Thermal Cracking Simulations of Aged Asphalt Pavements using Viscoelastic Functionally Graded Finite Elements

Transcription

1 Theral Cracking Siulations of Aged Asphalt Paveents using Viscoelastic Functionally Graded Finite Eleents E. V. Dave, W. G. Buttlar & G. H. Paulino Departent of Civil and Environental Engineering, University of Illinois, Urbana, Illinois, United States ABSTRACT: Low teperature or theral cracking is a ajor source of asphalt paveent deterioration in cold cliates and/or in regions where high cooling rates are present. As asphalt paveents age and becoe stiffer, the potential for therally induced cracks which initiate fro the paveent surface increases. The current state of practice in the siulation of theral cracking for design and analysis does not account for the presence of property gradients, which have been shown to exist in asphalt paveent surface courses as a result of teperature- and aging-induced gradients. These gradients need to be considered in order to better understand how they ay affect the initiation and propagation of theral cracks. A novel siulation technique utilizing finite eleents with viscoelastic graded eleents enable accurate and efficient siulation of viscoelastic functionally graded aterials (VFGM) such as those present in aged asphalt paveents. In the current study, aging and teperature induced property gradients in asphalt paveents are siulated in the context of low teperature cracking. Three paveent structures are siulated along with three ixture types. Cooling events with different peak cooling rates have been siulated for each of these paveent systes. Siulation results for VFGM cases are copared with results obtained using hoogeneous aterial properties as a function of depth in the paveent. The results deonstrate significantly different theral cracking predictions when aging gradients are considered, as the age stiffening significantly increases stress concentrations near the surface of the siulated paveents. The effect of paveent aging exained in this study provided new insight towards the echaniss of theral cracking in asphalt paveents. The techniques introduced can be readily adapted in existing theral cracking odels which utilize linear viscoelastic aterial properties. KEY WORDS: Theral cracking, asphalt concrete, aging, functionally graded aterials, finite eleents, viscoelasticity. 1 INTRODUCTION AND MOTIVATION Theral cracking or low teperature cracking of asphalt concrete paveents continues to be a leading cause of preature paveent deterioration in regions of cold cliate and/or where significant theral cycling occurs. Recent advances in fracture testing and odeling of asphalt concrete aterials have greatly aided in the understanding of the key echaniss behind this iportant paveent distress, which can greatly reduce paveent lifespan and the lifespan of subsequent rehabilitation cycles. Integrated laboratory testing and cracking siulation procedures have been successfully ipleented for theral cracking predictions (Marasteanu et al. 27, Dave et al. 28). However, previous studies on theral cracking

2 ignore age stiffening of asphalt concrete and corresponding property gradients across the paveent thickness. The constituents of asphalt concrete include asphalt binder (bituen) and ineral aggregates. Asphalt binder is derived fro crude oil as a by-product of fractional distillation. Due to its organic nature, asphalt binder undergoes oxidative aging as tie progresses, the effect of which is ost easily identified as hardening or stiffening of the binder, and subsequently, the ixture. The effect of aging creates graded aterial properties due to variation in the aount of aging through the depth of the paveent. The Strategic Highway Research Progra (SHRP) Project A-68 investigated cheical coposition changes occurring during binder aging. The final report fro this project identifies the process of age hardening as a non-reversible and continuous process that extends throughout the life of a paveent (Branthaver et al. 199). The aging and teperature induced property gradients have been well docuented by several researchers in the field of asphalt paveents (for exaple, Mirza and Witczak 1996 and Chiasson et al. 28). The effects of aging are ost pronounced at the surface of the asphalt layer. In general, theral cracks initiate and propagate fro the surface of paveent and progress downwards. Hence, aging gradients are expected to have a detriental effect on theral cracking distress, particularly with respect to crack initiation. Ignoring aging gradients in prediction odels can lead to the significant under prediction of a paveent s theral cracking potential. The accuracy and efficiency of functionally graded approaches in capturing aging related property gradients have been previously deonstrated in the context of paveent stress responses under tire loading (Buttlar et al. 2, Dave et al. 2). This paper describes the developent and application of a specialized finite eleent ethod that is suited for siulations of viscoelastic functionally graded aterials (VFGM), such as asphalt paveents that have property gradients caused by aging and teperature gradients. The forulation is briefly described followed by results fro verification studies and application exaples involving theral cracking siulations in flexible paveents, with property gradients as predicted by the Mechanistic Epirical Paveent Design Guide software. 2 VISCOELASTIC FUNCTIONALLY GRADED FINITE ELEMENT METHOD This section presents the forulation developed for VFGM finite eleent ipleentation. The subsections describe general functionally graded viscoelastic theory, details of the finite eleent forulations, and selected odel verification exaples. 2.1 Viscoelastic Theory General viscoelastic theory can be found in several textbooks and articles, for exaple, Christensen (1982). A generalized Maxwell odel is utilized in this study due to its flexibility in representing a wide variety of viscoelastic aterials as well as the availability of established forulations in the literature. The constitutive relationship for generalized Maxwell odel can be given as, t dεx, σ x, E x ε x, Et x, d (1) d where σ is stress, ε is strain, is reduced tie and E is fully relaxed odulus and E t is relaxation odulus for the Maxwell chains. The relaxation odulus for Maxwell units is given by,

3 M / t e τ x η x E E x ; τ x E x 1 th The aterial paraeters E, ηare spring coefficients and viscosities for the Maxwell unit. The spring coefficients and viscosities are related through relaxation ties τ and the total nuber of Maxwell units in the odel is given by M. The effect of teperature on the aterial properties is accounted for through use of tie-teperature superposition principle. The superposition is governed tie-teperature shift factor a T which is a aterial property. The real tie t is related to the reduced tie and teperature T as, t at, (2) dt () T t For isotropic conditions the above shown constitutive relationships can be re-written in for of deviatoric and voluetric stress-strain relationships as, d kk kk K x kk Kt x, d d d s sij 2G xij 2 Gt x, d d where, K, Kt, G, Gt are shear and bulk relaxation odulus coponents following the s siilar descriptions as shown before. The deviatoric strain coponents are shown by ij and the corresponding stress coponents by s ij, these are evaluated as, 1 s 1 sij ij kkij ; ij ij kkij () where, ij is Kronecker s delta. 2.2 VFGM Finite Eleents The VFGM finite eleents utilized in this study are based on the forulations developed by Dave et al. (2). The tie-integration approach in this forulation is based on the recursive increental schee developed by Yi and Hilton (199). Siilar schees have been utilized for solving viscoelastic finite eleent probles by several researchers (for exaple, Muliana and Khan 28). In field of asphalt concrete an increental-recursive schee has been utilized by Dai and You (29) for analysis of asphalt ixtures undergoing daage in lab sized speciens. The increental-recursive forulations (Zocher et al. 1997) rely on deterination of increental stress coponents ( dσ ) in response to the strain increent ( dε ) given by, s ij R, dσ K x dε dσ (6) where, the stiffness is given by K and the viscoelastic history effect is accounted through R residual stress ter dσ. Using the constitutive relationships shown in equation () and recursive-increental forulation in equation (6), the voluetric and deviatoric stress increents can be evaluated as, M Gx x d / x s R dsij 2G x 1 e dij dsij 1 d (7) M Kx x d / x R d kk K x 1 e d kk d kk 1 d At any reduced tie the increent in reduced tie d and the corresponding strain n ()

4 rates R can be approxiated as, 1 ; dε ε d n n R d. (8) The residual stress can be evaluated for deviatoric and voluetric coponents using the approxiations shown in equation (8) as, M R / R / ds (1 e x x ) S ; d (1 e ) V ij n n kk n n 1 1 where, sybols S and V represent viscoelastic (history) stress contributions at any given reduced tie. These effects account for hereditary contributions should be tracked for each stress coponent throughout the entire range of tie-steps used in a given siulation. Also notice that these ters are independent for each Maxwell unit in the aterial constitutive properties. The viscoelastic stress contributions are updated for each tie increent. Using the approxiate strain rate (equation (8)) and the expansion of equations () and (7) the viscoelastic stress contributions can be evaluated as, M x s S n 2G x x1 e Rij S n1 e x V n K x x1 e Rkk V n1 e / / / / x x Notice that in the above shown forulations, the aterial properties G, K, G, K, are a function of space ( x ), aking the forulation non-hoogeneous in nature. In order to create a sooth gradation of aterial properties, which is expected in the case of aged asphalt concrete paveent, it is necessary to capture the aterial gradation effect within the eleent. These types of specialized eleents are coonly referred to as graded eleents. In general, two approaches have been proposed for graded eleents: (a) direct sapling of aterial properties as Gauss points; and (b) Graded eleents using generalized iso-paraetric forulations (Ki and Paulino 22). Dave et al. (2) extended the generalized iso-paraetric forulations for viscoelastic finite eleents. Buttlar et al. (26) have utilized elastic graded eleents for the analysis of aged asphalt paveents. In the present paper, the aterial gradation within the eleent is accounted for through direct sapling of aterial properties at the Gauss points. 2. Ipleentation and Verification The VFGM finite eleent forulations discussed in the previous section has been ipleented in the coercial software ABAQUS by eans of a user defined aterial subroutine (UMAT). Coercial software is chosen to take benefit of the existing features in the code and to ensure coputational efficiency. In order to verify the forulations and their successful ipleentation, a series of verification exaples were conducted. The verifications were conducted in three stages, naely viscoelastic verifications, thero-viscoelastic verifications, and VFGM verifications. The verifications were conducted by coparing the response of VFGM siulations to analytical reference solutions. The viscoelastic verifications were first conducted using creep and relaxation behavior of hoogeneous finite eleents at a selected reference teperature to iposed traction and boundary conditions. The aterial properties utilized for the viscoelastic and thero-viscoelastic probles are shown in Figure 1. Notice that the tie-teperature superposition in these exaples is perfored through use of WLF equations (Christensen, 1982). Figure 2 shows the creep and relaxation response of the boundary value probles in the for of creep displaceent and stress relaxations. Identical results were obtained for analytical solutions and the VFGM finite eleents developed in this study. This deonstrates (9) ()

5 Displaceent, u x (t) () Relaxation Modulus (MPa) Shift Factor, Log(a T ) the veracity of the forulations and their ipleentation. Thero-viscoelastic verifications were perfored to verify the accuracy of the VFGM eleent forulations in the context of tie dependent teperature conditions and teperature dependent viscoelastic properties. The boundary value proble siulated in this case is siilar to the theral stress restrained specien test (TSRST), which is soeties used for the evaluation of theral cracking perforance of asphalt concrete (AASHTO TP-). In order to ensure good accuracy for theral cooling and waring conditions, the teperature boundary conditions were chosen to ipose both waring and cooling events. The results fro the VFGM eleents proposed in this study were copared with the results obtained fro the coercial software ABAQUS. The coercial software does not have graded eleent capability hence the proble was solved using hoogenous aterial properties. Figure shows the variation of teperature with tie as well as the corresponding theral stresses generated in the restrained viscoelastic body. The stress response is shown for the forulations and ipleentation fro the present study as well as those obtained using ABAQUS, showing excellent agreeent Teperature (C) 6 Tie -1 1 Reduced 2 (sec) Figure 1: Relaxation odulus astercurve utilized for verification exaples. (insert: Tie-teperature superposition shift-factors, WLF equation) y Analytical Solution Present Study x (t) = h(t) h(t)=heaviside Function Tie (sec) Figure 2a: Coparison of analytical and finite eleent solution for viscoelastic bar in creep loading conditions. The final verification exaple presented in this paper is for a VFGM proble. This is an iportant verification step since it ensures the accuracy of present approach for siulation of non-hoogeneous viscoelastic probles. Analysis is conducted for the creep response of an exponentially graded VFGM bar. The results fro the present study are copared with an

6 Displaceent, u y ( x - ) Displaceent, u x (t) () Noralized Stress, x (t)/ x () analytical solution available in the literature (Mukherjee and Paulino 2) for the proble shown in Figure. Based upon the excellent agreeent observed, the VFGM odel developed and ipleented in this study was considered to be successfully verified y x u(t) u(t) =u h(t) h(t) = Heavyside function Tie (sec) Figure 2b: Coparison of analytical and finite eleent solution for viscoelastic bar in fixed grip loading conditions (stress relaxation). Y T(t) X Figure : Coparison of finite eleent solutions fro present study and coercial software ABAQUS for theral restrained boundary value proble. y 2 (t) E(t,x) x σt =σ t Analytical Solution (Mukherjee and Paulino 2) Present Study t = sec t = 2 sec (t) = h(t) 1.2 y t = 1 sec (t) t = sec x () x Figure : Coparison of creep displaceent results evaluated using analytical solution and finite eleent ethod (present study) for an exponentially graded VFGM bar Tie (sec)

7 SIMULATION MODEL AND RESULTS.1 Paveent Sections, Materials and Cracking Model In the present study, two paveent sections fro Minnesota Departent of Transportation s Road Research Facility (MnROAD) are studied, naely, MnROAD cell and cell. The scheatics of the paveent sections are shown in Figure 6a. Fracture and theral voluetric expansion and contraction properties for these sections are reported by Marasteanu et al. (26). The global aging odel (GAM) by Mirza and Witczak (1996) was utilized for deterining the graded viscoelastic properties. Coplex odulus (E*) is predicted by GAM as a function of depth of asphalt concrete layer, the sae odel was utilized for deterined unaged aterial properties. Notice that the unaged predictions ade in GAM are based on the Witczak Predictive Equation, which is also utilized in the AASHTO MEPDG software. Relaxation odulus (E(t)) was evaluated fro coplex odulus using analytical interconversion procedure (Schapery and Park 1999). Two field aging levels were siulated using GAM, three years ( Year Aged) and six years (6 Year Aged). The unaged and aged relaxation odulus astercurves are shown in Figure. Notice that in case of aged astercurves the aterial behavior is graded through the paveent thickness, showing stiffer and less relaxant behavior near the paveent surface. Low teperature cracking behavior is evaluated using the VFGM finite eleent ethod presented earlier. In addition to the VFGM capabilities, several other coputational odels have been incorporated in the analysis, such as, cohesive zone fracture odel (Song et al. 26) and teperature dependent theral expansion and contraction coefficients (Marasteanu et al. 27, Dave et al. 28). A critical conditions approach was utilized in the present study, whereby critical low teperature events were identified and siulated; e.g., winter days involving a very high cooling rate and/or a very severe low teperature event. MnROAD cell experienced a critical cooling event during the 1st 2nd February, 1996 and MnROAD cell had a critical event during the th 1 st January 2. Detailed descriptions of the odel and the theral boundary conditions can be found in Dave et al. (28)..2 Siulation Results The theral cracking odeling approach utilized in this study siulates the foration and downward propagation of a single crack during the critical cooling event. The cracking potential is evaluated by coputing the extent of daage (softening) and cracking (coplete aterial separation) through the thickness of asphalt concrete. Previous studies have deonstrated a good correlation between this crack/daage depth and cracking potential of the paveent (for exaple, Paulino et al. 26). For the different paveent aging levels and sections siulated in this study the siulation results are presented in Table 1. For coparison purposes the observed field cracking for the test cells is also included in the table. The observed cracking is based on crack counts perfored in 2, which corresponds to thirteen and six years of service life and associated aging gradients developed over this tie frae for the respective sections. The lowest paveent teperature reached during the critical cooling event for each section is also listed in Table 1. The effect of aging on siulated cracking behavior is evident fro the results shown in Table 1. The predicted paveent response under a critical cooling event appears to be consistent with the observed field cracking. For instance, in Cell, it is deonstrated that the critical cooling event would produce significant daage and downward cracking due to the effects of therally induced stress on the aged paveent syste. Although the current odel has only been applied to a single critical event, it is clear that this section is vulnerable

8 Asphalt Concrete AC12/1 16 (Cell ) PG8-28 (Cell ) Granular Base 9 (Cell ) (Cell ) Subgrade Relaxation Modulus (MPa) to cracking under theral cycling in this cliate cobined with the additional stress iposed by vehicular traffic. As a result, the observed oderate cracking level (6. of transverse cracking per of paveent length) is not unexpected, given the propensity for cracking under a critical cooling event as predicted in the current odel. Also notice that at the tie of crack count Cell had been in service for thirteen years however, due to liited scope of this study the greatest aging level studied was liited to six years. For Cell, the paveent section was not predicted to incur any discrete cracking and even very little daage during the critical cooling event. This corresponds well to the observed field perforance, which indicates that negligible transverse cracking had been recorded as of the end of the evaluation period in 2. More work is needed to fully validate the odel developed herein, by predicting cracking over ultiple cooling cycles and by considering the effects of oving wheel loads on crack oveent. 16 (Surface) 12 8 Height () (Botto) 2 1 Reduced Tie (sec) (b) Relaxation odulus for unaged section Relaxation Modulus (MPa) Relaxation Modulus (MPa) (a) Paveent Sections (Surface) (Surface) Height () (Botto) Reduced Tie (sec) (c) Relaxation odulus for year aged section 8 Height () (Botto) Reduced Tie (sec) (d) Relaxation odulus for 6 year aged section Figure : Paveent sections and relaxation odulus for unaged and aged conditions at -2ºC (Trends plotted for Section as function of tie and depth fro paveent surface). The results of this analysis suggest that field aging gradients should be considered in the prediction of theral cracking. This is an iportant finding, as the current MEPDG procedure does not consider aging gradients in theral cracking predictions. The coonly utilized approach in paveent analysis of assigning hoogeneous property to an asphalt layer or considering it by eans of a layered approach will lead to under prediction of theral

9 cracking potential and ay require a very high aount of esh refineent in the vicinity of the paveent surface. Hence, a graded approach such as the VFGM ethod presented herein provides an efficient and accurate alternative to the conventional layered approach. Table 1: Siulation results (extent of asphalt layer thickness daaged and cracked), observed field cracking and lowest paveent surface teperature during cooling event. Siulation Results Observed Field Lowest Paveent MnROAD Cell Aging Level Daage Cracking Surface Teperature Cracking (%) (Softening) (%) (/) (deg. C) Unaged Year 1 6 Year 79 8 Unaged Year 6 6 Year SUMMARY, CONCLUSIONS AND RECOMMENDATIONS A finite eleent forulation based on a recursive-increental tie integration schee is presented for viscoelastic functionally graded aterials (VFGM). The VFGM finite eleents are ipleented in coercial software ABAQUS using user defined aterial subroutine. The forulation and ipleentation are verified through series of exaples. Verification exaples deonstrate good agreeent between present approach and reference solutions. The VFGM analysis procedure has also been applied for low teperature cracking odeling of asphalt paveents. Two paveent sections are studied, each with unaged conditions and two aging levels ( and 6 years). Siulations results deonstrate that paveent aging has a significant effect on the extent of predicted theral cracking. A reasonable correlation was noted when coparing the observed field cracking with the predicted daage and cracking for the two sections investigated. Based on this study it can be concluded that the field aging gradients should be considered when predicting theral cracking perforance of the paveent. This is an iportant observation as the current MEPDG procedure does not consider aging gradients in theral cracking predictions. Furtherore, the VFGM finite eleents provide an efficient way of considering the aterial gradations. The coonly utilized approach in paveent analysis of assigning hoogeneous property to an asphalt layer or considering it by eans of a layered approach will lead to under prediction of theral cracking potential and ay require a very high aount of esh refineent in the vicinity of the paveent surface. The present study is liited in ters of the aterials and paveent sections studied, and ore validation is still needed. More sections and aging levels are recoended to be evaluated in future studies to further explore the effect of aging on theral cracking as well as other paveent distresses. Traffic effects, ultiple teperature cycles, and three diensional odeling are also needed in future odel revisions. Many of these aspects are being considered in an ongoing FHWA Pooled Fund Study on low teperature cracking. Further research is also required in field of non-hoogeneous aterial characterization of asphaltic aterials, especially for paveent saples obtained fro field sections. REFERENCES Branthaver, J.F., Petersen, J.C., Robertson, R.E., Duvall, J.J., Ki, S.S., Harnsberger, P.M.,

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