Shear heating of a fluid-saturated slip-weakening dilatant fault zone 1. Limiting regimes

The one-dimensional model of Rudnicki and Chen [1988] for a slip-weakening dilating fault is extended to include shear heating. Because inertia is not included, instability (a seismic event) corresponds to an unbounded slip rate. Shear heating tends to increase pore pressure and decrease the effective compressive stress and the resistance to slip and consequently tends to promote instability. However, the decrease of effective compressive stress also reduces the magnitude of shear heating. Consequently, in the absence of frictional weakening and dilation, there exists a steady solution for slip at the tectonic rate in which the pressure does not change and the shear heating is exactly balanced by heat flux from the fault zone. In the absence of shear heating, dilatancy tends to decrease pore pressure and inhibit instability; more rapid slip weakening promotes instability. Analysis of undrained, adiabatic slip (characteristic of rapid slip or hydraulically and thermally isolated faults) reveals that the interaction of these effects can cause increased slip weakening to be stabilizing and increased dilatancy to be destabilizing. These counterintuitive effects are due to the dependence of the shear heating on the total shear stress (not just its change). They occur for small thermal expansivity and for material parameters within a plausible range for 0 - 10 km depth.