Abstract
This paper first reviews recent studies on constitutive formulations for shear failure. Noting that earthquake rupture is an general a mixed process between what is called frictional slip instability and fracture of initially intact rock in the fault zone, the paper then discusses how the constitutive law for earthquake rupture should be formulated to meet the physical principles and constraints to be imposed on the law. This leads to the conclusion that the constitutive law should be formulated as a slip-dependent law, which includes a scaling parameter Dc (critical slip displacement). Scale dependent physical quantities inherent in shear rupture, such as the breakdown zone size and the nucleation zone size, their duration, the slip acceleration, and the shear fracture energy, are consistently scaled by Dc, which in turn is prescribed by a characteristic scale representing the geometric irregularity of the fault zone. A physical model for earthquake generation is presented, which reconciles the observation that the mainshock seismic moment is scaled by the critical size of the nucleation zone. The constitutive law parameters depend on ambient conditions in the seismogenic layer, and therefore it is critical to evaluate the effects of the environmental factors on the constitutive law parameters in quantitative terms, in order that numerical simulation of a model earthquake could be useful for earthquake prediction in the real world.
