Frictional Stability of Heterogeneous Surfaces in Contact

Utilizing the principles of elastic-brittle fracture mechanics, stress-displacement relationships are derived for an elastic solid containing a slip plane consisting of various configurations of collinear arrays of cracks. These models take into account the heterogeneous nature of slip planes as observed in the lab and in the field, and are relevant to the behavior of rock containing faults, joints, bedding planes, and fractures. All of our models exhibit slip weakening behavior, and show regimes of both stable (aseismic) and unstable (seismic) deformation. For given configurations of cracks and applied boundary conditions, our results show explicit ly the energy released through unstable crack growth. For instance, it is found that two equal length cracks growing together release more seismic energy than, say, a large crack growing into a small crack. Also, by allowing cracks to coalesce, our models show multiple stick-slip events without crack healing or other geochemical means.