Slip instability of dilatant and fluid-saturated faults

The mechanisms of slip instabilities of dilatant and fluid-saturated faults remain controversial, particularly in low-permeability environments. Using a rate and state friction model including the effects of dilatancy, we conduct a linearized stability analysis of a one-dimensional spring-slider model and reexamine the critical stiffness (kc) of the fault zone as a function of fluid diffusivity and dilatancy factor. Our analytical results indicate that under fully-drained conditions, kcis independent of dilatancy factor, while under poorly-drained conditions, kcdepends on dilatancy factor and fluid diffusivity. Both analytical and numerical results show that a nonnegative kcalways exists, even for highly-dilatant and poorly-drained faults where kcis proportional to fluid diffusivity. This implies that dilatancy does not alter the inherent (in)stability of fault slip, and that a sufficiently low system stiffness can always produce unstable fault slips without a critical pore pressure or critical dilatancy factor. These findings may provide new insights into effects of dilatancy on fault instability. The numerical results further illustrate that the fault slip acceleration tends to be significantly suppressed by increasing dilatancy factor and decreasing fluid diffusivity. These results may explain ubiquitous slow-slip events on natural faults that vary in length.