Uniaxial Fatigue Testing of Diverse Asphalt Concrete Mixtures 1

Waleed A. Zeiada1, B. Shane Underwood

2, and Kamil E. Kaloush

3 2

（1Postdoctoral Scholar, Arizona State University, Department of Civil, Environmental and 3

Sustainable Engineering, PO Box 875306, Tempe, AZ 85287-5306, wzeiada@asu.edu) 4

(2Assistant Professor, Arizona State University, Department of Civil, Environmental and 5

Sustainable Engineering, PO Box 875306, Tempe, AZ 85287-5306, Shane.Underwood@asu.edu) 6

(3Associate Professor, Arizona State University, Department of Civil, Environmental and 7

Sustainable Engineering, PO Box 875306, Tempe, AZ 85287-5306, kaloush@asu.edu) 8

9

ABSTRACT 10

The uniaxial fatigue test is a useful method for developing constitutive models to 11

describe the fatigue behaviour of asphalt concrete mixture owing to the uniform states of stress 12

across the specimen section. As part of the NCHRP 944-A project, a proposed uniaxial fatigue 13

test protocol and software were developed to assess fatigue damage and healing. In this study, 14

the protocol was used to evaluate a wide range of conventional and modified asphalt mixtures 15

sampled from national and international projects as well as laboratory prepared mixtures with 16

different volumetric properties. The study mixtures included those modified with rubber, 17

polymer, fiber, warm mix additives, and combined rubber and warm mix. The fatigue analysis 18

was performed using the simplified viscoelastic continuum damage (S-VECD) approach where 19

the damage characteristic (C-S) curves were established for each mixture, and then used to 20

obtain the fatigue relationships through simulated predictions. Overall, the proposed uniaxial 21

fatigue test protocol was successfully used with respect to the S-VECD formulation to capture 22

fatigue behaviour of all tested mixtures. 23

Keywords: Uniaxial, Asphalt Mixture, Fatigue, Viscoelastic, Continuum Damage. 24

1. INTRODUCTION 25

Fatigue cracking, associated with repetitive traffic loading over time, is considered to be 26

one of the most significant distress modes in flexible pavements besides thermal cracking and 27

rutting. Fatigue cracking is a progressive distress and can be divided into three different stages. 28

An early stage of fatigue cracking consists of intermittent longitudinal wheel path cracks. An 29

intermediate stage of fatigue cracking called alligator cracking because the cracking pattern 30

resembles an alligator’s skin. A final stage of fatigue cracking is disintegration when potholes 31

form. 32

The fatigue life of an asphalt pavement depends directly on the properties of the materials 33

in the mix plus the complicated microstructure of asphalt concrete mixture, which is related to 34

the aggregate size and gradation [1,2], binder grade [3], air voids and binder content [4,5], 35

temperature [6,7], rest period [8,9,10,11], aging [12,13,14], and additives [15,16,17,18,19,20]. 36

As a result, the fatigue properties of asphalt mixtures are very complicated and sometimes 37

difficult to predict. 38

There are two main approaches that can be utilized to characterize the fatigue behavior of 39

asphalt concrete mixtures: phenomenological and mechanistic. Mechanistic approach is 40

inherently more complex than the Phenomenological one but it is more widely accepted because 41

2

it uses material properties based on stress-strain relationships [21]. The mechanistic approach 1

can be implemented through three main methods; dissipated energy [22,23,24], fracture 2

mechanics [25,26,27], and continuum damage mechanics [28,29,30,31,32,33,34]. 3

Different test methodologies have been developed over the past few decades for 4

measuring the fatigue behavior of asphalt concrete mixtures such as the beam fatigue test 5

[35,36], cantilever rotating beam test [37], trapezoidal cantilever beam test [38], supported 6

flexure test [39], uniaxial direct-tension test [40,41,42,43], uniaxial tension-compression test 7

(40,44,45], indirect diametrical test [46,47], triaxial test [48,49], and wheel track test [38]. 8

As part of the NCHRP 9-44A project, a uniaxial fatigue test protocol was developed to 9

evaluate the fatigue damage and healing of asphalt concrete mixtures. The development test 10

protocol includes several studies to identify appropriate sample fabrication procedures, gluing 11

materials and procedures, alignment, machine compliance impacts, strain wave shape, and strain-12

controlled method [50]. The main objective of this study was to evaluate the fatigue behavior of 13

diverse conventional and modified asphalt concrete mixtures tested by a developed uniaxial 14

fatigue test method using the simplified-viscoelastic continuum damage (S-VECD) analysis. 15

This analysis enables the prediction of the fatigue life relationships under both stain and stress 16

controlled mode of loading with fewer experiments. 17

2. MIXTURES AND SPECIMENS PREPARATIONS 18

2.1 Description of Projects and Mixtures 19 In this study, the fatigue behavior of a diverse set of asphalt concrete mixtures from four 20

main projects was evaluated by performing both dynamic modulus |E*| test and uniaxial fatigue 21

tests. All the tested specimens were compacted in the laboratory using the Superpave gyratory 22

compactor. Project 1 included the testing of four 19-mm conventional dense graded mixtures at 23

combinations of two levels of air voids (4.5 and 9.5%) and two levels asphalt content (4.2 and 24

5.2%). The main objective of the first project was to investigate the effect of changing the 25

volumetric properties on the fatigue behavior of asphalt concrete mixtures. Project two included 26

the testing of three 19-mm gap graded Asphalt concrete mixtures. The first mixture was a control 27

while the second and the third were polymer-modified and rubber-modified asphalt concrete 28

mixtures respectively. The main objective of this project was to study the effect of polymer and 29

rubber additives on the fatigue performance of asphalt concrete mixtures. Project three included 30

the testing of two 9.5-mm dense graded mixtures. The first mixture was a standard dense graded 31

mixture while the second mixture was the same mixture, but modified with 19-mm long fibers. 32

The objective of project three was to evaluate the effect of adding fiber on the fatigue 33

performance of asphalt mixtures. Project four included the testing of two asphalt mixtures. The 34

first mixture was a regular 9.5-mm dense graded warm mix asphalt (WMA) mixture using 35

Evotherm additive while the second mixture was a newly used 12.5-mm gap graded rubber-36

modified WMA mixture. The main objective of this project was to compare the fatigue 37

performance of both mixtures in order to investigate the replacement of the first mixture with the 38

second newly used mixture. The asphalt mixtures of project one were mixed and short term aged 39

in the laboratory while asphalt mixtures for the remaining projects were sampled from actual 40

field projects and then compacted in the laboratory. Table 1 presents the aggregate gradation 41

while Table 2 shows the design volumetric properties of the different mixtures. 42

Two different specimen geometries were manufactured for each test. For the |E*| test, 43

gyratory plugs were compacted into 150 mm diameter and 170 mm tall specimens. Then, one 44

100 mm diameter sample was cored from each gyratory plug. The sample ends were sawn to 45

3

arrive at typical test specimens of 150 mm in height. For uniaxial tension-compression fatigue 1

test, the compaction height was increased to 180 mm and the final specimen dimensions were 2

150 mm height and 75 mm in diameter. The main reason to increase the compaction height was 3

to allow for larger end cuts to produce a more homogeneous air void distribution which increases 4

the chances to have a middle failure in the uniaxial fatigue test. 5

TABLE 1 Aggregate Gradation of Tested Mixtures 6

Sieve

Size

mm

% Passing

Project 1 Project 2 Project 3 Project 4

19-mm Dense

Graded

Conventional

Mixture

19-mm Gap

Graded

Control and

Polymer-

Modified

Mixtures

19-mm

Gap

Graded

Rubber-

Modified

Mixture

9.5-mm Dense

Graded

Conventional

and Fiber

Mixtures

9.5-mm

Dense

Graded

WMA

Mixture

12.5-mm

Gap Graded

Rubber

WMA

Mixture

25.4 100.0 -- -- --

22.4 100 100

19.0 95.0 -- -- 100

16.0 98.0 98.0

12.5 80.0 100 100 97.0

11.2 65.0 68.0

9.5 59.0 96.0 95.0 84.0

8.0 38.0 44.0

4.75 39.0 55.0 59.0 30.0

4.0 23.0 24.0

2.38 29.0 38.0 45.0 22.0

2.0 21.0 22.0

1.2 23.0 26.0 27.0 14.0

0.6 17.0 17.0 17.0 9.0

0.3 10.0 9.0 12.0 7.0

0.15 5.0 5.0 8.0 6.0

0.075 3.3 4.1 5.5 5.0

0.063 10.5 7.5

TABLE 2 Design Volumetric Properties of Tested Mixtures 7

Volumetric

Property Project 1

Project 2

Project 3

Project 4

Control Polymer Rubber WMA Rubber-

WMA

Binder Grade PG64-22 ABS16

70/100

ABS16

50/100-75 GAP16 PG64-22 PG76-22

PG64-

22AP

Target Asphalt

Content (%) 4.5 5.9 5.9 8.7 5.9 5.7 8.1

Theoretical Max.

Sp. Gr. (Gmm) 2.467 2.464 2.456 2.359 2.397 2.498 2.407

Design Air Voids

(%) 4.1 2.6 2.6 2.4 7.0 4 6

4

3. TEST METHODS 1

3.1 Dynamic Modulus Test 2 The |E*| tests, per AASHTO T342 were performed in the laboratory at five temperatures 3

-10, 4.4, 21.1, 37.8, 54.4 °C and six load frequencies: 25, 10, 5, 1, 0.5 and 0.1 Hz. The stress 4

levels were varied with the frequency to keep the specimen response within a linear viscoelastic 5

limit (recoverable microstrain below 150 microstrain). The test parameter values; dynamic 6

modulus and phase angle, were measured at different temperatures and frequencies. The average 7

dynamic modulus and phase angle values were summarized based on three replicates for each 8

mixture. Figure 1 shows a typical instrumented test specimens and the applied wave shape. 9

10

11

FIGURE 1 |E*| Test Setup and Applied Wave Shape 12

13

3.2 Uniaxial Tension-Compression Test 14 The first step prior to running the test included gluing end plates to the specimen using 15

the jig shown in Figure 2. The applied glue was Devcon plastic steel 5 minutes epoxy putty. The 16

test specimen was then instrumented with three LVDTs to monitor material response. The 17

uniaxial tension-compression fatigue test was conducted to evaluate the fatigue damage of the 18

tested mixtures using the viscoelastic and continuum damage model. A servo hydraulic testing 19

machine was used to load the specimens under an on-specimen strain-control mode of loading 20

(Figure 2). A sinusoidal strain (continuous wave) was applied. The test software was capable of 21

achieving and maintaining the target on-specimen strain based on the outputs from the three 22

LVDTs by dynamically changing the actuator strain level to solve the machine compliance issue. 23

New software was developed for Arizona State University by IPC (Industrial Process Control) 24

company and is designated as UST032-v1.01b S-VECD fatigue test [50]. The uniaxial tension-25

compression fatigue tests were conducted using two or more specimens for each mixture at 21.1 26

ºC. At each loading cycle, the software calculated the dynamic modulus and the phase angle plus 27

the stress and the strain values from the actuator and the three LVDTs. The uniaxial tension-28

compression fatigue test was run until a sudden decrease in phase angle is reached as possible. 29

30

5

1

FIGURE 2 Specimen Gluing Jig and Test Setup with Failed Specimen 2

4. TEST RESULTS 3

4.1 Dynamic Modulus Test Results 4 The |E*| master curves were constructed for the tested mixtures from the four projects as 5

shown in Figure 3. It can be observed from Figure 3(a) that the |E*| values were more 6

significantly affected by varying the air voids from 4.5 to 9.5% than by varying the asphalt 7

content from 4.2 to 5.2%. Figure 3(b) shows that at high test temperatures, the polymer- 8

modified mixture expressed the highest stiffness followed by the reference and rubber-modified 9

mixtures. In comparison, at low temperatures, the rubber-modified mixture had the highest 10

stiffness followed by reference and polymer-modified. The rubber-modified mixture exhibited 11

the lowest stiffness compared to the other two mixtures at 21 °C which is the test temperature 12

used for the uniaxial tension-compression test. Figure 3(c) indicates that for the particular 13

mixtures studied, the addition of fiber had almost no effect on the |E*| values. It can be observed 14

from Figure 3(d) that at lower and intermediate temperatures the rubber-modified WMA mixture 15

exhibits a lower |E*| values compared to the WMA mixture. However, at high temperatures, the 16

|E*| values of both mixtures are closer. This unique behavior of rubber-modified mixtures would 17

indicate an enhancement of their performance with respect to thermal and fatigue cracking at 18

lower and intermediate temperatures with a sensible rutting resistance at high temperatures. 19

20

21

6

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E-08 1.E-04 1.E+00 1.E+04 1.E+08

Dy

nam

ic M

od

ulu

s, k

Pa

Reduced Frequency, fr

4.2%AC, 4.5%Va

5.2 % AC, 4.5%Va

4.2 % AC, 9.5%Va

5.2 % AC, 9.5%Va

(a)

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E-08 1.E-04 1.E+00 1.E+04 1.E+08

Dy

nam

ic M

od

ulu

s, k

Pa

Reduced Frequency, fr

Control-Gap

Polymer-Modified

Rubber-Modified

(b)

1 2

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E-08 1.E-04 1.E+00 1.E+04 1.E+08

Dy

nam

ic M

od

ulu

s, k

Pa

Reduced Frequency, fr

Control

Fiber- Reinforced

(c)

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E-08 1.E-04 1.E+00 1.E+04 1.E+08

Dy

nam

ic M

od

ulu

s, k

Pa

Reduced Frequency, fr

WMA

Rubber-Modified WMA

(d)

3

FIGURE 3 Dynamic Modulus Master Curves of Tested Mixtures (a) Project 2; (b) 4

Project 2; (c) Project 3; and (d) Project 4 5

6

4.1 Uniaxial Fatigue Test Results 7 Table 3 includes a summary of the uniaxial tension-compression fatigue tests. It is 8

observed from this table that tensile strain levels were varied within the same project where it 9

was expected that the tested mixture would give totally different fatigue behavior. That judgment 10

was typically based on the relative difference in the dynamic modulus master curves. For only 11

project three, both control and fiber-reinforced mixtures were tested on the same strain level as 12

both exhibit similar dynamic modulus values. This issue does not affect the ability to make 13

comparisons between mixtures as measured data can be interpolated and/or slightly extrapolated 14

to the same conditions. The fingerprint data confirmed the findings from the dynamic modulus 15

tests, which can be seen by observing the |E*|FP column in Table 3. By comparing results of tests 16

conducted at close strain levels, it can be observed that the fatigue response asphalt concrete 17

mixtures in project one was not strongly affected by air void content (at a fixed strain level), but 18

did exhibit observable asphalt content effects. In project two, the polymer-modified and rubber 19

modified mixtures showed comparable fatigue performance and were better compared to the 20

control mixture. The results of project three showed the fiber-reinforced mixture exhibits a 21

superior fatigue resistance compared to the control mixture, however the dynamic modulus 22

values for both mixtures were similar. For project four, the new rubber-modified WMA as 23

expected showed an improved fatigue performance compared to the regular WMA mixture. It 24

7

was also noticed that the rubber-modified WMA mixture tolerated the highest tensile strain 1

levels among all the test mixtures with immense fatigue cycles. 2

3

TABLE 3 Uniaxial Fatigue Test Results for All Mixtures 4

Project

Number

Mixture

Type

Specimen

ID

Air

Voids

%

Tensile

Strain

με

|E*|FP

MPa

Machine

Compliance

Factor,

MCF

Initial

Stiffness

MPa

Initial

Degree

Cycles to

Failure, Nf

Project

1

4.2% AC,

4.5% Va

D-401 3.77 75 7856 5.74 6785.8 29.2 221,168

D-402 4.72 145 7598 5.29 5868.5 31.3 10,610

D-490 4.44 90 7711 4.55 6628.7 27.9 67,786

D-491 4.48 90 7295 4.50 6182.4 26.82 51,160

5.2% AC,

4.5% Va

D+402 3.46 105 7163 4.80 5812.2 31.2 201,846

D+404 3.37 175 6371 4.41 4624.1 34.3 28,404

D+406 3.54 75 6775 4.80 5828.2 32.5 676,100

D+449 4.79 122.5 6012 4.31 4684.3 33.0 140,182

D+461 3.94 122.5 6917 4.69 5732.5 28.4 166,602

4.2% AC,

9.5% Va

D-946 9.22 87.5 4468 3.46 3548.8 29.9 279,692

D-978 9.45 90 4639 3.45 3842.7 28.2 79,032

D-983 9.14 90 5301 4.27 3947.2 32.3 26,524

D-969 9.52 115 3712 2.83 2989.8 28.1 21,892

D-981 8.73 115 5030 3.58 4020.9 31.5 17,924

D-984 8.76 115 4970 3.56 3799.4 30.1 57,402

5.2% AC,

9.5% Va

D+943 9.52 95 3562 2.85 2822.4 31.4 213,804

D+944 8.92 125 4437 3.57 3330.5 31.2 137,514

D+948 9.34 200 4228 3.93 2460.6 36.3 2,940

D+949 9.99 187.5 3465 2.97 2264.3 39.0 9,090

D+961 9.66 155 4160 3.50 2986.3 34.6 57,402

D+9B2 9.34 155 3725 2.66 2847 33.5 49,234

Project

2

Control-

Gap

SWC03 3.65 125 10,978 6.78 8,609 25.3 131,830

SWC02 3.82 150 10,310 6.45 7,435 28.6 11,030

Polymer-

Modified

SWP05 3.55 150 8,479 5.08 6,707 21.8 138,570

SWP06 3.65 200 8,913 5.43 6,214 24.1 28,620

Rubber-

Modified

SWR04 2.81 150 6,710 4.45 5,296 24.9 126,380

SWR06 3.11 200 7,123 4.63 5,134 25.5 27,200

Project

3

Control PAC10 5.98 225 6,305 3.39 4,337 28.8 5,710

PAC11 6.07 225 6,613 4.06 4,888 26.4 10,000

Fiber-

Reinforced

PAF08 5.60 225 6,643 4.10 4,592 29.0 74,000

PAF09 5.51 225 6,084 3.86 4,261 29.2 134,000

Project

4

WMA PACW03 5.71 175 8,206 4.91 5,730 30.2 250,000

PACW11 6.42 250 6,708 4.09 4,873 31.2 98,480

Rubber-

WMA

PARW07 6.31 250 3,523 2.46 2,444 32.9 1,800,000a

PARW11 5.74 450 3,915 2.87 1,821 39.6 130,000b

a Test did not show reduction in phase angle and test was stopped 5 b 450 με was stopped at approximately 130,000 cycles and then strain levels were increased repeatidly until failure 6

5. DAMAGE CHARACTERISTIC (C-S) CURVE 7

The construction of C-S curves in this paper followed the most updated procedure to calculate 8

damage parameter, S [33]. For each mixture, the C-S curves were established from each test 9

sample. Then a single power model was fitted through the collapsed curves to represent the 10

model C-S curve for the mixture. A more favorable damage characteristic curve is the one that 11

8

has the greatest damage level for a given pseudo stiffness as it means that the rate of damage 1

growth for a given pseudo energy input will be less and thus the incremental loss in pseudo 2

stiffness will also be less. However, one cannot, or should not, use this curve alone to judge the 3

fatigue resistance of the three mixtures. Figure 4 shows the C-S curves of the mixtures for four 4

projects together. It can be observed from Figure 4(a) that, like the modulus response, the 5

damage characteristic relationship is more strongly affected by the 5% change in air void content 6

than it is by the 1% change in asphalt content. It can be also observed that mixtures with lower 7

air voids and higher binder contents produce favorable damage characteristic curve. Figure 4(b) 8

shows that the most favorably positioned damage characteristic curves are obtained from the 9

reference-gap and polymer-modified mixtures. 10

11

0.0

0.2

0.4

0.6

0.8

1.0

0.0E+00 2.0E+04 4.0E+04 6.0E+04 8.0E+04 1.0E+05

No

rmali

zed

Pse

udo

Sti

ffn

ess,

C

Internal State Damage, S

4.2%AC, 4.5%Va

5.2%AC, 4.5%Va

4.2%AC, 9.5%Va

5.2%AC, 9.5%Va

(a)

0.0

0.2

0.4

0.6

0.8

1.0

0.0E+00 5.0E+04 1.0E+05 1.5E+05 2.0E+05 2.5E+05

No

rmali

zed

Pse

udo

Sti

ffn

ess,

C

Internal State Damage, S

Control-Gap

Polymer-Modified

Rubber-Modified

(b)

12

0.0

0.2

0.4

0.6

0.8

1.0

0.0E+00 5.0E+04 1.0E+05 1.5E+05 2.0E+05 2.5E+05

No

rmali

zed

Pse

udo

Sti

ffn

ess,

C

Internal State Damage, S

Control

Fiber-Reinforced

(c)

0.0

0.2

0.4

0.6

0.8

1.0

0.0E+00 1.0E+05 2.0E+05 3.0E+05

No

rmali

zed

Pse

udo

Sti

ffn

ess,

C

Internal State Damage, S

WMA

Rubber-Modified WMA

(d)

13

FIGURE 4 Comparison of Damage Characteristic Curves for Study Mixtures (a) 14

Project 2; (b) Project 2; (c) Project 3; and (d) Project 4 15

16

It is interesting to observe in Figure 4(c) that both the control and the fiber-reinforced C-S 17

curves are very similar; however, the pseudo stiffness at failure, Cfailure, value for the control is 18

higher compared to the fiber-reinforced mixture. This may imply that the addition of fibers does 19

not appreciably change the internal structure of the mixture compared to other additives as 20

polymer and rubber. What may support this argue is the fact that the fiber has almost no effect on 21

the modulus obtained from either the dynamic modulus test or the uniaxial fatigue test. So, the 22

fiber role is to hold the microcracks which consequently delay the formation of the macrocracks 23

9

or the fatigue failure. For this particular mixture, microdamage that is affected by the fibers 1

might occur relatively late in the fatigue process, e.g., after a C value of approximately 0.4 has 2

been achieved. Figure 4(d) showed as anticipated that the rubber-modified WMA mixture 3

showed a favorable C-S curve compared to WMA mixture. 4

6. FATIGUE PERFORMANCE SIMULATION 5

Damage curves alone are not sufficient to judge the fatigue resistance of an asphalt 6

concrete mixture since they only indicate the resistance to damage. Under a given external 7

condition (i.e., load level or deformation magnitude, temperature, frequency of loading, and load 8

shape) the amount of pseudo strain energy created will vary by mixture. Therefore, one must 9

consider the damage curves and the |E*| of a mixture in order to evaluate its fatigue resistance. 10

The implication of this situation is simply that in order to gain useful information on fatigue 11

performance, one must perform simulated predictions of the fatigue life at specific conditions of 12

interest. In this paper, the simplified-viscoelastic continuum damage (S-VECD) theory is used to 13

derive formulas for predicting the material response to fully reversed constant stress and constant 14

strain loadings [33]. There formulas were verified using independent laboratory experiments and 15

showed good prediction of fatigue life [51]. 16

In this paper, only the simulation results for the controlled strain condition at 21 °C and 17

10 Hz frequency are presented as shown in Figure 5. In Figure 5(a), it is seen that there is little 18

overall effect from the 5% air void content change, but a noticeable effect from the 1% change in 19

asphalt binder content. Since the conditions simulated for these figures are very similar to the 20

experiments, this finding is not surprising. It is observed from Figure 5(b) that overall the asphalt 21

rubber mixture is expected to yield a longer laboratory fatigue life. Figure 5(c) showed a superior 22

fatigue resistance for the fiber-reinforced mixture compared to the control mixture however both 23

showed similar modulus values and C-S curve. Figure 5(d) showed that the addition of the 24

rubber to the WMA mixture enhance the fatigue behavior. 25

7. DISCUSIONS AND CONCLUSIONS 26

This paper presented research performed to compare properties and fatigue performance 27

characteristics of diverse asphalt mixtures from laboratory studies and field projects. The data 28

were used to compare the performance of the mixtures within each project using the simplified-29

viscoelastic continuum damage (S-VECD) approach. 30

Results from project one showed as expected that increases in asphalt content and air 31

voids reduced the modulus of the material. A 5% change in air void content was found to more 32

strongly affect the modulus of the study mixture than a 1% change in asphalt content. Controlled 33

on-specimen strain fatigue tests were also showed that the fatigue performance of the study 34

mixture was more strongly affected by the 1% change in asphalt content than the 5% change in 35

air void. The simulated fatigue behavior predicted in accordance with the viscoelastic continuum 36

damage theory supported the experimental findings for controlled strain loading. 37

For project two, dynamic modulus test results indicate that, at high test temperatures, the 38

polymer- modified mixture expressed the highest stiffness followed by the reference and rubber-39

modified mixtures. In comparison, at low temperatures, the rubber-modified mixture had the 40

highest stiffness followed by reference and polymer-modified. The S-VECD analysis clearly 41

showed the benefits of the rubber modified mixture in terms of laboratory fatigue resistance. 42

10

It was interesting in project three that both fiber-reinforced and control mixture showed 1

similar modulus and C-S curve, however the fatigue life of the fiber-reinforced mixture was 2

higher compared to the control mixture. That was mainly due to the elongated C-S curve of the 3

fiber-reinforced mixture compared to a shorter damage curve for the control mixture. 4

For the tested mixture in project four, the rubber-modified WMA mixture showed a 5

tendency to resist cracking and rutting more than the regular WMA by showing lower dynamic 6

modulus at low and intermediate temperature and meantime similar modulus to the WMA 7

mixture at high temperature. Both the uniaxial test result and the S-VECD analysis showed that 8

the rubber-modified WMA expressed much better fatigue resistance compared to the WMA 9

mixture. Overall, the results showed that the rubber-modified WMA mixture is by far the best 10

fatigue resistance mixture followed by the fiber-reinforced mixture. 11

In conclusion, the S-VECD analysis represents a more powerful tool to evaluate fatigue 12

resistance than the traditional method of examining only the number of cycles necessary to reach 13

a certain stiffness reduction. Such approaches inherently smear the effects of modulus and 14

damage into the analytical result. The rationality of the model with regards to air void content 15

and asphalt content changes as well as the effect of using different additives has been examined 16

in this paper. In addition, these results showed that the developed uniaxial fatigue test method 17

was successfully able to capture the true fatigue behavior of the assorted tested mixtures. 18

19

1.E+01

1.E+02

1.E+03

1.E+02 1.E+04 1.E+06 1.E+08

Ten

sile

Str

ain

(μ

ε)

Number of Cycles to Failure

4.2% AC, 4.5% Va

5.2% AC, 4.5% Va

4.2% AC, 9.5% Va

5.2% AC, 9.5% Va

(a)

1.E+01

1.E+02

1.E+03

1.E+02 1.E+04 1.E+06 1.E+08

Ten

sile

Str

ain

(μ

ε)

Number of Cycles to Failure

Control-Gap

Polymer-Modified

Rubber-Modified

(b)

20

1.E+01

1.E+02

1.E+03

1.E+02 1.E+04 1.E+06 1.E+08

Ten

sile

Str

ain (

με)

Number of Cycles to Failure

Fiber-Reinforced

Control

(c)

1.E+01

1.E+02

1.E+03

1.E+02 1.E+04 1.E+06 1.E+08

Ten

sile

Str

ain

(μ

ε)

Number of Cycles to Failure

WMA

Rubber-Modified WMA

(d)

21 22

FIGURE 5 Simulation Results for Controlled Strain Test (a) Project 1; (b) Project 2; 23

(c) Project 3; and (d) Project 4 24

11

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18