Analysis of slip-softening instability on a fault with asperities

Slip-softening instability on a vertical strike-slip fault with asperities has been analysed. The fault strength is uniform in depth, but the strength is nonuniform in the strike direction, i.e., there are asperities on the fault. These asperities and other segments of the fault have the same type of constitutive law but different peak stresses. The material surrounding the fault is represented by elastic plates, of which the top and bottom surfaces are stress-free.We use a finite element method to study the evolution of theoretical displacement, stress and strain field with a growing displacement applied at the remote plate ends. The slip and frictional stress are obtained as part of the solution. We have compared the difference of theoretical displacement, strain field and the distribution of frictional stress on the fault between unstable and stable slip. In addition, we have studied the effect of size and strength of asperities on instability, and the softening behaviour of asperities before instability.We find that (1) the failure of the fault zone may be due to either dynamic instability or rapid quasistable slip. A general characteristic of unstable mode is that slippage, on some parts of asperities increases indefinitely for a small finite increase in remote imposed displacement until, immediately before the unstable slip; (2) the size and peak strength of asperities have a large effect on instability. Reducing the size and peak strength of asperities tends to replace inertially unstable deformation with stable deformation; (3) the location with maximum acceleration during unstable slip, as the plausible nucleating seismic source, is in asperities; (4) the shapes of the changes in theoretical stress and strain at a given location, caused by the nonlinear constitutive property of the fault, are all similar whether instability, happens or not. This fact suggests that the changes of peak type or bend type in crustal deformation are not required for earthquake instability.