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49 cracks in the existing pavement and to develop mechanistic data within the overlay. Such a temperature model was incorpo- with which to "train" the ANN algorithms for crack growth. rated into the Design Program (characteristics of this model This was done by calculating a large set of stress intensity factor are described in detail in Appendix B). The temperatures calcu- data for a variety of overlay and pavement structures using lated by this program and those measured in the field rarely dif- a two-dimensional finite element approach with the transverse fered by more than 2 C. A complete set of weather data were third dimension being represented by a series solution. When assembled from databases available to the public for about 150 the calculated results were compared to the correct answers different locations within the United States and Canada for use generated by a full three-dimensional set of computational in the Design Program. results, the errors were acceptably small (discussion is provided in Appendix Q). The ANN models were found to fit all 18 sets Consistent Description of Reflection of computed databases very well (as described in Appendix F). Cracking Distress Neither the two- nor the three-dimensional finite element analysis was used within the Design Program because of the The S-shaped curve for the accumulating extent of reflec- long computational time that each requires. tion cracking adopted in this project matches the pattern that is observed in the progressive development of many kinds of distress. There are three curves that represent the extent and HMA Overlay Material Properties severity of the reflection cracks as they are observed in the The ANN algorithms were also used for generating the field. The curves show the one growth of the high severity material properties of a HMA overlay material as it responds reflection cracks; the sum of the percentages of the high and to traffic and thermal stresses. It was also necessary to use a well medium severity cracks; and the sum of percentages of the constituted and widely available database of HMA material high, medium, and low severity cracks. Each curve is plotted properties to represent these properties. The database assem- against the percent of the original length of transverse cracks bled and modeled by Witczak in 1999 and 2006 (2, 3) satisfied in the old pavement surface. The difference between the these criteria. Representing both models by an ANN algorithm curves represents the percentages of the individual levels of provided two models that were computationally fast yet have a distress severity. This S-shaped curve is defined by two better coefficient of determination (R2) than Witczak's regres- parameters: , the scale parameter, and , the shape param- sion models. By inputting binder properties, some aggregate eter. The scale parameter is the number of days required for gradation, volumetric composition of the mix, and frequency the percentage of reflected cracks to reach 36.8 percent (i.e., of loading and temperature into these ANN algorithms, HMA 1/e), of the original length of the transverse cracks or joints mixture properties over a wide range of loading times and tem- in the old pavement surface. The shape parameter deter- peratures can be generated quickly. The binder properties mines how steep the growth of the curve is as it reaches the used as reference properties within the program were binder 36.8 percent mark. properties extracted from field cores and reported earlier (4). This method allows a simple, consistent, and comprehensive Although the user may input other binder properties at the description of the distress history of an overlay. It also makes detailed Level 1 input, binder data from actual constructed the task of calibrating the calculated reflection cracking lives, pavements may be used for Level 2 or 3. The PG of the binder due to traffic and thermal stresses to the field observations, and the internal reference data may be used for Level 2 to possible. generate the remainder of the required data. The fracture properties of an asphalt mixture depend on Calibration of Calculated Overlay Life to simpler and more fundamental properties of that mixture as the Observed Distress shown by Schapery (36, 37) and confirmed in other studies (4), which calibrated to field fatigue cracking data. The calibration The two-step method used to develop calibration coeffi- coefficients that were developed in these studies were used in cients first involved linear regression analysis and observation this project without any alteration, even though the type of of the patterns of the predicted versus the observed values of distress was different. both and . If the coefficient of determination (R2) was acceptable and the scatter of the data was clustered around the line of equality, the calibration coefficients were considered Weather Data and Temperature Prediction acceptable. Otherwise, a second step was undertaken if there Accurate temperature prediction is key to making accurate was a non-random pattern of scatter around the line of equal- predictions of thermal crack growth, especially in an overlay. ity or R2 was unacceptable. Comparisons, between the temperature predictions and actual This approach had to be taken because only about 150 of temperatures measured in the field, demonstrated the need the sections were unique, the rest were similar in pavement for a higher degree of accuracy in calculating the temperature features (structure, materials), traffic, and weather, such that