Abstract

Here, we re‐examine the necessary and sufficient conditions for instability of frictional sliding based on a dynamic model derived from the Frenkel–Kontorova model and the rate‐and‐state frictional law. Two main findings follow from our analysis. First, sliding instability may be developed in velocity‐weakening as well as in velocity‐strengthening slidings in contrast to a common assumption only velocity‐weakening sliding may lead to instability. Instability in the velocity‐strengthening case is possible if there is a gradient of shear‐to‐normal stress ratio. Second, the nucleation size is smaller in the presence of the gradient compared with the case of no gradient, which leads to an apparent conclusion an earthquake is initiated in a place with maximal gradient. It is also shown nucleation size depends on the value of steady‐state friction. Our results support the point of view analysis of sliding stability, as well as quantitative studies of earthquake dynamics, should include stress heterogeneity.

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