Nonuniformity of crack-growth resistance and breakdown zone near the propagating tip of a shear crack in brittle rock: A model for earthquake nucleation to dynamic rupture

This paper reviews our recent studies on (i) slip failure nucleation, which leads to the mechanical instability that gives rise to a dynamically propagating shear rupture, (ii) constitutive behavior during the local breakdown process near the propagating tip of the slipping zone, and (iii) the physical modeling of the earthquake-source process based on the constitutive relation inferred from laboratory experiments. Laboratory studies were done using a simulated fault in rock in the brittle regime under a mode II crack-growth condition, to gain a deeper understanding of the earthquake-source process, which is considered to be dynamically propagating shear rupture in the earth. A stable but accelerating phase of nucleation locally precedes an unstable dynamically propagating rupture even in the brittle regime. The appearance of a sizable zone of such nucleation is related to a nonuniform distribution of the crack-growth resistance on the fault. The local shear strength degrades to a residual friction stress level with ongoing slip near the propagating tip of the slipping zone. This slip-dependent constitutive relation shows that there is a breakdown zone near the propagating tip over which shear stress, slip displacement, slip velocity, and slip acceleration are highly nonuniform. This nonuniformity is responsible for generating high-frequency elastic radiation. A model of the breakdown zone, which incorporates the laboratory-based constitutive relation, does not give rise to unrealistic singularities of slip acceleration and stresses at and near the dynamically propagating tip of the slipping zone. The breakdown zone model enables one to give a common interpretation to both small-scale slip failure in the laboratory and large-scale shear failure as earthquake faulting in the earth, and it can explain the earthquake-source strong motion characterized by the high-frequency content.