Continuity conditions for a fault consisting of obliquely aligned cracks

Abstract

SUMMARY Expressions exist for the continuity conditions that apply to a plane fault that is modelled as a distribution of circular cracks lying in the plane of the fault. These are conditions that apply when the wavelength of the incident wave is large compared with crack size and spacing, and they are approximate for a small number density of the cracks. In form they are identical to the ‘fault-slip’ conditions of Murty, Schoenberg and Pyrak-Nolte, Myer & Cook, in which the traction is proportional to the displacement discontinuity across the fault. It is possible to envisage a fault consisting of obliquely aligned cracks whose centres lie in the median plane of the fault but whose normals are not necessarily perpendicular to the fault. We have found the interface conditions for this model to be more complex than those for the fault-slip model and involve elements of the stress tensor other than the tractions on the plane of the fault. The continuity conditions are compared with those for a thin anisotropic layer and it is found that there is no equivalent material layer representation unless the cracks are parallel to the plane.