Modified Paris's Law to Predict Entire Crack Growth in Asphalt Mixtures

Paris's law is a well-known and widely used method for predicting crack growth in engineering materials. Currently, most Paris's law model forms are formulated on the basis of the growth of a single crack, which is not in accord with the actual damage in asphalt mixtures, which entails the propagation of a multitude of cracks. The parameters in these Paris's law model forms are determined either by extensive testing and curve fitting or by collecting data from a series of different tests. To predict the entire crack growth in an asphalt mixture, this paper proposes a modified Paris's law, which is defined by using the damage density. In addition, the procedure for determining the modified Paris's law parameters (A’ and n’) is simplified so that they are easily obtained from one test on one asphalt mixture specimen. The proposed modified Paris's law was applied to 20 types of asphalt mixtures. The results showed that A’ and n’ were highly correlated with each other for the materials tested. On the basis of this relationship, the damage density formulated in the modified Paris's law is proved to be related monotonically to n’ through a sensitivity analysis. This relationship suggests that n’ can be used directly to compare the damage density of different asphalt mixtures. Investigation of the effects of asphalt binder, air void content, and aging period on fatigue cracking in asphalt mixtures further confirms that n’ is a good indicator of the tendency of the material to crack and can be used solely in material comparison and selection for fatigue cracking; a smaller value of n’ is preferred.