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We examine the development of an instability of fault slip rate. We consider a slip rate and state dependence of fault frictional strength, in which frictional properties and normal stress are functions of position. We pose the problem for a slip rate distribution that diverges quasi-statically within finite time in a self-similar fashion. Scenarios of property variations are considered and the corresponding self-similar solutions found.
We present a model for dynamic weakening of faults based on local flash heating at microscopic asperity contacts coupled to bulk heating at macroscopic scale. We estimate the fracture energy G associated with that rheology, and find that for constant slip rate histories G scales with slip ? as at small slip, while at large slip. This prediction is quantitatively consistent with data from laboratory experiments conducted on dry rocks at constant slip rate.
AbstractWe examine the development of a frictional instability, with diverging sliding rate, at the interface of elastic bodies in contact. Evolution of friction is determined by a slip rate and state dependence. Following Viesca (2016 Phys. Rev. E 93, 060202(R). (doi:10.1103/PhysRevE.93.060202)), we show through an appropriate change of variable, the existence of blow-up solutions that are fixed points of a dynamical system.
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