13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Effects of a newly incorporated with a stress-weakening term in a revised RSF on earthquake nucleation Nobuki Kame1,*, Satoshi Fujita1, Masao Nakatani1, Tetsuya Kusakabe1 1 Earthquake Research Institute, the University of Tokyo, Tokyo 113-0032, Japan * Corresponding author: kame@eri.u-tokyo.ac.jp Abstract Quasi-static nucleation on a frictional fault embedded in an elastic medium is known to be sensitive to the frictional properties. Earlier works have employed ‘aging’ and ‘slip’ versions of rate- and state-dependent friction (RSF) law, but some clear flaws have been known; the aging law wrongly predicted linearly increasing slip-weakening distance with the amount of strength reduction, whereas the slip law could not reproduce observed time-dependent healing at very low velocities. Recently Nagata et al. [1] proposed a revised version of RSF by incorporating a stress-weakening effect newly found in laboratory experiments and by correcting the frictional parameters ‘a’ and ‘b’ largely, where ‘a’ and ‘b’ are the coefficients of RSF. It seems to be free from the previously known flaws and we here reexamined nucleation by using the revised RSF. From numerical simulations, two major differences were found. 1) For weakly velocity-weakening range of 0.85<a/b<1, nucleation has characteristics of both unidirectional slip-pulse regime found in the slip law case and crack-like expansion regime in the aging law case. 2) Fixed-length patch regime occurs over a wider condition of a/b up to 0.85 in contrast with the previously reported range of a/b<0.5 implying strongly velocity-weakening faults. Keywords Nucleation, Earthquake, Fault, Rate and State Friction 1. Introduction On the basis of laboratory rock friction experiments the rate- and state-dependent friction law (RSF) was introduced [2]. It has been widely used in modeling of earthquake occurrence and successfully explained the mechanics of seismic cycles [3], aftershock activities [4] and many others. In the present paper, we focus on the modeling of earthquake nucleation by careful attention to the RSF formulae. Quasi-static nucleation on a frictional fault buried in an elastic continuum is known to be sensitive to the frictional properties. Earlier works studied spontaneous nucleation under slow tectonic loading using ‘aging’ and ‘slip’ versions of rate- and state-dependent friction (RSF) law [5-7]. For strongly velocity-weakening faults characterized by a/b<0.5 (‘a’ and ‘b’ are the coefficients of RSF), nucleation occurs in a ‘fixed-length patch’ regime, where regions of quasi-static slip remains relatively small. For weakly velocity-weakening faults (0.5<a/b<1), nucleation must propagate spatially (Fig. 1). Propagation occurs in a form of an expanding crack in the aging law case and in a form of a migrating slip pulse in the slip law case. Both versions of RSF were proposed as descriptions of laboratory friction experiments, but some clear flaws are known; aging law’s slip-weakening distance increases linearly with the amount of strength reduction, while slip law does not reproduce time-dependent healing at very low velocities. Recently Nagata et al. [1] proposed a revised version of RSF by incorporating a stress-dependent term with a coefficient ‘c’ and by correcting the RSF parameters ‘a’ and ‘b’ largely. This new version of RSF seems to be free from the previously known flaws and is here employed to reexamine nucleation.
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