Stabilization of rapid frictional slip on a weakening fault by dilatant hardening

Frictional slip is often accompanied by dilatancy due to uplift in sliding over asperities and micro‐cracking in the adjacent material. If dilatancy occurs more rapidly than pore fluid can flow into the newly created void space, the local pore pressure is reduced and the effective normal stress is increased in compression, tending to inhibit further slip. This dilatant hardening is analyzed for a simple model. One surface of a slab is loaded by compressive stress and shear displacement and connected to a reservoir of pore fluid held at constant pressure. The other boundary is a frictional surface, assumed to have formed at peak stress, on which the shear stress decreases from a peak value τ p to a residual value τ r as slip increases from zero to δ 0 . In the absence of pore fluid effects an instability corresponding to an unbounded slip rate occurs when the slope of the shear stress versus slip relation is more negative than the unloading stiffness of the surrounding material. Dilatant hardening prevents this instability provided that the pore pressure in the reservoir is high enough. If the pressure in the reservoir is too low, the pressure at the fault surface can be reduced to the point at which the pore fluid bulk modulus decreases rapidly, eliminating the stabilizing effect. When the analysis is modified to include normal stress changes simulating those in the axisymmetric compression test, the prediction of the critical pressure in the reservoir agrees to within a factor of 2 or 3 with that observed by Martin in tests on Westerly granite. The predictions are also consistent with the trends observed by Martin of decreasing critical reservoir pore pressure with increasing effective confining stress and decreasing nominal strain rate.