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 is the first of a two-volume series documenting the first-ever application of Long

Term Pavement Performance (LTPP) data to the evaluation of mechanistically based

performance prediction procedures for flexible pavements. Volume II: Final ReportAppendices is available only through the National Technical Information Service (NTIS).

'This report will be of benefit to those interested in the development of mechanistically based

performance prediction and design procedures for flexible pavements. It will be of particular

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

Charles J.

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

FHW A-RD-98-012

4. Title and Subtitle 5. Report Date

MECHANISTIC EVALUATION OF TEST DATA

April 1998

FROM LTPP FLEXffiLE PAVEMENT TEST 6. Performing Organization Code

SECTIONS, Volume I: Final Report

7. Author!s) 8. Performing Organization Report No.

Hesham A. Ali and Shiraz D. Tayabji

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

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 Engineering Research and Development Final Report

Federal Highway Administration Feb. 1995 to Dec. 1997

6300 Georgetown Pike

Sponsoring Agency Code McLean, Virginia 22101-2296 14.

15. Supplementary Notes

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

16. Abstract

The study reported here was conducted to assess how well some of the existing asphalt pavement

mechanistic-empirical distress prediction models 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-l and GPS-2 experiments. The first phase of the data analysis involved using the deflection test

data to backcalculate pavement layer moduli values. Using representative values of the layer moduli,

structural analyses were performed for up to 140 axle-load configurations for the selected test sections.

Then, the Asphalt Institute and the Shell procedures were used to predict fatigue cracking and rutting

damage. The computed results were compared with observed values. Based on the results, new forms

of the fatigue cracking models have been proposed. Also, a new approach to predicting rutting has been

developed. This new procedure would account for rutting in each pavement layer and would consider

rate-hardening typically observed in the development of rutting.

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

can be used successfully to develop a better insight into pavement behavior and to improve pavement

performance.

This volume is the second in a series. The other volume in the series is:

FHW A-RD-98-Q20 Volume II: Final Report-Appendices

17. Key Words 18. Distribution Statement

Asphalt pavement, backcalculation, fatigue No restrictions. This document is available to

cracking, LTPP, NIMS, pavement performance, the public through the National Technical

pavement testing, rutting. Information Service, Springfield, VA 22161.

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

Unclassified Unclassified 108
•• •

APPROXIMATE CONVERSIONS TO SI UNITS APPROXIMATE CONVERSIONS FROM SI UNITS

Symbol WhenYou Know Multiply By To Find Symbol Symbol WhenYou Know Multiply By To Find Symbol

LENGTH LENGTH

in inches 25.4 millimel8rs mm mm millimel8rs 0.039 inches in

ft fee, 0.305 meters m m meters 3.28 feet ft

yd yards 0.914 meters m m meters 1.09 yards yd

mi miles 1.61 kilometers km km kilometers 0.621 miles mi

AREA AREA

in' squareinches 645.2 squaremillime18rs mm' mm' squaremillime18rs 0.0016 squareinches in'

ftI squarefeet 0.093 squaremeters m' m' squaremeters 10.764 squarefeet ftI

yrP squareyards 0.836 squaremeters m' m' squaremeters 1.195 squareyards ydl

ac aaes 0.405 hectares ha ha hectares 2.47 aaes ae

mil squaremiles 2.59 squarekilometers km' km' squarekilometers 0.386 squaremiles mi'

VOLUME VOLUME

fIoz fluidounces 29.57 millili18rs mL mL milliliters 0.034 fluidounces fl oz

gal gallons 3.785 liters L L liters 0.264 gallons gal

ftI cubicfeet 0.028 cubicmeters m3 m3 cubicmeters 35.71 cubicfeet ftI

yd' cubicyards 0.765 cubicmeters m3 m3 cubicmeters 1.307 cubicyards yfiJ

_. III

NOTE:Volumesgrea18rthan 1000I shallbe shownin m3.

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 shorttons(2000Ib) 0.907 megagrams Mg Mg megagrams 1.103 shorttons(2000Ib) T

(or"metricton") (or"r) (or or) (or"metricton")

TEMPERATURE (exact) TEMPERATURE (exact)

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

18mperature or (F-32Y1.8 temperature temperature temperature

ILLUMINATION ILLUMINATION

fc footoQndles 10.76 lux Ix Ix lux 0.0929 footoQndles fc

fI foot-lJlmberts 3.426 candelalm' cdlm' cdlm' candelalm' 0.2919 loot-Lamberts fl

FORCE and PRESSURE or STRESS FORCE and PRESSURE or STRESS

Ibl poundforce 4.45 newtons N N newtons 0.225 poundforce Ibf

IbflinZ poundforceper 6.89 kilopascels kPa kPa kilopascals 0.145 poundforceper Ibflin2

squareinch squareinch

• SI is the symbolforthe In18mationalSyS18mof Units.Appropriate (RevisedSeptember1993)

roundingshouldbemadeto oomplywithSection4 of ASTME380.
CHAPTER 1. INTRODUCTION 1

The LTPP PrograIIl 2

M-E Distress Modeling FundaII1entals 3

Scope of Work 6

Report Organization 7

CHAPTER 2. DATA ACQUISITION 9

Monitoring Data 9

Inventory Data .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Cross-Section Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Climatic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Materials Data 12

Traffic Data 12

Seasonal Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Data Variability 13

Missing Data 13

Test Sections 13

Experimental Cell Design 16

CHAPTER 3. PAVEMENT LAYER MODULI BACKCALCULATION 19

PADAL PrograIIl and Results 19

WESDEF PrograIIl and Results 19

MODULUS PrograIIl and Results 21

Deflection Basin Fit Criteria 21

AC Layer Modulus Temperature Adjustment 22

Mean Annual Pavement Temperature Calculation 22

Temperature Adjustment Algorithm 27

CHAPTER 4. PAVEMENT STRUCTURAL ANALYSIS 29

Introduction 29

Consideration of Spatial and Seasonal Variations in Pavement Layer Properties 29

Consideration of Traffic Loading 31

Calculation of Cumulative Traffic Application 33

Calculation of Critical Strains 36

CHAPTER 5. FATIGUE DAMAGE ANALYSIS 39

Introduction 39

Observed Fatigue Cracking 39

Asphalt Institute Fatigue Cracking Model 39

Comparison: Predicted Versus Observed Performance, GPS-l Sections 43

New Fatigue Cracking Model 43

Model Calibration 45
Linear Model 45

Exponential Growth Model 49

Fatigue Modeling Discussion 49

Fatigue Cracking Analysis, GPS-2 Sections 49

Summary 52

CHAPTER 6. RUTTING ANALYSIS 55

Introduction ' 55

Observed Rutting 55

Asphalt Institute Rutting Model 55

Comparison: Predicted Versus Observed Rutting 58

Summary 61

CHAPTER 7. THE SHELL MODELS 63

Introduction 63

Shell Fatigue Cracking Model Evaluation 63

Shell Rutting Model Evaluation 66

Summary 69

CHAPTER 8. CASE STUDY: COMPARING METHODS OF ASSESSING THE

EFFECTS OF SEASONAL VARIATIONS ON DAMAGE ANALYSIS 71

Case Study: LTPP Section 311030 71

Comparison: Approach 1 Versus Approach 2 75

CHAPTER 9. NEW RUTTING MODEL 77

Introduction 77

Model Formulation 77

Model Calibration 83

Model Calibration Results 83

Goodness of Fit 85

Model Validation 85

Summary 90

CHAPTER 10. SUMMARY AND RECOMMENDATIONS 91

General Observations 91

Fatigue Cracking: Mechanistic Prediction Procedures 91

Rutting: Mechanistic Prediction Procedures 93

LTPP Data Issues 94

Materials Data 94

Traffic Data 95

, Deflection Test Data 95

Distress Data 96
Sensitivity Data 96

Summary 96
1 Typical transverse profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 Flow chart of data analysis steps 14

3 Pavement layer models used in backcalculation analysis 20

4 Response points 32

5 Cumulative traffic consideration 34

6 Layer model used in the structural analysis 37

7 Plot of fatigue cracking versus damage ratio for GPS-l 44

8 Constrained growth model 46

9 Modified constrained growth model 47

10 Linear model 48

11 Exponential growth model 50

12 Fatigue damage versus fatigue cracking for GPS-2 51

13 Fatigue cracking, GPS-l versus GPS-2 53

14 Rutting for GPS-l 59

15 Rutting for GPS-2 60

16 The Shell fatigue model, GPS-l sections 64

17 The AI versus the Shell fatigue models, GPS-I sections 65

18 Shell rutting model, GPS-I sections 67

19 Comparison between the AI and the Shell rutting models 68

20 Seasonal variation effects on fatigue damage ratio 73

21 Seasonal variation effects on rutting damage ratio 74

22 Three-dimensional strain model 78

23 Histogram of residuals 86

24 Observed versus predicted rut depth 87

25 Observed versus predicted rut depth, based on validation data set 88

26 Rutting development for section 091047 (GPS-l) ; 89
1 Data elements and their source tables 10

2 Fatigue cracking in sections with traffic data 15

3 Fatigue cracking in sections missing traffic data 15

4 GPS-l sections in the analysis 17

5 GPS-2 sections in the analysis 18

6 PADAL versus WESDEF backcalculation results 22

7 Pavement layer thicknesses for GPS-l sections 23

8 Pavement layer thicknesses for GPS-2 sections 24

9 Layer moduli for GPS-l sections 25

10 Layer moduli for GPS-2 sections 26

11 Observed fatigue cracking in GPS-l sections 40

12 Observed fatigue cracking in GPS-2 sections 41

13 Observed rutting in GPS-l sections 56

14 Observed rutting in GPS-2 sections 57

15 T-test for the difference between the AI and the Shell fatigue models 66

16 T-test for the difference between the AI and the Shell rutting models 66

17 Effects of seasonal variations on damage analyses 72

18 Uncertainty factors and their expected effects on pavement performance 92

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 stresses, strains, or deformations that in

turn 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, such as fati~ue 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 highway.

Since the 1950s, as the techniques for analyzing pavement response to loading began to

be available, there have been many attempts to develop rational design procedures, now

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

development of specific distresses in pavements. Also, the proposed revision of the AASHTO

Guide for Design of Pavements, to be completed by the year 2002, will be based on M-E

procedures. The M-E procedures typically involve the following steps:

1. Establislup.ent of a hypothesis for the mechanism involved in the development of

the specific distress. For example, the development of fatigue cracking in AC

pavements is considered by many to be due to the repeated application of bottom

tensile strain in the AC layer. This is the most critical step, as all the subsequent

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

type of analysis needed to compute the critical response( s), as well as the material

and traffic characterizations needed for the analysis.

2. Comprehensive material characterization, 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. For each set of conditions, determination of critical responses (stresses, strains,

deformations) within the pavement layers when subjected to traffic and

environmental loadings.

4. Estimation of damage due to each set of conditions of traffic and environmental

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

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

different model is used for each distress and pavement type.
5. Evaluation of the damage accumulation over a period of time. Miner's fatigue

damage hypothesis [1] is generally used to account for this cumulative damage.

Based on predefined relationships between accumulated damage and distress

development, the amount of distress that may develop at the end of the selected

service life is estimated. The selected pavement may then be redesigned, if the

estimated amount of distress exceeds the acceptable level, or is significantly less

than that level.

6. Selection of the pavement design that results in acceptable levels of distresses at

the end of the target service/design life.

Similar steps are followed to evaluate the performance of existing pavements. If the

previous traffic loading, material properties, and environmental conditions are known (or can be

estimated), the six steps may be followed to estimate accumulated distress-specific damages in

the pavement and predict future pavement performance. Although these six steps may seem

simplistic, the actual process is very complex, because ofthe many still-undefinable factors

associated with pavement design and construction, traffic loading, and environmental conditions.

As part of an FHW A-sponsored project, a study was undertaken to use test data from the

currently ongoing Long Term Pavement Performance (LTPP) program in conjunction with

currently available M-E design procedures, to assess how well those procedures would perform

using that data. 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 then compared to the predicted

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

the accumulated damage to the observed level of distress.

This report presents the study results applicable to AC 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 used to compute the cumulative damage. Additional

background information related to this study is given in a companion volume. This companion

volume, FHW A Report No. FHW A-RD-98-020 (Mechanistic Evaluation of Test Data From

LTPP Flexible Pavement Test Sections, Volume II: Final Report - Appendices), contains

appendixes A to E.

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, the FHW A has assumed the

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

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

national pavement performance database 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 subgrade 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 pavementperformance database. 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-1 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 PCC pavements.

Unbonded PCC overlays on PCC pavements.

Details on the GPS experiments pertaining specifically to the study reported here are provided in

later sections of this 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 reported study. No

additional discussion on the SPS experiments is provided here.

As part of the LTPP program, an extensive data collection effort has been underway 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.
1. A structural analysis model that can consider the geometry of the pavement

(principally, the layered system), the loading condition (multiple wheel loads), and

the stress dependency of paving materials. The model must also be capable of

reliably determining the critical responses appropriate to the distress being

considered. For AC pavements, both linear-elastic and viscoelastic structural

analysis models are available. However, most of the M-E distress model work has

been done using linear-elastic models.

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

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

loading (e.g., equivalent single axle load [ESAL]), in which case all loadings are

transformed into a single load type using load equivalency concepts. However,

the use of such 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, also to account for

the"effect of internal-concrete temperature differentials on curling stresses.

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

characterized in terms of temperature effects and in terms of aging. 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-grained materials is very important. For PCG materials, seasonal effects

are not considered.

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

then to extrapolate those laboratory models to field conditions, using a shift factor

to account for different levels of distress development and other unaccounted for

factors. For example, for AC fatigue cracking, a model was developed on the

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

This model was then expanded to account for different levels of fatigue cracking,

as observed at the pavement surface. For example, the Asphalt Institute version of

the model uses 20 percent fatigue cracking.

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

method for combining various levels of damage done by a combination of traffic

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

damage is cumulative, and that a structure's fatigue life, defined by the allowable
number of load applications prior to failure, is finite. Each load application

consumes a small amount of fatigue life. When the actual number of 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

=L...J-'

Nj

Cumulative fatigue damage.

Actual number of load applications for a given set of conditions i.

Allowable number of load applications to failure for a given set of

conditions i.

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

determined as follows:

Damage ijk@= f (eijk@)

and

eijk@ = f (Ejk@)

Critical pavement structural response 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 Ejk! for each pavement layer.

Our capability for realistically modeling pavement behavior has seen much progress in

the last few decades. However, the capability to consider realistically the material

characterization (e.g., Ejk,) for the pavement layers remains less than desired, because of a lack of

knowledge of realistically accounting for seasonality effects, spatial variability, and deterioration

effects due to traffic loading and environment.

It should be noted that the steps described here are applicable to the use of the M-E

distress models for the design of new or rehabilitated pavements, or for checking such designs.

The application of the M-E distress models to existing pavements to validate/calibrate the models

further 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 the cumulative damage or distress

and comparing the predicted distress to the observed distress. Because a large number of AC

pavement distress prediction models have been developed, the study reported here was aimed at

validating or calibrating some of these models.

The overall objective of this study was to assess the performance of several existing M-Ebased distress prediction procedures when used in conjunction with LTPP data.

• Use deflection data to backcalculate the pavement layer moduli - an important

input to structural evaluation. The nonlinear behavior of the subgrade was

modeled by dividing it into five layers, to allow for different moduli at various

depths.

• Use a linear elastic program to calculate the critical strains. The horizontal tensile

strain at the bottom of the AC layer was used as a predictor of fatigue cracking,

and the vertical compressive strain at the top of the subgrade was used as a

predictor of rutting. Pavement response was calculated for each load level and

axle category.

• Although viscoelastic models may be the best for modeling the mechanical

behavior of AC mixtures, such models could not be used in this study, because the

viscoelastic analysis requires several parameters, such as the creep compliance of

the AC mix, that are not available in the LTPP database.

• Use existing transfer functions (i.e., those developed by the Asphalt Institute and

Shell Oil Company) 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 to the observed

pavement distresses to ascertain if there was a reasonable agreement between the

observed and the predicted distress levels. Also, since the current distress

prediction procedures only allow a "one-point" comparison (e.g., 20 percent

fatigue cracking when the fatigue damage approaches 100 percent), an attempt

was made to develop a continuous distress prediction function/model that would

relate the accumulated distress to the computed cumulative fatigue damage.

• The lack of fit between observed and predicted rutting prompted the development

of a theoretical rutting model, which was calibrated using the LTPP data. The

model was formulated such that traffic could be characterized by axle load/type

counts, rather than the commonly used ESALs.
As discussed, the study reported here was aimed at using LTPP data to assess the

applicability of several existing M-E analysis procedures, specifically, the Asphalt Institute and

Shell Oil Company procedures for predicting the development of fatigue cracking and rutting in

AC pavements. Chapter 2 details the process used to develop the necessary data needed for the

study, using the LTPP database. Chapter 3 describes the backcalculation procedure used to

establish representative layer moduli values for each LTPP test section used in the study.

Chapter 4 describes the structural analysis techniques used to compute the critical structural

responses in the LTPP sections due to traffic loading.

In chapter 5, analysis results are presented for an assessment of the Asphalt Institute

fatigue cracking prediction procedure. In addition, new continuous-function models are

presented that predict the amount of fatigue cracking as a function of computed fatigue damage.

In chapter 6, analysis results are presented for an assessment of the Asphalt Institute rutting

prediction procedure.

In chapter 7, the Shell fatigue cracking and rutting models are evaluated. Chapter 8

presents a case study of the different methods available to account for the seasonal variations in

damage analysis. The development, calibration, and validation of a new rutting model is

presented in chapter 9. This new model accounts for rutting in each pavement layer and

considers the "rate-hardening" typically observed in the progressive development of rutting.

Finally, chapter 10 presents a summary of the findings and includes a discussion of

improvements needed to advance the reliability of M-E procedures using LTPP data.

The final report also incorporates appendices A through E. These appendices are

contained in Volume II: Final Report - Appendices. The following appendices are included in

Volume II:

Appendix A - Test Sections With Missing Data

Appendix B - Sample of Backcalculation Output

Appendix C - Analysis of GPS-2 Sections With Other Base Treatment Than Asphaltic

Appendix D - Sample of WESLEA Output

Appendix E - Summary of Damage Ratio Values

The LTPP data used in this analysis were obtained from NIMS during February 1996

(Release 6.0 data). It was the most recent version of the data release, as of the date of this study.

The NIMS data is categorized into seven modules: inventory, environment, materials testing,

monitoring, maintenance, rehabilitation, and traffic. In each module, the data are stored in tables;

each table is given a name and contains a group of variables. This section briefly discusses the

data elements used in the analysis, the specific tables from which the data were obtained, the

manipulation performed on the data, and the test sections that were excluded from the analysis

because of the lack of data. More details are presented in chapters 3,4, and 5, as relevant.

The monitoring module contains data from various performance monitoring activities.

The falling weight deflectometer (FWD) deflection data, fatigue cracking data (from distress

surveys), and rutting data were obtained from the tables listed in table 1.

The pavement temperature during FWD testing was necessary to adjust the AC layer

backcalculated modulus to the mean annual pavement temperature. Pavement mid-depth

temperature was manually collected during FWD testing. Pavement temperature was collected at

approximately I-hour time intervals, whereas FWD testing was conducted at approximately 2- to

6-minute intervals. A linear regression process was used to estimate the pavement mid-depth

temperature during FWD testing. Pavement layer thicknesses and the mid-depth pavement

temperature were combined with the deflection data to perform the backcalculation.

Typical transverse profiles, as measured in the LTPP program, are shown in figure 1.

It should be noted that transverse profiles are measured using a photographic technique at a

spacing of about 15 m (50 ft). As such, the rut depth used for a given section is the average of

the 11 values. The precision of the rut depth measure has been reported to be ±2 mm (0.079 in).

The average rut depth was calculated from the cross profile data and was based on a 1.8-m (6-ft)

straightedge. The rut depth data were provided by Brent Rauhut Engineering (BRE), Austin,

Texas.

For the fatigue cracking analysis, data for all severity levels were grouped together.

Under the LTPP program, fatigue cracking is categorized as low, medium, and high severity. In

addition, in the field, fatigue cracking is measured using two procedures - the PASCO

photographic procedure, and manual surveys. It should be noted that the results of the two

methods have been found not to be consistent. For this study, the manual survey data were the

data of choice. For those sections missing manual surveys, the PASCO data were used. The last

distress survey for each section was used in the analysis, and the associated date was used in

estimating the cumulative traffic counts from the "traffic open" date to the date of the last

distress survey.
File

Data Element Table Name Extension Comments

Pavement layers and TSTL05B *.T32

material description.

Deflection testing. MON_DYNATEST_DROP _DAT *.M06

Pavement temperature at MON_TEMPERA TURE_TEMPS *.M22

various depths.

Temperature depths. MON TEMPERATURE DEPTH *.M21

- -

PASCO distress survey. MON_DIS_PADIAS_AC *.M15 These two

tables were

combined and

Manual distress survey. MON -

DISAC *.MI0 the last survey

was used.

Rutting transverse profile. MON RUT MASTER *.M23

- -

Rutting from profilometer MON RUT DEPTHS *.M24 Based on

- -

data. 1.8-m (6-ft)

straightedge.
Tr.n." ••.•• Loc.tlon, mm

Measurements obtained from test section 48B340 on March 4, 1993.
The inventory module supplies such data as the date the section was opened to traffic, the

construction date, material types, and layer thicknesses. The information regarding the traffic

opening date for each section were obtained from tabies INV_AGE. For those GPS sections that

were recently overlaid, a deflection analysis and the distress survey had to be interpreted

accordingly. Major improvements data were obtained from tables INV_MAJOR_IMP.

The cross-section data were obtained from table TST L05B. These data were based on

average values obtained from the test pits at each end of the test section. The data included layer

thicknesses and material types. All layers, including the AC layers, were reported separately.

The multiple AC layers were combined into one layer and the multiple granular subbase layers

were combined into one layer.

The environment data module contains statistical measures of selected climatic variables

for each section. The mean monthly air temperature (MMA T) data were available for a number

of years for each section, based on data extrapolated from adjacent weather stations. These

values were averaged for each section and were used to derive the mean monthly pavement

temperature and the mean annual pavement temperature. Table ENV_MONTHL Y_

PARAMETER was the source ofMMAT.

The descriptions of pavement layers (material types) were obtained from table

TST_L05B. Material descriptions were used to classify the treated base layers into cement-,

lime-, or asphalt-treated, soil cement, lean concrete, or others. Materials data, as developed

through laboratory testing, were not directly used in the study. The primary materials data

needed for the mechanistic analysis was the layer moduli data. These data were developed using

the deflection test data.

Traffic data were obtained from tables TRF MONITOR AXLE DISTRIB. The tables

- --

give the annual number of counts of a particular load/axle combination. There are 140 axle-Ioad/

type categories for each section. The axle categories include single, tandem, tridem, and fouraxle assemblies. The axle counts were extrapolated from the days of actual weigh-in-motion

(WIM) data. For example, if the counts were based on 350 days ofWIM data, then the reliability

of the annual figure would be higher than if the counts were based on, say, 14 days. Therefore, in

cases where counts were given for more than one year, the year with the maximum number of

WIM days was used to calculate the cumulative traffic counts. The number of WIM days was

given in tables TRF_MONITOR_ BASIC_INFO. The WIM data available were from 1990 to

1992. It should be noted that reliable traffic data are very critical for the development!
calibration/validation of mechanistically based design procedures. Although, there was a

concern about the reliability of the then-available monitored traffic data, those data are the best

available and a decision was made to use that data. A discussion of backcasting the traffic data

to the year each section was opened is given later.

The seasonal monitoring data were not available. at the time of the study. Therefore,

seasonal adjustments to account for changes in material properties were not directly incorporated

in the analysis. For the AC layer, the seasonality (temperature dependency) of the moduli values

was accounted for by using seasonally adjusted moduli values, as discussed later.

The LTPP data, similar to other pavement related data, incorporates a wide range of

variability in the various data elements. For the purpose of this study, only average values of the

data were used, as appropriate.

The total number of GPS-1 sections is 233 and the total number of GPS-2 sections is 144.

Some sections were missing traffic data, layer thickness data, deflection testing data, rutting data,

and/or distress survey data. These sections were not used. Appendix A contains a series of

tables that report the sections with missing data, grouped by the missing variables.

The pavement layer elastic moduli were backcalculated for all GPS-1 and GPS-2 sections

for which there was deflection and layer thickness data. Structural analysis was carried out on

the sections for which backcalculation was performed successfully (i.e., the deflection basin

match error was within tolerance, as discussed later in the backcalculation section) and for which

traffic and pavement temperature data were available. Figure 2 outlines the analysis steps.

The amount of fatigue cracking is an important variable in this analysis. The availability

or lack of fatigue cracking in the analysis sections has a significant influence on the analysis

results. Table 2 shows the sections in the analysis, categorized by the amount of fatigue cracking

(expressed as the ratio between cracked area to total area). The table shows that there was only

one GPS-I section with fatigue cracking greater than 5 percent and less than 25 percent, and

three sections had fatigue cracking greater than 25 percent. ~imilarly, there was only one GPS-2

section with fatigue cracking greater than 5 percent and less than 25 percent. The small number

of sections exhibiting fatigue damage constrained the effort to study the development of such

pavement distress. The number of data points in the failing region was less than the number

needed to build a reliable model. Further discussion on this matter is provided later.

Table 3 shows the amount of fatigue cracking in sections that were excluded from the

analysis for lack of traffic data. The table indicates that there were 13 sections in GPS-I that
All GPS-1 &

GPS-2

Sections

Sections Missing

Pavement

Temperature Data

Permanent

Deformation
GPS-l Sections GPS-2 Sections

Less than 25% and Greater than Less than 25% and Greater than

greater than 5% of area 25% of area greater than 5% of area 25% of area

261012 123997 014073

271019

341030

GPS-l Sections GPS-2 Sections

Less than 25% and Greater than Less than 25% and Greater than

greater than 5% of area 25% of area greater than 5% of area 25% of area

041007 014127 067491 283090

041018 014155 082008 721003

041037 041021 283085

068156 124102 482176

131001 231009

134111 371802

307088 451008

l;71024 451025

451011

481039

481093

481116

481168
exhibited fatigue cracking greater than 5 percent and less than 25 percent, and 8 sections had

fatigue cracking greater than 25 percent. Four of the GPS-2 sections exhibited fatigue cracking

greater than 5 percent and less than 25 percent, and two sections had fatigue cracking greater than

25 percent. The large number of sections exhibiting fatigue cracking and missing traffic data

stresses the need for obtaining traffic data so that these sections can be utilized in future analysis

and can be made productive.

Tables 4 and 5 show the experimental cell design of the analysis sections for GPS-l and

GPS-2 experiments, respectively. The cell assignment of the sections was based on inventory

data. Table 5 shows that many ofGPS-l sections were located in a wet-freeze zone. No sections

in the analysis represented the dry/no-freeze zone. There were no sections with fine subgrade in

the wet/no-freeze zone. Many sections had a moderate to high AC stiffness. The sections were

well distributed over traffic rate, AC stiffness, base thickness and AC layer thickness. Table 5

indicates that many of GPS-2 sections in the analysis were located in a wet/no-freeze zone. The

sections were well distributed over traffic rate, AC stiffness, base thickness, subgrade type, and

AC layer thickness.
MOISTURE WET DRY

TEMPERATURE FREEZE NO-FREEZE FREEZE NO-FREEZE

SUBGRADE TYPE F C F C F C F C

TRAFFIC RATE

AC Base AC

Stiff- Thick- Thickness ness ness

L 271016 531006

L

H 123996

L

L

H

H 851801 123997 081029

L 271019 121030 311030 836451

L 276251

M H 261012 871620 211010 261013 473075 011019 321021

291002 261004 341003 124106

511002 871622

L 501004 891127 881645 124099 081047 836450

H 081057

-

831801

H 341030 091803 341031 531008

421597 251003

L 211034 291010 271023 271028 531801 201005 201010

L 291008 511464 271029 271087

H 271085

H 171003 171002 511023 014126

181028

L 421605 331001

H

H 421599 251004 251002

501002 341011
MOISTURE

TEMPERATURE

SUBGRADE TYPE

TRAFFIC RATE

Binder Base Surface

Type Thick- Thickness

Bituminous

NonBituminous

ness

L 361644

501683

892011

H

L

H

L

H 512021

L

H

501681 341033 473110 014073 124108

881647 473109 479025

471028 479024

473108

124097 124096

124100
One of the most important structural parameters used in the M-E analysis is the modulus

of elasticity of pavement layers. To predict pavement stresses, strains, and distresses, structural

and damage analyses rely on the elasticity (resilient) moduli of the layers. Only a limited amount

of data on the laboratory-derived resilient modulus of pavement layers were available in the

LTPP database at the time of this study. The reliability of these data has been in question. For

instance, a recent study by BRE [2] showed that the laboratory-derived AC layer modulus

measured at 5°C appeared to be in error. Also, it is well known that pavement structural

properties may exhibit significant seasonal and spatial variations. Unlike laboratory testing, insitu deflection testing is performed over a longer period of time and at many testing points along

the section. The pavement layer moduli backcalculated from deflection testing were therefore

used in subsequent analysis, since they were derived using a larger sample size that covered

wider ranges of time and space.

Three backcalculation programs were used to analyze deflection data: PADAL [3],

WESDEF [4], and MODULUS [5]. It should be noted that the backcalculation results were

based on deflection testing at a 40-kN (9,000-lb) load magnitude. The following paragraphs

present a brief background and discussion of the assumptions made in the analysis of deflection

data.

PADAL was developed by Brown, et al., at the.University of Nottingham. The program

is a liner elastic layer program that accounts for the nonlinearity of the subgrade by dividing it

into five layers and assuming that the layer stiffness is a function of the stress state. The program

implements an efficient deflection-matching algorithm, which results in fast program execution.

PADAL was used to backcalculate the elastic layer moduli of all available test points.

Deflection testing is being performed 12 to 14 times a year, approximately every month, for

seasonal sections and once every few years for nonseasonal sections. Deflection testing is

conducted at 21 points along the wheelpath and along the lane centerline. Only the wheelpath

test data were used for the backcalculation analysis.

In that analysis, the pavement was modeled as a seven-layer structure, as shown in figure

3. The first layer is the surface layer, the second layer is the combined base and subbase layers,

and the third through the seventh layers are the subgrade layers, with thickness of 0.6, 1.0, 1.0,

2.0 m (23.6,39.4,39.4, 78.8 in), and'infinity, respectively. Appendix B shows a sample of the

output of PADAL.

WESDEF is a linear elastic program that was developed by the Army Corps of Engineers,

Waterways Experimental Station. The program uses a program calledWESLEA [12] to perform

a forward calculation of deflections. WESDEF implements an optimization method using least

square fit between the observed and calculated deflections. The program divides the subgrade
AC+'IB

BS+SB

AC+'IB

BS+SB

SO-1= 23.6 in

SO-2= 39.4 in

SO-3= 39.4 in

SO-4= 78.8 in
into two layers: an upper layer 6 m (240 in) deep, and a stiff lower layer. The layering

arrangement used is shown in figure 3. The optimization procedure stops when the absolute sum

of the percent differences between the computed and the measured deflections, or the predicted

change in modulus values, becomes less than 10 percent.

WESDEF was used to backcalculate the elastic moduli of pavement layers for the GPS-1

sections. The pavement was modeled as the surface layer, the combined base and subbase (if

available), the upper portion of the subgrade [6 m (240 in)], and the lower layer. Appendix B

shows a sample of the WESDEF output.

MODULUS [5] is a backcalculation program that can be applied to two-, three-, or fourlayer systems with or without a rigid bedrock layer. A linear elastic program is used to generate a

database of deflection bowls by assuming different modulus ratios. A pattern search routine is

used to fit the measured and calculated bowls. The solution is defined as the optimum set of

modulus ratios that minimizes the weighted sum of the difference between the observed and

calculated deflections.

MODULUS was used to backcalculate the pavement layer moduli for the GPS-2 sections

with a base layer treatment other than asphaltic. For these sections, the backcalculation error that

resulted from using WESDEF was too large to consider using the results in the subsequent

analysis. MODULUS was found to produce less error for these sections.

It is generally recommended that the error for each FWD sensor location be calculated as

the percent difference between the field deflection, and theoretical deflection, and runs with an

absolute error per sensor of more than 2 percent be considered unacceptable [6]. Hence, such

runs were excluded from further analysis. It was found that PADAL, in general, produced less

error than WESDEF. Therefore, it was decided to use the PADAL backcalculation results in the

pavement structural analysis.

Table 6 presents a comparison between the PADAL and WESDEF results for Section

11019. The table shows that the AC layer modulus derived by the two programs is similar. The

granular material, as calculated by the two programs, is shown to have a smaller modulus than

that of the subgrade. This trend was observed for much of the data.

The table also shows that the subgrade modulus, as calculated by PADAL, increases with

the layer depth (due to overburden pressure). It should be noted that WESDEF assumes the

existence of a stiff layer at a depth of 6 m (20 ft) in the subgra,de, whereas PADAL does not make

this assumption. Hence, the subgrade modulus values obtained by PADAL tend to be higher

than those obtained using WESDEF.

Some of the key summary data for GPS-1 and GPS-2 (with asphalt treated base) are

shown in tables 7 and 8.
AC Granular Subgrade Rigid

Program Error Layer Base (SG-l) SG-2 SG-3 SG-4 SG-5 Layer

t (in) 1 6.5 5.5 23.6 39.4 39.4 78.8 info n/a

PADAL

E (ksi) 414 14 37 41 44 47 53 n/a

t (in) 1.5 6.5 5.5 240 info

WESDEF

E (ksi) 401 20 29 1000

1 in= 25.4 mm

1 ksi = 6894 kPa

The layer moduli values given in tables 9 and 10 were obtained using the PADAL

program. The AC layer moduli values reported were corrected for the mean annual pavement

temperature, as discussed in the following sections.

The backcalculated moduli of GPS-2 sections with a base layer treatment other than

asphaltic were found to have a larger basin fit error than that of GPS-l and GPS-2 sections with

an asphalt-treated base course. It was necessary to relax the acceptance criterion for the

deflection fit basin to a 5-percent absolute error per sensor. As such, the analysis

(backcalculation, forward calculation, and damage analysis) of these sections is reported

separately in appendix C.

The backcalculated modulus of the AC layer corresponds to the temperature at which

deflection testing was conducted. To compare the modulus at different points and at different

sections, the modulus values at each test location were adjusted to a pavement temperature of

200C (680F). The modulus values were also adjusted to the mean annual pavement

temperature (MAPT), to arrive at an effective annual AC layer modulus. After adjustments to

200 C (680F), modulus values greater than practical limits [8.6 GPa (1,250,000 psi)] were

excluded from the analysis. The methcds used to perform the temperature adjustments are

discussed in the following paragraphs.

To calculate the MAPT using the Asphalt Institute (AI) method [7], the mean monthly air

temperature (MMA nis required. The mean monthly pavement temperature (MMPT) is first

calculated, and the MAPT is the mean value of the MMPT. The AI method, outlined here, was

used to estimate the MAPT.
Sbde SeclIon AC (In) TB(ln) GB(1n) GS(In) TS(In) SG_1(1n) SG-Z(In) lIG-3f1n) SGof(ln) SCW(ln) 1 lUlU 6.5 0 0 :>.:> u 23.6 JII.4 JII.4 '11.11 ..~ 1 4126 13.1 0 18.4 0 0 23.8 39.4 39.4 78.8 INF 8 1029 4.2 0 5.8 11 0 23.8 39.4 39.4 78.8 INF 8 1047 3.8 0 8.3 12.9 0 23.8 39.4 39.4 78.8 INF 8 1057 3.9 0 3.9 13.8 0 23.8 39.4 39.4 78.8 INF 9 1803 7.2 0 12 0 0 23.8 39.4 39.4 78.8 INF

12 1030 3.3

0 9.8 17.1

0 23.8 39.4 39.4 78.8 INF

12 39Il8 1.508 14.2

0 23.8 39.4 39.4 78.8 INF

12 3997 3.10 11.8 15

0 23.8 39.4 39.4 78.8 INF

12 4OIl9 3.80 10.5 11.2

0 23.8 39.4 39.4 78.8 INF

12 4108 8.2

0 10 14.5

0 23.8 39.4 39.4 78.8 INF

17 1002 13.2000

0 23.8 39.4 39.4 78.8 INF

17 1003 12.1

000 12 23.8 39.4 39.4 78.8 INF

18 1028 15.30

000 23.8 39.4 39.4 78.8 INF

20 1005 13.2

00

00 23.8 39.4 39.4 78.8 INF

20 1010 8.8

00

00 23.8 39.4 39.4 78.8 INF

21 1010 8.70

9.2

0

0 23.8 39.4 39.4 78.8 INF

21 1034 14.80

00

0 23.8 39.4 39.4 78.8 INF

25 1002 7.80

4 8.4

0 23.8 39.4 39.4 78.8 INF

25 1003 8.80 12.7

00 23.8 39.4 39.4 78.8 INF

25 1004 9.8

0 25.8

00 23.8 39.4 39.4 78.8 INF

26 1004 4.2

05

00 23.8 39.4 39.4 78.8 INF

26 1012 8.1

0 4.8 21.8

0 23.8 39.4 39.4 78.8 INF

26 1013 8.7

0 4.8 18.8

0 23.8 39.4 39.'1 78.8 INF

27 10183

0 8.50

0 23.8 39.4 39.4 78.8 INF

27 101950 8.4

0

0 23.8 39.4 39.4 78.8 INF

27 1023 10.5

04 8.8

0 23.8 39.4 311.4 78.1 INF

27 1028 9.80

00

0 23.8 39.4 39.4 78.8 INF

27 1029 8.400

0

0 23.8 311.4 39.4 78.8 INF

27 1085 11.300

00 23.8 311.4 3lIA 78.8 INF

27 1087 15.700

00 23.8 311.4 311.4 78.8 INF

27 8251 7.10 10.2

00 23.8 311.4 311.'1 78.8 INF

29 1002 8.8

0800 23.8 311.4 311.4 78.1 INF

29 1008 11.40 4.4

00 23.8 311.4 39.4 78.8 INF

29 1010 13.9 .0 4.2

0

0 23.8 311.4 311.4 78.1 INF

31 1030 7.2

0

000 23.8 311.4 311.4 78.8 INF

32 1021 7.10

2.1 3.2

0 23.8 311.4 311.4 78.8 INF

33 1001 8.4

0 18.3 14.4

0 23.8 311.4 311.4 78.8 INF

34 1003 7.50 7.4 Z4.9

0 23.8 311.4 311.4 "7B.I INF

34

-

1011

9

0 8.9 24.2

0 23.8 311.4 311.4 78.1 INF

34 1030

8

0 8.1 23.4

0 23.1 311.4 311.4 78.1 INF

34 1031 7.30 11

00 23.8 311.4 311.'1 78.8 INF

42 1587 8.40 18.4

00 23.8 311.4 311.4 78.1 INF

42 1_ 12.30 12

00 23.8 311.'1 311.4 78.1 INF

42 1805 8.10 18.2

00 23.8 311.4 311.'1 78.1 INF

47 30755

0 9.2

00 23.8 311.4 38.4 78.8 INF

50 1002 8.5

0 25.8

00 23.8 311.4 311.4 78.8 INf'

50 10048

0 24.3 22.1

0 23.8 39.4 311.4 78.8 INF

51 1002 5.70 7.7

00 23.8 311.4 311.4 78.8 INF

51 1023 10.10 5.8

0 8.4 23.8 311.4 311.4 78.8 INF

51 1484 8.4

0 5.1

0 5.4 23.8 311.4 311.4 78.1 INF

53 1008 3.40 3.3 3.8

0 23.8 311.4 311.4 78.8 INF

53 1008 3.4

0 3.1 9.8

0 23.8 39.4 39.4 78.8 INF

53 1801 9.20 3.7

0

0 23.8 311.4 39.4 78.1 INF

83 1801 4.4

0 5.8 13.2

0 23.8 39.4 39.4 78.8 INF

83 8450 4.4

0

4.5 4.2

0 23.8 311.4 39.4 78.8 INF

83 8451 4.1

0

7.2 3.7

0 23.8 39.4 39.4 78.8 INF

85 1801 3.20 9.9 11.2

0 23.8 39.4 39.4 78.8 INF

87 1820

5

0 5.7 23.9

0 23.8 39.4 39.4 78.8 INF

87 1822 5.80 8.8 26.3

0 23.8 39.4 39.4 78.8 INF

88 1845 8.40

3.5

0 11.7 23.8 39.4 39.4 78.8 INF

89 1127 4.9

0 18.4 23.4

0 23.8 39.4 39.4 78.8 INF
State 5ectIon AC(!n) TB(ln) GB(ln) GS(In) TS(ln) SG_1 (In) SG-2(ln) SG-3(ln) SG-4(ln) SG-5 1 ,021 3.' 4.:- 0 0 lr.4 23.6 39.4 3lI.4 18.1l INt- 1 4073 8.6 0 0 4.9 5.2 23.6 39.4 39.4 78.8 INF 5 3058 13.3 0 0 0 0 23.6 39.4 39.4 78.8 INF 5 3071 16.4 0 0 0 0 23.6 39.4 39.4 78.8 INF 8 7781 3.4 7.1 0 0 0 23.6 39.4 39.4 78.8 INF

12 4096 1.3 8.6

0

0 13.4 23.6 39.4 39.4 78.8 INF

12 4097 7.7 6.3

0 6.3

0 23.6 39.4 39.4 78.8 INF

12 4100 2.9 7.6

00 13.1 23.6 39.4 39.4 78.8 INF

12 4108 3.96

00 12.9 23.6 39.4 39.4 78.8 INF

28 3082 7.2 3.60 7.10 23.6 39.4 39.4 78.8 INF

32 1030 7.6 1.800 2.8 23.6 39.4 39.4 78.8 INF

32 7000 4.8 4.800 5.6 23.6 39.4 39.4 78.8 INF

34 1033 12 6.2

00 13.8 23.6 39.4 39.4 78.8 INF

34 1034 11.10

00

0 23.6 39.4 39.4 78.8 INF

36 1008 1.1 9.7

00 12 23.6 39.4 39.4 78.8 INF

36 1644 2.3 6.3

00 14.5 23.6 39.4 39.4 78.8 INF

40 4163 11.5

0

00

0 23.6 39.4 39.4 78.8 INF

40 4165 8.10

00

0 23.6 39.4 39.4 78.8 INF

47 1028 12.10

0

0 3.8 23.6 39.4 39.4 78.8 INF

47 3108 12.2

0

00 6.1 23.6 39.4 39.4 78.8 INF

47 3109 5.2 4.300 4.5 23.6 39.4 39.4 78.8 INF

47 3110 9.20

0

00 23.6 39.4 39.4 78.8 INF

47 9024 5.7 7.100

0 23.6 39.4 39.4 78.8 INF

47 9025 4.5 2.30

0 12 23.6 39.4 39.4 78.8 INF

50 1881 2.3 3.4

00 33.6 23.6 39.4 39.4 78.8 INF

50 1883 2.6 2.800 36 23.6 39.4 39.4 78.8 INF

51 1423 12 4.40

1 8.5 23.6 39.4 39.4 78.8 INF

51 2021 1.3 6200 3.6 23.6 39.4 39.4 78.8 INF

88 1647 1.5 5.40 6.9 62 23.6 39.4 39.4 78.8 INF

89 2011

3 3.30

0 36.9 23.6 39.4 39.4 78.8 INF
Table 9. Layer moduli for GPS-l sections.

E(ACITB) E(8SlSB) E( -1) E(SO-2) E(S04) E(S004)

8ecIIon E1_MPT !2 E3 E4 EI Et

1 4128 646,575 23,023 44,563 49,868 58,064 73,479 116,241

1 1029 794,334 16,633 15,329 15,373 15,418 15,451 15,528

1 1047 1,142,204 33,486 21,452 21,907 22,328 22,741 23,387

1 1057 1,283,462 23,464 18,158 18,204 18,220 18,228 18,245

8 1803 1,137,615 21,799 59,318 80,806 61,867 83,257 85,211

12 1030 775,995 74,725 40,358 40,822 41,227 41,853 42,281

12 3996 525,376 89,586 32,174 32,174 32,174 32,174 32,318

12 3997 521,828 21,024 28,880 30,380 31,849 33,586 31,232

12 4099 390,271 80,691 52,837 57,184 61,381 66,191 73,438

12 4106 670,550 39,193 32,105 32,457 32,795 33,202 33,798

17 1002 1,342,158 nla 12,808 22,831 43,253 98,178 358,244

17 1003 648,966 21,322 15,205 20,810 30,003 49,409 117,_

11 1028 771,186 nla 18,216 30,847 57,848 134,104 509,081

20 1005 780,485 nla 8,414 17,180 35,285 84,776 320,611

20 1010 1,107,375 nla 9,042 17,366 38,061 92,325 394,773

21 1010 800,613 13,222 24,083 38,684 58,129 104,030 281,977

21 1034 739,443 nla 19,843 53,133 131,016 383,517 1,595,587

25 1002 1,101,015 14,973 27,529 30,303 33,374 37,480 44,718

25 1003 1,082,895 25,206 30,219 32,895 35,437 38,372 42,708

25 1004 726,585 19,507 40,116 42,957 46,377 51,392 61,131

28 1004 1,525,389 49,522 29,725 35,435 40,305 45,587 53,015

28 1012 1,302,083 32,242 17,774 24,415 34,255 52,235 102,371

28 1013 629,004 28,648 31,228 33,380 36,015 40,317 51,187

27 1016 1,527,991 36,632 32,103 32,831 33,393 33,973 34,712

27 1019 550,371 39,434 22,161 22,398 22,602 22,813 23,013

27 1023 993,010 29,927 35,336 40,580 46,160 53,438 66,138

27 1028 1,865,525 nla 19,028 23,900 32,901 58,615 171,9.

27 1029 938,212 nla 16,036 21,932 35,797 80,098 330,923

27 1085 581,347 nla 5,686 15,737 41,492 124,443 599,.

27 1067 1,317,268 nIa 9,782 20,817 42,082 95,956 329,254

27 8251 1,319,399 34,167 33,882 34,906 35,856 36,987 36,611

211 1002 1,070,979 47,499 20,895 24,178 27,659 32,404 41,287

211 1008 669,239 24,804 35,996 37,831 39,474 41,985 46,490

211 1010 522,295 34,347 33,865 40,725 53,189 81,398 198,701

31 1030 684,059 nla 13,174 16,243 29,319 84,877 274,011

32 1021 91,0,676 17,446 15,744 20,408 28,482 36,834 85,534

33 1001 1,182,480 17,598 64,110 64,524 64,959 55,518 56,305

34 1003 494,996 20,380 56,939 59,983 83,280 67,501 74,475

34 1011 865,669 22,699 53,207 53,225 53,316 53,370 53,411

34 1030 911,m 15,845 52,573 85,991 87,223 131,173 285,387

34 1031 626,396 19,505 25,036 29,113 33,129 37,894 45,148

42 1597 1,303,033 13,897 56,394 66,828 77,783 94,591 130,734

42 1599 940,831 16,067 67,311 66,712 70,484 72,980 77,llO8

42 1805 1,180,891 19,010 59,735 60,774 61,766 82,947 84,114

47 3075 1,119,193 48,412 8,840 11,535 14,318 17,987 24,450

50 1002 1,469,430 19,865 27,490 28,473 29,871 32,153 37,881

50 1004 851,965 40,809 37,010 40,519 44,768 51,068 83,715

51 1002 839,167 19,553 21,328 26,861 33,093 41,640 57,000

51 1023 1,228,473 49,299 32,041 41,797 56,951 96,297 281,413

51 1484 598,023 69,876 40,106 40,995 41,799 42,701 44,012

53 1006 1,520,184 24,572 23,764 26,805 29,341 32,046 35,111

53 1006 1,709,669 25,694 23,844 29,489 34,969 41,483 51,553

53 1801 1,096,504 25,168 40,573 53,428 69,899 94,552 143,140

83 1801 963,427 28,802 22,222 23,157 24,068 25,207 27,078

83 6450 874,280 25,444 34,384 36,015 37,355 36,m 40,.

83 8451 1,125,872 28,891 26,522 29,457 31,913 34,486 37,ll2O

85 1801 1,684,822 22,629 24,719 53,206 109,103 243,996 771,1.

87 1820 1,437,536 19,486 9,928 13,194 17,684 25,150 43,561

87 1822 1,246,083 27,174 25,122 30,404 36,021 52,037 113.2ll6

II 1845 928," 21,184 34,385 38,490 42,932 41,781 58,911

89 1127 1,220,847 18,661 15,479 25,753 45,071 90,318 272,284

25
Table 10. Layer moduli for GPS-2 sections.

E(ACITB) E(BS/SB) E(SG-1) E(SG-2) E(SG-3) E(SG-4) E(SG-5)

State Section E1_MPT E2 E3 E4 E5 E8 E7

1 4073 740,395 27,977 77,388 79,961 82,505 85,439 89,802

5 3058 410,623 NlA 21,015 21,015 21,015 21,015 21,160

5 3071 791,852 NlA 17,841 45,798 110,408 301,527 1,272,007

8 7781 423,012 NlA 5,073 15,652 42,754 131,017 648,562

12 4096 691,455 11,907 21,829 22,263 22,709 23,334 24,382

12 4097 814,236 25,537 78,349 78,465 78,581 78,697 78,842

12 4100 846,805 17,952 21,430 21,498 21,537 21,595 21,662

12 4108 967,212 17,537 18,479 19,783 21,160 22,827 25,653

28 3082 862,677 299,504 55,631 65,620 77,259 94,572 131,017

32 1030 753,772 667,486 40,290 48,966 59,256 75,301 112,983

32 7000 545,391 24,707 38,940 43,792 48,414 53,845 62,129

34 1033 1,238,815 14,747 54,711 67,791 84,531 109,314 158,119

34 1034 841,128 NlA 16,232 22,151 32,823 59,788 184,870

36 1008 709,225 12,578 31,046 32,075 33,593 36,377 44,379

36 1644 637,480 35,347 23,778 30,202 39,842 59,765 132,730

40 4163 1,059,055 NlA 17,983 26,498 43,986 93,118 339,982

40 4165 1,057,564 NlA 22,935 25,979 28,841 32,319 37,863

47 1Q28 1,036,112 37,972 16,667 37,537 80,291 184,931 580,300

47 3108 1..195,673 339,142 41,831 53,576 70,659 103,063 197,346

47 3109 881,475 75,811 25,170 73,528 195,813 579,418 2,631,832

47 3110 585,750 NlA 34,682 36,522 38,015 39,624 41,928

47 9024 895,840 N/A 47,247 125,582 327,723 994,473 4,648,014

47 9025 735,498 31,049 34,694 69,856 132,834 276,984 839,981

50 1681 991,380 23,001 38,352 44,533 55,356 79,731 171,492

50 1683 672,518 20,100 21,081 28,911 40,642 62,643 127,153

51 1423 840,672 22,303 30,912 38,212 47,732 63,372 101,712

51 2021 540,233 633,569 13,959 14,390 14,787 15,241 15,912

88 1647 641,522 34,8118 55,173 56,202 57,080 57,lM1 59,101

89 2011 280,810 1&,512 33,107 36,126 39.503 44,001 52,083
(MMPT). = (MMAT). * [ 1 + 1 ] - 34 + 6

I I Z+4 Z+4

Depth at which temperature is to be predicted. (The mid-depth of the AC

layer was used for this analysis.)

Index representing the month of$e year.

1 12

MAPT = - :E (MMPT);

12 ;=1

The following equation, developed by Braun Intertec [8] based on LTPP data, was used to

adjust the AC modulus to 20° C (68° F) and to the MAPT:

Modulus at temperature T1°C (OF).

Modulus at temperature T2°C CF).

This model is similar to other temperature correction models. See, for example, Ali et aI.

[9], Kim et al. [10], and Stubstad et aI. [11].

This chapter presents details on the analysis of the critical structural responses to traffic

loading. Structural analysis is a pivotal component ofM-E analysis, and the successful

application of M-E distress prediction procedures depends on the selection of a reliable structural

analysis technique.

For this study, the WESLEA [12] program was used to calculate the critical strains (i.e.,

the horizontal tensile strain at the bottom of the AC layer, and the vertical compressive strain at

the top of the subgrade and other layers) due to traffic loading. Traffic loading is characterized

by 140 axle-load/type combinations and the annual count of each combination. Test sections

missing traffic data were excluded from the structural analysis. Also, for a competent structural

analysis, pavement structural parameters should be representative of the entire performance life

of the pavement. The seasonal, long-term, and spatial variations of pavement parameters were

considered in the analysis, as appropriate and as the data permitted. The consideration of the

seasonal and spatial variations is discussed in the following section.

The spatial variation of pavement layer moduli was determined by averaging the values at

all testing points in the section, after adjusting the surface layer modulus to temperature. The '

seasonal variation of temperature was assumed to exert considerable influence on the elastic

modulus of the AC layer. Therefore, the AC layer modulus was adjusted to the MAPT, as

described in chapter 3.

A pavement section was assumed to freeze when the AC layer mid-depth temperature

dropped below 0

0

C (320F). It was further assumed that traffic load repetition would cause

negligible damage during freezing. The number of load (axle) counts was reduced by a factor

equal to the ratio between the number of months with an MMPT of less than 0

0 C (320

F) to the

total number of months. For instance, if a section had 3 months a year of an MMPT of less than

0

0 C (320

F), then it was assumed that the pavement was frozen 25 percent of the time; hence,

25 percent of traffic had a negligible damage effect, and 75 percent of the axle counts were used

in the damage analysis. In so doing, it was also assumed that traffic was uniformly distributed

throughout the year. This assumption was made because there were no reliable data available to

characterize the seasonal variation in traffic.

Some approximate models (simulation-based) are available to adjust the modulus of the

unbound layers to moisture and precipitation conditions, or to the degree of saturation of the

sub grade (e.g., infiltration and drainage, and climate/material/structure models of the FHWA

integrated model). However, these models require parameters that were not available, especially

for nonseasonal sites. Moreover, the above models are still in the process of validation and are

viewed as only research tools. For instance, the CMS model may be used to predict changes in

the AC layer stiffness, the resilient modulus, and Poisson's ratio ofthe base, subbase, and

subgrade with time, given the sunshine percentage, wind speed, air temperature, solar radiation,
physical and thermal material properties, initial soil suction profile, initial soil temperature

profile, heat transfer coefficients, rainfall intensity coefficients, pavement infiltration parameters,

and pavement geometry. Obviously, a large number of the required variables are not available in

the LTPP data.

An approximate method to adjust the modulus of the unbound layers to moisture and

other seasonal climatic variations involves applying a seasonal factor to the backcalculated

moduli, to relate the stiffness of the pavement at a given time to that of the average, year-round

conditions. Pavement sections within the same LTPP experimental cells are subject to similar

environmental conditions and have similar design characteristics. Hence, it may be reasonable to

assume that their seasonal patterns are also similar. With this assumption in mind, the seasonal

adjustment factors derived from a seasonal section may be used to characterize the seasonality of

other nonseasonal sections falling in the same experimental cell. The seasonal adjustment factors

may be calculated as follows:

• For each seasonal site for which backcalculated monthly layer moduli are

available, the average modulus is calculated by:

• For every month, a seasonal factor (F;) is calculated as the ratio of the modulus for

that month to that of the average for the year (EAV)' that is:

E.

F.=-'

, E

AV

• The adjusted modulus for the nonseasonal GPS sites is then calculated as follows:

E

E =-'

AV F.

,

This approach may also be used to adjust the AC layer modulus to seasonal variations.

However, since the experimental cell design of the SMP program does not classify sites based on

temperature, the approach described earlier for the AC layer modulus seasonal adjustment may

be more accurate than the approach outlined here, especially when the nonseasonal site in

question is far enough away from the seasonal site that the temperature patterns at the two sites

are significantly different.

The initial analysis plan was intended to follow this approach. However, at the time of

the analysis, it was found that fewer than expected seasonal sections were available. The
seasonal sections that had traffic, deflection, and temperature data were not well-distributed

across the experimental cells (about 3 of 16 flexible pavement cells were available). It was then

decided that the best available estimate of the effective unbound layer modulus would be the

mean of the values taken in different seasons. Many of the nonseasonal sites had deflection

measurements taken in more than one month (in different years). Obviously, the reliability of the

modulus of the few seasonal sections is greater than that of the nonseasonal sections, since

deflection testing was conducted more frequently and covered more seasons.

Chapter 8 uses a case study to compare three different approaches to considering the

seasonal variations of the pavement moduli, and the effects of using such methods on pavement

damage. The first method uses individual modulus values, corresponding to individual seasons,

assuming that the moduli values of each season are representative of the year-round pavement

moduli. This is often the case when FWD testing is performed once a year, and the analyst does

not have a way to estimate the seasonal variability. The second method uses the average moduli

values of all seasons. The third sums the damages from all seasons, resulting from the

corresponding moduli values, the most theoretically 'appealing method.

In mechanistic evaluation, traffic is characterized as the number of passages of each axleload/type combination. There are 140 axle-load/type combinations in the database for single,

tandem, and tridem axles. The critical responses are calculated for a single application of each

axle-load/type combination.

A debate in the literature concerns how to calculate the maximum strain under multiple

loads, and whether a passage of one tandem axle should be considered as one or two passages of

a single axle. If the passage of each set of multiple axles is assumed to be one repetition, the

damage caused by an 80-kN (I8-kip) single axle is nearly the same as that caused by 160-kN (36-

kip) tandem axles or 240-kN (54-kip) tridem axles. On the other hand, if one passage of a

tandem axle is assumed to be two repetitions of a single axle and that of tridem axles to be three

:repetitions, the damages caused by 160-kN (36-kip) tandem and 240-kN (54-kip) tridem axles are

two and three times greater, respectively, than that caused by an 80-kN (I8-kip) single axle.

Both assumptions are apparently incorrect. The equivalent factors suggested by the Asphalt

Institute are 1.38,and 1.66 for tandem and tridem axles, respectively.

As recommended by Huang [13], a detailed process was used to calculate the critical

responses due to multiple axles. It was assumed that the passage of a tandem axle caused

primary damage corresponding to the strain magnitude under the first axle, and secondary

damage corresponding to the difference between the strain under the first axle and the strain

midway between the two axles. The total damage was the summation of the primary and

secondary damages. The ratio between the total tandem- or tridem-axle damage and the total

single-axle damage is the equivalent axle load factor (EALF). The process is described here:

• For single axles, single wheel: Calculate the tensile strain at the bottom of the AC layer

(et) and the compressive strain at the subgrade surface (ec) at point 1, as shown in figure

4.
1_." •__ 1. •

I

I I I :

4 ' 5'6' I - .--=~~. _._._._._._._._._._ .. , , ,

I I I

I

, ' I

II I

" y

II I

, " I

_ ..........•_.-. _. ---J' _. _. _. _. -.

4 5 6 I

I

Y

I

I

I
Use these values to calculate the number of repetitions to failure associated with this type

of loading, based on fatigue (Nf) and permanent deformation (Np). No data are available

in the LTPP database to identify this type of loading. Therefore, this case was not

considered in the analysis.

• For single axle, dual wheel: Calculate the tensile strain at the bottom of the AC layer (et)

and the compressive strain at the subgrade surface (eJ at points 1, 2, and 3, as shown in

figure 4. Use the maximum of the three values in the calculation of Nfand Np• It was

assumed that all axles consisted of dual wheels.

(a) Calculate et and ec at points 1,2, and 3, as shown in figure 4. Use the

maximum value of each response to calculate the required Nfand Npfor

the first of the two axles.

(b) Calculate et and ec midway between the two axles at the point located

along the path of the point of maximum response in step (a). For example,

if the maximum response in step (a) was at point 2, then point 5 should be

used to calculate the response in step (b). Calculate the Nfand Npof the

second axle based on the difference in the strain values between (a) and

(b), i.e., Nffor the "econdaxle =fjetofA - etofsJ and Npofthesecondaxle =f,,(ecofA - ecofsJ,

where jj and f" are the Asphalt Institute functions for fatigue and permanent

deformation, respectively. If the response in step (b) is in a different sign

from that of (a) (i.e., one is compressive and the other is tensile), we

considered the value of the strain at (b) to equal zero. This was done to

prevent the tandem-axle damage from being more than twice that of the

single axle.

(a) Calculate et and ec at points 1,2, and 3, as shown in figure 4. Use the

maximum value of each response to calculate the required ~.and Npfor

the first of the two axles.

(b) Follow the same procedure outlined previously in (b).

(c) Assume that the damage associated with the third axle equals that of the

second axle. (Use the same values obtained in (b).)

The annual number of axle-load/type passages is given for each axle-load/type category.

For some sections, traffic counts were available for more than one year. The year with the

maximum number of WIM days was selected as the best estimate of the annual traffic counts.

The total number ofload applications (cumulative up to the date of the last distress survey) for

each axle-load/type combination was calculated as follows:
Figure S. Cumulative traffic consideration.

Time Since

Operation in

Years
Figure 5 is a schematic showing the traffic growth function, where traffic (in load

applications) in the first year of operation is To. The traffic T, at any given year, is given by:

T = To (1 + r)(n-I)

where: r

n

Annual traffic growth rate, in percent (estimated by each state).

Number of years since the first year of operation.

N

Cumulative T = f To (1 + rin-

I

) dn

o

N

Cumulative T = To f B(n-I)dn

o

To (B N - 1)

Cumulative T = -----

BlnB

Example: A GPS section was opened to traffic in January 1970, and the last distress

survey was conducted in May 1994. In 1990, LTPP traffic data indicated that a lll-kN

(25-kip) single axle was counted 1000 times in that year. Calculate the cumulative counts

of this axle/load category for the period since the section was opened to traffic until the

date of the last distress survey. Assume that the annual traffic growth rate is 3 percent.
Solution: First calculate the initial traffic To = 1000/(1.03)(20-1)= 570 load applications in

1970. The cumulative count is calculated from the equation:

570 (1.0324.5 - 1) Cumulative T = ------~ = 19,902 applications

(1.03 in 1.03)

T

1

(B N - 1)

Cumulative T = -----

BN1lnB

Based on the estimated historical annual ESAL values, the annual growth rate was

calculated for each section. The rate was found to be highly variable from one year to the next

within the same section, and from one section to another. The growth rate ranged from -13

percent to +30 percent, and averaged 2.4 percent. It should also be noted that individual load

groups had different growth rates. However, it was not feasible to calculate the traffic growth

rate, because many sections only had monitoring traffic data for one year. Also, other sections

had an unrealistic variability in the counts of specific load groups from one year to the next. In

the calculation of the cumulative traffic applications, a simplifying assumption was made that the

annual traffic growth rate was 2 percent for all loading groups. The last survey dates (for rutting

and fatigue cracking) were used to project the axle counts up to that date.

The effect of traffic wander was accounted for by reducing the number of traffic load

counts by a factor of 10 percent. This adjustment factor was suggested by Brown et al. [14]. The

rationale behind this adjustment is that if we assume that each load application will result in a

maximum strain at a given point, the result will be an overestimation of the damage, because the

wheels do not always pass over the exact same path. The damage is therefore distributed over a

range of points.

A more accurate estimate of the effect of traffic wander may be obtained by developing

frequency charts (histograms) of the lateral wheel positions across the traffic lane. The

histograms could then be used to estimate the number of occurrences of the maximum strain

value. The development of such charts requires more data on the lateral locations of the traffic

loads.

Using the backcalculated elastic moduli of pavement layers (adjusted for temperature,

seasonal, and spatial variations) and traffic, characterized by the axle loads and configuration, the

WESLEA program calculated the critical pavement responses. The program output was the

maximum vertical compressive strain at the top of the subgrade and the maximum horizontal

tensile strain at the bottom of the AC layer, all resulting from one load application of each
Case 1: No base layer

AC

SO·l

·SO·2

SO·3 +SO·4

Case 2: Base layer

AC+TB

BS+SB

SO·l

SO·2+ SO·3 +80-4
axle-load/type category. These values were then used to perform damage analysis. Appendix E

shows a sample of WESLEA output.

To account for the nonlinearity of the subgrade layer, in the backcalculation, the subgrade

was modeled as a 5-layer system with thicknesses of 0.6, 1.0, 1.0, and 2.0 m, and infinity.

Additional backcalculation trials were run without dividing the subgrade layer. In general, the

backcalculation error was much larger than that of the divided subgrade. Thus, in subsequent

analyses, the 5-layer subgrade was retained as the better.pavement model. Since WESLEA is a

5-layer program, the layers were combined to form a total of 5 layers. Figure 6 is a schematic

showing the manner in which the layers were combined.

It should be noted that there are two cases, depending on the existence of a base layer. In

the first case, no base layer exists and the first layer is the AC layer. The second layer is the first

subgrade layer. The third is the second subgrade layer. The fourth is the third and fourth

subgrade layers together, combined using Odemark's transformation equation. The fifth is the

fifth subgrade layer. Odemark's transformation combines the layers as follows:

n 3

L hi fE;

i=l

Equivalent modulus.

Layer index.

Total number of layers to be combined.

Thickness of layer i.

Modulus of layer i.

where: Ee

i

n

hi

Ei

In the second case, a base layer does exist and the first layer is the AC layer combined

with the asphalt-treated base (if present). The second layer is the granular base and subbase

layers together, combined using Odemark's transformation equation. The third layer is the first

subgrade layer. The fourth is the second, third, and fourth subgrade layers together, again

combined using the Odemark transformation. Finally, the fifth layer is the fifth subgrade layer.

Since the tire pressure magnitude and distribution were not available in the database, the

tire pressure was assumed to be 689 kPa (100 psi). Also, Poisson's ratio was assumed to be 0.35

for the AC and asphalt-treated layers and 0.4 for the granular base and subgrade layers.

Additional WESLEA runs were performed later to calculate the vertical compressive

strain in the middle of each pavement layer, in conjunction with a new rutting model that

considered the deformation within each pavement layer. The new model development,

calibration, and validation is presented in chapter 9.
Fatigue cracking, one of the most common distresses in AC pavements, is a series of

interconnecting cracks caused by fatigue failure of the AC layer or a stabilized base, under

repeated traffic loading. The initiation and propagation of fatigue cracking has long been

correlated with horizontal tensile strain at the bottom of the surface layer. Fatigue cracking may

also be correlated with shear strain at the bottom of the AC layer. The objective of this study was

to evaluate how well existing fatigue damage models would predict the development of fatigue

cracks. Another important objective was to develop a continuous function relating the fatigue

damage ratio to the extent of fatigue cracking. It should be noted that many pavement engineers

believe that some of the fatigue cracking may be due to high tensile strains occurring at the top of

the surface layer. However, not much work has been done in the United States to validate this

hypothesis, and the phenomenon was not considered in the analysis of the LTPP fatigue cracking

data.

The horizontal tensile strain at the bottom of the AC layer, corresponding to each load

group, was calculated using the structural analysis procedure described in chapter 4. The

calculation of the fatigue damage was performed according to two well-established sets of

.models, the Asphalt Institute (AI) model and the Shell models. Fatigue damage analysis using

the AI model is presented in this chapter. Chapter 7 presents fatigue damage and rutting analyses

using the Shell models.

As mentioned earlier, many of the analysis sections have only been surveyed a few times

under the LTPP data collection efforts. Fatigue cracking data reported in the last survey (at the

time this analysis was conducted) were used in the analysis. The areas of low-, moderate-, and

high-severity cracking were added to produce one measure of fatigue cracking.

The total area of fatigue cracking is divided by the total area surveyed [over 152.4-m

(500-ft) length], to produce the percentage cracked area. Tables 11 and 12 show the percentage

fatigue cracking in the GPS-l and GPS-2 sections used in the analysis. The tables show that the

GPS-2 sections exhibited very little fatigue cracking compared to those of GPS-l.

The approach for developing M-E-based fatigue cracking models was based on fatigue

cracking models developed through laboratory beam-type testing. Laboratory fatigue test data

are typically expressed as follows:
Observed Observed

Number State Section Fatigue Number State Section Fatigue

Cracking Cracking

1 1 4126 0.000 25 29 1002 0.005

2 8 1029 0.007 26 29 1008 0.000

3 8 1047 0.000 27 29 1010 0.000

4 8 1057 0.000 28 31 1030 0.000

5 9 1803 0.000 29 32 1021 0.028

6 12 1030 0.008 30 33 1001 0.000

7 12 3996 0.011 31 34 1030 0.409

8 12 3997 0.780 32 42 1597 0.000

9 12 4099 0.000 33 42 1599 0.000

10 12 4106 0.000 34 42 1605 0.000

11 18 1028 0.002 35 47 3075 0.000

12 20 1005 0.000 36 50 1002 0.000

13 21 1034 0.000 37 50 1004 0.000

14 25 1002 0.008 38 51 1002 0.037

15 25 1003 0.000 39 51 1023 0.000

16 25 1004 0.000 40 51 1464 0.000

17 26 1012 0.069 41 53 1006 0.006

18 26 1013 0.000 42 53 1008 0.006

19 27 1019 0.544 43 53 1801 0.000

20 27 1023 0.000 44 85 1801 0.000

21 27 1028 0.000 45 87 1620 0.000

22 27 1029 0.000 46 87 1622 0.000

23 27 1085 0.000 47 89 1127 0.000

24 27 1087 0.000

Note: Observed fatigue cracking value is the total area exhibiting fatigue cracking

divided by the test section area.
Observed

Number State Section Fatigue

Cracking

1 1 1021 0.010

2 1 4073 0.102

3 5 3058 0.000

4 5 3071 0.000

5 8 7781 0.000

6 12 4096 0.000

7 12 4097 0.000

8 12 4100 0.000

9 12 4108 0.000

10 32 1030 0.000

11 32 7000 0.000

12 34 1033 0.000

13 34 1034 0.000

14 36 1008 0.000

15 36 1644 0.000

16 40 4163 0.000

17 40 4165 0.000

18 47 1028 0.000

19 47 3108 0.000

20 47 3109 0.000

21 47 3110 0.000

22 47 9024 0.000

23 47 9025 0.000

24 50 1681 0.000

25 50 1683 0.013

26 51 1423 0.000

27 51 2021 0.005

28 88 1647 0.000

" 29 89 2011 0.000

Note: Observed fatigue cracking value is the total area exhibiting fatigue cracking

divided by the test section area.
where: Nt =

e =

Eac =

KJ> K2, K3

Number of load repetitions to failure.

Repetitive tensile strain.

Dynamic modulus of elasticity of asphalt concrete.

= Constant depending on material properties.

Based on the results of extensive laboratory testing and on correlations with field

observations, the Asphalt Institute established the following model for AC pavements. The

model relates the number of load repetitions to failure, Nfl to the horizontal tensile strain, et, at

the bottom of the AC layer:

where: Nf =

Eac =

Vv =

Vb =

et =

N

f

= 18.4 *(lOM) *0.004325 *(etr3.291 *(EacrO.854

V

M = 4.84 *( b - 0.69)

Vv+ Vb

Number of load repetitions to failure.

Dynamic modulus of elasticity of asphalt concrete, in psi.

Percent volume of air voids.

Percent volume of asphalt.

Magnitude of tensile strain at the bottom of the AC layer.

Typically, Vv = 5 percent and Vb = 11 percent; then M= 0, and the equation for Nfmay be reduced

to:

Failure is defined as 45 percent fatigue cracking in the wheelpath, which is equivalent to

about 20 percent fatigue cracking of the total lane area. This equation was used to calculate the

number of load repetitions to failure associated with each axle-load/type combination. As

mentioned earlier, tandem axles were considered as two axles. The Nfvalue for the first axle is

that associated with the maximum tensile strain under the first axle (maximum of three points);

for the second axle, Nfis associated with the difference between the horizontal tensile strain

under the first axle and that midway' between the two axles. The third axle in tridem axles is

assumed to have a similar effect as the second axle.

Fatigue transfer functions indicate that the allowable number of applications of any axleload/combination is a function of the strain (horizontal tensile strain at the bottom of the AC

layer) caused by that load application. The pavement damage caused by a load combination is

expressed as the ratio of the actual to the allowable number of load applications of the load

combination. This is referred to as the damage ratio, DI' To accumulate the damages caused by

various axle-load/type combinations, Miner's cumulative damage hypothesis [1] was used.
Failure is expected when the cumulative damage ratio, Df

, equals or exceeds 100 percent,

according to the following expression:

Number of loading groups (axle-load/type combinations).

Cumulative number of passages of load group i.

Allowable number of passages to failure of load group i.

Appendix E contains a summary of the calculated cumulative fatigue damage ratios for

each GPS-I section.

According to the AI fatigue cracking transfer function, it is expected that less than 20

percent of the total pavement area will exhibit fatigue cracking when the damage ratio is less

than 100 percent. Figure 7 shows a plot of the fatigue damage ratio versus the percent of fatigue

cracking. It should be noted that fatigue cracking is given as the ratio of the total area of fatigue

'cracking (of all severity levels) to the total area surveyed.

Figure 7 shows that there were four sections with a damage ratio greater than 100 percent.

Two of these sections demonstrated a negligible amount of fatigue cracking, and the other two

showed fatigue cracking of greater than 20 percent. The section with the largest fatigue damage

ratio (Df= 17) showed the largest amount of fatigue cracking (78 percent of the area).

Although the AI fatigue model does well at predicting the formation of fatigue cracking at

a damage ratio greater than 100 percent (based on the limited amount of data), it does not really

define or quantify the amount of cracking to be expected at each damage ratio level. The only

defined point on the curve is 100 percent damage, corresponding to 20 percent fatigue cracking.

A continuous function is needed to correlate the two variables and to predict one in terms of the

other more accurately. The development and calibration of such a function is presented next.

Theoretically, fatigue cracking should be minor until the damage ratio approaches 100

percent. At this point, the reduction in the AC-Iayer effective modulus and the subsequent

increase in tensile strain leads to accelerated crack propagation. The cracking propagates until it

reaches a level that prompts the highway agency to take remedial action. However, the percent

of fatigue cracking as it forms in the wheel paths only may not exceed a practical value, say 80

percent of the total area, assuming that the wheel paths constitute 80 percent of the lane area. It

should be noted that the maximum observed value was 78 percent. Therefore, the shape of the

model should allow for stabilization at 80 percent fatigue cracking. The best form of model that

represents this behavior is the constrained growth model, which takes the following form:
- , ' ,..,., ,.., , ,.,.., , ,; ,., , ,., , l.., , ~ ~

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Explanatory variable (damage ratio).

Criterion variable (percent of cracked area).

= Regression coefficients.

The model vvas calibrated using GPS-l data. Figure 8 is a graphical presentation of the

model as it fits the data points. The calibrated model is:

0.021

0.027 + e (-O.8S*Df)

The goodness of fit statistics are: percent of variance accounted for, R

2

= 57 percent; and

the standard error of estimate, Se = 9.5 percent. The standard deviation of the observed fatigue

cracking is 15 percent. Hence the relative error of the model is 0.63, indicating that the model's

prediction is better than that obtained by using the average value in this data set. The model

indicates that vvhen the damage ratio is 100 percent, the expected fatigue cracking is 4.6 percent.

This is considerably less than vvhat vvould have been predicted by the AI model. The follovving is

a modified model to force fatigue cracking at zero, vvhen the damage ratio is zero:

0.0026 * D

% f Fatigue Cracking = -------

e (O.OOI47*Dj - 0.967

This model, illustrated in figure 9, has a slightly better fit; the explained variance (R2) is

60 percent, and the standard error of estimate is 9.4 percent. The model predicts 7.5 percent

fatigue cracking at a damage ratio of 100 percent.

A linear model vvasfitted to the data, as shovvn in figure 10. It should be noted that the

model appears to be nonlinear, because the scale of the horizontal axis is logarithmic. The model

is expressed as:

% Fatigue Cracking = 0.045 *Df
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The goodness of fit statistics are similar to those of the previous models: R

2

= 61 percent,

and Se = 9.5 percent. The shape of this model indicates that a fatigue cracking of higher than 100

percent is possible, which is not correct. However, the model is simpler and similar in its fit to

the previous models. It should be noted that at a damage ratio of 100 percent, the expected

fatigue cracking is less than 5 percent of the area.

An exponential growth model was also fitted to the data. The following is the model

after calibration:

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70 r a zgue rac zng = e - .

The model, presented in figure 11, is similar to the previous ones, with R

2

= 59 percent

and Se = 9.3 percent. The model predicts 7.5 percent fatigue cracking at a damage ratio of 100

percent.

It should be noted that there are only a few points with a damage ratio greater than 100

percent. Consequently, the part of the model that describes failure is not well defined; four

different models were fitted to the data and resulted in a comparable fit. This stresses the need

for analyzing additional failing sections, so that pavement deterioration may be modeled

accurately.

Based on the limited amount of data, a group of models was fitted to the data to construct

a continuous function between fatigue damage ratio and fatigue cracking. The linear constrained

growth and exponential growth models are comparable in terms of their goodness of fit.

However, the linear model is the simplest of all. It indicates that fatigue cracking, as a

percentage of the total pavement area, is about 4.5 percent of the fatigue damage ratio. All

models predicted less than 10 percent fatigue cracking at a damage ratio of 100 percent. This

leads to the conclusion that although the AI model can predict the general pattern, it

overestimates the amount of fatigue cracking.

Most of the pavement sections in the GPS-2 experiment had a stabilized base layer. In

the analysis reported in this chapter, only sections with an asphalt-stabilized base are considered.

The analysis results of those GPS-2 sections with other base treatments are presented in appendix

C.

It is expected that the GPS-2 sections resist fatigue cracking better because of the

stabilized base. Figure 12 shows that the GPS-2 sections had much less fatigue cracking than the

GPS-l sections. All sections in the analysis, both those with less fatigue damage than 100
-c:

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percent and those with more, had less than 10 percent fatigue cracking. Only two sections had a

fatigue damage ratio of more than 100 percent. It is obvious that there were not enough failing

sections to model fatigue cracking for these test sections. Therefore, unless more data are

available from pavements exhibiting large amounts of fatigue cracking, very little can be done to·

develop or validate fatigue cracking models using data from the GPS-2 sections.

To compare the performance of the GPS-l and GPS-2 sections, the fatigue cracking

versus fatigue damage ratio plot was generated for both .experiments on the same graph. Figure

13 shows that the GPS-l sections exhibited considerably more cracking than the GPS-2 sections,

especially at higher damage ratios. This is surprising, since the mechanistic analysis should have

accounted for the structural differences between the two pavement types and factored that into

the damage analysis .. A number of reasons may explain this observation. One is that the

pavement models used to represent the pavement structure in the backcalculation process may

not be accurate. For instance, combining the AC layer and the asphalt-treated base may affect the

damage analysis. Another reason might be that the assumptions of linear elasticity, material

homogeneity, and the stress mode under which the transfer functions were derived may not

necessarily be applicable for in-service pavements. It is conceivable that one type of pavement

may be more sensitive to the underlying assumptions than the other.

The GPS-l sections exhibited more fatigue cracking than the GPS-2 sections, for the

same damage ratio. The existence of a treated base in the GPS-2 sections may be responsible for

their superior performance. Theoretically, the structural analysis should account for the

differences between the two types of pavements, through the use of appropriate base-layer

moduli. However, the underlying assumptions under which the transfer functions were derived

may not apply to in-service pavements. One type of pavement may be more sensitive to those

assumptions than the other. Thus, there is a need to investigate the correctness of modeling AC

pavements with stabilized bases.

The Asphalt Institute fatigue cracking transfer function appears to model adequately the

fatigue behavior of GPS-l type pavements (AC on granular base). A lack of failing pavements

(with observed fatigue cracking in excess of 10 percent of the total area) made it difficult to

model more accurately the rate of pavement deterioration. It is recommended that this type of

analysis be performed again, after more of the pavement sections have started exhibiting higher

levels of fatigue cracking.

A group of models was fitted to the data, to construct a continuous function between

fatigue cracking damage ratio and observed fatigue cracking. The linear constrained growth and

exponential growth models were comparable in fit. However, the linear model is simpler. It

indicates that fatigue cracking is about 5 percent of the computed fatigue damage ratio. All

models predicted less than 10 percent fatigue cracking at a damage ratio of 100 percent. The

conclusion is that although the AI model can predict the general fatigue pattern, it overestimates

the amount of fatigue cracking.
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Rutting is another major failure mode for flexible pavements. Pavement engineers have

been trying for years to control and arrest the development of ruts. Many models are available to

relate pavement rutting to design features, load, and climatic conditions. These models range

form purely empirical to mechanistic. In this chapter, the AI model is used to predict the

development of rutting. In chapter 7, the Shell model is used to predict rutting, and the results

are compared with those obtained using the AI model.

Two approaches have been considered for the mechanistic modeling of rutting. The first

approach, typically referred to as the sub grade strain model approach, assumes that most of the

rutting is due to permanent deformation within the subgrade layer, and that the deformation

within the AC and base/subbase layers is negligible, as the quality of these layers is controlled

through mix design and construction specifications. The second approach considers permanent

deformation within each layer of the pavement. Although several techniques have been proposed

for the second approach, it has not been widely used because of the difficulty in obtaining elastoplastic or visco-plastic characterizations for the various paving materials.

Many of the sections used in the analysis have been surveyed several times under the

LTPP data collection efforts. Rut depths reported in the last survey (at the time this analysis was

conducted) were used in the analysis. The rut depth was calculated using the 1.8-m (6-ft)

straightedge method. The rut depth was averaged over 11 cross-profile measurements taken

along each section. Tables 13 and 14 summarize the observed average rut depths for the GPS-l

and GPS-2 sections, respectively.

The Asphalt Institute's permanent deformation model assumes that rutting takes place in

the subgrade and that rutting in other pavement layers is negligible. Hence, the model relates the

vertical compressive strain at the subgrade surface, ec' to the number of load repetitions to failure

due to permanent deformation, Np, according to the following expression:

Failure is defined as the development of 13 to 19 mm,(0.5 to 0.75 in) of rutting. Hence, it

is expected that a permanent deformation damage ratio of 100 percent would correspond to

rutting of 13 to 19 mm (0.5 to 0.75 in).
Observed Observed

Number State Section Rutting, in Number State Section Rutting, in 1 1 1019 0.539 32 27 6251 0.111 2 1 4126 0.183 33 29 1002 0.128 3 8 1029 0.239 34 29 1008 0.277 4 8 1047 0.156 35 29 1010 0.142 5 8 1057 0.151 36 31 1030 0.424 6 9 1803 0.169 37 32 1021 0.248 7 12 1030 0.180 38 33 1001 0.304 8 12 3996 0.224 39 34 1003 0.582 9 12 3997 0.723 40 34 1011 0.331

10 12 4099 0.306 41 34 1030 0.693

11 12 4106 0.154 42 34 1031 0.433

12 17 1002 0.200 43 42 1597 0.185

13 17 1003 0.143 44 42 1599 0.266

14 18 1028 0.594 45 42 1605 0.740

15 20 1005 0.218 46 47 3075 0.267

16 20 1010 0.415 47 50 1002 0.348

17 21 1010 0.224 48 50 1004 0.250

18 21 1034 0.178 49 51 1002 0.127

19 25 1002 0.216 50 51 1023 0.526

20 25 1003 0.162 51 51 1464 0.329

21 25 1004 0.329 52 53 1006 0.141

22 26 1004 0.106 53 53 1008 0.820

23 26 1012 0.314 54 53 1801 0.118

24 26 1013 0.287 55 83 1801 0.168

25 27 1016 0.239 56 83 6450 0.121

26 27 1019 0.252 57 83 6451 0.094

27 27 1023 0.211 58 87 1620 0.522

28 27 1028 0.277 59 87 1622 0.341

29 27 1029 0.193 60 88 1645 0.131

30 27 1085 0.220 61 89 1127 0.814

31 27 1087 0.118
Observed

Number State Section Rutting, in

1 1 1021 0.261

2 1 4073 0.159

3 5 3058 0.147

4 5 3071 0.202

5 8 7781 0.219

6 12 4096 0.159

7 12 4097 0.204

8 12 4100 0.330

9 12 4108 0.436

10 28 3082 0.207

11 32 1030 0.176

12 32 7000 0.126

13 34 1033 0.311

14 34 1034 0.228

15 36 1008 0.121

16 36 1644 0.092

17 40 4163 0.263

18 40 4165 0.237

19 47 1028 0.320

20 47 3108 0.213

21 47 3109 0.161

22 47 3110 0.062

23 47 9024 0.186

24 47 9025 0.208

25 50 1681 0.106

26 50 1683 . 0.134

27 51 1423 0.146

28 51 2021 0.391

29 88 1647 0.297

30 89 2011 0.266
Theoretically, the pavement rutting rate should decrease with time as the subgrade

reaches compaction and the AC layer hardens. The accumulated damage was calculated using

Miner's hypothesis, as described earlier for fatigue cracking. The allowable load repetitions were

computed for each strain level imposed by the axle-load/type combination, and the damage ratio

was computed for each axle-load/type combination. Appendix E contains a summary of the

calculated cumulative permanent-deformation damage ratios, for both the GPS-1 and GPS-2

sections.

The relationship between observed rutting and rutting damage ratio is expected to take an

S shape. The rate of pavement rutting starts at a high level and decreases with time. Therefore,

the point of 100 percent damage ratio does not have the same implication as that of fatigue. In

fatigue analysis, the 100 percent damage ratio, corresponding to about 20 percent cracking, is the

point at which the cracking starts to propagate progressively and the pavement starts to

deteriorate more quickly. Conversely, the 100 percent damage ratio for rutting is an arbitrary one

that corresponds to about 13 mm (0.5 in) of rutting. The rate of rutting development after this

point does not increase significantly. The 13-mm (0.5-in) rutting criterion is a functional, rather

than a structural, criterion.

Figures 14 and 15 show the relationship between observed rutting and the calculated

rutting damage ratio for the GPS-1 and GPS-2 sections, respectively. Figures 14 and 15 show

that, overall, the AI model appears to perform well. Most of the data points meet the one-point

AI model criterion; that is, the observed rutting is less than about 13 to 19 mm (0.5 to 0.75 in) if

the computed damage is less than 1.0, or 100 percent. Only 2 out of 61 GPS-1 sections did not

meet the AI criterion. Rutting in the GPS-2 sections did not exceed 13 mm (0.5 in), and the

maximum computed damage ratio was less than 1.0. However, there was a large scatter of the

data points in Figures 14 and 15. The AI model presumes that the pavement layers above the

subgrade do not contribute much to rutting. Consequently, the plastic characteristics of the upper

pavement layers are excluded from the analysis. In the absence of other predictor variables, this

may have resulted in the scatter of the data points.

Figures 14 and 15 show no consistent trend in the observed rutting versus the computed

damage ratio. Many sections with a small rutting damage ratio exhibited a large rut depth;

conversely, many sections with a large rutting damage ratio exhibited a small rut depth. It is

apparent that the AI damage ratio is not a good predictor of rut depth. In general, the data did not

exhibit the expected S-shaped curve that represents the hardening of the AC layer and rutting

stabilization with time.
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It is well known that rutting increases at an increasing rate during the initial years of

operation and then stabilizes with time. The AI model is limited in that while it appears to be

reliable in predicting a one-point event, it provides no indication of the behavior of rutting over

time or with the application of traffic loading. It also does not provide any indication of ratehardening, nor does it consider the contribution of the nonsubgrade layers to rutting. In order to

account for the rate-hardening and the contribution of all layers to rutting, a new rutting model

was formulated. The development of this new model is discussed in chapter 9.

In the forgoing analysis, the AI models were used to predict fatigue and permanent

deformation damage. In this section, the Shell transfer functions are used to predict both fatigue

cracking and rutting for the GPS-l sections.

The Shell transfer function (model) is very similar in form to the AI model. It relates the

fatigue damage to the horizontal tensile strain at the bottom of the AC layer, as follows:

Number of load repetitions to failure.

Modulus of asphalt concrete in psi.

Magnitude of tensile strain at the bottom of the AC layer.

Compared to the AI model, the Shell model places more emphasis (higher exponent) on

the tensile strain at the bottom of the AC layer and less emphasis on the elastic modulus of the

layer.

Figure 16 is a plot of the observed fatigue cracking versus fatigue damage ratio, based on

the Shell model. The plot is similar to that of the AI model in its shape and in predicting the

development of fatigue cracking for damage ratios higher than 100 percent. The Shell model

produced a higher damage ratio, especially at the higher end of the scale. As with the AI model

evaluation discussed in chapter 5, the lack of sections exhibiting significant amounts of fatigue

cracking did not allow for a detailed evaluation of the accuracy of the Shell models. Table 15

presents the results of a comparative t-test for the difference between the predictions of the AI

model and the Shell model. The test showed that for a 95-percent confidence level, the mean

value of the difference between the two predictions was not different from zero. In other words,

the two models did not produce significantly different results. The significance level (probability

of error) at which the two models produce different results is 22 percent. This is shown in the

rightmost column of table 15.

Figure 17 is a combined scatter plot of the damage ratio versus the observed fatigue

damage for both models. The figure shows that the two models produced a similar trend. For

some sections, the AI model produced higher damage ratios than the Shell model, and the

situation was reversed for other sections.
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Model Mean Dev. Readings Diff. Difference t Dr P

AI 0.8175 2.53 62

~0.552 3.51 -1.235 61 0.221

Shell 1.3694 5.97 62

The revised (1985) Shell transfer function for rutting relates the rutting damage to the

vertical compressive strain at the top of the subgrade, as follows:

Number ofload repetitions to failure (rutting equal to 13 mm [0.50 in]),

corresponding to 50-percent reliability.

Vertical compressive strain at the top of the subgrade.

A permanent-deformation damage analysis was performed using this model. Figure 18 is

a plot of the rut depth versus the total damage ratio. Similar to the AI rutting model, the Shell

model met the one-point criterion ofless than 13 mm (0.5 in) rutting if the damage ratio is less

than 1.0. The expected S-shape trend in data points was not observed. The wide vertical scatter

of the data points suggests that other nonsubgrade layers may contribute significantly to rutting.

Figure 19 compares the AI and Shell models. It is clear that the AI model produced

larger damage ratios than those of the Shell model. Table 16 shows the results of a t-test to

compare the difference between the predictions of the two models. The test indicated that at 95-

percent confidence, the two models produce significantly different results (p-Ievel is less than

0.05). The AI model is more conservative in evaluating the damage than the 50-percentreliability Shell model.

Std. Number of Std.

Model Mean Dev. Readings Diff. Difference t Dr p

AI 0.0453 0.127 62

0.04 0.113 2.8 61 0.0067

Shell 0.0049 0.013 62
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1 in= 25.4 mm

Shell

AI
The Shell fatigue cracking model is comparable to the AI fatigue cracking model in

predicting the fatigue behavior of pavements. Although the Shell model produced slightly higher

damage ratios than the AI model, the t-test showed that the two models did not produce

significantly different results.

The Shell 50-percent-reliability permanent-deformation transfer function appears to

perform as well as the AI model in predicting the rut depth within the limitation of the one-poi~t

criteria. Both models neglect the contributions to rutting by the upper pavement layers. The ttest showed that the two models produce significantly different damage results, with the Shell

model producing low~r damage values.

The large scatter in the plots of observed versus computed rutting damage for both the AI

and the Shell rutting models indicates that the damage ratio calculated by these models is not a

good predictor of rut depth. It was hypothesized that if the models considered the contribution of

the nonsubgrade layers to the measured rutting, a better match would result.

CHAPTER 8. CASE STUDY: COMPARING METHODS OF ASSESSING THE

EFFECTS OF SEASONAL VARIATIONS ON DAMAGE ANALYSIS

One of the assumptions made in the damage analysis is that the average pavement layer

moduli values may be used as an estimate of the effective year-round values. If pavement moduli

are available at only one random point of time, then this value would be used as a representative

of the effective (true) values. Ifseveral values, representing different seasons, are available (as in

the case of the seasonal sections), two approaches may be used in the damage analysis:

• The first involves dividing the analysis period into seasons. In each season, the

moduli values are used to calculate the damage ratio. The damage ratios are then

summed over all seasons. If seasonal traffic variation is known, then traffic

volume in each season is associated with the moduli values in that season;

otherwise, a uniform traffic distribution is assumed.

• The second involves calculating the best estimate of the effective year-round

moduli and then using these values in the damage analysis. A good estimate of

the effective moduli is the weighted average of the seasonal values, with the

weights proportional to the traffic volume in each season. For the purpose of this

analysis, the weights are considered equal, since the seasonal variation of traffic

volume is not known (only annual traffic counts are available in the LTPP

database).

Although the first method is more appealing than the second, it is more calculationintensive. For example, for a seasonal section with 12 seasonal pavement moduli values and 100

axle/load categories (there are actually a total of 140 axle/load categories in the LTPP database),

it would be necessary to perform the structural analysis 1200 times. However, using the second

approach, it would only be necessary to perform the structural analysis 100 times. Two

important questions addressed in the following case are: How significant is the difference

between the results of the two methods? Also, what if only one set of values of the pavement

moduli, taken at a random point in time, was used in the analysis?

Section 311030 is a seasonal section located in Nebraska. For this section, nine sets of

pavement layer moduli, taken in different years and seasons, are available.

Damage analysis was conducted using three scenarios, outlined in Table 17. Figures 20

and 21 graphically show the results of the fatigue cracking damage analysis and the permanentdeformation damage analysis, respectively. The first and second analysis approaches listed in the

table are as previously outlined. The third scenario listed in the table uses the individual value

taken at one given day. This analysis approach is used when the section is not a seasonal section

and is visited only once every few years.

As the table shows, depending on the day at which FWD testing was done, the results

differ. The fatigue damage ratio ranged between 0.035 and 0.15. The permanent-deformation
Fatigue

Approach Used in Structural Damage Permanent-Deformation

and Damage Analyses Ratio Damage Ratio

1. Using all seasonal moduli. 0.096 0.118

2. Using the average moduli. 0.078 0.065

3. Using a single reading taken on:

8/8/89 0.125 0.280

11/29/90 0.035 0.017

11/20/91 0.101 0.098

12/11/91 0.080 0.072

1/16/92 0.043 0.019

2/26/92 0.106 0.107

3/23/92 0.151 0.207

4/16/92 0.149 0.193

4/20/93 0.075 0.072
~

o

-o

~ 0.10

CD

fl

E 0.08

as

C

CD:J

g 0.06 If

........................................ 1'.................... . ~ ~ ~. . .

~ ~ ~

....................................... ~ ··· ..············ ..·1 ·· ··· ..······:·t·········· ···l · .

All seasons included : 1 ~

in the analysis: 0,= 0.096 . :

........... ,, ~ ····T· .., , 'To............... . , ,.... .. . ~ of··········, ··f········· . .

.......... ,- ~ ,."':':' . ~.. . ;................... . : '';'" ? ~... !' . A~~~~~~··~~~~/~~~ ! ·····j···············1' "[ ·······t···············!···············l··············· .

. m ~ an~s: Df= 0.078 : 1 ·········1···· , , , , .

........... ,. . "f" ! '1' '1" ~ ····t··· ! .

j I j I I:

11129190 12/11/91 2/26/92 4/16192

8/8/89 11120/91 1/16/92 3123/92 4120193

Date of Deflection Testing
0.30

0.26

'it

0

:;:;

-0 0.22

as

a:

CD

C) 0.18 as

E

as

C

0.14 c

0

:;:;

as

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.....:I .g

~ CD

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c 0.06

CD

c

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-0.02

......................................... ; ; .

· .

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......................................... ~....... . ~ r···················· r . .

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All seasons included :::

...in the analysis: Dp= 0.118 [ i , ~ .

· .

· .

· .

· .

· . · .

· .

· .

· .

· .

· .

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...Average moduli used . : : : : .

in the analysis: Dp = 0.065 I!: [

. . . . .

. . . . . .

. . .

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",:""

11/29/90 12/11/91 2/26/92 4/16/92

8/8/89 11/20/91 1/16/92 3/23/92 4/20/93

Date of Deflection Testing
damage ratio ranged from 0.017 to 0.28. The implication of such variation is that pavement life

expectancy may be greatly under- or over-estimated, depending on the time at which pavement

testing is conducted. This stresses the need for quantifying the seasonal effects and considering

them in damage analysis.

Table 17 shows that for the same traffic magnitude, the fatigue damage ratio equals 0.096

if all the seasonal values are used, and equals 0.078 if the average pavement moduli are used. A

single t-test was used to compare a single value of 0.078 to a population with a mean value of

0.096 and a variation expressed by the 9 points (given in approach 3). However, more data

points would be required to arrive at a definitive conclusion. Based on the limited data available,

the test fails to show that the two values are significantly different compared to the seasonal

variation of the damage ratio.

The same test was conducted to compare the permanent deformation damages using

approaches 1 and 2 versus the seasonal variation of the damage ratios. Similar results were

obtained. That is, the two values (0.118 and 0.065) were not significantly different. It should be

noted, however, that assumptions of normality and sample independence were made. The

comparison also indicates that the second approach yielded lower damage values than the first

approach. This indicates that, in this case, the first approach is more conservative.

• A lack of seasonal data (layer moduli) may lead to a too-large or too-low estimate

of pavement damage. A difference of up to 16 times the magnitude was observed

when different sets of pavement layer moduli, taken at different points in time,

were used individually in the analysis.

• The damage ratio obtained using all seasonal moduli values did not appear to be

significantly different from that obtained using the average moduli values.

However, the former approach tended to yield more conservative results.

These conclusions are based on the assumption that traffic volume is uniform throughout

the year. It is expected that if the seasonal fluctuations in traffic volume are considered in the

damage analysis, the methods described for considering the seasonal variation effect on

pavements may produce even more different results.

As discussed in chapters 6 and 7, the subgrade-strain-based rutting models developed by

the Asphalt Institute and Shell have serious limitations. These models neglect the contributions

of the AC layer, the base, and the subbase layers to rutting, and they do not account for ratehardening in the progression of rutting over time. Data from the AASHO road testexperiments

showed that the subgrade contributed only about 9 percent of the total measured rutting. The AC

layer, the base, and the subbase layers contributed about 34 percent, 14 percent, and 45 percent,

respectively [15]. In general, the contribution of each layer to rutting will depend on such factors

as the layer compaction, modulus, shear strength, shear and normal stresses and strains, the layer

position in the pavement and the corresponding stress levels, permanent deformation parameters,

etc. Therefore, it is important to consider the contribution of all pavement layers to rutting.

A number of models are available for considering the additive permanent deformation

from all pavement layers. The direct method [13], the VESYS model [16], and the Ohio State

[17] model are examples. However, none of the available model forms directly allows for using

axle-load/type combinations to characterize traffic. In addition, they require material parameters

that are not available in the LTPP database. The following section describes the development

and calibration of a mechanistic-based rutting model that can consider the actual axle load

spectrum.

Assume that we have k loading groups (axle/load combinations) and that each load group

i is associated with a vertical elastic compressive strain €e i•.i in pavement layerj (there are L

pavement layers). Each load group i has ni axles. The plastic strain is assumed to be a linear

function of the plastic deformation; and it is related to the number of load applications by a

negative power model. The negative power relationship reflects the pavement hardening effect

due to repetitive loading. The following model relates: (a) the vertical compressive plastic strain

cP i•.i in a given layer resulting from one load increment of axle group i, to (b) the elastic

compressive strain €eiJ in layerj resulting from the load passage and the number of load

applications N.

-ex

= ll·*Ee .. *N j

} IJ

where: P.i

-a,;

= Slope of the elastic-strain/plastic-strain line for layer j.

= Negative exponent reflecting hardening of layer j with repetitive loading.

Figure 22 represents the three-dimensional plastic strain model. In each loading group i,

the amount of plastic strain differs from one axle to the next, while the elastic strain is constant

for the group. That is, the first axle causes more permanent deformation than the second,
Plastic strain

Elastk strain

N Load Applications
because of the hardening effect. The total plastic strain in layer j due to the first load group is

calculated by:

n\

ep;=I,j = JJljeel;NajdN

Jl.eel· I-a.

} 'J n J

I

1 - a.

}

n

1J+n2J

ep;=2, j = J Jljee2,;NajdN

where: nJ,I' = Equivalent number of applications of the first load group in the second

group's space (scale) for layerj.

Then, nJJ'may be calculated from the following assumption:

nl,j

,

That is, the ratio between two load counts equals the ratio between the number of repetitions of

each needed to cause critical damage. The critical plastic strain €Pc.! at layerj is calculated by:

Jl.ee I . I-a

ep . = } J NI'/J' J

CJ 1 - a. J'

}
N . = (epcil - (1,)] I~«J

11,J J.l.ee

l

.

J ,J

_ ( ee. I';] I~«. _ __ J

ee2,;

Similarly, the cumulative plastic strain in layer j resulting from nkaxle applications of

load group k is:

J.ljeek';~ , )1-«" ~')I-«"] ep =~--n +n J-n J

k,; I _(1,. k,; k,; k,;

J
This equation is the equivalent number of load applications of all previous load groups in the k

group scale.

k

=E

i=1

J.Ljeej ~ .'. + )1-U1 _ ~ .'.r -U1]

---, n

'J n. . n

1 'J - (X. IJ

1

The parameters Pj and ~ are constant for each layer. If we have L layers, each having hj

thickness, then the total plastic deformation Ppis obtained by:

The coefficients P and IX for each layer may be evaluated by laboratory testing, or by using

numerical optimization techniques, given rutting and traffic data.

To simplify this equation, it may be prudent to convert the number of applications of all

load groups to a single load level, using equation 30. The concept was applied here to convert

the counts of a previous load group to an equivalent count in terms of the group in question.

Equation 38 may be used for this purpose. For example, we may convert the counts of all load

groups into an equivalent count of the first load group, as follows:

k

=E

i=1

(

n.. __eeiJ) I~U1

IJ ee.

1
where: NeJJ The equivalent number of applications of all groups, in terms of the first

group.

In this case, we convert the number ofload applications into Ne (corresponding to Ee). If

Eej = EeJJ, i.e., converting any load group to the first load group, then the first term in equation44

equates to nJJ• The cumulative plastic strain corresponding to Ne1J applications may'be

calculated by:

Multiplying the plastic strain of each layer by the layer thickness to obtain the plastic

deformation and substituting Ne1J from equation 45 gives:

Cumulative permanent deformation in all layers from all load groups (i.e., rut

depth).

Vertical compressive strain in the middle of layer j due to the passage of an

axle of group i.

Thickness of layer j.

The subgrade may be divided into several layers and the calculations performed until the vertical

elastic strain = 0, the subgrade thickness is then determined accordingly.

It should be noted that this mc>deldoes not account for the lateral flow resulting from the

horizontal shearing strain in the layers. The model may be modified to use the shearing strain as

another predictor of rutting. However, the regression coefficients of the model will partially

compensate for the absence of this second predictor. It is also possible to formulate a model in

terms of the elastic deflection within each layer.
The parameters )J; and ~ may be determined for each layer using numerical optimization.

To perform this task, a forward elastic layer analysis program, such as the WESLEA program,

must be used to calculate the vertical compressive strain at the mid-depth of each layer.

Finding the set of parameters P and afor each layer involves solving the following

optimization problem:

s

Minimize: F = L(p; - RD;)2

;=1

where: PI

RDi

S

= Calculated cumulative rut depth from the rutting model, for section i.

= Observed rut depth in section i.

= Total number of sections.

The result of this calibration is a set of Pj and ~ values (average values) for each layer of the

pavement. If such values yield an accurate rutting prediction (small standard error of estimate),

. then the model and the coefficients may be used to produce an estimate of rutting.

It should be noted that, ideally, ~ and )J; are site-specific. That is, each section or project

should have its own unique parameters. However, there are not enough data points to support the

calibration of the model for each section individually. For example, a section with 5 layers has

10 unknowns, 2 for each layer, but only one rutting value. The availability of time-series traffic

and distress survey data is necessary to perform site-specific calibration.

If the average plastic parameters (Pi and ai), rather than the actual site-specific values, are

used to predict rutting, a rutting estimation error is expected. The standard error of estimate Se

may be used to assess the magnitude of error expected from the model. Such magnitude

encompasses: the error due to using the average, rather than the actual, parameters; the modeling

error; and the measurement error. Hence, Se is calculated in both the calibration and validation

of the model.

A total of 61 GPS-1 sections were used to calibrate the model. Vertical elastic

compressive strains were calculated at the mid-depth of each layer, assuming that the mid-depth

strain represents the layer's average strain. The subgrade was divided into a number of layers

until the strain value approached zero for the lowest layer. Given that WESLEA is a five-layer

program, the sub grade was divided into three or four layers, depending on the existence of a base

layer, and the upper subgrade layers were considered to have finite thickness. The thickness of

such layers was large enough that the strain values approached zero at the lowest layer.
An error minimization algorithm was implemented to find the parameters aand f.l for

each pavement layer such that the squared deviation between observed and calculated rutting was

minimal. The following are the calibration results.

Combined Granular Base

AC and Subbase Subgrade

a

0.10 0.95 0.644

)l 1.03*10-4 1.163 8.0* 10-3

h

flAC (~ I. )I-~AC] 1 - CX

AC

Pp = AC 1 LJ nj \eej,AC

- aAC j=1

(

1 ] l-cxBaw

II k --

h rBase 't"" I. )1-CXBa""

+ Base 1 _ a ~_ nj \eej,Base

Base I 1

+ h flSubgrade (~n I. ) I-cx.\.:'hgrade] l-cx

Suhgratk

Subgrade 1 _ a LJ j \eej,subgrade

Subgrade 1=1

where: Pp =

i =

k =

h =

AC, Base,

Subgrade =

f.lj =

t1j =

EeiJ =

Total cumulative rut depth (in the same units as the layer thickness h).

Subscript denoting load groups (e.g., single axle with 44.5 kN).

Number ofload groups.

Layer thickness.

Subscripts denoting the AC layer, the combined base/subbase layer, and

the subgrade, respectively.

Layer parameter representing the slope of the elastic/plastic strain line.

Layer parameter reflecting the hardening of layer j with repetitive loading.

Vertical compressive elastic strain in the middle of layer j, corresponding

to load group i.

Substituting the applicable coefficients in this equation gives:

(

k ) 0.9 ( k ) 0.05

Pp = 0.00011 *hAC ~ nj (eej,Ac)l.Il1 + 23.26*hBase ~ nj (eej,Base}o

(

k ) 0.356

+ 0.022 *hSubgrade ~ nj (eej,subgrade}·81
The sum of the squared error is 961 mm squared (1.49 in squared). The standard error of

estimate is 4.14 mm (0.164 in). This is not much larger than the error in measuring the rut depth

[about 2 mm (0.08 in)]. The relative error (Le., the ratio between the standard error of estimate

of the model and the standard deviation of observed rutting) is 0.87; hence, the model provides

improved prediction, compared to the mean rut depth.

Figure 23 shows that the residuals are normally distributed. The bias (mean residual) is

0.7 mm (0.027 in). Fifty-five percent of the observations were within an error of2.5 mm (0.1

in). Eighty percent of the observations were within 5 mm (0.2 in) error.

Figure 24 is a plot of the predicted versus observed rutting values. The observations are

distributed with a constant variance around the 45-percent degree line, an·indication of a good fit

between the model and the data. The plot indicates that the model underpredicted rut depth .

values in excess of20 mm (0.8 in).

The Wilcoxon Matched Pair test, a nonparametric alternative to the t-test, was performed

to test the hypothesis that the observed and predicted rutting values are drawn from the same

distribution. The test is significant at the 0.01 level. The test shows that the p-Ievel (significance

level) is 0.316. Hence, the distributions of the observed and predicted values are not different at

this level of significance.

The model parameters indicate that the AC layer contribution to surface rutting is

marginal for the sections considered in the analysis. The combined base/subbase layer

contributed the most to the measured rutting. In-addition, the contribution of the subgrade to the

measured rutting was greater than that of the AC layer, but much less than that of the

base/subbase layer. However, the vertical elastic strain values may not be the same in all layers,

and this comparison was based on the value of the constant multiplied by the strain value of each

layer. It should also be noted that the model is very sensitive to the layer moduli used. For

example, the apparent higher contribution of the base/subbase layer to rutting may be due to the

fact that the backcalculated moduli for the base/subbase were generally low; in many cases, they

were lower than the subgrade moduli values.

The rutting model described here was calibrated using the rut depth, as measured in the

last rutting survey, and the traffic loading counts projected up to the date of the last survey. To

evaluate the model's accuracy in predicting the rut depth, the model was used to predict the rut

depth at the first rutting survey date, given the traffic loading counts projected up to that date.

The predicted versus observed values are plotted in Figure 25. The standard error of estimate of

the rut depth was 3.55 mm (0.14 in), which is lower than that of the calibration set.

Section 091047 was selected randomly to compare its actual measured rutting values to

rutting development as a function of time, as predicted by the model. Figure 26 is a graphical

presentation of the comparison. The figure shows the expected rutting of the pavement at ages
Histogram of Residuals

y = 61 * 0.1 * normal (x, 0.023512, 0.155123)

(I)

c: 12 o

:p

~ 10

J

o

'0

ci

z

o

-0.4
0.9

0.8

0.7

- 0.6 c

:.:-

=i 0.5

c

'S0:: 0.4 "

00 !

-..I

1 0.3

a.•••

O~2

0.1

......................... , :; .

:·:.0

· .

· .

· .

· .

· .

· .

· .

· .

· .

· .

........................._ _..························1····················································1····················: , ·····················0························· .

.......................... ~ "f'" : j ~"·0··················· j···························t········o········· . .

i i 0 i i 0 i i i

~ ex> ~ : 0 ~ ~ i

......................... , , : , : , .

~ ~ i 0 ~o ~o ~ i 0

~ 0 ()()oj 1 . 1 1

.........................j ············:·i·· ·0·············· .; ~ ! ~ ~ {.......................... .··(f·················

· . (:) . . . .

rOOO~r;:~I~Lr~l[

°8~ ~~ °o~ : :. ~~ : .:

j 0 j ~

0.0

0.0 0.3 0.4 0.5

Observed Rut Depth (in)

Fipre 14. ObIerved ven1ll predicted rat •• &.
-c:

c

.c:

-c.

G)

C

-~

a::

00

00

"~

=0

!

a.

"Ii

••••••.•••••••••••••••••••••• j •••••••••••••••••••••••••••••• :•..•

~ ~ Observed = Predicted ~

: ~:

·····························1······························;······························f················ ~ ~ ························0··············· ..············ .

· . .

· . .

· . .

· . .

: : 0 :

· . .

~ ~ ~ . o. . 0

............................ '1' ·0 1 · 0 r~ \ ~ [ ~ .

, ~ ~ ~ 0 ~ ~

............................ j ~ .\ Q of). ~ C'. ~ l l............................. . .

~ 0 ~o ~ i 0 0

~ 0 ~ ~ ~

............................. : o ..~.· ······ooo····..···o·,,~···················~····L ····················\······························f·· .

~ ~ 0 ~ ~ ~ :

............................ 1: · ·8..00 0.1 ,: ~~o.Q ",::,,~..' ~o.~.~· ~ ,I ~, .

. o~ 0 ~ 0: ~ : ~

: 0 ~ 0 ~;;

o ~ ~ ~ ~

0.0

0.0 0.3 0.4 0.5

Observed Rut Depth (in)
-r:::

c 0.12

.l:

-Co

(I)

C

00 -::::J

\0 a::: 0.08

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18 20 22 ····0···· Observed Rutting
between 0 and 20 years. Two points are plotted on the graph to represent the actual rutting

values, corresponding to the first and last rutting surveys. As the figure shows, the observed and

predicted rut depths match closely.

In summary, the proposed rutting model was developed based on the assumption that the

relationship between the plastic and elastic strains is linear for all pavement layers. It further

assumes that this relationship is nonlinearly related to the number of load applications. Two

parameters are required to characterize the permanent deformation in each layer. These

parameters were not available in the LTPP database, nor were there enough data to estimate the

site-specific layer pat;ameters. However, there were enough data to calibrate the model for the

entire data set. The result was a set of rough estimates, or average values, of these parameters for

the surface, base, and sub grade layers. The calibrated model fits reasonably well with the data

points, with a standard error of estimate not much larger than the measurement error of the rut

depth.
The primary objective of the study reported here was to evaluate the accuracy of some

well-known, mechanistic-empirical models for predicting the performance of in-service AC

pavements. Two distress types were considered in this study: fatigue cracking, and rutting.

Another objective was to develop and calibrate new performance prediction models, as deemed

necessary.

In this analysis, when data were not available, assumptions were made to estimate the

missing data. For instance, annual traffic growth rate, long-term variations in the pavement layer

moduli, seasonal variations of the unbound pavement layers, aging of the AC layers, lateral

distribution of traffic, and vehicle tire pressure are examples of key factors for which there were

not enough data; yet, these factors significantly influence the results. To evaluate the sensitivity

of the output to each assumption, it would be necessary to repeat the analysis; changing only one

assumption at a time, and examine the output. Although such a sensitivity analysis requires

more time and resources, it would be useful in establishing the level of accuracy required for the

key design parameters. Table 18 summarizes the uncertainty factors, and their expected effects

on fatigue cracking and rutting damage computations.

The following are some of the important observations, based on the analysis of fatigue

cracking:

• The GPS-l sections exhibited more fatigue and rutting than the GPS-2 sections,

for the same level of computed damage ratio. The existence of a treated base in

the GPS-2 sections may have been responsible for their superior performance.

Theoretically, the structural analysis accounts for the difference between the two

types of pavements by means of the base layer modulus. However, the

assumptions of linear elasticity, material homogeneity, and the stress mode

(constant stress versus constant strain) under which the transfer functions were

derived may not necessarily hold in real pavements. It is conceivable that one

type of pavement may be more sensitive to the underlying assumptions than the

other. The structural differences that may contribute to differences in

performance between the two pavement types need further investigation.

• The Asphalt Institute fatigue model appeared adequately to model the fatigue

behavior of GPS-l type pavements. The lack of failing pavements (Le.,

pavements with an observed fatigue cracking in excess of 10 percent of the total

area) made it difficult to model the rate of pavement deterioration. It is

recommended that this analysis be performed again at a later date, after more

pavement sections have started exhibiting higher levels of fatigue cracking.
I

Factor I Effect on Damage I

Seasonal variation in traffic. Depends on the magnitude and timing of the

seasonality relative to the seasonality of the

layer moduli.

Effect of traffic wander. Reduction in computed damage.

Seasonal variation in the modulus of unbound Depends on the magnitude and timing of the

layers. seasonality relative to the seasonality of

traffic.

Long-term variation in elastic modulus of the Depends on the direction of change.

surface layer (including aging effects). Age-hardening of the surface layer may

decrease or increase fatigue damage. The

development of cracks, on the other hand,

may accelerate the damage.

Pavement layers backcalculated moduli may Could have a significant effect on damage,

be sensitive to the modeling assumptions, the since the elastic moduli of the pavement

program used, the specified closure error, and layers are major inputs to structural and

the layer thickness variation. There is damage analyses. The direction of the effect

concern that there is no unique solution to a is not predictable, due to compensating errors.

given deflection basin, within a given

tolerance of the closure error.

Tire pressure. Increases with tire pressure.
• A group of models was fitted to the data to construct a continuous function

relating the fatigue damage ratio to the amount of fatigue cracking. The linear

constrained growth and exponential growth models were comparable in terms of

goodness of fit. However, the linear model is the simplest; it indicates that fatigue

cracking, as a percentage of the total pavement area, is about 5 percent of the

fatigue damage ratio.

• The Shell fatigue model is comparable to the AI fatigue model in its adequacy in

predicting the fatigue behavior of pavements. Although the model produced

slightly higher damage ratios than the AI model, the t-test showed that the two

models did not produce significantly different results.

• The Asphalt Institute permanent-deformation transfer function appears to satisfy

the Asphalt Institute one-point criterion for rutting in both GPS-l and GPS-2

pavement sections. However, there was a large scatter of the data points in the

plot showing the permanent-deformation damage ratio versus observed rut depth

plot. The models are not capable of estimating rutting in the early stages. The AI

model presumes that all pavement layers above the sub grade do not contribute

much to rutting. Consequently, the plastic characteristics of the upper pavement

layers are excluded from the analysis.

• The 50-percent-reliability Shell permanent-deformation transfer function also

appears to satisfy the one-point criterion for rutting in GPS-l sections. This

model is also not capable of estimating rutting in the early stages. It is similar to

the AI model in neglecting the rutting in the upper pavement layers. The t-test

shows that the two models produce significantly different damage results, with the

Shell model producing lower damage values.

• The large scatter in the results from the AI and Shell rutting models may indicate

that these models do not correctly estimate rutting. Also, they are only applicable

to pavement sections that do not exhibit permanent deformation in any of the

layers above the subgrade. Hence, they need to be used cautiously.

• A new mechanistic model was developed to predict rut depth as a function of the

vertical compressive elastic strain in all pavement layers. The model was derived

from a well-established plastic deformation functional form. To be compatible

with mechanistic analysis, the model allows the characterization of traffic in terms

of loading groups, rather than ESALs. The proposed model was developed based

on the assumption that the relationship between the plastic and elastic strains is

linear for all pavement layers. It further assumes that this relationship is

nonlinearly related to the number of load applications. Two parameters are

required to characterize the permanent-deformation behavior of each layer. These
parameters were not available in the LTPP database, nor were there enough data

to estimate the site-specific layer parameters. However, there were enough data to

calibrate the model for the entire data set (61 GPS-l sections); the result was a set

of rough estimates, or average values, of these parameters for the surface, base,

and sub grade layers.

• The calibrated model reasonably fits the data points, with a standard error of

estimate not much larger than the measurement error of rut depth. The model

parameters indicate that the AC-Iayer contribution to surface rutting is marginal.

The combined base/subbase layer contributes the most to the measured rutting.

The contribution of the subgrade to the measured rutting is greater than that of the

AC layer, but less than that of the base layer.

• The model was validated using a different set of data from the same sites, but

obtained at different times. The results showed a reasonable agreement between

predicted and observed rut depths. Future enhancement to the model may be

realized by calibrating it to specific material types. For instance, the parameters a

and fJ could be calibrated separately for fine-grained and coarse-grained

subgrades. Treated bases also need a separate calibration. It is also recommended

that the laboratory permanent-deformation parameters be compared to those

derived from the mechanistic analysis.

In the following paragraphs, issues relating to specific data elements are discussed. The

purpose of this discussion is to provide feedback to the LTPP data collection efforts, identify

areas of improvement, discuss the rationale behind selecting specific sources of data when

options were available, and identify future research needs to fill the gaps.

Only a limited amount oflaboratory-derivedresilient modulus data was available;

therefore, these data were not used in the analysis. As discussed, the moduli data used were

based on backcalculation analyses of the deflection data. It is well known that pavement

structural properties may exhibit significant seasonal and spatial variations. Deflection testing is

performed at different times and at many testing points along a section. The pavement layer

moduli backcalculated from deflection testing were used in this study, since they were derived

using a larger sample size that covered wider ranges of time and space.

Future research should be directed towards relating the material properties derived from

laboratory testing to those obtained by field testing at different seasons. A study of the spatial

variability of pavement structural properties is needed, to help construct confidence bands on the

values measured at any point along the test section.
In this analysis, traffic was characterized as annual counts of an array of specific loading

groups. The analysis was thus complicated, since there were up to 140 loading groups. The

annual growth rate was calculated for each section based on the estimated, historical annual

ESAL values. The rate was found to be highly variable within the same section, from one year to

the next and from one section to another. The growth rate ranged from -13 percent to +30

percent, and it averaged 2.4 percent. It should also be noted that individual load groups had

different growth rates. However, it was not feasible to calculate the traffic growth rate because

many sections only had monitoring traffic data for 1 year. Other sections had an unrealistic

variability in the counts of specific load groups from 1 year to the next. In the calculation of the

cumulative traffic applications, a simplifying assumption was made that the annual traffic growth

rate was 2 percent for all loading groups.

Future improvement to traffic data would include providing traffic counts for each

season. This would help in matching the seasonal variation in the structural properties of

pavements with the seasonal variation in traffic applications, to calculate more accurate damage

values.

Traffic wander is another factor that needs to be studied. In this study, a 10-percent

reduction in traffic counts was used to account for the lateral distribution of the wheels. This

adjustment coefficient was suggested by Brown et al. [14]. The rationale behind this adjustment

is that if we assume that each load application will result in a maximum strain at a given point,

that will result in overestimating the damage, because the wheels will not always pass over the

same exact path; therefore, the damage will be distributed over a range of points. A more

accurate estimate of the effect of traffic wander may be obtained by developing frequency charts

(histograms) of the lateral wheel positions across the traffic lane. The histograms could then be

used to estimate the number of occurrences of the maximum strain value. The development of

such charts requires that more data be collected on the lateral locations of the traffic loads.

Deflection data were used to backcalculate the elastic layer moduli of pavement sections.

One limitation of the analysis reported here was that there was no basis for adjusting the modulus

of the unbound layers for the seasonal variations, since deflection data were only available for

one or two seasons ofthe year. In a case study reported in chapter 8, it was shown that the

seasonal variations in the layer moduli could have significantly affected the expected pavement

damage and performance.

Future research efforts should be directed toward evaluating and possibly modeling the

seasonal variations in the pavement layers moduli, and relating those variations to readily

available environmental variables. Moreover, the long-term variations in pavement moduli need

to be investigated.
There were some concerns about the quality of the distress data. It was observed that

some sections had less distresses at a later time. This inconsistency may be explained by

measurement errors, incorrect distress identifications (e.g., longitudinal, block, and fatigue

cracks), and environmental effects.

A study is needed to quantify the magnitudes of errors in distress data, investigate the

seasonality of distress data, and in the case of significant seasonality, provide guidelines as to

when and how to measure distresses. A study is underway to compare manual and photographic

distress surveys and address the variability and reliability of distress data.

In an attempt to evaluate the sensitivity of the damage analysis results to the method used

for including the seasonal variation of pavement moduli, a seasonal section was studied using

three different methods (chapter 8). Two lessons were learned from this case study. First, the

lack of seasonal data (FWD data) may lead to a too-large or too-low estimate of pavement

damage. A difference of up to 16 times the magnitude of damage was observed when different

sets of pavement layer moduli, obtained from FWD testing at different points in time, were used

individually as being representative of the year-round layer moduli. Second, the damage ratio

obtained using all seasonal moduli value did not appear to be significantly different from that

obtained using the average moduli values. However, the former approach tended to yield more

conservative results. These conclusions were based on the assumption that traffic volume was

uniform throughout the year. It is expected that if the seasonal fluctuations in traffic volume are

considered in damage analyses, the methods used here for considering the seasonal variation

effect on pavements may produce even more different results.

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

as follows:

Damage ijkt = f (eijkt)

and

eijkt = f (Ejk,)

= Critical pavement structural response 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 Ejk/for each pavement layer. Our capability for realistically modeling

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

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

than desired because of the lack of knowledge on realistically accounting for seasonality effects,

spatial variability, and deterioration effects 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 traffic data, in terms of reliability and completeness, and the

many approximations that had to be made to develop an appropriate characterization of the

pavement layer properties in terms of Ejk!" Future endeavors in the LTPP and other pavement

research programs should attempt to minimize these serious inadequacies.

The LTPP database 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 a better insight into pavement behavior and ultimately to improve

pavement performance.

1. M.A. Miner, "Cumulative Damage in Fatigue," Transactions of ASME, Vol. 67, 1945, pp.

AI59-AI64.

2. H.V. Quintus, and B. Killingsworth, "Analysis Relating to Pavement Material

Characterization and Their Effects on Pavement Performance," Report Number FHWARD-97-85, Federal Highway Administration, August 1996.

3. F.S. Brown, S.W. Tam, and J.M. Brunton, "Structural Evaluation and Overlay Design:

Analysis and Implementation," Paper presented at the 6th International Conference on

Structural Design, Ann Arbor, MI, 1986.

4. F.J. Van Cauweleaert, D.R Alexander, T.D. White, and W.R Baker, "Multilayer Elastic

Program for Backcalculation Layer Moduli in Pavement Evaluation," STP 1026,

American Society for Testing and Materials, 1989, pp. 171-188.

5. J. Uzan, T. Scullion, C. Michalek, M. Paredes, and R Lytton, "General Procedure for

Backcalculating Layer Moduli," STP 1026, American Society for Testing and Materials,

1989, pp. 217-228.

6. Deflection Testing and Backcalculation Expert Task Group Meeting, Washington, DC,

June 29, 1994.

7. Asphalt Institute, Research and Development of the Asphalt Institute's Thickness Design

Manual (MS-l), Ninth Edition, Research Report No. 82-2, August 1982.

8. Erland Lukanen, "Temperature Adjustment for Backcalculated Asphalt Moduli,"

Facsimile Memorandum received from Braun Intertec Corporation, July 1996.

9. Hesham Ali and Aramis Lopez, "Statistical Analyses of Temperature and Moisture Effect

on Pavement Structural Properties," Paper presented at the Annual Meeting of the

Transportation Research Board, Washington, DC, January 1996.

10. Y. Richard Kim et aI., "Temperature Correction of Deflection and Backcalculated

Moduli," Paper presented at the Annual Meeting of the Transportation Research Board,

Washington, DC, January 1995.

11. RN. Stubstad, S. Baltzer, E.G. Lukanen, and H.J. Ertman-Larsen, "Prediction of AC Mat

Temperatures for Routine Load/Deflection Measurements," Proceedings of the Fourth

International Conference of Bearing Capacity, Minneapolis, MN, July 1994.

12. WESLEA Structural Analysis Program, U.S. Army Engineer Waterways Experimental

Station, Vicksburg, MS, 1989.
13. Yang H. Huang, Pavement Analysis and Design, Prentice Hall, Englewood Cliffs, NJ,

1993.

14. S.F. Brown, J.M. Brunton, and A.F. Stock, "The Analytical Design of Bituminous

Pavement," Paper 8834, Transportation Engineering Group, May 1985.

15. Per Ullidtz, "Pavement Analysis," Developments in Civil Engineering Series, #19,

Elsevier, 1987.

16. William J. Kenis, "Predictive Design Procedures, A Design Method for Flexible

Pavements Using the VESYS Structural Subsystem," Proceedings, Fourth International

Conference on the Structural Design of Asphalt Pavements, Ann Arbor, MI, 1977.

17. K. Majidzadeh et aI., Implementation of a Pavement Design System, Final Report,

Volumes 1 and 2, Research Project Number EES 579, Ohio State University, Columbus,

OH,1981.