Dilatancy Toughening of Shear Cracks and Implications for Slow Rupture Propagation

Dilatancy associated with fault slip produces a transient pore pressure drop which increases frictional strength. This effect has been argued to be at least partially at the origin of slow slip events in subduction zones. Recent experimental results have demonstrated that dilatancy hardening has the potential to stabilise rupture in rocks, but laboratory results need to be upscaled to account for large scale variations in slip along faults. Here, we analyze the dilatant hardening in a steadily propagating rupture model that includes frictional weakening, slip-dependent fault dilation and fluid flow. A fracture mechanics approach is used to show that dilatancy hardening tends 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. The competing effect of thermal pressurization 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-derived parameters, we show that the dilatancy-toughening effect leads to rupture dynamics that is quantitatively consistent with the dynamics of observed slow slip events in subduction zones.