The days in which we can significantly advance the science of pavement engineering through

purely empirical approaches are over. Instead, we must turn to mechanistically-based analyses,

which seek to explain the mechanisms associated with pavement deterioration. This fact is

reflected in the requirement that the 2002 Guide for Design of New and Rehabilitated Pavement

Structures (2002 Guide, currently under development through the National Cooperative Highway

Research Program) be based on mechanistic concepts.

This report documents the application of Long Term Pavement Performance (LTPP) data to the

evaluation of mechanistically-based performance prediction procedures for jointed concrete

pavements. It will be of benefit to those interested in the development of mechanistically-based

performance prediction and design procedures for jointed concrete pavements. It will be of

particular interest to those involved in the development of the 2002 Guide.

Charles 1. Nemmers, P.E.

Director

Office of Engineering

Research and Development

This document is disseminated under the sponsorship of the Department of Transportation in the

interest of information exchange. The United States Government assumes no liability for its

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

The United States Government does not endorse products or manufacturers. Trademarks or

manufacturers' names appear herein only because they are considered essential to the object of

this document.
ee mea eport oeumentation Pa

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

FHWA-RD-98-094

4. Title and Subtitle 5. Report Date

MECHANISTIC EVALUATION OF TEST DATA June 1998

FROM LTPP JOINTED CONCRETE PAVEMENT 6. Performing Organization Code

TEST SECTIONS

7. Author(sl 8. Performing Organization Report No.

Y. Jane Jiang, Shiraz D. Tayabji, and Chung L. Wu

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

ERES Consultants, Inc.

9030 Red Branch Road, Suite 210 11. Contract or Grant No.

Columbia, Maryland 21045 DTFH61-95-C-00028

12. Sponsoring Agency Name and Address 13. Type of Report and Period Covered

Office of Research & Development Final Report

Federal Highway Administration Feb 1995 - Dec 1997

6300 Georgetown Pike

14. Sponsoring Agency Code McLean, Virginia 22101-2296

15. Supplementary Notes

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

The faulting analysis was performed by Construction Technology Laboratories (CTL), Skokie, Illinois, under

a subcontract to ERES. Dr. Chung L. Wu served as the Project Manager and Mr. Paul Okamoto served as

the Administrator of the CTL subcontract.

16. Abstract

This study was conducted to assess how well some of the existing concrete pavement

mechanistic-empirical based distress prediction procedures performed when used in conjunction

with the data being collected as part of the national Long-Term Pavement Performance (LTPP)

program. As part of the study, appropriate data were obtained from the National Information

Management System (NIMS) for the GPS-3 and GPS-4 experiments. Structural analysis was

performed for up to 140 axle load configurations for the selected test sections. Then,ILUCON

and the Portland Cement Association (PCA) procedures were used to predict fatigue cracking

and joint faulting damage, respectively. The computed results were compared with observed

values.

This study has shown that, even given the many current limitations in the LTPP database, the

LTPP data can be used successfully to develop better insight into pavement behavior and to

improve pavement performance.

17. Key Words 18. Distribution Statement

Concrete pavement, fatigue cracking, joint No restrictions. This document is available to

faulting, LTPP, mechanistic-empirical procedures, the public through the National Technical

NIMS, pavement distress, pavement performance, Information Service, Springfield, Virginia

pavement testing, structural analysis. 22161.

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

Unclassified Unclassified 77
•• •

APPROXIMATE CONVERSIONS TO SI UNITS APPROXIMATE CONVERSIONS FROM SI UNITS

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

lENGTH lENGTH

in inches 25.4 m~fimefllrs mm mm m~limefllrs 0.039 inches in

ft feet 0.305 meters m m meters 3.28 feet ft

yd yards 0.914 meters m m meters 1.09 yards yd

mi m~es 1.61 kilometers km km kilometers 0.621 miles mi

AREA AREA

in' square inches 645.2 square m~limeters mm' mm' square m~limeters 0.0016 square inches in'

ftZ square feet 0.093 square meters m' m' square meters 10.764 square feet ftZ

ycJZ square yards 0.836 square meters m' m' square meters 1.195 square yards ycJZ

ac aaes 0.405 hectares ha ha hactares 2.47 aaes ac

mil square miles 2.59 square kilometers km' km' square kilometers 0.386 square miles mi'

VOLUME VOLUME

lIoz lIuidounces 29.57 milliliters mL mL milliliters 0.034 lIuidounces II oz

gal galons 3.785 Uters L L Uters 0.264 gallons gal

ft' cubic feet 0.028 cubic meters m3 mZ cubic meters 35.71 cubic feet ft'

_. ycJZ cubic yards 0.765 cubic meters m3 mZ cubic meters 1.307 cubic yards ydl

III

_.

NOTE: Volumes greater than 1000 I shaH be shown in mZ.

MASS MASS

oz ounces 28.35 grams g g grams 0.035 ounces oz

Ib pounds 0.454 kilograms kg kg kilograms 2.202 pounds Ib

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

(or "metric ton") (or T) (or or) (or "metric ton")

TEMPERATURE (exact) TEMPERATURE (exact)

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

temperature or (F-32Y1.8 temperature temperature temperature

IllUMINATION IllUMINATION

Ie foot-candlel 10.76 lux Ix Ix lux 0.0929 foot-candles Ie

II foot-t...amberts 3.426 candelalm' cdIm' cd'm' candeIaIm'

0.2919 foot-Lamberts II

FORCE and PRESSURE or STRESS FORCE and PRESSURE or STRESS

Ibf poundfon:e 4.45 newIons N N newtons 0.225 poundforce lb.

IbfllnZ poundfon:e per 6.89 kiIopascall kPa kPa kiIopascals 0.145 poundforce per IbflinZ

Iqu8I8 inch square inch

I

• SI is the symbol for the Intemation81 Syllllm of Units. Appropriate (Revised September 1993)

rounding should be made to comply with Section 4 of ASTM E380.
CHAPTER 1 - INTRODUCTION 1

The LTPP Program 2

Fundamentals ofM-E Distress Modeling 3

Scope of Work 5

Report Organization 6

CHAPTER 2 - DATA BASE ACQUISITION 7

Inventory/Section Data 7

Material Characteristics 7

PCC Modulus of Elasticity, E 7

PCC 28-day Flexural Strength, M, 9

Poisson's Ratio ofPCC, v 10

Base Elastic Modulus 11

Modulus of Subgrade Reaction, k 12 ' I

LTPP Traffic Data 12

Backcasting Traffic 13

Cumulative Traffic Determination 15

Lateral Distribution of Traffic 15

Climatic Data 16

Transverse Cracking Data 16

Joint Faulting Data 20

Sections with Missing Data 20

CHAPTER 3 - FATIGUE CRACKING ANALYSIS 21

Introduction 21

Stress Calculation 21

Load Stress 22

Equivalent Single-Axle Radius 23

Slab Size Effect 25

Tied Concrete Shoulder 26

Stabilized Base 26

Widened Outer Lane 27

Curling Stress 28

Warping Stresses ...............................•................. 29

Combined Stress 29

Structural Model 30

Fatigue Damage Calculation 30

Correlation Between GPS-3 Fatigue Cracking and the Calculated Fatigued Damage " 31

Sensitivity Analysis 32
TABLE OF CONTENTS

(continued)

CHAPTER 4 - JOINT FAULTING ANAL YSIS 39

Introduction 39

Background 39

Development of Faulting Prediction Models Based on the Erosion Factor 42

Faulting at Aggregate-Interlock Joints 45

Faulting at Doweled Joints 50

PCC Modulus of Elasticity 54

Modulus of Subgrade Reaction 54

Traffic Data 54

Predicted Faulting versus Measured Faulting for Aggregate-Interlock Joints 55

Predicted Faulting versus Measured Faulting for Doweled Joints 55

Discussion of Results 55

Summary 60

CHAPTER 5 - SUMMARY AND RECOMMENDATIONS 61

General Observations 61

Prediction of Fatigue Cracking and Joint Faulting Using Mechanistic Procedures 61

LTPP Data Issues 62

Materials Data 62

Traffic Data 62

Distress Data 62

Summary 63

APPENDIX A - DATA BASE FOR ANALYSIS OF TRANSVERSE CRACKING (GPS-3

DATA) 69
1 An example of temperature difference distribution of a wet-freeze section

for an average year 18

2 An example of temperature difference distribution of a wet no-freeze section

for an average year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3 An example of temperature difference distribution of a dry-freeze section

for an average year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4 An example of temperature difference distribution of a dry no-freeze section

for an average year ' . . . . . . . . . . . 19

5 Axle configurations analyzed 24

6 Fatigue analysis results ofLTPP GPS-3 data 33

7 Sensitivity of the cumulative fatigue with traffic counts 33

8 Sensitivity plot of the fatigue damage with change of modulus of rupture 34

9 Sensitivity plot of the fatigue damage with change of elastic modulus of the slab 34

10 Sensitivity plot of the fatigue damage with change of the PCC thermal expansion

coefficient 35

11 Sensitivity plot of the fatigue damage with change of Poisson's ratio of the slab 35

12 Sensitivity plot of the fatigue damage with change of subgrade k-value 36

13 Faulting prediction error distribution for aggregate-interlock joints 47

14 Faulting versus accumulated erosion for aggregate-interlock joints with gravel coarse

aggregate in dry region 47

15 Faulting versus accumulated erosion for aggregate-interlock joints with crushed

coarse aggregate in dry region 48

16 Faulting versus accumulated erosion for aggregate-interlock joints with gravel

coarse aggregate in wet region 48

17 Faulting versus accumulated erosion for aggregate-interlock joints with crushed

coarse aggregate in wet region 49

18 Faulting prediction error distribution for doweled joints 52

19 Faulting versus accumulated erosion for doweled joints in wet region 52

20 Faulting versus accumulated erosion for doweled joints in dry region 53

21 Faulting prediction error distribution for aggregate-interlock joints 56

22 Predicted faulting versus measured faulting for aggregate-interlock joints 56

23 Faulting prediction error distribution for doweled joints 57

24 Predicted faulting versus measured faulting for doweled joints 57

25 Sensitivity analysis of annual traffic growth rate on computed faulting 59
LIST OF TABLES

Table Paee

1 Inventory data elements and the corresponding LTPP tables 8

2 Thermal properties of aggregate 11

3 Selected elastic moduli for the base layer of GPS-5 sections 12

4 Summary of the GPS-3 sections with traffic monitoring data 14

5 Data elements needed for the CMS model and the corresponding LTPP tables 17

6 Summary of states surveyed 43

7 Climatic zone classification 43

8 Sensitivity of faulting to variable change for non-doweled joints 46

9 Sensitivity of faulting to variable change for doweled joints 50
Over the years, pavement engineers have been attempting to develop "rational" design

procedures for both flexible and rigid pavements. These rational procedures have focused on

using mechanistic considerations to explain the behavior of pavements under traffic and

environmental loadings. The basic assumption of these rational procedures is that the primary

pavement distresses are a result of damage induced by the state of stress, strain, or deformation

that result from traffic and environmental loadings. Under normal operating conditions, damage

to the pavement occurs from a large number of repetitive traffic and environmental loadings over

a period of time. Thus, each incremental loading results in some damage to the pavement, and

the cumulative effect of the damage over a period of time results in the manifestation of specific

distress, for example, fatigue cracking in asphalt concrete (AC) and portland cement concrete

(PCC) pavements, rutting in AC pavements, and faulting in PCC pavements. A pavement is

considered to have failed when the distress level (severity and extent or magnitude) reaches or

exceeds a predefined acceptable level for that distress for a given category of the highway.

Since the 1950's, as techniques for analysis of pavement response to loading began to be

available, many attempts have been made to develop these rational design procedures, now

commonly referred to as mechanistic-empirical (M-E) procedures, to define/describe the

development of specific distresses in pavements. During the late 1980's, extensive evaluation

was performed ofM-E procedures as part of the National Cooperative Highway Research

Program (NCHRP) 1-26 study. In addition, the proposed revision oftheAASHTO Guidefor

Design of Pavements to be completed by 2002 will be based on M-E procedures. The M-E

procedures typically involve the following steps:

1. Establishing a hypothesis for the mechanism for the development of the specific

distress. For example, the development of fatigue cracking in PCC pavements is

considered by many to be due to repeated application of bottom tensile strain in

the PCC layer. This first step is the most critical because all the subsequent steps

depend on the correctness of the hypothesis. The hypothesis determines the type

of analysis that needs to be conducted to compute the critical response(s) and the

material characterization and traffic characterization needed as input for the

analysis.

2. Comprehensively characterizing materials by incorporating changes in material

properties as a function of the state of stress (stress dependency), environmental

conditions (temperature and moisture), aging, and continual deterioration under

traffic loading.

3. Determining critical responses (stresses, strains, deformations) within the

pavement layers when subjected to traffic and environmental loadings.

4. Estimating damage from each "set/condition" of traffic and environmental

loading. This is typically done using distress prediction models or transfer

functions that relate a critical structural response to distress-specific damage. A

different model is used for each different distress and for each pavement type.
5. Accumulating the damage over a period of time. Miner's hypothesis is generally

used to account for cumulative damage. Based on predefined relationships

between the accumulated damage and amount of distress development, the

amount of distress that may develop at the end of the selected service life is

estimated. At this time, the selected pavement may be redesigned if the estimated

amount of distress exceeds the acceptable level or is significantly less than the

acceptable level.

6. Selecting as a candidate design a pavement section that results in acceptable levels

of distresses at the end of the target service/design life. More than one section

may be identified as candidate designs.

Although the above steps seem simple enough, the actual process is very complex

because of many still-undefined factors associated with pavement design and construction, traffic

loading, and environmental conditions.

As part of a Federal Highway Administration (FHWA) sponsored project, work was

undertaken to use test data from the on-going Long-Term Pavement Performance (LTPP)

program in conjunction with currently available M-E design procedures to assess how well these

M-E procedures perform. In essence, the LTPP test data were used to perform a reality check on

the validity of several M-E based distress prediction procedures. Under this study, existing M-E

design procedures were used to determine cumulative damage in relation to a specific distress in

each applicable LTPP test section. The estimated distress was compared with predicted distress.

In addition, an attempt was made to develop calibrated distress models that relate the

accumulated damage to the observed level of distress.

This report presents the results of the study applicable to jointed PCC test sections from

the LTPP program. In the subsequent sections, details are presented on the LTPP program, the

LTPP data used in the study, and the procedures undertaken to compute the cumulative damage.

The LTPP program is a 20-year program established under the now-completed Strategic

Highway Research Program (SHRP). The first 5 years of the LTPP program (mid-1987 to mid1992) were funded under the SHRP funding; since mid-1992, FHW A has assumed the

management and funding of the LTPP program. Although the LTPP program was conceived to

meet many needs of the pavement engineering community, one major objective was to develop a

national pavement performance data base that could be used to develop and/or validate pavement

design procedures. The study reported here was aimed at fulfilling that objective.

The LTPP program is collecting information on the long-term performance of various

pavement structures under a range of traffic loadings, climatic factors, and sub grade soils. The

LTPP program includes two fundamental classes of studies: the General Pavement Studies

(GPS) and the Specific Pavement Studies (SPS). The GPS experiments are a series of selected

in-service pavement studies structured to develop a comprehensive national pavement

performance data base. These studies are restricted to pavements that incorporate materials and
designs representing good engineering practice and that are in common use across the United

States and Canada. Studies included in GPS are:!

First Performance Period

GPS-l Asphalt Concrete (AC) on Granular Base

GPS-2 AC on Bound Base

GPS-3 Jointed Plain Concrete

GPS-4 Jointed Reinforced Concrete

GPS-5 Continuously Reinforced Concrete

Overlays

GPS-6

GPS-7

GPS-9

AC Overlays on AC

AC Overlays on Portland Cement Concrete Pavements

Unbonded PCC Overlays on PCC Pavements

Specific details on the GPS-3 and GPS-4 experiments as pertaining to the study reported

here are provided in later sections of the report. The SPS program involves the study of specially

constructed, maintained, or rehabilitated pavement sections incorporating a controlled set of

experimental design and construction features. Test data from the SPS experiments were not

included in this study. As such, no additional discussion on the SPS experiments is provided

here.

As part of the LTPP program, an extensive data collection effort has been under way

since about 1989. These data types are classified within the LTPP program as follows:

1. Inventory

2. Materials Testing

3. Climatic

4. Monitoring

5. Traffic

6. Seasonal

In addition, as appropriate, maintenance, rehabilitation, and construction data are also

collected.

The M-E distress modeling approach for PCC pavements involves the following

elements:

1. A structural analysis model that can consider the geometry of the pavement, the

loading condition (multiple wheel loads), and load transfer effectiveness at joints

and that is capable of reliably determining the critical responses appropriate to the

distress being considered. For PCC pavements, most of the M-E distress model

work has been done using plate on elastic (liquid or Winkler) foundation

approach.
2. A fairly reliable estimate of traffic loading. Advanced M-E procedures consider

the axle loading spectra while other models are based on use of equivalent loading

(e.g., ESAL) in which case all loadings are transformed into a single load type

using load equivalency concepts. The use of equivalent traffic loading limits the

usefulness of many of these models in developing rational design procedures.

The traffic loading data may need to be available on a seasonal basis and,

in the case of concrete pavements, on a diurnal basis as well as by lateral

placement along the width of the traffic lane.

3. A fairly reliable estimate of seasonal climatic conditions to account for changes in

material properties and, in the case of concrete pavements, to also account for the

effect of temperature differentials within the concrete slab on curling stresses.

4. Comprehensive material characterization. The PCC material properties need to be

characterized in terms of aging. For PCC materials, seasonal effects are not

considered. The granular material properties need to be characterized in terms of

stress dependency and in terms of seasonal variation as a result of seasonal

moisture and temperature variations within these materials. For example, the

spring-thaw characterization for fine-grai~ed materials is very important.

5. Availability of "calibrated" mechanistic distress models or transfer functions that

incorporate mechanistic responses. The general approach has been to develop

"absolute" models based on laboratory testing and laboratory failure criteria and to

extrapolate these laboratory models to field conditions using a shift factor to

account for different levels of distress development and other unaccountable

factors. For example, for PCC fatigue cracking, early models were developed on

the basis of laboratory testing and the first crack initiation as the failure criterion.

These models were then expanded to account for field observations and to

incorporate different levels of fatigue cracking (e.g., in terms of number of slab

panels exhibiting cracking).

6. Acceptance of Miner's fatigue damage hypothesis. Miner's hypothesis allows a

method for combining various levels of damage from the combination of traffic

and environmental loadings. Miner's hypothesis states that the structural fatigue

damage is cumulative and that a structure's fatigue life is finite, defined by the

allowable number of load applications prior to failure. Each load application

consumes a small amount of fatigue life. When the actual load applications equal

the number of allowable load applications, the fatigue damage is 1.0 or 100

percent and failure occurs. Miner's hypothesis is typically stated as follows:

~ n.

Fatigue Damage, Df= LJ-'

N;
where: Df

nj

Nj

Cumulative fatigue damage.

Actual number of load applications of load group i.

Allowable number of load applications to failure of load group i.

In an ideal M-E procedure, damage (in relation to a specific distress) should be

determined as follows:

Damage ij/d = f (eij/d)

and

eij/d = f (Ej/d)

Critical structural response in the pavement that is considered to be a

predictor of the distress under consideration for the ith axle group at the jth

time period of the kth month of the Ah year.

Modulus of elasticity of each layer of the pavement system at the jth time

period of the kth month of the Ah year.

Thus, a major consideration in developing and using M-E procedures is the appropriate

characterization of Ejkl for each of the pavement layer. Our capability for realistically modeling

pavement behavior has seen much progress in the last few decades. However, the capability to

realistically consider material characterization (e.g., Ejkl) for the pavement layers remains less

than desired because of the lack of knowledge on how to realistically account for seasonal

effects, spatial variability, and effects of deterioration due to traffic loading and environment.

It should be noted that the above steps are applicable for use of the M-E distress models

for design of new/rehabilitated pavements or for checking such designs. The application of the

M-E distress models to existing pavements to further validate/calibrate the models creates an

entirely different set of problems. Such an effort requires very reliable data on material

properties, pavement section layering, past traffic loading history, past environmental conditions,

and distress manifestation.

The validation/calibration process involves predicting cumulative damage or distress and

comparing the predicted distress to observed distress. The study reported here was aimed at

validating or calibrating the distress prediction models for transverse fatigue cracking in jointed

plain PCC pavements and for faulting in jointed PCC pavements.

The overall objective of the study was to assess how well some of the existing M-E based

distress prediction procedures performed when used in conjunction with the LTPP data.

Specifically, it was decided to assess the transverse cracking prediction procedure developed at

the University of Illinois as part of the NCHRP 1-26 study and the joint faulting prediction

procedure developed by the Portland Cement Association.
• Use of deflection data to backcalculate the pavement layer moduli - an important

input to structural evaluation. The base/subbase/subgrade was modeled as a liquid

foundation and was therefore characterized in terms of the modulus of subgrade

reaction, k.

• Use of an algorithm based on finite-element analysis of jointed slabs on elastic

foundation to calculate the critical responses. The horizontal tensile strain at the

bottom of the PCC layer at mid-slab edge was used as a predictor of fatigue

cracking and the deflections at joints were used as a predictor of rutting.

Pavement response was calculated for each load level and axle category.

• Existing transfer functions (those developed by the University of Illinois and the

Portland Cement Association) were then used to predict the damage associated

with each load level. The damage was summed over all load groups and over the

entire service life of the pavement. The resulting total damage was then compared

with the observed pavement distresses to ascertain if there was a reasonable

agreement between the observed and predicted distress levels.

As discussed, this study was aimed at using LTPP data to assess the applicability of

several existing M-E analysis procedures. Specifically, the University of Illinois procedure for

predicting the development of fatigue cracking and the Portland Cement Association procedure

for predicting the development of faulting in jointed PCC pavements were considered. Chapter 2

details the process used to develop the necessary data needed for the study using the LTPP data

base. In chapter 3, analysis results are presented for assessment of the University of Illinois

(NCHRP 1-26) fatigue cracking prediction procedure. In chapter 4, analysis results are presented

for assessment of the Portland Cement Association's joint faulting prediction procedure. Chapter

5 presents a summary of findings and provides a discussion on improvements that need to be

made to further advance the reliability ofM-E procedures using LTPP data.
The LTPP data used in the analysis reported here were obtained from the National

Information Management System (NIMS) during February 1996 (Release 6.0 data). The data

were the most recent version of the data release as of the date of this study. The NIMS data are

categorized into seven modules: inventory, environment, material testing, monitoring,

maintenance, rehabilitation, and traffic. In each module, the data are stored in tables that contain

a related set of data elements. This section briefly discusses the data elements used in the

analysis, the specific tables from which the data were obtained, the manipulations performed on

the data, and the test sections that were excluded from the analysis because of the lack of data.

Inventory data include general information about each LTPP section, such as section

identification, pavement construction date, original design, etc. The key inventory data elements

with the corresponding LTPP table names and file extensions used in NIMS are shown in table 1.

Most inventory data variable values were retrieved directly from the NIMS data base

except for the slab thickness. If slab thickness data were available from the concrete cores taken

from the field, the average core thickness was used. Otherwise, the thickness value from the

inventory table was used.

The material properties that are typically used in the mechanistic evaluation of transverse

fatigue cracking are listed below:

'. PCC modulus of elasticity.

• PCC 28-day flexural strength.

• PCC Poisson's ratio.

• PCC coefficient of thermal expansion.

• Stabilized base modulus of elasticity.

• Modulus of subgrade reaction, k.

Backcalculated slab elastic moduli for the LTPP sections were available from a previous

study conducted by ERES Consultants, Inc., under FHW A Contract No. DTFH61-94-C-00218.

However, because of too many unreasonably high values (greater than 55,000 MPa) from the

backcalculation results, these were not used in this study. The following procedure therefore was

adopted to estimate the concrete elastic modulus for each section:

1. Obtain the elastic modulus from LTPP data table TST_PC04 (file extension

*.TI2). The test results were obtained in the laboratory using field cores. This
Data Element LTPP Table Name File Extension

Section identification information INV ID *.100

-

Traffic open date INV AGE *.104

Slab thickness TST PC06 *.T2

INV LAYER *.103

Slab length INV PCC JOINT *.106

- -

Slab width INV GENERAL *.101

28-day flexural strength TST PC02 *.Tll

INV PCC STRENTH *.109

- -

PCC slab elastic modulus TST PC04 *.TI2

INV PCC STRENTH *.109

- -

Slab Poisson's ratio TST PC04 *.TI2

Shoulder type INV SHOULDER *.102

Base type INV LAYER *.103

Base thickness INV LAYER *.103
applies to 129 GPS-3 and GPS-4 sections out of the total of 192 GPS-3 and GPS4 sections.

2. If laboratory test results were not available, then the elastic modulus was

extrapolated using the 28-day flexural strength values obtained from the table

INV_PCC_STRENGTH (file extension •••.109). Fifteen sections fall into this

category.

3. If neither of the above two options were available, a value of27,580 MPa was

assigned to the section. This value has typically been used to represent the elastic

modulus for pavement concrete. The default value of27,580 MPa was used for

48 sections.

The PCC 28-day flexural strength is a very critical variable in mechanistic evaluation of

concrete pavements. The following steps, as prioritized, were taken to determine the 28-day

concrete flexural strength for each LTPP section:

1. Calculate the Mrfrom the splitting tensile strength (OT) test data in table

TST_PC02 (file extension •••.Tll). Mris calculated using the following equation:2

Mr(leS/) = 210 + 1.02(0T)

where: Mr(,e8t) =

or

Flexural strength, psi.

Splitting tensile strength, psi.

where: M,(28-days)

T

= Flexural strength at 28 days, psi.

= Age of the pavement at test, yr.

The 28-day flexural strength was calculated for 128 GPS-3 and GPS-4 sections

using this approach.
2. Estimate the 28-day flexural strength from the inventory flexural strength data of

different ages in table INV_PCC_STRENGTH (file extension *.109). Typically,

the data were for 7 or 14 days. Therefore, 7-day strengths were multiplied by a

coefficient of 1.3 in order to estimate the 28-day strength; 14-day strengths were

multiplied by 1.1 to estimate the 28-day strength; i.e.4

Mr(28 days) = Mr(test, 7 days)* 1.3

Mr(28 days) = Mr(test, 14 days)* 1.1

where: Mr(test, 7 days)

M,.(test, I4 days)

= 7-day flexural strength.

= 14-day flexural strength.

The 28-day flexural strength values were obtained using this method for 28

sections.

3. Estimate the 28-day flexural strength from the inventory compressive strength

data at different ages from table INV_PCC_STRENGTH (file extension *.109).

Again, the compressive strength data were normally measured at7 or 14 days, so

7-day strengths were multiplied by a coefficient of 1.3 to estimate the 28-day

compressive strengths and 14-day strengths were multiplied by 1.1 to estimate the

28-day compressive strengths. The 28-day flexural strengths were estimated from

the 28-day compressive strengths (f'e) by using the following equation:

M = 10*[fle]0.5 r(28 days)

The 28-day flexural strength value was determined for 13 sections using this

method.

4. If no data were available, a value of 4.48 MPa was chosen as a default value for

the 28-day flexural strength. This applied to 32 GPS-3 and GPS-4 sections.

Furthermore, all the data were reviewed for either very high or very low values.

Values in the range of3.45 MPa to 5.52 MPa were considered acceptable for the

analysis. Any values outside these limits were not used, and the default value of

4.48 MPa was used for these sections.

The following two steps, as prioritized, were taken to estimate the Poisson's ratio of the

concrete:
1. Estimate Poisson's ratio of the section from the data in the LTPP test table

TST_PC04 (file extension *.TI2). If the tested value was greater than 0.20, then

0.20 was used. The minimum Poisson's ratio obtained from the test table was

0.11, which was considered acceptable. The test values were available for 128

GPS-3 and GPS-4 sections.

2 A value of 0.20 was chosen iftest data were not available. Sixty four sections fell

into this category.

The coefficient of thermal expansion is a variable depending on the concrete mix design

and the type of aggregate used. As shown in table 2, the coefficient of thermal expansion of the

aggregates varies and affects the overall coefficient of thermal expansion of concrete.4

Generally, the thermal expansion coefficient of the concrete is between 6.3*10..(i/PCand

.l3.5*1O-6/

oC. Laboratory tested coefficient of thermal expansion values were not available.

Also, the aggregate type and cement content values were not available for many sections in the

NIMS data base. Therefore, a value of9.9*1O-6/oC was assigned to each section.

Coefficient of Thermal

Expansion,lO-6;oC

Aggregate

Granite 7-9

Basalt 6-8

Limestone 6

Dolomite 7-10

Sandstone 11-12

Quartzite 11-13

Marble 4-7

When the base layer is a stabilized material with an elastic modulus comparable to the

elastic modulus of concrete slab (EBas)Eslab >0.1), then the base layer can have an effect on the

slab response to load. However, this is not a very critical variable in the transverse cracking

evaluation. For this study, base elastic moduli for stiff stabilized base were estimated using the

material code and description of the base course from table INV_LAYERS (file extension *.103),

as shown in table 3.
Elastic

LTPP Modulus,

Description Code MPa

Soil Cement 27 1,379

AC Bound Base (dense graded, hot laid, central plant mix) 28 3,103

AC Bound Base (dense graded, cold laid, central plant mix) 29 1,379

AC Bound Base (open graded, hot laid, central plant mix) 31 1,379

Cement-Aggregate Mixture 37 6,895

Lean Concrete « 3 sacks cement/cy) 38 13,790

Limerock, Caliche (soft carbonate rock) 41 1,379

Pozzolanic-Aggregate Mixture 44 3,448

Deflection data were used to backcalculate the dynamic k values in a recently finished

LTPP data analysis project. 5 Two methods were used in the project to determine the subgrade k

value. One method was the AREA method currently used in the AASHTO Guide for the Design

of Pavement Structures, by which the slab radius of relative stiffness, f, is estimated as a function

of the AREA of the deflection basin. The second method was a best-fit method, which solves for

the combination of f and k and produces the best possible agreement between the predicted and

measured deflections at each sensor. Several sensor configurations also were considered to

investigate the significance of sensor configuration to backcalculation results. The effect of the

finite slab size also was corrected for in the backcalculation results.

On the basis of the results of the comparison of the plate load data and other soils data

available in the LTPP data base, the AREA method with seven sensor configurations and slab

size corrections was selected for estimation of the dynamic k values. The static k values were

then estimated by dividing the mean calculated dynamic k values after data screening by 1.97.5

Traffic data are one of the most important data elements for the mechanistic evaluation of

the distress data. To determine the amount offatigue and faulting damage accumulated at the

crititallocation, the following data items are needed to represent traffic conditions: axle type,

axle weight, number of the axle passes, and lateral traffic distribution.
Intensive efforts are being made to obtain quality traffic data for the LTPP studies. Site

monitored traffic data for some sections have recently become available, including Automatic

Vehicle Classification (AVC) and Weight-In-Motion (WIM) data. Only the WIM data were used

in this study. The data relevant to this study are included in the following two tables:

TRF _MONITOR_AXLE_DISTRIB (file extension *.F04)

TRF_MONITOR_BASIC_INFO (file extension *.F01)

The first table provides information on the axle type, axle weight, and the total number of

axles passes for the monitoring year; the second table includes the information on the number of

days with WIM monitoring in a given year. The total count is extrapolated based on the number

of passes on the WIM monitoring days. Some sections had only 1 year of traffic monitoring data,

while others had 2 or 3 years of traffic monitoring data. The monitoring year with the highest

number of days with WIM data was selected to represent the traffic condition of the section in

one specific year. This was generally the last year ofthe traffic monitoring data available. There

are 140 axle load/type categories for each section. The axle categories include single, tandem,

tridem, and four-axle assemblies.

For the fatigue cracking evaluation study, a total of 52 jointed plain concrete pavement

(JPCP) sections from a total of 129 sections in the GPS-3 experiment had at least 1 day of traffic

monitoring data in 1 year. Table 4 provides a list of sections with traffic monitoring data for the

year with the highest number of days of WIM data.

Since the traffic data obtained from the LTPP NIMS data base were available only for a

few years, the traffic data for the remaining years had to be backcasted to the year when the

pavement was opened to traffic in order to estimate the cumulative traffic.

To calculate the cumulative fatigue damage, the cumulative traffic passes for each axle

weight in each axle group were needed. As discussed previously, for the sections with traffic

data, only 1 year of monitored data was selected. Therefore, it was necessary to backcast traffic

data to the year the section was opened to traffic. In this study, a constant growth factor of 2

percent was assumed for all the sections. The use of the 2 percent growth factor was considered

conservative as it results in a higher level of cumulative traffic loading. The following equation

incorporating the 2 percent growth factor was used to calculate the estimated traffic at the

beginning year for the test section:

where: To

Tc

n

Estimated traffic at the time of opening to traffic.

Traffic for the monitored year.

Age at the time of the traffic monitoring year.
State SHRPID Traffic Monitorin2 Year Number of Days with WIM Data

5 3011 1993 42

6 3030 1992 29

6 3042 1992 66

8 3032 1993 161

12 3804 1993 14

12 3811 1993 14

12 4000 1993 343

12 4057 1993 333

12 4059 1993 315

12 4109 1993 317

12 4138 1993 343

13 3015 1993 6

13 3018 1993 3

18 3002 1993 168

18 3003 1993 227

18 3030 1993 304

18 3031 1993 135

19 3006 1993 59

19 3009 1993 6

19 3028 1993 5

20 3013 1992 5

20 3015 1993 201

21 3016 1993 146

26 3068 1993 318

26 3069 1993 317

27 3003 1993 219

27 3013 1992 362

29 5393 1993 7

31 3018 1993 9

31 3023 1993 9

31 3028 1993 7

31 3033 1993 6

32 3010 1990 20

32 3013 1992 6

32 7084 1992 14

38 3005 1993 168

38 3006 1993 79

40 4160 1993 31

40 4162 1993 29

42 1623 1991 5

42 3044 1993 3

46 3012 1993 130

53 3011 1993 351

53 3013 1993 343

53 3014 1992 314

53 3019 1992 324

53 3812 1993 362

53 3813 1993 365

53 7409 1993 330

83 3802 1993 205

89 3015 1993 125

R9 1016 1992 172
To be consistent with the backcasting approach, a constant growth rate of2 percent was

again assumed to calculate the cumulative traffic at the time of the distress survey. The

following equation was used to compute the cumulative traffic:

1(1 + 0.02)n-l I}

Cumulative Traffic Passes = To * -

0.02

A GPS section was opened to traffic in January 1970 and the last distress survey was

conducted in May 1994. In 1990, the LTPP traffic data indicate that a 111.2 kN single axle was

counted 1000 times during that year. Assuming that the traffic growth rate is 2 percent, the

cumulative numbers of axle applications are computed as follows:

1970111.2 kN Single Axle Loadings, To = 1000/(1.02/20-1)

= 686 applications

Cumulative Axle Loadings to 1994 = 686 [(1.02/4.

5

- 1]/0.02

21,418 applications

The knowledge of lateral distribution of trucks in the traffic lane is critical for computing

fatigue cracking damage because of the high longitudinal edge stresses that develop when the

truck loading is applied at or near the edge. The truck lateral distribution is a function of width

of the traffic lane, location of edge stripe, paved or unpaved shoulders, edge restraints such as

retaining walls, and the existence of curbs and gutters. Ideally, the lateral distribution should be

measured for local conditions. However, this information is not available in the LTPP data base,

and the following general approach was taken to consider the lateral distribution of truck traffic.

It was assumed that the lateral wander of truck traffic is normally distributed about the

mean wheelpath. Then, the lateral distribution of the trucks was determined by the mean wheel

location and the standard deviation of the traffic wander. Studies by Emery in 1975 showed a

mean wheel location of 406 to 457 mm from the edge with a standard deviation of 254 mm on

rural lane interstate highways.6 The lateral distribution was shown to be approximately normal. 3

This results in about 10 percent ofloads that were within 152 mm of the slab edge. Another

study conducted by Benekohal et al. in 1990 showed an average wheel location of559 mm from

the pavement edge with a standard deviation of213 mm.7 These results were based on 1,300

observations. This results in about 3 percent of loads that were within 152 mm of the slab edge.

For this study, a conservative value of 8 percent of the loads within 152 mm of the slab edge was

selected to account for the truck lateral distribution effect. Thus, for fatigue cracking analysis,

only 8 percent of the axle loads were considered with the load located right along the slab edge.
Climate is another important factor that affects pavement performance. With respect to

fatigue cracking, the most significant factor is the temperature differential or thermal gradient

between the top and the bottom of the slab and the moisture in the slab. The thermal gradient can

be either positive (i.e., the top of the slab is warmer than the bottom, or negative, with the top of

the slab cooler than the bottom). A positive thermal gradient causes the top to curl downward,

which is resisted by the support. This creates restraint tensile stress at the bottom of the slab with

the maximum stress level midway between the joints. A negative thermal gradient causes the

comers of the slab to curl upward, and this is resisted by the weight of the slab. This results in

tensile stress at the top of the comer region of the slab. The downward curling of the slab caused

by the positive thermal gradient adds to the loading stress caused by the traffic. This can increase

the critical stresses in the concrete slab dramatically, especially with large positive thermal

gradients. The fatigue damage caused during the negative temperature gradients is negligible as

the curling stresses subtract from the load stresses. Therefore, only the positive thermal gradients

were considered in this study.

The temperature gradient in the pavement slabs change continuously through the day.

The main factors affecting the magnitude of temperature gradients are air temperature, wind

speed, and the amount oftime the slabs are exposed to the sun. To adequately account for the

effect of temperature gradients, hourly temperature gradient data for the entire year from the

representative years were needed. The Climatic-Materials-Structural (CMS) pavement analysis

program was used to generate the needed data from the monthly derived climatic data in the

LTPP data base.8 The CMS model has been validated and has been shown to predict

temperatures in pavement slabs reasonably well. The CMS model calculates the thermal gradient

with depth considering air temperature, radiation heating and cooling, convection, cloud cover,

wind speed, and material properties. From the LTPP climatic data base, the variables used to

calculate the thermal gradients using the CMS model are shown in table 5.

Examples of the histograms of temperature differential versus frequency of occurrence in

percent time of the year for a few sections are given in figures 1 through 4. Average monthly

maximum temperature and average monthly minimum temperature were available for most of

the JPCP sections. However, only 56 sections out of a total of 129 sections in the GPS-3

experiment had percent sunshine data and only 81 sections had wind speed data. For the sections

without either percent sunshine data or wind speed data, the average value of these parameters

for other sections in the same State or the surrounding States were used instead.

The manual transverse cracking data are stored in the table MON_DIS_JPCC_REV (file

extension *.M08). The data elements used in the evaluation are TRANS_CRACK _NO _L,

TRANS _CRACK_NO _M, and TRANS_ CRACK_NO _H. The parameter of interest is the

percent slabs cracked in the 152.4-m section, which can be calculated as:
Data Element LTPP Table Name File Extension

Average monthly maximum ENV MONTHLY PARAMETER *.E03

- -

temperature (1959 to 1989)

Average monthly minimum

temperature (1959 to 1989)

Average monthly wind speed

(1959 to 1989)

Average monthly percent

sunshine

(1959 to 1989)

PCC slab thickness TST PC06 *.T2

INV LAYER *.103

Latitude INV ID *.100
0.10

~

5j 0.08

::::J 10

.

06

0.04

I-MO 5393, WF. 8-ln slab I

Figure 1. An example of temperature difference distribution of a wet-freeze

section for an average year.

0.16

0.14

0.12

,- FL 3811, WNF, 9-ln slab I

~ 0.10

c

CDt 0.08

u. 0.06

0.04

0.02

0.00

Figure 2. An example of temperature difference distribution of a wet no-freeze

section for an average year.
IIIco 3032, OF, 8-in slab I

~

55 0.08

~

tr

~ 0.06

u.

Figure 3. An example of temperature difference distribution of a dry-freeze

section for an average year.

IIICA 3042, ONF, 9-in slab I

~

55 0.08

~

~ 0.06

u.

Figure 4. An example of temperature difference distribution of a dry no-freeze

section for an average year.
% slabs cracked = (Total TRANS CRACKED NO) * average joint spacing, m

- - 152.4

where: TOTAL TRANS CRACK NO = TRANS CRACK NO L + - --

TRANS CRACK NO M + - --

TRANS CRACK NO H.

- --

For the sections with traffic data but no manual transverse cracking data, the

photographic distress data in the table MON_DIS_PADIAS_JC (file extension *.M17) were

used. No attempt was made to differentiate between midslab and non-midslab transverse

cracking or random cracking (construction related) as these data were not readily available. It

was assumed that a very low amount, if any, of random cracking was present in the GPS-3

sections.

The joint faulting data were derived from the table MON_DIS_JPCC_FAULT (file

extension *.M09). The table lists the values for joint faulting at the comer and at the wheelpath

at each joint. The values used in the analysis were the comer values, averaged along the l52.4-m

length of the section.

The total number of GPS-3 sections is 129 and the total number of GPS-4 sections is 68.

Only GPS-3 sections were used for the analysis of fatigue cracking. For joint faulting analysis,

both GPS-3 and GPS-4 were used. However, as discussed, many sections were missing key data

such as traffic and distress data. These sections were not used in the analysis. For analysis of

fatigue cracking, data from 52 sections (with traffic data availability) were used. For the analysis

of faulting data, data from 57 sections (20 with aggregate interlock joints and 37 with doweled

joints) were used.

It should be clear from the information presented in this chapter that LTPP test sections

have zero utility if any of the critical data elements are missing or are of questionable quality.
Transverse fatigue cracking is one of the most important distress measures that affects the

pavement performance for JPCP. This occurs as a result of repeated application of high stresses

in the concrete slabs that induces fatigue failure. The high stress levels are caused by the

combined effects of the shrinkage of the concrete slab, thermal curling, moisture warping, and

traffic loading. Fatigue cracking is caused by the repeated application of traffic and

environmental loadings at stress levels lower than the failure stress level. This section

documents the mechanistic evaluation of the fatigue cracking that occurred in LTPP JPCP

sections.

The keys to the evaluation of the transverse fatigue cracking in JPCP include the

following:

• Reliable determination of the stresses at the critical location under both traffic

loading and the environmental effects; and

• Accurate prediction of the fatigue damage using a reliable fatigue damage model.

In this study, the fatigue analysis was conducted assuming that the transverse cracks

observed in JPCP are the result of fatigue failure initiated at the slab bottom near the mid-slab

locations. Therefore, for normal3.66-m-wide sections, the critical damage location is at the

bottom of the longitudinal edge, halfway between the two transverse joints that border the slab.

The maximum wheel-load stress occurs at the longitudinal edge when the load is placed right

along the edge. The stresses resulting from slab temperature curling also add significantly to the

load stresses when the slabs are exposed to high positive temperature gradients. Combined, the

magnitude of stresses at the longitudinal edge is so much greater than the stresses at any other

location that fatigue cracking in JPCP is controlled by the few axle loads that pass along or near

the slab edge while the slab is subjected to a large positive temperature gradient.

There are many procedures to calculate the stresses induced in the concrete slab. Finite

element analysis technique is the most accurate technique for the calculation of slab stresses. In

the NCHRP 1-26 study, a procedure was developed to determine the structural responses that can

consider different pavement conditions and different loading conditions based on the plate on

liquid [Winkler foundation model (the Westergaard model)].9 The stresses calculated from the

Westergaard model are modified using results from the finite element model, ILLI-SLAB, to

make the necessary adjustments for joint spacing, load transfer, load location, load configuration,

slab curl, etc.10,II,12 All these modifications were validated using factorial matrixes of the key

variables.9 This approach was selected in this study to calculate the critical tensile stresses in the

concrete slab.
The NCHRP 1-26 equations start with Westergaard's "new" formula for edge loading for

a circular load. 13 This approach is based on medium-thick plate theory on a dense liquid

foundation. The closed form solution for the edge load stress, ae, is given below:

a = 3(l+~)P [In Eh

3

+ 1.84 _ 4~ + 1-~ + 1.18(1+2~)a] (11)

e 1t(3+~)h2 100ka4 3 2 ~

where: P =

~ =

E =

h =

k =

a =

~ =

where: E =

h =

~ =

k =

Total applied load, Ibf.

Poisson's ratio.

Modulus of elasticity of PCC, Ibf/in2•

Slab thickness, in.

Modulus of subgrade reaction, Ibf/in2/in.

Radius of the applied load, in.

Radius of relative stiffness, in, defined as follows:.

[

Eh3 ] 0.25

~ = 12(1 - ~2)k

Modulus of elasticity of PCC, Ibf/in2•

Slab thickness, in.

Poisson's ratio.

Modulus of subgrade reaction, Ibf/in2/in.

(Note: 11bf= 4.448 kN, Ilbf/in2 = 0.895 kPa, 1 in = 25.4 mm,

Ibf/in2/in = 0.27 MPalm)

The load stresses are determined by applying various adjustment factors to the edge stress

calculated using Westergaard's equation (equation 1). The adjustments are made for the slab size

effect, widened lane, tied concrete shoulder, and stabilized base. Regression equations are

available for determining each of these factors. The final load stress is computed as follows:

where: aload

!slab> /nose'

fWlJfTied Adjustment factors for slab size, stabilized base, widened lane, and

tied concrete shoulder.

Stress obtained using Westergaard's edge load equation for circular

loads, Ibf/in2•
The equivalent single-axle radius (ESAR) concept is used to handle multiple wheel loads,

and adjustments are made to account for the slab size effect, widened traffic lane, tied concrete

shoulder, and the presence of a stabilized base.

The ESAR is the equivalent single wheel radius for a multiple wheel load that will

produce the same stress intensity as the single circular wheel load having a radius of loaded area

equal to ESAR at the critical location. The application of the ESAR concept allows the use of a

closed form solution to determine the maximum stress under a multiple wheel load. The axle

configurations analyzed in this study are shown in figure 5.

The equivalent single-axle radius for the dual wheel load is obtained using the following

equation:9

a

eq = 0.909 + 0.339485 S + 0.103946 a _ 0.017881( s) 2_ 0.045229( s) 2

a

a a ~ a a ~

+ 0.000436( ~) 3_ 0.301805 ~( ~) '. 0.034664( :) '. 0.001( ~) 3~

o ~(S/a) ~ 20

o ~ (a/~ ~0.5

where: aeq

a

S

~

Equivalent single axle radius of dual wheels.

Radius of the applied load.

Dual wheel spacing.

Radius of relative stiffness.

The equivalent single-axle radius for the dual wheel tandem axle load is given by the

following equation:9

Limits: 4 < (tla) < 16

0.05 < (all) < 0.5
Single Wheel

Single Axle

Dual Wheels

Single Axle ®®

TraM"'" Wheel

®®

Spacing

It t!

84 in

Dual Wheels ®® ® Longitudinal

Tandem Axle 48 in Wheel

®® ®® Spacing

14 in

Dual Spacing

14 III

®® ® Longitudinal

Wheel

Dual Wheels ®® ®® Spacing

Trldem Axle

®® ®®

(1 in = 25.4 mrn)

Figure 5. Axle configurations analyzed.
The regression equation for the equivalent single-axle radius for the dual wheel tridem

axle load is given by the following equation:9

Q;: = 1.542864 + 0.56744~ ~) + 5.465697( ~) + 17.37141~ ~ r

-Oo70471~ ~) - 2061563( 1) + Oo087538( ~) (~) - OoOOO35~~) (~r

3 5 (8/a) 515

45 (t/a) 510

0.05 5 (all) 50.3

Edge stress calculated by the Westergaard solution is for slabs of infinite size. Ioannides

et al. introduced a normalized length term, VZ, to correct the Westergaard edge stresses for slab

size.14 In the NCHRP 1-26 study, a factorial was designed for the key variables affecting the

stress, and a regression equation was developed to account for the finite slab size, as shown

below:9

:: = 0.582282 - 0.53307' n + Oo18170~ ~) - Oo01982~ ~ r

+ Oo109051( ~) ( ~)

3 5(Ul) 55

0.05 5 (all) 50.3

ILLI-SLAB edge stress for finite slab.

Westergaard edge stress for infinite slab.

Radius of relative stiffness.

Slab length.
The following two equations were developed in NCHRP 1-26 to correct for the effect of a

tied shoulder:9

(JAGG = 0.99864 _ 0.SI237( a) _ 0.0762[ln( AGG)] +

(JAGG=O I kl

0.00315[ln2( A~) 1 + 0.015936[( ;)' In2( A~)]

5 ~ (AGG/kl) ~ 50000

0.05 ~ (all) ~ 0.3

and

= 1 - 0.02516' A~) _ 0.08603~ ;)( A~G)

o ~ (AGG/kl) ~ 5

0.05 ~ (all) ~ 0.3

Aggregate-interlock factor.

Edge bending stress with aggregate interlock at AGG/kl.

Free edge bending stress.

When base layer is a stabilized material with an elastic modulus comparable to the elastic

modulus of concrete slab (EBas/ESlab >0.1), then the base layer can have a significant effect on the

slab response to load. Two cases were considered in the NCHRP 1-26 study, namely a bonded or

unbonded base. The following regression equation was developed to correct the effect of an

unbonded base:9

a~:,= 0.0477629 + 0.26526~ ;) + 0.953195( :~ r

_ 0.26083( ;) ( hh~)-2

Limits: 1 ~ {he/h)2 ~ 1.6

0.05 < (all) < 0.3

26
where: oil/ = ILL! -SLAB edge stress with a base.

°west = Westergaard edge stress without a base.

hefft = Effective thickness.

heff

2 2E2h2

= hl

+ hl--

Elhl

hI = Slab thickness.

h2 = Base thickness.

For the bonded base case, an equivalent layer can be calculated based on the transformed

section concept. The following equations can be used to calculate the effective slab thickness:

(~)hl(hl + 11,)

hI + ~ ::]

hlf =

h2f =

hI =

h2 =

Transformed slab thickness.

Transformed base thickness.

Slab thickness.

Base thickness.

On widened lane sections, the critical location for fatigue damage is the bottom of the

slab, directly under the wheel path and at the midslab location. Studies have shown that the slabs

are almost never loaded at the outer edge on widened lane sections.7 Therefore, the following
adjustment factor was used to obtain the maximum stress directly under the wheel load for the

few cases of widened lanes:9

= 0.454147 + 0.013211 + 0.386201!!-

DN D

_ 0.24565( ~) 2 + 0.053891 ( ~) 3

Adjustment factor for widened lane.

1.0 if standard-width lane of3.66 m.

Radius of loaded area.

Mean wheel location, in from outer edge.

Radius of relative stiffness.

The curling stress is determined using the following equation and then combined with the

load stress using a regression coefficient in the NCHRP 1-26 procedure:

where: 0c =

C =

E =

aT =

LIT =

C E aT !:iT

2

Curling stress.

Curling stress coefficient.

Concrete modulus of elasticity.

Concrete coefficient of thermal expansion.

Temperature difference between the top and bottom of the slab.

This equation was developed by Westergaard, and Bradbury developed the coefficients

for solving this equation.1S,16 For maximum stress at the longitudinal edge, the curling stress

coefficient is given by the following equation:

where: L

~

C = 1 - 2 COSAcoshA (tanA + tanhA)

2 sinA sinhA

Slab length.

Radius of relative stiffness.
Warping is the result of non-uniform shrinkage between the top and bottom of the slab.

The top of the slab is usually drier than the bottom throughout the year. Therefore, moisture

gradient generally tends to cause lifting of the slab corner or warping. The warping is resisted by

the slab weight, causing warping restraint stresses in the slab. The moisture gradients could be

treated as equivalent temperature gradients, but insufficient research is available to adequately

quantify this effect.

During initial construction, as concrete dries it will shrink in volume and thus cause

upward warping and warping stresses. The shrinkage normally occurs during concrete's initial

curing phase, and before it has attained its full strength. Since the shrinkage warping stresses

occur early in the concrete aging cycle, and the stresses are long term, some of the warping

stresses may be relieved by concrete creep. Again, there is not enough information to quantify

the effect. Therefore, the warping stresses are not considered in this evaluation. It was assumed

that the warping effects are indirectly accounted for during the calibration/validation of the

procedure.

Combined edge stress.

Load stress.

Regression coefficient.

Curling stress.

where: 0combined

O/ood

R

The regression coefficient R is determined using the following equation:9

R = 1.062 - 0.015757 dT - 0.0000876 k - 1.068 L + 0.387317 dT L

Q Q

+ 1.17x10-11E dTk - 1.81x10-12E dT2k - 1.051X10-9E( ~) 2kdT

+ 1.84xlO-11E dT2~ k - 1.7487( ~) 2dT + 0.000034351dT3

• 86.97( ~) 3_ O.00816396dT' ~

aATx 105•

Concrete coefficient of thermal expansion, E/oF.

where: dT

ex
AT =

k =

L =

~ =

E =

Temperature difference through the slab, OF.

Subgrade modulus of reaction, Ibf/in2/in.

Slab length, in.

Radius of relative stiffness, in (equation 11).

Concrete modulus of elasticity, Ibf/in2•

(Note: Ie/OF = 1.8e/oC, 1°F = 0.56°C, llbf/in2/in = 0.27 MPalm, 1 in = 25.4 mm,

1 Ibf/in2= 6.895 kPa)

The coefficient R is needed because the load and curling stresses are not directly additive.

Curling causes various parts of the slab to lift off of the base, invalidating the full contact

assumption made in the load stress calculation. The regression coefficient R provides the

necessary adjustment to the curling stress to give the correct combined stress.

Several fatigue models are available to calculate the total number of a specific load

coverages to failure.3,9 The fatigue model developed in the NCHRP 1-26 study was used in this

project. The model, which gives the mean number of coverages to failure, defined as 50 percent

slabs cracked, is of the following form:

LogN = -1.7136R + 4.284 for R > 1.25

LogN = 2.8127R -1.2214 for R < 1.25

Ratio of flexural stress, due to load and climatic factors, to the mean

modulus of rupture of the concrete.

Number of coverages to 50 percent slabs cracked.

where: FD =

nijk =

Nijk =

i =

FD = L

Total fatigue damage at the critical location in the slab.

Number of load repetitions of z-thaxle grouP,J-th load level, and JCh

temperature gradient.

Number of allowable load repetitions of z-thaxle group,Jib load level, and JCh

temperature gradient.

A counter for axle group (single dual, tandem dual, and tridem dual).
A counter for axle load magnitude, total of 83 axle load levels in the LTPP

data base for the single, tandem, and tridem axles.

A counter for temperature gradient levels, total of 15 levels used.

The number of load repetitions, nijb was computed using traffic data from the LTPP

traffic data base for different axle load group and load magnitude. It was corrected for the truck

lateral distribution. Temperature gradient was represented by the frequency of the different

temperature difference happenings in a typical year, as discussed previously. Therefore, the

number of load repetitions of a specific axle load group and load level, for a specific temperature

gradient level, can be formulated as follows:

Load repetition count from the LTPP data base for a specific load

group and magnitude.

Lateral truck distribution factor for loads within 6 in from the edge

(8 percent).

Frequency of a specific temperature gradient happening in a typical

year.

A spreadsheet was developed to calculate the allowable number of load repetitions for

each axle load group at each load level for a specific temperature gradient. This was then used

with the actual load repetition in each group to calculate the total fatigue damage. The calculated

load and curling stresses were compared with the results from the computer program ILLI-CONC

developed under the NCHRP 1-26 project to ensure the correctness of the spreadsheet. It is

worth noting that, since there were 83 total load levels and 15 temperature gradient levels used

for the fatigue damage calculation, a total of 1,245 calculations for each LTPP section was

needed to obtain the cumulative fatigue damage.

At the time of the analysis, a total of 52 JPCP (GPS-3) sections had at least 1 year of

traffic monitoring data. Only these 52 sections were used in the analysis. The specific data used

in the analysis for these 52 sections are given in appendix A. The fatigue analysis results of the

52 GPS-3 test sections are shown in figure 6. Also shown in the graph is a transverse cracking

model recently developed as part of a completed FHWA concrete pavement performance study.17

This model is based on field observations from 303 in-service concrete pavements in the United

States and Canada in 1987 and 1992. A total of 465 data points were used to develop the model.

The model is listed below:

100

1 + 1.41FD 1.66
As shown in figure 6, there were only 15 sections with traffic data in GPS-3 showing

some form of transverse cracking. The sections with fatigue cracking generally follow the trend

of the model except for a couple of outliers. There also are many sections with large

theoretically calculated fatigue damage values but with no transverse cracking present, indicating

that the fatigue damage procedure used and/or the input data used do not fully simulate the

fatigue cracking process in JPCP.

This section is concerned with the sensitivity of the fatigue damage calculation as a

function of some key data elements such as traffic counts, modulus of rupture of the concrete,

concrete elastic modulus, concrete thermal expansion coefficient, and subgrade modulus of

reaction. A Missouri section, SHRP ID of 5393, was selected to conduct the sensitivity analysis.

The following results are all based on the data from this pavement section.

Traffic counts represent the loading conditions of the pavement over time. The

availability and accuracy of the traffic spectrum data are always a great concern in the

mechanistic evaluation of the pavement distresses. When Miner's hypothesis is used to calculate

the cumulative fatigue damage as given in equation 20, the total cumulative fatigue damage is the

linear combination of the traffic counts divided by the allowable number of repetitions under the

specific condition. Figure 7 shows the variation of the cumulative fatigue damage when the

traffic counts are all doubled or halved uniformly for all load configuration and load levels.

Modulus of rupture of the concrete is another very important variable in the mechanistic

evaluation. Figure 8 gives the sensitivity plot of the fatigue damage with the variation of the

modulus of rupture of the concrete. As shown, small changes in Mr will significantly affect the

final calculated fatigue damage. Similarly, as shown in figure 9, variation in the elastic modulus

value will have a significant effect on the calculated fatigue damage. The sensitivity plot of the

PCC thermal expansion coefficient (figure 10) also shows a significant effect on the calculated

fatigue damage.

Figures 11 and 12 show the fatigue damage as a function of concrete Poisson's ratio and

the subgrade k-value. As shown, within the range of values commonly used, fatigue damage

computation is not dependent on either Poisson's ratio or modulus of subgrade reaction used.

Analysis of the LTPP fatigue cracking data indicates that the LTPP data have a high

potential for supporting the development ofM-E procedures for the prediction of fatigue

cracking. The analysis presented was limited to showing the potential for use of the LTPP data

for calibrating/validating existing M-E procedures. No specific calibration of the NCHRP 1-26

model/procedure for prediction of fatigue cracking was attempted because it was considered

premature to do so at this time, for the following reasons:
100

90

80

i 70

~

e!

0

60

fIl ,g

50 .!!!

fIl

-r:: 40

~Q) 30

ll.

20

10

0

1.0E-Q7 1.oe-Q6 1.0E-Q5 1.0E-Q4 1.0E-Q3 1.0E-Q2 1.0E-Q1 1.0E+00 1.0E+01 1.0E+02

Fatigue Damage

IfIl ,g

.!!!

fIl

C

~ 30

ll.

100

90

80 AActual data

70 ZTrafficl2

60 XTraffic*2

50

40

o f-6-X~%-6-~ I Z ~~X-%~ ,

1.0E-07 1.0E-06 1.0E-Q5 1.0E-Q4 1.0E-Q3 1.0E-Q2 1.0E-01 1.0E+00 1.0E+01 1.0E+02

Fatigue Damage
800

700

600

500

1 400 i

300

200

100

o

1.OEo07 1.0E-QI 1.0E-QI 1.0E-04 1.0E-G3 1.0E.Q2 1.0E-G1 1.OE.ao 1.OE+01 1.0E+02

F•••• o.m.ge

Fipre 8. Sensitivity plot of the fatigue damage with change of modulus of rupture.

10

9

8

'R 7

c: 6

/

,g

E 5

.&i 4 .!!

.n 3

2

O+------1f----+---+---+----t---+---+---j------;

1.oeo07 1.oe-Q8 1.oe-05 1.0E-04 1.0Eo03 1.OEo02 1.0E.Q1 1.0E+OO 1.OE+01 1.OE+02

Flltigue OarN1g8

Figure 9. Sensitivity plot of the fatigue damage with change of elastic

modulus of the slab.
0.5

0.45

0.4

0.35

t

0.3

i

0.25

0.2

I

D.

0.15

0.1

0.05

O+----+----f-----I---+---+----+----+----+-----j

1.0E-Q7 1.0E-Q6 1.0E-05 1.0E-04 1.0E-Q3 1.0E-Q2 1.0E-Q1 1.0E+OO 1.0E+01 1.0E+02

Fatigue Damage

Figure 10. Sensitivity plot of the fatigue damage with change of the

PCC thermal expansion coefficient.

/

O+----1I-----+----+-__ +-_--+~ _ __+_-~+_--+__-__1

1.0E-07 1.0E-Q6 1.0E-Q5 1.0E-Q4 1.0E-Q3 1.0E-Q2 1.0E-Q1 1.0E+OO 1.0E+01 1.0E+02

Fatigue Damage

Figure 11. Sensitivity plot ofthe fatigue damage with change of

Poisson's ratio of the slab.
450

400

350

300

250

200

150

100

50

o

1.0E-Q7 1.0E-Q6 1.0E-Q5 1.0E-Q4 1.0E-Q3 1.0E-Q2 1.0E-01 1.0E+OO 1.0E+01 1.0E+02

Fatigue Damage

Figure 12. Sensitivity plot of the fatigue damage with

change of subgrade k-value.
2. Concern with the quality of the extrapolated traffic data. Even though weigh-inmotion data are beginning to be available for many GPS test sections, the

sampling precision, the reliability of the axle load measurements, lateral

distribution of traffic, and the backcasting of traffic need further clarity.

3. Concern with the fatigue cracking distress data. The fatigue data need to be reevaluated to ensure that random cracking data are omitted from the fatigue

cracking data.

5. A better characterization needs to be developed to incorporate curling and

warping effects. The availability of site specific coefficient of thermal expansion

for the concrete would greatly aid in this effort.

In summary, it is concluded that the NCHRP 1-26 approach for predicting fatigue

cracking (in terms of pertinent slabs cracked) appears to be reasonable, given the many

unknowns that continue to hinder a complete development of the prediction methodology. As

the LTPP data base is progressively improved upon, both in terms of quality and in terms of data

coverage, it is expected that the NCHRP 1-26 approach will be improved and that a more reliable

and better calibrated fatigue cracking prediction procedure will be developed.

Transverse joint faulting is the difference in elevation of two adjacent slabs at a joint.

Typically, the leave slab is at a lower elevation than the approach slab. Many jointed PCC

pavements experience serious faulting with time. A faulting level in excess of 6 mm is

considered unacceptable for high-volume highways. Faulting is significantly affected by the

presence of dowel bars and permeable/non-erodible base, joint spacing, and subdrainage

conditions.

Over the years, many studies have been conducted to research the development of

faulting. Various models have been developed to predict faulting. Typically, these models have

been empirical in form and incorporate the use of the equivalent single-axle load parameter to

represent the traffic loading. The only mechanistic-based faulting prediction procedures are

those developed under the sponsorship of the Portland Cement Association (PCA). These

mechanistic-based models were the ones used in the analysis of the LTPP faulting data, as

reported here.

Prior to 1984, mechanistic thickness design procedures for concrete pavements were

based on the principle of limiting the flexural stresses in a slab to avoid flexural fatigue cracks

due to load repetitions. Erosion criteria were incorporated into the 1984 PCA design procedure

since some modes of pavement distress, such as pumping, faulting, and shoulder distress, are

unrelated to fatigue. Distress due to erosion is considered to be more closely related to slab

deflections than to flexural stresses. At slab comers and edges in the presence of water and many

repetitions of heavy axle loads, pumping (erosion of subgrade, subbase, and shoulder materials),

voids under and adjacent to the slab, and faulting of pavement joints (especially in pavements at

nondoweledjoints) can occur. Voids or the loss of uniform support increase slab stresses and

strains and can lead to premature cracking.

Attempts to correlate comer deflections to AASHO Road Test performance data, where

all pavement sections were doweled, and to faulting studies were not successful. 18 The principal

mode of failure at the AASHO Road Test was pumping of the granular subbase from under the

slabs. It was found that, to be able to predict the AASHO Road Test performance, different

values of deflection criteria would have to be applied to different slab thicknesses, and to a

smaller extent, different slab support values.

Better performance prediction was obtained by correlation of the subbase pressure

multiplied by the slab comer deflection. Subbase pressure at the slab-foundation interface is

computed as the modulus of subgrade reaction, k, multiplied by the slab deflection. Power, or

rate of work, with which an axle load deflects the slab is the parameter used for the erosion

criterion. For a unit area, the power term incorporates the product of pressure and deflection
divided by a measure of the length of the deflection basin (radius of relative stiffness, I). The

concept is that a thinner pavement with its shorter deflection basin receives a faster punch than a

thicker slab. At equal products of deflection and pressure, the thinner slab is subjected to a faster

rate of work or power.

Successful correlation to AASHO Road Test performance data was developed in which

the number ofload repetitions, N, decreases with power, as defined in the following equation:19

constant

kO.0633

p = ---------

Ie

truckspeed

268.7 * p2

t

kO.73

where: P =

P

=

w =

t =

Ie =

k =

Power (rate of work).

Pressure at slab-foundation interface, psi.

Comer deflection, in.

Slab thickness, in.

Radius of relative stiffness for elastic subgrade, in.

Modulus of subgrade reaction, pci.

Truck speed is not a design variable but is used to introduce the length of deflection basin

in time units. The selection of the elastic radius of relative stiffness for a Winkler subgrade and

the addition of the modulus of subgrade reaction were arbitrarily selected to produce a single

criteria that explained the performance of slabs with different thicknesses and foundation

strengths at the AASHO Road Test.

Comer deflections (w) used in this model were computed based on a comprehensive

finite element analysis of jointed concrete pavements.19 In this analysis, comer deflections

caused by applying a single axle load or a tandem axle load at the comer of concrete pavements

with different parameters, such as concrete slab thickness, modulus of subgrade reaction, etc.,

were computed. Both doweled joints and aggregate-interlock joints were considered in the

analysis. The effects of using tied concrete shoulder also was evaluated. From this

comprehensive pavement analysis, equations were developed to compute comer deflections in

the pavements when subjected to different axle loads. Essentially, comer deflections were

expressed in terms of the radius of relative stiffness (I) of the pavement system under

consideration.
The development of the 1984 design erosion criteria was also generally related to studies

on joint faulting. These studies included pavements in Wisconsin, Minnesota, North Dakota,

Georgia, and California, and included a range of variables not found at the AASHO Road Test.

Additional variables such as increased amounts of truck traffic, non-doweled pavements, a wider

range of pavement service life, and stabilized subbases were included in the erosion criteria

verification.

The analysis of data from the AASHO Road Test and available faulting studies resulted

in the following erosion prediction equation:

log Nj = 14.524 - 6.777 * (C1* Pj- 9.0)°·103

Allowable load repetitions to end of design period for axle-group i.

Power term for axle-group i.

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

The constant C] is an adjustment factor that has a value close to 1.0 for normal granular

subbases and decreases to approximately 0.90 for high-strength subbases.

EROSION, % = 100 * :En; * ( ~]

Accumulated erosion, percent.

Expected number of axle-load repetitions for axle-group i.

Allowable number of repetitions for axle-group i.

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

tied concrete shoulder.

Truck wheel loads placed at the outside pavement edge create more severe deflection

conditions than any other load position. As the truck placement moves inward a few millimeters

from the edge, the effects decrease substantially. Only a small fraction of all the trucks run with

their wheels placed at the edge. Studies on pavement edge encroachment show that most trucks

are driven with the outside wheels placed about 0.6 m from the edge.6,7 For the design procedure

the most severe condition noted in encroachment studies of 6 percent of trucks at pavement edges

was assumed. This added an additional factor of safety and accounted for recent changes in the

United States permitting wider trailers. At increasing distances inward from the pavement edge,

the frequency of load applications increases while the magnitude of stress and deflection

decreases.

Where there is no tied concrete shoulder, comer loadings are critical. When a concrete

shoulder is used, the greater number of loadings inward from the pavement comer are critical.
Most conventional analyses of concrete pavement systems assume that subbase-subgrade

layers do not exist beyond the pavement edge. The MATS finite element computer program was

used to investigate the effect and contribution of subbase-subgrade support away from the

pavement edge.20 For different moduli of subgrade reaction and slab thicknesses, the free comer

deflections were equal to or less than 89.6 percent of those conditions without the outside

subgrade-subbase support. The 10.4 percent comer deflection reduction factor was incorporated

into the PCA erosion design charts for pavements without a tied concrete shoulder. For slabs

with a concrete shoulder, the subgrade support outside the shoulder edge is too far from the truck

traffic to have any beneficial effect on reducing deflections.

During 1992, data from existing performance data bases were used to develop faulting

prediction models to include the PCA erosion criteria as a parameter. Transverse joint data were

collected from existing State Department of Transportation (DOT) pavement management data

bases and pavement performance research data bases.21.22.23Joint faulting measurements obtained

by the Construction Technology Laboratories also were added to the PCA data base.

The collection of faulting and traffic data used in the analysis is summarized by region

and State in table 6. Survey data were collected in dry-freeze, dry non-freeze, wet-freeze, and

wet non-freeze sections of the United States. Joint faulting data from a total of 509 projects were

collected. Region classification criteria for wet or dry and non-freezing or freezing are

summarized in table 7.24

The accumulated percent erosion was correlated with degree of faulting for each

pavement section. Modulus of subgrade reaction (k-value) and increases in support due to

granular and stabilized subbases were calculated using the PCA thickness design guideline

procedures.2s Truck load distribution and frequency were selected for each project from W-4

load tables. One-way average daily traffic (ADT) was used to estimate the proportion of trucks

in the right lane. Erosion for several load categories was accumulated from the truck

proportions, load frequency, and average daily truck traffic (ADTT).

Important environmental factors included in the analysis were the levels of moisture and

temperature range. Levels of moisture were categorized by the freezing index (degree-days

below O°C), average annual precipitation, soil drainability (AASHTO soil type), and presence of

longitudinal edge drains. Some previous research work has indicated that joint opening was

statistically significant in predicting faulting only at non-doweled pavement joints. The degree of

joint opening affecting joint load transfer and potential for faulting is a function of annual

temperature range (maximum daily temperature minus minimum temperature), slab length

(broadly categorized into jointed reinforced, JRCP, and jointed plain concrete pavement, JPCP),

concrete coefficient of thermal expansion, and concrete drying shrinkage.

A statistical analysis computer program was used to develop the relationships between

accumulated erosion and joint faulting. Non-linear regression analysis techniques were used in

development of the faulting prediction model. An initial set of power parameters and variable
Climatic No. of No. of Data

State Reldon Projects Points Data Source

Arizona Dry Non-Freeze 7 7 ref. 22

California Dry and Wet Non-Freeze 85 814 DOT, refs.21 & 22

Connecticut Wet-Freeze 7 9 DOT

Florida Wet Non-Freeze 50 283 DOT, refs. 22 & 23

Georgia Wet Non-Freeze 28 65 ref. 21

Iowa Dry and Wet Freeze 38 38 DOT

Illinois Wet-Freeze, Wet Non-Freeze 8 15 DOT

Louisiana Wet Non-Freeze 28 297 ref. 21

Michigan Wet-Freeze 12 12 ref. 22

Minnesota Dry-Freeze 105 921 DOT, refs.21 & 22

North Carolina Wet Non-Freeze 13 63 DOT, ref. 22

New York Wet-Freeze 21 21 refs. 22 & 23

Ohio Wet-Freeze 59 59 refs. 22 & 23

Pennsylvania Wet-Freeze 5 5 ref. 22

Utah Dry-Freeze 33 231 ref. 21

Wisconsin Dry and Wet Freeze 10 10 DOT

Total 509 2850

Annual Rainfall, Freezing Index,

Climatic Zone in. F De2ree-Days

Wet Non-Freeze Greater than 28 Less than 100

Wet-Freeze Greater than 28 Greater than 100

Dry Non-Freeze Less than 28 Less than 100

Dry-Freeze Less than 28 Greater than 100
coefficients were defined. A Taylor series expansion of the model was used near the initial set of

parameters. Using partial derivatives with respect to each parameter and ignoring higher order

terms, an approximation for the original function was derived that is linear in the power

parameters and can then be solved with standard linear regression analysis techniques. This

process was repeated until the sum of squared errors falls below a preselected minimum value.

Linear regression techniques were then used to generate coefficients for the transformed variable

(raised to nonlinear power coefficient). Statistically insignificant variables (t-statistic less than

2.0) were eliminated from the model. The nonlinear regression analysis to generate power

coefficients and linear regression analysis to generate variable coefficients were repeated until all

remaining variables were statistically significant in the prediction of joint faulting. The two joint

faulting prediction models are presented below:

FAULT = (EROSION * 2)'·25 * [0.0032233 * ( P~~IP) 1.8412I

+ 0.0048573 * JSO.38274]

where: FAULT

EROSION

PRECIP

JS

Faulting at doweled transverse pavement joints, in.

Calculated accumulated erosion (Eqs. 3 & 4, Ref. 26), percent.

Annual precipitation, in.

Average joint spacing, ft.

R

2

adj= 0.703.

SEE (standard error of estimate) = 0.047 in.

n (no. of data points) = 281.

FAULT = EROSIONo.25 * [9.75873 * 10-4 * (PRECIP)O.91907

+ 0.0060291 * JSO.54428 - 0.016799 * DRAIN]

where: FAULT

EROSION

PRECIP

JS

DRAIN

faulting at aggregate-interlock transverse pavement joints, in.

calculated accumulated erosion (Eqs. 3 & 4, Ref. 26), percent.

annual precipitation, in.

average joint spacing, ft.

drainage dummy variable, 0 for none, 1 for edge drains.

R

2

adj= 0.743.

SEE (standard error of estimate) = 0.055 in.

n (no. of data points) = 582.
Detailed information related to the development of the above two models can be found in

references 26 and 27.

In addition to the variables used in the development of the 1992 PCA faulting models,

other parameters, such as type of coarse aggregate, may be important in development of faulting

in jointed concrete pavements. To account for these variables, attempts were made as part of this

study to acquire additional information related to types of coarse aggregate used in the concrete

for all the pavement sections used in developing the two equations. Both the coarse aggregate

component and geology composition were identified. Types of aggregate component included

gravel, crushed stone, slag, manufactured lightweight aggregate, and combinations of the above.

For the pavement sections considered, the coarse aggregate was either gravel or crushed stone.

This information was used in the revision of the faulting models. Coarse aggregate of different

geologic composition will have different coefficients of thermal expansion. This information

was used in calculating the joint opening for JPCP pavement sections that was used in the

revision of the faulting prediction models.

With the additional variables included, the BMDP statistical analysis computer program

was again used for the revision of the models. The procedure was similar to that used in the

development of the original models (equations 35 and 36). Essentially, a non-linear regression

technique was first performed on the data to determine the power terms of the equations. A

linear regression technique was then used to determine the coefficients for the transformed

variables.

For aggregate-interlock joints, it was observed that coarse aggregate shape (round or

crushed) had a significant effect on joint faulting. The use of crushed stone seemed to slow the

progress of joint faulting compared with pavements with gravel aggregate. Even with the

inclusion of different coefficient of thermal expansion values in computing the joint opening,

there was no significant effect on the compacted faulting of aggregate-interlock joints. The

revised faulting prediction equation for aggregate-interlock joints is as follows:

FAULT = EROSIONo.2s * [-0.113924 * PRECIP -0.167423

+0.0332380 * JSO.46103S- 0.0186867 * DRAIN - 0.0268094 * CAe]

where: FAULT

EROSION

PRECIP

JS

DRAIN

CAC

Faulting at aggregate interlock transverse joints, in.

Calculated accumulated erosion (equations 5 & 6), percent.

Annual precipitation, in. '

Average joint spacing, ft.

Drainage dummy variable, 0 for none, 1 for edge drains.

Coarse aggregate component, 0 for gravel, 1 for crushed stone.
SEE (standard error of estimate) = 0.048 in.

n (no. of data points) = 683.

Compared with the original 1992 peA faulting prediction equation for aggregateinterlock joints, the revised equation shows some improvement in terms of both the adjusted

coefficient of determination (R2

adj) and the standard error of estimate (SEE). The revised

prediction equation should therefore provide better estimation of joint faulting. As presented in

figure 13, an approximately normal distribution centered around zero is observed for the

prediction error.

For aggregate-interlock joints, a sensitivity analysis indicates that faulting increases with

an increase in the value of the variable in question. Results of the sensitivity analysis for nondoweled joints are shown in table 8.

Inde endent Variable

Increase in erosion

Increase in reci itation

Increase in .oint s acin

Use of crushed coarse

a re ate

Use of ed e drains

Effect on Faultin

Increase

Increase

Increase

Increase

Sensitivi

varies with erosion

medium

hih

medium

Plots of faulting versus accumulated erosion for aggregate-interlock joints are shown in

figures 14 through 17 for pavements using different coarse aggregate (crushed stone or gravel)

and for pavements in wet regions (annual precipitation of 1016 mm) and in dry regions (annual

precipitation of 508 mm).

The annual precipitation has a significant effect on joint faulting. For example, at 100

percent erosion for a 4.6-m-Iong slab in a region with an annual precipitation of 1016 mm the

predicted j oint faulting for a pavement using gravel coarse aggregate, as shown in figure 16, is

4.4 mm. For the same conditions but with a lower precipitation of 508 mm, the aggregate

interlock model shown in figure 14 predicts faulting of 3.8 mm when no edge drains are present.

A 50 percent reduction in precipitation results in a 14 percent reduction in faulting.

Joint spacing also has a significant effect on predicted aggregate-interlock joint faulting.

For example, at 100 percent erosion for a 12.2-m-Iong slab in a region with an annual

precipitation of 508 mm the predicted faulting fQr a pavement with gravel coarse aggregate, as

shown in figure 14, is 9.1 mm when edge drains are not used. For the same conditions but with a

smaller joint spacing of 4.6 m the aggregate-interlock joint model, as shown in figure 14, predicts

faulting of 3.8 mm. A 63 percent reduction in joint spacing results in a 58 percent reduction in

faulting.
200

Number

or

Cases

ISO

100

SO

Predicted Faultlna Minus Observed Faulting, In.

(1 in = 25.4 mm)

Figure 13. Faulting prediction error distribution for

aggregate-interlock joints.

Pavement with -a,rea_te-Interlock Joints

Gravel coane aaarea_te

Dry region

Precipitation = 20 In No Edge Drain

Joint Spacing. 40 ft

With Edge Drain

Joint Spacing. 40 ft

Faulting,

in

No Edge Drain

Joint Spacing. IS ft

With Edge Drain

Joint Spacing. IS ft

0.0

o

Erosion Damage, percent

(l in = 25.4 mm, 1 ft = 305 mm)

Figure 14. Faulting versus accumulated erosion for aggregate-interlock

joints with gravel coarse aggregate in dry region.
Faulting,

in

Faulting,

in

Pavement with aggregate-interlock joints

Crushed coarse agaregate

Dry region

Precipitation = 20 in

0.0

o

Erosion Damage, percent

(1 in = 25.4 mm, 1 ft = 305 mm)

No Edge Drain

Joint Spacing = 40 ft

With Edge Drain

Joint Spacing = 40 ft

No Edge Drain

Joint Spacing = 15 ft

With Edge Drain

Joint Spacing = 15 ft

80 100

Figure 15. Faulting versus accumulated erosion for aggregate-interlock

joints with crushed coarse aggregate in dry region.

Pavement with aggregate-interlock joints

Gr•••.el coarse aggregate

Wet region

Precipitation = 40 in

0.0

o

No Edge Drain

Joint Spacing. 40 ft

With Edge Drain

Joint Spacing. 40 ft

No Edge Drain

Joint Spacing • 15 ft

With Edge Drain

Joint Spacing = 15 ft

Figure 16. Faulting versus accumulated erosion for aggregate-interlock

joints with gravel coarse aggregate in wet region.
Faulting,

in

Pavement with aggregate-interlock joints

Crushed coarse aggregate

Wet region

Precipitation = 40 in

0.0

o

No Edge Drain

Joint Spacing = 40 ft

With Edge Drain

Joint Spacing = 40 ft

No Edge Drain

Joint Spacing = 15 ft

With Edge Drain

Joint Spacing = 15 ft

Figure 17. Faulting venus accumulated erosion for aggregate-interlock

joints with crushed coane aggregate in wet region.
Also shown in these figures, the use of longitudinal edge drains and the use of crushed

stone coarse aggregate were statistically significant in reducing aggregate interlock joint faulting.

However, the effectiveness of these two parameters in reducing aggregate-interlock faulting is

dependent on the percent erosion level. They become more effective as percent erosion

increases.

For pavements with doweled joints, statistical analysis showed that the coarse aggregate

type (crushed stone or gravel) had significant effects on the predicted joint faulting. However,

when compared with the 1992 PCA faulting prediction equation, the new prediction equation,

with the inclusion of coarse aggregate type as a predictor, had lower R

2

adj (0.648) and higher SEE

(0.072). It was therefore determined that the coarse aggregate type need not be included as a

predictor in estimating faulting for doweled joints. Instead, the 1992 PCA faulting prediction

equation (equation 35) was selected for use in this study. The equation is given below:

FAULT ~ (EROSION *2)0.2' * 0.0032233 * ( P~~IP) L84121

+ 0.0048573 * JSO.38274

where: FAULT

EROSION

PRECIP

JS

Faulting at doweled transverse pavement joints, in.

Calculated accumulated erosion (equations 5 and 6), percent.

Annual precipitation, in.

Average joint spacing, ft.

R

2

adj= 0.703.

SEE (standard error of estimate) = 0.047 in.

n (no. of data points) = 281.

The predicted faulting error distribution is shown in figure 18. Again, the prediction

errors are symmetrically distributed around zero.

Similar to the aggregate-interlock joints, a sensitivity analysis indicates that faulting

increases with an increase in the value of the variable in question. Results of the sensitivity

analysis for doweled joints are shown in table 9.

Effect on Faultin

Increase

Increase

increase

Sensitivi

varies with erosion

hih

medium
Plots of faulting versus accumulated erosion are shown in figures 19 and 20 for wet

regions (annual precipitation of 1016 rnm) and dry regions (annual precipitation of 508 rnm),

respectively. Figures 14 through 17, 19 and 20 should not directly be used for comparing the

effectiveness of dowel bars in reducing faulting since they are plotted as a function of erosion.

Erosion is computed using erosion factors that include the benefits (higher amount of allowable

loads) of dowel bars.

Again, the annual precipitation has a significant effect on joint faulting for doweled

joints. For example, at 100 percent erosion for a 4.6-m-long slab in a region with an annual

precipitation of 1016 rnm the predicted faulting as shown in figure 19, is 5.3 rnm. For the same

conditions but with a lower precipitation of 508 rnm the doweled model shown in figure 20

predicts faulting of 2.4 rnm. A 50 percent reduction in precipitation results in a 50 percent

reduction in faulting.

Joint spacing also has a significant effect on predicted faulting. For example, at 100

percent erosion for a 12.2-m-long slab in a region with an annual precipitation of 508 rnm the

predicted faulting for doweled joints, as shown in figure 20, is 3.0 rnm. For the same conditions

but with a smaller joint spacing of 4.6 m the doweled joint model shown in figure 20 predicts

faulting of 2.4 rnm. A 63 percent reduction in joint spacing results in a 19 percent reduction in

faulting.

Evaluation of the Revised 1992 peA Faulting Models Using SHRP LTPP Data (GPS-3 and

GPS-4)

Data obtained from the LTPP data base for GPS-3 (JPCP) and GPS-4 (JRCP) test

sections were used in evaluating the revised faulting models. Types of information required from

the LTPP data base included the following:

• Pavement structural design parameters

PCC thickness

PCC modulus of elasticity

Modulus of subgrade reaction

Coarse aggregate types

Type and thickness of base or subbase layers

Type of pavement shoulder

Joint type, doweled or aggregate-interlock

Average joint spacing

• Traffic information

Axle load distribution

Annual precipitation

Freezing index
Number

or

Cases

Faulting,

in 0.15

0.00

o

Predicted Faulting Minus Observed Faulting, in

(1 in = 25.4 mm)

Figure 18. Faulting prediction error distribution for doweled joints.

Pavement with doweled joints

Wet region

Precipitation = 40 in

Figure 19. Faulting versus accumulated erosion for doweled joints in wet region.
Faulting,

in

Pavement with doweled joints

Dry region

Precipitation = 10 in

0.00

o
Most of the data were extracted from the data base (as discussed in chapter 2) and directly

used in the analysis. However, some manipulation was required for some of the data before they

could be used in the evaluation process.

Attempts were first made to use the measured concrete modulus of elasticity data in the

evaluation. However, too many missing data made this approach impossible. As the second

step, PCC moduli of elasticity backcalculated from falling weight deflectometer (FWD) test data

were considered. However, a closer examination of the backcalculated concrete modulus values

revealed that most of the values were much too high, with some reaching 90,000 MPa. Since

the computed erosion factor caused by traffic loads on pavement systems will be affected by the

concrete modulus of elasticity, the use of unrealistically high values was considered inadequate.

For the purpose of this analysis, the best possible material testing data available at the

time of analysis appeared to be the 28-day compressive strength of concrete specimens. For most

of the test sections evaluated in this study, the 28-day compressive strength data were used to

estimate concrete modulus of elasticity. For a few cases, the 28-day compressive strength data

were not available and the concrete modulus of rupture (flexural strength) data were used to

estimate the modulus of elasticity values for that section.

The modulus of subgrade reaction values backcalculated from FWD deflection tests were

available for all the pavement sections considered in this analysis. For pavements with a

stabilized or granular base or subbase layer, their backcalculated k-values were adjusted to

account for the increased support provided by the presence of base and/or subbase layers using

the PCA thickness design guideline procedures.29

To compute the accumulated erosion of a pavement system, the axle load distribution

over its service life for all the weight categories is required. Unfortunately, very limited traffic

data were available. The lack of axle load distribution data reduced the number of test sections

that could be evaluated. A total of 57 pavement sections were included in this study, consisting

of20 pavements with aggregate-intedockjoints and 37 with doweled joints. Furthermore, the

data available were mostly for a single year only. To estimate the total amount of traffic traveled

on a pavement during its entire service life, an annual traffic increase rate of 2 percent was

assumed in the analysis (as discussed in chapter 2). This assumption somewhat overestimates

the joint faulting. The effect of annual traffic growth rate on the predicted joint faulting is

presented in a latter section.
With all the information obtained and derived from the LTPP data base, the predicted

faulting for aggregate-interlock joints was computed using the revised 1992 joint faulting

equation. As mentioned earlier, complete information was obtained for 20 pavement sections.

The differences between the predicted and observed faulting (prediction errors) ranged from -1.5

mm to 1.32 mm, with a mean value of -0.76 mm and a standard deviation of 0.79 mm. As

presented in figure 21, the prediction errors are distributed approximately symmetrically around

zero, indicating reasonable predicting power of the faulting model.

A paired-t test also was performed to further evaluate the adequacy of the prediction

equation. It was concluded that, at the 95 percent confidence level, the null hypothesis of no

difference between the predicted and observed faulting could not be rejected. In fact, the null

hypothesis could not be rejected even at the 70 percent confidence level. This conclusion

suggested that the developed faulting prediction model is reasonable for predicting faulting for

aggregate-interlock joints. The comparison of the predicted and the observed faulting for

aggregate-interlock joints is shown in figure 22. In the figure, the solid line represents the line of

equality and the two dashed lines are one standard deviation away from the line of equality. It is

observed that most of the data points fall within ±1 standard deviation from the line of equality.

Joint faulting was computed using the 1992 joint faulting equation and data obtained

from the LTPP data base for doweled joints. A total of37 pavement sections having the needed

data were evaluated. The differences between the predicted and observed faulting (prediction

errors) ranged from -1.7 mm to 3.0 mm, with a mean value of 0.56 mm and a standard deviation

of 1.24 mm. Plotted in figure 23, the prediction error distribution for doweled joints shows

skewness toward the positive side, indicating an overestimate of the predicted faulting. A pairedt test further revealed that the null hypothesis of no difference between the predicted and

observed faulting was rejected at the 95 percent confidence level. It can therefore be inferred that

there is a difference between the predicted and observed faulting.

The predicted faulting is plotted against the observed faulting in figure 24. It is observed

that most of the measured faulting values are in the range between 0.00 and 1.27 mm. The use of

doweled joints seemed to significantly reduce joint faulting. It is also clear that, at this lower

range, the prediction equation tends to overestimate joint faulting for doweled joints. For

measured faulting greater than 1.27 mm, the equation seems to provide better faulting estimates

for doweled joints.

As presented in the previous sections, the aggregate-interlock model provided reasonably

good estimates for j oint faulting for the 20 LTPP sections evaluated. Statistically, no difference

could be claimed between the predicted and observed faulting for aggregate-interlock joints.

However, an overestimate of the faulting was evident for doweled joints, as indicated by the

positive skewness of the faulting prediction error distribution shown in figure 23.
6

S

4

Number

or

Cues

3

0.00

U.OO

•

•

a. standard deviation

or prediction errors

• 0.031 In

Measured 'aultlna, In

(1 in = 25.4 mm)

Figure 22. Predicted faulting versus measured faulting for

aggregate-interlock joints.
Number

or 6

Cues

Predicted Faultlnl Minus Observed Faulting

(l in = 25.4 mm)

a = standard deviation

or prediction errors

= 0.049 In

Measured Faulting, In

(l in = 25.4 mm)
The PCA faulting prediction equation utilizes the concept of erosion damage of the

pavements caused by traffic loads. Erosion damage is determined based on traffic load-induced

comer deflections in the pavements. Among other parameters, concrete modulus of elasticity is

important in determining the comer deflections. However, site specific data were not available at

the time of analysis. In this study, concrete modulus of elasticity was estimated from its 28-day

compressive strength. It is believed that use of actual measured concrete modulus of elasticity

data will increase the prediction accuracy.

Similar to other mechanistic-based procedures, the joint faulting prediction equations

require the use of traffic axle load distribution in the analysis. Converted traffic indices, such as

80-kN ESAL currently used in the AASHTO design procedure, cannot be used. At the time of

analysis, the LTPP data base contained traffic axle load distribution data for a very limited

number of pavement sections. Furthermore, for these limited number of test sections, axle load

distribution data were only available for a particular year, and the cumulative amount of traffic

volume on the pavements had to be estimated using a 2 percent annual traffic growth rate, as

discussed in chapter 2. This assumption was believed to be conservative and might have

contributed to the overestimate of the doweled joint faulting. Reliable traffic data (in terms of

axle loadings) are essential for any pavement evaluation using the LTPP data base.

Sensitivity analyses of annual traffic growth rate on computed faulting were performed

for both doweled and aggregate-interlock joints, and are presented in figure 25. It can be

observed that traffic growth rate only slightly affects the predicted faulting for both types of

joints. As the annual traffic growth rate increases from 2 to 15 percent, the computed faulting

decreases from 1.32 mm to 1.14 mm and from 1.60 mm to 1.50 mm for the aggregate-interlock

joint and the doweled joint, respectively. It should be noted that because traffic is backcasted

from a current year, higher growth rates result in lower cumulative traffic loadings. The

prediction errors may be reduced slightly if annual growth rate of traffic can be estimated

reliably.

The lack of required material testing and traffic data reduced the number of LTPP test

sections that could be evaluated. However, the quality of the faulting data may be a more serious

deficiency of the data base. For instance, faulting observed at two consecutive years at many

sections had a difference in excess of 2.54 mm. In some cases, faulting measured at the wheel

path was very different from that measured at the comer. These inconsistencies make the use of

the LTPP data difficult. The following are a few examples of inconsistencies of the faulting data:

• Pavement section 1-3028

Faulting at wheel path: 0.000 mm

Faulting at comer: 3.28 mm

• Pavement section 12-4138

Faulting at wheel path: 0.000 mm

Faulting at comer: 5.13 mm
0.08

Doweled Joint

Test Section 34-4042

••

0.06 •

•

Computed •

Fa'!lting,

..

an

Aggregate-Interlock 10int •

0.04 Test Section 6-3042

0.00

o

Figure 25. Sensitivity analysis of annual traffic growth rate on

computed faulting.
• Pavement section 1-4084

Faulting measured in 1991 (21 years): 4.29 mm

Faulting measured in 1993 (23 years): 8.79 mm

• Pavement section 34-4042

Faulting measured in 1991 (24 years): 4.70 mm

Faulting measured in 1992 (25 years): 5.56 mm

Faulting measured in 1993 (26 years): 3.58 mm

In general, the LTPP data base provides valuable information that can be used to develop,

calibrate, and/or validate mechanistic-based pavement analysis and design procedures. However,

the issues of lack of material testing and traffic data, and the quality of the performance data need

to be addressed.

The two faulting prediction models, one for aggregate-interlock joints and the other for

doweled joints, developed in 1992 were revised in an attempt to include coarse aggregated type

as a predictor. Reasonable coefficients of determination (greater than 0.70) were obtained. For

doweled joints, important factors that will influence faulting include erosion, precipitation, and

joint spacing. For aggregate-interlock joints, erosion, precipitation, joint spacing, the use of edge

drains, and coarse aggregate types were found to be significant in affecting joint faulting.

Sensitivity analyses of the two joint faulting prediction equations have revealed that

faulting will increase with increased erosion, precipitation, or joint spacing for both doweled and

aggregate-interlock joints. The use of edge drains and crushed stone coarse aggregate will reduce

faulting.

The two faulting prediction equations were evaluated using data obtained from GPS-3

and GPS-4 test sections. A total of 57 pavement sections, consisting of 20 aggregate-interlock

joints and 37 doweled joints, were evaluated. The prediction equation for aggregate-interlock

joints was found to provide reasonable estimates of joint faulting compared with the observed

values. However, an overestimate, especially in the lower range of measured faulting ofless than

1.27 1IUll, was observed for doweled joints.
The primary objective of the study reported here was to evaluate the reliability of some

widely used M-E models for predicting the performance ofin-service PCC pavements. Two

distress types were considered in this study: fatigue cracking for jointed plain concrete pavements

and joint faulting for jointed plain and reinforced concrete pavements. Another objective was to

develop and calibrate new performance prediction models, as deemed necessary.

• Both the NCHRP 1-26 approach for prediction of fatigue cracking (based on

cracking initiating at slab bottom) and the PCA type approach for prediction of

joint faulting.appear reasonable within the context of the validation attempted

using LTPP test data. However, as more data become available, it may also be

possible to consider other hypotheses for development of fatigue cracking in

jointed concrete pavements.

• The PCA joint faulting procedure incorporates mechanistic elements (especially

the "damage" caused by the different axle loads), but is also dependent on certain

site-specific features. In an ideal mechanistic approach, all site-specific features

should be incorporated within the mechanistic parameters that represent the

structural characteristics of the pavement, specifically within seasonally adjusted

modulus of elasticity values for the various paving materials.

• The incorporation of curling and warping effects in both the fatigue cracking

analysis and the joint faulting analysis need major advancement. This is

especially true with regard to the assumption of linear temperature gradient in the

concrete slab and the complete omission of moisture warping stresSes. Similarly,

better understanding of how to estimate loss of support and joint load transfer

effectiveness and how to incorporate these estimates into the structural analysis is

needed. The estimate of the fatigue cracking damage is very sensitive to the

computation of the total flexural (bending) stresses in the slab. Also,

consideration of the loss of support and load transfer effectiveness can

significantly affect the estimate of the faulting damage.

• The development of joint faulting is very similar to that of rutting in asphalt

pavements. The rate of faulting is high in the early years and decreases with time.

No practical approaches have been developed to allow consideration of this nonlinear relationship between faulting and the number of load applications.
Issues relating to the specific data types are discussed in the following paragraphs. The

purpose of this discussion is to provide feedback to the LTPP data collection efforts, help

identify areas of improvement needed in the data collection effort, and identify future research

needs to fill data and knowledge gaps within the context of the M-E analysis/design procedures.

The key materials data needed for both the fatigue cracking and joint faulting analysis

include concrete modulus of elasticity values, the coefficient of subgrade reaction, the concrete

coefficient of thermal expansion, and the concrete flexural strength values. As indicated

previously, at the time of the study, the site-specific coefficient of thermal expansion values were

not available and a single value was used for all test sections. Also, the concrete modulus of

elasticity and flexural strength values were extrapolated. No seasonal adjustments were made to

these values nor were long-term aging effects considered. The backcalculated layer moduli

values for concrete were not considered appropriate because many of these values were higher

than normally expected. Finally, material variability effects were not considered. Future

improvements are needed to establish these values to be used for M-E data analysis.

In this analysis, traffic was characterized as annual counts of an array of specific axle

loading groups. The analysis is thus complicated, since there are up to 140 axle loading groups

in the LTPP data base. Although it is conceivable that individual loading groups may have

different growth rates, a simplifying assumption was made that the annual traffic growth rate is 2

percent for all load groups. Also, another assumption that needs further study is the seasonal

variation in traffic load applications to ensure that seasonal traffic is matched to seasonal

variation in the structural properties of the various pavement layers. Finally, traffic wander

(lateral distribution) needs to be established for each site to ensure that appropriate traffic data

are used for both the fatigue analysis and the faulting analysis.

Concerns remain about the quality of the distress data. These concerns include the

following:

2. Cleaning up the joint faulting data, including discrepancies between faulting

magnitudes at comer locations versus wheelpath locations and a few cases of

negative faulting values.
In an ideal M-E procedure, damage (in relation to a specific distress) should be

determined as follows:

Damage ij/d = f (eij/d)

and

eijk~ = f (Ej/d)

Critical structural response in the pavement that is considered to be a

predictor of the distress under consideration for the ith axle group at the jth

time period of the kth month of the All year.

Modulus of elasticity of each layer of the pavement system at the jth time

period of the kth month of the All year.

Thus, a major consideration in developing and using M-E procedures is the appropriate

characterization of Ejkl for each pavement layer. Our capability for realistically modeling

pavement behavior has seen much progress in the last few decades. However, the capability to

realistically consider material characterization (e.g., ~kl) for the pavement layers remains less

than desired because of the lack of knowledge of how to realistically account for seasonality

effects, spatial variability, and effects of deterioration due to traffic loading and environment.

In this study, distress-specific damage was estimated for a segment of LTPP test sections.

However, as discussed in the report, the damage estimation was seriously handicapped by two

primary factors: lack of adequate (in terms of reliability and completeness) traffic data and the

many approximations that had to be made to develop an appropriate characterization of the

pavement layer properties (in terms of Ejkl). Future endeavors in the LTPP and other pavement

research programs will attempt to improve these serious inadequacies.

The LTPP data base is one of the most important advances made in improving pavement

technologies. This study has shown that, even given the many limitations, the LTPP data can be

used successfully to develop better insight into pavement behavior and to ultimately improve

pavement performance.

1. Rowshan, S., and Harris, S., Long-Term Pavement Performance Information

Management System Data Users Guide, FHWA-RD-93-094, Federal Highway

Administration, Washington, DC, 1993.

2. Hammitt, G.M., II, Concrete Strength Relationships, U.S. Army Corps of Engineers

Waterways Experiment Station, Vicksburg, MS, 1971.

3. Darter, M.l., and Barenberg, EJ., Design of Zero-Maintenance Plain Jointed Concrete

Pavement, Volume i-Development of Design Procedures, FHWA-RD-77-111,

Washington, DC, 1977.

5. Hall, K.T., Darter M.l., Hoerner, T.E., and Khazanovich, L., LTPP Data Analysis, Phase

I: Validation of Guidelines for k Value Selection and Concrete Pavement Performance

Prediction, Interim Report, DTFH61-94-C-00218, Federal Highway Administration,

Washington, DC, 1996.

6. Emery, D.K., A Preliminary Report on the Transverse Lane Displacement for Design

Trucks on Rural Freeways, Paper presented to the ASCE Pavement Design Speciality

Conference, Atlanta, GA, June, 1975.

7. Benekohal, RF., Hall, K.T., and Miller, H.W., Effects of Lane Widening on Lateral

Distribution of Truck Wheels, Transportation Research Record 1286, Transportation

Research Board, Washington, DC, 1990. .

8. Dempsey, B.J., Herlache, W.A., and Patel, A.J., The Climatic-Materials-Structural

Pavement Analysis Program User's Manual, FHWAIRD-82/126, Federal Highway

Administration, Washington, DC, 1986.

9. Salsilli, RA., Barenberg, EJ., md Darter, M.I., Calibrated Mechanistic Design

Procedure to Prevent Transverse Cracking of Jointed Plain Concrete Pavements,

Proceedings of the 5

th International Conference on Concrete Pavement Design and

Rehabilitation, Purdue University, 1993.

10. Tabatabaie-Raissi, A.M., Structural Analysis of Concrete Pavement Joint, Ph.D. Thesis,

University of Illinois, Urbana, 1977.

11. Ioannides, A.M., Thompson, M.R, and Barenberg, E.J., Finite Element Analysis of Slabon-Grade Using a Variety of Support Models, Proceedings of the Third International

Conference on Concrete Pavement Design and Rehabilitation, Purdue University, 1985.

12. Korovesis, G.T., Analysis of Slabs- on-Grade Pavement Systems Subjected to Wheel and

Temperature Loadings, Ph.D. Thesis, University of Illinois, Urbana, Illinois, 1990.
13. Westergaard, H.M., "New Formulas for Stresses in Concrete Pavements of Airfields,"

Transactions, American Society of Civil Engineers, Volume 113, 1948.

14. loannides, A.M., Thompson, M.R., and Barenberg, E.J., Westergaard Solutions

Reconsidered, Transportation Research Record 1043, Transportation Research Board,

Washington, DC, 1985.

16. Westergaard, H.M., "Analysis of Stresses in Concrete Pavements Due to Variations of

Temperature," Proceedings, Sixth Annual Meeting, Highway Research Board,

Washington, DC, 1926.

17. Yu, H.T., Darter, M.I., Smith, K.D., Jiang, Y.l, and Khazanovich, L., Performance of

Jointed Concrete Pavements, Volume III: Improving Concrete Pavement Performance,

Final Report, DTFH61-91-C-0053, Federal Highway Administration, Washington, DC,

August 1996.

18. The AASHO Road Test, Highway Research Board Special Report No. 61E,

Transportation Research Board, Washington, DC, 1962.

19. Packard, R.G., and Tayabji, S.D., Mechanistic Design of Concrete Pavements to Control

Joint Faulting and Subbase Erosion, Paper presented at the International Seminar on

Drainage and Erodability at the Concrete Slab-Subbase-Shoulder Interfaces, Paris,

France, March 1983.

20. Computer Program for the Analysis and Design of Foundation Mats and Combined

Footings, SR100D, Portland Cement Association, Skokie, Illinois, 1971.

21. Darter, M.I., Becker, J.M., and Smith, R.E., Portland Cement Concrete Pavement

Evaluation System COPES, Report prepared by the University of Illinois, UrbanaChampaign, for the National Cooperative Highway Research Program (NCHRP), Report

277, September 1985.

22. Smith, K.D., Mueller, A.L., Darter, M.I., and Peshkin, D.G., Performance of Jointed

Concrete Pavements, Volumes I through VI, Report prepared by ERES Consultants, Inc.,

for the Federal Highway Administration (FHWA), FHWA/RD-89/136 through 89/141,

Washington DC, July 1990.

23. Majidzadeh, K., and lIves, G.J., Correlation of Quality Control Criteria and Performance

of PCC Pavements, Report prepared by Resource International, Inc., for the Federal

Highway Administration (FHWA), FHWA/RD-83/014, Washington DC, March 1984.

24. Heinrichs, K.W., Liu, M.I., Darter, M.I., Carpenter, S.H., and loannides, A.M., Rigid

Pavement Analysis and Design, Report prepared by the University of Illinois, Urbana-
Champaign, for the Federal Highway Administration (FHWA), FHW AIRD-88-068,

Washington DC, June 1989.

25. Thickness Designfor Concrete Highway and Street Pavements, Portland Cement

Association, Engineering Bulletin EBI09.01P, Skokie, Illinois, 1984.

26. Wu, C.L., and Okamoto, P.A., Refinement of the Portland Cement Association Thickness

Design Procedure for Concrete Highway and Street Pavements, Report Prepared for

Portland Cement Association, PCA R&D Serial No. 1916, December 1992.

27. Wu, C.L., Mack, J.W., Okamoto, P.A., and Packard, R.O., Prediction of Faulting of

Joints in Concrete Pavements, Proceedings of the Fifth International Conference on

Concrete Pavement Design and Rehabilitation, Purdue University, Indiana, April, 1993.

APPENDIX A - DATA BASE FOR ANALYSIS OF TRANSVERSE CRACKING (GP8-3

DATA)

e;. slabs Age MR Dslab Eslab, Poisson's Thermal Subarade Slab

State SHRP_ID expansion k-value length, cracked year psi in IOA6 psi ratio cod., IF psi ft

5 3011 0 11.6 607 10.0 4.0 0.15 5.55E-6 222 15

6 3030 21.7 19.2 609 8.5 3.9 0.14 5.55E-6 276 15.5

6 3042 12.4 16.5 714 8.8 3.5 0.13 5.55E-6 143 15.5

8 3032 37.2 16.3 615 8.0 3.8 0.20 5.55E-6 394 15.5

12 3804 62.4 6.3 553 12.0 4.0 0.19 5.55E-6 211 19.5

12 3811 64 18.6 502 9.4 3.1 0.17 5.55E-6 300 20

12 4000 0 18.4 469 8.1 3.6 0.15 5.55E-6 158 20

12 4057 0 4.7 537 13.3 3.8 0.17 5.55E-6 354 15.5

12 4059 0 4.0 765 6.0 4.4 0.20 5.55E-6 303 14

12 4109 0 4.0 629 7.0 4.2 0.20 5.55E-6 300 14

12 4138 16 18.4 480 8.0 3.3 0.20 5.55E-6 182 20

13 3015 0 15.2 679 10.0 3.9 0.20 5.55E-6 243 20

13 3018 3.9 21.3 507 9.9 2.0 0.13 5.55E-6 201 19.5

18 3002 0 19.5 674 9.5 5.7 0.18 5.55E-6 147 15.5

18 3003 0 16.3 584 10.1 4.8 0.20 5.55E-6 176 20

18 3030 0 13.6 700 8.0 4.0 0.20 5.55E-6 226 15.5

18 3031 0 18.0 558 10.2 4.9 0.20 5.55E-6 139 15.5

19 3006 16 18.9 655 8.5 3.7 0.20 5.55E-6 95 20

19 3009 8 17.8 576 10.6 4.5 0.20 5.55E-6 135 20

19 3028 0 9.8 654 9.5 3.7 0.20 5.55E-6 106 20

20 3013 0 10.7 520 10.2 4.3 0.16 5.55E-6 304 15

20 3015 0 3.6 515 9.2 4.2 0.20 5.55E-6 129 15

21 3016 0 9.2 640 11.7 5.1 0.18 5.55E-6 174 15

26 3068 0 14.6 650 9.0 4.0 0.20 5.55E-6 300 15.5

26 3069 0 19.9 650 9.0 4.0 0.20 5.55E-6 165 14.5

27 3003 0 3.7 579 7.6 5.0 0.20 5.55E-6 78 15

27 3013 0 3.0 719 8.0 5.5 0.14 5.55E-6 72 15

29 5393 48 31.2 650 8.0 4.0 0.20 5.55E-6 88 30

31 3018 0 10.0 650 12.0 4.0 0.20 5.55E-6 159 15.5

31 3023 65.1 11.3 556 11.9 3.8 0.16 5.55E-6 167 15.5

31 3028 0 14.4 550 8.4 4.9 0.20 5.55E-6 110 15.5

31 3033 3.1 7.1 650 9.0 4.0 0.20 5.55E-6 132 15.5

32 3010 3.1 11.9 606 9.7 3.4 0.17 5.55E-6 105 15.5

32 3013 21.7 12.9 579 8.3 5.4 0.19 5.55E-6 323 15.5

38 3005 0 8.3 587 8.0 4.8 0.14 5.55E-6 83 13.8

38 3006 0 7.8 620 8.4 5.0 0.13 5.55E-6 125 14

40 4160 0 15.4 650 9.0 4.0 0.20 5.55E-6 110 15

40 4162 0 9.4 650 9.0 4.0 0.20 5.55E-6 118 15

42 3044 0 4.6 580 12.7 3.4 0.16 5.55E-6 505 20

46 3012 3 12.1 555 10.1 4.9 0.19 5.55E-6 240 15

53 3011 0 12.1 784 9.0 4.0 0.20 5.55E-6 180 11.4

53 3013 0 23.9 650 7.8 4.0 0.20 5.55E-6 159 15.5

53 3014 0 12.2 770 10.4 4.7 0.19 5.55E-6 108 11.5

53 3812 0 24.3 540 9.0 4.0 0.20 5.55E-6 195 15

53 3813 9.3 29.3 650 7.8 4.0 0.20 5.55E-6 89 15.5

83 , 3802 0 9.8 618 9.8 4.7 0.20 5. 55E-6 88 15

89 3015 0 10.8 655 8.0 4.0 0.20 5.55E-6 73 16

89 3016 0 12.7 585 8.6 4.6 0.20 5.55E-6 89 16
Widened If widened Tied

If tied, Base Base

Dbase State SHRP_ID lane? distance-to-edge shoulder? stabilized? bonded? Ebase, psi

(YorN) in (YorN) AGGIkI (YorN) (U orB) in

5 3011 0 N 0 Y U 6.9 1000000

6 3030 0 y 0.1 Y U 4.3 1000000

6 3042 0 N 0 Y U 5.5 1000000

8 3032 0 Y 0.1 Y U 5.0 2000000

12 3804 0 N 0 Y U 7.6 2000000

12 3811 0 N 0 Y U 7.6 200000

12 4000 0 N 0 y U 5.7 200000

12 4057 0 N 0 N 7.0 20000

12 4059 0 Y 0.1 N 9.8 200000

12 4109 0 Y 0.1 N 9.8 200000

12 4138 0 Y 0.1 Y U 5.9 200000

13 3015 0 y 0.1 Y U 6.0 200000

13 3018 0 Y 0.1 Y U 6.8 1000000

18 3002 0 N 0 N 7.0 30000

18 3003 0 Y 0.1 Y U 6.5 100000

18 3030 0 Y 0.1 Y U 5.4 450000

18 3031 0 N 0 Y U 5.6 450000

19 3006 0 N 0 Y U 5.0 1000000

19 3009 0 y 0.1 y U 5.7 200000

19 3028 0 y 0.1 Y U 5.0 2000000

20 3013 0 y 0.1 Y U 5.0 1000000

20 3015 0 N 0 y U 5.2 450000

21 3016 0 Y 0.1 N 7.0 30000

26 3068 0 N 0 Y U 5.0 450000

26 3069 0 y 0.1 Y U 5.0 200000

27 3003 y 24 N 0 N 6.0 30000

27 3013 Y 24 Y 0.1 N 6.0 30000

29 5393 0 N 0 N 4.0 30000

31 3018 0 y 0.1 Y U 6.0 200000

31 3023 0 N 0 Y U 5.0 1000000

31 3028 0 y 0.1 y U 4.0 100000

31 3033 0 Y 0.1 Y U 5.8 450000

32 3010 0 y 0.1 Y U 6.6 1000000

32 3013 0 y 0.1 y U 4.7 1000000

38 3005 0 N 0 N 3.0 30000

38 3006 0 Y 0.1 N 5.0 30000

40 4160 0 N 0 Y U 4.0 0

40 4162 0 N 0 y U 4.0 450000

42 3044 0 Y 0.1 N 9.0 30000

46 3012 0 Y 0.1 N 5.0 30000

53 3011 0 N 0 N 5.8 30000

53 3013 0 Y 0.1 N 4.0 30000

53 3014 0 N 0 N 6.0 30000

53 3812 0 N 0 N 3.0 30000

53 3813 0 N 0 N 3.4 30000

83 3802 0 N 0 N 7.0 30000

89 3015 0 N 0 N 10.0 30000

89 3016 0 N 0 N 10.0 30000