Fatigue of asphalt binder, mastic and mixture at low temperature

RESEARCH ARTICLE

Fatigue of asphalt binder, mastic and mixture at lowtemperatureDong WANGa,*, Linbing WANGb, Guoqing ZHOUc

a Virginia Tech Transportation Institute, Blacksburg VA 24061, USAb The Via Department of Civil and Environmental Engineering, Virginia Polytechnic Institute and State University, Blacksburg VA

24061, USAcGuangxi Key Laboratory for Spatial Information, Guilin University of Technology, Guilin 541004, China*Corresponding author. E-mail: [email protected]

© Higher Education Press and Springer-Verlag Berlin Heidelberg 2012

ABSTRACT The fatigue damage is one of the most common distresses observed on the asphalt concrete pavement. Tothoroughly understand the fatigue of asphalt concrete, the behaviors of the major components of asphalt concrete undercyclic loading are investigated respectively in this study. A new experiment method is developed to evaluate theperformances of asphalt binder, mastic and fine aggregates mixture under cyclic tensile loading. The fatigue test results ofasphalt binder show that the fatigue performance of asphalt binder is closely related with loading magnitude, temperatureand loading rate. Mastic specimens with different filler content are tested and the results indicate that mastic specimenswith 30% filler content show better fatigue resistance and higher permanent strain. The micro-structure analysis of masticand mixture indicates that the fatigue resistance is closely related with the air void content of specimen. 3D digitalspecimens are developed to model the fatigue of the asphalt binder, mastic and mixture specimens based on the finiteelement method (FEM). Fatigue damage of asphalt concrete is simplified by a damage model. With proper selection ofdamage parameters, the simulation results agree well with laboratory test results and can be used as a basis for futurefatigue research.

KEYWORDS fatigue, asphalt mixture, asphalt binder, mastic, finite element method (FEM), X-ray tomography

1 Introduction

Asphalt concrete pavement is susceptible to crackingdamages. Micro-cracks usually initiate deep within thepavement structure where detection is very difficult. Due tothe repeated external loading, these invisible micro-crackspropagate and connect to each other, leading to mechanicaldegradation of asphalt materials. The micro-cracks accu-mulate until visible cracks appear. Then maintenance andrehabilitation work become mandatory and extremelycostly. Fatigue cracking is one of the main crackingdamages observed on the asphalt concrete pavements. It isdefined as failure of pavement structure due to repeatedstresses which are not large enough to cause immediatefracture. Generally, fatigue cracking is described as a

process where micro-cracks accumulate and connect toeach other until visible cracks are formed and thenpropagate through the pavement. This is a complicatedphenomenon because the initiation and propagation offatigue cracking is very difficult to detect. To thoroughlyunderstand the mechanism of this distress, an investigationof each component of the asphalt mixture during thefatigue process is necessary. Aggregate is a majorcomponent forming the skeleton of the asphalt mixture.Due to the high stiffness, damage of aggregate caused byfatigue is very limited. Compared with the aggregate, thestiffness and strength of the binding medium are muchlower which make the binding medium among aggregatesmore vulnerable and sensitive to fatigue damage. In thiswork, the fatigue behaviors of binding medium includingasphalt binder and mastic will be evaluated. The fatiguebehaviors of binding medium will be compared with theasphalt mixture using a unified test methodology with theArticle history: Received Dec. 21, 2011; Accepted Apr. 9, 2012

Front. Struct. Civ. Eng. 2012, 6(2): 166–175DOI 10.1007/s11709-012-0157-7

X-ray tomography incorporated. A model based on FEM isdeveloped to simulate the fatigue of asphalt materials andwill serve as a basis for further research.

2 Background

Traditional research about the fatigue of asphalt mixturewas focus on the theoretical model development andexperimental test to evaluate the fatigue life of asphaltmixture. The major theoretical models can be classifiedinto four categories: Experiment-dependent models [1],Models based on dissipated energy concept [2–6], modelsbased on fracture mechanics [7–13] and models based ondamage mechanics [14–19]. Other theoretical models usedto describe the fatigue of the asphalt mixture include thedamage model based on mixture bonding energy [20],artificial neural network approach [21] and fuzzy-logicalapproach [22].As the major laboratory test method to evaluate the

fatigue properties of the asphalt mixture, repeated flexuralbending test recommended by American Association ofState Highway and Transportation Officials (AASHTO) iswidely used in the research of the asphalt concrete fatigue[23–28]. However, research about fatigue of asphalt binderand mastic is much less compared with fatigue researcheffort to asphalt mixture. One main reason that keptresearchers from focusing on the asphalt binder fatigue isthat it is challenging to apply repeated loading to the stickyasphalt binder. Although Strategic Highway ResearchProgram (SHRP) has accepted Dynamic Shear Rheometer(DSR) as the experimental tool to evaluate the fatigueproperties of asphalt binder, some research has shown thatthere exist limitations with using the DSR as test method tostudy the fatigue properties of asphalt binder [29–31].Since most of the research about the fatigue of asphaltmastic is also conducted using DSR [32,33], the under-standing of fatigue properties of binding medium will be

affected due to these limitations. Furthermore, as onecommon form of fatigue damages, the top-down crackingis generally caused by tensile loading which is not capablefor the DSR test. Another disadvantage of DSR test is thatthe asphalt mixture specimen cannot be tested in DSR,which makes the test method of asphalt mixture andbinding medium not unified. An important initiative of thisstudy is to develop a test device which is able to applycyclic tensile loading on both binding materials and asphaltmixture.

3 Methodology

3.1 Experiment design

Direct Tension Tester (DTT) from Interlaken Company(Fig. 1(a)) provides a software package, Test Builder (TB),which is able to develop customized test procedure forusers. It configures the DTT machine to step through userdefined test procedure and build up a user-defined test (Fig.1(b)). Loading mode option of the TB enables a cyclictensile loading to be applied on the specimen with loadinglevel and loading frequency specified. The test temperatureis controlled by a climate chamber.For the new fatigue test procedure developed in this

work, there are four major steps. First, a small loadingcommand, 0.01 N, is given so that the driving motor can besmoothly started. The loading rate is a relatively smallvalue 0.01N/s. When the desired load is reached, the testproceeds to the next step in which a 2 N loading is appliedon the loading end of the specimen at a rate of 0.1N/s (Fig.1(c)). A good contact between loading pin and thespecimen is achieved by the application of the loading.After the desired load value is reached, the test proceeds tothe next step. Both the loads applied on the loading end andthe axial displacements of specimen are measured after thisstep. Then, a stress-controlled fatigue test is started and a

Fig. 1 (a) Direct tension tester; (b) main screen of the tester builder; (c) loading end of the load frame

Dong WANG et al. Fatigue of asphalt binder, mastic and mixture at low temperature 167

cyclic tensile loading is applied at this step from level 1 tolevel 2 following a sinusoidal curve. Level 1, which is thelower loading level of the sinusoidal loading, is 2 N whichis the same with the previous step. Level 2 is the peak valueof the sinusoidal loading, which will be determined later.The frequency of the cyclic loading is also specified. Aftercertain number of loading cycles, the specimens break andthe results data including both loading history and axialdeformation of the specimen during the test process areautomatically recorded. The axial deformation of thespecimen can be used to calculate the axial strain of thematerial after the fatigue process.

3.2 Sample preparation

The asphalt binder, mastic and mixture specimens areprepared respectively following similar specimen prepara-tion procedure for direct tension test [34]. The asphaltbinder used in the fatigue test is PG70-22 binder based onsuperpave binder specification. The binder is heated at300°F (149°C) for 45 min and then poured into the bone-shaped specimen mold used for direct tension test (Fig. 2).The effective length of the specimen is 0.04 m and thecross section of the specimen is a square with area36�10–6 m2. Asphalt mastic specimens are prepared bymixing those very fine aggregates referred as fillers andheated asphalt binder. The major component of the fillers isquartz which is very common in fine aggregates. The sizeof the filler is smaller than 0.075 mm controlled by #200sieves. The amount of the fillers added into the binder iscontrolled by the weight ratio between the filler and asphaltbinder. For the preparation of asphalt mixture specimen,the sizes of the aggregates added into the asphalt binder orasphalt mastic to prepare the mixture specimen are limitedsince the size of the specimens is determined by thespecimen mold. So, relatively fine aggregates passingthrough #4 sieves but retained on #35 sieves are used toprepare asphalt mixture specimen in this study, which have

a size ranging from 0.5 to 4.76 mm. Since limited sizeaggregates are used, the amount of aggregates added intothe asphalt binder and mastic specimen is not controlled bygradation curve but by the weight ratio between theaggregates and asphalt binder. After the samples areprepared, the climate chamber is turned on. The climatechamber will reach the specified test temperature fortesting. The samples are placed into the climate chamberfor one hour conditioning and then placed on the loadingframe to perform the fatigue test procedure describedabove.

3.3 Digital test development

To obtain the internal structure of the mastic and fineaggregates mixture, specimens are scanned using X-raytomography system SkyScan 1174. SkyScan 1174 (Fig. 3)is a compact X-ray CT system with 6 um spatial resolutioncapability. The maximum X-ray source energy of thesystem is 50 kV and it scans sample up to 30 mm indiameter and 50 mm in length. Since the temperature of theX-ray system cannot be controlled and it is observed thatthe asphalt materials deform quickly in room temperature,only a 10mm long section of each kind of specimens is cutand scanned to avoid any significant deformation causedby long scanning time and self-weight of the specimen.Both mastic and mixture specimen are scanned at roomtemperature. After the scanning process is finished, a seriesof 2D images showing the cross-section of the specimenwill be obtained. The scanned images are processed using adeveloped MATLAB code for the mesh generation ofdigital specimens used in the further FEM–based simula-tion. The basic principle to reconstruct the 3D internalstructure of a specimen is as following: the X-rayattenuation is different for each component of the material;pixels on the images belonging to different components ofthe mixture have different values. For a binary image, thepixel value range is from 0 to 255, 0 refers to black and 255

Fig. 2 Preparation of asphalt binder specimen Fig. 3 SkyScan 1174 compact CT system

168 Front. Struct. Civ. Eng. 2012, 6(2): 166–175

refers to white. Dense materials such as aggregates areshown as brighter pixels and the pixel value is close to 255.Air voids with negligible density are shown as darkerpixels and the pixel value is close to 0. The binder whichhas an intermediate density is shown as gray color. Twothreshold values are determined to discriminate these threemajor components of the asphalt mixture material. Thehigher threshold value determines all the pixels belongingto the aggregates and fillers, while the lower thresh holdvalue determines all the pixels belong to air voids. The restpixels with values between the higher and lower thresholdvalues represent the asphalt binder. In this work, since theair void content of the small size specimen cannot bemeasured directly, the pixels with pixel value lower than70 are considered as air voids. The higher threshold valueis determined by a trial and error process. For each masticor mixture sample, the weights of the asphalt binder, fillersand aggregates are measured. The density of binder used inthis study is 1.03 g/cm3 and the density of the quartz fillersand limestone aggregates are same which is 2.56 g/cm3. Apreset higher threshold value is given and all the pixelshave value larger than this are counted. All the pixels havepixel value lower than 70 are also counted. The rest of thepixels are belonging to asphalt binder. Based on thestereology theory [35], the area of an object in a 2D imagecan be extended to give volume of the object. The volumesof the asphalt binder and aggregates are obtainedrespectively. The weight ratio of aggregates and fillersover asphalt binder can be calculated with knowndensities. Repeat this process as many as necessary untilthe calculated weight ratio from the image processing isequal to the weight ratio used in the laboratory test.The developed Matlab code gives element and node

information required for FEM modeling through amapping between the 3-D reconstructed voxel and FEMmesh (Fig. 4).

4 Results

4.1 Fatigue test of asphalt binder

Fatigue of asphalt binder is measured under differentloading and environmental conditions. The direct tensiontest provides the tensile strength of the asphalt binderspecimen at a specified temperature. With known effectivecross-section area of a specimen, the maximum tensileloading can be applied on a specimen is calculated. Thepeak value of the cyclic tensile fatigue loading is set to be75% of the maximum tensile loading. In this work, asphaltbinder specimens are tested at three different loadinglevels, three test temperatures and three loading rates. Thefinal axial strain and number of loading cycles aredocumented. For each test condition, three specimens areprepared and tested respectively; average results for threespecimens are calculated. Each test condition andcorresponding fatigue test results for each group ofspecimens are listed in the Table 1. External loading isclosely related with the fatigue performance of asphaltbinder. At lower loading level, asphalt binder shows betterfatigue performance. It is also found that the fatigueresistance of asphalt binder increases significantly whenthe test temperature increases, the fluid behavior of asphaltbinder is more dominant at higher temperature whichmakes the specimen less sensitive to cyclic loading.Compared with loading level and temperature, the

Fig. 4 Image processing and 3D reconstruction


influence of loading rate is not very significant at lowtemperature. The number of loading cycles and final strainslightly decreases when the loading rate is increased.

4.2 Effect of filler content to the fatigue of asphalt mastic

Mastic specimens are prepared with different fillercontents. The weight ratio between the filler and asphaltbinder is ranging from 10% to 50%. The peak value of thecyclic loading applied on the mastic specimen, testtemperature and loading frequency are same with thefirst group of asphalt binder specimens for comparison,20N, – 20°C and 0.5 Hz respectively. Three specimens areprepared and tested for each kind of mastic. The averagetest results are listed in the Table 2. It is found that theintroduction of the fillers changes the fatigue property ofthe asphalt binder significantly. Both the final strain and thetotal number of loading cycles are increased comparedwith asphalt binder specimen. It is also found that the

fatigue resistance of the mastic is not linearly increased asthe filler content increases. The final strain and number ofloading cycles reach the maximum values when the masticcontains 30% of fillers (Fig. 5). It is also observed thatwhen the filler content of mastic is higher than 50%, themastic specimen becomes brittle and the fluidity decreasessignificantly which causes failure of sample preparation.

4.3 Fatigue of fine aggregates asphalt mixture

Two kinds of asphalt mixture samples are prepared forfatigue test. One is asphalt binder directly mixed withlimestone aggregates, while the other is asphalt bindermixed with both quartz filler and limestone aggregates.The amount of aggregates added into the asphalt binder iscontrolled by the weight ratio between aggregates andasphalt binder, which is 50% for both kinds of mixture inthis work. The peak value of cyclic loading, testtemperature and the loading rate are same with previoustests for mastic. Three specimens are prepared and testedfor each kind of asphalt mixture. The average final strainand number of loading cycles for each kind of asphaltmixture are listed in the Table 3. It is found that theaddition of aggregates into the asphalt binder improves thefatigue resistance of asphalt binder. However, the perfor-mances of asphalt mixture are very different due to theaddition of the fillers. The addition of the fillers strengthensthe material and forms a better skeleton together withaggregates so the mixture with fillers added retains higherstrain level and larger number of loading cycles.

4.4 Micro-structure analysis of asphalt mastic and mixture

From the fatigue test results shown above, it can be seenthat both the fillers and fine aggregates added into theasphalt binder improve the fatigue resistance of thematerial. However, the performances of the asphalt masticand fine aggregates mixture are very different. Comparedwith mastic specimen, the mixture specimen composed ofasphalt binder and fine aggregates does not necessarilyshow better fatigue resistance. An important reason of this

Table 1 Fatigue test results of asphalt mastic

mastic filler content average final strain average number of load cycle

10% 0.0475 10559

15% 0.0536 13142

20% 0.0587 16395

25% 0.0660 17531

30% 0.0684 19208

35% 0.0666 18529

40% 0.0652 17457

45% 0.0614 16417

50% 0.0592 15484

Table 2 Fatigue test results of two kinds of mixture

specimen average final strain average number of loadingcycles

mixture with no filler 0.0275 8647

mixture with 30% filler 0.0459 12227

Fig. 5 Fatigue test results of mastic with different filler content


phenomenon is that compared with fillers, the texture andangularity of these fine aggregates are more complicatedwhich may cause the bonding problem between the asphaltbinder and aggregates so that the structure becomes morevulnerable to the fatigue loading. It is also observed thatthe addition of fillers helps to form a better structureskeleton together with aggregates and makes the mixturemore resistant to the fatigue damage.A further work is conducted to analyze the internal

structure of the asphalt mastic and asphalt mixturespecimens. Three kinds of specimens are scanned usingX-ray tomography system SkyScan 1174 respectively:mastic with 30% fillers, mixture with 30% fillers andmixture without fillers. After the 2D scanned images ofeach kind of material are obtained, 3D internal structure ofthe specimen is reconstructed. With same lower thresholdvalue, the elements belonging to air voids are counted foreach kind of specimen. The percentage of air voidselements is calculated. Three specimens are prepared foreach kind of material. 100 slices of scanned images areused to reconstruct the 3D model. It shows that asphaltmixture with no filler has 11.09% elements counted as airvoid, mixture with 30% filler has 4.75%, 30% filler mastichas lowest air void content among three kinds of materials,3.18%. Considering the fatigue test results of three kinds ofmaterial, the air void content is an important factor to affectthe fatigue resistance of the material. The asphalt masticspecimen, with lowest air void content among three kindsof materials, reaches the highest final strain and largestnumber of loading cycles. When the large size aggregatesare added, the air void content is increased and causes thedecrease of the fatigue resistance. The air voids can beconsidered as one of main sources of the initial microcracks, the material is more vulnerable to the fatigueloading with higher air void content.

4.5 Fatigue simulation in FEM

The fatigue tests of asphalt binder, mastic and mixture aresimulated using FEM-based software ABAQUS. Asphaltmastic and mixture are modeled as heterogeneousmaterials in which aggregates/filler and asphalt binderare treated with different constitutive models. The internalstructures of specimens are obtained through the imageprocessing and 3D mesh reconstruction. The air voidelements are removed in the model. 8-node linear brickelement is used to represent the voxel generated from 3Dmesh reconstruction. Fillers and aggregates are considered

as linear elastic materials with high stiffness. The elasticmodulus is 50 GPa and Poisson’s ratio is 0.25 for bothaggregates and filler. Considering the elastic behavior andthe unrecoverable deformation of the asphalt binderspecimen at this low temperature, an elasto-plastic modeldeveloped by Lemaitre and Chaboche [36] is used todescribe the mechanical behavior of asphalt binder. Theelastic part of the model is determined by elastic modulusand Poisson’s ratio. In this work, the elastic modulus ofasphalt binder is calculated from the linear part of thestress-strain curve which is 0.27 GPa, the Poisson’s ratio is0.35. The plastic part of the model is described by acombined isotropic/kinematic hardening model. The iso-tropic hardening component describes the change of thesize of the yielding surface as a function of equivalentplastic strain and the kinematic hardening componentdescribes the translation of the yield surface in stress spacethrough the backstress α. The isotropic component of themodel is expressed as below:

�0 ¼ �j0 þ Q1 1 – e – bεpl

� �, (1)

where σ0 is the size of the yield surface, σ|0 is the yieldstress at zero plastic strain, Q1 is the maximum change inthe size of the yield surface and b is the rate at which thesize of the yield surface changes as plastic strainingdevelops, εpl is the equivalent plastic strain.Determination of the model parameters is challenging,

details of the parameter calibration method can be found inthe ABAQUS Analysis User’s Manual [37]. For this newfatigue test procedure, the first half cycle is a unidirectionaltension process. Using the TB, this monotonic tensile testis conducted before the cyclic fatigue test. The initialyielding stress σ|0 can be determined at the point where theplastic deformation starts and the stress-strain curvebecomes nonlinear (Fig. 6). The average initial yieldingstress for three binder specimens tested is 0.45MPa. Thestress-strain data from last half cycle of cyclic tensile testfor three asphalt binder specimens are used to calculate thefinal yielding stress. The average result of three specimensis 0.81MPa. So the maximum change of yielding stress,Q1, is 0.36MPa. Every point after the initial yieldingpoint experiences both elastic and plastic strains. Theplastic part of the strain is calculated using Eq. (3).

εpli ¼ εi –�i

E, (2)

where εpli is the plastic strain, εi is the measured total strain,

Table 3 Plastic model parameters of asphalt binder

isotropic component �j0 Q1 b

0.45Mpa 0.45MPa 70

kinematic component σ1 εpl1 σ2 εpl2

0.4528Mpa 2.19�10–4 0.5151 9.97�10–4


σi is the measured total stress and the E is the elasticmodulus.In this uniaxial tensile fatigue test, the specimen is

stretched along the loading direction, so the equivalent

plastic strain εpli is equal to the plastic strain εpll . It isassumed that the very next point after initial yielding is onthe yield surface so the stress value of the point is σ0 .With

known σ0, σ|0, Q1, and plastic strain εpll , the parameter b iscalculated based on Eq. (1). The parameter b used in thiswork is 88.The kinematic component of the elasto-plastic model is

expressed as

_α ¼ C _εpl1

�0 � – αð Þ – γα _εpl, (3)

where C is the initial kinematic hardening modulus. εpl isthe equivalent plastic strain. σ0 is the size of the yieldingsurface defined in the isotropic hardeing component. γ isthe parameter which determines the rate at which thekinematic hardening modulus decreases with increasingplastic deformation. C and γ need to be determined todefine the evolution of the backstress α. The first half cycledata of the fatigue test are used to calibrate C and γ. Foreach data point (σi, εi) after the initial yielding, a value of αcan be calculated using Eq. (4).

αi ¼ �i –�0i , (4)

where �0i is the size of the yield surface at the

corresponding plastic strain for the isotropic hardeningcomponent. Integration of the backstress evolution lawover a half cycle yields the expression

αi ¼C

γð1 – e – γεpli Þ: (5)

As described before, the first half cycle of the fatigue testis a unidirectional tension process, the equivalent plasticstrain equals to the plastic strain which can be calculated

based on Eq. (2). With known αi and corresponding εpll , theC and γ can be determined. The very first point after initial

yielding and the end point of the half cycle are used tocalculate C and γ. The stress and corresponding plasticstrain used to calculate C and γ in this study are

σ1 = 0.4528MPa, εpl1 ¼ 2:19� 10 – 4, σ2 = 0.5151MPa,

εpl2 ¼ 9:97� 10 – 4. In Abaqus codes, these two pairs ofstress-strain data are inputs to calibrate parameters C and γ.All the parameters for the plastic part of the model ofasphalt binder are summarized in the Table 4.The fatigue damage of the asphalt binder is addressed by

using a damage model developed by Darveaux [38]. Thestiffness of the asphalt binder decreases once the fatiguedamage initiates. The fatigue damage initiates due to stressreversals and the accumulation of inelastic strain. Themodel is described by

N0 ¼ c1Δwc2 , (6)

where c1 and c2 are material constants. Δw is inelastichysteresis energy.The damage evolution is modeled by the rate of the

damage in a material point per cycle which is given by

dD

dN¼ c3Δw

c4

L, (7)

where c3 and c4 are material constants, and L is thecharacteristic length associated with an integration point.Dis damage variable which describes the stiffness decreaseof the material. The characteristic length L is determinedby the element geometry and formulation. For the firstorder element, it is typical length of a line across anelement.At any given loading cycle during the analysis the stress

σ in the material is given by the scalar damage equation

� ¼ ð1 –DÞ�, (8)

where � is the effective stress tensor when there is nodamage in the material. The load carrying capacity of thematerial is lost when D = 1.The parameters c1 c2 c3 c4 govern the fatigue damage

initiation and propagation of the model. Since it is notapplicable to scan the specimen when the fatigue test is inprogress, the damage model parameters c1 c2 c3 c4 cannotbe obtained directly from laboratory test results. Thedamage parameters used for joint solder material inDarveaux’s work are initially used. Same with theboundary condition of the laboratory fatigue test, cyclictensile loading is applied on the loading end of the beammodel along the axial direction. The other end of the beamsample is fixed in all degree of freedom. (Fig. 7). Thecyclic loading is following a sinusoidal curve where thepeak load and the loading rate are specified to be same withthe laboratory test condition. The loading level and numberof loading cycles applied in the simulation are as same aslaboratory fatigue test for each kind of specimen. Since thespecimen is tested in the environmental chamber which is


filled with ethanol and the self-weight does not cause anysignificant deflection of the specimen in the verticaldirection, the weight of the specimen is not considered inthe model. When the model reaches the same number ofloading cycles, the axial strain predicted by the model iscompared with laboratory test results. And the damageparameter c1 is determined when the simulation resultsagree with the laboratory test results. Similarly, the fatiguetests of mastic and mixture are also simulated. Mastic with30% fillers and mixture with 30% fillers are selectedrespectively for simulation. Since it is assumed that thefatigue damage occurs in the asphalt binder material only,c1 used for mastic and mixture model is much larger thanthe asphalt binder considering the introduction of theaggregate/filler elements makes the fatigue damage muchharder to initiate. The damage model parameters used andcorresponding simulation results of axial strain of eachmodel are listed in the Table 4. The percentage of asphaltbinder element whose stiffness is totally lost during thefatigue process is also listed in the table. The simulationresults of axial strain are compared with the laboratory testresults of axial strain for each kind of specimen. It can beseen that with same number of loading cycles, the axialstrain predicted by the models agree reasonably well withlaboratory test for each kind of specimen. In the numericalmodel, the number of loading cycles applied is same withthe laboratory test when the specimen fails. It is shown inthe model that most of the asphalt binder lost theirstiffness. With proper selection of model parameter, thecomplicated fatigue process of asphalt materials ismodeled by a relatively simple method. With the property

parameters calibrated by the laboratory test, the developeddigital specimen and digital fatigue test can serve as a basisfor further fatigue research in the future.

5 Conclusions

In this work, fatigue behavior of asphalt binder, mastic andmixture with fine aggregates at low temperature areinvestigated. The DTT from the Interlaken Company isaltered to develop a new fatigue test procedure which isable to apply cyclic tensile loading on the specimenprepared by the mold used for direct tension test. Theoutputs of the fatigue test are the number of loading cyclesand final axial deformation of the specimen when it breaksunder cyclic loading. The axial deformation is used tocalculate the axial strain of the specimen. The newdeveloped fatigue test provides a tool to evaluate thefatigue performance of the binding materials. It appliescyclic tensile loading which is believed to be majormechanism to cause fatigue damage. It also offers a unifiedmethodology to test the fatigue behaviors of bindingmaterials and mixture. FEM-based software ABAQUS isused to simulate the fatigue tests for different materials.Incorporated with X-ray tomography technology, theinternal structures of mastic and mixture specimens areobtained and used for the mesh generation of numericalmodels. The models are heterogeneous composites whichdescribe the aggregates, filler and asphalt binder withdifferent mechanical models. Fatigue damage caused bycyclic loading is addressed by a damage model applied toasphalt binder elements. Major finding of this researchinclude: 1) Fatigue behavior of asphalt binder is closelyrelated with external loading level, temperature, andloading rate. High external loading always causes morefatigue damage. When the temperature increases, theasphalt binder shows more fluid-like behavior and holdslonger number of loading cycles. The impact of loadingrate is not as obvious as loading level and temperature atthe test temperature, – 20°C. 2) The addition of fillerimproves the fatigue resistance of asphalt binder signifi-cantly which indicates that the mastic plays an importantrole in the fatigue resistance of binding materials. 3) Thefatigue performance of the mastic is closely related withthe filler content; mastic with 30% filler reaches the highestnumber of loading cycles and final strain when the

Table 4 Damage model parameters and simulation results

specimen damage parameterc1

damage parameterc2

damage parameterc3

damage parameterc4

laboratory test result ofaxial strain

simulation result ofaxial strain

asphalt binder 1750 – 1.45 5 1.15 0.0196 0.0221

asphalt mastic(30% filler)

10000 – 1.45 5 1.15 0.0656 0.0684

asphalt mixture(30% filler)

16500 – 1.45 5 1.15 0.0429 0.0459

Fig. 7 FEM simulation of fatigue test


specimen fails. 4) Mixture with fine aggregates also hasbetter fatigue performance than the asphalt binder.However, addition of fine aggregates into the masticspecimen does not necessarily improve the fatigueperformance of mastic. Micro-structure analysis of twokinds of specimens shows that the air void content is muchhigher in the mixture than the mastic which indicates thatthe large size aggregates introduces more air voids andweaken the bonding between aggregates and asphaltbinder. 5) The asphalt binder is described by an elasto-plastic model and the model parameters are quantitativelydetermined using laboratory test. The complicated fatigueprocess of asphalt mastic and mixture is simply modeledby using a damage model, with proper model parameterselection, the simulation results agree well with laboratorytest results. The developed digital specimen with labora-tory test determined material property and digital testprovide a basis for further fatigue research of asphaltmaterials.

Acknowledgements This paper was financially supported by GuangxiGovernor Grant under approval number of 2010-169, the National NaturalScience Foundation of China under Grant number of 41162011, GuangxiGrand Natural Science Foundation under contract number of2011GXNSFD018001, Guangxi Grand Natural Science Foundation underthe number of 2012GXNSFCB053005, and the grant of the Guangxi KeyLaboratory of Spatial Information and Geomatics under contract number,GuiKeNeng110-31-08-01. The authors would like to thank those who havegiven us technical advices and help in experimental design.

References

1. Ghuzlan K A, Carpenter S H. Traditional fatigue analysis of asphalt

concrete mixtures. In: Presented at the 2003 Annual Meeting of the

Transportation Research Board. Washington, D C, 2003

2. Aglan H A, Figueroa J L. Damage-evolution approach to fatigue

cracking in pavements. Journal of Engineering Mechanics, 1993,

119(6): 1243–1259

3. Bonnetti K S, Nam K, Bahi H U. Measuring and defining fatigue

behavior of asphalt binders. Transportation Research Record, 2002,

1810: 33–43

4. Si Z, Little D N, Lytton R L. Characterization of microdamage and

healing of asphalt concrete mixtures. Journal of Materials in Civil

Engineering, 2002, 14(6): 461–470

5. Daniel J S, Bisirri W M. Characterizing fatigue in pavement

materials using a dissipated energy parameter. American Society of

Civil Engineers, 2005, 199–208

6. Carpenter S H, Shen S. Dissipated energy approach to study hot-mix

asphalt healing in fatigue. Transportation Research Record, 2006,

1970: 178–185

7. Ghuzlan K A, Carpenter S H. Fatigue damage analysis in asphalt

concrete mixtures using the dissipated energy approach. Canadian

Journal of Civil Engineering, 2006, 33(7): 890–901

8. Majidzadeh K, Kauffman E M, Saraf C L. Analysis of fatigue of

paving mixtures from fracture mechanics viewpoint. American

Society for Testing and Materials (ASTM STP 508), 1972, 67–83

9. Abdulshafi A A, Majidzadeh K. J-integral and cyclic plasticity

approach to fatigue and fracture of asphaltic mixtures. Transporta-

tion Research Record, 1985, 1034: 112–123

10. Button J W, Little D N, Kim Y, et al. Mechanistic evaluation of

selected asphalt additives. Association of Asphalt Paving Technol-

ogists, 1987, 56: 62–90

11. Sulaiman S J, Stock A F. The use of fracture mechanics for the

evaluation of asphalt mixes. Association of Asphalt Paving

Technologists, 1995, 64: 500–533

12. Mull M A, Stuart K, Yehia A. Fracture resistance characterization of

chemically modified crumb rubber asphalt pavement. Journal of

Materials Science, 2002, 37(3): 557–566

13. Ramsamooj D V. Prediction of fatigue performance of asphalt

concrete mixes. Journal of Testing and Evaluation, 1999, 27(5):

3343–3348

14. Lee H J, Daniel J S, Kim Y R. Continuum damage mechanics-based

fatigue model of asphalt concrete. Journal of Materials in Civil

Engineering, 2000, 12(2): 105–112

15. Bodin D, Pijaudier-Cabot G, De La Roche C, et al. Continuum

damage approach to asphalt concrete fatigue modeling. Journal of

Engineering Mechanics, 2004, 130(6): 700–709

16. El-Basyouny M M, Witczak M. Calibration of alligator fatigue

cracking model for 2002 design guide. Transportation Research

Record, 2005, 1919: 77–86

17. Castro M, Sanchez J A. Damage based model for prediction of

asphalt concrete fatigue curves. Journal of Materials in Civil

Engineering, 2007, 19(8): 700–702

18. Suo Z, Wong W G. Analysis of fatigue crack growth behavior in

asphalt concrete material in wearing course. Construction &

Building Materials, 2009, 23(1): 462–468

19. Wen H, Bahia H. Characterizing fatigue of asphalt binders with

viscoelastic continuum damage mechanics. Transportation Research

Board, 2009, 2126( – 1): 55–62

20. Rodrigues R M. A Model for fatigue cracking prediction of asphalt

pavements based on mixture bonding energy. International Journal

of Pavement Engineering, 2000, 1(2): 133–149

21. Huang C, Najjar Y M, Romanoschi S. Predicting the asphalt

concrete fatigue life using artificial neural network approach. In:

Presented at the 2007 Annual Meeting of the Transportation

Research Board, Washington, D C, 2007

22. Tigdemir M, Karasahin M, Sen Z. Investigation of fatigue behaviour

of asphalt concrete pavements with fuzzy-logic approach. Interna-

tional Journal of Fatigue, 2002, 24(8): 903–910

23. Epps J, Monismith C L. Influence of mixture variables on the

flexural fatigue properties of asphalt concrete. Asphalt Paving

Technology, 1969, 38: 423–464

24. Monismith C L, Epps J A, Kasianchuk D A, et al.. Asphalt Mixture

Behavior in Repeated Flexure. Report TE 79–5 to Federal Highway

Administration, Berkeley: University of California, 1971

25. Sousa J B, Tayebali A A, Harvey J T, et al. Sensitivity of SHRP-

A003A testing equioement to mix design parameters for permanent

deformation and fatigue. Annual Meeting of the Transportation

Research Board, 1993

26. Tayebali A A. Fatigue Reponse of Asphalt-Aggregate Mixtures.

Report A404 to SHRP Project A003A. Strategic Highway Research


Program, National Research Council. Washington, D C, 1994

27. Harvey J,Tsai BW. Effects of asphalt content and air void content on

mix fatigue and stiffness. Transportation Research Board, 1996,

1543: 38–45

28. Sousa J B, Pais J C, Prates M, et al. Effect of aggregate gradation on

fatigue life of asphalt concrete mixes. Transportation Research

Record, 1998, 1630: 62–68

29. Deacon J A, Harvey J T, Tayebali A, et al. Influence of binder loss

modulus on pavement fatigue performance of asphalt concrete

pavement. Journal of the Association of Asphalt Paving Technol-

ogists, 1997, 66: 633–685

30. Anderson D A, Le Hir Y M, Marasteanu M O, et al. Evaluation of

fatigue criteria for asphalt binders. Transportation Research Record,

2001, 1766: 48–55

31. Shenoy A. Fatigue testing and evaluation of asphalt binders using

the dynamic shear rheometer. Journal of Testing and Evaluation,

2002, 30(4): 303–312

32. Smith B, Hesp S. Crack pinning in asphalt mastic and concrete:

regular fatigue studies. Transportation Research Record, 2000,

1728: 75–81

33. Kim Y R, Little D, Song I. Effect of mineral fillers on fatigue

resistance and fundamental material characteristics: mechanistic

evaluation. Transportation Research Record, 2003, 1832: 1–8

34. American Association of State and Highway Transportation

Officials. AASHTO T 314: Standard Method of Test for Determin-

ing the Fracture Properties of Asphalt Binder in Direct Tension

(DT), 2007

35. Bay B, Smith T, Fyhrie D, et al. Digital volume correlation: three-

dimensional strain mapping using X-ray tomography. Experimental

Mechanics, 1999, 39(3): 217–226

36. Lemaitre J, Chaboche J L. Mechanics of Solid Materials. Cam-

bridge: Cambridge University Press, 1990

37. ABAQUS Analysis Users’ Manual, Version 6.10

38. Darveaux R. Effect of simulation methodology on solder joint crack

growth correlation. In: Proceedings of Electronic Components and

Technology Conference. Las Vegas, 2000, 1048–1058


Documents

Fatigue of asphalt binder, mastic and mixture at low temperature