Shear heating of a fluid‐saturated slip‐weakening dilatant fault zone: 2. Quasi‐drained regime

Abstract

[1] This paper analyzes slip on a fluid-infiltrated dilatant fault for imposed (tectonic) strain rates much slower than the rate of fluid exchange between the gouge zone and the surroundings and for exchange of heat slower than of fluid, typical of interseismic or most laboratory loading conditions. The limiting solution, corresponding to the infinitely rapid drainage rate, developed in the companion paper by Garagash and Rudnicki [2003], yielded unbounded slip acceleration for sufficiently large slip weakening of the fault. Analysis for rapid but finite drainage rates (quasi-drained condition) reveals two types of possible instability. The first is inertial instability (a seismic event) characterized by an unbounded slip rate and attributed to the destabilizing effects of shear heating and fault slip weakening. The second corresponds to loss of uniqueness and arises from the small pressure increase caused by shear heating for rapid but finite rates of drainage. This instability emerges for even small amounts of thermomechanical coupling and a large range of dilatancy and slip weakening. Its resolution probably requires a more elaborate frictional description (e.g., rate and state), but within the slip-weakening framework here, leads to either slip arrest or inertial instability. The response is always unstable (in one of these two ways) for sufficiently large thermal coupling or initial stress regardless of the amount of slip weakening and dilatancy. The counterintuitive stabilizing effect of increased slip weakening or decreased dilatancy, similar to the effect in the companion paper, also occurs for nearly drained slip.

Influence of dilatancy on the frictional constitutive behavior of a saturated fault zone under a variety of drainage conditions

“…In some ways the work presented here is similar to previous numerical studies on the role of dilatancy in fault zones, in particular the ability of pore fluid decompression to stabilize fault zones by transiently increasing shear strength [ Garagash and Rudnicki , 2003a, 2003b; Hillers et al , 2006; Hillers and Miller , 2006; Segall et al , 2010]. Our work differs from that of Garagash and Rudnicki [2003a, 2003b] by way of our implementation of rate‐ and state‐dependent frictional behavior, rather than slip‐weakening behavior alone, which allows us to investigate the full evolution of shear strength in a fault zone with controlled fluid drainage parameters. Additionally, our work differs from the studies of Hillers et al [2006] and Hillers and Miller [2006] in that our intention is to analyze specifically the effective change in rate and state constitutive parameters resulting solely from fault zone dilatancy.…”

Effective normal stress alteration due to pore pressure changes induced by dynamic slip propagation on a plane between dissimilar materials

“…Induced pore pressure by poroelastic compression discussed here is one of a number of mechanisms that have been suggested for dynamic weakening of slip resistance during earthquakes. These include thermal pressurization of pore fluid [ Lachenbruch , 1980; Mase and Smith , 1987; Garagash and Rudnicki , 2003a, 2003b; Garagash et al , 2005; Rice , 2006], flash heating of asperity contacts [ Rice , 1999; Tullis and Goldsby , 2003; Rice , 2006] and others [ Sibson , 1975; Spray , 1993, 1995; Goldsby and Tullis , 2002; Chambon et al , 2002]. For the most part, these require rapid slip to generate heat sufficiently rapidly and relatively large slip to generate sufficiently high temperature (although Segall and Rice [2006] have shown that shear heating can be significant toward the end of the nucleation period, before slip velocities become seismic).…”

Stability regimes of a dilatant, fluid‐infiltrated fault plane in a three‐dimensional elastic solid

“…Continuity of fluid mass per unit volume m = ϕρ f is required, and by distinguishing between elastic and plastic pore deformation the resulting change in porosity can be written as the sum of an elastic and plastic (denoted by ( x , z , t )) component. Currently, we ignore possible shear heating effects [ Blanpied et al , 1998b] on pore pressure change, which could counteract rapid sliding induced compressibility of the pore fluid by its thermal expansion [ Taylor and Rice , 1998; Andrews , 2002; Garagash and Rudnicki , 2003a, 2003b]. The irreversible porosity reduction acts as a direct source term in the diffusion equation where β is the porosity times the sum of fluid and elastic pore compressibility, respectively.…”