NUMERICAL INVESTIGATION OF DESIGN STRATEGIES TO ACHIEVE LONG-LIFE PAVEMENTS

Transcription

1 NUMERICAL INVESTIGATION OF DESIGN STRATEGIES TO ACHIEVE LONG-LIFE PAVEMENTS By Grace G. Abou-Jaoude, Assistant Professor Department of Civil Engineering, Lebanese American University, Blat, Byblos - Lebanon PO Box 36- Phone: (961) grace.aboujaoude@lau.edu.lb & Ziad G. Ghauch, Undergraduate Student Department of Civil Engineering, Lebanese American University, Blat, Byblos - Lebanon PO Box zdghaouche@gmail.com

2 ABSTRACT Increasing the HMA base thickness and modifying the HMA mixture properties to improve the resistance to fatigue cracking are among the most popular methods for achieving long-lasting pavements. Such methods are based on the idea of reducing the tensile strain at the bottom of the HMA layer below the Fatigue Endurance Limit (FEL), a level of strain below which no cumulative damage occurs to the HMA mixture. This study investigates the effectiveness of several design strategies involved in long-life, perpetual pavement design. A 3D Finite Element model of the pavement involving a linear viscoelastic constitutive model for HMA materials and non-uniform tire contact stresses is developed using ABAQUS The effects of asphalt base course thickness and mixture type, rich binder layer, and aggregate subbase layer are examined. Four asphalt base course mixture types, namely dense graded, polymer modified, high modulus, and standard binder, are studied as a function of the asphalt base course thickness. The results underline a better performance of the high-modulus asphalt base, as compared to the other base course mixtures. The aggregate subbase layer on top of subgrade soil showed a relatively minor effect on the longitudinal and lateral strain response at the bottom of asphalt base course. The addition of a rich binder layer at the bottom of the asphalt base course showed a significant reduction in tensile strains. Tables are provided as a guideline to assess the different alternatives in design of long-life perpetual pavements. Keywords: long-life pavement, perpetual pavement, strain response, finite element method, linear viscoelastic theory, fatigue endurance limit 2

3 Introduction Research on long-life pavements, also known as perpetual pavements, has evolved over the last decade. APA (2002) defined a perpetual pavement as an asphalt pavement designed and built to last longer than 50 years without requiring major structural rehabilitation or reconstruction, and needing only periodic surface renewal in response to distresses confined to the top of the pavement. The advantages of such pavements were clear when Full-Depth1 and Deep-Strength2 asphalt pavements started showing superior performance after being in service for several decades. The design concept of Full-Depth and Deep-Strength pavements was based on the idea of substituting the thick layers of gravel in conventional pavements by layers of HMA, thus reducing the total pavement thickness (Yoder and Witczak 1975). The primary purpose of long-life pavements is two-fold: 1) resist bottom-up fatigue cracking in the hot-mix asphalt layers, and 2) resist rutting of the subgrade. They are considered the most cost-effective and long-lasting solution for roads subjected to heavy traffic. If properly rehabilitated through periodic repair for surface distress, these pavements present no major structural failures. A typical cross-section of a long-life pavement structure is shown in Figure 1. The description of each layer is based on the Asphalt Pavement Alliance definition of a long-life, perpetual, pavement (Harm 2001). Figure 1 - Typical cross section for a long life, perpetual pavement The long-lasting characteristics of these pavements has led researchers to investigate the presence of a Fatigue Endurance Limit (FEL) below which the HMA structure does not endure any permanent fatigue damage for an infinite number of load 3

4 repetitions. The concept of a FEL was based on the observation that bottom-up fatigue cracking does not occur in thick pavements where asphalt tensile strains were relatively low. Monismith and McLean (1972) and Thompson and Carpenter (2006) conducted a series of laboratory fatigue tests and observed from a log-log plot of strain versus bending cycles that the fatigue life dramatically increased below the FEL. Thompson and Carpenter (2006) considered the FEL as the balance point between healing and damage of the HMA. When the strains were below the FEL, the healing potential of the HMA overcame the damage inflicted by the loading cycles. For strains higher than the FEL, the healing potential of HMA was exceeded by the damage done. An extensive literature review on the value of the FEL showed that no single value existed for this limit; however numerous researchers talked about a range between 60 and 100 µε for flexible pavements depending on the mix type (Monismith and McLean (1972), Nunn (1997), Monismith and Long (1999), Nishizawa et al. (1997), Mahoney (2001), and Carpenter et al. (2003)). Most recently, the NCHRP 646 report, published in 2010, presented a detailed study that investigated the presence of an endurance limit and recommended a procedure to incorporate its effects into mechanistic pavement design methods. Moreover, this report underlined three strategies that were found successful in prolonging the pavement fatigue life: 1) use of high modulus asphalt mixtures in the base layer, 2) use of fatigue-resistant bottom layers, and 3) use of polymer modified asphalt binder. The effectiveness of these design strategies has been shown through laboratory and field experiments. Molenaar et al. (2009) showed that the use of a high modulus, stiff, base layer could reduce the asphalt thickness by up to 40%. Monismith et al. (2001) measured the fatigue life of asphalt mixtures using beam fatigue testing according to AASTHO T321, at 20. The results showed that the fatigue life approximately doubled as the asphalt binder content was raised by 0.5% and the air voids lowered by 3%. Anderson and Bentsen (2001) and Harvey et al. (2004) reported similar findings of increased fatigue life with higher asphalt binder content. Goodrich (1988) observed from flexural beam fatigue tests that the fatigue life of modified asphalt mixtures was an order of magnitude higher than that of conventional asphalt mixtures. Lee et al. (2002) observed a ten times greater fatigue life for mixtures made with SBS-modified PG asphalt binder, as compared to conventional asphalt binders. It is, thus, clear that prolonging the pavement design life is greatly dependent on limiting the flexural strain at the bottom of the asphalt base layer. Being able to meet this 4

5 goal without excessive costs is a critical issue. This paper presents a parametric study on the performance of Full-Depth and Deep-Strength pavements under a moving wheel load using three dimensional finite element modeling. The effect of asphalt base thickness and asphalt mixture type on the tensile strain response of the bottom asphalt layer is investigated. Four asphalt mixtures, namely dense graded, polymer modified, high modulus, and standard binder are used in the asphalt base layer. The advantage of using a rich bottom layer in the perpetual pavement section is also investigated. Visco-elastic material properties are used to characterize the HMA layers and to include the time and temperature dependent behavior of the asphalt material. This numerical investigation is intended to assess different design alternatives and to provide a roadmap for an efficient design based on the type and cost of available materials. Material Properties To achieve long-life asphalt pavement structures with typical service lives in excess of 50 years, the selection of proper materials for each of the surface course, intermediate course, and base course is crucial. Although resurfacing the pavement every 20 years or so is acceptable, each asphalt layer should provide minimum durability in order to sustain a long-lasting performance without structural failure. Newcomb et al. (2001) stated that the upper layers of the pavement should provide enough stiffness to eliminate rutting potential, while the lower layers of the asphalt pavement should provide enough flexibility in order to avoid bottom-up fatigue cracking. The total thickness of the pavement should be sufficient to ensure that tensile strains at the bottom of the asphalt layers are below the FEL. High performance graded (PG) binders, such as the stone matrix asphalt (SMA), are commonly used in the wearing course to provide proper aggregate-to aggregatecontact to achieve a load carrying capacity, and enough binder and filler content to provide the surface mix enough impermeability and stiffness. The High performance graded (PG) binders, such as the stone matrix asphalt (SMA), are commonly used in the wearing course to provide proper aggregate-to aggregate contact to achieve a load carrying capacity, and enough binder and filler content to provide the surface mix enough impermeability and stiffness. The intermediate course is usually composed of an asphalt mixture that combines the stiffness of the upper layer with the flexibility of the lower layers. The intermediate course provides a minimum level of rut resistance and durability. 5

6 The asphalt base layer must present enough flexibility and fatigue cracking resistance such that bottom up fatigue cracking does not initiate under traffic loading. In this study, the asphalt concrete mixture types and properties for all pavement layers were extracted from Liao (2007) and Al-Qadi et al. (2008). A rich binder mix was used in the parametric study to investigate the effect of high asphalt binder content on the tensile strains at the bottom of the asphalt base. Properties of this mix were also extracted from Liao (2007). Finite Element Model Two pavement structures were modeled in this study. The first model simulates a Deep-Strength asphalt pavement structure. It consists of a 50 mm surface course, a 50 mm intermediate course, a 100 mm to 250 mm asphalt base course, a 180 mm aggregate subbase, and a 2880 mm subgrade. The aggregate subbase layer was excluded in the second model to simulate a Full-Depth pavement. In order to assess the impact of using a rich binder mix in the base course, the parametric analysis included a 100mm thick rich binder layer as part of the total thickness of the base course layer. The dense graded mix, standard binder mix, polymer modified binder mix, and high-modulus mix were used to simulate a total of 58 analysis cases in order to quantify the strain response of Deep- Strength and Full-Depth pavements to a moving wheel load. The pavement models were developed using the finite element software ABAQUS 6.11 (ABAQUS 2011), as shown in Figure 2. The modeled section of the pavement was 4,750 mm in the transverse direction and 3,600 mm in the traffic direction. Such dimensions were selected as a compromise between minimizing boundary effect errors and achieving accurate results at the lowest computational cost. Only half of the pavement was modeled in the transverse direction. Symmetric boundary conditions were adopted along the longitudinal symmetry plane. Fixed boundary conditions were assigned for the remaining planes in the model. A graded mesh was implemented in order to achieve the highest accuracy without increasing the computational cost. A relatively fine mesh (20mm) was used in the upper pavement layer and in the vicinity of the vehicle load path. The length of elements in the wheel path was on average 10 mm in the transverse direction and 20 mm in the longitudinal direction. Larger elements were used farther from the loading path. A total of 44,100 C3D8R elements (8-node linear brick with reduced integration) were used in the model. 6

7 Figure 2-3D Finite Element mesh configuration of a Deep Strength pavement with 100mm rich binder layer included in the asphalt base course To simulate the movement of an 80 kn single axle dual-tire load passage at a speed of 8 km/h, a quasi-static approach was implemented by gradually shifting the contact area of the load along the loading path. A total of 170 increments, each with a duration of 9 milliseconds and a length of 20 mm, were used to model one full wheel load passage. Longitudinal and lateral strains at the bottom of the asphalt base layer were examined for one load passage. In order to simulate the most critical condition for fatigue failure, a relatively high pavement temperature distribution was adopted. Initially, the pavement temperature was set to 20 C, and subsequently, a 15 C increase in pavement surface temperature was simulated. An exponential function was used to simulate the thermal gradient such that the temperature at the top of the surface course was 35 C, and the temperature at the top of subgrade (for Full-Depth pavement) or aggregate base (for Deep-Strength pavement) was 20 C. Viscoelastic Material Characterization Flexible pavements have been traditionally modeled as multilayer linear elastic systems. However, the behavior of HMA materials is highly time and temperature dependent. At low temperatures and short loading duration, they behave as elastic solids, 7

8 while at high temperatures and long loading duration, they present viscous properties. At moderate temperatures and loading durations, HMA materials exhibit both the rigidity of elastic solids, and energy dissipation by frictional losses which are a characteristic of viscous fluids. In this study, viscoelastic properties of HMA materials are represented using a linear viscoelastic (LVE) constitutive model which is a simple yet sufficiently accurate tool for modeling the behavior of asphalt materials. All HMA materials used in the FE model are assumed to behave as thermorheologically-simple (TRS) materials, i.e, time-temperature superposition principle is valid. The latter implies that the material behavior at low temperatures is identical to that at high frequency loading, while the behavior at high temperatures is the same as that at low frequency loading. Based on this idea, the long-term behavior of viscoelastic materials is simulated at relatively high temperatures instead of performing laboratory tests over a long duration. For linear isotropic viscoelasticity, the basic hereditary integral formulation is expressed as follows: t ò 0 0 t.. s(t)= 2G( t - t ')ed t '+ K( t - t ') f d t ' ò Where t dt' t = ò a [T (t')] 0 T In the above equations, ø and e are the mechanical volumetric and deviatoric strains, respectively; K and G are the bulk and shear modulus, function of the reduced time τ; and at is a shift function dependent on the temperature T (ABAQUS 2011). The time dependent behavior of asphalt concrete is simulated in ABAQUS 6.11 using the Prony (or Dirichlet) series expansion expressed in the form of shear modulus. The shear modulus is calculated from the relaxation modulus using the following equation: E( t ) G( t )= 2(1+ u ) Where G(τ) is the shear modulus, E(τ) is the relaxation modulus, and ν is the Poisson s ratio of asphalt concrete, assumed constant (as for isotropic homogeneous materials). A 8

9 simple normalization of the obtained shear modulus G(τ) with respect to the instantaneous shear moduli is done to obtain a shear modulus ratio g(τ), expressed as: N t - t i i i=1 g( t )=1-å g (1-e ) Where N is the number of Prony series terms (N=9), τi is the retardation time, and gi is a dimensionless Prony series parameter. The temperature dependent behavior of asphalt concrete is modeled using a timetemperature shift factor. In ABAQUS 6.11, either the Arrhenius shift factor relationship or the Williams-Landel-Ferry (WLF) equation can be used. In this study, the WLF equation (Williams et al. 1955) is used: C (T -T ) 1 0 Log 10(a T )=- C 2 +(T -T 0 ) where at is the time-temperature shift factor, T0 is the reference temperature, C1 and C2 are regression coefficients obtained by fitting the WLF equation to the corresponding shift factors at various tests temperatures. Tire Contact Stresses Thompson and Carpenter (2006) observed that occasional overloads greater than the critical 80kN single axle dual-tire load (SAL) will not significantly reduce the HMA fatigue life and their limited occurrence will not eliminate the concept of no damage accumulation below the FEL. Thus, an 80 KN single axle dual-tire load (SAL) is used in this study. Also, knowing that the vertical stresses at the tire-pavement interface are not uniformly distributed throughout the contact area, measurements of tire-pavement contact stresses were obtained from the literature. The Goodyear 295/75R22.5 tire was used based on the measurements of contact stress distribution that were obtained from Park et al. (2005). Table 1 shows the tread contact stresses of the Goodyear 295/75R22.5 tire measured using the Vehicle Road Surface Pressure Transducer Array (VRSPTA). For the 80 kn single axle dual-tire assembly, each tire is loaded 20kN. The corresponding values of vertical pressure at each tread/tire are interpolated from the values in Table 1. Figure 3 shows the dimensions of the Goodyear 295/75R22.5 tire footprint and the corresponding vertical contact stress for each tread. 9

10 Table 1 - Table 1 Goodyear 295/75R22.5 tread contact stresses using VRSPTA (Park et al 2005) Figure 3 - Figure 3 Goodyear 295/75R22.5 tire imprint (dimensions in mm) 10

11 Results and Analysis Unless otherwise specified, the Deep-Strength pavement model with 100-mm Dense Graded Asphalt Base Course is used as the reference example for presenting and analyzing the results of this parametric study. Effect of Asphalt Base Binder Course Mix Type The effect of the asphalt base course mixture on the horizontal flexural strain at the bottom of the asphalt pavement is examined. As shown in Figure 4, the longitudinal tensile strains levels are lowest for the high-modulus asphalt base mixture. In percentages, the maximum tensile longitudinal strain for the high-modulus base course is 60.7 %, %, and % lower than that of dense graded, polymer modified, and standard binder courses, respectively. Similar variations are obtained for the maximum lateral strains when comparing the performance of high modulus asphalt to the other base course types. The maximum lateral tensile strain for the standard binder asphalt base is % higher than that of the high-modulus layer, while that of the polymer modified and dense graded asphalt base were % and 65.1 % higher, respectively. Effect of Asphalt Base Course Thickness The thickness of the asphalt base course is directly related to the reduction in horizontal strains at the bottom of the asphalt pavement section. Figure 5(a) shows how the values of longitudinal flexural strains drop at a decreasing rate with increasing thickness. The standard binder asphalt base course shows the steepest drop. The maximum tensile longitudinal strain decreases by 1.14µε/mm when the asphalt base thickness increases by 50 mm. This decrease becomes 0.85µε /mm for another 100 mm increase in thickness. Although the level of longitudinal flexural strain in the standard binder mixture is initially higher than that of the high-modulus mixture, an increase in asphalt base thickness is more effective in reducing the longitudinal strain for the standard binder asphalt base mixture. The same increase in thickness is least effective for the highmodulus asphalt base mixtures. In summary, as the asphalt base thickness increased from 100 mm to 250 mm, the level of longitudinal flexural strain in the standard binder asphalt base dropped by %, while it dropped by % in the high-modulus asphalt base mixtures. 11

12 Figure 4 - Effect of asphalt base course mix type on the longitudinal and lateral strains Figure 5(b) shows that as the asphalt base course thickness increases, the drop in lateral peak strain is more pronounced at high base thicknesses. For a standard binder asphalt base course, the maximum lateral strain drops by only 0.075µε/mm when the asphalt base thickness increases from 100 mm to 150 mm, while it drops by 0.43µε/mm as the asphalt base thickness increased from 150 mm to 250 mm. Similarly to longitudinal strains, the values of lateral strain are highest in the standard binder asphalt base and lowest for in the high-modulus asphalt base. With increasing asphalt base thickness, the lateral strain in the high-modulus asphalt base layer decreases at a slightly lower rate than the other asphalt mixtures. 12

13 Figure 4 - Maximum longitudinal and lateral strain values as a function of asphalt base course mix type and thickness Effect of Aggregate Subbase Layer The aggregate subbase layer in the Deep-Strength pavement model showed that it has a positive effect in reducing the tensile strain values when the base course thickness is small. Figure 6 shows the decrease in maximum longitudinal and lateral strains with increasing base course thickness for both Full-Depth and Deep-Strength pavements using the dense-graded base course mix. The results show that the aggregate subbase layer reduced the level of longitudinal strain by approximately the same amount for all asphalt base thicknesses. On average, the values of longitudinal flexural strain dropped by 34 % with the addition of the aggregate subbase layer. 13

14 Figure 5 - Maximum longitudinal and lateral strain values as a function of pavement type and asphalt basecourse thickness Effect of the Rich Binder Mix in the Asphalt Base Course Figure 7 shows that the effectiveness of including a rich binder layer decreases with increasing asphalt base thickness. For instance, for the deep-strength pavement with dense graded asphalt base, the level of longitudinal peak strain drops 2.2 times with the addition of the rich binder layer for a total thickness of asphalt base course of 150 mm, while it drops 1.9 times for a 250 mm total thickness. Similarly, by including the rich binder layer, the lateral flexural strain decreases 2.5 times for a 150 mm total thickness of asphalt base course, and 2.2 times for a 250 mm total thickness. It is thus clear that a rich binder layer placed at the bottom of the asphalt base course acts as a fatigue resistant 14

15 layer that significantly decreases the strain values at the bottom of the pavement section. The effectiveness of this layer, however, decreases as the total base course thickness increases. Figure 6 - Effect of rich binder layer as a function of asphalt base course thickness Table 2 - Maximum longitudinal strains for Deep Strength and Full Depth pavements without the 100 mm rich binder layer 15

16 Table 3 - Maximum lateral strains for Deep Strength and Full Depth pavements without the 100 mm rich binder layer Table 4 - Maximum longitudinal strains for Deep Strength and Full Depth pavements including the 100 mm rich binder layer Table 5 - Maximum lateral strains for Deep Strength and Full Depth pavements including the 100 mm rich binder layer 16

17 Maximum Longitudinal and Lateral Flexural Strain The results of the parametric study for the maximum longitudinal and lateral flexural strains of Deep-Strength and Full-Depth pavements are shown in Table 2 and Table 3, respectively. Table 4 and Table 5 show that the presence of a 100-mm rich binder mix at the base of the asphalt pavement section significantly reduces both longitudinal and lateral flexural strains. Knowing that the Fatigue Endurance Limit (FEL) for typical HMA mixtures varies between 60 and 100 µε depending on the mix type, values presented in these tables can be used as a guide in selecting design alternatives that would limit the tensile strain at the bottom of the HMA layer below the chosen FEL value in a particular design. As a general guideline, the longitudinal and lateral tensile strains at the bottom of the HMA layer are found to be most sensitive to a change in asphalt base course thickness. In addition, the rich binder layer is found to have a crucial role in reducing the maximum tensile longitudinal and lateral strain below 100 µε. The maximum longitudinal tensile strain drops approximately 1.7 times when the mix of the 100mm asphalt base is changed from a dense graded to a rich binder mix. Similarly, the rich binder mix layer decreases the maximum lateral strain by approximately 1.8 times. If the rich binder layer is not used, other design strategies can be selected in order to limit the maximum tensile longitudinal and lateral strain below the FEL. Conclusions and Recommendations This study examined different design alternatives used to achieve a long-life, perpetual pavement. A 3D FE pavement model involving Linear Viscoelastic (LVE) properties for HMA materials and non-uniform tire contact stresses was developed using ABAQUS. The results of the parametric study showed that the high modulus mix used in the asphalt base course outperformed all other asphalt mixtures. It presented the lowest levels of longitudinal and lateral strains. The dense-graded and polymer modified mixes ranked second in reducing the values of tensile strains at the bottom of the asphalt pavement. The longitudinal strain values in the standard binder mix were higher than that of the highmodulus mix; however, these values decreased significantly when the asphalt base course thickness was increased. The effect of varying the asphalt base course thickness was lowest for the high-modulus asphalt base mix. The aggregate subbase layer on top of subgrade soil was found to have a relatively small impact on the longitudinal and lateral strains at the bottom of the asphalt base layer. The addition of a rich binder layer at the bottom of the asphalt base course significantly reduced the longitudinal and lateral 17

18 strains. Increasing the asphalt base thickness was found more effective in reducing the strain levels in cases where the rich binder mix was not included. The results of this parametric study can be easily compared to the results of laboratory and field testing that were obtained from the literature review. Conclusions drawn from this numerical assessment of design strategies used in long-life, perpetual, pavements were found to complement the research findings of Molenaar et al. (2009), Monismith et al. (2001), Anderson and Bentsen (2001), Harvey et al. (2004), Goodrich (1988), and Lee et al. (2002), that were presented in the beginning of the paper. Finally, the values of longitudinal and lateral strains presented in Table 2 totable 5 were provided as a guideline to assess various design alternatives to achieve a long-life pavement. Knowing that a high positive pavement temperature distribution was used in this model, the measured flexural strains are expected to be the highest during the seasons of the year. Hence, values presented in Table 2 to Table 5 are considered to be conservative, since during most of the remaining of the year, the flexural strains at the bottom of the HMA layer will be of lower magnitude. References Perpetual Pavements: A Synthesis. Asphalt Pavement Allliance, Lanham, Md., Yoder, E.J., and M.W. Witczak. Principles of Pavement Design. 2nd ed., John Wiley & Sons, Inc., New York, 1975 Harm, E. Illinois Extended-Life Hot-Mix Asphalt Pavements. Perpetual Bituminous Pavements. Transportation Research Circular Number 503, Transportation Research Board, Washington, D.C., 2001, pp Monismith, C.L. and D.B. McLean. Technology of Thick Lift Construction: Structural Design Considerations. Proceedings: Association of Asphalt Paving Technologists. White Bear Lake, Minnesota., 1972, Vol. 41, pp Thompson, M.R., and S.H. Carpenter. Considering Hot-Mix-Asphalt Fatigue Endurance Limit in Full-Depth Mechanistic-Empirical Pavement Design. Proceedings: International Conference on Perpetual Pavements. CD-ROM. Ohio University, Columbus, 2006 Nunn, M. Long-life Flexible Roads. Proceedings: 8th International Conference on Asphalt Pavements, University of Washington, Seattle, August 1997, Vol. 1, pp Monismith, C.L. and F. Long. Mix Design and Analysis and Structural Section Design for Full Depth Pavement for Interstate Route 710. Technical Memorandum TM UCB PRC Pavement Research Center. Institute for Transportation Studies. 18

19 University of California, Berkeley, Nishizawa, T., S. Shimeno, and M. Sekiguchi. Fatigue Analysis of Asphalt Pavements with Thick Asphalt Mixture Layers. Proceedings: 8th International Conference on Asphalt Pavements, University of Washington, Seattle, August 1997, pp Mahoney, J.P. Study of Long-Lasting Pavements in Washington State. Perpetual Bituminous Pavements. Transportation Research Circular Number 503, Transportation Research Board, Washington, D.C., 2001, pp Carpenter, S.H., K.A. Ghuzlan, and S. Shen. Fatigue Endurance Limit for Highway and Airport Pavements. In Transportation Research Record: Journal of the Transportation Research Board, No. 1832, Transportation Research Board of the National Academies, Washington, D.C., 2003, pp Prowell B.D., E.R. Brown, R.M. Anderson, J.S.D.A.K. Swamy, H. Von Quintus, Sh. Shen, S.H. Carpenter, S. Bhattacharjee, and S. Maghsoodloo. Validating the Fatigue Endurance Limit for Hot Mix Asphalt. NCHRP Report 646, Transportation Research Board, National Research Council, Washington, DC, Molenaar, A.A.A., M.F.C. van de Ver, M.R. Poot, X. Liu, A. Scarpa, E.J. Scholten, and R. Klutz. Modified Base Courses for Reduced Pavement Thickness and Increased Longevity. Proceedings: International Conference on Perpetual Pavements. CD-ROM. Ohio University, Columbus, Monismith, C.L., F. Long, and J.T. Harvey. California s Interstate-710 Rehabilitation: Mix and Structural Section Designs, Construction Specifications. Journal of the Association of Asphalt Paving Technologists, Vol. 70, Clearwater Beach, FL, 2001, pp Anderson, R. M. and R. Bentsen. Influence of Voids in Mineral Aggregate (VMA) on the Mechanical Properties of Coarse and Fine Asphalt Mixtures. Journal of the Association of Asphalt Paving Technologists, Vol. 70, Clearwater Beach, FL, 2001, pp Harvey, J., C. Monismith, R. Hornjeff, M. Berjarano, B. W. Tsai, and V. Kannekanti. Long-Life AC Pavements: A Discussion of Design and Construction Experience Based on California Experience. In Proceedings of International Symposium on Design and Construction of Long Lasting Asphalt Pavements, National Center for Asphalt Technology, Auburn, AL, 2004, pp Goodrich, J. L. Asphalt and Polymer Modified Asphalt Properties Related to the Performance of Asphalt Concrete Mixes. In Proceedings of Association of Asphalt Paving Technologists Technical Sessions, Vol. 57, Williamsburg, VA, 1988, pp Lee, H. J., J. Y. Choi, Y. Zhao, and Y. R. Kim. Laboratory Evaluation of the Effects of Aggregate Gradation and Binder Type on Performance of Asphalt Mixtures. In Proceedings of the Ninth International Conference on Asphalt Pavements, Copenhagen, Denmark Newcomb, D.E., M. Buncher, and I.J. Huddleston. Concepts of Perpetual Pavements. Perpetual Bituminous Pavements. Transportation Research Circular 503, 19

20 Transportation Research Board, Washington, DC, 2001, pp Liao, Y. Viscoelastic FE Modeling of Asphalt Pavements and its Application to U.S. 30 Perpetual Pavement. Ph.D. dissertation, Ohio University, Al-Qadi, I.L., H. Wang, P.J. Yoo, and S.H. Dessouky. Dynamic Analysis and In Situ Validation of Perpetual Pavement Response to Vehicular Loading. In Transportation Research Record: Journal of the Transportation Research Board, No. 2087, Transportation Research Board of the National Academies, Washington, D.C., 2008, pp ABAQUS/Standard User s Manual, Version 6.11.Habbit, Karlsson & Sorenson, Inc., Pawtucket, R.I Williams, M.L., R.F. Landel, and J.D. Ferry. Time-Temperature Dependence of Relaxation Mechanism in Amorphous Polymers and Other Glass-Liquids. Journal of the American Chemical Society, Vol. 77, 1955, pp Park, D.W., A.E. Martin, and E. Masad. Effects of non-uniform tire contact stresses on pavement response. Journal of Transportation Engineering, 2005, Vol. 131, No. 11, pp