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7 These compatibility requirements automatically eliminate Process of Constructing a Calibrated a number of approaches such as the empirical model, extended Reflection Cracking Model multi-layer linear elastic program, equilibrium equations, and advanced models requiring use of supercomputers. The process of constructing a calibrated reflection crack- While this use may be desirable in the future when super- ing model (Figure 6) involves several steps: computer use becomes more widespread and the MEPDG · Select a sufficient number of overlay sections to provide a has been converted to such use, it is more desirable at the present to develop a model that uses the level of computa- good likelihood of having a sufficient amount of good qual- ity data (including sequential distress measurements; pave- tional power that is commonly available for state design ment structure and materials property data; and traffic and offices. After considering the different model features and weather data) to permit development of a set of calibrated compatibility requirements, the finite element plus fracture reflection cracking model coefficients. As a rule of thumb, at mechanics model was selected. However, the running time least 20 such sections are required to develop a complete set of a finite element program proved not to provide a practi- of calibration coefficients. cal tool for design so it was decided to incorporate the results · Collect pavement structure data (including layer thickness, of multiple runs into a faster algorithm. Nearly 100,000 runs construction dates, and nondestructive testing data on of a finite element program were made in order to obtain a each pavement section) and the mixture design data for the broad range of computed fracture mechanics results. These overlay. numerical results were then incorporated into a total of 18 · Collect pavement distress data (including the total length separate ANN algorithms. These algorithms provide accept- of cracking in the old pavement surface prior to overlay able computational speeds and are the core of the overlay and the lengths and levels of severity of reflection crack- reflection cracking model developed in this project. ing) for at least three (preferably more) sets of sequential The key concept in fracture mechanics is Paris and Erdogan's observations. Law (11) for modeling crack propagation, particularly for · Collect traffic data on each pavement section including the fracture-micromechanics applications. Expressed in Equa- input data used in the MEPDG program (i.e., the traffic tion 1, Paris and Erdogan's Law has been successfully applied load spectrum rather than the total 18-kip equivalent sin- to HMA by many researchers, for the analysis of experimental gle axle loads). test data and prediction of reflection- and low temperature- · Collect climatic data on each of the candidate sections of cracking (4, 12). overlay, including the data needed to accurately calculate the overlay temperature with depth below the surface dc = A ( K ) n (1) (i.e., hourly air temperature, solar radiation, and surface dN reflectance). · Develop a finite element mechanistic method for calculating where the SIF in overlays for thermal, bending, and shearing traf- c= the crack length; fic stresses as a crack grows up through different thicknesses N= the number of loading cycles; of overlay. A and n = fracture properties of the asphalt mixture; and · Develop a numerically accurate and computationally effi- K = the SIF amplitude (depends on the stress level, cient method of predicting the SIF computed by the finite the geometry of the pavement structure, the element method. fracture mode, and crack length). · Develop a method of dealing with different traffic loads and tire footprints in calculating the SIF. There are three fracture modes: tensile, shearing, and tearing. · Analyze the field distress data into a standard form to rep- The number of loading cycles, Nf , needed to propagate a resent the total length of reflected cracks that appear with crack (initial length, c0) through the pavement layer thick- time at the different levels of severity (i.e., low, medium and ness, h, can be estimated by numerical integration in the form high). At this point, the number of test sections with actual of Equation 2. observed reflection cracking data can be determined (in h some cases, not all levels of severity have been observed). dc Nf = A ( K ) n (2) · Develop a method for accurately calculating the hourly and C0 dailytemperaturesinanoverlay at the current tip of the crack. · Write a program to calculate the stiffness, tensile strength, Because the SIF is one of the key parameters in Paris and compliance, and fracture coefficients of the overlay mix- Erdogan's Law, the speed and accuracy of computing SIF val- ture using the mixture properties of volumetric contents of ues is a very critical aspect of crack propagation analysis and the mixture components, aggregate gradation, and binder the development of a reflection cracking model. master curve characteristics. These properties must be