Dilatancy, compaction, and slip instability of a fluid‐infiltrated fault

We analyze the conditions for unstable slip of a fluid infiltrated fault using a rate and state dependent friction model including the effects of dilatancy and pore compaction. We postulate the existence of a steady state drained porosity of the fault gouge which depends on slip velocity as ϕ ss = ϕ 0 + εln( v / v 0 ) over the range considered, where v is sliding velocity and ε and v 0 are constants. Porosity evolves toward steady state over the same distance scale, d c , as “state.” This constitutive model predicts changes in porosity upon step changes in sliding velocity that are consistent with the drained experiments of Marone et al. (1990). For undrained loading, the effect of dilatancy is to increase (strengthen) ∂τ ss /∂ln v by μ ss ε/(σ – p )β where μ ss is steady state friction, σ and p are fault normal stress and pore pressure, and β is a combination of fluid and pore compressibilities. Assuming ε ∼ 1.7×10 −4 from fitting the Marone et al. data, we find the “dilatancy strengthening” effect to be reasonably consistent with undrained tests conducted by Lockner and Byerlee (1994). Linearized perturbation analysis of a single degree of freedom model in steady sliding shows that unstable slip occurs if the spring stiffness is less than a critical value given by k crit = (σ‐ p )( b ‐ a )/ d c ‐ εμ ss F ( c *)/β d c where a and b are coefficients in the friction law and F ( C *) is a function of the model hydraulic diffusivity c * (diffusivity/diffusion length 2 ). In the limit c * →∞ F ( c *) → 0, recovering the drained result of Ruina (1983). In the undrained limit, c * → 0, F ( c *) → 1, so that for sufficiently large ε slip is always stable to small perturbations. Under undrained conditions (σ – p ) must exceed εμ ss /β( b ‐ a ) for instabilities to nucleate, even for arbitrarily reduced stiffness. This places constraints on how high the fault zone pore pressure can be, to rationalize the absence of a heat flow anomaly on the San Andreas fault, and still allow earthquakes to nucleate without concommitant fluid transport. For the dilatancy constitutive laws examined here, numerical simulations do not exhibit large interseismic increases in fault zone pore pressure. The simulations do, however, exhibit a wide range of interesting behavior including: sustained finite amplitude oscillations near steady state and repeating stick slip events in which the stress drop decreases with decreasing diffusivity, a result of dilatancy strengthening. For some parameter values we observe “aftershock” like events that follow the principal stick‐slip event. These aftershocks are noteworthy in that they involve rerupture of the surface due to the interaction of the dilatancy and slip weakening effects rather than to interaction with neighboring portions of the fault. This mechanism may explain aftershocks that appear to be located within zones of high mainshock slip, although poor resolution in mainshock slip distributions can not be ruled out.