavement being evaluated annually or biennially for networklevel pavement management system (PMS) purposes, high-speed measurement

using sophisticated profiling equipment has become the norm. This has forced

initial smoothness measurements to be made with the same type of high-speed

profiling equipment used in pavement management, or to be made with a

device that is highly correlated to the PMS high-speed profiler.

Although the AASHTO and NCHRP surveys showed increased use of the

profilograph between 1987 and 1994, they also showed an increase in usage of inertial

profilers (0 to 6 percent for asphalt pavements, 3 to 6 percent for concrete pavements).
166

More significantly, since the 1994 survey, the interest in inertial profilers for

construction acceptance testing has skyrocketed. At least 15 States, including Arizona,

Colorado, Florida, Kansas, Michigan, and South Dakota, have begun allowing the use

of inertial profilers on new construction jobs; several others are either encouraging their

use or are in the process of investigating their use.

Also of significance is the movement toward the reduction or elimination of

blanking bands in the computation of PI. Many States, such as Louisiana and Missouri,

have followed the lead of Kansas, which in 1992 implemented a PI0.0 specification for its

PCC pavements. This is considered a major improvement in smoothness

specifications.

Though the trend of construction acceptance testing appears to be moving away

from the use of profilographs and toward the use of inertial profilers and IRI, the upfront and operational expense of these inertial devices, as well as their complexities,

may cause the trend to be somewhat gradual in the short term. Hence, profilographs

should see continued use for at least a few years to come.

Smoothness Monitoring

Pavement smoothness over time is a vital component of the pavement management

process. By knowing the smoothness trends of many individual pavement sections

within a network, pavement managers can identify which pavements are approaching a

maximum tolerance level for roughness and can reasonably predict the time until those

pavements reach the established threshold. This information, in turn, helps in the

development of a coherent, long-term maintenance and rehabilitation (M&R) program

for the pavement network.

Key to the pavement smoothness monitoring process are the equipment and

procedures used to collect and report smoothness data. Without accurate, time-stable

smoothness measurements, the ability to predict future smoothness and develop a

sound M&R program is seriously compromised. Although past methods of

smoothness testing (e.g., Bureau of Public Roads [BPR] Roughometer, PCA Roadmeter,

Mays Ride Meter) may have met the needs of their era, only the inertial-type profilers

so common today are capable of providing the high-speed, quality measurements

needed for pavement management.

A 1998 survey of State practices showed that a large majority of States (36 of 37 total

respondents) used inertial profilers to collect smoothness data.

(59) Of the 13 nonresponding States, at least four had reported using inertial profilers in the 1994 NCHRP

survey.(45)

Though many different profiler models are currently being used, the most popular

are the International Cybernetics Corporation (ICC) profiler and the Roadware profiler,
167

each being used by 10 or more States.

(59) IRI is the statistic of choice for computing and

reporting pavement smoothness using the inertial profilers for nearly all of these

agencies.

With respect to sensor types, profilers with laser sensors are the most popular.

Two-thirds of the States responding to the 1998 smoothness survey indicated using this

type of sensor over ultrasonic, infrared, or incandescent sensors. In the matter of profile

filtering, most States use a 91.4-m (300-ft) filter—prior to roughness index calculation—

to remove long wavelengths that do not cause discomfort to highway users.

(59) And,

lastly, in the calculation of the chosen roughness statistic, a majority of States use the

profile data collected on both the left and right wheelpaths of a given travel lane.

It can be seen from these survey statistics that SHA's have set a course for the future

that includes high-speed, inertial-based profiling and utilization of the IRI statistic.

However, the fact that many different models of profilers are being used and are

commercially available, and that each model uses different profile measurement

instruments (e.g., sensors, accelerometers, distance measuring instruments [DMI's]) and

profile filtering methods, may result in less consistency among States with respect to

the measurement of smoothness.

PRELIMINARY INVESTIGATION—PAST STUDIES ON SMOOTHNESS

RELATIONSHIPS

To begin this investigation, a fairly extensive literature search was performed

focusing on National- and State-sponsored pavement smoothness studies conducted in

the past 15 years. The search resulted in the collection of more than 50 reports, papers,

or articles on the topic; however, only a small portion dealt specifically with the

correlation of IRI and PI. Even fewer involved the correlation of these indexes based

solely on the testing of JPCP.

Presented in this section are synopses of five documented studies and the PI-to-IRI

correlations developed in those studies. Though some of the studies included

examination of PI values obtained with a Rainhart profilograph, only the PI-to-IRI

correlations associated with the California profilograph are featured, because of the

California system’s predominant use.

Pennsylvania Transportation Institute Profilograph Calibration Study(58)

As part of a major effort to develop calibration procedures for profilographs and

evaluate equipment for measuring the smoothness of new pavement surfaces, the

Pennsylvania Transportation Institute (PTI) conducted a full-scale field testing program

on behalf of the FHWA. Concrete and asphalt pavements at five different locations

throughout Pennsylvania were selected for the experiment; each pavement was new or

newly surfaced. Multiple 0.16-km- (0.1-mi-) long pavement sections were established

at each location, resulting in 26 individual test sections over which 2 different types of

profilographs (California and Rainhart), a Mays Meter, and an inertial profiler were

operated. The resulting smoothness measurements were evaluated for correlation.
168

Figure 56 shows the relationship between the inertial profiler IRI and the PI5-mm

(PI0.2-in) determined manually from the California-type profilograph. As can be seen,

the resulting linear regression equation had a coefficient of determination (R2) of 0.57.

Figure 57 shows the relationship between the inertial profiler IRI and the computerIRI = 4.0238*PI + 70.13

R

2

 = 0.5654

N = 25

0

20

40

60

80

100

120

140

160

180

0 2 4 6 8 10 12 14 16 18 20

PI0.2-in (analog strip chart, manual reduction), in/mi

IRI, in/mi

PCC Pavements AC Pavements Linear (PCC and AC Pavements)

Figure 56. Relationship between IRI and manually generated PI in PTI profilograph

calibration study.

(58)

IRI = 2.4599*PI + 66.22

R

2

 = 0.5806

N = 25

0

20

40

60

80

100

120

140

160

180

0 4 8 12 16 20 24 28 32 36

PI0.2-in (computerized, continuous scale), in/mi

IRI, in/mi

PCC Pavements AC Pavements Linear (PCC and AC Pavements)

Figure 57. Relationship between IRI and computer-generated PI in PTI profilograph

calibration study.

(58)
169

generated PI5-mm from the California-type profilograph. Although the resulting linear

regression equation had a similar coefficient of determination (R2 = 0.58), its slope was

considerably flatter. For any given IRI, the data show a wide range of PI5-mm (PI0.2-in).

Although both of these relationships were based on measurements from both

concrete and asphalt pavement sections, neither one is considerably different from

regressions based solely on data from the concrete sections.

Arizona DOT Initial Smoothness Study(60)

In 1992, the Arizona DOT initiated a study to determine the feasibility of including

their K.J. Law 690 DNC Profilometer (optical-based inertial profiler) as one of the

principal smoothness measuring devices for measuring initial pavement smoothness

on PCC pavements. At the time, the DOT used a Cox California-type profilograph to

test newly constructed PCC pavements for compliance with construction smoothness

standards.

To examine the correlative strength of the Profilometer outputs (IRI) and the

profilograph (PI), a group of 12, 0.16-km (0.1-mi) pavement sections around the Phoenix

area were selected for testing. The smoothness levels of the sections spanned a range

that is typical of newly built concrete pavement—PI5-mm (PI0.2-in) between 0 and 0.24

m/km (15 in/mi). A total of three smoothness measurements were made with the

Profilometer over each wheelpath of each selected section, whereas a total of five

measurements were made by the profilograph over each wheelpath of each section.

The mean values of each set of three or five measurements were then used to correlate

the IRI and PI values.

Simple linear regression analyses performed between the left wheelpath, right

wheelpath, and both wheelpath sets of values indicated generally good correlation

between the two indexes. Figure 58 shows the scatter plots of each group, as well as

the regression line associated with the both wheelpath data group. As can be seen, the

R2 for the both wheelpath regression line was very high (0.93).

University of Texas Smoothness Specification Study(56)

In the course of developing new smoothness specifications for rigid and flexible

pavements in Texas, researchers at the University of Texas conducted a detailed field

investigation comparing the McCracken California-type profilograph and the Face

Dipstick, a manual Class I profile measurement device. The two devices were used to

collect smoothness measurements on 18 sections of roadway consisting of both asphalt

and concrete pavements. For both devices, only one test per wheelpath was performed.

Results of linear regression analysis showed a strong correlation (R2 = 0.92) between

the IRI and PI0.2-in values. The resulting linear regression equation had a higher

intercept
170

IRI = 6.1282*PI + 52.931

R

2

 = 0.9245

N = 12

0

20

40

60

80

100

120

140

160

180

0 2 4 6 8 10 12 14 16

PI0.2-in, in/mi

Left WP Right WP Both WP Linear (Both WP)

Figure 58. Correlation of IRI and PI in Arizona pavement smoothness study.

(60)

value than those obtained in the PTI and Arizona DOT studies, while the slope of the

equation was more in line with the slopes generated in the PTI study.

Florida DOT Ride Quality Equipment Comparison Study(61)

Looking to upgrade its smoothness testing and acceptance process for flexible

pavements, the Florida DOT undertook a study designed to compare its current testing

method (rolling straightedge) with other available methods, including the California

profilograph and the high-speed inertial profiler. A total of 12, 0.81-km- (0.5-mi-) long

pavement sections located on various Florida State highways were chosen for testing.

All but one of the sections represented newly constructed or resurfaced asphalt

pavements.

The left and right wheelpaths of each test section were measured for smoothness by

each piece of equipment. The resulting smoothness values associated with each

wheelpath were then averaged, yielding the values to be used for comparing the

different pieces of equipment.

The inertial profiler used in the study was a model manufactured by ICC. Because

one of the objectives of the study was to evaluate different technologies, the ICC inertial

profiler was equipped with both laser and ultrasonic sensors. Separate runs were

made with each sensor type, producing two sets of IRI data for comparison.
171

Figure 59 shows the relationships developed between the profilograph PI5-mm

(PI0.2-in) and the IRI values respectively derived from the laser and ultrasonic sensors.

As can be seen, both correlations were fairly strong (R2 values of 0.88 and 0.67), and the

linear regression equations were somewhat similar in terms of slope. As is often the

case, however, the ultrasonic-based smoothness measurements were consistently

higher than the laser-based measurements, because of the added sensitivity to items

such as surface texture, cracking, and temperature. This resulted in a higher y-intercept

for the ultrasonic-based system.

Ultrasonic IRI = 3.1539*PI + 52.196

R

2

 = 0.6665

N = 12

Laser IRI = 3.9519*PI + 39.927

R

2

 = 0.8846

N = 12

0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12 14

PI0.2-in, in/mi

IRI, in/mi

Laser Profilometer Ultrasonic Profilometer

Linear (Ultrasonic Profilometer) Linear (Laser Profilometer)

Figure 59. IRI–PI5-mm (PI0.2-in) correlations established in Florida’s ride quality

equipment study.

(61)

Figure 60 shows the correlations developed between IRI and PI0.1-in (PI2.5-mm) and IRI

and PI0.0. It is quite clear from this and the previous figure that the application of

smaller blanking bands results in higher PI values, since additional components of

roughness are considered. More significant, however, is the fact that both the slopes

and the y-intercept values in the resulting linear regression equations decrease with

smaller blanking bands. This is, again, the result of additional profile roughness being

considered.

It is reasonable to surmise from these observations that, if the PI0.0 was computed

from a more accurate pavement profile than the one generated by a profilograph, the yintercept would be much closer to zero. This is because the roughness associated with

long wavelengths (e.g., long dips or humps) is automatically filtered out as a result of

the short baselength of profilographs.
172

Ultrasonic IRI = 2.708*PI(0.1-in) + 37.969

R2 = 0.9568, N = 5

Laser IRI = 2.7345*PI(0.1-in) + 31.907

R2 = 0.9586, N = 5

Ultrasonic IRI = 2.1991*PI(0.0-in) + 19.361

R2 = 0.9016, N = 5

Laser IRI = 2.1899*PI(0.0-in) + 13.75

R2 = 0.8784, N = 5

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35 40

PI, in/mi

Laser IRI vs PI(0.1-in) Ultrasonic IRI vs PI(0.1-in)

Laser IRI vs PI(0.0-in) Ultrasonic IRI vs PI(0.0-in)

Linear (Ultrasonic IRI vs PI(0.1-in)) Linear (Laser IRI vs PI(0.1-in))

Linear (Ultrasonic IRI vs PI(0.0-in)) Linear (Laser IRI vs PI(0.0-in))

Figure 60. IRI–PI2.5-mm (PI0.1-in) and IRI–PI0.0 correlations established in Florida’s ride

quality equipment study.

(61)

Texas Transportation Institute Smoothness Testing Equipment Comparison Study(57)

As part of a multi-staged effort to transition from a profilograph-based smoothness

specification to a profile-based specification, the Texas Transportation Institute (TTI)

was commissioned by the Texas DOT in 1996 to evaluate the relationship between IRI

and profilograph PI. The study entailed obtaining longitudinal surface profiles

(generated by one of the Department’s high-speed inertial profiler) from 48 newly AC

resurfaced pavement sections throughout Texas, generating computer-simulated

profilograph traces from those profiles using a field-verified kinematic simulation

model, and computing PI5-mm (PI0.2-in) and PI0.0 values using the Pro-Scan computer

software.

A total of three simulated runs per wheelpath per section were performed, from

which an average PI value for each section was computed. The resulting section PI

values were then compared with the corresponding section IRI values, which had been

computed by the inertial profiling system at the time the longitudinal surface profiles

were produced in the field. Since both the PI and IRI values were based on the same
173

longitudinal profiles, potential errors due to differences in wheelpath tracking were

eliminated.

Figure 61 illustrates the relationships between the IRI and the simulated PI response

parameters. As can be seen, a much stronger trend was found to exist between IRI and

PI0.0 than between IRI and PI5-mm (PI0.2-in). Again, this is not unexpected since the

application of a blanking band has the natural effect of masking certain components of

roughness.

IRI = 4.0871*PI(0.2-in) + 52.735

R

2

 = 0.5909, N = 48

IRI = 2.1425*PI(0.0-in) + 19.328

R

2

 = 0.8532, N = 48

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35

Simulated PI, in/mi

IRI, in/mi

0.2-in blanking band 0.0-in blanking band

Linear (0.2-in blanking band) Linear (0.0-in blanking band)

Figure 61. Relationship between IRI and computer-simulated PI values in TTI

equipment comparison study.

(57)

In comparison with the other IRI-PI5-mm (IRI–PI0.2-in) correlations previously

presented, the one developed in this study is quite typical. The linear regression

equation includes a slightly higher slope but a comparable y-intercept value.

Summary of IRI–PI Relationships

Table 39 summarizes the various regression equations found in the literature

relating IRI from an inertial profiling system with PI statistics (PI5-mm [PI0.2-in], PI2.5-mm

[PI0.1-in], and PI0.0) generated by California-type profilographs. How these various

relationships compare visually with one another can be seen in figures 62 through 64.

Generally speaking, there is considerable disparity in the vertical positioning of each
174

trend, but the slopes are rather similar. The fact that different pavement types, different

roughness ranges, and different pieces of testing equipment are represented by the

various trends is believed to account in large part for the disparities observed.

Table 39. Summary of documented IRI–PI relationships.

Study*

Pavement

Types

No. Test

Sections Remarks

Linear Regression

Equation, Metric

(m/km)

Linear Regression

Equation, English

(in/mi)

IRI vs. PI5-mm (PI0.2-in)

PTI (1988)(58) AC &

PCC

26 Manually computed PI,

Laser-type profiler

IRI = 4.02*PI + 1.11 IRI = 4.02*PI + 70.13

Computer-generated PI,

Laser-type profiler

IRI = 2.46*PI + 1.04 IRI = 2.46*PI + 66.22

Arizona DOT

(1992)(60)

PCC 12 Computer-generated PI,

Laser-type profiler

IRI = 6.1*PI + 0.83 IRI = 6.1*PI + 52.9

University of

Texas

(1992)(56)

AC &

PCC

18 Manually computed IRI

(Dipstick)

IRI = 2.83*PI + 1.16 IRI = 2.83*PI + 73.7

Florida DOT

(1996)(61)

AC 12 Computer-generated PI,

Laser-type profiler

IRI = 3.95*PI + 0.63 IRI = 3.95*PI + 39.93

Computer-generated PI,

Ultrasonic-type profiler

IRI = 3.15*PI + 0.82 IRI = 3.15*PI + 52.20

TTI (1996)(57) AC

overlays

48 Computer-simulated PI,

Laser-type profiler

IRI = 4.09*PI + 0.83 IRI = 4.09*PI + 52.74

IRI vs. PI2.5-mm (PI0.1-in)

Florida DOT

(1996)(61)

AC 12 Computer-generated PI,

Laser-type profiler

IRI = 2.73*PI + 0.50 IRI = 2.73*PI + 31.91

Computer-generated PI,

Ultrasonic-type profiler

IRI = 2.71*PI + 0.60 IRI = 2.71*PI + 37.97

IRI versus PI0.0

TTI (1996)(57) AC

overlays

48 Computer-simulated PI,

Laser-type profiler

IRI = 2.14*PI + 0.31 IRI = 2.14*PI + 19.33

Florida

(1996)(62)

AC 12 Computer-generated PI,

Laser-type profiler

IRI = 2.19*PI + 0.22 IRI = 2.19*PI + 13.75

Computer-generated PI,

Ultrasonic-type profiler

IRI = 2.20*PI + 0.31 IRI = 2.20*PI + 19.36

* The number in parentheses indicates the year in which the study was conducted.

DETAILED INVESTIGATION—LTPP CORRELATION ANALYSIS

To further examine the relationship of IRI and PI, a detailed evaluation of LTPP

profile and smoothness data was performed. This evaluation consisted of the

following three steps:

1. Processing time-series profile data on GPS-3, SPS-2, and SPS-4 JPCP test sections

into PI5-mm (PI0.2-in), PI2.5-mm (PI0.1-in), and PI0.0 values using commercial

profilograph simulation software.
175

2. Developing scatter plots of the simulated PI values and corresponding IRI

values recorded in the LTPP database.

3. Performing regression analysis on each scatter plot to establish the respective

PI–IRI relationships.

0.00

0.50

1.00

1.50

2.00

2.50

0.00 0.05 0.10 0.15 0.20 0.25

PI5-mm

1992 AZDOT (PCC pvts) 1992 Univ. of Texas (PCC pvts)

1996 FLDOT (AC pvts, laser IRI) 1996 FLDOT (AC pvts, ultrasonic IRI)

1996 TTI (AC overlays) 1988 PTI (PCC & AC pvts, manual PI)

1988 PTI (PCC & AC pvts, computerized PI)

Figure 62. Graphical illustration of documented IRI–PI5-mm (PI0.2-in) smoothness relationships.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0.00 0.05 0.10 0.15 0.20 0.25

PI2.5-mm, m/km

IRI, m/km

1996 FLDOT (AC pvts, laser IRI) 1996 FLDOT (AC pvts, ultrasonic IRI)

Figure 63. Graphical illustration of documented IRI–PI2.5-mm (PI0.1-in) smoothness

relationships.
176

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

0.00 0.05 0.10 0.15 0.20 0.25

PI0.0, m/km

1996 FLDOT (AC pvts, laser IRI) 1996 FLDOT (AC pvts, ultrasonic IRI)

1996 TTI (AC overlays)

Figure 64. Graphical illustration of documented IRI–PI0.0 smoothness relationships.

As seen in table 40, a total of 152 JPCP test sections located in 11 States and 1

Canadian Province formed the basis for this evaluation. It should be noted that all the

States/Provinces in this table are located in the Midwest (comprehensive profile data

were only immediately available from the LTPP North Central Region, which

encompasses these and three other States/Provinces). In addition, the profile data

analyzed represented data collected by the North Central Regional Contracting Office

(NCRCO) since January 1997. Earlier data were not available due to the limitations of

the profiling equipment used prior to that time.

In keeping with the PRS subject pavement type, the LTPP correlation analysis was

limited to JPCP. In this way, the relationships developed between IRI and simulated PI

would not be skewed by measurements taken on other pavement types. As table 40

shows, the evaluation centered on 36 GPS-3 sections, 96 SPS-2 sections, and 20 SPS-4

sections.

LTPP Profile and Smoothness Data

The profile and smoothness data used in the LTPP correlation analysis were

collected using a K.J. Law T-6600 Profilometer from the North Central Region. This

device is equipped with infrared sensors spaced 1,680 mm (66 in) apart, so as to

measure the longitudinal profiles of the left and right wheelpaths of a travel lane.

Profile data were recorded on 25-mm (1-in) intervals, which is similar to the 33-mm

(1.25-in) interval currently used by computerized profilographs. This is also the
177

Table 40. Summary of JPCP test sections included in LTPP correlation analysis.

LTPP Experiment

State/Province GPS-31 SPS-22 SPS-43 Total

Indiana 2 0 0 2

Iowa 5 13 4 22

Kansas 3 13 0 16

Kentucky 1 0 2 3

Michigan 1 13 0 14

Minnesota 2 0 0 2

Nebraska 5 0 4 9

North Dakota 2 18 0 20

Ohio 0 20 3 23

South Dakota 6 0 7 13

Wisconsin 8 19 0 27

Manitoba 1 0 0 1

Total 36 96 20 152

Notes:

1

 Study of Jointed Plain Concrete Pavements.

2

 Study of Structural Factors for Rigid Pavements.

3

 Study of Preventive Maintenance Effectiveness of Rigid Pavements.

recording interval used by the K.J. Law lightweight inertial profiler. The T-6600

Profilometer is considered a class I accelerometer-established inertial profiling

reference based on ASTM E-950-98. Its capabilities for good repeatability and

compatibility with other LTPP Profilers are documented in several studies.

(62,63)

The data used for the analysis were based on 2,795 individual profile runs (1,111

GPS-3, 1,443 SPS-2, and 241 SPS-4 runs), covering the full 152.4 m (500 ft) of each test

section pavement. Each run included measurements of both the left and right

wheelpaths. The average IRI based on all of these profile runs was 1.64 m/km (103.8

in/mi). The range in IRI was from 0.63 m/km (39.9 in/mi) to 5.56 m/km (352.5 in/mi),

which is representative of new to very deteriorated JPCP. Individual data files were

created using the LTPP archived profile data. These data files followed the

Engineering Research Division (ERD) format developed for the RoadRuf software at

the University of Michigan Transportation Research Institute (UMTRI).

Development and Application of Simulation Software

To model profilograph traces and generate PI values from the LTPP profile data, a

software modeling system was needed. In 1995, K.J. Law developed software to model

California-type profilograph traces and output PI values. This software is now used

with their lightweight profilers to compute PI and IRI. K.J. Law’s lightweight profilers

use the same vertical elevation sensors that are mounted on the T-6600 Profilometer.
178

As of March 2000, K.J. Law lightweight profilers were approved for use in 12 States,

including Pennsylvania, New York, Utah, Texas, Arizona, and Michigan. Approval of

the system is pending in seven other States. The system has been calibrated against

California-type profilographs in Kansas, Arkansas, Indiana, Idaho, Minnesota,

Oklahoma, Utah, Arizona, and Georgia. Although there are several good lightweight

profilers and PI modeling systems available, the K.J. Law modeling software was

selected for this study to provide the most compatibility with the available LTPP

profile data.

Using the modeling and index computation software currently installed on their

commercial lightweight profilers, K.J. Law developed an interface for analysis of the

LTPP data. Named “Indexer,” the software computes PI, IRI, and ride number values

using ERD format input files. The size of the blanking band can be set by the operator.

Other factors that can be selected include:

• Blanking band filter (straight-line or selectable null filter).

• Smoothing filter (moving average or third-order Butterworth).

• Scallop filter (height, length, rounding).

Data Analysis

As discussed previously, the primary objective of the LTPP correlation analysis was

to establish relationships between IRI and three different variations of the PI statistic—

PI5-mm (PI0.2-in), PI2.5-mm (PI0.1-in), and PI0.0. The established relationships would then be

compared with the relationships identified and documented in past studies, in an

attempt to satisfy the overall goal of identifying reasonable PI-to-IRI conversions for the

PaveSpec user.

The analysis of data consisted of two parts. First, a baseline evaluation was done, in

which simulated PI computations were made using filter settings that provide the best

correlation with profilograph data from test track comparisons. These settings

consisted of a moving average smoothing filter set at 0.76 m (2.5 ft) and minimum

height, maximum height, and rounding scallop filters set at 0.9, 0.6, and 0.25 mm (0.035,

0.024, and 0.01 in), respectively. After modeling a California profilograph response to

these filtered profiles, straight-line blanking band filters of 0, 2.5 mm (0.1 in), and 5 mm

(0.2 in) were used to compute the associated values.

The second part of the analysis involved a look at the sensitivity effect of different

filter types and filter settings on the IRI–PI relationships. In this sensitivity analysis,

PI0.0, PI2.5-mm (PI0.1-in), and PI5-mm (PI0.2-in) parameters were computed using profilograms

from profile traces generated using moving average filters set at 0.31, 0.76, and 1.22 m

(1.0, 2.5, and 4.0 ft). These same three parameters were also computed using a thirdorder Butterworth filter set at 0.76 m (2.5 ft). Minimum height, maximum height, and
179

rounding scallop filter settings in this analysis were kept at the same levels as in the

baseline evaluation.

Baseline Evaluation

Figures 65 through 67 show the resulting IRI–PI scatter plots and linear regression

equations corresponding to the baseline PI computations. Each plot consists of more

than 5,000 data points, again spanning a range of IRI between 0.63 and 5.56 m/km (39.9

and 352.5 in/mi).

There is a strong fit among each data set (all R2 values > 0.75) and an increasingly

stronger correlation associated with PI values derived from smaller blanking-band

sizes. In addition, as was observed with the Florida DOT and TTI smoothness study

correlations, both the slope and y-intercept values given by the linear regression

equations decreased with the application of smaller blanking bands.

Figures 68 through 70 provide for a direct visual comparison of the smoothness

relationships developed in past studies with the LTPP-derived relationships. In each

figure, a band width envelope centered one standard deviation around the LTPPderived regression line has been transposed over the individual regression lines of the

past documented smoothness studies. Though the LTPP relationships represent a

wide range of smoothness, only the levels typical of new construction (IRI < 2.0 m/km

[126.8 in/mi]) are illustrated in figures 68 through 70.

IRI = 2.6252 * PI(5-mm) + 1.1915

R

2

 = 0.7577

N = 5590

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40

Simulated PI5-mm, m/km

IRI, m/km

Simulated PI based on 0.76-m moving-average smoothing

Figure 65. Graphical illustration of LTPP IRI–PI5-mm (PI0.2-in) smoothness relationship.
180

IRI = 2.2396 * PI(2.5-mm) + 0.9174

R

2

 = 0.7909

N = 5590

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40

Simulated PI2.5-mm, m/km

IRI, m/km

Simulated PI based on 0.76-m moving-average smoothing filter

Figure 66. Graphical illustration of LTPP IRI–PI2.5-mm (PI0.1-mm) smoothness relationship.

IRI = 2.2334 * PI(0.0-mm) + 0.4031

R

2

 = 0.8045

N = 5590

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40

Simulated PI0.0, m/km

IRI, m/km

Simulated PI based on 0.76-m moving-average smoothing filter

Figure 67. Graphical illustration of LTPP IRI–PI0.0 smoothness relationship.
180

IRI = 2.2396 * PI(2.5-mm) + 0.9174

R

2

 = 0.7909

N = 5590

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40

Simulated PI2.5-mm, m/km

IRI, m/km

Simulated PI based on 0.76-m moving-average smoothing filter

Figure 66. Graphical illustration of LTPP IRI–PI2.5-mm (PI0.1-mm) smoothness relationship.

IRI = 2.2334 * PI(0.0-mm) + 0.4031

R

2

 = 0.8045

N = 5590

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40

Simulated PI0.0, m/km

IRI, m/km

Simulated PI based on 0.76-m moving-average smoothing filter

Figure 67. Graphical illustration of LTPP IRI–PI0.0 smoothness relationship.


183

are still key factors in trend discrepancies, it appears that reducing the blanking band

has the effect of producing more harmonious relationships.

Sensitivity Analysis

As discussed previously, PI can be computed from a longitudinal profile using

various types of filters and filter settings. To examine the effects of some of the more

commonly available filtering routines on the IRI–PI relationship, the following PI

computations were performed on the LTPP profile data using the K.J. Law

profilograph simulation software:

• PI5-mm (PI0.2-in)

- 0.31-m (1-ft) moving average filter.

- 1.22-m (4-ft) moving average filter.

- 0.76-m (2.5-ft) third-order Butterworth filter.

• PI2.5-mm (PI0.1-in)

- 0.31-m (1-ft) moving average filter.

- 1.22-m (4-ft) moving average filter.

- 0.76-m (2.5-ft) third-order Butterworth filter.

• PI0.0

- 0.31-m (1-ft) moving average filter.

- 1.22-m (4-ft) moving average filter.

- 0.76-m (2.5-ft) third-order Butterworth filter.

As with the baseline evaluation of IRI and PI derived using a 0.76-m (2.5-ft) moving

average filter, the computed PI values were plotted against the corresponding actual

IRI values, and linear regressions were performed. Table 41 lists all of the relationships

developed between IRI and simulated PI5-mm (PI0.2-in), PI2.5-mm (PI0.1-in), and PI0.0 values,

along with the corresponding R2 values. Note: PI is expressed in metric units of m/km

and English units of in/mi.

Figures 71 through 73 show the series of trends for each blanking band PI, covering

only the levels of smoothness typical of newly constructed pavement (again, IRI < 2.0

m/km [126.8 in/mi]). In each figure, it can be seen that the trends associated with the

short wavelength (0.31-m [1-ft]) moving average filter and the third-order Butterworth

filter are nearly identical, and both are a little lower than the corresponding baseline

filter (0.76-m [2.5-ft] moving average) trends. The trends associated with the long

wavelength (1.22-m [4-ft]) moving average filter, on the other hand, are a little higher

than the corresponding baseline trends.

Table 42 summarizes the percent differences between the baseline filter IRI–PI

trends and the alternative filter trends at discrete levels of initial smoothness. Though

the percent differences are appreciable in some cases, they are, for the most part,

considerably smaller than the percentages characterized by the IRI–PI relationships of
184

Table 41. Summary of IRI–PI relationships based on different filter types and settings.

Filter Type Filter Setting

Linear Regression

Equation (Metric,

m/km)

Linear Regression

Equation (English, in/mi) R2

IRI vs. PI5-mm (PI0.2-

in)

Moving Average 0.31 m (1 ft) IRI = 2.350*PI + 1.164 IRI = 2.350*PI + 73.823 0.77

0.76 m (2.5 ft) IRI = 2.625*PI + 1.192 IRI = 2.625*PI + 75.541 0.76

1.22 m (4 ft) IRI = 2.834*PI + 1.221 IRI = 2.834*PI + 77.437 0.73

Third-Order Butterworth 0.76 m (2.5 ft) IRI = 2.367*PI + 1.151 IRI = 2.367*PI + 72.946 0.79

IRI vs. PI2.5-mm (PI0.1-

in)

Moving Average 0.31 m (1 ft) IRI = 2.021*PI + 0.875 IRI = 2.021*PI + 55.481 0.80

0.76 m (2.5 ft) IRI = 2.240*PI + 0.917 IRI = 2.240*PI + 58.163 0.79

1.22 m (4 ft) IRI = 2.407*PI + 0.953 IRI = 2.407*PI + 60.446 0.78

Third-Order Butterworth 0.76 m (2.5 ft) IRI = 2.052*PI + 0.871 IRI = 2.052*PI + 55.233 0.82

IRI vs. PI0.0

Moving Average 0.31 m (1 ft) IRI = 2.033*PI + 0.351 IRI = 2.033*PI + 22.279 0.81

0.76 m (2.5 ft) IRI = 2.233*PI + 0.403 IRI = 2.233*PI + 25.557 0.80

1.22 m (4 ft) IRI = 2.387*PI + 0.440 IRI = 2.387*PI + 27.915 0.79

Third-Order Butterworth 0.76 m (2.5 ft) IRI = 2.135*PI + 0.319 IRI = 2.135*PI + 20.219 0.81

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.05 0.10 0.15 0.20 0.25

Simulated PI5-mm, m/km

IRI, m/km

0.31-m Moving Average 0.76-m Moving Average

1.22-m Moving Average 0.76-m 3rd-Order Butterworth

Figure 71. Comparison of IRI–PI5-mm (PI0.2-in) relationships for different filter types and

settings.
185

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Simulated PI2.5-mm, m/km

IRI, m/km

0.31-m Moving Average 0.76-m Moving Average

1.22-m Moving Average 0.76-m 3rd-Order Butterworth

Figure 72. Comparison of IRI–PI2.5-mm (PI0.1-in) relationships for different filter types and

settings.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.20 0.30 0.40 0.50 0.60

Simulated PI0.0, m/km

IRI, m/km

0.31-m Moving Average 0.76-m Moving Average

1.22-m Moving Average 0.76-m 3rd-Order Butterworth

Figure 73. Comparison of IRI–PI0.0 relationships for different filter types and settings.
186

Table 42. Effects of alternative filter types and settings on IRI–PI relationships.

% Difference in IRI Between Baseline Filter Trend and Alternative

PI Filter Trend at:

Paramete

r Filter Setting and Type

PI = 0.0

m/km

PI5mm = 0.237

m/km

PI2.5mm = 0.37

m/km

PI0.0 = 0.5

m/km

0.31-m (1-ft) Moving Avg. 2.27% 5.09%

0.76-m (2.5-ft) Moving

Avg.

— —

1.22-m (4-ft) Moving Avg. -2.51% -4.38%

PI5-mm

0.76-m (2.5-ft) Third-Order

Butterworth

3.43% 5.63%

0.31-m (1-ft) Moving Avg. 4.61% 7.06%

0.76-m (2.5-ft) Moving

Avg.

— —

1.22-m (4-ft) Moving Avg. -3.93% -5.60%

PI2.5-mm

0.76-m (2.5-ft) Third-Order

Butterworth

5.04% 6.63%

0.31-m (1-ft) Moving Avg. 12.82% 9.98%

0.76-m (2.5-ft) Moving

Avg.

— —

1.22-m (4-ft) Moving Avg. -9.23% -7.51%

PI0.0

0.76-m (2.5-ft) Third-Order

Butterworth

20.89% 8.76%

past smoothness studies. Moreover, if the alternative filter trends were added to

figures 68 through 70, they would easily fall within the band width envelopes centered

one standard deviation around the LTPP baseline trends. Hence, it is reasonable to

believe that the effects of profiler equipment characteristics and pavement types have a

greater influence on the IRI–PI relationship than the PI simulation filter types and

settings.

SUMMARY AND RECOMMENDATIONS

In the search for reasonable, practical relationships that link IRI with PI derived

from different blanking bands, a comprehensive evaluation was made of trends

documented in past pavement smoothness studies, as well as trends developed in this

study from vast amounts of LTPP profile and smoothness data. The background and

results of these studies were presented and discussed in this chapter.

Although past documented IRI–PI relationships were rather limited (particularly

with respect to IRI–PI2.5-mm (PI0.1-in) and IRI–PI0.0 relationships) and showed varying

degrees of disparity, factors such as pavement type, equipment characteristics, and

filtering methods contributed significantly to those disparities.

A much broader and more controlled evaluation using more than 5,000 LTPP

smoothness data points showed IRI–PI trends generally similar to the past study

trends. The data points consisted of IRI and simulated PI values computed from the
187

same longitudinal profiles measured multiple times for 152 LTPP JPCP test sections.

Based on a standard filtering routine (a 0.76-m [2.5-ft] moving average smoothing filter)

and the application of 5-mm (0.2-in), 2.5-mm (0.1-in), and zero blanking bands, the

following PI-to-IRI conversion equations (in metric units of m/km) were developed:

IRI = 2.6252*PI5-mm + 1.1915 R2 = 0.76 (109)

IRI = 2.2396*PI2.5-mm + 0.9174 R2 = 0.79 (110)

IRI = 2.2334*PI0.0 + 0.4031 R2 = 0.80 (111)

These will be included as the default relationships in the new PaveSpec 3.0 software

and will serve as practical alternatives for agencies that lack their own reliable

conversion algorithms. However, it should be emphasized that these relationships are

based on profile data collected by one distinct piece of inertial profiling equipment

(K.J. Law T-6600 Profilometer) and on simulated PI values derived from those profile

data. The use of other profiler models will likely result in slightly different

relationships, because of the inherent differences in vehicle characteristics, profile

measurement instruments (e.g., sensors, accelerometers), and profile filtering methods.

Similarly, the use of actual PI data (i.e., data collected in the field using a profilograph)

will likely produce slightly different relationships because of differences in the

measured profile and the profile filtering methods used.
189

CHAPTER 9: GUIDELINES FOR MODEL CALIBRATION AND

DEVELOPMENT

INTRODUCTION

Many SHA's are wary about using distress or smoothness prediction models that

were not developed using data from their agency. This is a valid concern because local

construction, materials, and specific design situations may vary significantly from

national averages. Thus, there is a significant need for the capability to evaluate and

tailor distress indicator models to better reflect local conditions and circumstances

(remove bias and improve precision). Every construction project represents a unique

combination of pavement type, pavement design, material properties, subgrade

support, mix design, climatic variables, traffic, and construction quality. It is, therefore,

naive to think that one set of performance prediction models based on national data

will be completely accurate for all projects. To address this limitation, this chapter

outlines guidelines that may be used by a SHA to either 1) calibrate a national distress

indicator model to better reflect the specific local conditions associated with a project,

or 2) develop a new distress indicator model using SHA data. These two methods of

model improvement are discussed separately below.

GUIDELINES FOR CALIBRATING AN EXISTING DISTRESS INDICATOR

MODEL

IF SHA's believe that the performance of their pavements is not being accurately

predicted by the PRS performance models, they may want to consider calibrating the

models to an actual data set in which they have confidence. This section describes all

aspects of a procedure that a SHA may use to successfully complete such a calibration.

The model calibration approach chosen as the basis for these guidelines is similar to

that used in the World Bank HDM4 software.

(64)

 As expressed in the World Bank

report, the calibration of a distress indicator model consists of finding adjustment

factors that allow model predictions to best approximate measured data. Actual SHA

performance data are plotted against the predicted performance data from the same

pavement sections. A linear regression of the predicted versus actual plot is

conducted, and linear regression coefficients (A and B) are determined. Regression

coefficients are calculated in such a way as to minimize the total error between the

calibrated model and actual observed distress for each pavement section. The results

coming from the calibrated model are then computed using the following equation:
190

Calibrated Distress Value = A + B * (Original Model Distress Value) (112)

where:

A and B = Calibration factors determined from regression of predicted distress

vs. actual distress using actual SHA data to minimize the error in

prediction.

A calibrated model will often remove bias present in the national model, as well as

reduce some scatter in the results (i.e., improve precision). Figure 74 illustrates the

results of a model calibration procedure in which a Condition Rating Survey (CRS—

distress rating) model for the Illinois DOT was calibrated with a new data set.

(65) The

two plots shown in figure 74 show predicted versus actual data for both the before

calibration (existing model) and after calibration (calibrated model) scenarios. The

calibrated model corrects both bias and scatter about the one-to-one line. The detailed

steps required to successfully calibrate a distress indicator model to an external data

set are discussed in the following section.

Figure 74. Illustration of predicted vs. actual CRS both before calibration and after

calibration with new data.

(65)

Step 1—Compile the Calibration Data Set

The first step in the model calibration process is to compile a data set that best

represents current performance trends (distress versus time) for a chosen distress

indicator model. This data set must include not only data representing all of the inputs

required by the distress model in question, but also actual measured distress values at

different points in time. The local conditions represented by the compiled data set

should closely represent those local conditions expected at the project for which the
191

calibrated model will be used. Each data point within the calibration data set

represents the unique combination of pavement section inputs and one measured

distress value influenced by the associated n data input values. An example of the

format for this calibration data set is shown in table 43. LTPP data from sections in the

State should be adequate for this purpose.

Table 43. Format for a calibration data set.

Data Point Input 1 Input 2 * * * Input n

Measured

Distress Value

1

2

3

4

*

*

*

m

Step 2—Compute Corresponding Predicted Values

The second step in the process involves computing predicted distress values using

the original distress indicator model being investigated. Predicted distress values are

computed for each of the m data points (reflecting the associated values identified for

the n inputs) in the calibration data set. The comparison of these predicted distress

indicator values to the actual measured distress values will become the basis of the

calibration procedure. An example of the updated calibration data set (updated to

include the predicted distress values) is shown in table 44.

Table 44. Example calibration data set table with predicted values included.

Data Point Input 1 Input 2 * * * Input n

Measured

Distress

Value

Predicted

Distress

Value

1

2

3

4

*

*

*

m

Step 3—Plot Predicted vs. Measured Distress Values

Predicted distress values are then plotted versus actual measured distress values.

The construction of this predicted versus actual plot allows a user to visually evaluate

the data by identifying any potential bias, lack of precision, or unwanted trends

associated with the original model.
192

Step 4—Statistical Analysis of Predicted vs. Measured Distress Values

A simple statistical analysis (paired t-test) is performed to determine if there is a

significant difference between the sets of predicted and actual distress values. The

paired t-test is used to test the null hypothesis (Ho) that there is no difference between

the means of the measured and predicted distress values (predicted using the original

distress model). For this analysis, the null hypothesis being tested is that presented in

equation 113.

Ho: μACTUAL – μPREDICTED = 0 (113)

where:

μACTUAL = Mean of measured values.

μPREDICTED = Mean of values predicted using the original distress indicator model.

To run a paired t-test on the data set, the user first has to decide on chosen level of

significance. Typically, a significance level of 5 or 10 percent (i.e., 95 or 90 percent

confidence) is recommended. Thus, the null hypothesis is rejected if the determined pvalue is less than 0.05 or 0.10, respectively. The p-value represents the smallest

significance level at which a null hypothesis can be rejected.

(65) A stand-alone statistical

software package may be used to easily conduct the t-test. (Note: most spreadsheet

software packages such as Microsoft Excel also have statistical tools for completing

such analyses.)

If the null hypothesis is not rejected, there is no significant difference (for the chosen

confidence interval) between the predicted and actual data; therefore, the agency may

use the national distress indicator model with confidence. If the hypothesis is rejected,

there is a significant difference between the predicted and actual data. For this case, it

is recommended that the SHA complete the remaining steps of this calibration process.

Step 5—Determine Calibration Coefficients A and B

The calibration coefficients (A and B) are determined by running a linear regression

on the predicted versus measured data values. A statistical or spreadsheet software

package contains statistical tools to successfully complete a linear regression through a

given data set. The coefficients (A and B) simply represent the y-intercept and slope of

the determined best-fit regression line.

Step 6—Determine Calibrated Distress Values

Calibrated distress values are computed as a function of the original distress model

predicted values and the calibration coefficients determined under step 5 of this

process. Specifically, the calibrated values are determined using the previously
193

displayed equation 112. For convenience, equation 7 is displayed here again as

equation 114.

Calibrated Distress Value = A + B * (Original Model Distress Value) (114)

where:

Original Model Distress Value = Predicted value computed using the original

distress indicator model (calculated in step 2 of this process).

A = Calibration coefficient that represents the y-intercept of the linear regression

line fit through the predicted versus actual distress data.

B = Calibration coefficient that represents the slope of the linear regression line fit

through the predicted versus actual distress data.

Step 7—Plot Calibrated vs. Measured Distress Values

Plotting the calibrated versus actual measured distress values allows the user to

again visually evaluate the data. A side-by-side comparison of the original predicted

versus actual plot (step 3) and calibrated versus actual plot gives an initial indication of

the improved effectiveness of the calibrated model.

Step 8—Statistical Analysis of Calibrated vs. Measured Distress Values

The same paired t-test analysis discussed in step 4 is again used to determine if

there is a significant difference between the sets of calibrated and actual measured

distress values. For this case, the null hypothesis (Ho) is that there is no significant

difference between the means of the measured and calibrated distress values (this null

hypothesis is shown in equation 115). The paired t-test is used to determine if this null

hypothesis can be rejected using a significance level of 5 or 10 percent.

Ho: μACTUAL – μCALIBRATED = 0 (115)

where

μACTUAL = Mean of measured values.

μCALIBRATED =Mean of calibrated values (calibrated values are those determined using equation 1

If the hypothesis is not rejected, there is no significant difference (for the chosen

confidence interval) between the calibrated and actual data sets; therefore, the agency

may use the calibrated model with confidence. If the hypothesis is rejected, there is a

significant difference between the calibrated and actual data. This should not occur if

calibration is properly performed. If this occurs, an evaluation of the data and
194

procedures used must be made to determine if any errors have been made. If no errors

are identified, the SHA may want to proceed with the development of a new model.

GUIDELINES FOR DEVELOPING NEW DISTRESS INDICATOR MODELS

This section is provided as a general guide for those SHA's that are interested in

developing new distress indicator models that are specific to a SHA data set. If a SHA

is not satisfied with the performance of one of the national distress indicator models, it

is strongly recommended that the SHA first try to calibrate existing national distress

indicator models with a specific data set. If the SHA is still not satisfied with the

performance of the calibrated model, a new distress indicator model can be developed

using the general procedure outlined in this section.

Distress Indicator Prediction Model Types

Generally, two types of prediction models can be developed: empirical and

mechanistic-empirical. The details of each of these are discussed below.

Empirical Models

Ideally, empirical models are developed using statistical regression methods and

basic engineering principles and judgment; however, they do not model the basic

mechanisms of the distress. They are simply the best relationship that allows

prediction of an explanatory or dependent variable (i.e., a distress indicator) from a set

of independent variables based on the available data. The model obtained does not

necessarily signify a cause-and-effect relationship between the independent variables

and the dependent variable; however, the analyst can use the engineering knowledge

available and experimental results to improve this empirical aspect of the model.

One of the ways to improve empirical models is to include as independent

variables one or more mechanistic parameters or clusters. These clusters are functions

of independent variables and should be identified using engineering mechanics and

dimensional analysis techniques. An example of a cluster variable used in many

transverse joint faulting models is the radius of relative stiffness (l).

4

2

3

12 (1- ì )k

E h

l = (116)

where:

l = The cluster of terms that is appropriate to use in predicting the slab's radius

of relative stiffness, in.

E = PCC modulus of elasticity, psi.

h = Slab thickness, in.
195

μ = PCC Poisson's ratio (assumed to be equal to 0.15).

k = Modulus of subgrade reaction, psi/in.

One of the advantages of using a cluster variable is that it accounts for the relative

contribution of its components in a rational manner.

Mechanistic-Empirical Models

Mechanistic-empirical models 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 formulated that attempts to describe both

the occurrence and progression of the 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 mechanistic-empirical model is its potential to

extrapolate beyond the limits of the data used in its development.

Basic Principles to Developing Improved Distress Indicator Prediction Models

When conducting any model development/improvement activities, a number of

basic principles should be applied in order to optimize the

development/improvement process. Some of these basic principles are as follows:

• Past efforts of predictive model building should be fully considered, including

model functional forms, independent and dependent variables, interaction of

variables, and model accuracy achieved.

• The results of the t-test and multivariate analysis should be accounted for in the

process of selecting independent variables.

• The very best predictive models are those that are first formulated using

principles of mechanics and then calibrated using the extensive new field

database. An attempt should be made to identify the underlying mechanistic

functional form of the model and variables prior to use of the database. Modern

statistical model building techniques should also be utilized.(66)

• Comprehensive sensitivity analyses should be conducted for each model. This

includes developing plots of each independent variable (X-axis) versus the

dependent variable (distress on Y-axis) to show its relative effect. Sometimes, a

statistical test will show that some X-variable is significant, but from an

engineering standpoint its effect on the Y-variable is insignificant. This can be

readily seen from these plots. Any interactions or colinearity between

independent variables (such as age and traffic loads) should be directly

considered in the sensitivity analysis.
196

• Both the direction of the effect and its magnitude should be examined for each Xvariable in the model. A comparison of the general magnitude of each of these

effects with the results obtained from the major experimental projects where

direct comparisons can be made should be considered, as should current

pavement engineering knowledge. For example, if a faulting model shows that

a permeable base has no effect on joint faulting, but several of the major

experimental sections show the opposite, a "red-flag" would be raised. Such an

inconsistency should be fully explored to attempt to determine an explanation

for the discrepancy.

• The performance of a new model should be compared with existing time-series

performance data. The time-series data allow monitoring of the progression of

distresses in individual pavement sections. The amount and accuracy of

available time-series distress data will greatly influence the performance of the

developed model.

Figure 75 shows a flow chart that incorporates the above-mentioned basic principles

into an overall step-by-step procedure that can be used to develop pavement distress

indicator prediction models.

(14) More information regarding the specific methods used

to develop pavement distress indicator models may be found in a number of sources,

including those by Lee(66) and Simpson et al.(14)
197

Step 1: Select Distress/IRI Model

and Conduct Literature Review of Previous

Models and Distress Mechanism

Step 2: Identify and Define Potential Variables

ü Dependent Variable (Definition)

ü Independent or Explanatory Variables

Step 3: Assemble Database

(Determine specific subset of data to use)

Step 4: Identify Missing Data Items for

Variables

(Decide which variables have too little data to keep

in the analysis)

Step 5: Explore Dataset and Clean Data

ü Statistics (mean, min., max., etc.)

ü Two-Dimensional bivariate plots

ü Correlation matrix of all variables

ü Three-Dimensional multivariate plots

ü Identify types of relationships between variables

ü Identify erroneous and potential problem data

ü Optional: Create mechanistic variable cluster

Step 6: Model Building

ü Identify functional form of distress/IRI model

ü Identify boundary conditions

ü Select potential variables and transformations

for initial evaluation

ü Conduct linear regression with all variables

(observe significance levels, collinearity, residual

and predicted vs. actual plots)

ü Add and test various interactions

ü Observe 2-D and 3-D plots of variables (observe

relationships, consider additional

transformations)

ü Identify potential outliers

ü Conduct further regression analyses

ü Select tentative model

Step 7: Sensitivity Analysis

ü Set variables at their means

ü Increase/decrease each variable by one standard

deviation and compute distress/IRI for each

ü Sensitivity is difference between plus and minus

standard deviation

ü Repeat for all variables

ü Plot sensitivity graph

ü Evaluate reasonableness of direction of variables

on distress/IRI

ü Evaluate reasonableness of sensitivity of each

exploratory variable

ü Judge adequacy of tentative model

ü Revise model if deficient

Figure 75. Flow chart for developing pavement distress models for rigid pavements.

(14)
199

CHAPTER 10: SUMMARY AND RECOMMENDATIONS

SUMMARY

One of the key benefits of a PRS continues to be the identification of rational pay

adjustments (incentives and disincentives) related to the predicted AQC-influenced

future performance of an as-constructed pavement project. The continued focus on

linking future pavement performance to the quality of the measured AQC's will lead to

improved construction quality, reduced future maintenance and rehabilitation, and the

subsequent reduction in LCC's (those incurred by both the agency and the user). The

implementation of PRS is expected to improve construction quality, similar to the way

in which incentives have improved smoothness over the past several years.

Under this research project, the prototype PRS (developed under previous FHWA

research) was improved.(5,8,9,10,11) Specifically, this study focused on improving the key

distress indicator and smoothness prediction models used in the prototype PRS for

JPCP demonstrated in version 2.0 of the PaveSpec software. This report discussed all

aspects of the research, including:

• Completed model improvement (validation/calibration) efforts, details of the

improved models, and their associated sensitivity analyses.

• Results of a study that investigated relationships between different methods of

measuring initial smoothness and initial IRI.

• Development of guidelines that can be used to calibrate national distress

prediction models to reflect local conditions.

The PaveSpec 2.0 PRS demonstration software was also improved under this study.

Specific improvements in the PaveSpec 3.0 software include:

• Incorporation of the improved distress indicator models.

• Capability to calibrate or modify a national distress indicator model to better

reflect a project's local conditions.

• Inclusion of sensitivity analysis capabilities.

• Ability to produce project-specific expected pay charts used to assess risks to

both the contractor and agency.

• Incorporation of an online user's guide.
200

Based on the research conducted under this project, the following conclusions and

recommendations were compiled.

Improved Performance Prediction Models

The PRS methodology has been under development by the FHWA for several years

and has now reached a level at which it can be implemented by SHA's to improve the

quality of their jointed concrete pavements. However, the adequacy of the key

performance models included in the PRS has been of concern to SHA’s. To resolve this

issue, performance models included in the PaveSpec 2.0 software were evaluated and

substantially improved under this project. Specifically, the models chosen to be

improved include:

• Transverse joint faulting.

• Transverse slab cracking.

• Transverse joint spalling.

• IRI.

The evaluation and improvement of the above performance models were

accomplished using JPCP performance data compiled from the following data sources:

• LTPP JPCP database (GPS-3) (134 sections).

• FHWA RPPR JPCP database (303 sections)

• NCHRP 1-19 (COPES) database (152 sections).

• Extended AASHO Road Test (25 sections).

• Mn/ROAD database (sections included in LTPP).

Combined, these data sources included more than 600 sections located in 40 different

States and Canadian Provinces.

The improved performance prediction models are the most comprehensive and

robust models developed to date and can be used with relative confidence to predict

key distresses and smoothness of JPCP. Each improved distress indicator model is

summarized below.

• Transverse Slab Cracking. Fatigue damage was accumulated at the slab edge on

the basis of key pavement structural and climatic factors. This damage was then

correlated with measured slab cracking from the many database sections. The

final model included the following key variables: slab thickness (an AQC), slab

concrete strength (an AQC), base type and subgrade support, joint spacing,

longitudinal joint load transfer (widened lane or tied shoulder), thermal

gradients in the slab, and built-in thermal gradient, which produces an upward

curling of the slab.
201

• Transverse Joint Faulting. The erodibility of the base course along with key

structural and climatic factors were directly considered in the development of

the improved JPCP transverse joint faulting model. The database used to

develop this model included data from LTPP, RPPR, NCHRP 1-19, and the

extended AASHO Road Test. The final transverse joint faulting model included

the following key variables: slab thickness (an AQC), slab concrete strength (an

AQC), base type and subgrade support, transverse joint spacing, transverse joint

load transfer, widened slab, temperature factors, and moisture factors.

• Transverse Joint Spalling. Transverse joint spalling was modeled empirically

using LTPP data from GPS-3 supplemented by laboratory data obtained from a

previous FHWA PRS contract.

(5,6,7) The laboratory study specifically

investigated the effects of materials properties (air content and PCC percent

consolidation) and cumulative freeze-thaw cycles on the transverse joint spalling

of PCC slabs.(5,6,7) The final transverse joint spalling model determined under

this project was obtained from nonlinear regression and included the following

key variables: age of the concrete, air content (an AQC), slab thickness (an AQC),

compressive strength of the concrete (an AQC), type of joint sealant, average

annual number of air freeze-thaw cycles, and concrete water/cement ratio.

• International Roughness Index. The prediction of IRI was based on the premise that

the IRI over time was dependent on the initial IRI (measured immediately after

construction), the other distress indicators that develop over time, and

additional site factors. The final model included the following key variables:

initial IRI after construction, transverse cracking, transverse joint spalling,

transverse joint faulting, and specific site factors (fines content in the subgrade

soil, freezing index, and age since construction).

Investigation of Initial Smoothness Relationships

The relationships between initial IRI and PI (using 0.0-, 2.5-, and 5.0-mm [0.0-, 0.1-,

and 0.2-in] blanking band widths) were studied and subsequently greatly improved

using LTPP data. This makes it possible to more accurately express initial smoothness

in terms of an IRI that is then directly used in the prediction of IRI over time. These

determined correlations are intended to give SHA's more confidence in using the IRI

model (included in PRS) to predict smoothness over time.

The IRI versus PI correlations utilized data from LTPP that included more than

5,000 data points. Results showed that good correlations were obtained over a wide

range of IRI and PI values; however, increasingly better correlations were obtained as

the PI was computed with smaller and smaller blanking bands. The correlation

between IRI and PI was best at a zero blanking band.

Distress Indicator Model Calibration Guidelines

Distress indicator model calibration guidelines were also developed so that a given

State could calibrate any of these models to better reflect their pavement performance
202

data (local conditions). For example, a State could utilize its LTPP sections, other

research test sections, or sections selected from its pavement management data to

calibrate each of the performance models included in the PRS (faulting, spalling,

cracking, IRI).

Development of PaveSpec 3.0

The PaveSpec PRS demonstration software was upgraded to version 3.0 under this

project. The improved PaveSpec 3.0 software demonstrates all aspects of the current

PRS methodology by providing the following general capabilities:

• Development of a Specification. The PaveSpec 3.0 Specification Wizard leads the user

through the development of all aspects of the PRS (for JPCP) for a given project.

The overall focus of the development process is to provide guidance on

determining rational LCC-based pay factor curves associated with each AQC

(concrete strength, slab thickness, concrete entrained air content, initial smoothness,

and percent consolidation of concrete around dowel bars).

• Evaluation of a Developed Specification. PaveSpec provides two tools for evaluating a

developed specification: sensitivity analysis and expected pay charts. A

specification-dependent sensitivity analysis is used to investigate the effects of AQC

changes on pay factors, while expected pay charts help analyze the risks for both the

agency and the contractor.

• Use of a Developed Specification. Performance-related lot pay factors (and pay

adjustments) may be computed based on actual AQC field data.

RECOMMENDATIONS FOR FUTURE RESEARCH

Although the current PRS methodology has been advanced over the past decade,

many improvements to the existing PRS for JPCP are still needed. The implementation

of the current PRS is anticipated to be a major effort, and obstacles are to be expected.

To overcome these obstacles, the results of future research must continue to be

incorporated into the current methodology. The following are identified areas of the

existing PRS that could be addressed under future research efforts:

• More Comprehensive User Cost Models. The user cost models currently used in the

PRS methodology are relatively simple. It is recommended that future PRS

research strive to include a more robust user cost method.

• Improved or Additional Distress Indicator Models. Although the current PRS distress

indicator models were greatly improved under this research project, continual
203

efforts are needed to develop improved mechanistic-based models for the

prediction of key distress types and smoothness.

A specific example of ongoing model improvement work (under another

research effort) is the development of a transverse slab cracking prediction

model that predicts bottom-up and top-down cracking. Top-down cracking has

recently been recognized as a very important distress for JPCP as it has occurred

on several projects. PaveSpec 3.0 only includes bottom-up cracking of JPCP as a

key performance indicator. The inclusion of top-down cracking would add a

valuable construction curling variable to the PRS in that built-in curling would

be directly controlled by the contractor.

• Inclusion of Additional AQC’s. As researchers continue to develop distress

indicator models that are more mechanistic, the possibility of identifying and

including new AQC's into the PRS methodology increases. Influential AQC's

that currently cannot be incorporated into the PRS include joint sawing depth,

surface texture, concrete mixture components (e.g., cement, aggregates), base

course quality, and subgrade quality. It is recommended that additional AQC's

be incorporated into the PRS methodology as reliable and practical

measurement methods of these potential AQC's become available, and as new

distress indicator models are developed as a function of one or more of these

potential AQC's.

• PRS for Additional Pavement Types. The current prototype PRS is only valid for

JPCP. The same concepts could be applied in future research to develop PRS for

pavement types such as continuously reinforced concrete pavement (CRCP) and

unbonded concrete overlays.

• Inclusion of Other Pavement Features. Currently, the PRS methodology is

applicable to the mainline pavement only. It is recommended that future

research address the inclusion of the pavement shoulders.

• Additional AQC Sampling and Testing Methods. As new AQC sampling and testing

methods become reliable and practical, they should be considered for use within

the PRS. The PRS would benefit greatly from the incorporation of sampling and

testing methods that are more rapid, nondestructive, and inexpensive.

• Use of Pavement Management System Data to Support PRS Implementation. Such

aspects as calibration of distress models, validation of distress models, and

validation and improvement of M & R life-cycle costing are important.

• PRS Training. Considerable training in PRS concepts and practice will be needed

for SHA, contractor, and industry personnel.
205

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