Critical nucleation length for frictional slipping of an elastic layer over an elastic half-space

The interplay of geological forces and shear resistance of slipping surfaces leads to the expansion of earthquake ruptures, which nucleate in creeping zone patches. Once the dimension of the nucleating creeping zone exceeds a critical length, ruptures accelerate dynamically. The present work provides an analytic model to determine the critical nucleation length of a slip rupture. It is determined by performing a linear stability analysis of steady-state sliding of an elastic layer (having a finite height) over an elastic half-space in the quasi-static regime. Interfacial frictional behaviour is modelled using a rate- and state-dependent friction law with velocity weakening behaviour in the steady state, mimicking the experimental observations of interfacial friction. Results for critical nucleation length at the interface with similar and dissimilar materials across the interface are presented and the effect of layer height on the critical nucleation length is explored numerically.