Parameter interdependence of dynamic self-similar crack with distance-weakening friction

SUMMARY In several analytical and numerical studies, the slip rate function and energy release rate for dynamic self-similar crack growth have been investigated, and the results obtained have contributed to a theoretical understanding and estimation of on-fault energetics. However, the relationships among physical parameters, including stress state, process zone size, rupture velocity, peak slip rate and energy release rate, are still unclear. Therefore, the aim of this study is to derive an analytical solution of the slip rate distribution of antiplane self-similar crack growth under distance-weakening friction that mimics slip-weakening friction. To satisfy the condition that the slip rate starts from zero at the rupture front, a trade-off relationship among rupture velocity, process zone size and breakdown stress-to-stress drop ratio is proposed. The peak slip rate, slip-weakening distance and fracture energy obtained using the proposed model provide a possible mechanism for the determination of the rupture velocity and the estimation of the fracture energy of the self-similar crack growth, based on the seismic observables.