Two basic models which represent faulting in the medium with a barrier (asperity) are analyzed. The first model consists of two interacting colinear cracks (colinear Volterra dislocations) separated by a high rigidity inclusion and refers to faulting in the medium with a barrier of high rigidity and strength which is not initially fractured. The second model, which describes the mechanical state of the medium when the barrier is broken, is a single crack (Volterra dislocation) which crosses the inclusion. The models are further divided into symmetric and asymmetric cases as far as the position of the outer ends of the fracture zone, with respect to the inclusion, is concerned.
The dislocation density and slip on the cracks as well as stresses due to the cracks and the Volterra dislocations are computed and compared with the corresponding quantities for the homogeneous medium models. The results provide further quantitative insight into the mechanics of processes in tectonically active regions. The stress intensity factors are significantly influenced when a crack approaches a medium inhomogeneity, even that of small size. There is a distinct stress concentration, especially of the tectonic stress component, within an intact barrier of high rigidity. Once the barrier is broken, a substantial increase of stresses in the vicinity of ends of the fracture zone takes place. The asymmetric location of a barrier results in a distinctly asymmetric stress pattern. The stresses due to faulting obtained for the dislocation models are qualitatively similar to those for the corresponding crack models but considerably different quantitatively, especially for the model of a single fracture crossing a barrier.