Slip on wavy frictional faults: Is the 3rd dimension a sticking point?

The formulation for the 3D triangular displacement discontinuity boundary element method with frictional constraints is described in detail. Its accuracy in comparison to analytical solutions is then quantified. We show how this can be used to approximate stress intensity factors at the crack tips. Using this method, we go on to quantify how slip is reduced on fault surfaces with topography, where the asperities are approximated as a sinusoidal waveform, i.e. corrugations. We use stress boundary conditions (compressive) orientated such that frictional contacts shear. We show that slip reductions relative to planar faults for 2D line and 3D penny-shaped crack models are comparable within 10% when slip is perpendicular to the corrugations. Using the 3D model, we then show how slip is reduced more when corrugation wavelengths are doubled compared to the reduction due to corrugation alignment with the slip direction. When slip is parallel with the corrugation alignment we show that reducing the out-of-plane stress, from the normal traction acting on the fault when planar to that resolved on a perpendicular plane, has the same effect as halving the length of the corrugation waveform in terms of slip reduction for a given amplitude.