Shear resistance and near-field stresses on rough faults

Natural faults are rough at all scales and can be described with fractal geometry. This deviation from planarity results in geometric asperities and a heterogeneous stress field. Analytical and numerical studies have shown that roughness introduces additional shear resistance on the fault and promotes failure in the medium surrounding the fault because of the elevated stresses. These studies generally assume a small slip on the fault, i.e., much smaller than the minimum roughness wavelength, λ_min. It is important to examine the effects of roughness on shear resistance and near-fault stresses at large sliding, as well as the assumptions incorporated in the derivation of the analytical solutions.

In this study, we examine the effects of fault geometry on the shear resistance and near-fault stresses at large sliding numerically, using a method that is based on the mortar finite element formulation, in which non-matching meshes are allowed across the fault, and the contacts are continuously updated. This enables modeling slip larger than λ_min and the overriding of asperity contacts. We begin with simulations of an elastic medium and show that, indeed, the roughness results in large and heterogeneous stresses on and off the faults, which increase with the roughness level. However, except for small slip values, the increase of shear resistance with slip is much smaller than the linear increase predicted by the analytical models, which assume small and uniform slip. For self-similar geometry, with Hurst exponent of H = 1, the average shear resistance increases with slip at a decreasing rate. For self-affine geometry, with H < 1, it initially increases with slip, then decreases at a slip larger than λ_min /2. Although overriding of asperities is allowed in the simulations, as slip increases, significant stress concentrations are developed on the fault, which may not be realistic for natural rock surfaces. To account for that, we implement wear laws into the method and model the evolution of stresses during a quasistatic slip and cycles of dynamic earthquakes. The wear process redistributes and bounds the stresses on the fault and allows a more realistic characterization of stress distribution near the fault.