Application of a unified rate and state friction theory to the mechanics of fault zones with strain localization

Abstract

is •n Cn(O)/AP•Cn(AT). The theoryis complete in the sense that the complete earthquake cycle is represented and that there are no unmeasurable state parameters. The theory was applied to investigate earthquake quenching by fluid pressure decreases associated with frictional dilatancy and the related topic of strain localization and delocalization within fault zones. It was found that strain localization will occur when b > a. Such strain localization tends to destabilize sliding within drained faults by reducing the effective value of the critical displacement. Fault zones that are hydraulically sealed from the country rock but internally hydraulically connected are also destabilized because strain localization reduces the fluid pressure decrease from frictional dilatancy. Two mechanisms that delocalize strain once sliding is well underway were investigated. Strain rate strengthening at high-strain rates leads to a high strain zone that gradually broadens throughout an earthquake. An increase in the coefficient of friction with temperature leads to a high strain rate zone that moves through the fault zone from hot regions created by frictional heating to cold regions.

Rate and state dependent friction and the stability of sliding between elastically deformable solids

“…It is now generally assumed to be descended from an Arrhenius activated rate process describing creep at asperity contacts. That interpretation had been mentioned earlier by Stesky (1977), was implicit in Chester (1994), and was suggested explicitly, in the rate and state framework, by Heslot et al (1994), Brà echet and Estrin (1994), Baumberger (1997), Sleep (1997), Persson (1998), Baumberger et al (1999), Lapusta et al (2000), and Nakatani (2001). In such an interpretation, for the simple case of a single activated process, we write the slip rate as…”

“…That is, for rapid enough changes in V so as for the surfaces to be at the same population of asperity contacts (i.e., at a constant value of the state variable), the variation of friction strength with slip rate V is generally found to involve a positive proportionality to ln(V ). This dependence is plausibly attributed to the presence of a thermally activated creep process at stressed asperity contacts (Stesky, 1977;Heslot et al, 1994;Chester, 1994;Brà echet and Estrin, 1994;Baumberger, 1997;Sleep, 1997;Persson, 1998;Baumberger et al, 1999;Lapusta et al, 2000;Nakatani, 2001) as discussed further. We also demonstrate how compromises from the full rate and state constitutive framework, in the direction of classical friction laws like pure velocity-dependent friction, of velocity-weakening type, do not allow a quasi-static range and, in fact, lead to paradoxical prediction of supersonic propagation of slip pulses (as recognized already by Weertman, 1969, andKnopo andLandoni, 1998), or to ill-posedness, depending on the strength of the velocity weakening.…”

Physics of friction and strain rate localization in synthetic fault gouge

“…Data on synthetic fault gouge previously collected by Richardson and Marone [1999] were compared with the predictions of a unified theory for rate-and state-dependent friction compiled by Sleep [1997]. The theory treats the gouge as a continuum one-dimensional fluid sheared between parallel plates.…”

Rate‐ and state‐dependent friction of intact rock and gouge

“…The failure of natural and simulated faults depends on the previous history of slip, not just the instantaneous stress state [e.g., Dieterich, 1994 Sleep [1997], represents the effects of sudden changes in normal traction [Linker and Dieterich, 1992] and temperature [Chester, 1994[Chester, , 1995 on friction.…”

“…The purpose of this paper is to unify deformation theories for gouge with those for intact rock. I retain the notation of Sleep [1997] who uses strains and strain rates rather than displacements and velocities with minor changes to avoid conflicts with new variables.…”