Mechanics of discontinuous faults

Fault traces consist of numerous discrete segments, commonly arranged as echelon arrays. In some cases, discontinuities influence the distribution of slip and seismicity along faults. To analyze fault segments, we derive a two-dimensional solution for any number of nonintersecting cracks arbitrarily located in a homogeneous elastic material. The solution includes the elastic interaction between cracks. Crack surfaces are assumed to stick or slip according to a linear friction law. For an array of echelon cracks the ratio of maximum slip to array length significantly underestimates the difference between the driving stress and frictional resistance. The ratio of maximum slip to crack length slightly overestimates this difference. Stress distributions near right- and left-stepping echelon discontinuities differ in two important ways. For right lateral shear and left-stepping cracks, normal tractions on the overlapped crack ends increase and inhibit frictional sliding, whereas for right-stepping cracks, normal tractions decrease and facilitate sliding. The mean compressive stress between right-stepping cracks also decreases and promotes the formation of secondary fractures, which tend to link the cracks and allow slip to be transferred through the discontinuity. For left-stepping cracks the mean stress increases; secondary fracturing is more restricted and tends not to link the cracks. Earthquake swarms and aftershocks cluster near right steps along right lateral faults. Our results suggest that left steps store elastic strain energy and may be sites of large earthquakes. Opposite behavior results if the sense of shear is left lateral.

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