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

Abstract

[1] We investigate in a systematic parameter space study dilatant effects on slip evolution of a fluid-infiltrated fault in the continuum limit. The fault is governed by rate-and state-dependent friction and an empirical law for porosity evolution. We focus on the response of systems as a function of fluid-related parameters, such as the degree of overpressurization, dilatancy and diffusivity. This study emphasizes the exploration of the parameter space for homogeneous along-strike properties to investigate the evolution of spatiotemporal slip depending on hydromechanical processes. Three types of responses emerge. First, system-wide unstable stick-slip develops for drained conditions, and for undrained conditions if mechanisms leading to an increase in pore space are less effective. The critical stiffness depends on hydraulic diffusivity and dilatancy, which is shown to correspond with interevent times of simulated stick-slip events. During instabilities the evolution of hydraulic variables differ significantly between drained and undrained conditions. Second, stable creep is a result of dilatant processes. Third, systems situated in transitional stability regimes develop nonuniform slip pattern in space and time, revealing a possible explanation for rupture termination and observed stable afterslip. Although these patterns are produced by models located in transition zones of the parameter space, the occurrence of heterogeneous slip evolution is persistent for an extensive range of parameter values. Since transition zones contain an broad range of plausible conditions in the crust, they do not represent extreme cases.Citation: Hillers, G., and S. A. Miller (2006), Stability regimes of a dilatant, fluid-infiltrated fault plane in a three-dimensional elastic solid,

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, such regions of efficient dilatancy hardening would tend to arrest the propagation of shear rupture, similar to those regions described as conditionally stable by Scholz [1998]. This type of spatial complexity in fault zone drainage state was shown to result in realistic spatiotemporal complexity in earthquake nucleation in the numerical analyses of Hillers et al [2006] and Hillers and Miller [2006, 2007] on simulated dilatant fault zones with spatial variations in fault constitutive parameters and was in part attributed to large values of D C , which we have shown can be effectively produced by efficient dilatant hardening, leading to increases of several orders of magnitude.…”

“…In order to vary the drainage state of the simulated fault zone we systematically alter the permeability ( k ) from 10 −15 to 10 −21 m 2 based on previous works [ Wibberley , 2002; Wibberley and Shimamoto , 2003, Wibberley et al , 2008; Mitchell and Faulkner , 2008; Tanikawa et al , 2010], the dilatancy coefficient (ɛ) from 10 −5 to 10 −3 [ Marone et al , 1990; Samuelson et al , 2009; J. Samuelson and C. Marone, Laboratory measurements of the frictional dilatancy coefficient for natural and simulated fault zones manuscript in preparation, 2011], and the load point velocity ( v lp ) from 10 to 30, 100, 300, and 1000 μ m/s to simulate the velocity stepping experiments of the Penn State biaxial/triaxial apparatus [e.g., Mair and Marone , 1999; Ikari et al , 2009; Samuelson et al , 2009]. Hillers and Miller [2006] point out that the dilatancy measurements of Marone et al [1990] were done at slip velocities within the realm of the nucleation of dynamic slip (1–10 μ m/s), and subsequently surmised that ɛ may be far smaller at the lower velocities more typical at nucleation. Contrary to that notion, the more recent experiments of Samuelson et al [2009], which measured the dilatancy coefficient over a range of velocity step sizes from 1 to 100 μ m/s showed no strong correlation between velocity and ɛ, suggesting that using a dilatancy coefficient on the order of 5 × 10 −4 is appropriate for those simulations in which ɛ is not the control variable.…”

“…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. To do this, we use a numerical simulation of a laboratory experiment performed under the in situ conditions of a natural fault zone.…”

Two‐dimensional model calculations of earthquake cycle on a fluid‐infiltrated plate interface at a subduction zone: Focal depth dependence on pore pressure conditions

“…In experimental and theoretical studies, however, the pore pressure fluctuates due to pore dilatation and compaction [ Marone et al , 1990] or thermal pressurization [e.g., Noda and Shimamoto , 2005]. For numerical studies using the rate‐ and state‐dependent friction law, how pore dilatation and compaction affect slip instability has been investigated in a simple spring slider model [ Segall and Rice , 1995] and also in a vertical strike‐slip model [ Shibazaki , 2005; Hillers and Miller , 2006].…”