Additional shear resistance from fault roughness and stress levels on geometrically complex faults

Abstract

The majority of crustal faults host earthquakes when the ratio of average background shear stress τb to effective normal stress σeff is τb/σeff≈0.6. In contrast, mature plate‐boundary faults like the San Andreas Fault (SAF) operate at τb/σeff≈0.2. Dynamic weakening, the dramatic reduction in frictional resistance at coseismic slip velocities that is commonly observed in laboratory experiments, provides a leading explanation for low stress levels on mature faults. Strongly velocity‐weakening friction laws permit rupture propagation on flat faults above a critical stress level τpulse/σeff≈0.25. Provided that dynamic weakening is not restricted to mature faults, the higher stress levels on most faults are puzzling. In this work, we present a self‐consistent explanation for the relatively high stress levels on immature faults that is compatible with low coseismic frictional resistance, from dynamic weakening, for all faults. We appeal to differences in structural complexity with the premise that geometric irregularities introduce resistance to slip in addition to frictional resistance. This general idea is quantified for the special case of self‐similar fractal roughness of the fault surface. Natural faults have roughness characterized by amplitude‐to‐wavelength ratios α between 10−3 and 10−2. Through a second‐order boundary perturbation analysis of quasi‐static frictionless sliding across a band‐limited self‐similar interface in an ideally elastic solid, we demonstrate that roughness induces an additional shear resistance to slip, or roughness drag, given by τdrag=8π3α2G∗Δ/λmin, for G∗=G/(1−ν) with shear modulus Gand Poisson's ratio ν, slip Δ, and minimum roughness wavelength λmin. The influence of roughness drag on fault mechanics is verified through an extensive set of dynamic rupture simulations of earthquakes on strongly rate‐weakening fractal faults with elastic‐plastic off‐fault response. The simulations suggest that fault rupture, in the form of self‐healing slip pulses, becomes probable above a background stress level τb≈τpulse+τdrag. For the smoothest faults (α∼10−3), τdrag is negligible compared to frictional resistance, so that τb≈τpulse≈0.25σeff. However, on rougher faults (α∼10−2), roughness drag can exceed frictional resistance. We expect that τdrag ultimately departs from the predicted scaling when roughness‐induced stress perturbations activate pervasive off‐fault inelastic deformation, such that background stress saturates at a limit (τb≈0.6σeff) determined by the finite strength of the off‐fault material. We speculate that this strength, and not the much smaller dynamically weakened frictional strength, determines the stress levels at which the majority of faults operate.