Micromechanical finite element framework for predicting viscoelastic properties of asphalt mixtures

Transcription

1 DOI.117/s ORIGINAL ARTICLE Microechanical finite eleent fraework for predicting viscoelastic properties of asphalt ixtures Qingli Dai Æ Zhanping You Received: Deceber / Accepted: 7 August 7 Ó RILEM 7 Abstract A icroechanical finite eleent (FE) fraework was developed to predict the viscoelastic properties (coplex odulus and creep stiffness) of the asphalt ixtures. The two-diensional (D) icrostructure of an asphalt ixture was obtained fro the scanned iage. In the ixture icrostructure, irregular aggregates and sand astic were divided into different subdoains. The FE esh was generated within each aggregate and astic subdoain. The aggregate and astic eleents share nodes on the aggregate boundaries for deforation connectivity. Then the viscoelastic astic with specified properties was incorporated with elastic aggregates to predict the viscoelastic properties of asphalt ixtures. The viscoelastic sand astic and elastic aggregate properties were inputted into icroechanical FE odels. The FE siulation was conducted on a coputational saple to predict coplex (dynaic) odulus and creep stiffness. The coplex odulus predictions have good correlations Q. Dai Departent of Mechanical Engineering-Engineering Mechanics, Michigan Technological University, Houghton, MI 9931, USA e-ail: qingdai@tu.edu Z. You (&) Departent of Civil and Environental Engineering, Michigan Technological University, Houghton, MI 9931, USA e-ail: zyou@tu.edu with laboratory uniaxial copression test under a range of loading frequencies. The creep stiffness prediction over a period of reduced tie yields favorable coparison with specien test data. These coparison results indicate that this icroechanical odel is capable of predicting the viscoelastic ixture behavior based on ingredient properties. Keywords Microstructure Microechanical odeling Finite eleent ethod Asphalt ixture Viscoelasticity Coplex odulus Creep stiffness 1 Introduction Heterogeneous asphalt ixtures coprise of graded aggregates bound with astic (asphalt binder plus fine aggregates and fines). For such aterials, the acro properties depend on the aggregate and astic icrostructure. Iportant icro behaviors related to astic properties include: volue percentage, viscoelastic and viscoplastic responses, icrocracking, and bonding strength. The icrostructural features of aggregate include: ineralogy, elastic odulous, size, shape, texture, and packing geoetry. Chen et al. [1] evaluated the internal structures of asphalt ixtures constituting of four different percentages of flat and elongated (F&E) aggregates, and studied how the engineering properties of these ixtures change in ters of rut depth, particle oveent and

2 orientation, and strain. The experiental procedure used in their study relied on the two-diensional (D) iages subjected to wheel loading. It was concluded that the low percentages of F&E aggregates result in a stable internal structure that could develop stone-on-stone contact and provide a better interlocking echanis [1]. Because of the heterogeneous nature of asphalt ixtures, a icroechanical odel for asphalt concrete ixtures is needed to study and characterize their properties. Microechanical odels can predict fundaental aterial properties based upon the properties of the individual constituents such as the astic and aggregate. Microechanical odels have treendous potential benefits in the field of asphalt technology, for reducing or eliinating costly tests to characterize asphalt-aggregate ixtures and design purposes. Since these odels allow a ore thorough exaination of icrostructural aterial behavior, such as strain distribution within the aggregate skeleton and asphalt atrix, they can ultiately provide a powerful tool for optiizing ixture design on the basis of echanistic perforance. The use of icroechanical odels to predict properties of asphalt ixtures and astics has drawn increasing attention over the past years, and a nuber of approaches have been investigated. Asphalt ixture was investigated by non-interaction particle icroechanics odels without specified geoetry [ ], as well as, with specified geoetry [7 ]. Discrete eleent ethod (DEM) was eployed on ceented particulate aterials in recent years [11 1]. A D icro-fabric discrete eleent odel (MDEM) concept was developed to predict the stiffness of asphalt ixtures [19 1]. The MDEM holds proise to balance the advantages of icrostructural odel resolution with all the benefits of the discrete eleent approach including the siulation of aggregate cracking, debonding between aggregates and astic, and icrocracking initiation and propagation. However coplex contact laws need to be developed for predicting coplex astic constitutive behavior. In addition, it is a challenge to use circular eleent to siulate the irregular shaped aggregate. On the other hand, finite eleent odeling of asphalt concrete icrostructure potentially allows accurately odeling of aggregate and astic coplex constitutive behaviors and icrostructure geoetries. Research work has been conducted using FE techniques [ 31]. In addition, soe research have been reported on the three-diensional (3D) icrostructure of asphalt ixture [9, 3 3]. A displaceent discontinuity boundary eleent approach was applied in the odeling of asphalt ixtures [35]. An equivalent lattice network approach was developed and applied, where the local interaction between neighboring particles was odeled with a special frae-type FE [3 39]. A ixed FE approach was developed to study asphalt ixtures by using continuu eleents for the effective asphalt astic and rigid body defined with rigid eleents for each aggregate []. A unified approach for the rateindependent and rate-dependent daage behavior was developed using Schapery s nonlinear viscoelastic odel. Properties of the continuu eleents were specified through a user aterial subroutine within the ABAQUS code and this allows linear and daage-coupled viscoelastic constitutive behavior of the astic ceent to be incorporated. In these odels, the icrostructure of real asphalt aterials was siulated with idealized elliptical aggregates and polygonal effective astic zones [1]. Using iage processing and ellipse fitting ethods, particle diensions and locations were deterined fro digital photographs of the saple s icrostructure. These odels have been proising in predicting the ixture behavior, however, the aggregate shape is idealized as ellipse. Even though any research studies have been conducted on icroechanical odeling of asphalt ixtures, the irregular shape of the aggregate in the ixture still has not been successfully odeled to capture the icroechanical aggregate-to-aggregate contact behavior. Objectives The objectives of this study are to (1) develop a icrostructure-based FE odel for heterogeneous asphalt ixture, and; () predict viscoelastic ixture properties (e.g., coplex odulus and creep stiffness) by using the FE odel with the input of the viscoelastic properties of sand astic and elastic odulus of the aggregates.

3 3 Scope The asphalt ixture in this study is odeled as irregular shaped aggregates bonded with sand astic. The icrostructure of the ixture was obtained fro the D scanned iage of a sawn asphalt concrete. Therefore, the iage of the asphalt ixture includes the coarse aggregate and sand astic. The sand astic is a ixture of fine sand and asphalt binder. Coparing with the coarse aggregate, the sand particles are so sall that they can distribute in the asphalt binder uniforly. Therefore, it is reasonable treat the sand astic as a hoogonous coposite. The FE esh was generated within each aggregate and astic subdoains by sharing nodes on the aggregate boundaries. Viscoelastic properties of the astic eleents are calibrated with the laboratory experiental test data and inputted into a user aterial subroutine within the ABAQUS code. Then the viscoelastic astic was cobined with elastic aggregates to predict the properties of asphalt ixtures. It should be noted that the air void in the ixture is ignored in this D odel due to the liitation of sooth sawn iage. Ongoing siulation work is conducted on X-ray scanned iages with the indication of air void distribution. Microstructure of asphalt ixture In this study, the D icrostructure of asphalt concrete was obtained by optically scanning soothly sawn asphalt ixture speciens. A highresolution scanner was used to obtain grayscale iages fro the sections. Iage processing technique was used to process and analyze iages. Figure 1 deonstrates the iage processing on an asphalt specien (with the noinal axiu aggregate size of 19 ). Figure 1a shows an optical scanning iage of a ixture specien with width and height. A scanner with 1 3 Dots Per Inch (DPI) optical resolution was used. After iproving the iage contrast, the outlines of aggregates were converted into anysided polygons using a custo developed acro progra in Iage Pro Plus to define the icrostructure of asphalt ixture [15]. The average of the polygon diaeter was chosen as a threshold to deterine which aggregates would be retained on a given sieve (i.e., the rest of the aggregates would be passed the given sieve), although soe other easureent paraeters were also attepted in analyzing the gradation of the aggregates []. The polygons used in the icroechanical odel were treated as coarse aggregates. Figure 1b is the coarse aggregate retained on 1.1 sieve (i.e., No. 1), where the fine aggregates passing 1.1 were filtered as sand astic. Elastic properties of aggregates [, 1, ] were assigned to aggregate subdoains, and viscoelastic astic properties were also evaluated with astic creep tests. Finite eleent siulation was conducted to predict the ixture behavior by cobining aggregate and astic properties. Fig. 1 Microstructure of an asphalt ixture specien surface. (a) An original iage of the surface, (b) The aggregate skeleton (sieving size [1.1 )

4 5 Mastic viscoelastic odel Generalized Maxwell odel was widely used for viscoelastic solids such as asphalt ixture. The generalized Maxwell odel was applied to siulate the linear and daage-coupled viscoelastic behavior of asphalt ixture []. The linear constitutive behavior for this Maxwell-type odel can be expressed as a hereditary integral Z t de ij ðsþ r ij ¼ E 1 e ij þ E t ds ð1þ ds where E t is expressed with a Prony series E t ¼ XM E e ðt sþ q ; and q ¼ g E ðþ In these equations, E 1 is the relaxed odulus, E t is the transient odulus as a function of the tie, E, g and q are the spring constant, dashpot viscosity and relaxation tie respectively for the th Maxwell eleent. The reduced tie (effective tie) is defined by using the tie-teperature superposition principle as Z t 1 nðtþ ¼ ds ð3þ a T where the ter a T ¼ a T ðtðsþþ is a teperaturedependent tie-scale shift factor (Fig. ). Three-diensional behavior can be forulated with uncoupled voluetric and deviatoric stress strain relations. A displaceent-based increental FE odeling schee with constant strain rate over each increent was developed in the following forat: Dr ¼ K De þ Dr R ðþ Where Dr and De are increental stress and strain, K is the increental stiffness and Dr R is the residue stress vector. The voluetric constitutive relationship is expressed with the voluetric stress r kk and strain e kk in the general for Z n r kk ðnþ ¼3K 1 e kk ðnþþ 3K t ðn n Þ de kkðn Þ dn dn ð5þ where K 1 ¼ E 1 =3ð1 Þ is the relaxed bulk odulus, K t ðn n Þ¼ P M K e ðn nþ q is the transient bulk odulus, and K = E /3(1 ) is the bulk constants for the spring in the th Maxwell eleent. The increental forulation of the voluetric behavior is obtained with constant voluetric strain rate R kk ¼ De kk Dn ; " Dr kk ¼ 3 K 1 þ XN K q 1 e Dn q De kk þ Dr R kk Dn ðþ and the residual part Dr R kk can be expressed in a recursive relation with the history variable S, Dr R kk ¼ XM 1 e Dn q S ðn n Þ; and S ðn n Þ¼3K R kk q 1 e Dn q þ S ðn n 1 Þe Dn q ð7þ E E1 E E3 E M 1 EM For the initial increent, the history variable S (n 1 ) equals to 3K R kk q 1 e Dn q and is siilar to the following forulations. For the deviatoric behavior, the constitutive relationship is written using deviatoric stress ^r ij ¼ r ij 1 3 r kkd ij and strain ^e ij ¼ e ij 1 3 e kkd ij ; η1 η η3 η M 1 η M Fig. The generalized Maxwell viscoelastic odel for the sand astic Z n ^r ij ðnþ ¼G 1^e ij ðnþþ G t ðn n Þ d^e ijðn Þdn dn ðþ where G 1 ¼ E 1 =ð1 þ Þ is the relaxed shear odulus, G t ðn n Þ¼ P M G e ðn nþ q is the transient shear odulus, and G = E /(1 + ) is the shear constants for the spring in the th Maxwell eleent.

5 The forulation of the deviatoric behavior is obtained with constant deviatoric strain rate ^R ij ¼ D^e ij Dn ; " D^r ij ¼ G 1 þ XN G q 1 e Dn q D^e ij þ D^r R ij Dn ð9þ and the residual part D^r R ij can be expressed in the recursive relation D^r R ij ¼ XN 1 e Dn q S ðn n Þ; and S ðn n Þ¼G ^R ij q 1 e Dn q þ S ðn n 1 Þe Dn q ðþ The increental noral stresses can be then forulated by cobining the voluetric and deviatoric behavior. For exaple, Dr xx ¼ " 1=3Dr kk þ D^r xx ¼ K 1 þ XN K q 1 e Dn q De kk " Dn þ G 1 þ XN G q 1 e Dn q D^e xx Dn þ 1=3Dr R kk þ D^rR xx ð11þ where De kk and Dr kk are the increental voluetric strain and stress, D^e xx and D^r xx are the increental deviatoric strain and stress coponents, and Dr R kk and D^r R xx are the recursive part of the voluetric and deviatoric behavior given in Eqs. and 9. Increental stresses Dr yy and Dr zz are deterined in the sae anner. The increental shear stress can be forulated by using only the deviatoric behavior. For exaple, Dr xy ¼ D^r " xy ¼ G 1 þ XM G q 1 e Dn q D^e xy þ D^r R xy Dn ð1þ where D^e xy and D^r xy are the increental shear deviatoric strain and stress coponents, and the recursive ter D^r R xy is also given in Eq. 9. Once the increental stress coponents are developed, the increental stiffness ters can be calculated and then the increental 3D linear viscoelastic behavior was forulated as Dr xx K 1 K K De xx Dr yy K 1 K De yy Dr zz K 1 De Dr ¼ zz xy K 3 De xy Dr yz 5 K 3 5 De yz 5 Dr xz K 3 De xz Dr R kk þ 3 D^rR xx Dr R kk þ D^rR yy Dr R kk þ þ D^rR zz D^r R ð13þ xy 7 5 D^r R yz D^r R zx where " K 1 ¼ K 1 þ XN K q 1 e Dn q " Dn þ 3 G 1 þ XN G q 1 e Dn q " Dn K ¼ K 1 þ XN K q 1 e Dn q " Dn 3 G 1 þ XN G q 1 e Dn q " Dn K 3 ¼ G 1 þ XN G q 1 e Dn q Dn ð1þ This viscoelastic odel was defined in the ABAQUS user aterial subroutine for astic subdoains. A displaceent-based tie-dependent FE analysis was conducted by integrating elastic aggregate and viscoelastic astic subdoains to predict the global behavior of asphalt ixture. Laboratory tests of aggregates, sand astic, and copacted asphalt ixture The purpose of this section is to easure and evaluate the aterial properties of sand astic, aggregate (rock), and copacted asphalt ixture through laboratory tests. The uniaxial copression laboratory tests of sand astic and aggregate

6 (cylinder specien) were conducted to provide aterial input paraeters for the FE odels. The goal of the ixture test is to provide a coparison with the odel prediction in order to validate the FE odel siulation. The input paraeters for the FE odels include not only the icrostructure inforation but also the aterial properties of the aggregate and astic at different loading conditions. In this study, a odulus of 55.5 GPa [, 1, ] for the liestone was used for different teperatures and loading frequencies. The uniaxial copression creep test was conducted on the sand astic and ixture saples under different teperatures ( C, C, and C). The astic contains aggregates passing sieve 1.1 and asphalt content is about 1% [, 1, ]. The sand astic was coprised of the portion of the aggregate gradation finer than the 1.1 sieve cobined with the volue of binder norally used in the entire asphalt concrete ixture. The creep stiffness at different loading tie and teperatures were obtained fro the inverse of creep copliance. A regression fitting ethod was eployed to evaluate astic viscoelastic properties with a generalized Maxwell odel at the reference teperature of C, and the tie shift factors were calculated for C and C. Master stiffness curves were generated for astic and asphalt ixture fro creep tests [3]. The shifted creep stiffness and fitted aster curve for sand astic at the reference teperature C are shown as Fig. 3. The odel for sand astic includes one spring and four Maxwell eleents in parallel. The viscoelastic paraeters of the sand astic are: E 1 ¼ 59:7 MPa; E 1 = 57. MPa, (GPa) Creep Stiifness Mastic 1E+ 1E+1 1E+ 1E-1 1E+ 1E+1 1E+ 1E+3 Reduced Tie (sec) C Test Data - C Test Data - C Test Data Fitted Model 1E+ 1E+5 Fig. 3 The shifted creep stiffness and fitted aster curve for the sand astic s 1 =. s, E = 75.1 MPa, s = s, E 3 = 19 MPa, s 3 = 17. s, E = 73.9 MPa, and s = s. The relaxed and transient oduli are deterined fro the aster curve of astic creep stiffness. Uniaxial behavior was extended to ultiaxial (3D) constitutive forulation with the uncoupled voluetric and deviatoric Eqs. 5 and. The elastic bulk and shear oduli are K ¼ E 31 t ð Þ and G ¼ E ð1þtþ : The ters K 1 and G 1 are the relaxed bulk and shear oduli, and K and G are the bulk and shear constants for the spring in the th Maxwell eleent. The Poisson s ratio is assued as.3 for asphalt ixture. Therefore, the ulti-axial properties were connected with the uniaxial easureents. For the gyratory copacted ixture speciens, uniaxial copression tests were conducted to easure coplex (dynaic) odulus and creep stiffness with a nuber of ixture speciens. The coplex oduli were easured at different teperatures and loading frequencies. The creep stiffnesses were calibrated over a period of loading tie at different teperatures. This database was used to validate FE odel for prediction of ixture coplex oduli and creep stiffness at different loading conditions. 7 Developent of icroechanical finite eleent odels for asphalt ixtures As entioned previously, the icrostructure of the asphalt ixture was divided into different aggregate and astic subdoains. The FE esh was generated within the subdoains of aggregates and astic and along the subdoain boundaries. Due to the very irregular aggregate and coplex astic distribution, the three-node triangle eleents were used in the FE esh for the coplex geoetry. Figure shows the FE eshes in the aggregate and astic subdoains of a specien surface. Finite eleents in the neighboring subdoains share the nodes on irregular boundaries as shown in Fig., and therefore the displaceents of neighboring subdoains were connected through the shared nodes. For this D FE esh, plane stress eleents with a solid section thickness were applied for both aggregate and astic subdoains. After the FE odel has been developed, uniaxial copression test was siulated. For the copression siulation, the x- and y-displaceents of the nodes

7 Fig. The asphalt ixture iage and the three-node triangle FEM eshes for the aggregate and astic subdoains. (a) A scanned iage of the specien surface, (b) The finite eleent eshes of the specien surface, (c) Enlarged eshes for the aggregates and astic on the botto layer and the x-displaceents of the nodes on the top layer were constrained. The constant or dynaic force loading was evenly divided and iposed on nodes of the top layer. The generalized Maxwell odel paraeters for astic and the elastic odulus of aggregates were inputted to the FE odel. Siulation was conducted to predict the global viscoelastic properties of the asphalt ixture. In the siulation, axial strain was calculated by dividing the average vertical displaceent of top particles with the initial height of the undefored specien, and axial stress was obtained by dividing the constant loading force on the top layer with the specien initial cross-section area. One of the benefits of the icroechanical odel is to present the detailed stress and strain distributions within the icrostructure of the ixture saple. Figure 5 shows the copression strain distribution contour in a portion of the digital specien under a uniaxial constant copression force loading. The aggregate skeletons are indicated in the figure with the skeleton curves. The high copression strains were generated in the vertical astic gap between neighboring aggregates. The coputational results show that the highest local strain is about eight ties of average strain for this portion of the coputational saple. Figure shows the shear strain distribution contours in the sae portion of the digital specien Fig. 5 The copression strain contour in a portion of the digital specien

8 Fig. The shear strain contour in the sae portion of the digital specien under a constant copression force loading. This figure indicates that high shear strain zones are distributed in horizontal narrow astic gap along the large-size aggregates. Fro our previous study, it was found that under the echanical loading, the cracks initiate in the narrow gap between coarse aggregates of asphalt ixture specien. These strain distributions agree with the laboratory observations. The strain contours help exaine icro aterial behavior, such as strain intensities within the asphalt astic and aggregate phases. They also can provide useful inforation in analyzing crack initiation and optiizing ixture design on the basis of echanistic perforance for further study. Coplex odulus siulation and results Sinusoidal cyclic loading was iposed to the siulation specien for calculating the coplex odulus under the different loading frequencies ( Hz, 5 Hz, 1 Hz and.1 Hz) as shown in Fig. 7. In the siulation, the loading cycles were taken as 3 for.1 Hz, 5 for 1 Hz, 5 Hz, and Hz. In these figures, the constant cyclic curve is the iposed stress load with the right-side axial scale, and the other curve indicates the strain response with the left-side axial scale. For better illustration, the final several cycles were agnified in the right-side figures for each frequency. The coputation points are indicated in the right-side figures. The agnitude of the dynaic odulus was calculated using the last ten cycles for each frequency. As indicated in these figures, the strain increases with the loading tie for each frequency. Coparing different frequency responses, it was found that the strain value deceases with the loading frequencies. It also indicates the coplex odulus value increases with the loading frequencies due to decreasing relaxation tie. Figure shows the coplex odulus coparisons between FE siulation results and test data for different loading frequencies at a test teperature of C. As entioned previously, the astic aster curve was obtained at the reference teperature C. Therefore the FE siulation with the input astic properties generated the ixture behavior at this selected teperature. The coparisons indicate that the siulation results are reasonable and applicable for coplex odulus prediction although it slightly under predicted the ixture odulus. The differences between the predictions and easureents ay cause by the following reasons: (1) the aggregates sieved fro the D iage ay reduce the real aggregate content/percentage, and () the D ixture icrostructure odel ay underestiate the

9 (a) (GPa) Copression (GPa) Copression 1 1 (b) Loading Tie (s) Loading Tie (s) Copression Copression C opression (GPa) Copression (GPa ) Loading Tie (s) Loading Tie (s) C opression Copression Strai n (c) (Gpa) Copression Loading tie (s) Copression Copression (GPa) Loading tie (s) t Copression (d) (GPa) Copression Copression Copression (GPa) Copression Loading Tie (s) Loading Tie (s) Fig. 7 The FEM siulation results under sinusoidal loading. (a) loading frequency = Hz, (b) loading frequency = 5 Hz, (c) loading frequency = 1 Hz, (d) loading frequency =.1 Hz aggregate-aggregate contact or aggregate interlock effects. With the developent of 3D odeling and the additional calibration of astic and aggregates, the odel prediction perhaps will be closer to the test data with ore capacity to describe ixture coplex behavior. In order to copare the FE prediction, the authors also conducted the discrete eleent odeling to predict the ixture coplex odulus with the input of the easured astic coplex oduli at different loading frequencies and test teperatures, and aggregate odulus [19 1, 3]. It was found that the

10 M ixture Coplex Modulus (GPa). 1 Test Data (-C) FEM Siulation.1 1 Loading Frequency (Hz) Fig. The coplex odulus coparison with the FEM siulation and the test data at a teperature C coplex odulus predictions fro the FE odels had a good agreeent with the DEM and the lab easureents. 9 Creep stiffness siulation and results In this section, the creep stiffness siulation by using the icroechanical FE odel was discussed. In addition, the predictions fro the icroechanical FE odel, a icrostructure based discrete eleent odel (DEM) [1] and a icrostructure based FE network odel (FENM) were copared. Microechanical FE siulation was conducted with a constant force loading condition to predict the creep stiffness of asphalt ixture. When the constant force was applied to the icrostructure-based FE odel, the creep displaceent responses were captured over a period of tie. Then the acro creep strain and creep stiffness of the asphalt ixture were coputed. The creep stiffness (reverse of the creep copliance) varies with tie. FE odel siulation was copared with the easureents of the aster curve of creep stiffness of the ixture across a reduced tie up to s as shown in Fig. 9. TheFE odel had a good coparison with test easureents, and slightly underpredicted the creep stiffness (perhaps due to the liitation of D odel). In this case study, the authors consider that the ajor contributions to creep deforation are viscoelastic properties. It also exits slight unrecoverable deforation caused by the viscoplastic behavior for real asphalt ixture. In the ongoing work, the authors study the viscoplastic-viscoelastic behavior by (GPa) Relaxation Modulus.. FEM DEM (c=.), Calibrated DEM (c=.55), Calibrated Test Data Reduced Tie (s) Fig. 9 Prediction fro the FEM and the calibrated DEM siulation, and the laboratory easureents of the asphalt ixture creep stiffness for a reduced tie up to s replacing the elastic spring with a viscoplastic-elastic eleent in the presented odel. In order to copare the creep stiffness prediction of a icrostructure based discrete eleent odel (DEM) [1], the discrete eleent odel predictions with the coarse aggregate volue concentration ratios (i.e, c =.55 and c =.) were copared with the aster curve of the creep stiffness of the ixture as shown in Fig. 9. A calibration ethod was applied to reduce the possibility of under-counting the aggregate particles in the ixture odel, since the D odeling approach ay count insufficient aggregate-aggregate contact or interlock. The calibration ethod was adding extra fine aggregate particles (between. and 1.1 ). Therefore, the extra fine aggregate particles were part of the original aggregate skeleton, and therefore the ixture s coarse aggregate volue concentration ratio increased. When coparing with the aster curve of the creep stiffness fro discrete eleent odels, the odel prediction was iproved with the increasing aggregate volue concentration ratio. Finite eleent network odel (FENM) using elliptical aggregates was developed to study asphalt ixture behavior including creep stiffness [1,, 5]. In the FENM odel, the icrostructure of asphalt aterials is siulated with idealized elliptical aggregate and polygonal effective astic zone. FENM integrates viscoelastic astic eleents with rigid elliptical aggregates to predict global ixture behavior. Figure shows the coparison aong ixture creep stiffness predictions fro the FE and idealized FENM siulation, and the laboratory easureents. It was observed fro the figure that the FENM slightly over-predicted ixture creep

11 (GPa) Modulus Relaxation.. FEM FENM Test Data Reduced Tie (s) Fig. Coparison aong ixture creep stiffness prediction fro the FEM, and the idealized FENM siulation, and the laboratory easureents stiffness especially in the beginning of the loading tie. This occurs due to the odel assuption of rigid aggregates with infinity stiffness and idealized particle and astic zone shapes. The easureents of the creep stiffness are between the FE and FENM prediction bounds. Although soe liitations within D icroechanical FE and FENM predictions, the FE odel predictions in general, are reasonable by coparing the easureents of ixture creep tests. odulus and creep stiffness of the asphalt ixture were used to copare the odel predictions. In general, icroechanical FE odels provided reasonable predictions of the coplex odulus over a range of frequencies, and creep stiffness across a period of reduced loading tie. In order to show the different odel predictions, coparisons have been conducted aong the FE odel, a DEM and a FE network odel (FENM). FENM slightly overpredicted creep stiffness especially in the beginning of loading tie due to the odel assuption of rigid aggregates and idealized aggregate and astic zone shapes. Based upon the predictions fro FE and DE odels, it was found that these odels slightly underpredicted ixture odulus and creep stiffness, because of the liitation of aggregate-to-aggregate contact and interlock effects in the D odels. As future odeling efforts are extended to three-diensions, the prediction will be iproved with larger aount of inter-particle contacts and ore easureents of aggregates and astic. Acknowledgeent The authors acknowledge Dr. Willia Buttlar s assistance in the laboratory tests at the University of Illinois at Urbana-Chapaign. Conclusions The icrostructure-based FE odel was developed and applied to predict viscoelastic properties (coplex odulus and creep stiffness) of heterogeneous asphalt ixture. The D icrostructure of asphalt ixture was obtained by optically scanning the soothly sawn surface of asphalt speciens. In the icrostructure, aggregates and sand astic were divided into different subdoains. Finite eleent esh was generated within each aggregate or sand astic subdoain. Therefore the very irregular aggregate geoetry and astic doains are odeled using a nuber of FEs. Then the viscoelastic astic with specified properties in an ABAQUS user subroutine was cobined with elastic aggregates to predict the global viscoelastic properties of asphalt ixtures. An experiental progra was developed to easure the properties of the aggregates, sand astic, and asphalt ixture for FEM siulation and validation. The astic viscoelastic properties and aggregate elastic odulus were inputted for FE siulation. The laboratory easureents of the coplex References 1. Chen JS, Wong SY, Lin KY (5) Quantification of oveents of flat and elongated particles in hot ix asphalt subject to wheel load test. Mater Struct/Materiaux et Constructions 3:395. Voigt W (19) Ueber die Beziehung zwischen den beiden Elasticitatsconstanten isotroper Korper, pp Hashin Z, Shtrikan S (193) A variational approach to the theory of the elastic behaviour of ultiphase aterials. J Mech Phys Solids 11:137. Schapery R (197) Extension and replaceent of asphalt ceent sulfur. FHWA, US Departent of Transportation 5. Buttlar WG, Roque R (199) Evaluation of epirical and theoretical odels to deterine asphalt ixture stiffnesses at low teperatures (with discussion). Assoc of Asphalt Paving Tech 5: Buttlar WG, Roque R (1997) Effect of asphalt ixture aster copliance odeling technique on theral cracking perforance evaluation using superpave. University of Washington, Seattle, pp Hashin Z (195) Viscoelastic behaviour of heterogeneous edia. J Appl Mech Trans ASME 9:3 3. Christensen RM, Lo KH (1979) Solutions for effective shear properties in three phase sphere and cylinder odels. J Mech Phys Solids 7: Buttlar WG, Bozkurt D, Al-Khateeb GG, Waldhoff AS (1999) Understanding asphalt astic behavior through

12 icroechanics (with discussion and closure). Transportation Research Board, pp Shashidhar N, Needha SP, Chollar BH, Roero P (199) Prediction of the perforance of ineral fillers in stone atrix asphalt. J Assoc Asphalt Paving Tech : Chang GK, Meegoda JN (1997) Microechanical siulation of hot ixture asphalt. ASCE J Eng Mech 13: Chang GK, Meegoda JN (1999) Micro-echanic odel for teperature effects of hot ixture asphalt concrete. J Trans Res Record Natl Res Counc, Washington, DC 17: Rothenburg L, Bogobowicz A, Hass R (199) Microechanical odelling of asphalt concrete in connection with paveent rutting probles. In 7th International Conference on Asphalt Paveents, pp Trent BC, Margolin LG (199) Modeling fracture in ceented granular aterials. Geotechnical Special Publication, vol 3. ASCE, pp Buttlar WG, You Z (1) Discrete eleent odeling of asphalt concrete: a icro-fabric approach. Journal of the Transportation Board, National Research Council, Washington, DC, 1757: Ullidtz P (1) A study of failure in cohesive particulate edia using the discrete eleent ethod. Proc th Transportation Research Board Meeting, Washington, DC 17. Sadd MH, Qiu L, Boardan WG, Shukla A (199) Modelling wave propagation in granular edia using elastic networks. Int J Rock Mech Mining Sci Geoech Abstracts 9: Sadd MH, Gao JY (1997) The effect of particle daage on wave propagation in granular aterials, echanics of deforation and flow of particulate aterials. In: Chang CS, Misra A, Liang RY, Babic M (eds) Proc McNu Conference, Trans. ASCE, Northwestern Univ. 19. You Z, Buttlar WG () Discrete eleent odeling to predict the odulus of asphalt concrete ixtures. J Mater Civil Eng ASCE 1:1 1. You Z, Buttlar WG (5) Application of discrete eleent odeling techniques to predict the coplex odulus of asphalt-aggregate hollow cylinders subjected to internal pressure. J Trans Res Board Natl Res Counc 199:1 1. You Z, Buttlar WG () Microechanical odeling approach to predict copressive dynaic oduli of asphalt ixture using the distinct eleent ethod. Transportation Research Record. Journal of the Transportation Research Board, National Research Council, Washington, DC 197:73 3. Stankowski T (199) Nuerical siulation of failure in particle coposite, coputers and structures. Coput Struct Great Britain : 3. Sepehr K, Harvey OJ, Yue ZQ, El Husswin HM (199) Finite eleent odeling of asphalt concrete icrostructure. Proc 3rd Int Conf Coputer-Aided Assessent and Control Localized Daage, Udine, Italy. Bazant ZP, Tabbara MR, Kazei Y, Pijaudier-Cabot G (199) Rando particle siulation of daage and fracture in particulate or fiber-reinforced coposites, vol 9. Dallas, TX, USA: Publ by ASME, New York, NY, USA, pp Mora P (199) A lattice solid odel for rock rheology and tectonics. In The Seisic Siulation Project Tech., vol. Institut de Physique du Globe, Paris, pp 3. Budhu M, Raakrishnan S, Frantziskonis G (1997) Modeling of granular aterials: a nuerical odel using lattices, echanics of deforation and flow of particulate aterials. In: Chang CS, Misra A, Liang RY, Babic M (eds) Proc McNu Conference, Trans. ASCE, Northwestern Univ. 7. Guddati MN, Feng Z, Ki R () Toward a icroechanics-based procedure to characterize fatigue perforance of asphalt concrete. Transportation Research Record, pp Bahia HU, Zhai H, Onnetti K, Kose S (1999) Non-linear viscoelastic and fatigue properties of asphalt binders. Association of Asphalt Paving Technologists, pp Papagiannakis AT, Abbas A, Masad E () Microechanical analysis of viscoelastic properties of asphalt concretes. Transportation Research Record, pp Mustoe GGW, Griffiths DV (199) An equivalent odel using discrete eleent ethod (DEM). In Proc 1th ASCE Engineering Mechanics Conf., La Jolla, CA 31. Kose S, Guler M, Bahia HU, Masad E () Distribution of strains within asphalt binders in HMA Using Iage and finite eleent techniques. J Trans Res Record National Research Council, Washington, DC, Wang L, Frost JD, Shashidhar N (1) Microstructure study of westrack ixes fro X-ray toography iages. J Trans Res Rec Natl Res Counc, Washington, DC 177: Wang L, Paul HS, Haran T, D Angelo J () Characterization of aggregates and asphalt concrete using X-ray coputerized toography a state of the art report, vol 73. Association of Asphalt Paving Technologist, pp Masad E () X-ray coputed toography of aggregates and asphalt ixes. Mater Eval : Birgisson B, Soranako C, Napier JAL, Roque R (3) Siulation of fracture initiation in hot-ix asphalt ixtures. Transportation Research Record, pp Sadd MH, Dai Q, Paraeswaran V, Shukla A () Siulation of asphalt aterials using finite eleent icroechanical odel with daage echanics. Transportation Research Record, pp Sadd MH, Dai Q, Paraeswaran V, Shukla A () Microstructural siulation of asphalt aterials: odeling and experiental studies. J Mater Civil Eng 1: Dai Q, Sadd MH () Paraetric odel study of icrostructure effects on daage behavior of asphalt saples. Int J Pav Eng 5: Dai Q, Sadd MH, Paraeswaran V, Shukla A (5) Prediction of daage behaviors in asphalt aterials using a icroechanical finite-eleent odel and iage analysis. J Eng Mech 131: 77. Dai Q, Sadd MH, You Z () A icroechanical finite eleent odel for viscoelastic creep and viscoelastic daage behavior of asphalt ixture. Int J Nueric Anal Meth Geoech 3: Dai Q () Microechanical odeling of constitutive and daage behavior of heterogeneous asphalt aterials. University of Rhode Island

13 . You Z (3) Developent of a icroechanical odeling approach to predict asphalt ixture stiffness using discrete eleent ethod. University of Illinois at Urbana- Chapaign, Departent of Civil and Environental Engineering, UMI, a Bell & Howell Inforation Copany, Ann Arbor, MI 3. Dai Q, You Z (7) Prediction of creep stiffness of asphalt ixture with icroechanical finite eleent and discrete eleent ethods. J Eng Mech ASCE 133(): Dai Q, You Z, Sadd MH () A icroechanical viscoelaso-plastic odel for asphalt ixtures. Geotech Special Publication (GSP): Asphalt Concrete: Siul Model Exp Characterization. A Soc Civil Eng (ASCE), 1 5. Sadd MH, Dai Q, Paraeswaran V () Microstructural siulation of asphalt aterials: odeling and experiental studies. J Mater Civil Eng 1:7 115