Fatigue of asphalt binder, mastic and mixture at low temperature

Abstract

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

Keywords

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

Introduction

Asphalt concrete pavement is susceptible to cracking damages. Micro-cracks usually initiate deep within the pavement structure where detection is very difficult. Due to the repeated external loading, these invisible micro-cracks propagate and connect to each other, leading to mechanical degradation of asphalt materials. The micro-cracks accumulate until visible cracks appear. Then maintenance and rehabilitation work become mandatory and extremely costly. Fatigue cracking is one of the main cracking damages observed on the asphalt concrete pavements. It is defined as failure of pavement structure due to repeated stresses which are not large enough to cause immediate fracture. Generally, fatigue cracking is described as a process where micro-cracks accumulate and connect to each other until visible cracks are formed and then propagate through the pavement. This is a complicated phenomenon because the initiation and propagation of fatigue cracking is very difficult to detect. To thoroughly understand the mechanism of this distress, an investigation of each component of the asphalt mixture during the fatigue process is necessary. Aggregate is a major component forming the skeleton of the asphalt mixture. Due to the high stiffness, damage of aggregate caused by fatigue is very limited. Compared with the aggregate, the stiffness and strength of the binding medium are much lower which make the binding medium among aggregates more vulnerable and sensitive to fatigue damage. In this work, the fatigue behaviors of binding medium including asphalt binder and mastic will be evaluated. The fatigue behaviors of binding medium will be compared with the asphalt mixture using a unified test methodology with the X-ray tomography incorporated. A model based on FEM is developed to simulate the fatigue of asphalt materials and will serve as a basis for further research.

Background

Traditional research about the fatigue of asphalt mixture was focus on the theoretical model development and experimental test to evaluate the fatigue life of asphalt mixture. The major theoretical models can be classified into four categories: Experiment-dependent models [1], Models based on dissipated energy concept [2-6], Models based on fracture mechanics [7-13] and Models based on damage mechanics [14-19]. Other theoretical models used to describe the fatigue of the asphalt mixture include the damage model based on mixture bonding energy [20], artificial neural network approach [21] and fuzzy-logical approach [22].

As the major laboratory test method to evaluate the fatigue properties of the asphalt mixture, repeated flexural bending test recommended by American Association of State Highway and Transportation Officials (AASHTO) is widely used in the research of the asphalt concrete fatigue [23-28]. However, research about fatigue of asphalt binder and mastic is much less compared with fatigue research effort to asphalt mixture. One main reason that kept researchers from focusing on the asphalt binder fatigue is that it is challenging to apply repeated loading to the sticky asphalt binder. Although Strategic Highway Research Program (SHRP) has accepted Dynamic Shear Rheometer (DSR) as the experimental tool to evaluate the fatigue properties of asphalt binder, some research has shown that there exist limitations with using the DSR as test method to study the fatigue properties of asphalt binder [29-31]. Since most of the research about the fatigue of asphalt mastic is also conducted using DSR [32,33], the understanding of fatigue properties of binding medium will be affected due to these limitations. Furthermore, as one common form of fatigue damages, the top-down cracking is generally caused by tensile loading which is not capable for the DSR test. Another disadvantage of DSR test is that the asphalt mixture specimen can’t be tested in DSR, which makes the test method of asphalt mixture and binding medium not unified. An important initiative of this study is to develop a test device which is able to apply cyclic tensile loading on both binding materials and asphalt mixture.

Methodology

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 for users. It configures the DTT machine to step through user defined test procedure and build up a user-defined test (Fig. 1(b)). Loading mode option of the TB enables a cyclic tensile loading to be applied on the specimen with loading level and loading frequency specified. The test temperature is controlled by a climate chamber.

For the new fatigue test procedure developed in this work, there are four major steps. First, a small loading command, 0.01 N, is given so that the driving motor can be smoothly started. The loading rate is a relatively small value 0.01N/s. When the desired load is reached, the test proceeds to the next step in which a 2 N loading is applied on the loading end of the specimen at a rate of 0.1N/s (Fig. 1(c)). A good contact between loading pin and the specimen is achieved by the application of the loading. After the desired load value is reached, the test proceeds to the next step. Both the loads applied on the loading end and the axial displacements of specimen are measured after this step. Then, a stress-controlled fatigue test is started and a cyclic tensile loading is applied at this step from level 1 to level 2 following a sinusoidal curve. Level 1, which is the lower loading level of the sinusoidal loading, is 2 N which is the same with the previous step. Level 2 is the peak value of the sinusoidal loading, which will be determined later. The frequency of the cyclic loading is also specified. After certain number of loading cycles, the specimens break and the results data including both loading history and axial deformation of the specimen during the test process are automatically recorded. The axial deformation of the specimen can be used to calculate the axial strain of the material after the fatigue process.

Sample preparation

The asphalt binder, mastic and mixture specimens are prepared respectively following similar specimen preparation procedure for direct tension test [34]. The asphalt binder used in the fatigue test is PG70-22 binder based on Superpave binder specification. The binder is heated at 300oF (149oC) 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 the cross section of the specimen is a square with area 36×10^-6 m². Asphalt mastic specimens are prepared by mixing those very fine aggregates referred as fillers and heated asphalt binder. The major component of the fillers is quartz which is very common in fine aggregates. The size of the filler is smaller than 0.075 mm controlled by #200 sieves. The amount of the fillers added into the binder is controlled by the weight ratio between the filler and asphalt binder. For the preparation of asphalt mixture specimen, the sizes of the aggregates added into the asphalt binder or asphalt mastic to prepare the mixture specimen are limited since the size of the specimens is determined by the specimen mold. So, relatively fine aggregates passing through #4 sieves but retained on #35 sieves are used to prepare asphalt mixture specimen in this study, which have a size ranging from 0.5 to 4.76 mm. Since limited size aggregates are used, the amount of aggregates added into the asphalt binder and mastic specimen is not controlled by gradation curve but by the weight ratio between the aggregates and asphalt binder. After the samples are prepared, the climate chamber is turned on. The climate chamber will reach the specified test temperature for testing. The samples are placed into the climate chamber for one hour conditioning and then placed on the loading frame to perform the fatigue test procedure described above.

Digital test development

To obtain the internal structure of the mastic and fine aggregates mixture, specimens are scanned using X-ray tomography system SkyScan 1174. SkyScan 1174 (Fig. 3) is a compact X-ray CT system with 6 um spatial resolution capability. The maximum X-ray source energy of the system is 50 kV and it scans sample up to 30 mm in diameter and 50 mm in length. Since the temperature of the X-ray system cannot be controlled and it is observed that the asphalt materials deform quickly in room temperature, only a 10mm long section of each kind of specimens is cut and scanned to avoid any significant deformation caused by long scanning time and self-weight of the specimen. Both mastic and mixture specimen are scanned at room temperature. After the scanning process is finished, a series of 2-D images showing the cross-section of the specimen will be obtained. The scanned images are processed using a developed MATLAB code for the mesh generation of digital specimens used in the further FEM–based simulation. The basic principle to reconstruct the 3D internal structure of a specimen is as following: the X-ray attenuation is different for each component of the material; pixels on the images belonging to different components of the mixture have different values. For a binary image, the pixel value range is from 0 to 255, 0 refers to black and 255 refers to white. Dense materials such as aggregates are shown as brighter pixels and the pixel value is close to 255. Air voids with negligible density are shown as darker pixels and the pixel value is close to 0. The binder which has an intermediate density is shown as gray color. Two threshold values are determined to discriminate these three major components of the asphalt mixture material. The higher threshold value determines all the pixels belonging to the aggregates and fillers, while the lower thresh hold value determines all the pixels belong to air voids. The rest pixels with values between the higher and lower threshold values represent the asphalt binder. In this work, since the air void content of the small size specimen can’t be measured directly, the pixels with pixel value lower than 70 are considered as air voids. The higher threshold value is determined by a trial and error process. For each mastic or mixture sample, the weights of the asphalt binder, fillers and aggregates are measured. The density of binder used in this study is 1.03 g/cm³ and the density of the quartz fillers and limestone aggregates are same which is 2.56 g/cm³. A preset higher threshold value is given and all the pixels have value larger than this are counted. All the pixels have pixel value lower than 70 are also counted. The rest of the pixels are belonging to asphalt binder. Based on the stereology theory [35], the area of an object in a 2D image can be extended to give volume of the object. The volumes of the asphalt binder and aggregates are obtained respectively. The weight ratio of aggregates and fillers over asphalt binder can be calculated with known densities. Repeat this process as many as necessary until the calculated weight ratio from the image processing is equal to the weight ratio used in the laboratory test. The developed Matlab code gives element and node information required for FEM modeling through a mapping between the 3-D reconstructed voxel and FEM mesh (Fig. 4).

Results

Fatigue test of asphalt binder

Fatigue of asphalt binder is measured under different loading and environmental conditions. The direct tension test provides the tensile strength of the asphalt binder specimen at a specified temperature. With known effective cross-section area of a specimen, the maximum tensile loading can be applied on a specimen is calculated. The peak value of the cyclic tensile fatigue loading is set to be 75% of the maximum tensile loading. In this work, asphalt binder specimens are tested at three different loading levels, three test temperatures and three loading rates. The final axial strain and number of loading cycles are documented. For each test condition, three specimens are prepared and tested respectively; average results for three specimens are calculated. Each test condition and corresponding fatigue test results for each group of specimens are listed in the Table 1. External loading is closely related with the fatigue performance of asphalt binder. At lower loading level, asphalt binder shows better fatigue performance. It is also found that the fatigue resistance of asphalt binder increases significantly when the test temperature increases, the fluid behavior of asphalt binder is more dominant at higher temperature which makes the specimen less sensitive to cyclic loading. Compared with loading level and temperature, the influence of loading rate is not very significant at low temperature. The number of loading cycles and final strain slightly decreases when the loading rate is increased.

Effect of filler content to the fatigue of asphalt mastic

Mastic specimens are prepared with different filler contents. The weight ratio between the filler and asphalt binder is ranging from 10% to 50%. The peak value of the cyclic loading applied on the mastic specimen, test temperature and loading frequency are same with the first group of asphalt binder specimens for comparison, 20N, -20°C and 0.5 Hz respectively. Three specimens are prepared and tested for each kind of mastic. The average test results are listed in the Table 2. It is found that the introduction of the fillers changes the fatigue property of the asphalt binder significantly. Both the final strain and the total number of loading cycles are increased compared with asphalt binder specimen. It is also found that the fatigue resistance of the mastic is not linearly increased as the filler content increases. The final strain and number of loading cycles reach the maximum values when the mastic contains 30% of fillers (Fig. 5). It is also observed that when the filler content of mastic is higher than 50%, the mastic specimen becomes brittle and the fluidity decreases significantly which causes failure of sample preparation.

Fatigue of fine aggregates asphalt mixture

Two kinds of asphalt mixture samples are prepared for fatigue test. One is asphalt binder directly mixed with limestone aggregates, while the other is asphalt binder mixed with both quartz filler and limestone aggregates. The amount of aggregates added into the asphalt binder is controlled by the weight ratio between aggregates and asphalt binder, which is 50% for both kinds of mixture in this work. The peak value of cyclic loading, test temperature and the loading rate are same with previous tests for mastic. Three specimens are prepared and tested for each kind of asphalt mixture. The average final strain and number of loading cycles for each kind of asphalt mixture are listed in the Table 3. It is found that the addition of aggregates into the asphalt binder improves the fatigue resistance of asphalt binder. However, the performances of asphalt mixture are very different due to the addition of the fillers. The addition of the fillers strengthens the material and forms a better skeleton together with aggregates so the mixture with fillers added retains higher strain level and larger number of loading cycles.

Micro-structure analysis of asphalt mastic and mixture

From the fatigue test results shown above, it can be seen that both the fillers and fine aggregates added into the asphalt binder improve the fatigue resistance of the material. However, the performances of the asphalt mastic and fine aggregates mixture are very different. Compared with mastic specimen, the mixture specimen composed of asphalt binder and fine aggregates does not necessarily show better fatigue resistance. An important reason of this phenomenon is that compared with fillers, the texture and angularity of these fine aggregates are more complicated which may cause the bonding problem between the asphalt binder and aggregates so that the structure becomes more vulnerable to the fatigue loading. It is also observed that the addition of fillers helps to form a better structure skeleton together with aggregates and makes the mixture more resistant to the fatigue damage.

A further work is conducted to analyze the internal structure of the asphalt mastic and asphalt mixture specimens. Three kinds of specimens are scanned using X-ray tomography system SkyScan 1174 respectively: mastic with 30% fillers, mixture with 30% fillers and mixture without fillers. After the 2D scanned images of each kind of material are obtained, 3D internal structure of the specimen is reconstructed. With same lower threshold value, the elements belonging to air voids are counted for each kind of specimen. The percentage of air voids elements is calculated. Three specimens are prepared for each kind of material. 100 slices of scanned images are used to reconstruct the 3D model. It shows that asphalt mixture with no filler has 11.09% elements counted as air void, mixture with 30% filler has 4.75%, 30% filler mastic has lowest air void content among three kinds of materials, 3.18%. Considering the fatigue test results of three kinds of material, the air void content is an important factor to affect the fatigue resistance of the material. The asphalt mastic specimen, with lowest air void content among three kinds of materials, reaches the highest final strain and largest number of loading cycles. When the large size aggregates are added, the air void content is increased and causes the decrease of the fatigue resistance. The air voids can be considered as one of main sources of the initial micro cracks, the material is more vulnerable to the fatigue loading with higher air void content.

Fatigue simulation in FEM

The fatigue tests of asphalt binder, mastic and mixture are simulated using FEM-based software ABAQUS. Asphalt mastic and mixture are modeled as heterogeneous materials in which aggregates/filler and asphalt binder are treated with different constitutive models. The internal structures of specimens are obtained through the image processing and 3-D mesh reconstruction. The air void elements are removed in the model. 8-node linear brick element is used to represent the voxel generated from 3D mesh reconstruction. Fillers and aggregates are considered as linear elastic materials with high stiffness. The elastic modulus is 50 GPa and Poisson's ratio is 0.25 for both aggregates and filler. Considering the elastic behavior and the unrecoverable deformation of the asphalt binder specimen at this low temperature, an elasto-plastic model developed by Lemaitre and Chaboche [36] is used to describe the mechanical behavior of asphalt binder. The elastic part of the model is determined by elastic modulus and Poisson’s ratio. In this work, the elastic modulus of asphalt binder is calculated from the linear part of the stress-strain curve which is 0.27 GPa, the Poisson’s ratio is 0.35. The plastic part of the model is described by a combined isotropic/kinematic hardening model. The isotropic hardening component describes the change of the size of the yielding surface as a function of equivalent plastic strain and the kinematic hardening component describes the translation of the yield surface in stress space through the backstress α. The isotropic component of the model is expressed as below:

(1){\sigma }^{\mathrm{0}}=\sigma {\mathrm{|}}_{\mathrm{0}}+Q_{\infty }\left(\mathrm{1}-e^{-b{\overline{ϵ}}^{pl}}\right),

where σ⁰ is the size of the yield surface, σ|₀ is the yield stress at zero plastic strain, Q_∞ is the maximum change in the size of the yield surface and b is the rate at which the size of the yield surface changes as plastic straining develops, {\overline{ϵ}}^{pl} is the equivalent plastic strain.

Determination of the model parameters is challenging, details of the parameter calibration method can be found in the Abaqus Analysis User’s Manual [37]. For this new fatigue test procedure, the first half cycle is a unidirectional tension process. Using the TB, this monotonic tensile test is conducted before the cyclic fatigue test. The initial yielding stress σ|₀ can be determined at the point where the plastic deformation starts and the stress-strain curve becomes nonlinear (Fig. 6). The average initial yielding stress for three binder specimens tested is 0.45 MPa. The stress-strain data from last half cycle of cyclic tensile test for three asphalt binder specimens are used to calculate the final yielding stress. The average result of three specimens is 0.81MPa. So the maximum change of yielding stress, Q_∞, is 0.36 MPa. Every point after the initial yielding point experiences both elastic and plastic strains. The plastic part of the strain is calculated using Eq. (3).

(2){ϵ}_i^{pl}={ϵ}_i-{\displaystyle \frac{{\sigma }_i}{E}},

where {ϵ}_i^{\mathit{p}\mathit{l}} is the plastic strain, ϵ_i is the measured total strain, σ_i is the measured total stress and the E is the elastic modulus.

In this uniaxial tensile fatigue test, the specimen is stretched along the loading direction, so the equivalent plastic strain {\overline{ϵ}}_{\mathit{i}}^{\mathit{p}\mathit{l}} is equal to the plastic strain {ϵ}_{\mathit{l}}^{\mathit{p}\mathit{l}}. It is assumed that the very next point after initial yielding is on the yield surface so the stress value of the point is σ⁰ .With known σ⁰, σ|₀, Q_∞, and plastic strain {ϵ}_{\mathit{l}}^{\mathit{p}\mathit{l}}, the parameter b is calculated based on Eq. (1). The parameter b used in this work is 88.

The kinematic component of the elasto-plastic model is expressed as

(3)\dot{\alpha }=C{\dot{\overline{ϵ}}}^{pl}{\displaystyle \frac{\mathrm{1}}{{\sigma }^{\mathrm{0}}}}(\sigma -\alpha )-\gamma \alpha {\dot{\overline{ϵ}}}^{pl},

where C is the initial kinematic hardening modulus. {\overline{ϵ}}^{pl} is the equivalent plastic strain. σ⁰ is the size of the yielding surface defined in the isotropic hardeing component. γ is the parameter which determines the rate at which the kinematic hardening modulus decreases with increasing plastic deformation. C and γ need to be determined to define the evolution of the backstress α. The first half cycle data of the fatigue test are used to calibrate C and γ. For each data point (σ_i, ϵ_i) after the initial yielding, a value of is α can be calculated using Eq. (4).

(4){\alpha }_i={\sigma }_i-{\sigma }_i^{\mathrm{0}},

where {\sigma }_{\mathit{i}}^{\mathrm{0}} is the size of the yield surface at the corresponding plastic strain for the isotropic hardening component. Integration of the backstress evolution law over a half cycle yields the expression:

(5){\alpha }_i={\displaystyle \frac{C}{\gamma }}(\mathrm{1}-e^{-\gamma {ϵ}_i^{pl}}),

As described before, the first half cycle of the fatigue test is a unidirectional tension process, the equivalent plastic strain equals to the plastic strain which can be calculated based on Eq. (2). With known α_i and corresponding {ϵ}_{\mathit{l}}^{\mathit{p}\mathit{l}}, the C and γ can be determined. The very first point after initial yielding and the end point of the half cycle are used to calculate C and γ. The stress and corresponding plastic strain used to calculate C and γ in this study are σ₁ = 0.4528 MPa, {ϵ}_{\mathrm{1}}^{\mathit{p}\mathit{l}}=\mathrm{2.19}\times {\mathrm{10}}^{-\mathrm{4}}, σ₂ = 0.5151 MPa, {ϵ}_{\mathrm{2}}^{\mathit{p}\mathit{l}}=\mathrm{9.97}\times {\mathrm{10}}^{-\mathrm{4}}. In Abaqus codes, these two pairs of stress-strain data are inputs to calibrate parameters C and γ. All the parameters for the plastic part of the model of asphalt 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]. The stiffness of the asphalt binder decreases once the fatigue damage initiates. The fatigue damage initiates due to stress reversals and the accumulation of inelastic strain. The model is described by:

(6)N_{\mathrm{0}}=c_{\mathrm{1}}\mathrm{\Delta }{w}^{C_{\mathrm{2}}},

where c₁ and c₂ are material constants. Δw is inelastic hysteresis energy.

The damage evolution is modeled by the rate of the damage in a material point per cycle which is given by

(7){\displaystyle \frac{dD}{dN}}={\displaystyle \frac{c_{\mathrm{3}}\mathrm{\Delta }{w}^{c_{\mathrm{4}}}}{L}},

where c₃ and c₄ are material constants, and L is the characteristic length associated with an integration point. D is damage variable which describes the stiffness decrease of the material. The characteristic length L is determined by the element geometry and formulation. For the first order element, it is typical length of a line across an element.

At any given loading cycle during the analysis the stress σ in the material is given by the scalar damage equation:

(8)\sigma =(\mathrm{1}-D)\overline{\sigma },

where \overline{\sigma } is the effective stress tensor when there is no damage in the material. The load carrying capacity of the material is lost when D = 1.

The parameters c₁c₂c₃c₄ govern the fatigue damage initiation and propagation of the model. Since it is not applicable to scan the specimen when the fatigue test is in progress, the damage model parameters c₁c₂c₃c₄ can not be obtained directly from laboratory test results. The damage parameters used for joint solder material in Darveaux’s work are initially used. Same with the boundary condition of the laboratory fatigue test, cyclic tensile loading is applied on the loading end of the beam model along the axial direction. The other end of the beam sample is fixed in all degree of freedom. (Fig. 7). The cyclic loading is following a sinusoidal curve where the peak load and the loading rate are specified to be same with the laboratory test condition. The loading level and number of loading cycles applied in the simulation are as same as laboratory fatigue test for each kind of specimen. Since the specimen is tested in the environmental chamber which is filled with ethanol and the self-weight does not cause any significant deflection of the specimen in the vertical direction, the weight of the specimen is not considered in the model. When the model reaches the same number of loading cycles, the axial strain predicted by the model is compared with laboratory test results. And the damage parameter c₁ is determined when the simulation results agree with the laboratory test results. Similarly, the fatigue tests of mastic and mixture are also simulated. Mastic with 30% fillers and mixture with 30% fillers are selected respectively for simulation. Since it is assumed that the fatigue damage occurs in the asphalt binder material only, c₁ used for mastic and mixture model is much larger than the asphalt binder considering the introduction of the aggregate/filler elements makes the fatigue damage much harder to initiate. The damage model parameters used and corresponding simulation results of axial strain of each model are listed in the Table 4. The percentage of asphalt binder element whose stiffness is totally lost during the fatigue process is also listed in the table. The simulation results of axial strain are compared with the laboratory test results of axial strain for each kind of specimen. It can be seen that with same number of loading cycles, the axial strain predicted by the models agree reasonably well with laboratory test for each kind of specimen. In the numerical model, the number of loading cycles applied is same with the laboratory test when the specimen fails. It is shown in the model that most of the asphalt binder lost their stiffness. With proper selection of model parameter, the complicated fatigue process of asphalt materials is modeled by a relatively simple method. With the property parameters calibrated by the laboratory test, the developed digital specimen and digital fatigue test can serve as a basis for further fatigue research in the future.

Conclusions

In this work, fatigue behavior of asphalt binder, mastic and mixture with fine aggregates at low temperature are investigated. The DTT from the Interlaken Company is altered to develop a new fatigue test procedure which is able to apply cyclic tensile loading on the specimen prepared by the mold used for direct tension test. The outputs of the fatigue test are the number of loading cycles and final axial deformation of the specimen when it breaks under cyclic loading. The axial deformation is used to calculate the axial strain of the specimen. The new developed fatigue test provides a tool to evaluate the fatigue performance of the binding materials. It applies cyclic tensile loading which is believed to be major mechanism to cause fatigue damage. It also offers a unified methodology to test the fatigue behaviors of binding materials and mixture. FEM-based software ABAQUS is used to simulate the fatigue tests for different materials. Incorporated with X-ray tomography technology, the internal structures of mastic and mixture specimens are obtained and used for the mesh generation of numerical models. The models are heterogeneous composites which describe the aggregates, filler and asphalt binder with different mechanical models. Fatigue damage caused by cyclic loading is addressed by a damage model applied to asphalt binder elements. Major finding of this research include: 1) Fatigue behavior of asphalt binder is closely related with external loading level, temperature, and loading rate. High external loading always causes more fatigue damage. When the temperature increases, the asphalt binder shows more fluid-like behavior and holds longer number of loading cycles. The impact of loading rate is not as obvious as loading level and temperature at the test temperature, -20°C. 2) The addition of filler improves the fatigue resistance of asphalt binder significantly which indicates that the mastic plays an important role in the fatigue resistance of binding materials. 3) The fatigue performance of the mastic is closely related with the filler content; mastic with 30% filler reaches the highest number of loading cycles and final strain when the specimen fails. 4) Mixture with fine aggregates also has better fatigue performance than the asphalt binder. However, addition of fine aggregates into the mastic specimen does not necessarily improve the fatigue performance of mastic. Micro-structure analysis of two kinds of specimens shows that the air void content is much higher in the mixture than the mastic which indicates that the large size aggregates introduces more air voids and weaken the bonding between aggregates and asphalt binder. 5) The asphalt binder is described by an elasto-plastic model and the model parameters are quantitatively determined using laboratory test. The complicated fatigue process of asphalt mastic and mixture is simply modeled by using a damage model, with proper model parameter selection, the simulation results agree well with laboratory test results. The developed digital specimen with laboratory test determined material property and digital test provide a basis for further fatigue research of asphalt materials.

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. Transportation Research Record, 1985, 1034: 112–123

[10] Button J W, Little D N, Kim Y, Mechanistic evaluation of selected asphalt additives. Association of Asphalt Paving Technologists, 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, 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. International 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, 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 B W. 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, 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, Influence of binder loss modulus on pavement fatigue performance of asphalt concrete pavement. Journal of the Association of Asphalt Paving Technologists, 1997, 66: 633–685

[30] Anderson D A, Le Hir Y M, Marasteanu M O, 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 Determining the Fracture Properties of Asphalt Binder in Direct Tension (DT), 2007

[35] Bay B, Smith T, Fyhrie D, 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. Cambridge: 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

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg