Strain Response of Hot-Mix Asphalt Overlays for Bottom-Up Reflective Cracking

Transcription

1 Strain Response of Hot-Mix Asphalt Overlays for Bottom-Up Reflective Cracking Z. G. Ghauch and G. G. Abou Jaoude Department of Civil and Environmental Engineering, Lebanese American University, Byblos, Lebanon Abstract This paper examines the strain response of typical HMA overlays above jointed PCC slabs prone to bottom-up reflective cracking. The occurrence of reflective cracking under the combined effect of traffic and environmental loading significantly reduces the design life of the HMA overlays and can lead to its premature failure. In this context, viscoelastic material properties combined with cyclic vehicle loadings and pavement temperature distribution were implemented in a series of FE models in order to study the evolution of horizontal tensile and shear strains at the bottom of the HMA overlay. The effect of several design parameters, such as subbase and subgrade moduli, vehicle speed, overlay thickness, and temperature condition, on the horizontal and shear strain response was investigated. Results obtained show that the rate of horizontal and shear strain increase at the bottom of the HMA overlay drop with higher vehicle speed, higher subgrade modulus, and higher subbase modulus. Moreover, the rate of horizontal strain accumulation increases with higher overlay thickness. Although initial strain values were higher at positive pavement temperature distributions, the corresponding rate of strain increase were higher at negative pavement temperatures. Finally, an extrapolation of the strain history curve for various pavement design parameters was used to estimate the number of cycles for bottom-up crack initiation. Keywords: finite element method, reflective cracking, rigid pavement, viscoelasticity, HMA overlays, strain response. 1

2 1 Introduction 1.1 Background The most common rehabilitation technique for deteriorated pavements is the placement of an HMA overlay on top of the old Portland Cement Concrete (PCC) or Asphalt concrete (AC) pavement. This resurfacing technique is a quick and costeffective solution. It requires relatively low initial construction costs and short construction time. It re-establishes the surface smoothness, restores the skid resistance, strengthens the bearing capacity of the existing pavement, and provides a barrier against moisture infiltration. However, the advantages of HMA overlays are counterbalanced by the development of reflection cracks shortly after pavement rehabilitation. Reflective cracking refers to the propagation of cracks in the HMA overlay in a pattern that reflects the cracks and joints of the old pavement. Vertical and horizontal movements of the underlying pavement are commonly understood to be the basic mechanisms leading to reflective cracking [1]. These movements are associated with both traffic and environmental loadings. In fact, moving traffic loading, temperature cycling, and subgrade moisture variations induce stresses that can quickly reduce the life of an overlay. Figure 1 shows how bending and shear stresses develop in the HMA overlay due to a wheel load. Figure 1 also depicts how the crack or joint expand and contract due to temperature variations. In addition to that, existing cracks and joints in the old pavement reduce the bending stiffness of the resurfaced pavement and act as stress concentrators, further increasing the overlay stresses. The occurrence of reflective cracking under the combined effect of traffic and environmental loading significantly reduces the service life of the HMA overlay and can lead to any of the following consequences: 1) loss of surface water-tightness which causes moisture to infiltrate through the pavement, reduces its structural capacity, and potentially deteriorates the subgrade; 2) increase in deformations at the jointed concrete pavement discontinuity, which induces higher stresses and strains throughout the pavement structure; and 3) loss of serviceability associated with the deterioration of the wearing course and stripping of asphalt overlay at joints. Several field tests, laboratory tests, and FEM analysis have been conducted in order to investigate the effectiveness of various treatment strategies to mitigate reflective cracking. Such strategies include increasing HMA overlay thickness [2], using an asphalt rubber membrane [3], cracking and seating [4], rubblizing the concrete pavement, and using open-graded HMA mixtures [5]. In addition, placing stress relieving interlayer systems such as stress absorbing membrane interlayer (SAMI), interlayer stress absorbing composite (ISAC) [6], or geosynthetics like fabrics and grids, have been applied to reduce reflective cracking. Although some techniques have proven to be successful in delaying reflective cracking, others have failed to do so. The 2

3 results have underlined a significant variability in the performance of various reflective cracking control systems and have concluded that the effectiveness of a treatment is presumably dependent on many project-related factors. To date, none of the current treatment techniques have proven to be successful in preventing reflective cracking [7]. ΔT HMA Overlay PCC Slab Subbase Several design methods have been proposed in order to model the development of reflective cracking in HMA overlays. Existing design methods can be divided into three categories: 1) empirical design methods that are limited to certain field conditions; 2) purely mechanistic design methods that are difficult to conduct in routine projects and can be time-consuming; 3) mechanistic-empirical (ME) design methods that have an increasing popularity since they combine the mechanistic analyses derived from the FEM models with the required field experience to validate the models. Several researchers have proposed ME design methods for the purpose of quantifying the total number of load repetitions required to fail the overlay. However, a rigorous performance model that can be used to evaluate the effectiveness of different design alternatives against reflective cracking is yet to be found. 1.2 Objective And Scope Shearing Stress Bending Stress Figure 1: Idealized flexural and shear stress profile caused by the passage of a wheel load on rigid pavement and expansion-contraction of the pavement structure due to temperature variation The purpose of this study is to examine the strain state in typical asphalt concrete overlays on rigid pavements. Since reflective cracking is mostly described by Mode I (opening) and Mode II (shearing) failures, both imum horizontal and shear strains at the bottom of the HMA overlay are monitored. Emphases are placed on the rates of horizontal and shear strain accumulation. The effect of HMA overlay thickness, 3

4 subbase and subgrade moduli, seasonal temperature distribution, and vehicle speed on the imum horizontal and shear strain at the bottom of the HMA overlay are examined. Analyses are performed for both symmetric and edge wheel load positions. A total of 96 numerical simulations are performed in order to quantify the strain response of HMA overlays as shown in Table 1. HMA Thickness = 84, 120, 144mm Temperature Winter (temperature at HMA overlay: top = -18 C, bottom = 9 C) Spring (temperature at HMA overlay: top = 12 C, bottom = 5 C) Modulus of Subgrade (MPa) Modulus of Subbase (MPa) Speed (km/hr) 180 8, , , , , , , , 48 Table 1: Cases Investigated for each HMA overlay thickness, for both symmetric and edge load positions 2 Material Properties 2.1 Linear Viscoelastic (LVE) Constitutive Model HMA materials exhibit time and temperature dependent properties. At low temperatures and high frequency loading, HMA materials behave like elastic solids, while they behave as viscous fluid at high temperatures and low frequency loading. At intermediate temperatures and loading frequencies, these materials present viscoelastic properties, characterized, by a certain degree of elastic rigidity along with a dissipation of energy through frictional losses. Several researchers have successfully used a linear viscoelastic (LVE) constitutive model to represent HMA properties [8, 9]. Elseifi et al. [10] concluded that the elastic theory, as compared to the LVE theory, greatly underestimates the pavement responses, therefore pinpointing the need for a viscoelastic constitutive model. In this study, the HMA overlay is considered as a linear isotropic viscoelastic material, with a time-dependent stress represented as follows: σ t 2G τ τ ėdτ K τ τ ǿdτ where ǿ and ė are the mechanical volumetric and deviatoric strains, respectively, K and G are the bulk and shear modulus, function of the reduced time τ [11]. 1 4

5 The temperature dependent behavior is modeled by using a time-temperature shift factor. In ABAQUS, either the Arrhenius shift factor relationship or the Williams- Landel-Ferry (WLF) equation can be used. In this study, the WLF equation was used, and it can be expressed as follows: Log 10 a T C 1 T T 0 C 2 T T 0 2 where a T is the time-temperature shift factor, T 0 is the reference temperature (-10 C), C 1 and C 2 are regression coefficients obtained by fitting the WLF equation to the corresponding shift factors at various tests temperatures as shown in Figure 2. Figure 2: Fitting the WLF equation to the corresponding The Generalized Maxwell Model represents the viscoelastic behavior of the HMA overlay. This model is composed of a finite number [M] of Maxwell units and one spring element connected in parallel. A Maxwell unit is composed of a spring and dashpot connected in series to model elastic and viscous behavior, respectively. Each spring element is assigned a relaxation modulus E i, while each viscous dashpot is assigned a friction resistance η i. The relaxation function of the generalized Maxwell model is the following: E ξ Eo Ei e ξ τ where E i is the i th spring elastic modulus, τ i is the relaxation time of the i th Maxwell unit defined as τ i =η i /E i, and ξ=t/a T is the reduced time, function of the time t and a timetemperature shift factor a T. This equation is known as the Prony (or Dirichlet) series expansion. Using the Prony series expansion, the shear and bulk relaxation moduli are expressed in function of reduced time as follows: 3 5

6 GR t G0 1 gi 1 e τ τ KR t K0 1 ki 1 e τ τ 4 5 where k i and g i are dimensionless Prony series parameters, N is the number of parameters, K 0 and G 0 are the instantaneous bulk and shear relaxation moduli, respectively, and K R (t) and G R (t) are the bulk and shear relaxation moduli, respectively. Values of dimensionless shear relaxation moduli (g i ) and corresponding relaxation time (τ i ) are obtained from Reference [12] and are presented in Table 2. g 1 g 2 g 3 g 4 g 5 g 6 g 7 g 8 g τ 1 τ 2 τ 3 τ 4 τ 5 τ 6 τ 7 τ 8 τ 9 1.0E E E E E E E E E+04 Table 2: Prony Series parameters [12] (T ref =-10 C) All other material characteristics required for the model are assumed to exhibit isotropic linear elastic behavior, with typical values of Young s modulus (E) and Poisson s ratio (ν) selected from the literature (see Table 3). The Poisson s ratio of HMA materials is assumed constant with time. Elastic Modulus (MPa) Poisson's Ratio HMA Overlay PCC Subbase Subgrade Table 3: Typical material properties of pavement layers 3 Pavement Finite Element Model 3.1 2D FE Model A two-dimensional Finite Element (FE) plane strain model is used to simulate the pavement structure using the commercial FE software ABAQUS. A typical pavement transverse cross-section is chosen for this study. It consists of a 120mm thick HMA overlay, a 180mm thick PCC slab, a 250mm granular base, and a 2302 mm subgrade. A total of plane strain elements are used in the FEM model. A biased 6

7 mesh is implemented, with the smallest elements (2mm) in the zones of high stress and strain gradients, i.e. near the existing joint (see Figure 3). In order to simulate the most critical condition for reflective cracking, no load transfer devices are inserted between adjacent PCC slabs. This situation represents a jointed PCC slab with no load transfer mechanisms such as dowel bars and aggregate interlock, or a deteriorated jointed PCC slab whose load transfer efficiency is poor. Finally, all layers are assumed perfectly bonded. The limitations of a 2D FE model are well known. Among other shortcomings, the assumption of plane strain implies that the traffic load is infinite in the out-of-plane direction, leading to an overestimation of the stresses and strains in the pavement [13]. However, due to its low computational cost, a 2D FE model can be effectively used for a qualitative study of pavement response. Figure 3: (a) Plane strain FE model, and (b) constructed mesh near the PCC joint 3.2 Traffic and Temperature Loading Traffic loading is simulated as a 194mm single axle vehicle load. With one vehicle passage, the imum tire-pavement contact stress reaches a typical value of 700 KPa. In order to simulate cyclic loading, the load amplitude is varied with time, with alternating periods of loading and unloading, as shown in Figure 4. A haversine function is used to model the variation of load intensity with time. The duration of loading d, function of the speed s and the tire contact radius r, is determined as d=12r/s [14]. Three vehicle speeds of 8, 32, and 48 Km/h (5, 20, and 30 mph) are investigated. A total of 50 loading-unloading cycles, each with duration of 1s, are used to identify the time-dependent viscoelastic response of HMA overlays. A imum time increment of 0.025s is used in the FEM analysis. 7

8 Two temperature distributions are envisaged: a negative temperature distribution simulating a winter season, and a positive temperature distribution representing a spring season. Temperature differentials are included for the purpose of tracking the appropriate viscoelastic properties with temperature variation (Kim and Buttlar, 2002). Hence, thermal strains are not considered in this study. The main purpose is to examine the effect of a temperature e differential on the strain state in the HMA overlay after several vehicle passages. A bilinear temperature function is used to idealize the temperature distribution within the pavement structure. Figure 4: Variation of moving load intensity with time for a vehicle speed of 8km/h (2 cycles) 4 Results 4.1 Design Parameters In order to investigate the response of HMA overlays under subcritical cyclic loading, the following design parameters are included in the study: (1) overlay thickness, (2) vehicle speed, (3) subbase and subgrade moduli, and (4) temperature condition. The PCC slab modulus and thickness, the joint spacing, and the crack width are fixed. Unless otherwise specified, reference values are adopted as follows: 60 MPa subgrade moduli, 180 MPa subbase moduli, winter temperature condition, and 8km/hr vehicle speed. Results are shown at the point in the HMA overlay above the PCC joint where imum horizontal and shear strain occur. 4.2 Regression Model The horizontal bending strain resulting from a symmetric load and the shear strain resulting from an edge load are monitored at the bottom of the HMA overlay 8

9 above the PCC joint. Figure 5 visualizes the variation of total tensile and shear strain from 50 vehicle passages. The total strain shown may be divided into time-dependent and time-independent components (or recoverable and irrecoverable constituents). In other words, the total strain can be expressed as: 6 where ε t is the total or imum strain, ε c is the creep strain that is time-dependent and partly recoverable, ε e is the elastic strain, that is time-independent and recoverable. Permanent deformations are due to the irrecoverable part of creep strain. (a) (b) Figure 5: Strain History for (a) horizontal strain, and( b) shear strain for 50 loading cycles at reference values Peak values of corresponding horizontal and shear strains are selected and plotted on a natural logarithmic time scale. A regression analysis is performed on the plot showing the imum horizontal and shear strains versus the number of cycles. A natural logarithmic regression curve is found to best fit the data obtained for both the imum horizontal and shear strains, as shown in Eqs [7] and [8], respectively. ε N. ln N γ N C γ. ln N γ o In the above equations, ε is the peak horizontal bending strain, γ is the peak shear strain, N is the number of cycles, is the regression slope of the ε ln (N) plot, C γ is the regression slope of the γ ln (N) plot, ε 0 is the regression intercept of the ε ln (N) plot, and γ 0 is the regression intercept of the γ ln (N) plot. The regression slopes and C γ represent the rate of imum horizontal and shear strain increase, respectively. The regression intercepts ε 0 and γ 0 represent, 7 8 9

10 respectively, the magnitude of the imum horizontal and shear strain at the beginning of the loading period. In order to avoid obtaining negative values on the logarithmic plot, the first loading cycle is omitted and the regression analysis is performed from the second loading cycle onwards. 4.3 Effect of Individual Design Parameters on Strain Reponse In order to study the effect of HMA overlay thickness on the imum strain response, three overlay thicknesses were investigated as shown in Figure 6. As expected, an increase in HMA overlay thickness reduces both the imum initial horizontal and shear strains ( and γ o ) above the PCC joint. However, the rate of horizontal strain accumulation increases with higher asphalt overlay thicknesses, whereas the rate of shear strain accumulation decreases with higher overlay thicknesses. For a 144mm thick HMA overlay, the rate of horizontal strain accumulation is approximately 39% higher than that of an 84mm thick overlay (Figure 6a), while the rate of imum shear strain accumulation is 19% lower (see Figure 6b). The effect of subgrade strength is investigated using two subgrade moduli of and 60 MPa, while keeping all other parameters fixed. A drop in subgrade modulus from 60 to MPa causes an 8% increase in the initial imum horizontal strain level, and a 12.7 % increase in the rate of imum horizontal strain accumulation. The same drop in subgrade modulus causes a 7.7 % increase in the imum initial shear strain γ o and a 9.4 % increase in the rate of imum shear strain accumulation. The effect of subbase strength is examined using two subbase moduli of 180 and 275 MPa, with all other parameters fixed. An increase in modulus reduces the imum initial horizontal strain by approximately 10% and the rate of imum horizontal strain increase drops by 18%. Similarly, it can be observed that both the imum initial shear strain and rate of shear strain accumulation drop by 8.5% and 11.3%, respectively, as the subbase moduli increased. The effect of vehicle speed on the HMA overlay strain response is also examined. A well known fact is that low vehicle speeds inflict relatively important damage to the pavement structure [16, 17]. Clearly, as vehicle speed increases, viscoelastic HMA materials exhibit a higher strength due to increasing loading frequency. Also, the duration of application of tire-pavement contact stresses decreases with higher vehicle speeds. From Figure 7a, it can be observed that an 8km/hr speed, as compared to 48 km/hr, creates not only a higher initial imum horizontal strain, but also a higher rate of tensile strain increase, approximately 6 times larger. A very similar trend was observed for the shear strain response, as shown in Figure 7b. Finally, the effect of temperature condition on the HMA strain response is examined. As mentioned earlier, thermal strains are not envisaged since the purpose of the temperature differential is solely to include the proper viscoelastic properties. It can 10

11 be observed that the imum initial horizontal and shear strain magnitudes, and γ o, in spring are approximately 35% higher than that of winter. The rate of shear strain accumulation for a positive temperature distributions (spring) is found to be more (a) (b) Figure 6: Effect of HMA overlay thickness on (a) imum horizontal strain, and (b) imum shear strain state for a MPa subgrade moduli Figure 7: Effect of vehicle speed on (a) imum horizontal strain, and (b) imum shear strain at reference values than 2 times higher than that of a negative temperature distribution (winter), while the rate of horizontal strain accumulation is found the same for both temperature distributions. 11

12 4.4 Horizontal Bending Strain A total of 16 numerical simulations are performed for each HMA overlay thickness, with the vehicle load placed symmetrically over the pavement structure. Values of the slope of the logarithmic regression curve ( ), and the imum horizontal initial strain ( ) are presented in Tables 4, 5, and 6. Figure 8 plots the values of as a function of HMA overlay thickness for various design parameters. The following observations are made: Figure 8: Rate of imum horizontal strain increase as a function of asphalt concrete overlay thickness for subgarde moduli of MPa and winter temperature condition 1. All curves show an increasing trend, thus the rate of strain accumulation, represented by the slope of the logarithmic regression curve, increases with higher HMA overlay thicknesses, as shown in Figure The imum strain rate increase occurs at the lowest vehicle speed and subbase modulus. A 60% drop is noted in the average rate of horizontal strain increase as the vehicle speed increases from 8km/hr to 48km/hr for 60 MPa subgrade modulus and 180 MPa subbase modulus. Also, a 19% drop in the average strain rate increase is observed as the subbase modulus increased from 180 to 275 MPa, for a 60 MPa subgrade modulus. 3. A decrease in the subgrade modulus inflicts a higher rate of horizontal strain increase. For an 8km/hr vehicle speed and 180 MPa subbase modulus, the average rate of strain increase drops by exactly 13% as the subgrade modulus increases from to 60 MPa. 12

13 Winter Spring Modulus of Subgrade (MPa) Modulus of Subbase (MPa) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-04 Table 4: Logarithmic regression parameters for HMA overlay thickness of 84mm (symmetric load) Winter Spring Modulus of Subgrade (MPa) Modulus of Subbase (MPa) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-04 Table 5: Logarithmic regression parameters for HMA overlay thickness of 120mm (symmetric load) 13

14 Winter Spring Modulus of Subgrade (MPa) Modulus of Subbase (MPa) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-04 Table 6: Logarithmic regression parameters for HMA overlay thickness of 144mm (symmetric load) In addition, the rate of imum tensile strain increase found at negative pavement temperatures is higher than that found at positive temperatures, as shown in Figure 9. For all HMA overlay thicknesses, the higher rate of tensile strain increase at winter temperatures is more pronounced at low vehicle speed. As the vehicle speed increases, the difference between the rate of tensile strain increase measured at winter and spring decreases. Figure 9: Comparison of the rate of tensile strain increase at winter and spring temperature conditions as a function of subbase modulus and vehicle speed for a 120 mm HMA overlay and MPa Subgrade 14

15 4.5 Vertical Shearing Strain The same analyses are repeated for an edge load, and the corresponding imum shear strain in the overlay directly above the PCC joint is recorded. A natural logarithmic regression is also performed on the imum shear strain-time plot. Values of C γ, regression slope, and, imum initial shear strain, are presented in Tables 7, 8, and 9. The following observations are made: 1. No specific relationship is observed between the rate of imum shear strain accumulation and the asphalt concrete overlay thickness. In fact, the rate of shear strain accumulation is found dependent on the pavement temperature distribution. For a positive temperature distribution (spring), the rate of imum shear strain accumulation is found to increase with overlay thickness, whereas for negative temperature distributions (winter), the rate of shear strain increase drops with increasing overlay thickness. For a 275 MPa subbase, 48km/hr vehicle speed, MPa subgarde, and winter temperature condition, the rate of shear strain accumulation drops by 4.3% as the overlay thickness increases from 84 to 144mm. In spring conditions, the rate of shear strain accumulation increases by 14.7%, with all other parameters fixed. 2. The imum rate of shear strain accumulation is also found to occur at the lowest speed and subbase moduli. For a 60 MPa subgrade and a 180 MPa subbase, the rate of shear strain increase drops by more than 5 times as the vehicle speed increases from 8 to 48 km/hr. Moreover, for an 8 km/hr vehicle speed, the rate of shear strain accumulation drops by 13.6% as the subbase modulus increases from 180 to 275 MPa. 3. Finally, the rate of shear strain increase is found to drop with higher subgrade moduli. In fact, for an 8 km/hr vehicle speed and 180 MPa subbase modulus, the rate of shear strain accumulation drops by approximately 9% as the subgrade modulus increases from to 60 MPa. The rate of imum shear strain increase C γ found at negative pavement temperatures is higher than that found at positive temperatures at low vehicle speeds only (see Figure 10). However, as vehicle speed increases from 8 to 48 km/hr, the rate of shear strain accumulation is found higher in spring than in winter temperatures conditions. 15

16 Winter Spring Modulus of Subgrade (MPa) C γ γ 0 C γ γ 0 C γ γ 0 C γ γ 0 Modulus of Subbase (MPa) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-04 Table 7: Logarithmic regression parameters for HMA overlay thickness of 84mm (edge load) Winter Spring Modulus of Subgrade (MPa) Modulus of Subbase (MPa) E E E E E E E E-05 C γ γ 0 C γ γ E E E E E E E E C γ 2.106E E E E-06 γ E E E E-05 C γ 2.394E E E E-06 γ E E E E-04 Table 8: Logarithmic regression parameters for HMA overlay thickness of 120mm (edge load) 16

17 Winter Spring Modulus of Subgrade (MPa) C γ γ 0 C γ γ 0 C γ γ 0 C γ γ 0 Modulus of Subbase (MPa) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-05 Table 9: Logarithmic regression parameters for HMA overlay thickness of 144mm (edge load) Figure 10: Comparison of the rate of shear strain increase at winter and spring temperature conditions as a function of subbase modulus and vehicle speed for 120 mm HMA overlay and MPa Subgrade 4.6 Framework of a New Design Method Current design methods do not explicitly tackle the problem of reflective cracking, though one of the major causes of early pavement distress. Due to the lack of a proper design method against reflective cracking, fatigue equations of the form N f = C 1 (ε -C 2) 17

18 where C 1 and C 2 are constants, N f is the number of loads to failure, and ε is the imum bending strain, have been used in reflective cracking problems. This has underlined the fact that research is needed for the establishment of a new practical mechanistic design method against reflective cracking. This research may constitute the initial step in defining the framework of a new practical model for estimating the number of cycles for bottom-up crack initiation. Simply said, by knowing the rate of strain increase at the bottom of the HMA overlay for specific pavement parameters and loading conditions, and by knowing a typical value of the failure strain ε f of HMA overlays, one can provide an estimate of the remaining number of cycles for bottom-up cracking. By defining parameters and ε 0 for imum horizontal strain and C γ and γ 0 for imum shear strain, Equations (7) and (8) can be used to express the strain evolution in asphalt concrete overlays. By equating Equation (7) to the expected failure tensile strain ε f of typical asphalt mixtures, and solving for N f, number of cycles for bottom-up crack initiation, one can provide a reasonable estimate of the remaining number of cycles for bottom-up cracking. Equation (7) can be rearranged as follows: ε f. ln N ε f Cε. ln N f N 0 N f N 0 e ε ε 9 where N o is the number of cycles at the start of the loading period, ε 0 is the corresponding imum initial strain level, is the natural logarithmic regression coefficient, as presented in Tables 4, 5, and 6. Once N f is known, design iterations would have to be performed for various overlay thicknesses until the number of cycles for bottom-up reflective cracking initiation found from the above equation exceeds the expected design life of HMA overlays against reflective cracking. 5 Conclusion In retrospect, a plane strain FE model is constructed including (1) a moving traffic wheel load applied in a cyclic pattern, (2) a temperature differential simulating typical seasonal pavement temperature distributions, and (3) a linear viscoelastic constitutive model for simulating the time dependent properties of the HMA overlay. The LVE model is implemented using Prony series expansion parameters characteristic of typical HMA overlays. The objective is to investigate the strain response in asphalt concrete overlays above jointed PCC slabs for various design parameters. The various cases of pavement responses presented in this study are used to compare the pavement performance for different design parameters. The following conclusions are made: (1) 18

19 the rates of tensile and shear strain accumulation are found to decrease with higher vehicle speeds, higher subgrade and subbase moduli; (2) the rate of tensile strain increase at the bottom of the HMA overlay is found to increase with higher overlay thicknesses; (3) the rate of horizontal strain increase is high at negative pavement temperatures, as compared to positive ones, especially at low vehicle speeds; (4) the rate of shear strain accumulation is found to increase with overlay thickness for positive pavement temperatures, and to decrease for negative ones; and (5) the rate of shear strain accumulation found at winter temperature conditions is higher than that found at spring conditions for low speeds only (8km/hr); as the speed increased to 48 km/hr, the opposite was true. Due to the limitations of current computational resources, this study only examines the overlay strain response for a relatively very low number of cycles with respect to the expected design life of overlays. Values of N f found using equation [8] are too high, underlining the fact that laboratory tests, field measurements, and numerical simulations will have to be further conducted to be able to perform an extrapolation of the strains to a higher number of cycles. Until then, equations [7] and [8] can be used to predict the strain level in HMA overlays on rigid pavements for a certain limited number of cycles, well below that responsible for bottom up cracking initiation. Future research will have to include, among other things, 3D FE models calibrated with field strain measurements, as well as interface conditions allowing sliding and debonding. Acknowledgments We would like to thank Mr. Nadim Haddad, Head of the Geotechnical and Heavy Civil Engineering Department, Dar Al-Hansadah (Shair and Partners) for his insight and feedback on the research topic. References [1] Wu, R Finite element analysis of reflective cracking in asphalt concrete overlays. Ph.D. dissertation, University of California, Berkeley. [2] Sherman, G. (1982). Minimizing reflection cracking of pavement overlays. Technical Report NCHRP Synthesis 92, Transportation Research Board, National Research Council, Washington, D.C. National Cooperative Highway Research Program. 19

20 [3] Vallerga, B., Morris, G., Huffman, J., and Huff, B. (1980). Applicability of asphalt-rubber membranes in reducing reflective cracking. In Proceedings Association of Asphalt Paving Technologists Technical Sessions, volume 49, pages , Louisville, Kentucky. [4] Rajagopal, A., Minkarah, I., Green, R., and Morse, A. (2004). Long-term performance of broken and seated pavements. Transportation Research Record, (1869):3-15. [5] Hensley, M. (1980). Open-graded-asphalt concrete base for the control of reflective cracking. In Proceedings Association of Asphalt Paving Technologists Technical Sessions, volume 49, pages , Louisville, Kentucky. [6] Bozkurt, D., and Buttlar W. Three-dimensional finite element modeling to evaluate benefit of interlayer stress absorbing composite for reflective crack mitigation, Presented at 2002 Federal Aviation Administration Airport Technology Transfer Conference, Atlantic City, NJ, May, [7] Button, J. W. and Lytton, R. L. (2007). Guidelines for using geosynthetics with hot-mix asphalt overlays to reduce reflective cracking, Proceedings of the 86th Annual Meeting of the Transportation Research Board (CD-ROM), Washington, D.C. [8] Baek, J. and I. L. Al-Qadi. Mechanism of overlay reinforcement to retard reflective cracking under moving vehicular loading, Proc., Sixth RILEM International Conference: Cracking in Pavements, (I. L. Al-Qadi, T. Scarpas, and A. Loizos, eds.) Chicago, IL, 2008, pp [9] Kim, J., Roque, R., Byron, T., (2009). Viscoelastic analysis of flexible pavements and its effects on top-down cracking. Journal of Materials in Civil Engineering, Vol. 21, No. 7, pp [10] Elseifi, M. A., Al-Qadi, I. L., and Yoo, P. J. (2006). Viscoelastic modeling and field validation of flexible pavements. J. Eng. Mech., Vol 132 (2), pp [11] ABAQUS. (2009). Abaqus/Standard User s Manual, Version Dassault Systèmes, [12] Baek, J. (2010). Modeling reflective cracking development in hot-mix asphalt overlays and quantification of control techniques. Ph.D. dissertation, University of Illinois at Urbana-Champaign. 20

21 [13] Kim, J., and Buttlar, W. G., (2002). Analysis of reflective crack control system involving reinforcing grid over base-isolating interlayer mixture. J. Transp. Eng., 128 (4), [14] Huang, Y. H. (2004). Pavement analysis and design, Prentice-Hall, Upper Saddle River, N.J. [15] Sebaaly, P.E., Tabatabae, N., Kulakowsky, B.T., and Scullion, T., (1991). Instrumentation for flexible pavements-field performance of selected sensors. Final Report No. FHWA-RD , Vols. 1 and 2, Federal Highway Administration, Washington, D.C., Sep. [16] Zafir, Z., Siddharthan, R., and Sebaaly, P.E., (1994). Dynamic pavement-strain histories from moving traffic load. Journal of Transportation Engineering, Vol. 120, No. 5, pp