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

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85 CHAPTER 4 FINDINGS: THE HMA-FM-BASED SYSTEM The primary feature of the HMA-FM-based crack propagation model was to account for effects of macro cracks during crack propagation. This model was comprised of the following key elements: 1. A critical condition concept that can more accurately capture field observations and significantly reduces the computation time required for long-term pavement performance prediction. 2. Material property sub-models that account for changes in near-surface mixture properties with aging [e.g., increase in stiffness (stiffening), reduction in fracture energy (embrittlement), and reduction in healing potential] which make pavements more susceptible to top-down cracking. 3. A thermal response model that predicts transverse thermal stresses that can be an important part of the top-down cracking mechanism. 4. A pavement fracture model that predicts crack growth with time, accounting for the effect of changes in geometry on stress distributions. In addition, a simplified fracture energy-based approach for crack initiation (i.e., a crack initiation model without considering damage zone effects) was developed and integrated with the HMA-FM-based model to illustrate the capabilities of a completed system (which was named the top-down cracking performance model). 4.1 Framework As shown in Figure 0-1, the overall framework of the integrated system has five main parts: (1) the inputs module, (2) the material property model, (3) indirect tensile test, (4) pavement response model, and (5) pavement fracture model.

86 Figure 0-1. Framework of the top-down cracking performance model 4.1.1 Inputs Module and Indirect Tensile Test The inputs module provides pavement material and structural properties, temperatures within HMA layer (as predicted using an enhanced integrated climatic model), and traffic volume (in ESALs). Because the use of load spectra to represent the traffic would have significantly increased the complexity of model development and its use on model accuracy was unknown, the research team decided to express the traffic in terms of EASLs (assuming an even spacing of ESALs over time). Table 0-1 summarizes the sub-models of the HMA-FM-based system along with the input requirements. Crack Amount (3) SUPERPAVE IDT AMOUNT OF CRACKING (5) PAVEMENT FRACTURE MODEL Crack Initiation Model Crack Growth Model Model (1) INPUTS MODULE (4) PAVEMENT RESPONSE MODEL (2) MATERIAL PROPERTY MODEL

87 Table 0-1. Input required for sub-models of the HMA-FM-based system Sub-model Sub-model component Input requirement Material property model AC stiffness aging model - Basic mixture characteristics (gradation, binder type, mix volumetrics) - Temperature, loading time, and aging time AC tensile strength aging model - Stiffness (from AC stiffness aging model) - Material coefficients an Fracture energy limit aging model - Stiffness (from AC stiffness aging model) - Initial fracture energy - Aging parameter k1 (to be determined in calibration) Healing model - Stiffness (from AC stiffness aging model) - Initial fracture energy - Critical stiffnesses. Pavement response model Load response model - Structural properties of each layer (thickness, modulus, and Poison's ratio) - Stiffness (from AC stiffness aging model) - Equivalent single axle load Thermal response model - Structural property of AC layer (thickness) - Relaxation modulus master curve parameters: Ei, λi, ηv - Temperature and thermal contraction coefficient

88 Table 0-1. Continued Sub-model Sub-model component Input requirement Pavement fracture model Crack initiation model - Load and thermal-induced stresses (from response models) - Creep compliance master curve parameters: m, D1, ηv - Mixture fracture and healing properties (from material property model) - Traffic (in ESALs) Crack growth model - Time and location of initial crack (from crack initiation model) - Structural properties of each layer (thickness, modulus, and Poison's ratio) - Stiffness (from AC stiffness aging model) - Thermal-induced stresses (from thermal response model) - Stress intensity factor for an edge crack - Creep compliance master curve parameters: m, D1, ηv - Mixture fracture and healing properties (from material property model) - Traffic (in ESALs) Crack amount model - Change of crack depth over time (from crack growth model)

89 The Superpave indirect tensile test (IDT) developed as part of the Strategic Highway Research Program (SHRP) (29) was used to determine damage and fracture properties on field cores as part of the calibration efforts. Three types of tests were performed with the Superpave IDT: resilient modulus, creep compliance (for damage rate), and tensile strength (for fracture energy limit). 4.1.2 Material Property Model Based on a brief review of the HMA-FM model and its relevant material property models, four important sub-models were developed, including aging models for asphalt concrete (AC) stiffness, tensile strength, and fracture energy (FE) limit, and a healing model. A summary of these sub-models is presented below (details of the development of the new models are presented in Appendix B). The AC stiffness aging model was developed on the basis of a binder aging model (24) and a dynamic modulus model (30). In this model, the following empirical equation was identified to consider the aging effect on mixture stiffness, * * 0 0 log | | | | log t tE E η η = (0-1) where |E*|t and |E *|0 represent the stiffnesses corresponding to aged and unaged conditions, respectively, and ηt and η0 correspond to the aged and unaged binder viscosity. The AC tensile strength aging model was developed by directly relating tensile strength to the AC stiffness aging model based on the following relationship developed by Deme and Young (31), ( )∑ = ⋅= 5 0 log n n fnt SaS (0-2)

90 where Sf is the tensile stiffness at a loading time of 1800 seconds that can be obtained from the AC stiffness aging model by considering a reduction factor from compression to tension. The constants an are 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 = = − = = − = = − The FE limit surface aging model was conceived and expressed in the following form: ( ) [ ] 1)()( min kniif tSFEFEFEtFE ⋅−−= (0-3) where, FEi is the initial fracture energy. FEmin is the minimum value of the FE limit after a sufficiently long aging period tinf. In this research, FEmin was determined based on experience (field specimens) to be 0.2 kJ/m3, and tinf was chosen as 50 years. 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 − − = (0-4) where S(t) is the stiffness at the surface of the AC layer. S0 and Smax are S(t) when t is set as 0 and 50 years, respectively. Therefore, it can be seen that Sn(t) is a parameter that varies between zero and one. The following relationship was conceived to describe the FE limit versus depth relation: ( )[ ] )(/),(),( tSztStFEFEFEztFE fiif ⋅−−= (0-5) where S(t,z) is the general expression for AC stiffness. Based on the FE limit aging model, the DCSE limit aging model was developed and is expressed as follows: ( ) ( ) ( )[ ] ( )[ ]ztSztSztFEztDCSE tff ,2/,,, 2 ⋅−= (0-6) where, St(t,z) is the general expression for AC tensile strength.

91 The development of a healing model was completed in two steps. First, a mixture level healing model was obtained based on the research by Kim and Roque (32). As a further step, possible improvements to this model for application in real pavement sections were investigated. This effort resulted in a simplified empirically based healing model that has three components: (1) a maximum healing potential aging model, (2) a daily-based healing criterion, and (3) a yearly-based healing criterion. The maximum healing potential surface aging model developed in this study is described by the following relationship: ( ) ( )[ ] 67.1/1 iFEnym tSth −= (0-7) where t is time in years. The maximum healing potential versus depth relation is ( ) ( )[ ] ( )( )tS ztSthzth ymym , 11, ⋅−−= (0-8) where S(t,z) is the general expression for AC stiffness, and S(t) is the stiffness at the surface of AC layer. The 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−= (0-9) 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. Thus ( )dninduceddremaind hDCSEDCSE −⋅= 1__ (0-10)

92 The daily normalized healing parameter depends on depth, time, and temperature. In this study, hdn was correlated with the daily lowest stiffness (Slow) of the AC layer because the healing potential is believed to be closely related to the AC material’s capacity to flow. Given that 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 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−= (0-11) 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. Thus ( )yninducedyremainy hDCSEDCSE −⋅= 1__ (0-12) 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). 4.1.3 Pavement Response Model The pavement response model has two sub-models: (1) a load response model and (2) a thermal response model. A brief summary of these sub-models is presented below (a detailed illustration of these two models is given in Appendix B). The load response model was primarily used to predict bending-induced maximum surface tensile stresses away from the tire. The model first estimated the AC modulus based on the temperature profiles and aging conditions. The load-induced tensile stresses at the pavement

93 surface were then predicted using 3-dimensional (3-D) linear-elastic analyses (LEA). The model automatically searched for the maximum tensile stress on the surface of the AC layer. The LEA was used strictly for predicting stress distribution. For small strain problems in systems that allow for stress relaxation between loading events, as is the case for pavement systems subjected to truck loading, there was no difference in the stress distribution predicted by LEA and viscoelastic analysis. A viscoelastic model, which is part of the HMA-FM-based model, was then used to predict strain and energy based on the predicted stress. Therefore, the error associated with using LEA should be negligible. The thermal response model was developed based on a thermal stress model for predicting longitudinal thermal stresses and thermal cracking (33). Because top-down cracking (known to occur in the longitudinal direction) is particularly relevant to transverse thermal stresses, the existing thermal stress model was revised to account for transverse thermal stresses, which are limited by the maximum frictional resistance that can develop between the HMA surface and base layers. 4.1.4 Pavement Fracture Model The pavement fracture model has three sub-models: (1) a crack initiation model, (2) a crack growth model, and (3) a crack amount model. These sub-models are summarized below (details regarding each of these models are presented in Appendix B). The fracture energy-based crack initiation model was developed to predict the location and time of crack initiation in HMA layers, in conjunction with the material property model and pavement response model. In the 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

94 ( ) ( )∫= 1.0 0 max 10sin10sin/ dtttcycleDCSE pAVEL πεπσ  (0-13) where σAVE is the average stress within the zone being analyzed to determine crack initiation and ε pmax is the creep strain rate. • The thermal-associated damage over the time interval from (t - ∆t) to t (or, DCSET/∆t) is expressed as ( ) ( )[ ] ( ) ( )[ ] 2// tttttttDCSE crcrT ∆−−⋅∆−−=∆ εεσσ (0-14) where εcr is creep strain at time t. It can be expressed as ( ) ( ) ( ) ( )[ ] ( ) ( )[ ]ttttttttt v crcr ∆−+⋅∆−−⋅ +∆−= σσξξ η εε 2 1 where ξ is the reduced time and ηv is the coefficient of mixture viscosity. The energy-based failure criterion for crack initiation is as follows: ( ) ( )( ) 0.1≥= tDCSE tDCSEtDCSE f remain norm (0-15) 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 (0-16) where n is number of load cycles in ∆t. The crack growth model was developed to predict the increase of crack depth with time in HMA layers, in conjunction with the material property model and thermal response model. In this model, load-induced tensile stresses ahead of the crack tip were predicted using a displacement discontinuity boundary element (DDBE) program (34); near-tip thermal stresses

95 were estimated by applying the stress intensity factor (SIF) of an edge crack to the thermal stresses predicted using the thermal response model. For each step of crack growth, the load- associated damage and the thermal-associated damage were calculated in the same manner as used in the crack initiation model, and the same failure criteria as used for crack initiation were used for crack propagation. Some key terms used during simulation of the step-wise crack growth follow: • 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, or about 6 mm. Therefore, 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. The crack amount model was developed based on the assumption of a linear relationship between the crack amount and the crack depth over AC layer thickness ratio (C/D) because, generally, the crack mouth opening gets wider as a crack gets deeper. 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 model was used to convert the crack depth versus time relationship to that of crack amount versus time.

96 4.1.5 Outputs The outputs for the predictive system are presented in the forms of (1) crack depth versus time and/or (2) crack amount versus time. 4.1.6 Model Integration The integration of sub-models was performed based on a critical condition concept, which is central to the cracking perform model. It 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. Figure 0-2 shows the stepwise pattern of crack propagation based on this concept, which is in direct contrast to traditional fatigue theory that assumes cracking is a continuous process. The integration process was completed in two phases. In Phase One, a critical condition identification (CCI) module was developed based on the critical condition concept. Figure 0-3 shows the flowchart of this module and its three components: (1) material property aging sub-models, (2) damage computation process (in terms of normalized dissipated creep strain energy: DCSEnorm), and (3) a healing model. The critical condition is identified by checking the DCSEnorm (after healing) against the threshold. As also shown in Figure 0-3, the damage computation function has two options. Option A is used to compute damage before the onset of cracking and Option B is for damage computation during crack propagation. Accordingly, two follow-up modules were formed: (1) a crack initiation simulation (CIS) module using Option A and (2) a crack growth simulation (CGS) module using Option B. These are described in the following two subsections.

97 D is tr es s Loads/Age Failure Critical Condition Crack Initiation Before Onset of Crack Crack Propagation Figure 0-2. Critical conditions for crack initiation and propagation Figure 0-3. Flowchart of CCI module In phase two, the integration was continued to illustrate the effects of healing and thermal stress using two example simulations: (1) healing effects in one pavement section in FDOT’s APT facility and (2) thermal effects in one pavement section in the Washington D.C. area (see Appendix B). 4.1.6.1 Module for crack initiation simulation (CIS) The CIS module was developed by directly making use of the CCI module (with Option A for damage computation). As shown in Figure 0-4, the AC pavement structure is analyzed using Healing Model Check DCSEnorm against Threshold Option A: Based on Pavement Response & Crack Initiation Models Option B: Based on Thermal Response & Crack Growth Models Material Property Aging Models Damage (DCSEnorm) Computation

98 a 3-D LEA program. The CCI module is called to compute the amount of induced damage, as well as damage recovery and accumulation in a step-wise manner until the critical condition is identified (usually in several years). Whenever starting a yearly period (which starts from July 1st of each year and ends with June 30th of the following year), mixture properties are updated with the material property aging models. Upon completion of the simulation, crack initiation time, as well as the location of the initial crack will be reported. DCSEnorm >= 1.0 End of Simulation Pavement Structure Analysis using 3-D LEA Call: CCI Module (Option A) No Yes Go to next time step Critical Condition Identified Figure 0-4. Flowchart of CIS module 4.1.6.2 Module for crack growth simulation (CGS) The CGS module was developed on the basis of the CCI module (with Option B for damage computation). Figure 0-5 shows the flowchart for this module. DCSEnorm >= 1.0 Pavement Structure Analysis using DDBE Update Crack Depth (CD) Call: CCI Module (Option B) End of SimulationCD >= CDc No Yes No Yes Go to next time step Critical Condition Identified Go to next model Critical Crack Depth (CDC) Reached Figure 0-5. Flowchart of CGS module

99 Knowing the initiation time and location of the initial crack, the CGS module starts by discretizing the pavement structure using 2-D displacement discontinuity boundary elements. The CCI module is then called to compute damage accumulation for each time step. If the critical condition is identified, the crack depth increases by a distance of one zone [selected as 6 mm (0.25 in.)] because lab testing revealed 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, or about 6 mm. The updated crack depth is then checked against the critical crack depth (preset to be one- half the depth of the HMA layer as field observations showed that top-down cracking generally does not exceed one-half depth of the layer): • If the crack depth is less than the critical crack depth, a new pavement structure with the updated crack depth will be discretized and another simulation is performed using the same steps as mentioned above. For modeling using the displacement discontinuity (DD) boundary element method (BEM), remeshing of the whole pavement structure is not required. The increase in crack depth can be simply addressed by replacing the zone next to the current crack-tip with a few DD elements. • Once the critical crack depth is reached, the simulation is completed and the time and applied loads corresponding to each crack depth increment will be reported. 4.2 Model Evaluation: Parametric Study The top-down cracking performance model was intended to predict crack initiation (time and location) as well as crack propagation (increase of crack depth or crack amount with time) for calibration and validation using asphalt concrete pavements. However, because of model complexity, it was necessary to know how various factors affected predicted results and which factors had the largest influence on performance. Specifically, it was important to identify factors that could alter the cracking mechanism used in the model (e.g., bending versus near-tire mechanism). Therefore, a parametric study was conducted using a broad range of input

100 parameters to evaluate these factors. To limit the number of runs, the following conditions were assumed: • A pavement structure used to demonstrate the thermal effect was selected. As shown in Figure 0-6, it consists of five layers: three asphalt concrete sub-layers, base, and subgrade. • The base thickness, subgrade modulus and thickness, and Poisson’s ratio for each of the layers were not changed for all analyses conducted. • The variation in AC creep compliance was obtained by varying binder viscosity (i.e., by changing binder type only). However, the other material characteristics (e.g., aggregate gradation, air void, and effective binder content of asphalt mixture), which also influence creep compliance, were not changed. These conditions reduced the input requirements to parameters in three input categories: Material and structural properties, including Initial fracture energy Fracture energy aging parameter Binder viscosity Base modulus AC layer thickness Traffic volume: number of ESALs per year. Climatic information: a mean annual air temperature (MAAT) and its companion hourly temperature data at four different depths of AC layer for a whole year. Figure 0-6. Pavement structure selected for use in parametric study AC layer Base Subgrade 1h 2h 3h H1 H2

101 The values selected for each variable are listed in Table 0-2. For each variable, the value used in the example to demonstrate the thermal effect is indicated by shading. In other words, the example was selected as a reference (or baseline) case to illustrate the effects of various factors. So, the input information for this example was reproduced in Table 0-3, which was used in conjunction with Table 0-2 to conduct this analysis. Then, each parameter included in the analysis was individually varied relative to the values given in Table 0-2, while the remaining parameters were held constant at the values used for the reference case. In total, the influence of individual parameters was investigated using 16 cases including the reference case. However, interactions and combined effects were not considered in this analysis. Table 0-2. Range of parameters selected for sensitivity analysis Variables Values Initial Fracture Energy FEi (Kpa) 2 5 10 Fracture Energy Aging Parameter k1 1 3 5 Binder Type 58-28 67-22 76-22 Base Modulus (Ksi) 20 40 60 AC Layer Thickness (in) 2.5 5 7.5 10 Traffic Volume (106 ESALs per year) 0.175 0.438 0.876 MAAT (°F) 50 60 75 Table 0-3. Data for material property aging models Parameter Value Aggregate % passing by weight (sieve 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

102 4.2.1 Effects of Material and Structural Properties The material and structural properties investigated included initial fracture energy, fracture energy aging parameter, binder viscosity, base modulus, and AC layer thickness. The influence of each is discussed in the following subsections. 4.2.1.1 Effect of Initial Fracture Energy The initial fracture energy (FEi) is the starting value (also maximum value) of any fracture energy aging curve (see Figure 0-7) and it controls the initial degradation rate of any maximum healing potential aging curve (see Figure 0-8). Therefore, it was expected to have a strong influence on pavement cracking performance. To examine such influence, a broad range of initial fracture energies was selected. Figure 0-7. FE limit aging curves for different FEi (k1 = 3) 0 2 4 6 8 10 0 10 20 30 40 50 Age (year) Fr ac tu re E ne rg y Li m it (K pa ) 2 5 10 FE i (Kpa) : `

103 Figure 0-8. Maximum healing potential (surface) aging curves for different FEi Plots of crack depth versus time predicted by the model for different values of initial fracture energy are shown in Figure 0-9. As the figure shows, pavement with higher initial fracture energy exhibits better cracking performance (i.e., longer crack initiation time ti and propagation time). For pavements with the same AC layer thickness, comparison was also made with respect to an average crack growth rate, which was defined as p ic t t CDCDC −= (0-1) where, Ct is average crack growth rate, CDc is critical crack depth, CDi is initial crack depth of 0.25 inch, and tp is crack propagation time to the critical crack depth. The average crack growth rate is essentially the slope of the curves shown in Figure 0-9. It is clear from the figure that a higher FEi value leads to a lower average crack growth rate, representing better cracking performance. 0 0.2 0.4 0.6 0.8 1 0 10 20 30 40 50 Age (year) M ax im um H ea lin g P ot en tia l 2 5 10 FE i (Kpa) :

104 Figure 0-9. Effect of initial fracture energy on cracking performance 4.2.1.2 Effect of Fracture Energy Aging Parameter Fracture energy aging parameter k1 is an input parameter that governs the shape of the fracture energy aging curve. For a constant initial fracture energy, a larger k1 value corresponds to a lower rate of degradation in fracture energy with aging (i.e., higher resistance to fracture, see Figure 0-10). Figure 0-10. FE limit aging curves at different k1 (FEi = 2 Kpa) 0 0.5 1 1.5 2 0 10 20 30 40 50 Age (year) Fr ac tu re E ne rg y (K pa ) 1 3 5 k 1 : 0 0.5 1 1.5 2 2.5 3 3.5 0 5 10 15 20 25 30 35 40 45 C ra ck d ep th (i nc h) Age (year) 2 5 10 FE i (Kpa) : FEi (Kpa) 2 5 10 ti (yr) 9.9 18.7 26.9 Ct (in/yr) 0.35 0.23 0.16

105 The effect of the fracture energy aging parameter is shown in Figure 0-11. As shown, the increase of k1 value results in longer time to crack initiation and a shallower slope of the crack growth curve. Figure 0-11. Effect of fracture energy aging parameter on cracking performance 4.2.1.3 Effect of Binder Viscosity A typical range of binder types (from soft to stiff) was selected for the analysis of cracking performance. Figure 0-12 shows that crack initiation time is not affected by the change in binder viscosity. Also a softer binder results in a slightly higher crack growth rate because of the higher creep rate of the mixture with the softer binder. However, binder stiffness also affects AC stiffness such that a softer binder will contribute to lower AC stiffness, which can offset the effect of higher creep rate. Therefore, the overall change in the average crack growth rate is small, and pavement cracking performance is not sensitive to the change of binder viscosity. However, this result does not consider the contribution of the softer binder to an increased mixture fracture energy, which was kept constant in this analysis. 0 0.5 1 1.5 2 2.5 3 3.5 0 5 10 15 20 25 C ra ck d ep th (i nc h) Age (year) 1 3 5 k 1 : k1 1 3 5 ti (yr) 6.9 9.9 11.8 Ct (in/yr) 0.47 0.35 0.30

106 Figure 0-12. Effect of binder type on cracking performance 4.2.1.4 Effect of Base Modulus The effect of base modulus was investigated using the material properties listed in Table 0-3 and the values of base modulus given in Table 0-2. Pavement cracking performance predicted by the model is given in Figure 0-13, which shows that the pavement with higher base modulus has better performance (i.e., longer crack initiation time and lower crack growth rate). This was expected because a stiffer base tends to reduce the load-induced tensile stresses at the surface of the pavement. For the range of base modulus values studied, the effect of base modulus is fairly strong. 0 0.5 1 1.5 2 2.5 3 3.5 0 5 10 15 20 25 C ra ck d ep th (i nc h) Age (year) 58 - 28 67 - 22 76 - 22 Binder type : Binder 58-28 67-22 76-22 ti (yr) 9.9 9.9 10.0 Ct (in/yr) 0.39 0.35 0.33

107 Figure 0-13. Effect of base modulus on cracking performance 4.2.1.5 Effect of AC Layer Thickness The following AC layer thicknesses were selected for this analysis (see Table 0-2): 2.5 in. for a thin AC layer. 5 in. for a medium thickness AC layer. 7.5 in. and 10 in. for thick AC layers. The predicted pavement cracking performance for the first three AC layer thickness values are shown in Figure 0-14, which shows that the pavement with thicker AC layer had better cracking performance, i.e., longer time to crack initiation. Because the crack growth rate generally increases with crack length for any crack, it was determined that this parameter was not suitable to be directly compared for pavements with different AC layer thicknesses, which by definition have different total crack lengths. However, the influence of AC layer thickness on crack growth may be examined in the following two cases: (1) Comparison of a staged crack growth rate (Ct1) for the crack depth of 1.25 in. for all three AC layers (2.5, 5.0, and 7.5 in.), which are 0.25, 0.24, and 0.20 in./year, respectively; and (2) Comparison of another staged crack growth rate (Ct2) for the crack depth of 2.50 in. for two AC layers (5.0 and 7.5 in.), which are 0 0.5 1 1.5 2 2.5 3 3.5 0 5 10 15 20 25 C ra ck d ep th (i nc h) Age (year) 20 40 60 E 2 (ksi) : E2 (ksi) 20 40 60 ti (yr) 7.4 9.9 12.6 Ct (in./yr) 0.51 0.35 0.29

108 0.35 and 0.32 in./year. It can be seen from these comparisons that, in general, crack growth is slower in a thicker layer. Figure 0-14. Effect of AC layer thickness on cracking performance However, the predicted location of the initial crack for the thick AC layer was more than 36 inches from the center of one tire. In this case, the initial crack was actually predicted to be either in the other traffic lane or in the compressive zone of the other tire (e.g., location A or C due to Tire 1, as indicated in Figure 0-15), which did not seem realistic. Therefore, the bending mechanism used for model prediction may not be appropriate for the thick AC layer pavement. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 5 10 15 20 25 C ra ck d ep th (i nc h) Age (year) 2.5 5 7.5 H 1 (inch) : H1 (in.) 2.5 5.0 7.5 ti (yr) 3.7 9.9 13.8

109 Traffic Lane 12 ft Passing Lane Shoulder   AC Layer (≥ 7.5 in.) (Potential) location of initial crack A: • Not in traffic lane (bending mechanism) • Maximum tension is low • Not critical (Potential) location of initial crack C: • In compressive zone of tire  (bending mechanism) • Maximum tension is low • Not critical (Potential) location of initial crack B: • Next to tire  (near- tire mechanism) • Critical Tire 1 Tire 2 Figure 0-15. Change in top-down cracking mechanism from bending to near-tire The near-tire mechanism, accounting for shear-induced tension at the tire edge, was thus considered for use in thick AC layer. This mechanism stipulated initial cracks located just next to the tire edge (e.g., location B due to Tire 1 in Figure 0-15). The major driving force for crack initiation and propagation is the shear-induced principal tensile stress. However, a crack growth simulation tool based on this mechanism was not available at this time. Therefore, the CGS module was used as a surrogate to predict crack growth with time. Due to the localized nature of the shear-induced tension at the tire edge, the critical crack depth was redefined to be one fourth of the AC layer depth. Then, a simplified model with the near-tire mechanism was used to predict cracking performance for the 7.5 in. thick AC layer and a 10 in. full depth AC pavement. The predicted cracking performance shown in Figure 0-16 indicates that both pavements have almost identical performance (i.e., same crack initiation time and similar crack propagation time). This is expected because the principal tensile stress of 25 psi predicted based on actual tire stresses was the same for both pavements. In fact, this stress was found to be independent of AC thickness and the stiffness ratio of AC-to-base layer.

110 A comparison of Figure 0-16 and Figure 0-14 suggests that thick pavements may perform even worse than a pavement with a medium thickness AC layer. However, the simplified model does not address some potential factors affecting the near-tire mechanism, including the effects of the wander and stress state, which will result in less damage than predicted, and therefore, the comparison may not be accurate without considering these factors. Figure 0-16. Predictions based on tire-edge cracking mechanism 4.2.2 Effect of Traffic As shown in Table 0-2, three traffic levels were selected for this analysis: a high traffic level with 0.876 million ESALs/year; a medium traffic level with 0.438 million ESALs / year; and a low traffic level with 0.175 million ESALs/year. The high, medium, and low traffic levels are equivalent to 100, 50, and 20 ESALs / hour, respectively. The predicted pavement performance, shown in Figure 0-17, indicates that the pavement subjected to the highest traffic level had the worst performance (i.e., shortest time to crack initiation and highest crack growth rate). Overall, the effect of traffic is strong. 0 0.5 1 1.5 2 2.5 3 0 2.5 5 7.5 10 12.5 15 C ra ck d ep th (i nc h) Age (year) 7.5 10 H 1 (inch) : Mechanism: Shear - induced tension at tire - edge H1 (in.) 7.5 10.0 ti (yr) 6.6 6.6

111 Figure 0-17. Effect of traffic volume on cracking performance 4.2.3 Effect of Climate Three typical climatic environments were selected for this analysis: a hard-freeze (HF) environment as that of Fargo, ND; a freeze-thaw (FT) environment as that of Washington, DC, and a non-freeze (NF) environment as represented by the climate of Melrose, FL. The mean annual air temperature (MAAT) values for these climatic environments are given in Table 0-2. For each climate, the MAAT value and the corresponding temperature data file containing hourly temperature history at four depths of the AC layer for a whole year were used as input for model prediction. The predicted pavement performance, shown in Figure 0-18, indicates similar pavement cracking performance for both the HF and FT environments. However, the pavement in the NF environment exhibits slightly later time to crack initiation, but a higher crack growth rate than those for the other two environments. Overall, the effect of climatic environment (more specifically, temperature) is not significant. 0 0.5 1 1.5 2 2.5 3 3.5 0 5 10 15 20 25 C ra ck d ep th (i nc h) Age (year) 0.876 0.438 0.175 Traffic : (10 6 ESALs/Yr) Traff ic (ESALs) 175000 438000 876000 ti (yr) 14.8 12.4 9.9 Ct (in./yr) 0.25 0.29 0.35

112 Figure 0-18. Effect of climatic environment on cracking performance This finding was expected because the climatic environment influences damage development in the pavement in two ways. Colder weather leads to higher thermal stresses and thus higher thermally induced damage. But, colder weather results in lower creep rate and thus lower load-induced damage. However, transverse thermal stresses were used to compute thermally induced damage in the thermal response model. Therefore, the resulting thermally induced damage is not as high as that caused by longitudinal thermal stresses. When both thermally induced damage and load-induced damage are combined, the two opposite effects of climatic environment tend to offset each other. To verify this trend, the thermal response sub-model was turned off in the top-down cracking performance predictive system, which was then used to predict cracking performance for the same pavement under these three climatic environments (i.e., the climate was allowed to influence load-induced damage only). The results presented in Figure 0-19 indicate that the climate did not have much influence on crack initiation time. However, it did strongly affect the crack growth rate. As can be seen, the pavement in the warmer climatic environment has a higher crack growth rate than the one in 0 0.5 1 1.5 2 2.5 3 3.5 0 5 10 15 20 25 C ra ck d ep th (i nc h) Age (year) NF FT HF Climate type : Climate NF FT HF ti (yr) 10.9 9.9 9.9 Ct (in./yr) 0.49 0.35 0.35

113 the colder climate because the pavement in the warmer climate is subjected to a higher creep rate for longer time and thus more damage. Figure 0-19. Effect of climatic environment (w/o thermally induced damage) on cracking performance 4.3 Model Calibration and Validation The top-down cracking performance model was calibrated and validated to determine whether the model could reasonably predict the cracking performance of asphalt concrete pavement for different pavement material and structural properties, traffic volume, and climatic information. 4.3.1 Summary of Top-down Cracking Performance Model Data Calibration of the top-down cracking performance model was conducted by matching as closely as possible top-down cracking predictions with observed cracking performance in the field, more specifically crack initiation time. To complete the calibration, input data were needed to make top-down cracking predictions, and observed field performance data of each pavement section was required for comparison with model predictions. This section presents the data used for model calibration. 0 0.5 1 1.5 2 2.5 3 3.5 0 5 10 15 20 25 C ra ck d ep th (i nc h) Age (year) NF FT HF Climate type : No Thermal Damage was Considered Climate NF FT HF ti (yr) 12.4 11.3 12.2 Ct (in./yr) 0.33 0.24 0.18

114 4.3.1.1 Selection of pavement sites Thirteen pavement sections were used for calibration/validation. These sections were selected based on quality of data in terms of both laboratory testing and field observation. Only sections for which material property data obtained from Superpave IDT tests performed on field core were used. In addition, only sections for which pavement performance data could be confirmed through direct field observations were used. According to the climatic condition, these pavement sections fell into two groups. Group I included eleven sections in Florida (Non-Freeze climate), and Group II had two sections in Minnesota (Hard-Freeze climate). The locations of these test sections are presented in Table 0-4. Table 0-4. Field test sections under Non-Freeze climate of Florida Group Section Section Code County Location / No. No. Name Section Limits I 1 Interstate 75 I75-1A Charlotte MP 161.1 - MP 171.3 Section 1 2 Interstate 75 I75-1B Charlotte MP 149.3 - MP 161.1 Section 1 3 Interstate 75 I75-3 Lee MP 131.5 - MP 149.3 Section 3 4 Interstate 75 I75-2 Lee MP 115.1 - MP 131.5 Section 2 5 State Road 80 SR 80-1 Lee From Hickey Creek Bridge Section 1 To East of Joel Blvd. 6 State Road 80 SR 80-2 Lee From East of CR 80A Section 2 To West of Hickey Creek Bridge 7 Interstate 10 I10-8 Suwannee MP 15.144 - MP 18.000 Section 8 8 Interstate 10 I10-9 Suwannee MP 18.000 - MP 21.474 Section 9 9 State Road 471 SR471 Sumter The northbound lane three miles north of the Withlacoochee River 10 State Road 19 SR19 Lake The southbound lane five miles south of S.R. 40 11 State Road 997 SR997 Dade The northbound lane 7.6 miles south of US-27 II 12 Interstate 94 I94-4 - located near Albertville, Minnesota Cell 4 (40 miles northwest of the Twin Cities) 13 Interstate 94 I94-14 - located near Albertville, Minnesota Cell 14 (40 miles northwest of the Twin Cities)

115 The parametric study presented in Section 4.2 showed that AC layer thickness governs the cracking mechanism. For pavements with thin to medium thickness AC layers such as those of Group I (which ranges from 2 to 8 in.), the bending mechanism was appropriate. But, for full- depth AC pavements such as those of Group II (which ranges from 8 to 12 in.), the near-tire mechanism had to be used. In this project, Group I was used for calibration/validation of the bending mechanism, and Group II was used to evaluate the reasonableness of the near-tire mechanism. 4.3.1.2 Data obtained from SuperPave IDT The Superpave indirect tensile test (IDT) developed as part of the Strategic Highway Research Program (SHRP) (29) was used to determine tensile properties on field cores obtained from the 13 test sections (i.e., properties at the age when coring was conducted). Nine specimens (from nine cores) were selected from each section to test the mixture at three temperatures (i.e., three replicate specimens at each temperature). The Superpave IDT includes three types of tests: resilient modulus, creep compliance, and tensile strength. • The resilient modulus test was performed in a load-controlled mode by applying a repeated haversine waveform load to the specimen for a period of 0.1 second followed by a rest period of 0.9 seconds. The load was selected to keep the repeated horizontal strain between 100 and 300 micro-strain during the test (35). The resilient moduli of mixtures (MR) determined at 10°C are presented in Table 0-5. • The creep compliance test was also performed in the load-controlled mode by applying a static load to the specimen for a period of 1000 seconds. The load was selected to maintain the accumulative horizontal strain below 1000 micro-strain (36). The creep compliance master curve power law parameters (m and D1) (determined based on tests conducted at 0, 10, and 20°C) are presented in Table 0-6. Plots for the master curves are provided in Appendix B (Section B.4). • The strength test was performed in a displacement-controlled mode, in which loading was applied at a rate of 50 mm/min. The fracture properties determined at 10°C are also shown in Table 0-5, including tensile strength (St), failure strain (εf), FE limit (FEf), and DCSE limit (DCSEf).

116 Table 0-5. Data from SuperPave IDT resilient modulus and tensile strength tests at 10°C Section MR St εf FEf DCSEf Aged Time Code (Gpa) (Mpa) (µε) (Kpa) (Kpa) (year) I75-1A 11.14 1.65 1028.05 1.1 1.0 15 I75-1B 10.91 2.01 1437.44 2.0 1.8 14 I75-3 11.58 1.68 715.74 0.8 0.7 15 I75-2 10.29 1.89 1066.72 1.3 1.1 14 SR80-1 13.39 1.59 495.27 0.3 0.2 16 SR80-2 13.45 2.39 679.15 1.0 0.8 19 I10-8 9.85 1.56 386.00 0.4 0.3 7 I10-9 10.21 1.27 415.00 0.4 0.3 7 SR471 7.67 1.79 2040.00 2.5 2.3 3 SR19 9.30 1.71 1338.00 1.6 1.4 3 SR997 11.74 2.33 594.00 0.9 0.7 40 I94-4 8.18 1.35 1203.56 1.1 1.0 13 I94-14 9.44 1.78 1760.25 2.4 2.2 13 Table 0-6. Data from SuperPave IDT creep compliance tests at 0, 10, and 20°C Section m D1 AT(3) * AT(2) AT(1) Code (1/Gpa) I75-1A 0.441 0.027 251.19 35.48 1 I75-1B 0.471 0.029 177.83 19.95 1 I75-3 0.485 0.022 281.84 14.13 1 I75-2 0.460 0.021 562.34 56.23 1 SR80-1 0.445 0.014 354.81 25.12 1 SR80-2 0.368 0.014 501.19 35.48 1 I10-8 0.441 0.013 112.202 8.913 1 I10-9 0.503 0.006 141.254 14.125 1 SR471 0.783 0.001 223.872 63.096 1 SR19 0.595 0.012 89.125 8.913 1 SR997 0.349 0.019 63.096 3.981 1 I94-4 0.462 0.018 − 44.668 1 I94-14 0.456 0.019 − 79.433 1 *AT(3) denotes the inverse of shift factor at the highest temperature. 4.3.1.3 Data for material property model As introduced in Section 4.1.2, the material property model consists of four sub-models: the AC stiffness (creep compliance) aging model, the tensile strength aging model, the fracture energy (dissipated creep strain energy) limit aging model, and the healing model.

117 The AC stiffness aging model estimates the stiffness of the asphalt mixture as a function of temperature and time. The input information for this model is as follows: • Percent passing 3/4, 3/8, #4, and #200 sieves by weight • Binder type and mean annual air temperature (MAAT) • Effective binder content (Vbeff, % by volume) and air void (Va, % by volume) The values used for the above parameters are shown in Table 0-7. The AC tensile strength aging model uses the stiffness predicted by the stiffness aging model and the correlation between stiffness and strength to calculate the tensile strength of asphalt mixture. Table 0-7. Data used by the material property model Section Percent passing by weight Vbeff Va MAAT Binder Code 3/4 in 3/8 in # 4 # 200 (%) (%) (°F) type I75-1A 100.0 91.8 73.6 5.9 10.7 5.4 75 67-22 I75-1B 100.0 93.7 74.6 5.6 10.7 3.2 75 67-22 I75-3 100.0 86.2 65.1 5.5 8.2 7.2 75 67-22 I75-2 100.0 92.5 68.9 5.0 8.4 6.9 75 67-22 SR80-1 100.0 80.4 59.0 5.8 8.6 5.7 75 67-22 SR80-2 100.0 84.8 64.4 6.2 8.9 7.5 75 67-22 I10-8 100.0 90.0 60.2 4.8 10.3 8.7 75 67-22 I10-9 100.0 90.0 60.2 4.8 9.1 9.9 75 67-22 SR471 100.0 90.0 60.2 4.8 13.3 5.7 75 67-22 SR19 100.0 90.0 60.2 4.8 14.2 4.8 75 67-22 SR997 100.0 90.0 60.2 4.8 11.4 7.6 75 67-22 I94-4 100.0 82.1 65.6 5.2 10.3 4.4 50 58-28 I94-14 100.0 83.4 68.3 5.0 11.1 3.7 50 58-28 The fracture energy limit aging model also uses the stiffness predicted by the stiffness aging model, but in a normalized form. The model has two unknowns: the aging parameter k1 which is to be determined from calibration, and the initial fracture energy FEi which is in general obtained from unaged cores using SuperPave IDT tests. However, since unaged mixture was not available for the field sections used in this study, FEi was backcalculated from tests performed on aged cores. As an example, an FEf value of 1.1 Kpa is obtained by testing cores from Section

118 I75-1A, which was 15 years old at the time of coring. Then, the FEi value of the mixture can be determined by using Equation 0-3, in which the normalized stiffness Sn(t) is estimated on the basis of material characteristics of the mixture (see Table 0-7) and the aging parameter k1 has to be assumed. For a k1 value of 3, the FEi is determined to be 4.5 Kpa, with which the entire FE limit aging curve is determined (see Figure 0-20). 0 5 10 15 20 25 30 35 40 45 50 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 FE f ( kJ /m 3 ) X: 15 Y: 1.1 t (year) Figure 0-20. FE limit aging curve (k1 = 3) for Section I75-1A The healing model has three components: the maximum healing potential aging model and two criteria for determining healing by day and by year: • The maximum healing potential aging model uses the normalized stiffness and initial fracture energy to estimate the loss of maximum healing potential due to aging. • The criterion for determining healing by day, hdn, uses the lowest stiffness, Slow, of any day (predicted by the stiffness aging model) and two critical values, Scr1 and Scr2 (estimated to be 320 and 2,000 ksi), to determine the healing potential of the day. The daily-based healing is bounded by zero and the maximum value hym determined by the maximum healing potential aging model.

119 • The criterion for determination of yearly based healing, hyn, is identical to the criterion for daily based healing except an averaged daily lowest stiffness, Slowa, for a prolonged period was used instead of Slow to obtain the healing potential of any year. Details of these models are provided in Appendix B. 4.3.1.4 Data for pavement response model The pavement response model consists of two sub-models: (1) a load response model and (2) a thermal-response model. The load-response model estimates load-induced stresses due to traffic loads. It requires the following input parameters: • Layer thickness of AC, base, and subbase • Modulus of base, subbase, and subgrade • Poisson’s ratio of AC, base, subbase, and subgrade • Equivalent single axle load • Hourly temperatures within the AC layer The values used for layer thickness, modulus, and yearly traffic are listed in Table 0-8. Poisson’s ratios of 0.3, 0.35, 0.35, and 0.4 were assumed for AC, base, subbase, and subgrade, respectively. It was determined that the effect on load response due to slight changes in Poisson’s ratio is negligible. The hourly pavement temperatures were estimated by the enhanced integrated climatic model (EICM), using typical pavement material and structural properties and local climatic information. The thermal-response model estimates thermally induced stresses caused by changes in pavement temperatures. It requires the following input parameters: • Thickness of AC layer • The relaxation modulus master curve parameters • Hourly pavement temperatures within the AC layer

120 • The coefficient of thermal contraction of the asphalt concrete mixture The values used for thickness and hourly pavement temperatures are similar to those described for the load-response model. The coefficient of thermal contraction was assumed to be 1.2E-5 ε/°C for all test sections. It was determined that slight changes in the coefficient of thermal contraction do not significantly influence transverse thermal stresses (predicted by the thermal-response model) which are limited by the maximum frictional resistance that can develop between surface and base layers. Table 0-8. Data used by the pavement response model Section Layer thickness (in) Layer modulus (ksi) Yearly traffic Code AC Base Sub-base Base Sub-base Sub-grade (103 ESAL) I75-1A 6.54 12 12 54.8 50.1 30.1 573 I75-1B 6.24 12 12 63.6 51.4 36.1 558 I75-3 6.48 12 12 59.6 34.8 36.2 674 I75-2 7.42 12 12 107.4 90.3 31.4 576 SR80-1 3.38 12 12 51.3 40.0 39.7 221 SR80-2 6.30 12 12 57.3 45.6 18.8 207 I10-8 7.20 12 12 55.7 54.5 38.9 392 I10-9 7.40 12 12 65.2 41.4 46.6 392 SR471 2.58 12 12 43.0 34.0 33.6 26 SR19 2.40 12 12 50.7 13.0 12.6 51 SR997 2.18 12 12 109.0 53.0 52.7 89 I94-4 9.10 − − − − 3.2 488 I94-14 10.90 − − − − 3.2 782 4.3.1.5 Data for pavement fracture model The pavement fracture model consists of three sub-models: (1) a crack initiation model, (2) a crack growth model, and (3) a crack amount model. The crack initiation model uses (1) the load-induced and thermally-induced stresses predicted by the pavement response model and (2) the rule for determination of crack initiation to predict crack initiation time and location. During the process, the mixture fracture and healing properties determined by the material property model are required.

121 The crack growth model uses the load-induced stresses predicted by the 2-D DDBE program, thermally induced stresses predicted by the thermal response model combined with the stress intensity function for an edge crack, and the energy-based failure criterion to compute the increase of crack depth with time. The mixture fracture and healing properties determined by the material property model are also required during the process. The crack amount model converts the crack depth-versus-time relationship predicted by the crack growth model to a crack amount-versus-time relationship. Detailed information on these models is provided in Appendix B. 4.3.1.6 Observed pavement performance data The input data presented in Sections 4.3.1.2 to 4.3.1.5 was used to predict the performance of each of the 13 test sections in two phases. In Phase One, the predictions for the 11 sections of Group I were compared with observed performance to calibrate the model. The field performance for each of the sections was obtained from the following two sources: • Visits were made to each test section to observe and photograph its performance and take cores in 2003. Some sections exhibited a moderate amount of cracking and others showed no cracking. An inspection of core samples from the cracked sections indicated the presence of top-down cracking (i.e., cracks initiated from the surface and moved downward). • The crack rating history for each test section was obtained from the flexible pavement condition survey database maintained by the Florida Department of Transportation (FDOT) (37). The crack rating is a pavement performance parameter used by the FDOT to monitor cracking development in the field. The index value starts at 10 (indicating no cracking) and drops to 0 with increasing severity of cracking. The crack rating history of the 11 Florida sections used in the project is given in Appendix B.5. The crack initiation time listed in Table 0-9 for each test section was determined on the basis of the gathered information (see Appendix B).

122 In Phase Two, predictions obtained using the calibrated model were presented and compared with field observations for all test sections, including those of Group II (also presented in Table 0-9), which was obtained from Minnesota Department of Transportation (MnDOT). Table 0-9. Observed top-down cracking initiation time Section Section Crack Initiation No Code Time (year) 1 I75-1A 10 2 I75-1B 12 3 I75-3 11 4 I75-2 17 5 SR80-1 13 6 SR80-2 22 7 I10-8 8 8 I10-9 8 9 SR471 2 10 SR19 1 11 SR997 38 12 I94-4 4 13 I94-14 6 Based on the observed crack initiation time, pavement cracking performance can be categorized according to one of five performance levels: Level I: 1 to 5 years before crack initiation. Level II: 6 to 10 years before crack initiation. Level III: 11 to 20 years before crack initiation. Level IV: 21 to 30 years before crack initiation. Level V: greater than 30 years before crack initiation. The intent of presenting the performance data according to levels was simply to provide an alternate way to illustrate the goodness of fit of the model, since R2 values are sometimes difficult to visualize (see Section 4.3.2). Four boundaries (i.e., 5, 10, 20, and 30 years), defining five levels were selected to differentiate the expected range of cracking performance. Admittedly, the boundaries selected by the research team are not unique. Different boundaries could have been selected and the illustration might have been slightly different. However, the

123 general message would be the same. In short, slight changes in these boundaries will not significantly affect model calibration/validation results. 4.3.2 Model Calibration Model calibration was accomplished by matching as closely as possible top-down cracking predictions for 11 pavement sections (Group I) with observed top-down cracking in the field. Given that the aging parameter (k1) was included as an unknown parameter within the fracture energy aging model, R2 of the predicted initiation times of top-down cracking was determined for each assumed k1 value, using linear regression with a constant intercept (more specifically, the error between predicted and measured data was examined relative to the line of equality, which by definition has an intercept of 0). A series of such linear regressions was conducted with k1 values ranging from 0.5 to 5. The k1 value resulting in the best fit (highest R 2) of observed initiation times of cracking with predicted times was chosen for the final model. (For brevity, the constant intercept linear regression used in the calibration was simply termed linear regression in the discussion that followed.) 4.3.2.1 Calibration procedure The calibration procedure included a matrix of runs of the top-down cracking performance model to obtain crack initiation time predictions for each selected section at 8 values of the aging parameter k1 ranging between 0.5 and 5, as determined by a trial-and-error process. A k1 value of 0.5 resulted in longer time to crack initiation for most of the pavement sections, including those sections known to have poor observed performance. Similarly, a k1 value of 5 resulted in shorter time to crack initiation for most of the sections, including those sections known to have good observed performance. The data obtained from these runs is shown in Table 0-10.

124 Table 0-10. Predicted versus observed cracking performance for different k1-values (all test sections in Group I) Section Observed Predicted ti' (year) No. ti k1-value (year) 0.5 1 1.5 2 2.5 3 3.5 5 1 10 14.7 14.7 13.8 12.7 11.8 10.9 10.7 9.6 2 12 13.9 13.9 13.9 13.9 13.8 12.9 12.7 11.0 3 11 8.9 8.0 6.9 6.5 5.9 5.5 4.9 4.0 4 17 19.0 19.0 18.8 17.8 16.8 16.0 15.7 14.6 5 13 3.0 2.3 2.2 1.7 1.3 1.2 1.2 1.1 6 22 25.7 25.7 25.7 24.7 23.7 22.8 22.6 20.9 7 8 7.6 6.6 5.9 5.8 5.6 5.6 4.9 4.6 8 8 7.9 6.9 6.7 6.6 5.9 5.8 5.7 4.7 9 2 6.9 5.8 5.5 4.9 4.8 4.8 4.8 4.7 10 1 5.6 4.6 4.3 3.9 3.8 3.8 3.7 3.5 11 38 34.8 34.8 34.8 34.8 34.8 34.8 34.8 34.7 R² 0.807 0.803 0.802 0.809 0.802 0.801 0.791 0.767 Also, for each aging parameter, a linear regression routine was used to determine R2 by examining the error between the observed initiation time and the predicted time of crack initiation relative to the line of equality. The k1 value that resulted in the largest R 2 (i.e., best match or lowest error between predicted crack initiation time and the time observed in the field) was chosen as the optimum k1. 4.3.2.2 Initial calibration results Linear regressions were performed to determine the R2 (for each aging parameter k1). Thus, eight values were obtained (see Table 0-10), and eight models (each of which has different k1 and R 2 values) were assembled. The model with the highest R2 value (i.e., 0.809) had a k1 value of 2.0 Another means for evaluating the goodness of fit of the model is by comparing the predicted levels of cracking performance to those observed, as described in Section 4.3.1.6. The results of this comparison are shown in Figure 0-21 and are summarized as follows:

125 • Two of the two Level I sections were predicted to be level I sections. • Two of the three Level II sections were predicted to be Level II sections and one section was predicted to be a Level III section. • Two of the four Level III sections were predicted to be Level III sections, one was predicted to be a Level II section, and one was predicted to be a Level I section. • The Level IV section was predicted to be a Level IV section. • The Level V section was predicted to be a Level V section. Observed Cracking Performance Level I II III IV V Pr ed ic te d C ra ck in g Pe rf or m an ce L ev el I 2 1 II 2 1 III 1 2 IV 1 V 1 Figure 0-21. Predicted versus observed cracking performance (All 11 sections) This comparison shows a strong correlation between predicted and observed cracking performance. As shown in Figure 0-21, eight predictions matched the observed performance, two predictions were off by one level, and only one prediction was off by two levels. Thus, predicted performance in terms of crack initiation time was relatively good for 10 out of 11 sections. The difference by two levels prediction for Test Section 5 apparently had a strong influence on R2, which was not very sensitive to the k1 value such that the prediction for Test

126 Section 5 may have overwhelmed the sensitivity of the results. Therefore, Test Section 5 was excluded from the final calibration, but it was included in the validation process. 4.3.2.3 Final calibration A final calibration that excluded Section 5 was made and linear regressions were performed to determine eight different values of R2 (one for each aging parameter). The model with the highest R2 value (i.e., 0.933) had a k1 value of 3.0 (see Table 0-11). Table 0-11. Predicted versus observed cracking performance (without Test Section 5 in Group I) Section Observed Predicted ti' (year) No. ti k1-value (year) 0.5 1 1.5 2 2.5 3 3.5 5 1 10 14.7 14.7 13.8 12.7 11.8 10.9 10.7 9.6 2 12 13.9 13.9 13.9 13.9 13.8 12.9 12.7 11.0 3 11 8.9 8.0 6.9 6.5 5.9 5.5 4.9 4.0 4 17 19.0 19.0 18.8 17.8 16.8 16.0 15.7 14.6 6 22 25.7 25.7 25.7 24.7 23.7 22.8 22.6 20.9 7 8 7.6 6.6 5.9 5.8 5.6 5.6 4.9 4.6 8 8 7.9 6.9 6.7 6.6 5.9 5.8 5.7 4.7 9 2 6.9 5.8 5.5 4.9 4.8 4.8 4.8 4.7 10 1 5.6 4.6 4.3 3.9 3.8 3.8 3.7 3.5 11 38 34.8 34.8 34.8 34.8 34.8 34.8 34.8 34.7 R² 0.902 0.911 0.914 0.930 0.931 0.933 0.924 0.901 A comparison of predicted and observed performance is presented in Figure 0-22, which shows that no prediction was off by more than one level. Eight out of the ten predictions matched the observed performance and the other two were one level off the observed performance. Thus, the predicted performance in terms of crack initiation time was good for all ten test sections. This finding indicates that the top-down cracking performance model appears to adequately represent and account for the most significant factors that influence top-down cracking in the field.

127 Observed Cracking Performance I II III IV V Pr ed ic te d C ra ck in g Pe rf or m an ce I 2 II 2 1 III 1 2 IV 1 V 1 Figure 0-22. Predicted versus observed cracking performance levels (without Section 5) 4.3.3 Validation of Model The previous section showed strong correlation between top-down cracking predictions and observed crack initiation time in the field. The final step in the model-development process was validating the model, i.e., assessing its ability to accurately predict top-down cracking for sections other than those used in developing the model. Three methods are commonly used in validating a regression model: (1) collection of new data, (2) data splitting, and (3) prediction sum of squares (PRESS). The first method requires the use of a different data set. The second requires a large data set that can be divided for calibration and validation. The third method is suitable for small data sets; it has been successfully used in other studies such as validation of the thermal cracking model (29). Because a different data set

128 could not be obtained in the project and the available data set was small such that it could not be split, the PRESS method was selected for use in this study. 4.3.3.1 PRESS procedure In the PRESS procedure, the unknown parameters in the model are estimated when one data point is removed at a time from the data set (i.e., for a data set with n data points, the model is calibrated with (n-1) data points at a time). The model is then used to predict the value of the removed point, and the process is repeated for all the data points in the data set. The predicted values obtained are then compared with the actual values. The R2 (PRESS) is calculated for the predicted and actual values as follows:                 iwoi ii p YY YY R ˆ 12 (0-1) Where Y(i) is the observed response for the ith data point, )(ˆiY is the predicted response for the ith data point, and )(iwoY is the average of the predicted responses of (n-1) data points without the ith data point. Because the PRESS procedure uses (n-1) data points to estimate the unknown parameters, the R2 (PRESS) will always be lower than the R2 obtained from the full model which uses n data points. The degree of closeness of R2 (PRESS) to R2 (Full model) serves as a measure of the model’s predictive ability (i.e., good models will have an R2 from the PRESS procedure close to the R2 from the full model). 4.3.3.2 Validation process using PRESS For validation purposes, the performance model used to predict crack initiation for any one particular test section was calibrated using data of the other test sections. For example, the model used to predict crack initiation in Test Section 1 was calibrated using the data set without including Section 1.

129 The validation process involved two steps. First, similar to the final calibration of the performance model presented in the Model Calibration section, Test Section 5 was excluded; only the other ten test sections were included. The calibration procedure (described in the section) was conducted ten times (once for each data set, including nine test sections). The ten models obtained were then used to make independent predictions, and the R2 (PRESS) was computed using Equation 4-1. In Step Two, the crack initiation time of Test Section 5 was predicted using the model calibrated with all ten test sections and the error associated with this prediction was added to the R2 (PRESS). As an example, the top-down cracking performance model used to predict crack initiation for Test Section 1 was calibrated with data from the other nine test sections (i.e., Test Sections 2 through 11 except for Section 5). Linear regressions were performed to determine eight different values of R2 (one for each aging parameter) using the data from these sections. The performance model used to predict crack initiation for Test Section 1 was selected as the one having the k1 value that resulted in the highest R2. This process was repeated ten times such that a total of 80 linear regressions were performed during this step. A similar process was used in the second step, where linear regressions were performed to determine eight different values of R2 using the data from all ten test sections used in the first step. The top-down cracking performance model used to predict crack initiation for Test Section 5 was selected as the one that resulted in the highest R2. This process was applied once in the second step. The R2 for each linear regression is presented in Table 0-12. A shaded area identifies the largest R2 for each pavement section and the predicted cracking performance level. The resulting 11 models were used to make an independent prediction of the top-down cracking initiation time for each test section. The independent predictions were compared with

130 the observed initiation time to evaluate the predictive capability of the model. Results of this evaluation are presented in the following sub-section. Table 0-12. Predicted cracking performance for various aging parameters using PRESS procedure Section No. Observed Performance Level Predicted Performance Aging Parameter k1 0.5 (R2) 1.0 (R2) 1.5 (R2) 2.0 (R2) 2.5 (R2) 3.0 (R2) 3.5 (R2) 5.0 (R2) 1 II (0.923) (0.932) (0.927) III (0.937) (0.934) (0.933) (0.924) (0.900) 2 III (0.906) (0.915) (0.917) (0.934) III (0.934) (0.934) (0.924) (0.902) 3 III (0.906) (0.920) (0.929) (0.949) (0.956) II (0.962) (0.959) (0.948) 4 III (0.904) (0.913) (0.916) (0.930) (0.930) III (0.933) (0.924) (0.905) 5 III (0.902) (0.911) (0.914) (0.930) (0.931) I (0.933) (0.924) (0.901) 6 IV (0.907) (0.917) (0.920) IV (0.931) (0.928) (0.927) (0.917) (0.893) 7 II (0.900) (0.911) (0.916) (0.934) (0.935) II (0.937) (0.931) (0.910) 8 II (0.900) (0.910) (0.913) (0.931) (0.934) II (0.936) (0.927) (0.909) 9 I (0.914) (0.914) (0.915) (0.930) (0.930) I (0.932) (0.921) (0.895) 10 I (0.909) (0.911) (0.911) (0.928) (0.928) I (0.930) (0.919) (0.891) 11 V (0.736) (0.763) (0.771) (0.821) (0.824) V (0.829) (0.802) (0.734) * Shaded cells identify the largest R2 value for each section and the predicted performance level. 4.3.3.3 Validation results The R2 value obtained from the PRESS procedure was 0.82; and an R2 value of 0.93 was obtained for the full model (i.e., the model determined from the final calibration). These values suggest that the performance model has strong predictive ability. Figure 0-23 shows the

131 independent predictions (using PRESS) for crack initiation time compared with predictions from the full model, which demonstrates the predictive ability of the model. 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 C ra ck In iti at io n Ti m e P re di ct ed U si ng P R E S S ( ye ar ) Crack Initiation Time Predicted Using Full Model (year) Figure 0-23. Predicted crack initiation time using PRESS versus that using full model The data were also evaluated by comparing the independent performance predictions with the observed performance levels. The results presented in Figure 0-24 show that only one prediction was off by two levels. Of the other ten predictions, eight matched the observed performance, and two were off by one level. Thus, the predicted cracking performance was good for ten of eleven test sections. Based on these results and the R2 (PRESS) value of 0.82, the predictive capability of the model appears to be good. The final predictions using the calibrated/validated model are presented in the next section.

132 Observed Cracking Performance Level I II III IV V Pr ed ic te d C ra ck in g Pe rf or m an ce L ev el I 2 1 II 2 1 III 1 2 IV 1 V 1 Figure 0-24. Predicted versus observed cracking performance levels (from PRESS) 4.3.4 Final Model Predictions Final model predictions were conducted using the calibrated model; the results are presented in Table 0-13. The following sections discuss (1) predicted versus observed cracking performance in terms of both crack initiation time and cracking performance level, (2) predicted crack propagation time versus predicted crack initiation time, and (3) predicted cracking performance of all sections in terms of crack amount development with time.

133 Table 0-13. Predicted crack depths versus time for an aging parameter (k1) of 3.0 Section I75-1A I75-1B I75-3 I75-2 SR80-1 SR80-2 Thickness (inch) 6.54 6.23 6.47 7.42 3.38 6.29 Year Opened 1988 1989 1988 1989 1987 1984 Observed Crack Initiation Time (year) 10 12 11 17 13 22 Predictions C.D.* C/D + Y.C.@ C/D Y.C. C/D Y.C. C/D Y.C. C/D Y.C. C/D Y.C. 0.25 0.04 10.9 0.04 12.9 0.04 5.5 0.03 16.0 0.07 1.2 0.04 22.8 0.50 0.08 12.7 0.08 14.6 0.08 6.3 0.07 18.4 0.15 1.7 0.08 25.6 0.75 0.11 13.2 0.12 15.1 0.12 6.8 0.10 18.9 0.22 1.9 0.12 26.5 1.00 0.15 13.5 0.16 15.4 0.15 6.9 0.13 19.3 0.30 2.0 0.16 26.9 1.25 0.19 13.7 0.20 15.7 0.19 6.9 0.17 19.6 0.37 2.1 0.20 27.4 1.50 0.23 13.9 0.24 15.9 0.23 7.0 0.20 19.8 0.44 2.1 0.24 27.7 1.75 0.27 14.1 0.28 16.0 0.27 7.0 0.24 20.0 0.52 2.4 0.28 27.9 2.00 0.31 14.2 0.32 16.2 0.31 7.1 0.27 20.1 0.32 28.3 2.25 0.34 14.3 0.36 16.3 0.35 7.1 0.30 20.3 0.36 28.5 2.50 0.38 14.5 0.40 16.4 0.39 7.2 0.34 20.4 0.40 28.6 2.75 0.42 14.7 0.44 16.7 0.43 7.2 0.37 20.6 0.44 28.8 3.00 0.46 14.8 0.48 17.0 0.46 7.3 0.40 20.7 0.48 29.2 3.25 0.50 15.1 0.52 17.2 0.50 7.5 0.44 20.8 0.52 29.4 3.50 0.47 20.9 3.75 0.51 21.1 * C.D. designates Crack Depth (inch); + C/D designates Crack depth over AC thickness ratio; @ Y.C. designates time to each crack depth (year) from opening to traffic.

134 Table 0-13. Continued Section I10-8 I10-9 SR471 SR19 SR997 I94-4 I94-14 Thickness (inch) 7.20 7.40 2.58 2.39 2.17 9.10 10.90 Year Opened 1996 1996 2000 2000 1963 1994 1994 Observed Crack Initiation Time (year) 8 8 2 1 38 4 6 Predictions C.D.* C/D + Y.C.@ C/D Y.C. C/D Y.C. C/D Y.C. C/D Y.C. C/D Y.C. C/D Y.C. 0.25 0.03 5.6 0.03 5.8 0.10 4.8 0.10 3.8 0.12 34.8 0.03 4.2 0.02 6.0 0.50 0.07 6.6 0.07 6.9 0.19 5.2 0.21 4.7 0.23 39.6 0.05 5.9 0.05 7.2 0.75 0.10 6.8 0.10 7.3 0.29 5.7 0.31 4.9 0.35 41.4 0.08 6.0 0.07 7.4 1.00 0.14 7.0 0.14 7.5 0.39 6.0 0.42 5.0 0.46 42.8 0.11 6.2 0.09 7.9 1.25 0.17 7.1 0.17 7.6 0.48 6.3 0.52 5.1 0.58 43.2 0.14 6.3 0.11 8.0 1.50 0.21 7.3 0.20 7.7 0.58 7.0 0.16 6.9 0.14 8.3 1.75 0.24 7.4 0.24 7.8 0.19 7.1 0.16 8.8 2.00 0.28 7.5 0.27 7.9 0.22 7.2 0.18 9.0 2.25 0.31 7.5 0.30 8.0 0.25 7.7 0.21 9.2 2.50 0.35 7.6 0.34 8.1 0.23 9.3 2.75 0.38 7.7 0.37 8.2 0.25 9.9 3.00 0.42 7.7 0.41 8.3 3.25 0.45 7.7 0.44 8.4 3.50 0.49 7.8 0.47 8.5 3.75 0.52 7.9 0.51 8.5 * C.D. designates Crack Depth (inch); + C/D designates Crack depth over AC thickness ratio; @ Y.C. designates time to each crack depth (year) from opening to traffic.

135 4.3.4.1 Predicted versus observed cracking performance The predicted cracking performance for all test sections is compared with the observed performance in terms of both crack initiation time and cracking performance level in Figure 0-25. As shown, the predictions generally agree well with the observed performance levels (except for Section SR80-1 which is off by two levels). 0 5 10 15 20 25 30 35 40 45 SR19 SR471 I94-4* I94-14* I10-8 I10-9 I75-1A I75-3 I75-1B SR80-1 I75-2 SR80-2 SR997 Ti m e to In iti at io n (Y ea r) Sections Observed Predicted Worst Best Performance Level I (1 - 5 Yr) Level II (6 - 10 Yr) Level III (11 - 20 Yr) Level IV (21 - 30 Yr) Level V (> 30 Yr) Figure 0-25. Predicted versus observed crack initiation time for all test sections 4.3.4.2 Predicted crack propagation time versus initiation time The initial depth of top-down cracking was determined to be 6 mm (0.25 in.), and the critical crack depth was defined as the depth equal to one-half of the AC layer thickness (see Appendix B). Therefore, for a vertical crack, the crack propagation time, tp, can be obtained by computing the difference between the time to initial crack depth (i.e., crack initiation time) and that to critical crack depth.

136 The crack propagation time determined for each test section using the calibrated model was plotted against the corresponding crack initiation time (Figure 0-26). As shown, the crack propagation time appears to increase linearly with the initiation time such that for pavement sections that start to crack after 10 to 20 years in service, the propagation time to failure is about 4 to 5 years (this is consistent with typical observations in the field). For test sections with an earlier crack initiation, the propagation time tends to be shorter; and for pavements that last for more than 20 years, the time to critical crack depth is longer. 0.0 2.5 5.0 7.5 10.0 0 5 10 15 20 25 30 35 40 Predicted Initiation Time (year) P re di ct ed P ro pa ga tio n Ti m e (y ea r) Group I Group II Linear (Group I) Figure 0-26. Predicted crack propagation time versus crack initiation time Because reliable field data on crack development cannot be obtained, no further calibration was performed on predicted crack propagation time. However, the comparison shown in Figure 0-26 provides a means for assessing the reasonableness of the model for predicting propagation time.

137 4.3.4.3 Crack amount development with time The final model predictions are expressed in terms of crack amount versus time for each test section and presented according to the performance level (I to V) with respect to observed performance in Figures 0-27 to 0-30. These predictions may be summarized as follows: • The amount of cracking of a thin pavement at initiation is greater than that of a thicker pavement. This indicates that crack initiation may be more easily identified in thinner pavements than in thicker ones in the field. • For test sections of Group I (governed by the bending mechanism), predictions for sections of lower performance levels are generally consistent with field observations (Figures 0-27 and 0-28). The relatively high creep rate combined with high surface tensile stresses are believed to contribute to the severe cracking conditions in these sections within a relatively short period. Predictions for sections of higher performance levels agree reasonably with observations in the field, except for Section 5 (i.e., SR80-1) (Figures 0-29 and 0-30). The relatively low creep rate and high fracture energy of the asphalt mixtures combined with the relatively low traffic in these sections resulted in longer service life. • For test sections of Group II (governed by the near-tire mechanism), predictions of crack initiation for both sections of this group agree well with field observations (Figures 0-27 and 0-28). The trend between predicted propagation and predicted initiation time appeared to be different than observed for the bending mechanism. However, this observation should be considered preliminary because there were only two sections in Group II, which did not allow for calibration and/or validation of the near-tire mechanism. 4.4 Summary of Findings An HMA-FM-based model for predicting top-down cracking propagation in HMA layers was developed in this project. Several key elements were identified, developed, and then incorporated into the existing HMA-FM model, including material property sub-models that account for changes in mixture properties (e.g., fracture energy, creep rate, and healing) with aging, and a thermal-response model that predicts transverse thermal stresses. In addition, a simplified fracture energy-based crack initiation model (without considering damage zone effects) was developed and integrated with the HMA-FM-based model to illustrate the capabilities of a completed system.

138 Parametric studies have shown that the system can reasonably capture the effects of climate, traffic, and material and structural properties on top-down cracking performance. It was also shown that structural characteristics may define the form of possible top-down cracking mechanisms (bending mechanism − suitable for HMA layers with thin to medium thickness, and near-tire mechanism − dominant for thick HMA layers). A limited calibration using data from field sections was performed by matching as closely as possible top-down cracking predictions with observed top-down cracking. Only one calibration factor (i.e., the aging parameter, k1) was included in the calibration process. The results showed that the system appears to reasonably represent and account for the most significant factors that influence top-down cracking. The validation efforts using the PRESS procedure confirmed the viability of the predictive model. The finalized system was used to predict the increase of crack depth (and crack amount) with time for all 13 field sections included in this project. In general, it was found that the predicted crack propagation time for test sections (Group I) was linearly proportional to the crack initiation time. This relationship indicated that the system can reasonably predict crack propagation time. Predictions for the two full-depth test sections (Group II), governed by the near-tire mechanism, were reasonable. However, some important factors (e.g., wander and effect of stress state on damage rate) were not considered.

139 SR19 0 50 100 150 200 250 300 350 400 0 2.5 5 7.5 10 Time (year) A C (f t/1 00 ft ) SR471 0 50 100 150 200 250 300 350 400 0 2.5 5 7.5 10 Time (year) A C (f t/1 00 ft ) InitiationInitiation I94-4* 0 25 50 75 100 125 150 175 200 0 2.5 5 7.5 10 Time (year) A C (f t/1 00 ft) Initiation Figure 0-27. Predicted crack amount versus time for test sections of level I (∗ The maximum amount of cracking was reduced to 165 ft /100 ft for full depth pavement (near-tire mechanism).)

140 I10-8 0 50 100 150 200 250 300 350 400 0 2.5 5 7.5 10 12.5 15 17.5 20 Time (year) A C (f t/1 00 ft ) I10-9 0 50 100 150 200 250 300 350 400 0 2.5 5 7.5 10 12.5 15 17.5 20 Time (year) A C (f t/1 00 ft ) I75-1A 0 50 100 150 200 250 300 350 400 0 2.5 5 7.5 10 12.5 15 17.5 20 Time (year) A C (f t/1 00 ft ) Initiation Initiation Initiation I94-14* 0 25 50 75 100 125 150 175 200 0 2.5 5 7.5 10 12.5 15 17.5 20 Time (year) A C (f t/1 00 ft ) Initiation Figure 0-28. Predicted crack amount versus time for test sections of level II (∗ The maximum amount of cracking was reduced to 165 ft /100 ft for full depth pavement (near-tire mechanism).)

141 I75-1B 0 50 100 150 200 250 300 350 400 0 5 10 15 20 25 Time (year) A C (f t/1 00 ft ) I75-3 0 50 100 150 200 250 300 350 400 0 5 10 15 20 25 Time (year) A C (f t/1 00 ft ) I75-2 0 50 100 150 200 250 300 350 400 0 5 10 15 20 25 Time (year) A C (f t/1 00 ft ) SR80-1 0 50 100 150 200 250 300 350 400 0 5 10 15 20 25 Time (year) A C (f t/1 00 ft ) Initiation Initiation InitiationInitiation Figure 0-29. Predicted crack amount versus time for test sections of level III

142 SR80-2 0 50 100 150 200 250 300 350 400 0 5 10 15 20 25 30 35 40 45 Time (year) A C (f t/1 00 ft ) SR997 0 50 100 150 200 250 300 350 400 0 5 10 15 20 25 30 35 40 45 Time (year) A C (f t/1 00 ft ) Initiation Initiation Figure 0-30. Predicted crack amount versus time for test sections of levels IV and V