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17 aggregate interpenetration through the grid from above and underlying old asphalt surface for the thermal stress case. below to lock the grid into place. The grid will provide no rein- ANN Model 4 provides a compliant interlayer (SAMI) between forcing function if there is slippage between the grid and the the overlay and the old asphalt surface layer for the thermal overlay material. For this reason, in all finite element runs the stress case. Model 5 provides a no-slip condition between the reinforcing interlayer was placed within the overlay on top of a overlay and the underlying old asphalt surface for the thermal leveling course. stress case. Model 6 provides a no-slip condition between the overlay and an underlying jointed concrete pavement for the thermal stress case. ANN Models 7 through 12 provide the Method of Predicting SIF Bending SIF for a tire located directly above the crack or joint The method chosen to model the computed results from in the old pavement surface; dual and single tire models are the finite element runs was the ANN algorithm. The formu- provided. ANN Models 13 through 18 provide the Shearing lation of an accurate and computationally efficient algorithm and Bending SIF that occur when the leading or trailing edge using the ANN approach is described in the literature (22, 23, of the tire is above the crack or joint in the old pavement sur- 24). The final model is a multi-layered equation which can face layer; both dual and single tire models are provided. The achieve very good fits to the original data. A total of 18 differ- ANN Models 8, 10, and 12 are designated by the term "Only ent ANN models were constructed for use in this program Positive" (i.e., only tensile SIF are modeled). This condition (see Table 10). Details of the ANN models of SIF for the dif- occurs when the crack is still small and in the bottom part of ferent pavement structure and thermal and traffic cases is the overlay. Negative SIF can be calculated and occur in com- provided in Appendix F, including graphs of the computed pressive stress areas where cracks will not grow. Figure 11 shows SIF versus those predicted by the ANN algorithms. The coef- the different pavement structures and traffic or thermal stress ficient of determination (R2) of all of these models was above cases that apply to each ANN model. 0.99 except for one case of pure bending in an asphalt over- An example of the fit of an ANN model to the SIF data that lay over a jointed concrete pavement. For this model, the R2 was calculated by the finite element program is given in Fig- value was 0.83 because tensile stresses rarely occur in asphalt ure 12 for the case of thermal stress in a HMA overlay over an overlays due to pure bending and as a consequence there were old cracked asphalt pavement surface for which the R2 was very few data points. 0.9982. Appendix F provides similar graphs for all of ANN As noted in Table 10, ANN Models 1, 2, and 3 provide dif- models and describes the variations and ranges of overlay pave- ferent degrees of interlayer slip between the overlay and the ment structure and the material and interface properties used Table 10. Artificial neural network models for stress intensity factors. Model No Model Name Load Case 1 AC_over_AC_Interlayer_slip_L Thermal 2 AC_over_AC_Interlayer_slip_M Thermal 3 AC_over_AC_Interlayer_slip_H Thermal 4 AC_SC_AC Thermal 5 AC_over_AC Thermal 6 AC_over_PCC Thermal 7 Pure_Bending_AC_over_AC_Dual_Tire_Together Traffic 8 Pure_Bending_AC_over_AC_Dual_Tire_Together_Only_Positive Traffic 9 Pure_Bending_AC_over_AC_Single_Tire_Together Traffic 10 Pure_Bending_AC_over_AC_Single_Tire_Together_Only_Positive Traffic 11 Pure_Bending_AC_over_PCC_Single_Tire_Together Traffic 12 Pure_Bending_AC_over_PCC_Single_Tire_Together_Only_Positive Traffic 13 AC_Over_AC_Shearing_Bend_Part_Dual_Tire Traffic 14 AC_Over_AC_Shearing_Shear_Part_Dual_Tire Traffic 15 AC_Over_PCC_Shearing_Shear_Part_Dual_Tire Traffic 16 AC_Over_AC_Shearing_Bend_Part_Single_Tire Traffic 17 AC_Over_AC_Shearing_Shear_Part_Single_Tire Traffic 18 AC_Over_PCC_Shearing_Shear_Part_Single_Tire Traffic

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18 AC InterLayer LevelingCourse AC-H AC Inter Layer LevelingCourse AC AC InterLayer LevelingCourse AC-M AC InterLayer LevelingCourse AC-L Thermal Cases AC Over AC and AC Mill AC AC Over PCC AC Over SC Over AC Pure_Bending_ACoverAC_DualTire_Together Pure_Bending_ACoverAC_DualTire_Together (Only Positive) Pavement Model Pure_Bending_ACoverAC_SingleTire_Together Pure Bending Load Cases Pure_Bending_ACoverAC_SingleTire_Together (Only Positive) Pure_Bending_ACPCC_SingleTire_Together Traffic Load Pure_Bending_ACPCC_SingleTire_Together (Only Positive) Cases AC_AC_Shearing_BendPart_dualTire AC_AC_Shearing_ShearPart_dualTire AC_PCC_Shearing_ShearPart_dualTire Shearing AC_AC_Shearing_BendPart_singleTire Load Cases AC_AC_Shearing_ShearPart_singleTire AC_PCC_Shearing_ShearPart_singleTire Figure 11. ANN models applications to overlaid pavement structures.