Top-Down Cracking of Hot-Mix Asphalt Layers: Models for Initiation and Propagation (2010)

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B-i APPENDIX B. DEVELOPMENT OF THE HMA-FM-BASED MODEL

B-ii TABLE OF CONTENTS page TABLE OF CONTENTS ............................................................................................................ B-ii APPENDIX B DEVELOPMENT OF THE HMA-FM-BASED MODEL ...................................................B-1 B.1 Introduction ....................................................................................................................B-1 B.1.1 HMA Fracture Mechanics Model ........................................................................B-1 B.1.1.1 HMA fracture mechanics ...........................................................................B-1 B.1.1.2 HMA fracture mechanics-based crack growth simulator ..........................B-2 B.1.1.3 Energy ratio approach ................................................................................B-4 B.1.1.4 Modified energy ratio approach ................................................................B-5 B.1.1.5 Summary of existing HMA-FM model .....................................................B-6 B.1.2 Material Property Models ....................................................................................B-6 B.1.2.1 Binder aging model ...................................................................................B-7 B.1.2.2 Dynamic modulus model ...........................................................................B-7 B.1.2.3 Tensile strength model ...............................................................................B-8 B.1.2.4 Healing model ............................................................................................B-8 B.2 Development of Model Components ...........................................................................B-11 B.2.1 Material Property Model ....................................................................................B-11 B.2.1.1 AC stiffness (creep compliance) aging model .........................................B-11 B.2.1.2 AC tensile strength aging model .............................................................B-13 B.2.1.3 FE limit (DCSE limit) aging model .........................................................B-14 B.2.1.4 Healing model ..........................................................................................B-17 B.2.2 Pavement Response Model ................................................................................B-24 B.2.2.1 Load response model ...............................................................................B-24 B.2.2.2 Thermal response model ..........................................................................B-25 B.2.3 Pavement Fracture Model ..................................................................................B-27 B.2.3.1 Crack initiation model .............................................................................B-27 B.2.3.2 Crack growth model ................................................................................B-29 B.2.3.3 Crack amount model ................................................................................B-30 B.3 Integration of Model Components ...............................................................................B-31 B.3.1 Integration of Healing Model ............................................................................B-31 B.3.1.1 Background of experiments for evaluating healing effect .......................B-31 B.3.1.2 Material and structural properties ............................................................B-32 B.3.1.3 Model predictions without healing ..........................................................B-35 B.3.1.4 Determination of critical values for daily lowest AC stiffness................B-38 B.3.1.5 Model predictions with healing ...............................................................B-39 B.3.2 Integration of Thermal Response Model ...........................................................B-42 B.3.2.1 Selection of climatic environment ...........................................................B-42 B.3.2.2 Material and structural properties ............................................................B-43 B.3.2.3 Traffic information ..................................................................................B-46

B-iii B.3.2.4 Model predictions without thermally induced damage ...........................B-46 B.3.2.5 Model predictions with thermally induced damage ................................B-48 B.4 Creep Compliance Master Curves from the SuperPave IDT .......................................B-52 B.5 Determination of Crack Initiation Time .......................................................................B-55 B.6 List of References ........................................................................................................B-59

B-1 CHAPTER 2 DEVELOPMENT OF THE HMA-FM-BASED MODEL B.1 Introduction B.1.1 HMA Fracture Mechanics Model The continuing development of the HMA fracture mechanics (HMA-FM) model, which was determined to be necessary to include effects of aging, healing, and thermal stress on top- down cracking performance, represented a significant proportion of the effort of the researchers at the University of Florida (UF). The enhancements made to this model to make it suitable for use in a MEPDG framework will be reviewed following the sequence of each new development. B.1.1.1 HMA fracture mechanics Recently, researchers at UF (1, 2) developed the HMA fracture mechanics model. In this model, a fundamental crack growth law (named HMA fracture mechanics) was developed that allows for predicting the initiation and propagation of cracking, including top-down cracking, in asphalt mixture. This law is based on a critical condition concept which specifies that crack initiation and growth only develop under specific loading, environmental, and healing conditions that are critical enough to exceed the mixture’s energy threshold/limit. A dissipated creep strain energy limit (DCSEf) has been identified suitable to serve as the energy limit in the law, which can be determined using the SuperPave Indirect Tension Test (IDT). Figure 2-1 shows a typical stress-strain response of mixture from IDT tensile strength test. The fracture energy limit (FEf) is determined as the area under the stress-strain curve (Area OAB). The elastic energy at fracture (EE) is calculated as the triangular area (CAB), in which the elastic modulus of the mixture (MR) is determined using IDT resilient modulus test. The DCSEf is then obtained by subtracting the EE from the FEf, which can be expressed as following, ( )Rtff MSFEDCSE ⋅−= 2/2 (2-1)

B-2 Where, St is the tensile strength of the mixture. It has been shown that DCSEf is independent of mode of loading. Once the damage in asphalt mixture is equal to (or larger than) the threshold, the critical condition is triggered, which results in crack initiation (or propagation). MR A C BO Dissipated Creep Strain Energy Limit (DCSEf) Elastic Energy (EE) σ ε St εo εf Fracture Energy Limit (FEf) = DCSEf +EE Figure 2-1. Determination of dissipated creep strain energy B.1.1.2 HMA fracture mechanics-based crack growth simulator Based on the HMA fracture mechanics, Sangpetngam et al. (3, 4) developed a crack growth simulator to predict crack propagation in HMA pavements. In this simulator, the displacements and stresses at any point of a pavement section are determined using the displacement discontinuity boundary element method (DDBEM). The DDBEM requires meshes only on the boundaries of an object (including cracks), and addresses crack growth by simply adding a few elements in the region of crack propagation. Figure 2-2 shows the typical boundary discretization in a two-dimensional BEM model for a pavement structure. Figure 2-3 illustrates the structure of the simulator and the associated modeling steps: (i) model the problem by placing displacement discontinuity (DD) elements on the boundaries, with

B-3 the location(s) of possible crack initiation specified; (ii) define the process zone in front of the critical location(s); (iii) use the BEM to calculate the tensile-mode dissipated creep strain energy (DCSE) step by step; (iv) check the accumulated DCSE to determine whether the crack will grow or not: if the accumulated DCSE reaches or exceeds the damage threshold (i.e., DCSE limit), a macro-crack forms in the critical zone and causes the crack to grow by length of the zone (6 mm or 0.25 in.). The resulting simulator is capable of evaluating relative cracking performance among asphalt pavements of similar ages. Figure 2-2. BEM model for a typical four-layer pavement structure

B-4 Create model of structure and boundary conditions Numerical Analysis Obtain: σ, ε, u Calculate DCSE in critical zones from this load cycle (i.e. DCSE/cycle) Accumulate DCSE/cycle in total DCSE DCSE > threshold? Update crack geometry Next loading cycle Yes No Define location and length of critical zone Figure 2-3. Flowchart of the HMA fracture mechanics-based crack growth simulator B.1.1.3 Energy ratio approach Roque et al. (5) derived a parameter termed the energy ratio (ER) based on a detailed analysis and evaluation of 22 field test sections in Florida using the HMA fracture mechanics (HMA-FM) model. The ER was defined as follows: min/ DCSEDCSEER f= (2-2) Where, DCSEf is the dissipated creep strain energy limit of the mixture, and DCSEmin is the minimum dissipated creep strain energy required for the number of cycles to failure to exceed 6000, which can be determined as follows: ADmDCSE /1 98.2 min ⋅= (2-3)

B-5 Where, m and D1 are the creep compliance power law parameters (determined using SuperPave IDT creep compliance test at 10 °C), and parameter A is a function of tensile strength St and tensile stress in the asphalt concrete pavement, which is expressed as follows: ( ) 810.3 1046.236.60299.0 −− ×+−⋅⋅= tSA σ (2-4) It is noted that the SuperPave IDT tensile strength and resilient modulus tests at 10 °C are required to determine St and resilient modulus MR. The tensile stress is predicted using the measured MR and other layer moduli as determined from falling weight deflectometer (FWD) tests for a typical pavement structure. As can be seen from the above definitions, the ER accounts for effects of both damage and fracture properties on top-down cracking performance. A higher ER implies better cracking performance. B.1.1.4 Modified energy ratio approach Due to the fact that ER was developed based on the evaluation of load-induced cracking performance, it may not provide a reliable basis to assess pavements located in areas where the thermal effect cannot be neglected. In order to combine the effects of load and thermal, Kim et al. (6) developed a method to calculate thermally induced damage and the failure time (FT) to 100 mm crack length for a thin plate subject to specified thermal loading conditions. This method was then used in conjunction with the HMA-FM model to perform a detailed analysis and evaluation of 11 field test sections in Florida, which resulted in a new parameter termed the modified energy ratio (MER) defined as follows: MTRIFTMER /= (2-5) Where, MTR is the minimum time requirement used to discriminate the performance of cracked and uncracked pavement sections. IFT is the integrated failure time expressed as follows:

B-6 ( ) ERMTVAMTFTIFT ⋅⋅= / (2-6) Where, AMT is the annual mean air temperature and MTV is the mean temperature variation, which are correction factors to account for temperature inputs other than the single harmonic function used to calculate FT. ER is the energy ratio. It is clear that the MER approach essentially introduced a correction factor into the ER equation such that both load and thermal effects can be accounted for during evaluation of top- down cracking performance. B.1.1.5 Summary of existing HMA-FM model In summary, these research efforts formed the existing HMA-FM model. However, the effect of aging and healing on top-down cracking performance during the entire service life of asphalt concrete pavements was not considered, which certainly cannot be ignored for more accurate prediction of top-down cracking. Furthermore, transverse, instead of longitudinal, thermal stresses needed to be considered for prediction of top-down cracking, since unlike thermal cracking, top-down cracking generally occurs in the longitudinal direction. In addition, the thermally induced damage needed to be directly involved in the computation of damage accumulation, so that damage recovery due to healing can be applied in a more consistent way as compared with the indirect approach used in the MER method. B.1.2 Material Property Models In this part, several existing mixture property sub-models, which were suitable for further development into mixture aging and healing models for incorporation into the HMA-FM model, are reviewed.

B-7 B.1.2.1 Binder aging model Asphalt aging is sometimes quantified by change in binder viscosity, which is directly related to the prediction of dynamic modulus and the creep properties, as discussed below. The binder viscosity at mix/laydown condition (t = 0) is estimated using the following equation (24): log log ( ) log ( )RA VTS Tη = + × (2-7) where η is the binder viscosity in centipoises (10-2 poise), TR is the temperature in Rankine, and A and VTS are regression constants. Typical values of A and VTS for three commonly used asphalt binders are given below (see NCHRP 1-37A design guide): PG 64-22: A = 10.98 VTS = –3.68 PG 67-22: A = 10.6316 VTS = –3.548 PG 76-22: A = 9.715 VTS = –3.208 For aged conditions, the viscosity of the asphalt binder at the pavement surface (depth z = ¼ in) can be estimated from the following in-service surface aging model (24): 0log log ( ) log log ( ) 1 t f aged AV f A t F B t η η = + = × + (2-8) where t is the time in months, FAV is the air void adjustment factor, and Af and Bf are field aging parameters that are functions of the in-service temperature and the mean annual air temperature (MAAT). The expressions for these parameters can be found in the current design guide (8). The viscosity-depth relation is given as: )0308.0exp(82.23 )1(4 )41)(()4( 0 , MaatEandzE zEE tt zt ⋅−=⋅+ −−+ = = ηη η (2-9) B.1.2.2 Dynamic modulus model The dynamic modulus |E*| of asphalt concrete is used to analyze the response of pavement systems. Numerous attempts have been made to develop regression equations to calculate the dynamic modulus from conventional mixture volumetric properties. The predictive equation

B-8 developed by Witczak and Fonseca (30) is one of the most comprehensive mixture dynamic modulus models available today. This model is used in the current ME design guide. According to Witczak’s model, the dynamic modulus |E*| can be represented by a sigmoidal function as follows: *log 1 e xp ( l og )r E t αδ β γ = + + + (2-10) where |E*| is in psi; tr is reduced time in seconds (1/f, f is loading frequency) at a reference temperature; δ, α, β, γ are fitting parameters. Detailed expressions for δ, α, β, γ in terms of the gradation and volumetric properties of the mixture can be found in Witczak and Fonseca (30). B.1.2.3 Tensile strength model In their work on evaluation of mixture low temperature cracking performance, Deme and Young (31) found that the tensile strength of mixture (St) is well correlated with the mixture stiffness at a loading time of 1800 second, i.e., S1800. They had extensive data in the temperature range of -40 to 25 °C. Based on these data, the following relation was obtained between the mixture stiffness (in psi) and the tensile strength (in Mpa) through regression: ( )∑ = ⋅= 5 0 log n n fnt SaS (2-11) Where Sf is the tensile stiffness that can be obtained from the dynamic modulus |E*| by taking t = 1800 s. The constants an are shown as follows, 0 1 2 3 4 5 a 284.01, a 330.02, a 151.02, a 34.03, a 3.7786, a 0.1652 = = − = = − = = − B.1.2.4 Healing model The concept of healing to increase mixture fatigue life has been observed and has been more widely accepted by researchers (11 - 22) in recent years. Button et al. (11) conducted

B-9 controlled displacement crack growth testing in asphalt concrete mixes modified with various additives. They found an increase in work was required to open cracks after rest periods due to both relaxation in the uncracked body and chemical healing at the micro-crack and macro-crack interface. Zhang (12) conducted fracture tests using the Indirect Tensile Test and showed there is a critical energy level that distinguishes micro-damage from macro-damage; micro-damage is healable and macro-damage is not. Daniel and Kim (15) used a third point bending beam machine to induce flexural damage in beam specimens subjected to cyclic loading. They found the calculated flexural stiffness increased after the specimens were subject to rest periods. Figure 2-4 shows that healing increased the ultimate number of cycles the specimen endured before failure at 20 °C. Figure 2-4. Flexural stiffness versus number of cycles to failure with and without rest periods (after Daniel and Kim (15)) Recent research by Kim and Roque (32) focused on development of experimental methods to evaluate healing properties of asphalt mixture. First, the DCSE associated with healing during unloading was determined by developing relationships between changes in resilient deformation and DCSE. The healing process was then expressed in terms of DCSE versus time. Figure 2-5

B-10 presents healing results at 20 °C for different applied DCSEs in the same mixture. Based on these results, they defined a healing rate hr, which can be expressed as ( ) ( )ttDCSEh healedr ln/= (2-12) where, DCSEhealed(t) is the recovered DCSE at time t, which is defined as, ( ) ( )tDCSEDCSEtDCSE remaininducedhealed −= (2-13) where, DCSEinduced is the total energy dissipated at the end of the loading period, and DCSEremain(t) is the dissipated energy remaining at time t during the rest period. As a further step, they identified a normalized healing rate hnr, which was defined as, inducedrnr DCSEhh /= (2-14) Substituting Eqn (2-12) into Eqn (2-14), leads to the following form, ( ) ( )t DCSE tDCSEh induced remain nr ln/1       −= (2-15) The normalized healing rate was found to be independent of the amount of damage incurred in the asphalt mixture. It was also found to increase with increasing temperature. Figure 2-5. Healing tests at different DCSE for modified mixture: loading with 55 psi & healing at 20 °C (after Kim and Roque (32))

B-11 B.2 Development of Model Components The model components developed in this project included: material property models, pavement response models, and pavement fracture models. Detailed descriptions of each of the developments are summarized in the sections below: B.2.1 Material Property Model As can be seen from Section B.1 (Introduction), no existing model is available to predict damage and fracture properties, or the changes of these properties with aging. However, development, calibration, and validation of a mixture model to predict damage, healing, and fracture properties is clearly a major research effort in its own right, and well beyond the scope of the current study. Therefore, the goal of this research was to develop rudimentary (place- holder) relationships between basic mixture characteristic and these properties for use when measured properties cannot be obtained. The material property aging models and healing model developed for this purpose will be introduced in the following sub-sections. The plots used to illustrate the implementation of the models were generated using material and structural properties of one pavement section in the Washington D.C. area (see Section B.3.2 for detailed information of that pavement). B.2.1.1 AC stiffness (creep compliance) aging model An AC stiffness aging model was developed on the basis of binder aging model and dynamic modulus model (at a loading time of 0.1 s). In this model, the aging effect on mixture stiffness was considered using the following empirical equation, * * 0 0 log | | | | log t tE E η η = (2-16) where |E*|t and |E *|0 represent the stiffnesses corresponding to aged and unaged conditions, respectively; ηt and η0 correspond to the aged and unaged binder viscosity.

B-12 As an example, Figure 2-6 gives three predicted AC stiffness curves as a function of time (in days), i.e., daily lowest, mean, and highest AC stiffness at surface of the pavement section of Washington D.C. area during Year one (started from July 1st). The AC stiffness curves of the same mixture at Year five (i.e., after being aged for five years), are shown in Figure 2-7. It can be seen from a comparison of these two plots that the effect of aging on AC stiffness is considerable, as expected. With the AC stiffness aging model, creep compliance values at 1, 2, 5, 10, 20, 50, 100, 200, 500, and 1000 sec for three temperatures (e.g., 0, 10, and 20°C) were obtained by taking inverse of the AC stiffness values at the corresponding time and temperature, which resulted in three creep compliance curves for 1000 sec. Figure 2-8 shows the predicted creep compliance curves at multiple temperatures for the same pavement section at Year one. These were used to generate master curve (17) to obtain creep compliance rate, and to predict thermal stresses (33, 19, 20). 0 50 100 150 200 250 300 350 1.5 2 2.5 3 3.5 4 t (day) lo g- st iff ne ss (k si ) Daily Stiffness of AC at Yr1 S High S Av e. S Low Figure 2-6. Daily AC stiffness of one pavement section in Washington D.C. area (Year one)

B-13 0 50 100 150 200 250 300 350 1.5 2 2.5 3 3.5 4 t (day) lo g- st iff ne ss (k si ) Daily Stiffness of AC at Yr5 S High S Av e. S Low Figure 2-7. Daily AC stiffness of one pavement section in Washington D.C. area (Year five) 0 100 200 300 400 500 600 700 800 900 1000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 x 10 -5 t (sec) D (t) (1 /p si ) Creep compliances (3-T) Vs. time at Yr1 -10 oC 0 oC 10 oC Figure 2-8. 1000 second creep compliance curves at three temperatures B.2.1.2 AC tensile strength aging model The AC tensile strength aging model was developed by directly relating tensile strength to the AC stiffness aging model based on the relationship developed by Deme and Young (31). As

B-14 an example, Figure 2-9 (c) shows the variation of AC tensile strength with age at the surface of the pavement section. It was obtained based on the AC stiffness aging curve determined at 10°C, as shown in Figure 2-9 (d). B.2.1.3 FE limit (DCSE limit) aging model It was shown by our testing results (21) that fracture energy limit (FEf) generally decreases at a decreasing rate with age, and reaches some minimum value after sufficiently long time. So, the FE limit function was assumed to begin with an initial fracture energy (FEi) at the starting point of Year one (t = 0), and end with a minimum value (FEmin) after a sufficiently long aging time (tinf). Also, it was assumed that the normalized change of FE limit was related to the normalized change of stiffness by a power of k1, which are expressed as following, ( ) [ ] 1)( min k n i fi tS FEFE tFEFE = − − (2-17) The item on the left hand side of Equation (2-17) represents the normalized change of FE limit, in which FEi is the initial fracture energy. FEmin is the minimum value after an aging period of tinf. In this research, FEmin was determined to be 0.2 kJ/m 3 based on experience from field specimens, and tinf was chosen as 50 years. On the right hand side, k1 is an aging parameter to be determined from calibration. Sn(t) is the normalized change of stiffness at the surface of the AC layer, and is expressed as, 0max 0)()( SS StStSn − − = (2-18) where, S(t) is the stiffness at the surface of the AC layer. S0 and Smax are S(t) when t is 0 and 50 years, respectively. It can be seen that Sn(t) is a parameter that varies between zero and one. With a simple manipulation, the FE limit surface aging function was then obtained from Equation (2-17) as follows:

B-15 ( ) [ ] 1min )()( kniif tSFEFEFEtFE ⋅−−= (2-19) It was also observed from testing of field cores that FE limit (FEf(t,z)) generally increases with depth after a period of aging. So, at t = 0 when no aging is applied, FEf(0,z) (or, FEi) was assumed to be independent of depth. Then, at any age after that (i.e., t > 0), the FEf(t,z) was assumed to increase with depth such that the ratio of the difference between FEi and FE limit at depth z to the difference between FEi and FE limit at surface (z = 0) was equal to the ratio of the stiffness at depth z to the stiffness at surface (z = 0), which are expressed as following, ( ) ( ) ( ) ( )tS ztS tFEFE ztFEFE fi fi ,, = − − (2-20) where, FEf(t,z) and S(t,z) are FE limit and AC stiffness at depth z, respectively. With a simple manipulation, the FE limit aging function at depth z was obtained from Equation (2-20) as follows: ( )[ ] )(/),(),( tSztStFEFEFEztFE fiif ⋅−−= (2-21) Based on the FE limit aging function, the DCSE limit aging function was developed and is expressed as follows, ( ) ( ) ( )[ ] ( )[ ]ztSztSztFEztDCSE tff ,2/,,, 2 ⋅−= (2-22) where, St(t,z) is a general expression for AC tensile strength. It is noted that this equation is a generalized form of Equation (2-1), in which MR is approximated by AC stiffness (at 10 Hz). As an example, Figure 2-9 (a) shows the variation of FE limit with age at the surface of the pavement in the Washington D.C. area. Correspondingly, the DCSE limit aging curve is given in Figure 2-9 (b).

B-16 0 10 20 30 40 50 0 0.5 1 1.5 2 FE f ( kJ /m 3 ) 0 20 40 0 0.5 1 1.5 2 D C S E f ( kJ /m 3 ) 0 10 20 30 40 50 0 1 2 3 t (yr) S t ( M pa ) 0 10 20 30 40 50 0 10 20 30 t (yr) S (G pa ) 10 30 50 D C S E f ( kJ /m 3 ) (a) (b) (c) (d) Figure 2-9. Variation of energy limits, tensile strength and stiffness with age Clearly, the initial fracture energy FEi and aging parameter k1 of Equation (0-3) are key parameters that govern the trend of the FE limit aging curve. Figure 0-7 gives FE limit curves at three different values of FEi (for a constant k1 value of 3). As shown, generally the FE limit value decreases with time. For a larger FEi, the entire FE limit curve moves upward (in the plot). But, the initial degradation rate of the curve also becomes larger. Figure 0-10 presents FE limit curves at three different values of k1 for a constant FEi value of 2. It can be seen that a larger FE limit value is associated with a larger k1. And, the initial degradation rate of the curve is smaller for a larger k1 value.

B-17 0 2 4 6 8 10 0 10 20 30 40 50 Time (year) Fr ac tu re E ne rg y (K pa ) 2 5 10 FEi (Kpa) : ` Figure 2-10. FE limit aging curves at different FEi (k1 = 3) 0 0.5 1 1.5 2 0 10 20 30 40 50 Time (year) Fr ac tu re E ne rg y (K pa ) 1 3 5 k1 : Figure 2-11. FE limit aging curves at different k1 (FEi = 2 Kpa) B.2.1.4 Healing model The development of a healing model for use in this research was completed in two steps. First, a mixture level healing model was obtained based on the research by Kim and Roque (32). The application of this model was illustrated using a simulated SuperPave IDT repeated load test on an HMA specimen.

B-18 As a further step, possible improvements to this model for application in real pavement sections were investigated, which resulted in the development of a simplified empirically-based healing model for use in this research. A model based on laboratory healing tests As stated in Section B.1 (Introduction), the normalized healing rate hnr is a mixture- dependent material property, which can be determined using the laboratory healing test developed at the University of Florida (32). If hnr is known a priori, the remaining dissipated energy after healing time t can be estimated using the following equation, which was derived from Equation (2-15), ( ) ( )[ ]thDCSEtDCSE nrinducedremain ln1 ⋅−⋅= (2-23) where, DCSEinduced is the dissipated energy at the end of the loading period. Based on Equation (2-23), a healing model was developed with the following assumptions, • Micro-damage can only be healed during rest periods. • For cyclic loading condition with more than one rest period, the damage induced during one loading period continuous to be healed during any successive rest period, until it vanishes. • A constant temperature condition was assumed for this healing model since shift factors for computing normalized healing rate at different temperatures had not been established because of limited test results. • The normalized healing rate is independent of mixture aging. This model was then used in conjunction with the existing HMA-FM model to predict crack initiation for an HMA specimen during a simulated IDT repeated load fracture test. The input information is given in Table 2-31.

B-19 As shown in the table, a constant healing period of 300 s was introduced between every 300 loading cycles. Each of the loading cycles was composed of 0.1 s of haversine loading and 0.9 s rest period. It was assumed that no healing occurred during loading. Table 2-31. Input for a synthetic IDT test Parameter Value Loading period* (sec) 300 Healing period (sec) 300 Temperature (°C) 10 m 0.505 D1 (10-6 1/Kpa) 0.101 DCSEf (Kpa) 0.978 hnr (1/ln(sec)) 0.1 * It includes 300 loading cycles. Each cycle lasts 1-second. Figure 2-12 shows the predicted DCSE versus number of load cycles for the with and without healing conditions. As shown, the damage accumulation when healing was accounted for is much slower than that without considering healing. The healing model based on Equation (2-23) was then incorporated into the existing HMA-FM model to more accurately predict cracking performance. 0 0.2 0.4 0.6 0.8 1 0 1500 3000 4500 6000 7500 9000 load cycle D C S E (k J/ m 3 ) DCSE Limit w ithout healing w ith healing Figure 2-12. Predicted damage accumulations with and without healing

B-20 However, it is emphasized that this model may not be suitable for direct application in field conditions due to the following reasons: • Variation of hnr (i.e., healing rate) with age was not taken into account in the model. • Similarly, variation of hnr with temperature was not considered in the model. • It is very hard to determine healing period and loading period in the field, which have varying lengths and are randomly distributed. • Even if constant healing periods and loading periods are assumed, it is not trivial to track the decrement of damage generated in each loading period with time. In other words, the current model is somewhat computationally inefficient. Healing model for use in this research Since the lab test based healing model is not suitable for application in real pavements, possible improvements were investigated, which resulted in the development of an empirically- based and less computationally involved healing model, which is composed of three components: • Maximum healing potential aging model. • Daily-based healing criterion. • Yearly-based healing criterion. Each of the components is introduced as follows. Maximum healing potential aging model The following relationship describes the maximum healing potential surface aging model: ( ) ( )[ ] 67.1/1 iFEnym tSth −= (2-24) where, FEi is the initial fracture energy, Sn(t) is the normalized change of stiffness at the surface of the AC layer, and t is time in years. The maximum healing potential versus depth relation is: ( ) ( )[ ] ( )( )tS ztSthzth ymym , 11, ⋅−−= (2-25)

B-21 where, S(t,z) is the general expression for AC stiffness, and S(t) is the stiffness at surface of AC layer. As shown in Eqn (0-7), the maximum healing potential hym was controlled by the initial fracture energy. As an example, Figure 0-8 gives maximum healing potential surface aging curves for three different values of FEi. As shown, a higher hym is generally associated with a larger FEi. And, the initial degradation rate of hym decreases with the increase of FEi value. 0 0.2 0.4 0.6 0.8 1 0 10 20 30 40 50 Time (year) M ax im um H ea lin g P ot en tia l 2 5 10 FEi (Kpa) : Figure 2-13. Max. healing potential surface aging curves at different FEi Daily-based healing criterion A daily-based healing criterion was developed to estimate the recovered damage on any particular day. It was assumed that the damage generated in a day would be healed according to a daily normalized healing parameter hdn which is defined as, inducedd remaind dn DCSE DCSE h _ _1−= (2-26)

B-22 where, DCSEd_induced is the dissipated energy induced during the day, and DCSEd_remain is the dissipated energy remaining at the end of the day after healing, which can be obtained by rearranging Eqn (0-9) as follows, ( )dninduceddremaind hDCSEDCSE −⋅= 1__ (2-27) The daily normalized healing parameter is dependent on depth, time, and temperature. In this study, hdn was correlated with the daily lowest stiffness Slow of the AC layer. The rationale is that healing potential is believed to be closely related to the AC material’s capacity to flow. Since Slow is the lowest stiffness of a day, it represents the highest flow capacity of the material on that day, which was used to estimate the material’s healing potential. The daily lowest stiffness can be determined using the daily highest temperature at any depth of the AC layer (refer to AC stiffness aging model). As an example, Figure 2-14 gives the variation of daily highest temperature at the surface of the pavement in the Washington D.C. area. 0 50 100 150 200 250 300 350 -10 0 10 20 30 40 50 time (days) Te m pe ra tu re (o C ) Figure 2-14. Variation of daily highest temperature

B-23 The corresponding daily lowest stiffness Slow for five successive years (each year was started from July 1st), after taking the effects of aging into account, are plotted in Figure 2-15. In addition, two critical stiffness values Scr1 and Scr2 are also shown in the figure, which divide the Slow profile into three zones, • Scr1 is the Lower Bound Value. It was assumed that the daily normalized healing parameter hdn reached the maximum value of a year, i.e., hym representing the highest healing potential of the mixture for that year, when: Slow ≤ Scr1 (i.e., when Slow falls into Zone A). hym was determined using the maximum healing potential aging model. • Scr2 is the Upper Bound Value. It was assumed that hdn reached the minimum value of a year, i.e., zero representing the lowest healing potential of the mixture, when: Slow ≥ Scr2 (i.e., when Slow falls into Zone C). • For any Slow value that is between Scr1 and Scr2 (i.e., when Slow is in Zone B), hdn can be determined by linear interpolation between zero and hym, representing intermediate healing potentials. • Determination of Scr1 and Scr2 is discussed in Subsection B.3.1. 0 1 2 3 4 5 1 1.5 2 2.5 3 3.5 4 time (year) lo g- st iff ne ss (k si ) Scr1 Scr2 Figure 2-15. Daily lowest AC stiffness (Slow) profile and two critical values (Scr1 & Scr2) Zone B Zone A Zone C

B-24 Yearly-based healing criterion In the daily-based healing criterion, the damage generated in any particular day will be healed only once during that day, after which no healing will be applied to remaining damage. This does not agree well with the observation from laboratory healing tests (32) which indicated that damage can be healed successively during any rest period that follows. Thus, a yearly-based healing criterion was developed to address continuous healing. In this healing criterion, it was assumed that all damage accumulated during a yearly period (started from July 1st) can be at least partially healed according to a yearly normalized healing parameter hyn which is defined as, inducedy remainy yn DCSE DCSE h _ _1−= (2-28) where, DCSEy_induced is the dissipated energy induced during the year, and DCSEy_remain is the dissipated energy remaining at the end of the year after healing, which can be obtained by rearranging Eqn (0-11) as follows, ( )yninducedyremainy hDCSEDCSE −⋅= 1__ (2-29) The yearly normalized healing parameter hyn was determined based on an averaged daily lowest stiffness Slowa over a prolonged period Tp (i.e., the last 40 days of the yearly period being analyzed). B.2.2 Pavement Response Model The pavement response model is composed of two sub-models: load response model and thermal response model. Details of each are explained below. B.2.2.1 Load response model The load response model was primarily aimed to predict bending-induced maximum surface tensile stresses, since the bending mechanism was the main focus of the HMA-FM-based

B-25 model. A 9-kip circular load was applied repeatedly to the surface of a pavement to simulate the cyclic traffic load. Each cycle included 0.1 s haversine loading period and 0.9 s resting period. The model first estimated the AC modulus (see Section B.2.1) based on the temperature profiles and aging conditions. The stiffness gradient due to the temperature and aging effects was taken into account by dividing the AC layer into multiple sub-layers with different stiffnesses. The bending-induced tensile stresses at the pavement surface were then predicted using 3- dimensional (3-D) linear elastic analyses (LEA). The model also automatically searched for the maximum tensile stress on the surface of the AC layer. Figure 2-16 shows the bending-induced surface tensile stress away from the tire. Figure 2-16. Schematic plot for load response at the surface of the AC layer B.2.2.2 Thermal response model The thermal response model predicts the thermally induced stresses in the transverse direction of asphalt concrete pavement. It was developed based on a thermal stress model for predicting thermal cracking (33). The existing thermal stress model was developed on the basis of the theory of linear viscoelasticity. In this model, the asphalt layer was modeled as a thermorheologically simple material. Based upon Boltzmann superposition principle for linear viscoelastic materials, the time-temperature constitutive equation at time t can be expressed as follows, ' ' )'( ))'()(()( 0 dt dt tdttEt t εξξσ ⋅−= ∫ (2-30) Lσ Load response: AC

B-26 where ( ')E ξ ξ− is the relaxation modulus at reduced time 'ξ ξ− ; and the reduced time ξ is: / Tt aξ = where Ta is the temperature shift factor. The strain ε(t') can be expressed as [ ]0( ') ( ')t T t Tε α= − where α is the linear coefficient of thermal contraction, T(t') and T0 are pavement temperature at time t' and the reference temperature corresponding to stress-free condition. The following finite difference solution to Equation (2-30) can be obtained by using the generalized Maxwell model representation of the relaxation modulus (Equation (2-32)) which was converted from the Prony series representation for creep compliance (Equation (2-33)), ∑ + = = 1 1 )()( N i i tt σσ (2-31) where ( )/ /( ) ( ) 1i iii i it e t t E eξ λ ξ λλσ σ ε ξ −∆ −∆= − ∆ + ∆ − ∆ and ε∆ , ξ∆ are the changes in strain and reduced time, respectively. 1 1 2 1 11 2 1 ( ) exp( ) exp( ) exp( ) exp( ) N N i iN i t t t tE t E E E E λ λ λ λ + + =+ = − + − + − = −∑ (2-32) - / 0 1 ( ) (1- )i N i i v D D D e ξ τ ξξ η= = + +∑ (2-33) where Ei and λi are relaxation moduli and relaxation times. Di, τi, ηv are Prony series parameters. The existing model was intended to predict thermal stresses in the longitudinal direction. However, top-down cracking is known to occur in the longitudinal direction, so transverse, as opposed to longitudinal, thermal stresses are of particular relevance. The difference in transverse

B-27 and longitudinal thermal stresses was caused by different boundary conditions to which the AC layer is subjected in these two directions: • The AC layer is subjected to a fixed boundary condition in the longitudinal direction, which can induce very high longitudinal thermal stresses, which are the main cause of thermal cracking. • However, the AC layer can move in the transverse direction once the maximum friction provided by the base is reached. Therefore, the transverse thermal stress, which contributes to top-down cracking, cannot exceed the friction limit. The limit value was determined to be 10 psi for typical HMA and base materials based on a separate calculation. Figure 2-17 shows the transverse thermal stresses due to change of temperature in an AC layer. Figure 2-17. Schematic plot for thermal response in the AC layer B.2.3 Pavement Fracture Model The pavement fracture model consists of three sub-models: (i) crack initiation model, (ii) crack growth model, and (iii) crack amount model. B.2.3.1 Crack initiation model The crack initiation model was developed on the basis of the threshold concept of the existing HMA fracture model. It was used to predict the crack initiation time and location in asphalt pavement sections, in conjunction with the material property model and pavement response model. Details regarding the joint use of all mentioned models were presented in Section 4.1.6 (Main Body). THσ Thermal response: AC

B-28 In the crack initiation model, the load-associated damage and thermal-associated damage is obtained based on the pavement response models as follows, • The load-associated damage per cycle (or, DCSEL/cycle) is calculated as: ( ) ( )∫= 1.0 0 max 10sin10sin/ dtttcycleDCSE pAVEL πεπσ  (2-34) where σAVE is the average stress within the zone being analyzed to determine crack initiation, and ε pmax is the creep strain rate, which is determined from IDT creep tests at 1000 second loading time. • The thermal-associated damage over the time interval from (t - ∆t) to t (or, DCSET/∆t) is expressed as: ( ) ( )[ ] ( ) ( )[ ] 2// tttttttDCSE crcrT ∆−−⋅∆−−=∆ εεσσ (2-35) where εcr is creep strain at time t. It can be expressed as: ( ) ( ) ( ) ( )[ ] ( ) ( )[ ]ttttttttt v crcr ∆−+⋅∆−−⋅ +∆−= σσξξ η εε 2 1 In the crack initiation model, the rule for crack initiation is given as follows, ( ) ( )( ) 0.1≥= tDCSE tDCSEtDCSE f remain norm (2-36) where, DCSEremain is the accumulated dissipated energy when taking healing into account, DCSEf is the DCSE limit accounting for its degradation with aging, and DCSEnorm is the normalized damage accumulation. The threshold for crack initiation is 1.0. The DCSEremain during each time interval ∆t can be further expressed as follows, ( ) ( ) ( ) ( )[ ]tDCSEcycleDCSEnhtDCSE TLdnremain ∆+⋅⋅−=∆ /1 (2-37) where n is number of load cycles in ∆t.

B-29 B.2.3.2 Crack growth model The crack growth model was developed on the basis of a two-dimensional (2-D) displacement discontinuity boundary element (DDBE) program (34) and the threshold concept of the existing HMA fracture mechanics model. It was used in conjunction with the material property model and thermal response model to predict increase of crack depth with time in asphalt concrete pavement. Details regarding the joint use of all models were presented in Section 4.1.6 (Main Body). In the crack growth model, load induced tensile stresses ahead of the crack tip were predicted using the DDBE model as follows: • The pavement structure was discretized using quadratic displacement discontinuity (DD) boundary elements. • An initial crack was assumed to have a length of 6 mm (0.25 inch), which is about one half of the nominal maximum aggregate size of typical asphalt mixtures. It was placed vertically at the location of the maximum surface tensile stress and discretized using DD boundary elements. • The load used for the 2-D model was adjusted so that the maximum tensile stress at surface of the pavement predicted by the 2-D model can be matched with the prediction by the 3-D LEA program. A similar strategy was used by Myers et al. (23) to account for 3-D effects on stress distribution by adjusting load applied to a 2-D pavement model. Meanwhile, the near-tip thermal stresses were estimated by applying the stress intensity factor (SIF) of an edge crack to the thermal stresses predicted using the thermal response model. The load associated damage and thermal associated damage were then calculated in a same manner as introduced in the crack initiation model. The same rule as used for determination of crack initiation was adopted in the crack growth model. Once the rule was satisfied (i.e., the DCSEnorm reached 1.0), the crack started to grow. Some key terms used during simulation of step-wise crack growth are explained below:

B-30 • Potential crack path: The potential crack path was predefined in front of the crack tip at the beginning of crack growth simulation. It was composed of a series of zones of constant length heading toward the bottom of the AC layer. • Zone (in the potential crack path): The zone is a means used to discretize the potential crack path to facilitate the calculation of crack growth. A constant zone length was used because it is far more computationally efficient than using variable zone lengths, with relatively little effect on the crack growth prediction. It was measured from lab testing that cracking develops in a stepwise manner in asphalt mixtures. For typical asphalt mixtures with a nominal maximum aggregate size (NMAS) of 12.5 mm, the stepwise developed crack length is about one half of the NMAS, which is about 6 mm. So, 6 mm (0.25 inch) was selected as the constant zone length. • Critical crack depth (CDc): The critical crack depth is the final crack depth in the crack growth model, which was preset to be one-half the depth of the AC layer, as field observations showed that top-down cracking generally does not exceed that depth. B.2.3.3 Crack amount model The crack amount model was developed based on the following assumptions: • For a 100 feet long pavement section, the maximum crack amount was assumed to be 330 feet. In other words, the pavement was determined to be severely cracked if total crack amount exceeded 330 feet. • The crack amount, between zero and the specified maximum value, was assumed to be linearly proportional to the crack depth over AC layer thickness ratio (C/D), which ranges from zero to 0.5 (i.e., when crack depth is equal to CDc). The rationale is that generally, as a crack gets deeper, the crack mouth opening gets wider. Also, for a crack of the same depth (i.e., same C), the crack mouth opening is wider in a thinner layer than in a thicker layer. Therefore, it seems logical to assume that the probability that a crack is visible and counted as a crack (and therefore the probability of increase in crack amount) increases as the C/D ratio increases. The assumption that the relationship is linear is a first order approximation. • In accordance with the definition for crack initiation in terms of the crack depth (refer to crack initiation model), the onset of a crack in terms of the crack amount was assumed to be triggered by observing an amount of cracking of at least 12 feet. Based on the above assumptions, the crack amount versus time relationship can be obtained from the crack depth versus time relation predicted by the crack growth model. Using this model, the predicted amount of cracking at initiation is greater than 12 feet for any pavement that has an HMA layer thickness of no larger than 12 inch.

B-31 B.3 Integration of Model Components B.3.1 Integration of Healing Model The material healing model was integrated into the performance model by determining the two critical values for daily lowest AC stiffness on the basis of a full-scale test conducted in the FDOT’s APT facility using the HVS. B.3.1.1 Background of experiments for evaluating healing effect Since Accelerated Pavement Testing (APT) offers great potential for evaluation of performance of asphalt mixture and pavement in relatively short periods of time, the Florida Department of Transportation (FDOT) has built an APT facility in Gainesville, Florida. The system includes a fully mobile Heavy Vehicle Simulator (HVS), and eight linear tracks (150 ft long by 12 ft wide). Figure 2-18 shows one typical test section subjected to HVS loading in FDOT’s APT facility. Figure 2-18. A typical HVS test section The University of Florida (UF) has been working on a research project with FDOT to assess cracking potential of asphalt mixture (21). In an effort to simulate aging of in-service pavement, a unit called the Accelerated Pavement Aging System (APAS) was developed and used to induce artificial aging of asphalt pavement test sections in the APT facility. One lane

B-32 (testing track 1) composed of a dense-graded mixture on limestone base and sand subgrade was divided into three test sections: 1A, 1B, and 1C. Each section was subjected to different levels of aging and HVS loading. Sections 1B and 1C were tested first to assess the capability of the APAS system and to determine whether top-down cracking could be induced within a reasonable period of time. It was found that these two sections, which were subjected to extensive loading with moderate aging, could not be cracked even after many heavy loads were applied. In addition to the excellent properties of the mixture and structure, healing was thought to be playing a major role. Therefore, an experiment was devised to severely age one part of section 1A so as to minimize healing potential. This severely aged part and a companion unaged part were subjected to the same loading conditions (load and temperature) to more definitively evaluate the effects of healing. The paired portions of section 1A, which were simply called the aged and unaged sections for brevity, were subjected to 18-kip HVS loads to maximize the potential for cracking within a reasonable period of time. Loading on both sections started on February 06, 2007. During February 16 to 19, transverse surface cracks were found in the aged section after around 140,000 passes (see Figure 2-19). Loading was continued until March 27, 2007 with around 488,358 passes, when cracks in the aged section were believed to have approached about half-depth of the AC layer (this was later verified by coring the cracked AC layer). No crack was observed in the unaged section for the entire loading period. B.3.1.2 Material and structural properties PG 67-22 binder was used in this study. Figure 2-20 shows binder recovery and viscosity measurements performed on cores obtained from the aged section at 0, 1, and 20 heating cycles of artificial aging. The binder viscosity of the unaged section corresponds to zero heating cycle

B-33 (i.e., only slightly aged). As can be seen, the aging level induced in the top of the aged section after 20 healing cycles was extremely high, the viscosity at which was much greater than any value determined from field cores in typical Florida pavement. Figure 2-20 also shows that the APAS was able to effectively create a stiffness gradient through the asphalt layer. Figure 2-19. Cracks observed in the aged section 0 50000 100000 150000 200000 250000 300000 350000 400000 450000 0* 1 20 Number of heating cycles (48 hr/cycle) Vi sc os ity (P oi se s) Top Middle Bottom Middle value N/A Figure 2-20. Recovered viscosity at different levels of aging Table 2-32 summarizes the Superpave Indirect Tension Test (IDT) results on cores from the paired sections. The same asphalt mixture with Georgia granite aggregate and 4.6% binder content was used for both sections.

B-34 Table 2-32. IDT test results (at 10°C) APAS m- value D1 Creep compliance at 1000 sec Creep rate 1/GPa FE DCSE HMA ER Unaged Top 0.491 4.90E-07 2.15 7.13E-09 2.7 2.4 1.88 Bottom 0.537 5.43E-07 3.27 1.19E-08 2.4 2.2 1.22 Aged Top 0.355 1.40E-07 0.29 5.74E-10 1.0 0.8 5.68 Bottom 0.377 4.16E-07 0.88 2.12E-09 1.1 1.0 2.03 The pavement structural and material properties for each layer of the aged section are given in Table 2-33. As shown, the AC layer was further divided into three sub-layers accounting for stiffness gradients due to aging and temperature. Table 2-34 shows creep compliance readings measured at 0, 10, and 20°C during 1000 second Superpave IDT creep tests. They were used to generate master curves for use in modeling viscoelastic material behavior. Table 2-33. Pavement structure and material properties in the aged section E H (psi) (in) AC-Top 2.40E+06 0.35 1.5 AC-Mid 1.20E+06 0.35 1.5 AC-Bot 6.00E+05 0.35 3 Base 4.00E+04 0.35 10.5 Subgrade 3.10E+04 0.4 Inf. Table 2-34. Creep compliance values for aged samples at 0, 10, and 20°C TOP BOTTOM TIME (SEC) 0°C 10°C 20°C 0°C 10°C 20°C 1 0.054 0.069 0.129 0.076 0.126 0.248 2 0.059 0.075 0.152 0.076 0.145 0.296 5 0.057 0.084 0.169 0.096 0.171 0.379 10 0.059 0.096 0.196 0.098 0.198 0.443 20 0.065 0.114 0.262 0.111 0.257 0.503 50 0.085 0.126 0.328 0.127 0.296 0.828 100 0.092 0.148 0.425 0.136 0.378 1.154 200 0.095 0.176 0.597 0.146 0.471 1.607 500 0.109 0.238 0.873 0.162 0.669 2.484 1000 0.110 0.282 1.168 0.160 0.884 3.443

B-35 B.3.1.3 Model predictions without healing Stage one: crack initiation When healing effect was not considered, the predicted load passes to induce crack initiation for the aged and unaged sections are given in Figure 2-21. As seen in the figure, predicted number of loads to cracking for the unaged section was only about 41,700, which was much less than the 128,300 loads for the aged section. The predictions in Figure 2-22 in terms of DCSEnorm versus time showed the same trend: the unaged section required less time for crack initiation than the aged one. 0 20 40 60 80 100 120 140 160 180 200 0 0.2 0.4 0.6 0.8 1 1.2 Load repetition (x103) D C S E no rm Aged Unaged Figure 2-21. Prediction of crack initiation w/o healing: damage versus load repetition

B-36 02/06 02/08 02/10 02/12 02/14 02/16 02/18 02/20 02/22 02/24 0 0.2 0.4 0.6 0.8 1 1.2 D C S E no rm Time (mm/dd) Aged Unaged Figure 2-22. Prediction of crack initiation w/o healing: damage versus time Stage two: crack propagation Figure 2-23 shows the step-wise increase of crack depth with load passes for both the aged and unaged sections. In general, the crack propagates at a relatively low rate initially (e.g., for the first zone). The rate of growth then increases for the next few zones, beyond which the rate slows down again. As also shown in Figure 2-23, the load repetition to the critical crack depth (i.e., 3 inch for these two sections) is about 129,200 for the unaged section. Meanwhile, the load to 3 inch depth of the aged section is about 295,900, which was much more than that for the aged section. Similar trends can be found from Figure 2-24, which shows crack growth as a function of time. Given the time to crack initiation obtained in stage I, an average crack growth rate in the unaged section can be estimated to be 0.34 in/day, which is more than 1.5 times of the value, i.e., 0.20 in/day obtained for the aged section.

B-37 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25 3.75 0 50 100 150 200 250 300 350 Load repetition ( x 103 ) C ra ck d ep th (i nc h) unaged aged Without Healing : Figure 2-23. Prediction of crack growth w/o healing: crack depth versus load repetition -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25 3.75 0 5 10 15 20 25 30 Time (day) C ra ck d ep th (i nc h) unaged aged Without Healing : Figure 2-24. Prediction of crack growth w/o healing: crack depth versus time It is clear that the predicted results in terms of both crack initiation and propagation in the unaged section do not make sense, since as mentioned before, no crack was observed in that section during the entire loading period. Therefore, a mixture healing model must be included in the top-down cracking performance model. However, the two critical values Scr1 and Scr2 of the healing model have to be estimated before it can be used.

B-38 B.3.1.4 Determination of critical values for daily lowest AC stiffness In order to determine these two critical values Scr1 and Scr2, the daily lowest AC stiffness curves in the aged and unaged sections are plotted in Figures 2-25 and 2-26, respectively. As shown, the stiffnesses of the aged section are much higher than the unaged section. Since the asphalt mixture at surface of the aged section was extensively aged, as indicated by the measured binder viscosity which was much greater than any value determined from field cores in typical Florida pavement, it was believed that no healing would occur in the mixture of this section. According to the definitions of healing zones (see Section B.2.1), the Slow values for this section should be close to Scr2. Therefore, the value for Scr2 was selected to be 2,000 ksi (see Figure 2-25). 0 5 10 15 20 25 30 35 40 45 50 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 t (day) lo g- st iff ne ss (k si ) S low S cr2 Figure 2-25. Daily AC stiffness of the aged section On the other hand, mixture in the unaged section was only slightly aged, as shown by viscosity test results. The mixture was thus believed to have full healing potential. According to

B-39 the definitions of healing zones, the Slow values for this section should be close to Scr1. As a result, Scr1 was selected to be 320 ksi (see Figure 2-26). 0 5 10 15 20 25 30 35 40 45 50 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 t (day) lo g- st iff ne ss (k si ) S low S cr1 S cr2 Figure 2-26. Daily AC stiffness of the unaged section B.3.1.5 Model predictions with healing Another set of predictions was made using the performance model after incorporating the healing model. Stage one: crack initiation The predicted damage in terms of DCSEnorm versus load passes for the paired sections are given in Figure 2-27. The figure clearly shows that no crack occurred in the unaged section, which is consistent with the observation in the full-scale HVS test. On the other hand, the predicted load passes to crack initiation for the aged section remained at 128,300. The similar prediction for the aged section using performance models with and without the healing model is expected, since the aged section had no healing potential due to extensive aging applied in the test. The predicted load passes of 128,300 were also found to be close to the actual number of

B-40 passes of 140,000 when the first crack was observed. The predictions in Figure 2-28 show the same trend: crack occurred in the aged section after about 12 days, and no crack occurred in the unaged section. 0 20 40 60 80 100 120 140 160 180 200 0 0.2 0.4 0.6 0.8 1 1.2 Load repetition (x103) D C S E no rm Aged Unaged Figure 2-27. Prediction of crack initiation with healing: damage versus load repetition 02/06 02/08 02/10 02/12 02/14 02/16 02/18 02/20 02/22 02/24 0 0.2 0.4 0.6 0.8 1 1.2 D C S E no rm Time (mm/dd) Aged Unaged Figure 2-28. Prediction of crack initiation with healing: damage versus time

B-41 Stage two: crack propagation Performance predictions accounting for healing were continued in the crack propagation stage. As shown in Figure 2-29, the crack in the aged section reached the critical crack depth after 296,600 passes of HVS loading. As expected, the number of load passes was slightly greater than the one predicted by the model without healing, since the healing potential, which increases with depth helped to prolong fatigue life. Figure 2-30 shows predicted crack growth in terms of crack depth versus time in the aged section, which follows a similar pattern as that of Figure 2-29. It took another 14 days for the crack to reach the critical crack depth. -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25 3.75 0 50 100 150 200 250 300 350 Load repetition ( x 103 ) C ra ck d ep th (i nc h) unaged aged With Healing : Figure 2-29. Prediction of crack growth with healing: crack depth versus load pass

B-42 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25 3.75 0 5 10 15 20 25 30 Time (day) C ra ck d ep th (i nc h) unaged aged With Healing : Figure 2-30. Prediction of crack growth with healing: crack depth versus time In summary, the predictions after incorporation of the healing model seemed quite reasonable, as they agreed well with observations from cores, which indicated that the crack had propagated to about half-depth of the AC layer of the aged section. B.3.2 Integration of Thermal Response Model Integration of the thermal response model was completed by simply activating this model in the CCI module. The significance of the thermal response model was illustrated by predicting cracking performance of one pavement section in the Washington D. C. area with and without thermally induced damage accounted for in the performance model. B.3.2.1 Selection of climatic environment Since the thermal response model was fully developed, the key for successful integration of this model was to show that the performance model cannot predict cracking performance accurately without accounting for thermal effects. In other words, it was necessary to demonstrate the need to include the thermal response model.

B-43 A limited investigation indicated that thermal damage induced in pavement sections subjected to a non-freeze climate as that of Florida was not high enough to alter the predicted top-down cracking performance of these sections. Therefore, a freeze-thaw climate as that of Washington, D.C., was selected to demonstrate the importance of including the thermal response model. The corresponding temperature data file was used as input for model prediction, containing hourly temperatures at different depths of the AC layer. The temperature data was generated based on the climatic condition and typical pavement material and structural properties using the enhanced integrated climatic model (EICM). Other types of climatic environment such as the hard-freeze climate of North Dakota were evaluated in Section 4.2 (Main Body). B.3.2.2 Material and structural properties The geometry and material properties for the pavement section are illustrated in Figure 2-31. To account for the effects of stiffness gradient due to temperature and aging, the AC layer was divided into 3 sub-layers with thickness h1, h2, and h3, respectively. Since the temperature and aging gradients are greatest near the surface and reduce with depth, the thickness values of the AC sub-layers were taken as h1 = h2 = H1/4 and h3 = H1/2. Figure 2-31. Geometry and material properties of a 3-layer pavement structure AC layer Base Subgrade 2 40 ksiE = 3 12 ksiE = 2 12 ''H = 1 5 ''H = 1h 2h 3h 35.02 =ν 4.03 =ν

B-44 The variation of asphalt concrete (AC) modulus with time was estimated using the AC stiffness (creep compliance) aging model. Meanwhile, the degradation of AC fracture properties and healing potential with time were predicted using the FE limit (DCSE limit) aging model and the healing model, respectively. The input information for these material property models is listed in Table 0-3. Table 2-35. Data for material property aging models Parameter Value Aggregate % passing by weight (seive size) 100.0 (3/4 in.), 90.0 (3/8 in.), 60.2 (# 4), 4.8 (# 200) Binder type 67-22 Mean annual air temperature, °F 60 Effective binder content, % by volume 12 Air void content, % by volume 7 Initial fracture energy, Kpa 2 Fracture energy aging parameter 3 Figure 2-32 shows the one-year temperature profile at the surface of the AC layer in the Washington D.C. area generated from the EICM. The first day shown in the figure corresponds to July 1st of the year. As an illustration, Figure 2-33 shows the estimated dynamic modulus at year one based on the temperature profile in Figure 2-32. The stiffness was calculated at a load frequency of 10 Hz (i.e., loading time 0.1 s). The variation of FE limit, DCSE limit, tensile strength and maximum healing potential with age (and depth) are given in Figure 2-34.

B-45 0 50 100 150 200 250 300 350 -10 0 10 20 30 40 50 time (days) Te m pe ra tu re (o C ) Figure 2-32. One-year temperature profile at the pavement surface (Washington D.C.) 0 50 100 150 200 250 300 350 0 200 400 600 800 1000 1200 1400 time (days) D yn am ic m od ul us (k si ) Figure 2-33. Variation of AC stiffness with time

B-46 0 20 40 0 0.5 1 1.5 2 FE f ( K J/ m 3 ) 0 20 40 0 0.5 1 1.5 2 D C S E f ( K J/ m 3 ) 0 20 40 0 1 2 3 t (yr) S t ( M pa ) 0 20 40 0 0.5 1 t (yr) h m y z=0" z=1" z=2.75" z=0" z=1" z=2.75" z=0" z=1" z=2.75" z=0" z=1" z=2.75" Figure 2-34. Variation of fracture and healing properties with age (and depth) B.3.2.3 Traffic information The pavement section was assumed to be subjected to 18 kip single axle wheel load at a rate of 100 cycles per hour, which is equivalent to 17.5 million ESALs per 20 years. B.3.2.4 Model predictions without thermally induced damage In this section, predictions for crack initiation and propagation in the pavement section were made without activation of the thermal response model. Stage one: crack initiation Figure 2-35 gives the results of load induced damage accumulation versus time during Year 12. As shown, crack initiation occurred in early October of that Year. The total load passes leading to crack initiation is about 9.9 million ESALs, which were obtained by adding the load passes predicted in Year 12, i.e., 223,700 to the product of the yearly traffic (i.e., 0.876 million ESALs) and 11 (meaning the past 11 years).

B-47 Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul 0 0.2 0.4 0.6 0.8 1 1.2 Damage accumulation at Yr12 D C S E no rm Time (month) Figure 2-35. Prediction of crack initiation w/o thermally induced damage Stage two: crack propagation The predicted crack propagation without thermally induced damage is shown in Figure 2-36. It started at a slow rate for the first few zones. Subsequently, it sped up and maintained a faster rate until it reached the critical crack depth (i.e., 2.5 in for this case). The process took about 9.5 years.

B-48 0 0.5 1 1.5 2 2.5 3 0 5 10 15 20 25 Time (year) C ra ck d ep th (i nc h) w ithout thermal WASH : Figure 2-36. Prediction of crack propagation w/o thermally induced damage B.3.2.5 Model predictions with thermally induced damage Another set of predictions were made when both load and thermally induced damage were accounted in the performance model. The thermal effect on predicted cracking performance was then evaluated based on a comparison of these results with those of the prior section. Stage one: crack initiation Figure 2-37 gives the predicted thermal stresses at four depths of the AC layer using the thermal response model. As shown, the thermal stresses at any depth of the AC layer were almost negligible during warmer months (i.e., Jul. to Sep., and Apr. to Jun.), but they were kept at 10 psi during most of the cold times (i.e., the other half of the yearly period), during which significant amount of thermally induced damage can be generated. It can also be seen from the figure that thermal stresses decrease with depth.

B-49 0 100 200 300 400 0 2 4 6 8 10 σT at Yr10 ( z = 0" ) σ T (p si ) 0 100 200 300 400 0 2 4 6 8 10 ( z = 1.25" ) 0 100 200 300 400 0 5 10 ( z = 2.5" ) t (day) σ T (p si ) 0 100 200 300 400 0 5 10 ( z = 5" ) t (day) Figure 2-37. Predicted thermal tresses at four depths of AC layer during Year 10 The damage accumulation during Year 10 is shown in Figure 2-38. It can be seen that crack initiation occurred in early June of that Year. After accounting for loads applied in prior years, the total loads leading to crack initiation were about 8.7 million. Stage two: crack propagation Figure 2-39 shows the increment of crack depth with time when thermally induced damage was considered (refer to the solid line). Again, the crack propagated at a relatively low growth rate through the first few zones. It then accelerated until it reached the critical crack depth. The process took about 6.4 years. For comparison purpose, the prediction for crack depth versus time without considering thermally induced damage was also presented in the same figure (see the dashed line).

B-50 Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul 0 0.2 0.4 0.6 0.8 1 1.2 Damage accumulation at Yr10 D C S E no rm Time (mon) Figure 2-38. Prediction of crack initiation with thermally induced damage 0 0.5 1 1.5 2 2.5 3 0 5 10 15 20 25 Time (year) C ra ck d ep th (i nc h) w ith thermal w ithout thermal WASH : Figure 2-39. Prediction of crack propagation with and without thermally induced damage Table 2-36 summarizes the predicted number of years (nyrs) and number of load passes (npas) leading to crack initiation, and location of the initial crack (xs) for two conditions: (a) with and (b) without thermally induced damage. It can be seen that without accounting for thermally induced damage, an additional 1.4 years or 1.2 million loads are needed to see

B-51 cracking in this pavement. Clearly, the thermal effect cannot be ignored for accurate prediction of crack initiation. Table 2-36. Thermal effect on crack initiation WASH nyrs npas (x 106) xs (in.) a: with thermal 9.9 8.7 27.5 b: without thermal 11.3 9.9 27.5 Table 2-37 summarizes the predicted number of years (nyrs), number of load passes (npas), and total increment of crack depth (∆a) for these two conditions during the crack propagation stage. Table 2-37. Thermal effect on crack propagation WASH nyrs npas (x 106) ∆a (in.) a: with thermal 6.4 5.6 2.25 b: without thermal 9.5 8.3 2.25 Without thermally induced damage, an additional 3.1 years or 2.7 million loads are required to complete the propagation stage. Therefore, the importance of incorporation of thermally induced damage in crack propagation was also emphasized. It is noted that the time for crack initiation will affect the propagation time, since FE limit (DCSE limit) reduces with age. For example, if the FE limit of Year 10 (when crack initiation was identified under condition (a)) was used as the starting FE value for predicting crack propagation under condition (b), additional time or loads are expected. In summary, predicted top-down cracking performance of one pavement section in the Washington D.C. area was compared for two different conditions: with and without thermally induced damage. Based on the comparison for both crack initiation and propagation, it was found that thermal effect is important for an accurate prediction. Therefore, it is necessary to incorporate the thermal response model into the performance model. The results also indicated

B-52 that the FE limit (DCSE limit) aging model played an important role in determining the time of crack initiation and the average crack grow rate. B.4 Creep Compliance Master Curves from the SuperPave IDT The creep compliance master curves in the form of power law determined based on SuperPave IDT tests are presented in Figures 2-40 to 2-45. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 0 5000 10000 15000 20000 25000 30000 D (1 /G pa ) t (sec) I75-1B I75-1A Figure 2-40. Sections I75-1A and I75-1B: Crack Rating History and Crack Initiation Time 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 0 5000 10000 15000 20000 25000 30000 D (1 /G pa ) t (sec) I75-3 I75-2 Figure 2-41. Creep compliance master curves for cores from Sections I75-2 and I75-3

B-53 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 5000 10000 15000 20000 25000 30000 D (1 /G pa ) t (sec) SR80-1 SR80-2 Figure 2-42. Creep compliance master curves for cores from Sections SR80-1 and SR80-2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 0 5000 10000 15000 20000 25000 30000 D (1 /G pa ) t (sec) I10-8 I10-9 Figure 2-43. Creep compliance master curves for cores from Sections I10-8 and I10-9

B-54 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 0 5000 10000 15000 20000 25000 30000 D (1 /G pa ) t (sec) SR19 SR471 SR997 Figure 2-44. Creep compliance master curves for cores from Sections SR471, SR19 and SR997 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 0 5000 10000 15000 20000 25000 30000 D (1 /G pa ) t (sec) I94-14 I94-4 Figure 2-45. Creep compliance master curves for cores from Section I94-4 and I94-14

B-55 B.5 Determination of Crack Initiation Time The crack initiation time for each of the eleven Florida sections (see Table 2-38) was determined on the basis of crack rating history (see Figures 2-46 to 2-51) obtained from the flexible pavement condition survey database maintained by the Florida Department of Transportation (FDOT) (37) and observations from our visits to the field sections in 2003. The approach taken was described as follows: • Data evaluation: • The crack rating is a pavement performance parameter used by the FDOT to monitor cracking development in the field. The index value starts from 10 (indicating no cracking) and reduces to 0 with increasing severity of cracking. Due to the inherent inaccuracy of crack measurements and the uncertainty in relating reported crack measurements to specific amounts of top-down cracking, the crack rating history was only suitable for use in determining crack initiation. • The observed cracking status at the time of our visits to field sections (see also Table 2-38) can serve as an independent data point to make confirmation with the crack rating data. • Threshold determination: a crack rating of 8 was determined to be the threshold for crack initiation. • Crack initiation determination: in general, the onset of cracking for each pavement section can be determined using the threshold. For cases in which crack initiation was not possible within the range of available data, linear extrapolation was used. Table 2-38. Top-down cracking initiation time Section Section Year Cracking Status* Crack Initiation No Code Opened (at time of visit) Time (year) 1 I75-1A 1988 C 10 2 I75-1B 1989 C 12 3 I75-3 1988 C 11 4 I75-2 1989 U 17 5 SR80-1 1987 C 13 6 SR80-2 1984 U 22 7 I10-8 1996 C 8 8 I10-9 1996 C 8 9 SR471 2000 C 2 10 SR19 2000 C 1 11 SR997 1963 C 38 * C stands for cracking; U stands for no cracking.

B-56 0 1 2 3 4 5 6 7 8 9 10 0 10 20 30 40 C ra ck R at in g Time (year) I75-1A I75-1B Crack Initiation at Year 12 Crack Initiation at Year 10 Figure 2-46. Sections I75-1A and I75-1B: Crack Rating History and Crack Initiation Time 0 1 2 3 4 5 6 7 8 9 10 0 10 20 30 40 C ra ck R at in g Time (year) I75-2 I75-3 Crack Initiation at Year 11 Crack Initiation at Year 17 (linear extrapolation) Figure 2-47. Sections I75-2 and I75-3: Crack Rating History and Crack Initiation Time

B-57 0 1 2 3 4 5 6 7 8 9 10 0 10 20 30 40 C ra ck R at in g Time (year) SR80-1 SR80-2 Crack Initiation at Year 13 Crack Initiation at Year 22 (linear extrapolation) Figure 2-48. Sections SR80-1 and SR80-2: Crack Rating History and Crack Initiation Time 0 1 2 3 4 5 6 7 8 9 10 0 10 20 30 40 C ra ck R at in g Time (year) I10-8 (or I10-9) Crack Initiation at Year 8 Figure 2-49. Sections I10-8 and I10-9: Crack Rating History and Crack Initiation Time

B-58 0 1 2 3 4 5 6 7 8 9 10 0 10 20 30 40 C ra ck R at in g Time (year) SR471 SR19 Due to resurfacing, crack rating returned to 10 (at Year 4). Initiation was determined at Year 1 Crack Initiation at Year 2 (linear extrapolation) Figure 2-50. Sections SR471 and SR19: Crack Rating History and Crack Initiation Time 0 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 C ra ck R at in g Time (year) SR997 Crack Initiation at Year 41 or earlier (Year 38 was selected) Figure 2-51. Section SR997: Crack Rating History and Crack Initiation Time

B-59 B.6 List of References 1. Zhang, Z., R. Roque, B. Birgisson, and B. Sangpetngam. Identification and Verification of a Suitable Crack Growth Law. Journal of the Association of Asphalt Paving Technologists, Vol. 70, 2001, pp. 206-241. 2. Roque, R., B. Birgisson, B. Sangpetngam, and Z. Zhang. Hot Mix Asphalt Fracture Mechanics: A Fundamental Crack Growth Law for Asphalt mixtures. Journal of the Association of Asphalt Paving Technologists, Vol. 71, 2002, pp. 816-827. 3. Sangpetngam, B., B. Birgisson, and R. Roque. Development of Efficient Crack Growth Simulator Based on Hot-mix Asphalt Fracture Mechanics. In Transportation Research Record: Journal of the Transportation Research Board, No. 1832, Transportation Research Board of the National Academies, Washington, D.C., 2003, pp. 105-112. 4. Sangpetngam, B., B. Birgisson, and R. Roque. Multilayer Boundary-element Method for Evaluating Top-down Cracking in Hot-mix Asphalt Pavements. In Transportation Research Record: Journal of the Transportation Research Board, No. 1896, Transportation Research Board of the National Academies, Washington, D.C., 2004, pp. 129-137. 5. Roque, R., B. Birgisson, C. Drakos, and B. Dietrich. Development and Field Evaluation of Energy-Based Criteria for Top-down Cracking Performance of Hot Mix Asphalt. Journal of the Association of Asphalt Paving Technologists, Vol. 73, 2004, pp. 229-260. 6. Kim, J., R. Roque, and B. Birgisson. Integration of Thermal Fracture in the HMA Fracture Model. Journal of the Association of Asphalt Paving Technologists, Vol. 77, 2008, pp. 631- 662. 7. Mirza, M. W., and M. W. Witczak. Development of a Global Aging System for Short and Long Term Aging of Asphalt Cements. Journal of the Association of Asphalt Paving Technologists, Vol. 64, 1995, pp. 393-430. 8. ARA, Inc., Guide for Mechanistic-Empirical Design of New and Rehabilitated Pavement Structures. Final Report - NCHRP Project 1-37A. National Cooperative Highway Research Program, Transportation Research Board, Washington, D.C., 2004. 9. Witczak, M. W., and O. A. Fonseca. Revised Predictive Model for Dynamic (Complex) Modulus of Asphalt Mixtures. In Transportation Research Record: Journal of the Transportation Research Board, No. 1540, Transportation Research Board of the National Academies, Washington, D.C., 1996, pp. 15-23. 10. Deme, I. J., and F. D., Young. Ste. Anne Test Road Revisited Twenty Years Later. Proceedings, Canadian Technical Asphalt Association, Vol. 32, 1987, pp. 254-283.

B-60 11. Button, J. W., D. N. Little, Y. Kim, and J. Ahmed. Mechanistic Evaluation of Selected Asphalt Additives. Journal of the Association of Asphalt Paving Technologists, Vol. 56, 1987, pp. 62-90. 12. Zhang, Z. Identification of Crack Growth Law for Asphalt Mixtures Using the Superpave Indirect Tensile Test (IDT). PhD Dissertation. University of Florida, Gainesville, 2000. 13. Daniel, J. S., and Y. R. Kim. Laboratory Evaluation of Fatigue Damage and Healing of Asphalt Mixtures. ASCE Journal of Materials in Civil Engineering, Vol. 13, No. 6, 2001, pp. 434-440. 14. Kim, B., and R. Roque. Evaluation of Healing Property of Asphalt Mixture. In Transportation Research Record: Journal of the Transportation Research Board, No. 1970, Transportation Research Board of the National Academies, Washington, D.C., 2006, pp. 84- 91. 15. Si, Z., D. N. Little, and R. L. Lytton. Characterization of Microdamage and Healing of Asphalt Concrete Mixture. ASCE Journal of Materials in Civil Engineering, Vol. 14, No.6, 2002, pp. 461-470. 16. Kim, Y. R., D. N. Little, and R. L. Lytton. Fatigue and Healing Characterization of Asphalt Mixtures. ASCE Journal of Materials in Civil Engineering, Vol. 15, No.1, 2003, pp. 75-83. 17. Buttlar, W. G., R. Roque, and B. Reid. Automated Procedure for Generation of Creep Compliance Master Curve for Asphalt Mixtures. In Transportation Research Record: Journal of the Transportation Research Board, No. 1630, Transportation Research Board of the National Academies, Washington, D.C., 1998, pp. 28-36. 18. Hiltunen, D. R., and R. Roque. A Mechanics-Based Prediction Model for Thermal Cracking of Asphaltic Concrete Pavements. Journal of the Association of Asphalt Paving Technologists, Vol. 63, 1994, pp. 81-117. 19. Park, S. W., and Y. R. Kim. Interconversion between Relaxation Modulus and Creep Compliance for Viscoelastic Solids. ASCE Journal of Materials in Civil Engineering, Vol. 11, No. 1, 1999, pp. 76-82. 20. Park, S. W., and Y. R. Kim. Fitting Prony-series Viscoelastic Models with Power-law Presmoothing. ASCE Journal of Materials in Civil Engineering, Vol. 13, No. 1, 2001, pp. 26-32. 21. Roque, R., A. Guarin, G. Wang, J. Zou, and H. Mork. Develop Methodologies/Protocols to Assess Cracking Potential of Asphalt Mixtures Using Accelerated Pavement Testing. Final Report, FDOT-BD545-49, University of Florida, Gainesville, 2007.

B-61 22. Sangpetngam, B. Development and Evaluation of a Viscoelastic Boundary Element Method to Predict Asphalt Pavement Cracking. PhD Dissertation. University of Florida, Gainesville, 2003. 23. Myers, L. A., R. Roque, and B. Birgisson. Use of Two-dimensional Finite Element Analysis to Represent Bending Response of Asphalt Pavement Structures. International Journal of Pavement Engineering, Vol. 2, 2001, pp. 201-214. 24. Flexible Pavement Condition Survey Handbook. State Materials Office, Florida Department of Transportation, 2003.