The stabilization of slip on a narrow weakening fault zone by coupled deformation-pore fluid diffusion

The transient stabilization of rapid slip on a very narrow weakening fault zone by the coupling of the deformation with pore fluid diffusion is investigated. More specifically, the fault zone is assumed to be so narrow that it can be idealized as a planar surface and the constitutive law is specified as a relation between stress on the fault τ_(f/t) and relative slip δ. The study considers only the stabilizing effect due to the time dependent response of the fluid-infiltrated elastic material surrounding the fault: the response is elastically stiffer for load alterations which are too rapid to allow for fluid mass diffusion between neighboring material elements (undrained conditions) than for those which occur so slowly that the local pore fluid pressure is constant (drained conditions). Calculations are performed to determine the length of the precursory period (the period of self-driven accelerating slip prior to dynamic instability) by assuming that the near-peak τ_(f/t) versus δ relation is parabolic and that the far-field tectonic stress rate is constant. An important result of the calculations is that the duration of the precursory period is predicted to decrease with increasing fault length for a plausible range of material parameters. Although this appears to disagree with results based on simple dimensional considerations, the result is due to the dependence of the constitutive law on a characteristic sliding distance necessary to reduce τ_(f/t) from peak to residual value. Calculated precursor times are very short, typically less than a few days for fault lengths of 1 to 5 km, a tectonic stress rate of 0.1 bar/year, and field diffusivities of 0.1 to 1.0 m^2/sec. The results are, however, sensitive to details of the τ_(f/t) versus δ relation which are, at present, poorly known