DILATANCY, COMPACTION, AND SLIP INSTABILITY OF A FLUID-INFILTRATED FAULT

We analyze the conditions for unstable slip of a fluid infiltrated fau lt using a rate and state dependent friction model including the effec ts of dilatancy and pore compaction. We postulate the existence of a s teady state drained porosity of the fault gouge which depends on slip velocity as phi(ss) = phi(o) + epsilon ln(v/v(o)) over the range consi dered, where v is sliding velocity and epsilon and v(o) 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 dr ained experiments of Marone et al. (1990). For undrained loading, the effect of dilatancy is to increase (strengthen) partial derivative tau (ss)/partial derivative lnv by mu(ss)epsilon/(sigma - p)beta, where mu (ss) is steady state friction, sigma and p are fault normal stress and pore pressure, and beta is a combination of fluid and pore compressib ilities. Assuming epsilon similar to 1.7 x 10(-4) from fitting the Mar one et al. data, we find the ''dilatancy strengthening'' effect to be reasonably consistent with undrained tests conducted by Lockner and By erlee (1994). Linearized perturbation analysis of a single degree of f reedom model in steady sliding shows that unstable slip occurs if the spring stiffness is less than a critical value given by k(crit) = (sig ma - p)(b - a)/d(c) - epsilon mu(ss)F(c)/beta 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 lim it c --> infinity F(c*) --> 0, recovering the drained result of Ruina (1983). In the undrained limit, c --> 0, F(c*) --> 1, so that for su fficiently large epsilon slip is always stable to small perturbations. Under undrained conditions (sigma - beta) must exceed epsilon mu(ss)/ beta(b - a) for instabilities to nucleate, even for arbitrarily reduce d stiffness. This places constraints on how high the fault zone pore p ressure can be, to rationalize the absence of a heat flow anomaly on t he San Andreas fault, and still allow earthquakes to nucleate without concommitant fluid transport. For the dilatancy constitutive laws exam ined here, numerical simulations do not exhibit large interseismic inc reases in fault zone pore pressure. The simulations do, however, exhib it a wide range of interesting behavior including: sustained finite am plitude oscillations near steady state and repeating stick slip events in which the stress drop decreases with decreasing diffusivity, a res ult 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 ef fects rather than to interaction with neighboring portions of the faul t. This mechanism may explain aftershocks that appear to be located wi thin zones of high mainshock slip, although poor resolution in mainsho ck slip distributions can not be ruled out.