Time-dependent failure of rock under cyclic loading

A simple model which describes the failure of brittle rock under cyclic compressive loading is presented. It is assumed that the damage incurred by the material during each stress cycle is due to the extension of tensile microcracks and that the specimen will fail when the microcrack damage reaches a critical level. Two mechanisms for crack extension, stress corrosion and cyclic fatigue are assumed to act simultaneously and independently. The rate of crack growth due to stress corrosion was determined from an empirical relationship for the static fatigue of glass. The equation describing the rate of crack growth due to cyclic fatigue was taken to be similar to those derived for structural metals. By combining the crack extension rates due to these two processes, the time to failure for a specimen subjected to a given cyclic loading program was computed. The time to failure was found to depend strongly on the mean differential stress and the magnitude of the stress change during each cycle. At high mean stress and low cycle amplitude, stress corrosion dominates, whereas at low mean stress and high cycle amplitude, cyclic fatigue dominates. The predictions of the model are in good agreement with existing experimental data. Further, the model explains the observed breakdown of discrete memory in dilatant rock under certain stress conditions.