The mechanics of static non-planar faults in linear elasticity

Fault geometry is a key factor in controling the mechanics of faulting. However, there is currently limited theoretical knowledge regarding the effect of non-planar fault geometry on earthquake mechanics. Here, we address this gap by introducing an expansion of the relation between fault traction and slip, up to second order, relative to the deviation from a planar fault geometry. This expansion enables the separation of the effects of non-planarities from those of planar faults. This expansion is realised in the boundary integral equation, assuming a small fault slope. It provides an interpretation for the effect of complex fault geometry on fault traction, for any fault geometry and any slip distribution. Hence the results are also independent of the friction that applies on the fault. The findings confirm that fault geometry has a strong influence on in-plane faulting (mode II) by altering the normal traction on the fault and making it more resistant to slipping for any fault geometry. On the contrary, for out-of-plane faulting (mode III), fault geometry has a much smaller influence. Additionally, we analyse some singularities that arise for specific fault geometries often used in earthquake simulations and provide guidelines for their elimination. To conclude this study, we discuss the limits of the small strain approximation when non-planar faults are considered.