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55 calibration coefficients can be entered into this design program thermal stresses are the principal mechanism from Position I up and can be used in the design of HMA overlays to represent to the surface of the overlay. Equation 43 is an example of the each unique combination of climatic zone and pavement form of the equation if bending stresses are assumed to be structure-overlay type. The remaining sets of calibration co- the principal cracking mechanism up to Position I and shear- efficients may be developed when a sufficient collection of field ing stresses are assumed to be the principal cracking mecha- distress, pavement structure and materials, and traffic and nism from Position I up to the surface of the overlay. All of weather data are assembled to repeat the process described in these forms of equation are tried and calibration co- Chapter 2. In order to assist in such calibration efforts, a Cali- efficients are found for each form of equation using linear bration Program has been assembled and the User's Guide is regression analysis. The form of equation that produces the provided in Appendix P. highest R2 value and its corresponding set of calibration co- It should be noted that if unrealistic input values are used, efficients are selected as the best set for that type of overlay. an unrealistic result can be expected from the predicted curves Experience has shown that bending stresses are the principal of reflection cracking extent and severity levels. Numerical tri- cracking mechanism up to Position I and thermal stresses are als in this project with the stress intensity factor and complex the principal cracking mechanism from Position I up to the modulus ANN models have shown that they provide accurate surface of the overlay, except for overlays with reinforcing extrapolations well beyond the values used to train them. These interlayers. From this overlay, bending is the principal mecha- ANN algorithms are an integral part of both the calibration nism up to Position I and shearing is the principal mechanism and design processes. However, they cannot be expected to from there up to the surface of the overlay. The reinforcing produce realistic results if the input values are too far outside interlayer reduced the influence of thermal stress on the rate the range of their training values. of crack growth in this type of overlay. As a general rule, at least 10 overlay sections which are distinctively different from one another in their traffic, layer Calibration of the Computational thicknesses, and overlay mix designs are needed to form a Model to Field Data set of calibration coefficients. Validation of the developed sets The process of developing calibration coefficients is de- of model coefficients involves the prediction of the distress scribed in Chapter 2 and details of the process are contained in of overlays that were not used in developing the original set of Appendices I through N. The Calibration Program, presented calibration coefficients. Such validation is desirable if sufficient in Appendix P, generates five computed pavement reflection additional overlay sections are available for this purpose. cracking lives that are required of each overlay in the original The shape of the extent-severity-life curves was chosen to field data set. limit the percentage of cracking to be no more than 100 per- At this point, the calibration process is completed by using cent. The rate of rise of these curves is also constrained by the linear regression analysis to produce the calibration coefficients magnitude of the shape factor . Generally, the scale factor for the overlay. The form of the model for the time scale value will be larger for the higher level of severity, although occasion- is seen in Equations 40 through 43 and the same form of ally the H and the M+H curves will cross because of inverted equation is used to model the shape factor . Equations 40 values of , as observed in Figures 49, 50, and 55. The logical through 42 are the form used if the principal cracking mecha- structure in the design program does not prevent two severity nisms are assumed to be bending stresses up to Position I and curves from intersecting and this will occur on occasion.