The onset of faulting around geometrically irregular faults

Geological and geophysical observations indicate that fault geometry is nonplanar, includes irregularities in all directions at many scales. The geometrical heterogeneity of faults is particularly critical during the interseismic stage of the earthquake cycle because it perturbs the stress field and thus affects the rupture nucleation along the fault zone and around it. We present a new analytical solution for the static stress field around a rough interlocked interface obtained under compressional stresses, and discuss its applications to faulting and seismic hazards. The model outputs are the local stress field and the Failure-Ratio, defined here as the susceptibility to failure of the bulk material around the interface. The calculations are then obtained by the following steps: First, the interface geometry is represented by a Fourier series. Then, the stress components around the irregular interface are calculated analytically using perturbation theory for any two dimensional far-field stress tensor. Finally, the Failure Ratio at any location near the interface is estimated by adopting a Coulomb failure criterion for the bulk material.

The model results can be applied to faulting mechanics because they demonstrate how the elastic stress field around rough fault is controlled by the geometry and by the tectonic stresses. We find that under a given tectonic stress state, stress heterogeneity increases with roughness. Therefore, some zones near rough faults are expected to yield at lower tectonic shear stress comparing to zones nearby smooth ones. However, the magnitudes of these events are expected to be relatively small, as they nucleate under relatively low tectonic stresses and fail as they propagating immediately to a stress shadow. This stress distribution promotes small seismic events near rough fault and therefore we suggest that increasing heterogeneity of the surface, contributes to increasing of the b-value in Gutenberg-Richter earthquakes distribution.

We compare the model predictions with results of experiments performed on rough rock surfaces and find good agreement between the locations of off-fault deformation zones and the calculated high Failure-Ratio values. We further test the model implications for stresses and failure around a natural fault system – the San Andreas Fault and find a first-order agreement between Failure-Ratio values and earthquake distribution around this fault system. We conclude that the proposed analytical approach is a useful and practical tool for evaluating the contribution of fault geometry to the seismic hazard potential around it.