Improved Method of Characterizing Fracture Resistance of Asphalt Mixtures Using Modified Paris’ Law: Development of Methodology

It is crucial to accurately determine the coefficients of the modified Paris’ law to accurately characterize the fracture properties of an asphalt mixture. However, the current methods reported in the literature are associated with two major deficiencies: (1) application of incompatible energy balance equations, and (2) abandonment of the relationship between the dissipated pseudostrain energy (DPSE) and the damage density. This study, which addressed these deficiencies, developed an improved method to determine fracture parameters of asphalt mixtures, including the coefficients of the modified Paris’ law and the damage density. Two controlled-strain repeated direct tension (RDT) tests were performed in sequence on four types of asphalt mixtures to determine the properties of the asphalt mixture specimens in the linear viscoelastic stage and the destructive stage, respectively. The pseudostrain and the apparent DPSE were calculated for each specimen in every load cycle in the second RDT test. A fitting model was established for the apparent DPSE versus the number of load cycles for each specimen. This fitting model was incorporated into the modified Paris’ law to derive the formulation of the coefficients of the modified Paris’ law and the damage density. According to the DPSE balance equation, the model for the apparent stress amplitude was established based on the formulation of the apparent DPSE and the damage density. Mathematical techniques were applied to seek the most appropriate solutions for the model parameters, which proved to be perfectly reasonable and accurate enough to predict the values of the apparent stress amplitude, especially after 20 load cycles. With the determined model parameters, the coefficients of the modified Paris’ law were determined for every specimen, and the models of the damage density were finalized for all specimens.