Dilatancy toughening of shear cracks and implications for slow rupture propagation

Abstract: Dilatancy associated with fault slip produces a transient pore pressure drop which increases frictional strength. This effect is analysed in a steadily propagating rupture model that includes frictional weakening, slip-dependent fault dilation and fluid flow. Dilatancy is shown to increase the stress intensity factor required to propagate the rupture tip. With increasing rupture speed, an undrained (strengthened) region develops near the tip and extends beyond the frictionally weakened zone. Away from the undrained region, pore fluid diffusion gradually recharges the fault and strength returns to the drained, weakened value. For sufficiently large rupture dimensions, the dilation-induced strength increase near the tip is equivalent to an increase in toughness that is proportional to the square root of the rupture speed. In general, dilation has the effect of increasing the stress required for rupture growth by decreasing the stress drop along the crack. Thermal pressurisation has the potential to compensate for the dilatant strengthening effect, at the expense of an increased heating rate, which might lead to premature frictional melting. Using reasonable laboratory parameters, the dilatancy-toughening effect leads to rupture dynamics that is quantitatively consistent with the dynamics of observed slow slip events in subduction zones.