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SUMMARY REPORT ON FATIGUE RESPONSE OF ASPHALT MIXTURES TM-UCB-A-003A-89-3 Prepared for Strategic Highway Research Program Project A-003-A by S. C. S. Rao Tangella, Assistant Research Engineer J. Craus, Professor of Civil Engineering J. A. Deacon, Professor of Civil Engineering C. L. Monismith, Professor of Civil Engineering Institute of Transportation Studies University of California Berkeley, California February 1990
Transcript

SUMMARY REPORT ONFATIGUE RESPONSE OF ASPHALT MIXTURES

TM-UCB-A-003A-89-3

Prepared for Strategic Highway Research ProgramProject A-003-A

by

S. C. S. Rao Tangella, Assistant Research EngineerJ. Craus, Professor of Civil Engineering

J. A. Deacon, Professor of Civil EngineeringC. L. Monismith, Professor of Civil Engineering

Institute of Transportation StudiesUniversity of California

Berkeley, California

February 1990

ABSTRACT

The purpose of this summary report is to evaluate test procedures for measuring the

fatigue response of asphalt paving mixtures and to summarize what is known about the

factors that influence fatigue response.

Available test methods are conveniently classified into the following categories:

simple flexure, supported flexure, direct axial, diametral, triaxial, fracture mechanics, and

wheel-track testing. Criteria used to evaluate each method for its potential use as a

laboratory standard included: (1) ability to simulate field conditions, (2) applicability of test

results for use in modelling pavement performance, (3) simplicity, and (4) correlation of

results with performance of in-service pavements. The three most promising methods are

considered to be simple flexure, diametral fatigue, and tests based on fracture mechanics

principles. Although not a fatigue test in itself, direct tension testing offers considerable

potential as a simple surrogate for more complex fatigue tests: French researchers have

achieved quite good correlations between direct tension and fatigue test results.

Factors affecting fatigue response include specimen fabrication, mode of loading,

mixture variables, and loading and environmental variables. Among the various fabrication

or compaction methods, rolling-wheel, kneading, and gyratory methods seem to best

duplicate field compaction. Although fatigue response is not expected to differ among

specimens compacted by these three methods, an evaluation of the possible effects of

compaction method on fatigue response is in order since prior compaction research has

focused on other engineering properties.

Mode of loading, typically either controlled-stress or controlled-strain for laboratory

testing, is one of the primary factors affecting fatigue response. Controlled-stress tests

essentially measure the loading necessary for crack initiation: longer fatigue lives are

recorded in controlled-strain tests because crack propagation is included as well.

Air void content and temperature--both affecting mixture stiffness--may have more

significant influence on fatigue response than any other variable(s). However, many mixture,

load, and environmental factors also influence fatigue response and must be considered both

in the development of test protocols and in the determination of asphalt and mixture

properties that are essential for fatigue-resistant pavements.

Finally, in most prior work, the maximum principal tensile strain has been used as

the cause or determinant of fatigue damage, and the linear summation of cycle ratios

hypothesis has been used to accumulate this damage under mixed traffic loading. Other

damage determinants, such as work strain as well as cumulative failure laws, such as

constancy of dissipated energy, offer possible alternatives.

ii

ACKNOWLEDGEMENTS

The work reported herein has been conducted as a part of project A-003A of the

Strategic Highway Research Program (SHRP). SHRP is a unit of the National Research

Council that was authorized by section 128 of the Surface Transportation and Uniform

Relocation Assistance Act of 1987. This project is entitled, "Performance Related Testing

and Measuring of Asphalt-Aggregate Interactions and Mixtures," and is being conducted by

the Institute of Transportation Studies, University of California, Berkeley, with Carl L.

Monismsith as Principal Investigator. The support and encouragement of Dr. Ian Jamieson,

SHRP Contract Manager, is gratefully acknowledged.

The draft of this report was reviewed by an Expert Task Group (ETG) which

includes the following members:

Ernest Bastian Eric E. Harm

Federal Highway Administration Illinois Department of Transportation

Campbell Crawford Charles S. HughesNational Asphalt PavingAssocation Virginia Highway and Transportation

Research Council

William Dearasaugh Dallas N. LittleTransportation Research Board Texas A&M University

Francis Fee Kevin Stuart

ELF Asphalt Federal Highway Administration

Douglas I. Hanson Roger L. YarbroughNew Mexico State Highway Department University Asphalt Company

Other reviewers included: Dr. R.G. Hicks, Dr. S.F. Brown, and Dr. P.S. Pell. Ms.

Joanne Birdsall prepared the final manuscript.

oo.

111

DISCLAIMER

The contents of this report reflect the views of the authors, who are solely responsible

for the facts and accuracy of the data presented. The contents do not necessarily reflect the

official view or policies of the Strategic Highway Research Program (SHRP) or SHRP's

sponsors. The results reported here are not necessarily in agreement with the results of

other SHRP research activities. They are reported to stimulate review and discussion within

the research community. This report does not constitute a standard, specification, or

regulation.

iv

TABLE OF CONTENTS

ABSTRACT ....................................................... i

ACKNOWLEDGEMENTS ............................................ iii

DISCLAIMER ..................................................... iv

TABLE OF CONTENTS .............................................. v

LIST OF TABLES .................................................. vii

LIST OF FIGURES ................................................. viii

1.0 INTRODUCTION .............................................. 1

1.1. Problem Definition ......................................... 1

1.2. Purpose ................................................. 11.3. Objectives ................................................ 1

2.0 BACKGROUND ............................................... 5

2.1. Factors Affecting Fatigue Response ............................. 52.1.1. Specimen Fabrication .................................. 52.1.2. Moad of Loading .................................... 142.1.3. Mixture Variables .................................... 15

2.1.4. Loading and Environmental Variables .................... 202.2. Limitations of Available Information ........................... 24

2.3. Overview of Test Methods and Their Development ................ 24

3.0 FATIGUE TEST METHODS .................................... 37

3.1. Simple Flexure ........................................... 383.1.1. Center-Point and Third Point Loading .................... 393.1.2. Cantilever Loading ................................... 393.1.3. Evaluation ......................................... 40

3.2. Supported Flexure ......................................... 473.3. Direct Axial ............................................. 49

3.3.1. Tension ........................................... 49

3.3.2. Tension/Compression ................................. 513.4. Diametral Test ........................................... 553.5. Triaxial ................................................. 603.6. Fracture Mechanics ........................................ 61

3.7. Wheel-Track Testing ....................................... 69

V

3.7.1. Laboratory Tests .................................... 693.7.2. Full-Scale Tests ..................................... 70

3.8. Evaluation of Test Methods ................................. 73

4.0 FAILURE CONCEPTS ................................. ........ 85

4.1. Unique Strain ............................................ 864.2. Deviator Stress ........................................... 874.3. Work Strain ............................................. 91

4.4. Constancy of Dissipated Energy ............................... 924.5. Work Strain and Dissipated Energy ........................... 100

5.0 CORRELATIONS AND SIMPLIFICATIONS ....................... 104

5.1. Direct Tension Test ...................................... 1045.2. Failure Envelope ......................................... 108

6.0 RELATIONSHIP BETWEEN TEST RESULTS AND FIELDPERFORMANCE ............................................ 115

6.1. Shift Factor ............................................. 1166.2. Fundamental Mixture Properties in Pavement Analysis ............ 1176.3. Further Challenges ....................................... 1226.4. Summary .............................................. 126

7.0 CONCLUSIONS AND RECOMMENDATIONS ..................... 128

7.1. Specimen Fabrication ..................................... 1287.2. Factors Affecting Fatigue Response ........................... 1287.3. Test Methods ........................................... 1297.4. Recommendations ........................................ 129

8.0 REFERENCES .............................................. 132

APPENDIX A ............................................... 140

A.1. Hypotheses ............................................ 140A.2. Test Program ........................................... 144

vi

LIST OF TABLES

2.1 Comparative Evaluation of Controlled-Stress andControlled-Strain Loading ....................................... 17

2.2 Factors Affecting the Stiffness and Fatigue Response ofAsphalt Paving Mixtures ......................................... 18

2.3 Effect of Shape of Waveform on Fatigue Life(Raithby and Sterling, 1972) ...................................... 22

2.4 Summary of Fatigue Test Characteristics ............................ 25

2.5 Chronology of Fatigue Testing and Evaluation ........................ 29

3.1 Comparison of Test Methods ..................................... 82

A.1 Significant Mixture and Test Variables for Fatigue Study ............... 146

A.2 Number of Samples for Fatigue Factorial Design ..................... 147

vii

LIST OF FIGURES

2.1 Influence of Compaction Method on Relative Mixture Stability(Vallerga, 1951) ................................................ 9

2.2 Principle of Compaction with the Gyratory Shear Compacting Press (Bonnot,1986) ....................................................... 10

2.3 Example of Compactive Effort Curves for Different Mixes Usingthe Mobile Steel Wheel Simulator (yon Quintus et al., 1988) ............. 13

2.4 Comparison of Laboratory Controlled-Strain and Controlled-StressFatigue Data (Monismith et al., 1977) .............................. 16

2.5 Types of Loading Patterns (Said, 1988) .............................. 21

2.6 Equivalent 'rime of Loading-Depth Relationship for Horizontal Stress(McLean, 1974) ............................................... 23

3.1 Third-Point Flexure Apparatus (Monismith et al., 1971) ................. 41

3.2 Center-Point Flexure Apparatus (van Dijk, 1972) ...................... 42

3.3 Load vs. Time and Deflection vs. Time Relationships forControlled-Stress Test Equipment (Monismith et al., 1971) ............... 43

3.4 Flexure Apparatus Used by Pell (1965) ............................. 44

3.5 Controlled-Strain Torsional Fatigue Machine (Pell, 1965) ................ 45

3.6 Bending Fatigue Test Machine (Bonnot, 1986) ........................ 46

3.7 Fatigue Test Apparatus (Barksdale, 1977) ............................ 50

3.8 Schematic Representation of Direct Axial Fatigue Test(Raithby and Sterling, 1972) ...................................... 53

3.9 Effect of Strain Reversal on Fatigue Life(Raithby arid Sterling, 1972) ...................................... 54

3.10 Loading Configuration and Failure in Diametral Test(Kennedy, 1977) ............................................... 58

oo°

VIII

3.11 Relative Stress Distributions and Element Showing Biaxial State of Stress for theDiametral Test (Kennedy, 1977) ................................... 59

3.12 Triaxial Load Fatigue Rig (Pell and Cooper, 1975) ..................... 63

3.13 Triaxial Apparatus Permitting Independent Control of Axial andRadial Loads (McLean, 1974) .................................... 64

3.14 Crack Tip Displacement Modes ................................... 67

3.15 Diagram for Fatigue Life Computations from FractureProperties (Salam, 1971) ........................................ 68

3.16 Schematic Representation of Wheel Tracking Machine(van Dijk, 1975) ............................................... 71

3.17 Details of Circular Test Track (Terrel and Kumar, 1970) ................ 74

3.18 Canterbury Test Track Showing Arrangement of Sections(Paterson, 1972) ............................................... 75

3.19 Linear Test Track - Nottingham University (Brown et al., 1977) ........... 76

3.20 TRRL Road Machine (Grainger, 1964) ............................. 77

3.21 Operational Layout of the ALF (Metcalf et al., 1985) ................... 78

3.22 Circular Track Facility for Fatigue Testing (LCPC) ..................... 79

4.1 Results of Fatigue Tests at Various Temperatures and Speeds(Saal and Pell, 1960) ........................................... 88

4.2 Strain-Life Fatigue Results for a Range of Mixes(Pell and Taylor, 1969) .......................................... 89

4.3 Typical Stress Difference-Fatigue Life Relationships for VariousTest Methods (Porter and Kennedy, 1975) ........................... 90

4.4 Relation of Energy Ratio and Mix Stiffness for an AsphalticConcrete (van Dijk, 1975) ....................................... 97

ix

4.5 Phase Angle, Energy Ratio, and Dissipated Energy Charts Showingthe Limits for the Base Course and Wearing Course and WearingCourse Mixes Tested (van Dijk et al., 1977) .......................... 98

4.6 Distortion Energy (Garretsen et al., 1987) .......................... 103

5.1 Direct Tension Testing Apparatus (Epps, 1969) ...................... 106

5.2 Typical Window Formed by Boundary Curves (Little and Richey, 1983) .... 111

6.1 Asphalt-Concrete Thickness vs. Tensile Stress for a TypicalFull-Depth Pavement .......................................... 120

6.2 Asphalt-Concrete Thickness vs. Tensile Stress for a TypicalPavement with Granular Base ................................... 121

6.3 Distortion Energy (Related to Work Strain) and Horizontal StrainDue to a Ve.rtical Load (Kunst, 1989) .............................. 127

A.1 Stress vs. Applications to Failure ................................. 142

A.2 Strain vs. Applications to Failure ................................. 142

X

1.0 INTRODUCTION

This summary report, focussing on the fatigue response of asphalt mixtures, is one

of a series prepared as a part of SHRP Project A-003A, "Performance Related Testing and

Measuring of Asphalt-Aggregate Interactions and Mixtures," to evaluate available

information on the fatigue, permanent deformation, thermal cracking, aging, and water

sensitivity characteristics of asphalt mixtures.

1.1 Problem Definition

Pavement distress resulting from repeated bending or fatigue of asphalt-concrete

pavements has been a well-recognized problem in the United States since 1948 (Hveem and

Carmany, 1948). In order to address fatigue distress in mixture and pavement design

procedures, it is necessary to describe the behavior of asphalt-concrete mixtures under

repeated stressing of the type encountered in situ. To this end, it is useful to evaluate

various laboratory fatigue tests with the objective of recommending a relatively simple test

(or tests) which can best simulate field conditions.

1.2 Purpose

The primary purpose of this research report is to review various fatigue test methods

and to recommend the most appropriate method for defining the fatigue response of

asphalt-concrete mixtures and for ultimate incorporation into an asphalt-aggregate mixture

analysis system.

1.3 Obiective_

This report includes an evaluation of factors affecting the fatigue characteristics of

dense-graded asphalt concrete together with an assessment of test methodologies used to

measure these characteristics.

Fatigue, as considered herein, is a form of cracking resulting from repeated traffic

loading. Cracking resulting from thermal stresses (non traffic associated) is described in

another summary report in this series.

From an evaluation of available information, it is evident that there are many

procedures, including both laboratory and field testing, to define the fatigue response of

asphalt-concrete mixtures. These procedures involve a variety of test techniques, equipment

types, specimen configurations, types and modes of loading, test conditions (for example,

frequency of loading, temperature, etc.), and analysis procedures.

Thus, the objectives of this study are to:

1. Review the factors affecting the fatigue performance of dense-graded

asphalt-concrete mixtures,

2. Summarize the steps necessary to measure fatigue lives and related

parameters which are useful in the structural analysis and design of

asphalt-concrete pavements,

3. Provide a listing of both the advantages and disadvantages of each test

method, and

4. Evaluate and list, in order of preference, the methods used to measure fatigue

response for mixture evaluation and design as well as for prediction of

pavement life in situ.

The methods which have been analyzed in this summary report include:

1. Simple flexure testing,

2

2. Supported flexure testing,

3. Direct axial testing,

4. Diametral testing,

5. Triaxial testing,

6. Fracture mechanics testing, and

7. Wheel-track testing.

Two additional considerations relative to fatigue are included. One is associated with

an indirect determination of an appropriate asphalt content for reasonable fatigue response

based on failure envelope defined for thermal cracking and permanent deformation. The

other is concerned with the phenomenon of load associated cracking which originates at or

near the surface of asphalt-concrete pavements.

This summary report is organized into seven sections. Section 1 contains the

introduction. Factors affecting the fatigue response of asphalt concrete, based on a review

of available information, are summarized in Section 2. Section 3 includes a summary of the

various methods to define fatigue, including a listing of their advantages and disadvantages.

It also provides the basis for evaluating alternate test methods in order to arrive at an initial

ranking for the laboratory studies to be conducted as a part of this project. Section 4

examines several fundamental concepts that may prove useful in developing a better

understanding of fatigue response of both laboratory specimens and in-situ materials.

Section 5 discusses alternate procedures having the potential for easing the burden of

laboratory fatigue testing and simplifying the analysis of pavement structures. Section 6

presents a discussion of the relationship(s) of test results to field performance. Finally,

3

Section 7 provides conclusions based on this detailed evaluation, a ranking of the existing

test methods, and an identification of some areas which may require additional investigation.

Appended to the report is the recommended laboratory study plan to evaluate the

various tests methodologies which have evolved as the candidate procedures.

4

2.0 BACKGROUND

The purpose of this section is to provide background information regarding the

fatigue response of asphalt mixtures. First, a summary is presented of the various factors

affecting fatigue response including the method of specimen fabrication (compaction), the

mode of loading, mixture variables, and, finally, traffic and environmental variables. Next,

the limitations of available information are briefly highlighted. The section concludes with

an overview of fatigue test methods and their development.

2.1 Factors Affecting Fatigue Response

Included herein is a brief summary of available information on factors affecting the

fatigue response of those types of asphalt paving mixtures that are comprised of asphalt

cements and of aggregates which produce dense mixtures when properly compacted.

Included are discussions of (1) methods of specimen fabrication, (2) mode of loading

considerations, (3) the influence of mixture variables on fatigue performance, and (4) the

influence of loading and environmental variables on fatigue response.

2.1.1 Specimen Fabrication

The primary objective of specimen fabrication or compaction is to produce "realistic"

test specimens, that is, specimens that reasonably duplicate the corresponding in-situ asphalt

paving in all major respects including composition, density, and engineering properties. The

effect of method of testing is examined more thoroughly in the following section.

Compaction methods presently being utilized to fabricate test specimens include the

following: (1) static compaction, (2) impact compaction, (3) kneading compaction, (4)

gyratory compaction, and (5) rolling-wheel compaction. The compaction temperature is

5

typically selected such that the asphalt viscosity is 500 +_. 50 cSt (ASTM D-3202). To

maintain this temperature during compaction, the mold, compaction foot, tamping rod, and

asphalt-concrete mix must be preheated. The NCHRP/AAMAS (Asphalt-Aggregate

Mixture Analysis System) study provides a recent evaluation of selected laboratory

compaction procedures (von Quintus et al., 1988).

Static t_ompaction. This procedure involves placing the loose asphalt mixture in a

mold of the desired shape and size and compressing the mixture under the gradual

application of a static load. To promote homogeneity, the mixture is generally "rodded" or

"spaded" prior to compaction, and the mold is made "free floating" by using a "double

plunger" arrangement. ASTM Test Method D-1074 describes such a double-plunger

compaction procedure. The primary advantage of this method, compared to kneading,

gyratory, and rolling-wheel compaction methods, is its simplicity. The major disadvantage

is that the orientation of aggregate particles is different from that obtained in the field and,

hence, in-situ conditions are not accurately simulated.

Impact Compaction. In this methodology, the mixture is compacted in a mold by

repetitive applications of impact loads, using a hammer of specified weight which is allowed

to free-fall a fixed distance. The number of blows is selected to reproduce densities

achieved in situ under roller and traffic compaction. The "Marshall" method (ASTM D-

1559-82) employs this procedure.

The advantage of impact compaction is that high energy can be applied with a rather

simple and low-cost, hand-operated unit that is portable, thus making it convenient to

fabricate specimens in the field as well as in the laboratory.

The primary disadvantage is that the high energy transfer on impact may cause (1)

the asphalt film to rupture and the aggregate particles to bear directly upon each other

which in turn leads to structural properties (for example, resistance to permanent

deformation) different from those of mixtures compacted in situ and/or (2) undue fracture

and degradation of the aggregate. Also, it is doubtful that the impact procedure can be used

to fabricate specimens which duplicate asphalt paving in the field after it has been subjected

to the compaction effects of rubber-tired traffic over a period of years (ARE, 1986).

Another potential disadvantage is the difficulty in preparing uniform and homogeneous

specimens of sizes and shapes other than short cylinders. No data or information exists on

this point.

Kneading Compaction. The kneading compactor was developed jointly by the

California Division of Highways and the University of California, Berkeley, under the

auspices of the Triaxial Institute.

Compaction is achieved by repetitive loading through a tamping foot, considerably

smaller in size than the specimen being compacted. During each application of the tamping

foot, the load is gradually increased, maintained for a short time interval, and then released.

Each subsequent loading is applied to a "fresh" portion of the exposed surface. This pattern

of loading induces deformations and particle orientation similar to those which take place

in situ. Kneading compaction is employed in the preparation of beam specimens for fatigue

testing (ASTM D-3202) and in preparing specimens for the stabilometer test (CALTRANS

Test 366).

Existing kneading compactors vary in size from small hand-operated units, through

7

portable hydraulic table models, to very elaborate mechanical-hydraulic models with the

capability of compacting beam specimens up to 30 in. in length as well as cylindrical

specimens with diameters up to 6 in. and heights to 12 in. Correlation studies have been

carried out indicating that laboratory-fabricated specimens have both physical and

mechanical properties equivalent to those of field cores (ARE Inc., 1986).

Results of Hveem Stabilometer tests on specimens prepared by impact, static and

kneading compaction, shown in Figure 2.1, illustrate that kneading compaction produces

mixes with a reasonable sensitivity of stability to changes in asphalt content.

Gyrator3' Compaction. Using gyratory shear, asphalt concrete is compacted by

subjecting a cylindrical specimen to gyratory motion of a compaction mold while pressure

is maintained at each end of the specimen by means of steel plungers with parallel faces

(Figure 2.2).

The main disadvantage of the gyratory compactor is its inability to fabricate test

specimens in other than cylindrical shapes. The NCHRP/AAMAS Study (von Quintus et

al., 1988) concluded that gyratory compaction produces specimens which are representative

of materials compacted in situ. This conclusion is based on a comparison of various stiffness

and strain parameters measured on cores obtained immediately after construction with the

same parameters obtained on specimens prepared in the laboratory to the same unit weights

as the field cores. According to the AAMAS analysis, kneading and rolling-wheel

compactors also adequately simulated field compaction. The specific ranking of compaction

devices in terms of their abilities to consistently simulate the engineering properties of field

cores is as follows:

8

6O

40 '.,

I,._3o I -_'-_--C-- o---_-_- _ _ _.

_ 20 1

•_ Legend,"=. _ Double plunger (2000psi)

/0 -- --°--D°ubleplunger(15OOps))......... Marshal/ /mpact '%-___'_ i

QC _ --Calif. Research Carp, _''. l---_Colif D/'v/s/on of Hwys.... Univ. of Calif. ( Triaxiol /nsDtute )

0 E I

3 4 5 6 7 8 9/_sphol/ Content - _o

Figure 2.1 - Influence of Compaction Method on Relative Mixture Stability (Vallerga, 1951)

9

Figure 2.2 - Principle of Compaction with the Gyratory Shear Compacting Press (Bonnot,

1986)

10

1. Gyratory-shear compactor

2. California kneading compactor

Mobile steel wheel simulator

3. Arizona vibratory\kneading compactor

4. Marshall hammer

Rolling-Wheel Compaction. Rolling-wheel compaction can closely simulate field

compaction conditions (von Quintus et al., 1988; Bonnot, 1986; and van Dijk, 1975). The

major advantage of this technique is that the orientation of the aggregate particles and

density of the mixture can be made to closely correspond to field compaction. This can be

accomplished by compacting the mixture in a large area using a roller that can impart com-

pacting pressures similar to those which occur in the field, and then extracting the required

specimens by sawing or coring from the large slabs. For such a large operation, a full scale

mixing machine must be employed. The disadvantage is that this is a costly procedure

requiring specialized equipment.

Alternatively, other small-scale compaction methods using a steel roller (Brown and

Cooper, 1984; von Quintus et al., 1988) or a pneumatic tire (Bonnot, 1986) are also

available. As an example, the procedure developed by the Laboratoire Central des Ponts

et Chauss6es (LCPC) of France utilizes a small wheel track to compact a slab-size sample

measuring 500 mm by 180 mm and having a thickness of 100 mm. The track is placed on

a metal frame and rests on a steel base plate. The wheels are fitted with rubber tires (400

mm by 8 mm) inflated and loaded appropriately to simulate field compaction pressures.

After compaction, specimens are sawed or cored from this slab.

11

An example of the steel-wheel rolling process is that used in the NCHRP/AAMAS

study. With such equipment, the rolling wheel applies a force to a portion of the free face

of an otherwise confined asphalt-concrete mix. Compactive forces are applied over the

entire specimen using a curved foot simulating the rolling pattern of a steel-wheel roller in

the field. The coarse aggregate particles move relative to one another in the partial free

surface, allowing the particles to orient themselves similar to that in the field.

Data from ttle NCHRP/AAMAS Study are shown in Figure 2.3. In this instance the

laboratory specimens were compacted using a steel-wheel compactor, controlling the number

of revolutions of th,e steel foot to determine the compactive effort required to produce the

average air void contents of field cores.

Evaluation. Based on the evaluation of compaction procedures, it would seem

reasonable to conclude the following:

1. While,. comparing various methods of laboratory compaction, rolling-wheel,

kneading, and gyratory methods produce test specimens more like the in-situ

pavement than either static or impact compaction.

2. Of the methods of compaction compared in Figure 2.1, kneading compaction

using the Triaxial Institute Kneading Compactor provides maximum sensitivity

of relative stability to asphalt content. Results of this type are not available

for comparable specimens prepared by the mechanized gyratory or rolling-

wheel compaction methods.

3. Possible effects of compaction method on the fatigue response of asphalt

mixtures have not been investigated. Accordingly, a fatigue testing program

12

MOBILE STEEL WHEEL SIMULATOR

250 i _ '_ I i

• C0-0009

O MI-0021

- k _ TX-0021 -

• VA-0621

® WY-0080

200

Coloradoz iS0

i Wyo

o

Virginia100

Z

50

0 I I I I I

0 2 4 6 8 i0 12

AIR VOIDS, %

Figure 2.3 - Example of Compactive Effort Curves for Different Mixes Using the Mobile

Steel Wheel Simulator (von Quintus et al., 1988)

13

should be carried out to define the relative effect of compaction method on

fatigue performance, using specimens compacted by

rolling-wheel, kneading, and gyratory methods. Orientation of the test

specimens relative to the compaction direction should be such as to insure

that the in-situ situation is correctly modelled; e.g., if a cylindrical core is to

be used from a rolled slab for direct tension fatigue testing, it should be

drilled horizontally from the slab.

2.1.2 Mode of Loading

In laboratory tests, fatigue response has been shown to be a function of mode of

loading, that is, the :method by which stress and strain are permitted to vary during repetitive

loading. Limits to the loading conditions range from the controlled-stress mode, where the

load or stress amplitude remains constant during testing, to the controlled-strain mode,

where the deformation or strain amplitude is maintained constant. Depending on

temperature (and hence mixture stiffness), the results of these tests may be quite different

(Figure 2.4). Test results may also lead to different mixture designs: accordingly, attempts

have been made to determine what mode of loading best simulates actual pavement

conditions (Monisrnith and Deacon, 1969, and Monismith et al., 1977).

One approach is to make use of a parameter termed the mode factor and defined

as"

MF _A-BA + B (2.1)

14

where MF is the mode factor, A is the percentage change in stress due to a stiffness

decrement of C percent, B is the percentage change in strain due to a stiffness decrement

of C percent, and C is an arbitrary but fixed reduction in stiffness resulting from the

accumulation of fatigue damage under repetitive loading. The mode factor assumes a value

of-1 for controlled-stress conditions and + 1 for controlled-strain conditions. Researchers

have evaluated several characteristics of the two modes of loading. A brief summary is

presented in Table 2.1.

2.1.3 Mixture Variables

A summary of the influence of selected mixture variables on fatigue response is

contained in Table 2.2. Results summarized in this table have been obtained from research

reported in a number of references (for example, Pell, 1972 and 1973; Monismith et al.,

1971 and 1981; Bazin et al., 1967; Freeme et al., 1973; Kirk, 1967; and Epps et al., 1972).

In general, for continuously graded mixes, the two primary factors affecting fatigue

response are asphalt content and air void content. Aggregate type seems to have less

influence. Thus, from a mix design standpoint, as much asphalt as possible should be

incorporated into the mixture. There is an upper limit to asphalt content because of

stability requirements; however, this upper limit should be approached in order to increase

fatigue resistance. In addition, adequate compaction is required to promote improved

fatigue resistance, that is, the mixture should be compacted to the design density at the time

of construction (for example, the void content in the compacted mixture should be of the

order of four percent).

15

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._ _"__ I • _""--_ /_'_ • '

Con/rolled Strdw_s, --J "___ ___ _'_ _ _ __ _ramp.,68 *C . ..... _'---_ ,' ' _ _ _ ....._

/vf• 4.68xlO"u( I/e')''" "_ _/0(7 I "_'-

{ I -_"

l

,o I IOz /03 /04 _ _

Number of Slres$ A_Ohcot/ons, N

Figure 2.4 - Comparison ofLaboratory Controlled-Strainand Controlled-StressFatigue Data

(Monismith et al., 1977)

16

Table 2.1 Comparative Evaluation of Controlled-Stress and

Controlled-Strain Loading

VARIABLES CONTROLLED-STRESS (LOAD) CONTROLLED-STRAIN (DEFLECTION)

Thickness of asphalt Comparatively thick asphalt bound layers Thin asphalt-bound layer; < 3 inchesconcrete layer

Definition of failure; Well-defined since specimen fractures Arbitrary in the sense that the test isnumber of cycles discontinued when the load level has been

reduced to some proportion of its initial

value; for example, to 50 percent of theinitial level

Scatter in fatigue test data Less scatter More scatter

Required number of Smaller Largerspecimens

Simulation of long-term Long-term influences such as aging lead to Long-term influences leading to stiffness

influences increased stiffness and presumably increased increase will lead to reduced fatigue lifefatigue life

Magnitude of fatigue life, Generally shorter life Generally longer lifeN

Effect of mixture variables More sensitive Less sensitive

Rate of energy dissipation Faster Slower

Rate of crack propagation Faster than occurs in situ More representative of in-situ conditions

Beneficial effects of rest Greater beneficial effect Lesser beneficial effect

periods

17

Table 2.2 Factors Affecting the Stiffness and Fatigue Response

of Asphalt Paving Mixtures a

Effect of Change in Factor

Factor Change in Factor On Stiffness On Fatigue Life in On Fatigue Life inControlled-Stress Mode Controlled-Stress Mode

of Testing of Testing

Asphalt Viscosity Increase Increase Increase Decrease(Stiffness)

Asphalt Content Increase Increase 2 Increase 2 Increase 3

Aggregate Open to Dense Increase Increase Decrease 4Gradation

Air Void Content Decrease Increase Increase Increase 4

Temperature Decrease Increase 5 Increase Decrease

aFor continuously graded mixtures.

2Reaches optimum at level above that required for stability.

3No significant data. Conflicting conditions of increase in stiffness and reduction inasphalt strain make this speculative.

4No significant data.

5Approaches limit at below-freezing temperatures.

18

For heavy-duty pavements (with thick asphalt-bound layers), a mix of high stiffness

should be utilized by incorporating a stiff asphalt--it may be necessary to temper this

requirement where thermal stresses can lead to cracking--and a dense gradation of

aggregate.

For light-duty pavements (with thin asphalt-bound layers), the mixture should be

made as flexible as possible, with lower stiffness asphalts and more open gradations (that

is, fewer fines). Alternatively, mixes containing a gap grading appear to produce better

fatigue response than the continuously graded mixes normally used in the United States

(Freeme et al., 1973).

Quantitatively, the effect of asphalt content and void content on the fatigue life of

asphalt mixtures can be ascertained by a correction factor proportional to (Pell et al., 1975):

Vm (2.2)(VB+ Vv)

where Vv is the air void volume (percent) and V B is the asphalt volume (percent) and

lib = [Past, "G, eg "(1 - Vv)] (2.3)[lOO + • ogg]

where Pasp is the percent by weight of asphalt (aggregate basis), Gas p is the specific gravity

of asphalt, and Gagg is the specific gravity of the aggregate. Santucci (1977) has analyzed

the data of Pell and Cooper (1975) and has noted that their relationship fits laboratory data

(Epps, 1969) for California mixes "reasonably" well.

19

2.1.4 Loading and Environmental Variabl¢_

Loading and environmental variables have both direct and indirect implications.

Direct implications include the shape and duration of the load pulse used in the laboratory

and the test temperature. Figure 2.5 and Table 2.3 show loading patterns generally used

in the laboratory. The relationship between loading time and thickness of the bituminous

layer for various vehicle speeds is given in Figure 2.6. From this figure, it appears that a

loading time in the range of 0.04 to 0.1 second is appropriate for fatigue testing.

For heavy-duty pavements, an increase in mixture stiffness increases the fatigue life,

provided other variables remain constant. Epps (1969) compared the fatigue performance

of specimens obtained from pavements subjected to actual traffic loading to that of

laboratory specimens of similar composition. He concluded that aging-induced stiffening

of the field mix increases its fatigue life to the extent that it offsets the effect of higher in-

situ air void contents and damage due to traffic. However, it should be pointed out that

stiffening of the asphalt due to aging would likely reduce its ability to resist cracking

(because of increased brittleness) in cold temperatures. The field projects of Epps' study

(Gonzales By-pass and Morro Bay) were not located in cold environments.

Densification of a paving mixture by traffic in service is also likely to affect its fatigue

response. Raithby and Ramshaw (1972) found, for example, that traffic compaction in a

large test slab increased fatigue life for a given stress level by a factor of three and increased

the dynamic stiffness by 60 percent. The effect on fatigue life is due both to the increase

in stiffness and the decrease in air voids.

20

0

time

time(a) sinusoidal

time

time8 (b) haversine

time

time(c) cyclic (oading

°_ F7 n F-I timeE

time(d) cyclic ,toeding

Figure 2.5 - Types of Loading Patterns (Said, 1988)

21

Table 2.3 Effect of Shape of Waveform on Fatigue Life

(Raithby and Sterling, 1972)

i

Geometric

Waveform Temp, *C Stress Amp Initial Mean Relative

MN/m 2 Strain Amp' Fatigue Lives

Life, Cycles

25 1.7 x 10"4 24,690 0.42

-+0.33

(48 psi)

25 1.2 x 104 58,950 1.0

/AN 25 0.67 x 104 85,570 1.45

'These represent values after approximately 200 cycles.

22

IO

Bocksdole- _t rio_TulorI

..... .._- "'30 mph

o.I - :---- _ _ _m-p_-.......... 30

00/ .----__ _ .-,_---E: ;-4,.-

1 Ror,#e of doto

ooo,....................II0 2 4 6 8 I0 12 14 /6 18 20

Depth -m.

Figure 2.6 - Equivalent Time of Loading-Depth Relationship for

Horizontal Stress (McLean, 1974)

23

2.2 Limitations of Available Informatign

Various researchers do not necessarily consider the same parameters--and even when

they do, the magnitudes are often different--in the investigations reported herein:

accordingly, it is difficult to compare the results of the various fatigue investigations and to

prepare a comprehensive summary of available information. For this reason, a limited

number of the available laboratory methods which are representative of the existing systems

have been selected for detailed evaluation herein.

2.3 Overview of Test Methods and Their Development

Table 2.4 provides a summary of the basic characteristics of the fatigue test methods

for the cases of third-point flexural, center-point flexural, cantilever flexural, rotating

cantilever, uniaxial, diametral, and supported flexure. These characteristics involve loading

configuration, stress distribution, loading wave form, loading frequencies, occurrence of

permanent deformation, state of stress, and presence of a zone of uniform stress. From this

table, it is apparent that the repeated-load diametral test is considerably different from the

others. Flexural, rotating cantilever, and axial tests have a uniaxial state of stress while the

diametral test has a biaxial stress state.

The rotating cantilever test has a continuous sinusoidal loading form. Flexural tests

typically employ pulsating loads of a variety of shapes (triangular, square, etc.), with or

without load reversal to eliminate permanent deformation. Axial tests use a sinusoidal or

a haversine pulse with or without a rest period. Rotating cantilever tests and axial tests

have used relatively higher frequencies than flexural and diametral tests. In a pavement a

rest period occurs after the application of each load pulse. A continuous loading pattern,

24

gl I.

iiNo_i __ _ .o .o _i

IO L. *p

o )))-,-I

_'j ee_ o o o oa._ Z Z Z Z

14 "7 "- w_, ..>

> I

_)_ _) E _ ,-., {'o ;; o \_ _ ° ,.-o- )

0 . ..... o.- (...-

o

_ .- t

• _ •

._ -o _,_ _o _ _,--'1 _ (n _..I ...,..,_.

'<'. _o _ • I-- i--V (/I

ill,-.,t

_ Li/

"o_ _ _*' = "" _'7-,._ 0 -,,* II 0 mI,- I_ t_ U Q. t/,. U e_' (.3

.-... _ o¢,- 0 *_ t'-,_ ¢/)

o _'E _,-,0 "-J .'_ X i.- 0,')

(/) ,p ,_

ca')(/) .._ nn

C0

U :1 o,-'- z =,_ _.-,,-I_ -Coo

0

0

A .__ _, ,- •['_ oL 0..

r,j

b_ _ _ ,(1)

0 m C

.,, > _

c :_ I---C'=.i

0 _)

_4 _ c

_ .o

r_ 0 '-.

• 1_-

-,-I,'-I

•0

(.3

0..I

"- _c ._.T. _-.-/,.-

such as that used in rotating cantilever tests, usually yields a smaller fatigue life:

consequently, laboratory tests are completed more quickly.

A major consideration in fatigue testing is the extent to which the specimen should

be allowed to deform inelastically under repetitive loading. Under traffic loading in service,

paving mixtures may inelastically deform as a result of densification, shear forces, and a

permanently yielding foundation. Nevertheless, in a properly designed and constructed

pavement, permanent deformations--particularly those associated with a yielding

foundation--will be small and eventually non-progressive.

Some forms of laboratory testing incorporate stress reversal to eliminate or reduce

cumulative deformation and to better simulate the stress patterns imposed by traffic loads

in situ. Others, particularly the diametral test and some types of axial and supported-flexure

tests, do not.

Three continuous loading pulses are applied by a moving wheel load over a pavement

rather than the single pulse so often applied in the laboratory fatigue test. At a critical

location on the bottom of the asphalt-concrete layer, the material is first subjected to a

compressive stress as the wheel approaches; then a tensile stress as the wheel moves over

the point; and, finally, a compressive stress again as the wheel moves away. The magnitude

of the initial compressive strain pulse on the bottom of the layer is approximately one-

seventh that of the tensile strain pulse (Raithby and Sterling, 1972). Without this smaller

initial compressive stress pulse, the decrease in fatigue life should be at most on the order

of only 10 to 15 percent (Barksdale, 1977).

27

As a result of the detailed literature review, chronological developments relative to

fatigue testing have. been shown in Table 2.5.

28

Table 2.5 Chronology of Fatigue Testing and Evaluation

YEAR _GATOR(S) TEST METHODS EVALUATION

AND CONDITIONS METHOD

1989 Rao Third-point flexure Controlled stressDr. Engg.,UC

Berkeley

1989 Scholz, Hicks, and Scholl Diametral Controlled stressOSU and

OregonDOT

1988 Gerritsen and Jongeneel Cantilever (trapezoidal) Controlled strainAAPT flexure

1987 Button, Little, Kim, and Flexure Controlled stress,AAPT Ahmed controlled strain, and

fracture mechanics

1986 Bonnot Direct tension and cantilever Controlled stressTRR 1096 (trapezoidal) flexure

1985 Monismith, Epps, and Finn Third-point flexure Controlled stress andAAPT controlled strain

Same Hugo and Kennedy Supported discs (elastic Intermediate mode offoundation) loading

Same Bjorklund Supported beams (rectangular, Intermediate mode ofelastic foundation) loading

1984 Molenaar Dynamic tensile Controlled stress andAAPT fracture mechanics

29

YEAR iNVF__TIGATOR(S) TEST METHODS EVALUATION

AND CONDITIONS METHOD

1983 Little. and Richey Diametral Controlled stress andfailure envelopeconcept

1982 Bonnaure, Gravois, and Center-point flexure Controlled strainUdron

1982 Mahoney and Terrel Suppported beam Intermediate mode of5th Intl (rectangular, rubber) with loadingConf on Str roiling-wheel loadingDes of AsphPavements

1981 Whitcomb, Hicks, and Diametral Controlled stressAAPT Boonders

1981 Monismith Third-point flexureAAPT

1980 Bonnaure, Gravois, and Statistical regression for 146 Controlled stress andUdron fatigue lines covering several controlled strain

major test methods andmixture variables of variousauthors

1979 Ulidtz Controlled stress,AAPT fracture mechanics,

and empiricalcorrelation factors

1978 Barksdale Supported beams (rectangular, Intermediate mode ofAAPT rubber) loading

1977 Classen, Edwards, Sommer, Dissipated energy method Limiting tensile strain4th Intl and Uge which is independent of test criteriaConf on Str conditions

Des of AsphPavements

30

YEAR INVESTIGATOR(S) TEST METHODS EVALUATION

AND CONDITIONS METHOD

Same Shell method Dissipated energy method Limiting tensile strainwhich is independent of test criteriaconditions

Same Finn, Sara, Kulkarni, Nair, AASHO Road Test results Limiting tensile strainSmith, and Abduilah and computer programs criteria

1977 Van Dijk Cantilever (trapezoidal) and Controlled stress,AAPT centerpoint (rectangular) controlled strain, and

flexure dissipated energytheory

Same Ruth, Gary, and Oslan Flexure (77* F, 41" F, and Controlled stress and23* F) and diametral (41" F) controlled strain

Same Kennedy Diametral Controlled stress

GIT-7305 Barksdale Supported beams (rectangular, Intermediate mode ofrubber) (same as 1978 AAPT) loading

1976 Majidzadeh Supported beams (elastic Fracture mechanicsFHWA-RD- foundation)76-91 and 92

1976 FinnAAPT

1975 Pell and Cooper Rotating flexure and axial Controlled stressAAPT fatigue

1973 Monismith Third-point flexure Controlled stress andHRB controlled strain

SpecialReport 140

31

YEAR INVESTIGATOR(S) TEST METHODS EVALUATION

AND CONDITIONS METHOD

Same Barksdale and Hicks Repeated load plate tests Numericalcharacterization

(layered theory andfinite elementapproaches)

Same Pell Rotating flexure Controlled stress withcomparison tocontrolled strain

Same Deacon State-of-the-art survey Suggested controlledstress, controlledstrain, and numericalmethods

Same Finn Serviceability index Numerical correlationbetween degree ofcracking and presentserviceability index

Same Terrel Examples of work from Controlled stress andMonismith, King,ham, and controlled strainKallas

Same Witczak Analysis of AASHO Road Allowable strainTest data criteria for a given

number of load

repetitions

Same The Asphalt Institute Same Same

Same Majidzadeh and Ramsamooj Supported beams (elastic Intermediate mode offoundation) loading and fracture

mechanics

Same Freeme and Marais Cantilever (rectangular and Controlled straintrapezoidal) flexure, 5 Hz, halfsinewave pulses

32

YEAR INVESTIGATOR(S) TEST METHODS EVALUATION

AND CONDITIONS METHOD

1972 Moore and Kennedy Diametral Controlled stress3rd IntlConf on Str

Des of AsphPavements

Same Pell and Brown Uniaxial tension-compression Controlled strainfatigue

Same Bennot Cantilever flexure Controlled stress andcontrolled strain

Same Kirk Third-point flexure Controlled strain

1972 Witczak Kingham's results of strain vs Allowable tensile3rd Intl fatigue life relationships for strain criteriaConf on Str full-depth asphalt concreteDes of Asph pavements of the AASHOPavements Road Test

Same Kingham and Kallas Center-point flexure Controlled stress andcontrolled strain

Same Van Dijk and Moreaud, Cantilever and center-point Controlled stress andQuedeville and Uge flexure controlled strain

Same Verstraeten Cantilever (trapezoidal) Controlled stressflexure

1972 Raithby and Sterling Cyclic axial tensile tests Controlled stress

RRL LR496 (prismatic samples)

1972 Monismith and Salam Third-point flexure Controlled stressAAPT

33

YEAR INVESTIGATOR(S) TE_T METHODS EVALUATION

AND CONDITIONS METHOD

1971 Salana Third-point flexure Controlled stress and

Ph.D., UC fracture mechanicsBerkeley

1971 Majidzadeh, Kauffman, and Center-point flexure Fracture mechanicsAAPT Ramsamooj

1971 Freeme Cantilever (trapezoidal) Controlled stress and

Ph.D., Univ flexure controlled strainof Natal

1969 Pell and Taylor Rotating cantilever flexure Controlled stressAAPT

1969 Epps Third-point flexure Controlled stress andPh.D., UC controlled strain

Berkeley

1969 Epps and Monismith Same Controlled stressAAPT

Same Santucci and Schmidt Third-point flexure Controlled strain

1968 Kennedy and Hudson Diametral Controlled stressHRR 235

1967 Bazin and Saunier Cantilever (rectangular and Controlled stress

2nd Intl trapezoidal) flexureConf on Str

Des of AsphPavements

Same Kirk Third-point flexure Controlled strain

Same Pell Rotating cantilever flexure Controlled stress

Same Vallcrga, Finn, and Hicks Third-point flexure Controlled stress

34

YEAR INVESTIGATOR(S) TEST ME-"I'HODS EVALUATION

AND CONDITIONS METHOD

Same Kallas and Riley Third-point flexure Controlled stress

1967 Deacon and Monismith Third-point flexure Controlled stressHRR 158

1965 Deacon Third-point flexure Controlled stress and

D. Engg., controlled strainUC

Berkeley

1964 Monismith Third-point flexure Controlled stress andTE-64-2, controlled strainITTE, UCBerkeley

1963 Monismith Third-point flexure Controlled strainTE-63-2,ITTE, UC

Berkeley

1962 Pell Flexure and torsion Controlled stress andlntl Conf on controlled strainStr Des of

AsphPavements

Same Jimenez and Gallaway Supported beams (oil Intermediate mode ofchamber) loading

1961 Monismith, Secor, and Supported beams (springs) Intermediate mode ofAAPT Blackmer loading

1959 Papazian and Baker Supported center-point flexure Intermediate mode ofAAPT loading

1958 Monismith Supported center-point flexure Intermediate mode ofAAPT (rubber) loading

35

YEAR INVESTIGATOR(S) TEST METHODS EVALUATION

AND CONDITIONS METHOD

1955 HveemHRBBulletin 114

1953 Nijboer and van der Poel Road vibration equipmentAAPT (recognition in Europe of

pavement distress from

repeated bending)

1948 Hveem and Carmany Recognition in U.S. ofHRB pavement distress from

repeated bending

36

3.0 FATIGUE TEST METHODS

In this section selected methodologies for measuring the fatigue behavior of asphalt

concrete are discussed. Included are brief descriptions of the test methodologies together

with a listing of the advantages and disadvantages of each. The general categories include:

1. Simple flexure with a direct relationship between fatigue life and stress/strain

developed by subjecting beams to pulsating or sinusoidal loads in either a third-

or center-point configuration; rotating cantilever beams; and trapezoidal

cantilever beams subjected to sinusoidal loading.

2. Supported flexure with a direct relationship between fatigue life and

stress/strain developed by loading beams or slabs that are supported in various

ways to directly simulate in-situ modes of loading and sometimes to simulate

a more representative stress state.

3. Direct axial with a direct relationship between fatigue life and stress/strain

developed by applying pulsating or sinusoidal loads, uniaxially, with or without

stress reversal.

4. Diametral with a direct relationship between fatigue life and stress/strain

developed by applying pulsating loads to cylindrical specimens in the diametral

direction.

5. Triaxial with a direct relationship between fatigue life and stress/strain

developed by testing similar to direct axial testing but with confinement.

6. Fracture tests and the use of fracture mechanics principles to predict fatigue

life.

37

7. Wheel-tracking tests, including both laboratory and full-scale arrangements,

with a direct relationship between the amount of cracking, the number of load

applications, and the measured and/or computed stress/strain. For full-scale

tests, both linear and circular track configurations have been used.

3.1 Simple Flexure

The majority of fatigue test data have been developed by simple flexure tests in which

the stress or strain "wasrepeatedly applied until the specimen failed or exhibited changes in

characteristics which rendered the mixture unsuitable.

Results of these tests have been expressed in the form of the following equations

(e.g., Pell, 1967; Monismith et al., 1966, 1981; and Pell et al., 1975).

iV/=a (1)b (3.1)e t

or

Iv:=c(!)d (3.2)flt

where e t and e t are, the magnitudes of tensile strain and stress repeatedly applied; a, b, c,

and d are material coefficients associated with the laboratory test methodology; and Nf is

the number of load applications to failure.

A number of' different types of flexural equipment have been developed to study the

fatigue characteristics of asphalt-concrete mixtures including (but not limited to):

38

1. Flexure tests in which the loads are applied repeatedly or sinusoidally under

center-point or third-point loading,

2. Rotating cantilever beams subjected to sinusoidal loads, and

3. Trapezoidal cantilever beams subjected to sinusoidal loads or deformations.

3.1.1 Center-P0int and Third-Point Loading

A simply supported asphalt-concrete beam specimen is subjected to a controlled load

or deflection under either third-point (Figure 3.1) or center-point (Figure 3.2) loading.

Examples of the equipment include that used by the University of California at

Berkeley and The Asphalt Institute (Figure 3.1). For the University of California

equipment, the specimens are 1.5 in. x 1.5 in. x 15 in. The Asphalt Institute uses larger

specimens, 3 in. x 3 in. x 15 in. Loads are applied at two locations as shown in Figure 3.1

to insure a uniform bending moment through the mid span of the beam. With this

equipment, pulsating loads, having a time of loading of 0.1 sec and a frequency of loading

of 100 repetitions per minute, are applied. Typical load and deflection traces are shown in

Figure 3.3. Both controlled-load (stress) and controlled-deflection (strain) tests have been

performed.

The Shell Laboratory at Amsterdam has used the center-point loading equipment .'

shown in Figure 3.2. Specimen dimensions are 30 mm (1.2 in.) x 40 mm (1.6 in.) x 230 mm

(9.2 in.), and specimens are tested in the controlled-deflection (strain) mode.

3.1.2 Cantilever Loading

Rotating Loads. At the University of Nottingham, U. K. (Pell et al., 1975 and 1973),

a rotating cantilever machine (Figure 3.4a) was used in which the specimen is mounted

39

vertically on a rotating cantilever shaft, a load is applied at the top, and the bending stress

of constant amplitude induced through the specimen. The majority of the tests were

conducted at a temperature of 10°C and a speed of 1,000 rpm. Dynamic stiffness was

measured using another machine (Figure 3.4b) by applying constant sinusoidal amplitude

deformations. Pell also used a controlled-strain torsional fatigue machine as shown in

Figure 3.5 for some fatigue tests on bituminous materials.

Trapezoidal Beams Loaded Sinusoidally. Tests on trapezoidal specimens have been

conducted by the Shell researchers (van Dijk, 1975), Belgium researchers (Verstraeten, 1972,

and Verstraeten et al., 1961), and by the LCPC (Bonnot, 1986). Figure 3.6 illustrates the

LCPC equipment.

The larger dimension of the trapezoidal specimen is fixed and the smaller end is

subjected to either a sinusoidally applied strain (Bonnot, 1986; van Dijk, 1975; and

Verstraeten, 1972) or stress (Kunst, 1989). By properly selecting the dimensions of the

trapezoid, the spec.imens will fail at about mid height where the bending stress is largest

rather than at the base where boundary conditions might adversely affect interpretation of

test results. Specimens tested by van Dijk, for example, had a base cross section of 55 mm

by 20 mm, a top cross section of 20 mm by 20 mm, and a height of 250 mm.

3.1.3 Evaluation

Advantages. The following are considered to be the primary advantages of simple

flexure tests:

1. This test method is well known, widespread in use, and readily understood.

2. The basic technique measures a fundamental properly that can be used for

40

/. ":i _m o,k _ _ "3

:.._ _ : -i, "04: __:. :,.

I

_ -%0

0

Key:

I. Reaction clamp .5. Bose plate 9. Double-acting. Bellofrom cylinder

2. Load clamp 6. Loading rod 10, Rubber washer

3, Restrainer 7'. Stop nut I I. Load bar

4. Specimen 8. Piston rod I 2. Thomson boll bushing

Figure 3.1 - Third-Point Flexure Apparatus (Monismith, et al., 1971)

41

9

11

8 _7

1. Specimen in steel clamps (see inset)

2. Thermostat

3. Fixed clamps

4. Vibrator sp/nd/e

5. E/ectrodynamic vibrator

6. Current meter and control for a.c.

7. E/ectrodynamic transducer

8. Phase angle meter 9. Voltmeter 10. Soft spring carrying 11

1I. Counter weight for 4, 5, 7 and middle clamp

Figure 3.2 - Center-Point Flexure Apparatus (van Dijk, 1972)

42

Time intervol between successive

/ood opp/icot/'ons

_Lood

--,,. _ durotiontr_Up stroka

[ I

(a) Idealized Load-Time Curve

Time

(b) Idealized Deflection-Time Curve

Figure 3.3 - Load vs. Time and Deflection vs. Time Relationships for Controlled-Stress Test

Equipment (Monismith et al., 1971)

43

pu#eys I

beot'ing

load,,ng

head

(a) Controlled-Stress Rotating Flexure (not to scale)

I[--."-v--_ ;_-: II _ I I

(b) Stiffness Machine

Figure 3.4 - Flexure Apparatus Used by Pell (1965)

44

! I

0 0 00 0

Figure 3.5 - Controlled-Strain Torsional Fatigue Machine (Pell, 1965)

45

C__=:_ _ __ _o__"_

Figure 3.6 - Bending Fatigue Test Machine (Bonnot, 1986)

46

both mixture evaluation and design.

3. The results can be used directly (with an appropriate shift factor) in the

structural design of pavements to estimate the propensity for cracking.

4. Results of controlled-stress testing can be used for the design of thick asphalt

pavements whereas results of controlled-strain testing can be used for the

design of thin asphalt pavements.

5. In third-point loading, failure of the specimen is initiated in the a region of

relatively uniform stress. This feature helps reduce the coefficient of variation

in the test results, requiring fewer samples.

Limitations. The major limitations of this methodology are:

1. Validation of laboratory results by comparison with in-situ pavement

performance is difficult due to the requirement for a shift factor as noted

above.

2. The method is costly, time consuming, and requires specialized equipment.

3. In center-point loading, initiation of failure in a relatively uniform tensile stress

region is not possible.

4. Unlike that within the pavement structure, the state of stress is essentially

uniaxial.

5. Elastic theory is usually assumed to compute the tensile strain or stress.

3.2 Supported Flexure

To more nearly duplicate in-situ stress and mode-of-loading conditions, several

researchers have used circular slab specimens supported either on a rubber mat (Majidzadeh

47

et al., 1971) or a cushion of air (Jimenez et al., 1962). A circular shaped repeated load is

applied to the center of the slab resulting in a stress state in the slab which is very similar

to that occurring in the pavement structure.

Additionally, beam fatigue tests were used by Barksdale (1977) to evaluate the fatigue

characteristics of asphalt-concrete bases. In his methodology, asphalt-concrete beams were

placed on a rubber mat to simulate the field support conditions (Figure 3.7). The fatigue

test equipment consisted of a loading frame, a 4 in. (102 mm) thick rubber mat (with a

modulus of subgrade reaction of 284 pci or 7,861 gm/cc) supporting the beam, and a

pneumatic loading system. The fatigue specimen and rubber support were enclosed in a

temperature control chamber maintained at 80*F + 1 °F (27°C). The beam specimens

were not subjected to stress reversals during testing. The load pulse had a duration of 0.06

second with an approximately haversine shape: one frequency, 45 cpm, was utilized.

Advantages. Advantages of this methodology include:

1. Better simulation of field conditions is possible.

2. The test offers a convenient means for examining modes of loading between

the extremes of controlled stress and controlled strain.

3. At higher temperatures, the problem of sagging due to specimen weight is

overcome.

4. Support of the specimen is expected to reduce the effects of minor

imperfections in the specimens and, hence, reduce the scatter of test results.

Disadvantages. Disadvantages of the methodology include:

1. For beam specimens, the state of stress is predominantly uniaxial, and,

48

depending on how the specimen is "clamped" in the test apparatus, it may not

be subjected to stress reversals (Barksdale, 1977).

2. The test is more time consuming than many other fatigue tests.

3. Compared to simple flexure, test equipment is more costly and more complex.

3.3 Direct Axial

3.3.1 Tension

The Transport and Road Research Laboratory (TRRL) of the United Kingdom has

performed uniaxial tensile tests without stress reversal using a loading frequency of 25 Hz;

a duration of 40 milliseconds; and rest periods varying from 0 to 1 sec. According to

Raithby (1972), starting from very short rest periods, fatigue life increases rapidly with an

increase in rest period before reaching a limiting value at about 0.4 second, beyond which

increasing the duration of the rest period had very little further effect. These tests were

conducted in the controlled-stress mode.

More recently, uniaxial tensile tests have been performed in the Netherlands (Kunst,

1989) at frequencies of 1 and 0.1 Hz using haversine loading in the controlled-strain mode.

Unfortunately, details of the Dutch tests are unavailable at this time.

Advantages. Advantages of direct axial tests include:

1. Specimens may be circular as well as rectangular in cross section.

2. In principle, results of axial tensile tests can be used both to evaluate mixtures

and to design the pavement for fatigue adequacy when proper shift factors

representing the field conditions are available.

3. When compared to flexural tests, these are simpler and less costly. Testing

49

LOAD

LOAD CELL

CELL LEADS

CUT-OFF LVDT LEADSM ICROSWITCH

LVDT

STRAIN GAUGELEADS

ASPHALT BLOCK WITHDUMMY STRAIN GAUGEFOR TEMPERATURECOMPENSATION

SR-4 TYPEC.;TRAIN GAUGE

/_/ RIGIDSTEE",'LATE--RUBBERPAD CONTROLLEDTEMPERATUREC,-,AM"E,__/_PHALT BEAM

SPECIMEN

Figure 3.7 - Fatigue Test Apparatus (Barksdale, 1977)

5O

time is shorter because fewer loading cycles can be sustained before failure.

4. Tensile stress and strain can be easily determined and in the case of strain,

measured directly.

Disadvantages. The primary disadvantage is that:

1. The loading condition does not necessarily represent the field conditions.

3.3.2 Tension/Compression

In this form of fatigue testing, developed at the TRRL (Raithby, 1972), axial tensile

and compressive loading was applied using in a servo-controlled electro-hydraulic machine.

Specimens were prismoidal, with 75 mm square cross sections and 225 mm lengths (Figure

3.8). Loading frequencies were 16.7 and 25 Hz, and the effects of rest periods, shape of

wave form, and the sequence of load application (compression/tension,

tension/compression, compression only, and tension only) were evaluated.

Raithby concluded that:

1. Short rest periods, such as occur in practice between successive axle load

applications, have an important effect on the fatigue life.

2. Compared with continuous cyclic loading at 25 Hz, the life to failure with one-

second rest periods was up to 25 times longer, the increase in life depending

largely on the test temperature. Above 25 °C, there appears to be a decrease

in the impact of short rest periods on fatigue life.

3. The effect of load form (for example, sinusoidal, trapezoidal, and triangular)

is not very great. Thus, for practical laboratory tests of asphalt concrete, a

sinusoidal load pulse would appear to be a reasonable representation.

51

4. Of the four loading sequences, pure compressive cyclic loading gives the largest

fatigue life followed by tensile/compressive cyclic loading, tensile cyclic loading,

and compressive/tensile cyclic loading. Between tensile/compressive cyclic

loading and compressive/tensile cyclic loading, the difference in fatigue life

attributable to the reversal of loading order is about 30 percent (Figure 3.9).

Advantages. Advantages include the following:

1. It is possible to simulate the loading pulse observed in the field

(compression/tension/compression).

2. The results can be used to evaluate mixture effects and, with field correlation

factors, to design pavements to control fatigue cracking.

Disadvantages. Disadvantages include the following:

1. The test does not well represent field conditions except the form of the loading

pulse.

2. When compared to direct tensile tests, reversed-stress tests require more time,

are more costly, and require more specialized equipment.

52

Temperature chamber

C.R.O.

LVDT IIIII

umming ICommand junction u._ Jsignal Load cell

Hydraulicactuator

Servo -valve

Hydraulicpowersupply

Figure 3.8 - Schematic Representation of Direct Axial Fatigue Test

(Raithby and Sterling, 1972)

53

WAVEFORM GEOMETRIC MEAN FATIGUE

LIFE CYCLES

TI ,-,/,_'N I /Stress

C 0 '_" " _"SI rainF

F I

i_'N /--\

--. _ 8,748

Peak stress 0.76/MN/m 2 in each case. Temperature 25* C.

Figure 3.9 - Effect of Strain Reversal on Fatigue Life (Raithby and Sterling, 1972)

54

3.4 Diametral Test "

The diametral fatigue test is an indirect tensile test conducted by repetitively loading

a cylindrical specimen with a compressive load which acts parallel to and along the vertical

diametral plane. This loading configuration develops a reasonably uniform tensile stress in

the specimen perpendicular to the direction of the applied load and along the vertical

diametral plane.

The test is simple to conduct and is considered by some to be an effective method

for characterizing materials in terms of "fundamental" properties. A number of investigators

have utilized this test for materials evaluations and pavement analyses (Kennedy et al., 1983

and 1968; Scholz, Hicks et al., 1989; Khosla and Omer, 1985; Schmidt, 1971; etc.).

Equipment and Pr0ccdur¢_. The loading configuration, illustrated in Figure 3.10, is

relatively simple, and loads can be applied with various devices including electro-hydraulic

and pneumatic systems. Usually a haversine load pulse is employed. Kennedy and Anagnos

(1983) used a loading time of 0.4 second and a rest interval of 0.6 second (60 repetitions per

minute). Khosla and Omer (1985) used a loading time of 0.05 second and a frequency of

20 repetitions per minute.

Test specimens are usually 4 in. in diameter and 2.5 in. high. Load is transmitted to

the sides of the right circular cylinder through a 0.5 in. wide loading strip (Figure 3.10).

Computed Stresses. According to Kennedy and Hudson (1968), under a line load of

sufficient magnitude, the diametral specimen would fail near the load line due to

compression. The compressive stresses are greatly reduced by distributing the load through

a loading strip, however, and a sufficiently large load will actually induce a tensile failure

55

along the vertical diameter.

Stresses at the center of the specimen under a strip load (Figures 3.10 and 3.11) are

as follows:

(2 _aP) a (3.3)o, = [(_ .--- h) ] • [sin 2a (_)1

(-6 • P))I " [sin 2.a - ---q--a•l (3.4)o, = a (2R)

where P is the applied load, a is the width of loading strip, h is the height of specimen, R

is the radius of specimen, 20, is the angle at the origin subtended by the width of loading

strip, e t is the indirect tensile stress (horizontal) at the center of the specimen, and ac is the

indirect compressive stress (vertical) at the center of the specimen. At the center of the

specimen, the vertical compressive stress is three times the horizontal tensile stress.

In addition to the biaxial state of stress, two more differences exist between the

flexural beam and diametral tests. These are: (1) permanent deformation which is usually

prohibited in flexural tests but permitted in diametral tests and (2) stress reversal which is

impractical in diametral tests. The likely effect of these differences is a smaller fatigue life

under diametral te,iting than under flexural testing.

Advantages. The diametral test offers a number of advantages:

1. The test is simple in nature.

56

2. Design of mixtures and pavements for fatigue adequacy is possible in principle

using the fatigue response measured by the test together with field correlation.

3. The equipment is applicable for other tests, for example, resilient modulus and

tensile strength.

4. Failure is initiated in a region of relatively uniform tensile stress. It should be

noted, however, that, according to Porter and Kennedy (1975), the governing

variable is (a t - ac); the uniform region for this variable is much smaller than

the uniform region for a t .

5. A biaxial state of stress exists, possibly of a type better representing field

conditions.

6. Tests can be performed not only on laboratory specimens but on field cores as

well.

Disadvantage_. Included among its disadvantages are:

1. Although a biaxial stress state exists at the center of the specimen, it is

impossible to vary the ratio of the vertical and horizontal components and,

hence, to replicate the stress state at critical locations within an in-situ

pavement.

2. This method significantly underestimates fatigue life if the principal tensile

stress is used as the damage determinant. Even when the stress difference, at -

ac, is used to predict fatigue life, the method still underestimates life relative

to other laboratory methods.

57

Figure 3.10 - I_x)adingConfiguration and Failure in Diametral Test (Kennedy, 1977)

58

Y

- 1.0 -

i

-.8 -

-,6 - fStress,

_ -.4 -b

u -.2 - / Vertical Stress_

0 .... X

',7,

I,- .4 -

.6 -

1.0 -

I I | I I l I / I I

1,0 .8 .6 ,4 2 0 ".2 -.4 -6 -.8 -_.0

Tltnilon _ Compreillon

Figure 3.11 - Relative Stress Distributions and Element Showing Biaxial State of

Stress for the Diametral Test (Kennedy, 1977)

59

3. There is possible concern about the absence of stress reversal and the

accumulation of permanent deformation.

3.5 Triaxial

An example of this form of fatigue testing equipment was developed at the University

of Nottingham (Pell and Brown, 1972, and Pell and Cooper, 1975) and is illustrated in

Figure 3.12. For this particular equipment, specimens are cylirtdrical in shape with a

diameter of 4 in. and a height of 8 in. Specimens are subjected to a sinusoidally varying

axial stress. This equipment has also been used for tension-compression testing with and

without confining stress. To accommodate tension, end caps are bonded to the specimen

providing an effective length for the measurement of vertical deformation of 6 in.

Another form of triaxial equipment in which the axial and radial stresses were

independently applied could be used for triaxial repeated tensile tests. McLean (1974)

developed such equipment (Figure 3.13) at the University of California, Berkeley to study

the rutting behavior of asphalt mixtures under combinations of normal tensile and

compressive stresses.

Also at the University of California, Sousa (1987) developed equipment which is

capable of applying shear strains by torsion (repeated or constant) together with radial

tensile stress using specimens fabricated as hollow cylinders. To date, only shear fatigue

(torsional) tests have been conducted. This equipment can be further developed to apply

repeated radial tensile stresses through the pulsating fluid within the hollow cylinder, thus

simulating the necessary conditions including shear stresses (through torsion) and vertical

stresses.

60

Advantages. Among the advantages of triaxial testing are the following:

1. It is possible to simulate the field loading condition in which compression is

followed by tension.

2. The results can be used for mixture design and, with field correlation factors,

for structural design.

3. The test better represents the state of stress in situ than most other laboratory

tests.

Disadvantages. Disadvantages include the following:

1. Shear strains must be controlled; otherwise, the predicted fatigue lives could

be considerably different than the field results.

2. These tests are costly, require specialized equipment, and are time consuming.

3.6 Fracture Mechanics

Another approach for characterizing the fatigue response of asphalt concrete makes

use of the principles of fracture mechanics (Majidzadeh et al., 1971; Salam, 1971; and

Monismith et al., 1973). In this method, fatigue is considered to develop in three phases:

(1) crack initiation, (2) stable crack growth, and (3) unstable crack propagation. It is

assumed that the second phase consumes most of the fatigue life and, consequently, it is for

this phase that quantitative models based on fracture mechanics have been proposed.

One of the basic relations used for this phase is

da- A(r_)_ (3.5)dN

61

where a is the crack length, K 1 is the stress intensity factor in mode 16 (stress x lengthl/2),

N is the number of load applications, and A and n are experimental coefficients.

This relation assumes that stable crack growth takes place between some initial crack

length, ao, and a critical length, ac, which terminates the fatigue life and is determined by

Klc, the critical value of K 1.

Equipment. Various equipment has been used to de.fine response by this

methodology. As an example, simple-flexure equipment like that shown in Figures 3.1 and

3.2 has been used 1:oassess the efficacy of this approach.

Test Methodology. The methodology using the above equipment has included both

fracture and fatigue; tests. For example, the fracture tests reported by Monismith and Salam

(1973) and Salam and Monismith (1971) were of two types:

1. Single-edge-notched flexure tests (1.5 x 2.0 x 15 inches)

2. Single-edge-notched tension tests (1.5 x 1.5 x 4.5 inches)

Notch-to-beam-depth ratios ranged from 0 to 0.4 in both types of fracture tests. In principle,

the methodology to predict the fatigue response uses the incremental technique shown in

Figure 3.15.

According to Majidzadeh (1971), the size of the plastic zone around a crack tip is

critical in the analysis of fatigue life during the crack propagation phase. If the plastic zone

is small compared to the crack size, linear elastic fracture mechanics (LEFM) can be used

to approximate conditions of failure: if the size of the plastic zone is several orders of

6Three crack tip displacement modes which are considered include the opening mode(I), the shear mode (II), and the tear mode (III) (Figure 3.14).

62

HydrauficLocal ram

ram t control

Couphng unit

Oil flow

return

Servo cutout

Servo vatve input

L_ _}_yio_utLoadcel I

Perspex cell _Jppk /Output

Water trap

Cei I

Figure 3.12 - Triaxial Load Fatigue Rig (Pell and Cooper, 1975)

63

Air pressure toI opp/y radio/ stress

Air- oil l _

pressure converter "_ --_ "_-----_ _- I-- Sample copwith Bertram diaphragm III /baited to ceil cap

I

/ _ Cellcap

LSample cop

-- Steelceil

4in. diametersample

-= Siliconefluid

4indiameter

Belofromsea/.

\_ Samplebose

.___ -_----Combined cell

Air pressure to base and loadingapply axial stress , cylinder

Double actingpiston wDn8e/ofrom seals

Figure 3.13 - Triaxial Apparatus Permitting Independent Control of

Axial and Radial Loads (McLean, 1974)

64

magnitude larger than the crack size, a nonlinear fracture mechanics approach is more

appropriate. In the first case, when brittle fatigue is assumed, the critical stress intensity

factor, Klc, defines the fracture characteristics of the material. In the second case, where

the nonelastic zone is large, either the J-integral or the C° line integral may be requested

to define crack propagation.

For the second case, one form that the crack propagation model (notched sample)

can take is as follows:

dc = A [._3__.] (3.6)dN (2U,)

where J is the path-independent mode contour J-integral, c is the crack length, Ue is the

total strain energy, A is a material constant, and N is the number of cycles at crack

length "c".

The steps are:

1. To establish experimentally a J-c curve, where Ue can also be found.

2. To establish a c-N relationship by performing fatigue tests on notched

specimens.

3. To differentiate this relationship in order to obtain the (dc/dN) vs. N

relationship.

4. For a given N, to obtain c and dc/dN.

5. For a given c, to obtain J = 2 Ue c.

6. To establish the relationship dc/dN, the slope of this relationship should be

A/2U e.

65

Experimental data necessary to calibrate this crack-growth model is considerable.

Advantages. Advantages include:

1. In principle the need for conducting fatigue testing is eliminated.

2. Strong theory explains crack propagation under low temperatures, for example,

below 40*F.

Disadvantages. Among the disadvantages are:

1. At high temperatures, due to the size of the plastic zone, the values determined

for Klc are affected by the plane-stress condition and Klc is not a material

constant.

2. The stable crack propagation stage may not explain a suitable range of the

entire fatigue spectrum. The exact contributions of crack initiation and

unstable crack propagation stages are not known.

3. Quantification of this method requires a considerable amount of currently

unavailable experimental data including:

a. Fracture toughness (Klc values).

b. Initial sizes of pavement cracks.

c. A calibration function which relates the stress intensity factor, K1, to

the applied loads. This function depends upon geometrical aspects of

the pavement layer and the loading parameter.

d. Bending moments or applied loads are needed to de/ermine the stress

intensity factor for any given crack size. The effects of variations of

loading patterns and the sequence of these variations on fatigue life

66

/ /z -/

-" [I

, f"

1Mode I Mode II Mode III

Figure 3.14 - Crack Tip Displacement Modes

67

r

ANALYSES ! -- o.< ,< fI"XPERIMENTS o < < n

_ i,.<r

i,r 1

CALIBRATIOH t /_ KI dii dN

FUNCTION, f(a/h) -- _-" _i

J I

Figure 3.15 - Diagram for Fatigue Life Computations

from Fracture Properties (Salam, 1971)

68

are yet to be established.

e. A fatigue crack growth law must be established for each material, thus

requiring experimental data to define the constants of the theoretical

model under consideration.

f. To represent field conditions accurately, a study of fracture in the

shear mode also needs to be conducted and an analytical procedure to

use these results in conjunction with those of opening mode needs to

be developed (Figure 3.15).

3.7 Wheel-Track T¢_ting

3.7.1 Laboratory Test_

In order to better simulate the effects of a rolling wheel on the pavement and to

better understand the pattern of crack initiation and propagation, a wheel tracking machine

has been developed to study fatigue characteristics of asphalt slabs (van Dijk, 1975) (Figure

3.16). In this device; a loaded wheel with a pneumatic tire is rolled back and forth over a

slab of asphalt concrete. The wheel has a diameter of 0.25 m and its path is 0.60 m long

with a width in the range of 0.05 to 0.07 m. The slab is supported by a rubber mat. The

tire contact area can be varied by changing either the inflation pressure or the load.

Suitable equipment ensures the measurement of the main characteristic, strains at the

bottom of slabs, and the detection of crack initiation and propagation.

Results can be expressed in terms of three fatigue stages associated with the

development of hairline cracks (N1), real cracks (N2), and failure of the slab (N3).

69

Fatigue data. obtained from a wheel tracking test7 have been presented by van Dijk

(1975). His results suggest that controlled-strain data may be more appropriate to define

pavement cracking than controlled-stress data since the former include the influence of

crack propagation on the number of load repetitions associated with unserviceability.

According to van Dijk, laboratory controlled-stress tests appear to provide conservative

results. He also noted that the difference between the development of hairline cracks, N1,

and the development of real cracks, N2, is related fairly well to the difference between

fatigue results measured under controlled-stress and controlled-strain conditions.

Wheel tracking devices like that at Nottingham University could also be used.

Advantages. Advantages include:

1. Better simulation of field conditions.

2. Both crack initiation and growth can be monitored.

Disadvantages. Among the disadvantages are:

1. The main limitation of the test is the speed of the rolling wheel.

2. For mixes of low stiffness, rutting becomes significant and may affect fatigue

measurements.

3. The test is time consuming, and special equipment is needed.

4. The test does not measure a fundamental mixture property.

3.7.2 Full-Scale Tests

In order to obtain full-scale field simulation, circular and longitudinal test tracks have

7The asphalt-concrete layer was 40 mm in thickness. The contact area of the tire loadwas approximately 25 cm2.

70

ROLLING WHEEL

.... .. ,.,i . i.'. ."- ;- "_ _." Mix

II

STRAIN GAUGES STEEL PLATE

Figure 3.16 - Schematic Representation of Wheel Tracking Machine (van Dijk, 1975)

71

been designed and constructed in a number of different countries. Well-known examples

include the circular tracks located at Nantes, France, and at Pullman, near the Washington

State University campus, and the Federal Highway Administration's ALF (Accelerated

Loading Facility). The tracks are often divided into sections, each with a different pavement

structure, and loads are applied by several sets of dual truck tires.

In the circular track, an eccentric mechanism ensures a lateral movement of the dual

tires in order to load the pavement surface in a manner more like real conditions. Other

examples of full-scale tracks include those in Australia (ARRB), United Kingdom (TRRL),

New Zealand (Canterbury), and Denmark, with the details as shown in Figures 3.17 through

3.22. The publication edited by Sparks (1980) provides a summary of a number of these

facilities.

Advantages. Advantages of full-scale testing include the following:

1. Excellent simulation of field conditions (actual pavement structure, full-scale

traffic loading incorporating lateral wander, use of different speeds, etc.).

2. Possibility of examining the effect of changes in the pavement structural section

on pavement performance.

3. One test track allows study of other forms of pavement distress in addition to

fatigue (for example, permanent deformation etc.).

Disadvantages. Disadvantages include the following:

1. The initial investment cost and annual operation and maintenance costs are

very high.

2. A parallel, supplementary laboratory testing program is still needed, since the

72

field track tests do not directly measure fundamental mixture properties.

3. In the circular field test track, wheel load speed is limited due to centrifugal

forces.

3.8 Evaluation of Test Mcth0d8

To establish a rating of the methods discussed in this report, the following criteria

were considered:

1. Simulation of field conditions,

2. Application of test results,

3. Simplicity, and

4. Field correlation.

In defining the simulation of field conditions, the following were evaluated:

1. To what extent do the characteristics and conditions of the specimen and the

load and their interaction simulate in-situ conditions?

2. To what extent do the parameters measured during the test maintain their

significance and reliability for a large range in temperatures?

3. To what extent do the frequency of loading and rest periods approximate real

traffic conditions on the road?

Simplicity of the test method included the following aspects:

1. Complexity of the needed equipment.

2. The possibility for using the same equipment for other tests.

3. The configuration and weight of specimens and the number required for the

test.

73

(a) Lateral wheel distribution showing coverages (b) Arrangement of Ring No. 2within traveled wheel path showing twelve pavement

sections

Figure 3.17 - Details of Circular Test Track (Terrel and Kumar, 1970)

74

• ' k,

Figure 3.18 - Canterbury Test Track Showing Arrangement of Sections (Paterson, 1972)

75

hydraulic molor

wire rope /

[ __-s 1 slrain?auge$_j [ I _ ) ----

• II 3,,,y/ '

7.3 _I,_ _ m pavemenl

SIDE VIEW OF PAVEMENT TESTING FACILITY

Figure 3.19 - Linear Test Track - Nottingham University (Brown et al., 1977)

76

Transition

o

uot _,!suoJJ.

PLAN

!= 3m _ i

38ramhot-rol led aspha It wearl ng course(B.s.sg4)-Iow stone content63.Smmhot-roJled asphalt basecourse ( I_ s.5g4)

FrT/'n _, -Five different materials-see plan

-Gravel -sand -clay

1.2m-Silty clay Subgrade

Concrete pit

' 150ram Clean gravel• _ _(_.. _._

CROSS-SECTION

Figure 3.20 - TRRL Road Machine (Grainger, 1964)

77

78

,'nt,',,,bl_ fournanl brat rand. bras carte., chariol_ barriOre do s4curit6

, _ _ _I]_r._o.,,_..---,_.,,_:<.,., ,..........7-_'% '-'-.... '" -

L- rernorque de / inlermediair_ principolmolorilollon e-.a nncau e.

b_lon

Figure 3.22 - Circular Track Facility for Fatigue Testing (LCPC)

79

4. The number of parameters to be measured for further application in mixture

and structural design.

5. If the needed parameters could be measured by the same equipment or by

different equipment.

Application of test results refers to the possibility of using the test results to design

a mixture or a pavement structure with fatigue as the major concern.

The summary table (Table 3.1) lists the advantages, disadvantages, and limitations

of each method considered in this report. These methods are evaluated based on simplicity,

ability to simulate the field conditions, and applicability of the test results to design the

pavement for fatigue adequacy. Necessary data on field correlations are not available;

hence, it was not possible to take this factor into consideration in the evaluation.

No attempt has been made to apply a weighting to the individual criteria listed

above. Rather, they were collectively considered and evaluated against the overall

objectives of the task to develop a test method to define fatigue response. Simply stated,

these objectives are to develop a test which properly reflects the influence on the asphalt

binder on the fatigue performance of in-service pavements and which can be used ih an

asphalt aggregate mixture analysis system (AAMAS). The final ratings shown in Table 3.1

represent the combined judgment of the authors of the report.

In arriving at the final rankings, it should be noted that some consideration was given

to the following as well. It is possible in the ranking process that a method which had not

been placed near the top of the ranking might utilize equipment and methodology

associated with a test method already highly ranked. For example, the dissipated energy

80

method includes similar methodology to that used to define fatigue response in flexural

fatigue which was considered to have good potential. Thus once the flexural fatigue test had

been ranked, it would seem reasonable to consider the dissipated energy as a candidate

procedure at a level near the flexural fatigue test methodology. Similarly, while the flexural

fatigue tests provide a better simulation of field conditions than the direct tension test, this

test is simpler, less costly, and requires less time than a flexure test. It is possible, as the

LCPC has demonstrated, to use the direct tension test results to predict fatigue response.

Hence, the two tests might be ranked together as shown in Table 3.1.

81

Table 3.1 - Comparison of Test Methods

Method Applicationo( Advanta_z Disadvantages ,_mulatioa ,_mplkiWTest Results and d lr_cld P.mfldng

I Jmltatiol_ ColldliilioQII

Repeated Yes 1.Well known, Costly, time 4 4 Iflexure test widespread, consuming,

ab or eb,Smix 2. Basic technique specializedcan be used for equipment needed.different concepts.3. Results can beused directly indesign.4. Options ofcontrolled stress orstrain.

Direct tension Yes (through 1. Need for In the LCPC 9 1 Itest correlation) conducting fatigue methodology:

e b or eb, Smix tests is eliminated, a. The correlations2. Correlations exist based on one million

with fatigue test repetitionsresults, b. Temperature only

at 10*C.c. Use of EQI(thickness ofbituminous layer) forone millionrepetitions only.

Diametral Yes 1.Simple in nature. 1. Biaxial stress state. 6 2 IIrepeated load 4ab and Smix 2. Same equipment 2. Underestimatestest can be used for other fatigue life.

tests.

3. Tool to predictcracking.

Dissipated O, *, Sraixand 1. Based on a 1.Accurate 5 5 IIIenergy method ob or _t, physical prediction requires

phenomenon, extensive fatigue test2. Unique relation data.between dissipated 2. Simplifiedenergy and N. procedures provides

only a generalindication of the

magnitude of thefatigue life.

82

Method Applicationof Advantages Disadvantages S_ation S_p_ty Ovc_Test _lt_ and o_ Field lhnlrin .u

llmilaliOIS Conditions

Fracture Yes 1. Strong theory for 1. At high temp., Kt 7 8 IVmechanics tests Kn, Sm_ curve low temperature, is not a material

(a/h - N); 2. In principle the constant.calibration need for conducting 2. Large amount of

function (also fatigue tests experimental dataKn) eliminated, needed.

3. Ku (shear mode)data needed. Link

between K! and KIt

to predict fatigue lifeto be established.

4. Only stable crack

propagation state isaccounted for.

Repeated Yes 1. Need for flexural 1. Comparedto 8 3tension or ob or e b, Smix fatigue tests direct tension test,tension and eliminated, this is time

compression consuming, costly,

test and specialequipment required.

Triaxial Yes 1. Relatively better 1. Costly, time 2 6

repeated O'd,a c, Smix simulation of field consuming, andtension and conditions, special equipmentcompression needed.

test 2. Imposition ofshear strains

required.

Repeated Yes 1. Relatively better 1. Costly, time 3 7

flexure test on ob or e b, Smix simulation of field consuming, and

elastic conditions, special equipmentfoundation 2. Tests can be required.

conducted at higher

temperatures sincespecimens are fullysupported.

Wheel track Yes 1. Good simulation 1. For low Smix 1 9

test o b or Eb of field conditions, fatigue is affected by(laboratory) rutting due to lack of

lateral wanderingeffects.

2. Special equipmentrequired.

Wheel track Yes 1. Direct 1. Expensive, time 1 10

test (field) a b or _b determination of consuming.fatigue response 2. Relatively fewunder actual wheel materials can be

loads, evaluated at onetime.

3. Special equipmentrequired.

83

NOTES:

ob = breaking stress (in fatigue or direct tension)

oa = deviator st:tess

Triaxial testsoc = confining stress

eb = breaking strain (in fatigue or direct tension)

S,._,= mix stiffness

= phase angle

= energy factor

84

4.0 FAILURE CONCEPTS

Fatigue cracking is considered to be a tensile phenomenon. It is the repetitive

application of tensile forces, at levels considerably below that required to induce immediate

fracture, that is responsible for the initiation and propagation of fatigue cracks. Early

fatigue research found that fatigue life was often better correlated with tensile strains than

with tensile stresses, and that the basic failure relationship could be characterized as follows:

N! = a(1) b (4.1)e t

where Nf is the fatigue life, et is the applied tensile strain, and a and b are constants,

determined from laboratory testing.

So that Equation 4.1 might be used in the analysis and design of pavement structures,

Et, the damage determinant, was assumed to be the maximum principal tensile strain, a

quantity identical to the maximum applied strain in uniaxial laboratory tests and determined

from the complex, multidimensional stress state imposed by traffic on pavements in service.

In an attempt to account for differences sometimes observed in the fatigue life-strain

relationship as loading frequency and temperature vary, a mixture stiffness term can be

added to Equation 4.1 as follows:

Nf = a(l) b (Smt_)c (4.2)e t

where Smix is the stiffness modulus of the asphalt mixture and c is a third calibration

constant.

85

Equation 4.2 is applicable for a specific value of the repetitively applied strain level,

Et. For pavements in service, strains induced in the structure vary widely as a result of

variations in the types of axles, their loaded weights, tire pressures, lateral placement, etc.

Accordingly, some means for accumulating the damaging effects of mixed loading is

required. The most common means is the linear summation of cycle ratios, described as

follows:

n 1 II2 nit n m+ + ... + + ... + (4.3)

82:

where i is the ith level of applied strain at a critical point within the pavement structure, ni

is the actual number of applications of strain i that is anticipated, and Nif is the number of

applications of strain i expected to cause fatigue failure if applied in a non-mixed loading

environment. Failure in the pavement under mixed loading is expected when the linear

summation of cycle ratios reaches one.

The primary purpose of this section is to review research developments directed

toward better understanding the cause or determinant of fatigue distress and the

accumulation of damage under mixed loading.

4.1 Unique Strain

Based on results of controlled-stress testing, Saal and Pell (1960) postulated a single,

unique relationship between strain and fatigue life independent of test temperature and

loading frequency (Figure 4.1). Tests to establish this relationship were conducted at low

temperatures within a relatively small range, that is, from -13.5 °C to 7 °C. Pell later showed

86

that unique strain relationships applied for different mixes over a temperature range 0*C

to + 20" C. There was some evidence that longer lives were obtained at higher temperatures

of + 30°C where some crack propagation occurred and non-linear stiffness behavior became

apparent (Figure 4.2).

According to Witczak (1976), all researchers reporting the existence of a unique

strain criterion applied continuous, sinusoidal loading. On the other hand, those who used

pulse loading with rest periods obtained a different fatigue life-strain relationship for each

combination of temperature and loading frequency. When loading conditions were such that

mixture response in the fatigue test was nonlinear, the fatigue relationships were not parallel

if the strains had been either measured directly with gauges or calculated using a stiffness

from deflection measurements. On the other hand, parallel curves were observed if strains

had been calculated using stiffnesses which ignored the actual nonlinearity, such as those

determined from the Shell nomographs or those measured under low stress levels typical of

dynamic-modulus testing.

4.2 Deviator Stress

Fatigue lives measured by diametral tests are smaller than those obtained by other

methods. Porter and Kennedy (1975) have suggested that these differences can be

attributed in part to the fact that specimens in the diametral test are subjected to a biaxial

stress state. Fatigue curves obtained by the diametral test more closely approximate those

obtained by other tests if the applied tensile stress, at, is replaced by a stress difference, a t -

crc (Figure 4.3). Accordingly, a combined stress theory should be used for a better

prediction of fatigue response. Kennedy et al. used a combined stress theory based on

87

/lO• lO_ lOe iOr lOa

CyclestoFailure(n)

Figure 4.1 - Results of Fatigue Tests at Various Temperatures

and Speeds (Saal and Pell, 1960)

88

Cyctcs to failure -Ns

TI_ Series G I Test 5,ri_s

T¢_. ="_" _ .... /rain

[Symbot [Symbot

Figure 4.2 - Strain-Life Fatigue Results for

a Range of Mixes (Pell and Taylor, 1969)

89

IO S1rels 011feren¢/o_N/cm2

ioe ,,I i I i , i , , i I i , 1 .L_..J__L LJ }

_'2 | I_ I_11_ _ N/_ z ) ' (14_*"I _

,o,. ,,. o)OMe,,,s,'-,_h et o0'_ \O _.....--- P_ e_ ae

.,,3._, e\. 8 • "_. k-,,6o -x;,i 55,10" _ ' \ _.;'3.8 ,Io _

,o6- s,....._'_1. \'_ "e..,,b. _-% _'%

• e".oo_,_ ,,."_ :'koO o k ..'_'""'-, N \n _ \ 0_-_II '_ "_ • %t _ ''ll'_"!

_" \ [] _ % -\l , \_- _\.,.---Mo..sm,tn .i el

I_ el oo

K__ OP'n.oloi,ngco_h.._.. \ 0 _ _] -_ i = _)OeF% ,_, e

Mo_,_.m,lh,i el I '%.<_ ....,. \ tO

tO _._Kennedy ef OI

_,,.c, _..,,,o- \ _': l 03 • iO'iJO " tROS4don $1t155 I T : 7_)e F

%-3 eeKI,4 76 • tOeT: 7_oF

I0

_l_ll s O,ffemJ'_ce ,DS,

Figure 4.3 - Typical Stress Difference-Fatigue Life Relationships for

Various Test Methods (Porter and Kennedy, 1975)

9O

Mohr's circle, an application of the maximum shear stress theory. The combined stresses

are given in terms of a deviator stress or stress difference (which is the maximum principal

stress minus the minimum principal stress). For the biaxial state of stress in diametral

testing (tension on one axis and compression on the other), the stress difference is

approximately four times the tensile stress.

It should be noted that other criteria are available to analyze the response of

materials to complex states of stress including, for example, octahedral shear stress. The

octahedral-shear-stress theory yields a smaller difference of stresses (approximately 3.6 times

the tensile stress) than the deviator-stress theory.

Nevertheless, the value of this approach is the fact that it suggests an alternative

damage determinant for biaxial states of stress.

4.3. Work Strain

To define the fatigue response of asphalt mixtures under multiaxial stress states, the

concept of work strain has been introduced by Deen and his co-workers (Deen, et al., 1980).

Use is made of strain energy density at a point and which is defined as follows for an elastic

material:

. 2 2 2. . 2 2 2, (4.4)6W = l/2_.e 2 + G (ex+ey+e z) + l/2G _,y_+yyz+y_z)

where:

6W = strain energy density or work per unit volume

e = Ex + £y "t- £z

ex, etc. = normal strains

91

y,,y,etc. = shear stress

= E.(1 + tt) (1- 2/_)

E,G = elastic and shear moduli, respectively

tt = Poisson's ratio

For a specific pavement structure, this parameter can be calculated at any point

within the system using parameters obtained from computations, assuming the pavement

responds to load elastically (e.g., from the ELSYM computer program).

The work strain, ew, is in turn defined as:

w=[ 2bW (4.5)eE

Deen et al. (1980), have shown that the work strain and tangential strain due to load on the

underside of an asphalt-bound layer are of the same order of magnitude.

This parameter can be related to load repetitions in the same manner as tensile

strain, e.g., as represented by equation (4.1).

4.4 Constancy of Dissipated Energy

An alternative to the accumulation of damage utilizing the linear summation of cycle

ratios concept is that considering the constancy of dissipated energy.

In this method the number of cycles to failure is related to the amount of energy

dissipated during repetitive loading. Available data (Figures 4.4 and 4.5) suggest that

loading mode, temperature, and frequency of loading do not have a significant influence on

the total energy dissipated prior to failure. Accordingly, it is argued that this approach

92

permits prediction of the fatigue response of a mixture over a wide range of conditions

based on a very few simple fatigue tests.

The initial dissipated energy per unit volume per cycle of bending (when loading is

sinusoidal), wL, is given by:

wv = _ • oo • e0 • sin _o (4.6)

where ao is the initial stress amplitude, e o is the initial strain amplitude, and _'ois the initial

phase angle between stress and strain.

During fatigue tests, the phase angle keeps changing and, therefore, the fatigue life

must be divided into fixed intervals, during each of which the phase angle is relatively

constant. For such conditions the dissipated energy for the interval under consideration

is wi and the total dissipated energy is given by

n

l,Vf,n. = __, w," (4.7)if1

The unique relationship between the number of load applications to failure and the

corresponding total dissipated energy per unit volume is given by:

Wtoua= A • N z (4.8)

where A and Z are constants representing mixture characteristics.

It should be noted that for an elastic material the dissipated energy is the same as

the strain energy due to distortion, 6W D. This parameter is determined by subtracting the

93

energy which causes change in volume from the total strain energy or from the strain energy

density, 6W, as represented by equation (4.4). For example, in terms of stress, this can be

determined from the following expression:

1+1_

(4.9)1 2 2 2

2G 0:xy + _z + _yz)

This equation reduces to the following for simple tension (in the x direction as an

example) in terms of stress:

6W ° _ 1 + IX o2 (4.10)3E

or in terms of stress and strain to:

6W ° _ 1 + tt o_ "e. (4.11)3

Equipment and Test Procedures. Tests used to explore the dissipated energy concept

have been flexural in nature. Center-point and third-point flexural tests could be used, with

either controlled-stress or controlled-strain loading modes. For cantilever bending tests,

trapezoidal specimens were used by van Dijk (test temperature up to 50°C) while

rectangular specimens were used in center-point flexure tests (test temperature up to 20 *C).

For these studies sinusoidal loads were applied at frequencies ranging from 0.1 to 100 Hz

and with a maximum ratio of loading period to rest period of 1:100.

Fatigue Life Prediction Using Ener_ Considcrations. The step-wise procedure to

predict fatigue life is as follows:

1. Conduct the flexural fatigue test and obtain the phase angle, 4,, and mixture

94

stiffness, SO.

2. Calculate the energy ratio, n, from the expression:

t_ - wi [_ " °° "e° "sin Cj- (4.12)(W_/_) AN(Z-l)

Then

1 2

N = [(n .S° " sin _,,)](z-l) . e_Z-1) (4.13)(A • t_)

and

(,4 • D) ]ltz . NE(Z-l)12] (4.14)ep = [ (_ .So sin ¢ o)

where % is the permissible strain and SOis the initial stiffness modulus, (a o / %).

Then,

n

W_,_ = _ w," (4.15)i=1

The relationship between fl and mixture stiffness is shown in Figure 4.4.

The total fatigue behavior--expressed by the relation for the permissible strain, ep,

as a function of stiffness modulus--can be fully predicted if the functions _ = f(Smix) and

f2 -- f(Smix) and the parameters A and Z are known.

95

In many cases, however, these data are not available. For these circumstances the

following is suggested:

1. Use the data for another mix which resembles the nfix in question, or

2. Carry out a set of fatigue tests when increased accuracy is required, or

3. Use the following simplified method (Figure 4.5):

a. Obtain # for the given initial Smix from the nomograph.

b. Obtain f_for the given initial Smix from the nomograph.

c. Taking mean values of fl = 1.22, Z = 0.66, and A = 4 x 104 J/m 3,

the relationship between permissible strain and fatigue life can be

obtained for a given set of initial stiffness and initial phase angle

values, as shown below:

NO._ 1.55x104 (4.16)el, . SO .sin _ o • =

This relationship is intended to give a general idea of the fatigue life

and cannot be used for accurate predictions. It should be noted that

the above equation is based on a sinusoidal loading pattern. This

equation would change for other patterns of loading.

Though only flexural fatigue tests have been used with energy considerations to date,

these principles can be applied to other types of fatigue tests, such as supported flexure, as

well. Further work is needed to establish and apply this methodology to pavement design.

Advantages. The following are considered to be advantages of this approach:

1. According to van Dijk (1975), the major advantage of this method is that

96

"W'INITIAL

V'= W_A.rmuE4

• 40/50 pen.BITUMEN5

V 80/100 ,, ,,

A 180/200 ,, ,,m

CONTROLLED STRAIN

• O-o" 8

V_1--

O.S

0.6 •_o •

• • CONTROLLED STRESS0.4

n n [ I I I I [ I I I I

6 8 109 2 4 6 8 101° Z 4 6 8 10It

MIX STIFFNESS MODULUS Smix, N/m 2

Figure 4.4 - Relation of Energy Ratio and Mix Stiffness

for an Asphaltic Concrete (van Dijk, 1975)

97

I_,de9

8C--

4O

20

108 109 1010

Sm_l, N/m2

(a)

1CONTROLLED STRAIN1.6

12 mlrL m_

1.0108 tO9 I010

Stall , Nlm2

(b)

WFAT, Jim 3

j

/ /7 _,h"

, , , I .... i , ,

103 104 105 106

NFAT

(c)

Figure 4.5 - Phase ,Angle, Energy Ratio, and Dissipated Energy Charts Showing the Limits

for the Base Course and Wearing Course and Wearing Course Mixes Tested (van Dijk et

al., 1977)

98

loading mode, temperature, frequency of loading, and occurrence of rest

period do not have a significant influence on the total dissipated energy. The

number of cycles to failure is mainly related to the amount of energy

dissipated during the test. If validated, this could lead to a dramatic reduction

in laboratory testing, and avoidance of the mode-of-loading issue in laboratory

work would be a great advantage.

2. This method is based on a physical phenomenon which explains the fatigue

behavior of viscoelastic materials through the accumulation of the distortion

energy resulting from load repetitions.

3. For both stress- and strain-controlled flexural tests, there exists a unique

relation between the total dissipated energy per unit volume and the number

of load applications to fatigue failure.

4. Prediction of fatigue life is possible as a first approximation if initial stiffness

and phase angle are known.

5. Structural design of an asphalt-concrete layer to consider fatigue effects is

possible as a first approximation.

Disadvantages. The disadvantages include:

1. Accurate prediction of fatigue behavior is not possible without conducting

detailed fatigue tests.

2. The simplified procedure proposed in this method cannot be considered as a

design technique; rather, it serves to indicate the general magnitude of the

fatigue life of a given asphalt mixture.

99

4.5. Work Strain and Dissipated Energy

Since work strain is a function of the strain energy density, there may be merit in

merging the concepts of work strain and dissipated energy into an integrated fatigue

concept.

As noted earlier, in a uniaxial test, the elastic distortion energy under a static load

is given by

5WB = (1/3) "(1 + I_) "o • ¢ (4.17)

where U is Poisson's ratio, a is stress, and e is strain.

The approximate dissipated distortion energy in a viscoelastic material under uniaxial

flexure is given by (Kunst, 1989):

8w_ = 2 • _ • sin • - 8w_

or

8Wz) = (3) • (1 + I_) " n • o .e • sin (I) (4.18)

where _ is the phase angle. 6WB can be computed with the help of multilayer programs

and ¢ can be derived from cyclic flexural tests.

As noted earlier, work strain is an alternative to tensile strain as the determinant of

fatigue response. _["nework-strain parameter has been used in pavement design and is

100

defined as follows (Deen et al., 1980):

ew = [2 8 WB]o.5 (4.19)s.,.

In a uniaxial test with a static load, work strain can be expressed as:

e w = e[(2) • (1 + Ix)]o.s (4.20)

and

e w = 0.95(e) for IX = 0.35 (4.21)

From the above relationships and Equation 4.6, the total dissipated distortion energy can

be expressed as:

N

Wt,,ua= __, 6W ° = (2) -(1 + Ix) " A " N z (4.22)i-I

In the dissipated energy method, using the work-strain concept, the predicted

pavement life is given by

[(3 •s.= .= -sin ,x,• e_)]cz_, (4.23)N(2-(1 + Ix).A-Q)

101

The major difference between this relationship and that given by Equation 4.8 is the

substitution of work strain, _w, for tensile strain, Eo. Based on analyses of various stress

and strain conditions in asphalt-bound layers subjected to traffic loads (Kunst, 1989;

Gerritsen, 1987), there is only a small difference between the work strain and the horizontal

tensile strain on the underside of the bound layer while there is a substantial difference

between these parameters at the pavement surface.

This difference can be explained by the fact that in a linear elastic multilayer system,

the distortion energy at the pavement surface due to a static load is almost the same as that

at the bottom of the asphalt layer as shown in Figure 4.6 (Gerritsen, et al., 1987).

According to this figure, it is apparent that distortion energy is large at both surfaces of the

asphalt layer, though crack growth occurs only under tensile octahedral normal stresses

(Majidzadeh, et al., 1971; and Paris, et al., 1963).

Determining whether work strain or tensile strain is the appropriate fatigue

determinant is not possible at this time. Nevertheless, the possibility of merging strain and

dissipated energy into an integrated measure of fatigue response is worth additional

investigation.

102

DISTORTION ENERGY (Jim 3)

0 50 100 150

o, I I

1;0

_kk._ _jj_25kN

IEt --"--4000 MPI

hl _)1= .35

I

J Eo= 100 MPa

____0 _o = .352,1.0

DEPTH (mm)

Figure 4.6 - Distortion Energy (Garretsen et al., 1987)

103

5.0 CORRELATIONS AND SIMPLIFICATIONS

Considerable effort and cost are required to measure the fatigue response of asphalt

mixtures using conventional laboratory procedures and to use the information so obtained

to design fatigue-resistant mixtures. Considered herein are alternative procedures having

potential for simplifying both testing and analysis procedures.

5.1 Direct Tension Test

The methodology by which direct tension test results have been correlated with

fatigue response was developed by the LCPC (Bonnot, 1986). Figure 5.1 illustrates test

equipment used to measure the necessary tensile properties. Specimens for the uniaxial

tension testing in tlhe LCPC procedure are cylindrical with a diameter of 80 mm and a

height of 200 mm. A range of asphalt-concrete mixtures has been tested using both the

direct tension test and a flexural fatigue test. The best regression on the admissible strain

at one million load cycles, e6, was found with the linearity loss, (1 - r), and modulus, S, as

follows:

e6T = 10-4[a0 + a1(1-1:) + a2 • 10-l° -S] (5.1)

where e6T is an estimate of the admissible tensile strain under flexural fatigue at one

million load repetitions (temperature of 10°C, frequency of 25 Hz); r is a nonlinearity

factor (the ratio of stiffness at a strain of 5 x 10-4 in./in, to stiffness extrapolated to a strain

of 0); (1 - r) is the linearity loss; and S is the modulus (stiffness) at a strain of 10-4 in.fin.

Both linearity loss and stiffness are measured at a 300-second loading time and 0 °C.

Each specimen in the direct tension tests is tested at four temperatures (from -10°C

104

to 20*C) and a range of loading rates. In order not to induce premature damage, loads are

first applied in minor strain fields, to define the time- and temperature-dependent moduli,

and then in a major strain field to the point of rupture, to deduce the nonlinearity factor.

The French method of mixture evaluation incorporates the following steps:

1. Conduct the direct tension tests, actually a sequence of 26 consecutive tests for

each specimen.

2. Calculate the linearity loss and the stiffness from results of the direct tension

testing.

3. Estimate the admissible strain at one million repetitions, e6T, from the

correlation equation (Equation 5.1).

4. Determine the IQE (Elastic Quality Indicator, the thickness of bituminous

concrete that gives a theoretical life of one million load repetitions of a 130-kN

axle when the subgrade modulus is 100 MPa), using an elastic, two-layer

computer program and assuming an effective temperature of 10°C and a 0.02-

second loading time. The IQE value decreases as the quality of the bituminous

mixture increases.

5. Although a temperature of 10°C has been found to be acceptable for

conditions normally encountered in France, the quality indicator concept can

be extended by defining a second IQE using annual temperature spectra and

adopting the hypothesis of invariability of the product e6 • (S)I/2.

It should be noted that direct tensile tests have been conducted by other investigators

as well (Epps, 1969, and Rao, 1989) using the apparatus shown in Figure 5.1 at a constant

105

|

_- Loading frame

Loadin 9 rod

Universal joint

_ Aluminum end cap

Epoxy

.._---Aluminum end cop

Load cell

Loading frame C_ l.t--- Universal jointandelectro - hydraulic

closed loop i I i _'_---

resting system "--7 Loading rod

Figure 5.1 - Direct Tension Testing Apparatus (Epps, 1969)

106

strain rate. These investigators have also attempted to relate test results (stress and/or

strain at break) to fatigue response.

Advantages. The following appear to be advantages of this approach:

1. In principle, the need for fatigue testing is eliminated, assuming that calibration

constants of Equation 5.1 are invariant for mixtures and asphalts of interest.

2. Based on the French experience, high correlation exists between direct axial

tensile strain and the fatigue tensile strain at one million load cycles.

3. In the direct tension test, failure of the specimen is initiated in a zone of

uniform stress (or strain).

Disadvantages include:

1. The correlation which allows use of the result of tensile tests for predicting

fatigue life is based on the admissible strain for one million load cycles only.

Forecasting the slope of fatigue life curves with acceptable accuracy proved

much more difficult.

2. The method assumes that the equivalent temperature of all bituminous

concretes is close to 10 °C. Therefore, the applicability of this method for

other temperature regimes must be established.

Discussion. Although the LCPC method seems to have been successfully used to

compare different bituminous mixtures, it has not been sufficiently developed to permit its

use as a versatile tool for predicting fatigue life or for designing pavements for fatigue

adequacy. However, the consistently high correlation between fatigue life and parameters

measured in the direct tension test is very important because of its potential for creating a

107

useful tool in predicting fatigue life through a relatively simple test.

In order to transform this principle into a practical method, a parallel laboratory

study will be undertaken to seek consistent correlations between results of flexural fatigue

and direct tension tests. The study will consider a range of parameters including those used

in the LCPC method. More work is needed to show that the effect of binder modifiers on

fatigue life is reflected in their effects on tensile properties.

5.2 Failure Envelope

The basic principle of this method is to draw an envelope through failure points of

stress-strain curves defined by diametral tests (Little and Richey, 1983). The design asphalt

content can be selected from a window of this envelope such that rutting and fatigue

distresses are at minimal levels. Monismith (1965) has shown that the ultimate tensile

properties of asphalt concrete superimpose to form a failure envelope in three dimensions

(compressive stress, tensile stress, and temperature) resulting in a solid enclosing the safe

or working stress region. Little and Richey (1983) developed a procedure to select an

asphalt content to mitigate fatigue distress.

For a range of asphalt contents bracketing the expected design value, a set of

boundary curves representing pavement distress could be superimposed on the plot to

determine the areas of satisfactory performance (Figure 5.2).

1. An initial estimate of the optimum asphalt content is made choosing the

asphalt content having the maximum toughness. To determine this estimate,

diametral tests are performed on specimens varying in approximately one-

percent increments of asphalt content. A range of five to six percent is usually

108

sufficient to bracket the optimum asphalt content. The diametral test is

performed at 77 °F with a loading rate of 2.0 in. per minute. The average

toughness (work to cause failure per unit volume) is plotted against the asphalt

content. The peak in the toughness curve indicates the range of one to two

percent in asphalt content that will be subjected to further analysis and testing.

2. The range of asphalt contents defined by the peak of the toughness curve in

Step I is subjected to an analysis for thermal cracking, permanent deformation,

and fatigue.

3. Boundary curves are selected for thermal cracking and permanent deformation.

The thermal-cracking boundary curve may be selected for the appropriate

binder and rate of cooling. The rate of cooling is determined from local

climatological data. The permanent-deformation boundary curve is selected for

the desired binder, climatic region, and traffic level. The traffic level on the

permanent-deformation design charts indicates the number of equivalent wheel

loads:

--2 x c x w,,,, (5.2)

where C is the ratio of total number of wheels/wheel track to the total number

of axle loads/lane and Wto t is the total number of commercial vehicles.

Failure envelopes generated by the diametral data from Step 2 are

plotted on a design chart with the desired thermal-cracking and permanent-

deformation boundary curves. A failure envelope which falls completely

109

within the window formed by the two boundary curves represents a

satisfactory mix.

4. The fatigue design chart is selected for the desired binder, the expected

subgrade modulus and pavement thickness, and the number of load

applications. Charts have been developed for subgrade moduli of 3,000 and

18,000 psi and for pavement thicknesses of 3 and 6 in. The number of load

applications indicated on the design charts is actually the number of standard

18-kip equivalent axle loads expected during the life of the pavement.

The number of equivalent standard axle loads is commonly obtained

by multiplying the number of axles in each class of axle load by a damage

factor, Fj. The damage factor is calculated as:

Fj-- (5.3)e s

where ej represents the tensile strain induced in the bottom of the pavement

layers by axle j, and es is the strain induced by the standard 18-kip single axle.

The exponent, n, ranges from 3 to 6.

Advantages. Advantages of this procedure include the following:

1. Diametral tests are easy to perform and, therefore, test data required for the

application of this procedure are easily obtained.

2. The method provides an asphalt content which is a compromise between

stability, thermal cracking, and fatigue life.

110

\Thermol Crocking Boundary Curve

103 _-(5" F/hr Coolie 0 Rote)\\

\ _ Tl_ermol Boundary Curve

_. _ _ Permanent' Deformofion

m 10 2

.===- \

3/, 5% I I_" I X 7%

I0 I I I I

I0" 5 I0" 4 I0- 3 I0" 2 I0" I

Failure Strain, In/in

Figure 5.2 - Typical Window Formed by Boundary Curves (Little and Richey, 1983)

111

Disadvantage. The primary disadvantage is as follows:

1. This method cannot determine the asphalt content for optimum fatigue life.

This method only permits an estimation of the fatigue life for the preselected

asphalt content based on the failure envelope which falls completely within

the window formed by the two boundary curves (obtained for permanent

deformation and thermal cracking) representing a satisfactory mix.

Direct tensile strength, compressive strength, and temperature could be used, as

shown by Monismith (1965), to develop a three-dimensional failure envelope as an alternate

to the use of diametral test results.

5.3 Other Simplifications

To predict fatigue performance for pavement design purposes, a number of simplified

procedures have been adopted including those developed by the Nottingham researchers

(Brown et al., 1982), Shell (Shell, 1978), and the Asphalt Institute (The Asphalt Institute,

1981).

The Nottingham researchers have developed a general relationship between tensile

strain, the number of loadings to failure, asphalt content (volume basis), and the ring and

ball softening point of the asphalt in the mix as follows:

14.39 log Vn + 24.2 log 7Rs - 40.7 - log Nlog e, = (5.4)

5.13 log Vn + 8.63 log TRn - 15.8

where:

112

et = allowable tensile stain

N = number of load applications to failure

Va = volume of asphalt binder, percent

TRB = ring and ball softening point temperature, °C

The Shell approach is to estimate the fatigue strain, from the following expression:

e t ---(0.856 x g B + 1.08) S_.°_ x N -°'2 (5.5)

where:

i_t = allowable tensile strain

N = number of load applications to faillure

VB = volume of asphalt binder, percent

Smi x = mix stiffness for particular time of loading and temperature; can

be estimated with the volume concentrations of the aggregate

and asphalt and the stiffness of the asphalt (Sasp) contained in

the mix.

In the Asphalt Institute methodology use is made of the expression:

N-- 18.4C[4.325 x 10-3(et) -3"291(Sin/x)-0"a54] (5.6)

The parameters £t, N, and Smi x are the same as above. The term C is a correction obtained

from:

113

C-- 10 u (5.7)

where:

M = 4.84 [. VB 0.69]vv ¬�”�and

V,, -- volume of air voids

In all of these relationships the property of the asphalt is reflected in either the ring

and ball softening point temperature or the asphalt stiffness. It must be emphasized,

however, that these relationships are merely approximations. Thus these should only be

considered for pavement design purposes and not for mix evaluation.

114

6.0 RELATIONSHIP BETWEEN TEST RESULTS AND FIELD PERFORMANCE

A major difficulty with fatigue testing is developing a meaningful relationship

between the results of the laboratory tests and field performance. Generally, fatigue

response determined from laboratory controlled-stress tests underestimates field

performance since such tests include relatively few repetitions for crack propagation. In situ,

on the other hand, it is possible that, after initial cracking, the asphalt-bound layer will

sustain additional repetitions (associated with crack propagation) because of the support

provided by the underlying layers. Allowance should also be made for the transverse

distribution of wheel loads; this factor is estimated to increase service life by a factor of

about 2.5 (Shell, 1978).

A major concern is the use of the laboratory test data to analyze the response of the

mixture in the pavement section. By defining fundamental material properties such as those

described herein, it is possible using analytical procedures to estimate field performance of

mixtures (including the influence of the binder). An example of such a methodology is

included herein for illustrative purposes.

Fatigue cracking is usually related to the magnitude of tensile strain occurring on the

underside of the asphalt-bound layer. In some circumstances, however, fatigue cracking may

be initiated above the underside of the layer, even at the pavement surface. To estimate

the potential for such cracking is a challenge also facing the pavement engineer.

Accordingly, some discussion of this problem is also included.

115

6.1 Shift Factor

To account for differences between laboratory and field response, shift factors are

necessary to translate laboratory fatigue characteristics to those considered to be

representative of in-situ performance. Unfortunately, there is no unique relationship. Shift

factors proposed by various researchers have varied from slightly more than one to 400 +.

The amount of shift appears to be dependent on the test type, test conditions, and the field

conditions to which the laboratory test results are being compared. In addition, it may also

be dependent on the asphalt characteristics. For example, for tests in which specimens have

been flexed at high rates in sinusoidal loading, factors of the order of 100 have been used.

For tests in which there are rest periods between load applications, considerably lower

values, usually less than 20, are used.

The shift factor also varies depending on the test configuration and the mode of

loading. A specimen subjected to repeated flexure has a fatigue life at least 50 percent

greater than the same material tested in direct tension (Bonnot, 1972). For the same

mixture, the shift factor is less for controlled-strain loading than for the controlled-stress

condition.

Temperature of test also has an influence (Rao, 1989). It appears that, at higher

temperatures, the shift factor may be less for laboratory fatigue data than when tests are

conducted at lower temperatures (e.g., 40* vs 20°C). In addition, the shift factor is

dependent on the thickness of the asphalt-bound layer increasing as the thickness of this

layer increases (Shell, 1978).

Little and his coworkers (e.g., Kim et al., 1990) have suggested that chemical healing

116

which is dependent on the asphalt may also contribute to the shift factor. This was also

briefly discussed by Bazin and Saunier (1967).

Brown et al. have attempted to quantify the shift factor (440) which they have used

(Brown et al., 1985) in the following terms:

a. factor of 20 for rest periods;

b. factor of 20 for crack propagation; and

c. factor of 1.1 to account for lateral distribution effects of wheel loads.

Generally, more is known about the fatigue response of asphalt mixtures from

laboratory testing than from field observations. Moreover, as noted above, established

correlations between laboratory data and field response are weak. This is a major area for

concern when attempting to utilize the results of laboratory investigations to define

performance criteria.

6.2 Fundamental Mixture Properties in Pavement Analysis

The fundamental "parameter" determined by fatigue testing is typically the

relationship between fatigue life and some damage determinant, such as the maximum

principal tensile strain. The following steps describe one approach for incorporating such

information into a performance-based design (or analysis) procedure:

1. The engineer first identifies the location of pavement to be constructed and

estimates the mean monthly air temperatures (MMATs) expected for each

month during the design life. If this is not possible, one of the environmental

conditions analyzed by Rao (1989) can be selected to represent the pavement

location.

117

2. Type of Pavement

The type of asphalt pavement must be preselected, that is, full depth or with

untreated (or treated) aggregate base. For many situations, the type of

pavement is dictated by available resources (Croney, 1977). There are,

however, several advantages of full-depth asphalt-concrete pavement as

explained in the MS-1 Manual (Asphalt Institute, 1981).

3. Estimation of Traffic

The engineer is required to estimate the total traffic in terms of equivalent

single axle loads (ESALs) for the design period.

4. First Trial Thickness

Trial thickness of the asphalt layer can be selected, using, for example, charts

shown in the MS-1 Manual (Asphalt Institute, 1981) or some other suitable

design procedure.

5. Calculation of Mean Monthly Pavement Temperatures (MMPTs)

For the trial thickness selected in the above step and the MMATs obtained in

Step 1, MMPTs can be calculated using Witczak's formula as given below:

1 4) ] [ 34 4) ]- + 6 (6.1)

MMPT= MMAT" [1 + (Z + (Z +

where Z is h/3 and h is the thickness of the asphalt layer in inches. MMPT

and MMAT are in *F.

This formula gives the average pavement temperature at one-third depth within

118

the pavement. Usually maximum tensile strain occurs at the bottom of the

asphalt layer. Therefore, results obtained using this formula may slightly

overestimate the design thickness. Alternately, using Barber's equation

(Barber, 1967), MMPTs at the bottom of asphalt-concrete layer could be

calculated.

6. Fatigue Tests

Conduct fatigue tests at a minimum of two temperatures, representative of the

MMPTs calculated above.

7. Shift Factor

Obtain the stress vs. fatigue life (or strain vs. fatigue life) from the laboratory

fatigue test data. Apply a proper shift factor to reflect differences between

field and laboratory conditions.

8. Tensile Stress (or Strain) at the Bottom of Asphalt-Concrete Layer

Determine the tensile stress or strain at the bottom of the asphalt-concrete

layer from the laboratory fatigue life data for the design traffic.

9. Asphalt-Concrete Layer Thickness

Determine the asphalt-concrete thickness for the tensile stress using graphs

such as illustrated in Figures 6.1 and 6.2. A more complete set of graphs is

available in Rao (1989). Similar charts could easily be developed for a tensile-

strain criterion.

10. Cumulative Damage Hypothesis

The ratio of the actual number of cumulative standard axles expected in a

119

_o.oo' _ ,.........................

iliiiii_I I

I l "

40.00 , ....... I............ i...............III I/\\ , t.l:<;,:..

- ']tt\\\ ' z - 40,,.0,,0 ,,._t3o.oo II_\\k'\......i....._-_oo.ooo,,..,.....

,I\\\\\ , 4 - i,,o.,,.,,,.,;i,_ ' I \\\\\ ' 5 - 5o.o,,o ,':;l

_ 20.00 L _ .k,_A_\\',,.,__ _,....................... _ \ \'\\_., _ \ \\_,

10.00 _ _ __._-_':-_ i, ............i G 5 , 4 _ _ l! !

! I

! I

0.00 -, ..... ,,, { .... ..... -m--J-,', b--v--,--v-1--v--v---v-v--v--v-r--v--,--,--r--

-50.00 0.00 50.00 I O0.UO 150.0(1ENSILE SIRESS AI 1lIE I1OIIOM ()F AC IA'¢lll. I':;i

Figure 6.1 - Asphalt-Concrete Thickness vs. Tensile Stress

for a Typical Full-Depth Pavement

120

30.0O m I

II

Q).E

n{20.00 i j L J _ _ _hi I

' >" i LEGEND ,

£) I = 800,000 Psi< 2 = 400,000 Psi

t,. 3 = 200,000 PsL0 4 = I00,000 Psi

in 5 = 50,000 PsiIn 6 = 20,000 Psi,,I 10.00 --- J L J___Z tY.U I.T.I-

6 t,

I t I

{5 4t _ e Z j 1

o.oo .... 1-,,,, I,,, .... ,, I ......... I.,, ....... ,., ....... .,,,,-5o.0o 50.00 150.00 250.00 350.00 450.00

IEHSILE STRESS AT THE BOTTOM OF AC LAYER, Psi

Figure 6.2 - Asphalt-Concrete Thickness vs. Tensile Stress

for a Typical Pavement with Granular Base

121

J..

given month to the possible cumulative number of standard axles for a given

thickness of AC layer gives the fraction of design life consumed in each

particular month.

Calculate the sum of fractions of life for all twelve months and obtain the

design thickness such that sum of fractions of life consumed in the design

period is less than unity.

By the use of such a procedure, it is possible to consider how different mixtures will

respond to traffic loading in a specific environment. In effect, by defining the appropriate

mix characteristics, the suitability of specific mixes with different binders can be determined

in advance, thus providing the potential for improved pavement performance.

6.3 Further Challenges

It must be emphasized that to properly define the effects of mix variables on the

fatigue performance of asphalt-bound layers, the use of a fundamental generalized approach

such as that described in the previous section permits the engineer to treat a wide variety

of materials, strucrares, traffic, and climates. Such an approach permits consideration of

fatigue cracking which, as noted earlier, may start at the bottom of the asphalt-bound layer

and progress to the: pavement surface. In addition, the methodology has the potential to

consider the possibility of surface cracking as well.

This surface cracking may result from tensile strains induced at or near the pavement

surface as a result of one or more of the following:

1. Horizontal shear forces in the contact area between tire and pavement,

2. Thermally induced stresses,

122

3. Dynamic load induced residual stresses, and

4. Relatively stiff underlying layers and relatively thin surface layers.

The combination of tensile stresses at or near the surface and high dissipation distortion

energy may initiate cracks in the upper region of the pavement (Kunst, 1989). Specific

conditions required for the initiation of such cracking as identified by various researchers

are summarized below.

Shell. Based on a series of calculations, Shell researchers have determined that the

depth in the asphalt layer at which the maximum strain occurs depends on the parameter

(Shell, 1978):

c = h I (E2) (6.2)E1

where E 1 is the stiffness of the asphalt-bound layer (Smix) in N/m 2, E2 is the modulus of

the unbound layer in N/m 2, and h 1 is the thickness of the asphalt layer in mm.

When c is greater than 133 mm, the maximum asphalt strain is not at the underside

of the layer. If h 1 is less than about 200 mm, the maximum strain occurs in the lower half

of the asphalt layer; whereas if h 1 is larger than 200 mm, maximum strain occurs in the

upper half of the asphalt layer. These findings are valid for the loading configuration used

by Shell researchers to develop their design charts, for three-layer structures with unbound

bases, and for hot climates (characterized by a weighted mean annual air temperature of

28°C).

123

Wallace. As summarized by Mortisrnith (1981), Wallace has also performed an

extensive analytical investigation of the location of maximum tensile strain in asphalt

pavement layers. The following range in parameters was investigated:

E1/E 2 < 10; hl/a < 1.0; and z/a < 1.5

where a is the radius of loaded area, z is the depth below the surface of pavement, and the

remaining variable.,; are as described above.

Some of the conclusions from this analysis are as follows:

1. Where shallow tensile strain exceeds the magnitude of strain at the underside

of the pavement layer, the maximum value of tensile strain at the load axis

occurs at a depth of about 0.8 to 1.0 times the radius of the contact area (0.8a

to 1.0a).

2. Higher tensile strains occur at shallower depths away from the load axis. At

a depth of 0.2a, beneath the edge of the contact area, the maximum principal

tensile strain is about 50 percent greater than at z = a on the load axis. These

shallower regions of high strain are more localized: thus the tensile strain at

z = a is used for design purposes.

3. Where the shallower strain is critical, its magnitude is given by the following

expression:

(_ -p)e,_ - (6.3)

(2 "En)

where p is the contact pressure and _1 is Poisson's ratio of the asphalt layer.

124

Gerritsen. According to Gerritsen et al. (1987), initiation of surface cracking is

possible under the following conditions:

1. Base layer is an asphaltic layer.

2. Ebase equal to or greater than Esurfac e.

3. Horizontal shear forces in the contact area.

4. Thermally induced stresses.

5. Dynamic load induced residual stresses.

Kunst. According to Kunst (1989) for structures with a bound base whose stiffness

exceeds that of the asphalt-bound surface, computations show that for all combinations of

thickness and asphalt-mixture stiffness used, the maximum tensile strain on the bottom of

the layer is exceeded by the maximum tensile strain at the surface.

Work-Strain Concept. Kunst (1989) and Gerritsen et al. (1987) have suggested that

work strain might be an appropriate failure parameter to predict pavement life reductions

due to surface cracking. Cores from in-service pavements have confirmed the existence of

crack initiation and growth at the upper level of the surface course. The work strain

concept has been described earlier.

Determining whether work strain or tensile strain is the correct fatigue determinant

may not be possible at this stage. Near the surface, while the horizontal strain is

compressive at the center of vertical loads, the work strain (since it directly related to the

distortion energy, equation [4.5]) can be of substantial magnitude as shown in Figure 6.3

(Kunst, 1989).

While there has been some confirmation of the applicability of this concept to explain

125

i...

surface cracking (Gerritsen, et al., 1987), it would seem desirable to further study this area,

particularly in light of the changes in axle loads and tire pressures which are occurring on

heavily trafficked pavements.

In conclusion, it should be noted that this phenomenon is different from that

observed by Anderson (1987). He demonstrated that in thin surfaces of asphalt concrete,

the highest tensile strains occur at the surface. As the thickness of the surfacing is

increased, the largest values shift and occur on the underside of the layer.

6.4. Summary

Thus, while there are a number of challenges facing the pavement engineer relative

to the fatigue problem, it should be apparent that procedures for defining mixture properties

in fundamental terms for use in analysis procedures which reflect the "real" pavement

situation provide an important opportunity for the engineer to design (and construct)

improved pavements using this improved methodology. In particular, such methodologies

have the potential to permit the engineer to realistically assess, in advance, the influence of

binder properties on pavement performance, one of the major goals of this project.

126

. DISTORTIONENERGYU/m ]

STRAIN[l_*/nd

-150 -100 -5C, 0 50 100 150

.............................I20 _.--_ ...._=-o_I[

\

E_ m 4000 UPeh_ _ :z .3S

2_,o . \

08=1'1'1lmml•

Figure 6.3 - Distortion Energy (Related to Work Strain)

and Horizontal Strain Due to a Vertical Load (Kunst, 1989)

127

7.0 CONCLUSIONS AND RECOMMENDATIONS

Conclusions obtained from this evaluation are presented in three parts: (1) specimen

fabrication; (2) factors which influence the fatigue response of asphalt paving mixtures; and

(3) evaluation of test methods.

7.1 Specimen Fabrication

For the SHRP program, it is considered important to examine the influence of

method of compaction on the response characteristics of laboratory prepared specimens.

Accordingly, a fatigue testing program will be conducted on specimens prepared by the three

most promising compaction techniques; kneading, gyratory, and rolling wheel.

7.2 Factors Affecting Fatigue Response

1. The controlled-stress mode of loading appears to represent the response of

thick asphalt pavements to repetitive loading while the controlled-strain

approach is suitable for thin pavements. The controlled-strain mode of testing

results in a greater fatigue life for the same mixture than controlled-stress

testing.

2. Air void content is an important factor which affects fatigue life of an asphalt

mixture and which should be as small as possible (but not less than the

minimum limit of 3.0 percent) to obtain the greatest fatigue life.

3. Another variable that can be controlled by the engineer and which has a

significant effect on the fatigue life is asphalt content. The optimum asphalt

content to obtain a maximum fatigue life is generally higher than the design

required for rutting considerations. Therefore, the asphalt content should be

128

as high as possible with due consideration to stability.

4. Asphalts should be quite stiff for thick asphalt pavements but relatively more

flexible for thin ones. For asphalt pavements of intermediate thickness,

asphalts of about 100 penetration (25 °C, 100 gr, 5 sec) are recommended.

5. Mixes containing dense-graded aggregates are recommended for use in

pavements containing thick asphalt layers while a more-open graded aggregate

(less fines) is recommended for pavements containing thin asphalt layers.

6. Higher temperature lowers fatigue life in the case of thick asphalt pavements

but increases fatigue life for thin pavements.

7.3 Test Methods

The various methods considered herein have been evaluated using the criteria

described earlier. This evaluation is summarized in Table 3.1. It will be noted that the

repeated flexure test received the highest ranking. The direct tension test was also included

in this category because of the possibility of using it to define fatigue response, following the

LCPC approach. The diametral test received a relatively high ranking, in part because of

its simplicity and in spite of the complex stress state which may exist, particularly at higher

temperatures. Also included in the first four categories are considerations of dissipated

energy and fracture mechanics.

7.4 Recommendations

This evaluation of existing information on the fatigue response of asphalt concrete

has suggested a set of competing alternatives which must be developed to establish a

suitable methodology for defining the fatigue response of asphalt-aggregate mixtures. This

129

program will involve the use of the tests and methodologies evaluated in Table 3.1 and rated

I to IV. In addition, as noted earlier, a study will be undertaken to assess the influence of

compaction method on fatigue response. The hypotheses to be tested and the associated

program are included as Appendix A.

This evaluation of existing information has also suggested other areas which require

additional investigation, some of which are beyond the scope of the SHRP research

endeavor. However, it is important to at least briefly describe them herein.

1. It is extremely important that the results of fatigue tests performed on

laboratory specimens be related to the fatigue performance of the same

materials in pavements in service. One approach to this problem is the use of

correlation (shift) factors.

2. The phenomenon of surface cracking should be investigated. This form of

distress may be related to high shear stresses developed near the pavement

surface. Accordingly, it is desirable to investigate the response of asphalt

concrete subjected to repeated shear stresses. While such an investigation will

not be conducted as a part of this program, there are sufficient examples of

pavements in which this distress has manifested itself to warrant further

investigation. Repeated shear tests can also take more effective account of the

types of load to which thin surface courses and interlayers are subjected.

3. According to van Dijk, loading mode, temperature, loading frequency, and

occurrence of rest periods do not have a significant influence on the cumulative

amount of energy dissipated before fatigue failure. As of this date, energy

130

considerations have been applied only to flexural fatigue tests. Further study

is needed (1) to apply energy considerations to other types of fatigue tests, like

diametral, direct axial, and supported flexure; (2) to determine the exact effects

of temperature and rest periods on the relationship between dissipated energy

and fatigue load, and (3) to apply energy considerations to the structural design

of asphalt pavements.

131

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APPENDIX A

HYPOTHESES AND RECOMMENDED TEST PROGRAM

A.1 Hypotheses

Based on this evaluation of the fatigue response of asphalt-aggregate mixtures, the

following hypotheses have been postulated relative to their fatigue response characteristics:

1. Cracking results from a tensile stress or strain (less than the fracture stress or

strain-at-break under one load application) at a specific number of stress (or

strain) applications, the number of load applications being larger as the

magnitude of the stress or strain is smaller, i.e.:

N = A(1/_t) t_ or N = C(1/at) a

The relationships are dependent on the temperature and mode-of-loading

[coefficients (A and b) and (C and d)] and must be established by some form

of repetitive load testing; or

2. Cracking results from repetitive stress (strain) applications when either the total

ener_ or the strain energy, of di_t0rtion reaches some limiting value regardless

of the mode of loading to which the specimen is subjected; or

3. A direct correlation can be established between the stiffness and fracture

characteristics of a mix and its fatigue response (e.g., similar to that established

by the LCPC of France); or

4. Results of fracture tests on notched specimens can be used to predict the

fatigue: response of asphalt concrete mixtures over a range in temperatures.

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From experimental evidence such as that illustrated in Figures A1 and A2, the

magnitude of tensile stress or strain repeatedly applied appears to be a reasonable

determinant of the cracking which occurs in asphalt-bound layers subjected to repetitive

trafficking. Since actual pavements are subjected to bending stresses, this model of loading

appears most reasonable to define fatigue response using laboratory test equipment.

While bending stresses are representative of in-situ conditions, other modes of

loading will also be utilized and include diametral and direct tension testing.

At the University of California at Berkeley, the bending fatigue tests will be

conducted at a rate of 100 repetitions per minute, a comparatively slow rate and one in

which the influence of rest periods has been shown to be negligible. Since it may be

desirable, should this method of testing be selected, to conduct a bending test at a faster

rate of loading, controlled-stress fatigue tests on pyramidal shaped specimens will be

conducted at SWK/Nottingham University at a rate approximately ten times as fast.

Since the bending mode of loading requires taht specimens be sawed to prismatic or

pyramid shapes, it was considered desirable to test specimens not requiring sawing; hence

the direct tension tests at SWK/Nottingham performed on cylindrical specimens.

When testing to define fatigue behavior, the mode of loading influences response

with specimens of comparatively low stiffness performing well in the controlled-strain mode

and specimens of high stiffness performing well in the controlled-stress mode. Since both

controlled-stress and controlled-strain tests will be performed at UCB, consideration will be

given to the determination of the total strain energy and the strain energy of distortion in

141

/0,000_ I I f t I i I I I I I i I i I I I i _ I I_

I/000

- l _Nf--/.55x/0_6(i/o_)_T _

- /-_ ___ -

IOC ._- _-_"_---- _ - ..... I_ _"-_ _

_ _-- Nf-3.97, I0,4 _-"'_-__(//__)5.36_ 7 68°F --

! I I I II0 I I I li I I r t i I I I I I I I

I02 i0_ 104 105 I06 I0z

Stress _ppl/cot/ons-Nf

Figure A1. Stress vs. Applications to Failure

#A.v'p,_ _ i i , ! [ i _ i I i I I i i i i

•_ --68"F

103 _ . ]i '"_, _ 4o2£ • I.-"-_,

_',_ - #:e35,,o_','d" "; _..o&_.

a,o, ..

_ _ _

/0 I I II I I I[ I I tl [ I II I I flI02 I03 I0 _ I0 5 I0 6 IC z

Stress ,_pplicotions- Nf

Figure A2. Strain vs. Applications to Failure

142

an attempt to eliminate the mode-of-loading variable. Such analyses will require a measure

of the complex modulus and phase angle for each mixture corresponding to the time of

loading and temperature of the fatigue test together with the stress/strain vs. number of

load applications to failure. While this approach still requires the conduct of fatigue tests,

it may have the potential to sort out mode-of-loading effects.

To reduce the amount of testing required to define fatigue response in the laboratory,

consideration will be given to the correlation developed by the LCPC between the fracture

characteristics of a mix in uniaxial loading and its fatigue response. In the LCPC

methodology, measurement of the stiffness characteristics of the specific mix at different

strain levels and temperatures are also required. An evaluation of the LCPC approach will

be made to determine its efficacy since the use of a direct tension test has the potential to

reduce considerably the time required to define fatigue response of asphalt-aggregate

mixtures as compared to repetitive load testing.

The use of fracture mechani¢_ principles has the potential to shorten the time

required in the laboratory to define fatigue response. Rather than conduct repetitive

loading fatigue tests, direct loading tests on notched specimens permit the determination of

specific material parameters from which the fatigue response can be estimated. Depending

on the size of the non-elastic zone at the crack tip, different interpretations are required.

If the majority of the material behaves elastically, the stress intensity factor, K, governs the

response. On the other hand, if the non-elastic zone is large, either the J-integral or the C'-

line integral may be required to define crack propagation. It is anticipated that the stress

intensity factor will be suitable to define fatigue response at low temperatures (i.e. 32"F).

143

At high temperatures, however, it may be necessary to consider either the J integral or the

C'-line integral; both will be evaluated.

By conducting the conventional fatigue tests together with the additional tests

described herein, sufficient data will have been obtained to permit the evaluation of all of

the above hypotheses permitting the selection of an appropriate methodology for further

development and evaluation.

A.2. Test Program

Tests. As outlined in the work plan (and modified based on the literature review),

the following tests will be evaluated:

AGENCY TEST

University of California Beams - controlled stress and controlledstrain

Direct tension - correlation with fatigue

University of Nottingham (SWK) Trapezoidal specimens - sinusoidalloading (controlled stress)Direct tension - sinusoidal loading(controlled stress)

North Carolina State University Diametral - pulsed loading (controlledstress and controlled strain)

It is now expected that each laboratory will prepare its own test specimens. In

addition, a limited test program will be conducted at Berkeley to evaluate the fracture

mechanics methodology. This program has not been defined at this time to the degree that

the repeated load test program has been and is described in the figllowing section.

144

Variables Considered. Table A-1 summarizes the significant variables for the fatigue

study. A total of ten variables were considered. Of these, four will be fixed (aggregate

gradation, grade of asphalt, aging, and moisture conditioning). Each of the others will be

evaluated at two levels. This results in a total number of combinations of 2 6 (or 64 cells)

for each test method.

Using principles of experimental design, it was determined that a 1/2

fraction of the complete factorial (i.e., 32 cells) would be necessary to estimate both main

effects and all two-factor interactions. To obtain estimates of purely experimental error,

these 32 factorial combinations will be replicated three times, for a total of 96 tests for the

beam testing, and twice (64 tests) for the other fatigue tests. The beam tests require greater

replication because of the larger variation expected as compared to the other tests.

The total number of samples contained in this testing program is 512. This testing

program is expected to be completed by June 1990. A summary of sample requirements is

shown in Table A.2.

Expected Results, The results of this study will provide insight as to which of the

fatigue test systems is most promising for implementation using the criteria stated at the

beginning of this chapter. The selected equipment will be used in the subsequent plans of

the project study.

145

Table A.1. Significant Mixture and Test Variables for Fatigue Study

Level of TreatmentVariable No of

Levels

1 2 3

Aggregate

Stripping potential Low High (2)

Gradation Medium (1)

Asphalt

Temperature susceptibility Low High (2)

Grade Medium (1)

Content Optimum High (2)

Compaction

Air voids 4 +_1/2% 8 + 1/2 % (2)

Test conditions

Temperature 32* F 68* F (2)

Stress Low ttigh (2)

Conditioning

Aging None (1)

Moisture None (1)

2_

146

Table A.2. Number of Samples for Fatigue Factorial Design

Number of SamplesTest Total

1/2 Fractional Repficates

University of California

• Flexural Beam, Controlled Stress 32 64 96

• Flexural Beam, Controlled Strain 32 64 96

• Direct Tension, Static 32 32 64

North Carolina State University

• Diametral, Controlled Stress 32 32 64

• Diametral, Controlled Strain 32 32 64

University of Nottingham (SWK)

• Direct Stress, Controlled Stress 32 32 64

• Trapezoidal Beam, Controlled Stress 32 32 64

Grand Total 512

Complete Factorial 26 = 641/2 Fractional = 32Total Number of Samples = 512Estimated Time for Testing = 6-9 months

147


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