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

Abstract

[1] The majority of crustal faults host earthquakes when the ratio of average background shear stress b to effective normal stress eff is b / eff 0.6. In contrast, mature plate-boundary faults like the San Andreas Fault (SAF) operate at b / eff 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 pulse / eff 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˛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 drag = 8 3˛2 G * / min , for G * = G/(1 -) with shear modulus G and Poisson's ratio , slip , and minimum roughness wavelength min . 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 b pulse + drag . For the smoothest faults (˛ 10 -3 ), drag is negligible compared to frictional resistance, so that b pulse 0.25 eff . However, on rougher faults (˛ 10 -2 ), roughness drag can exceed frictional resistance. We expect that drag 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 ( b 0.6 eff ) 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.Citation: Fang, Z., and E. M. Dunham (2013), Additional shear resistance from fault roughness and stress levels on geometrically complex faults,

Fault roughness and strength heterogeneity control earthquake size and stress drop

“…The observed decrease in average slip per stress drop due to fault roughness corresponds to a decreased frictional breakdown during sliding and thus a decrease in Δμ. Hence, fault roughness may be regarded as a bulk frictional agent [Griffith et al, 2010;Fang and Dunham, 2013], modifying the change in frictional resistance that is associated with a given stress drop (equation (5)). …”

The minimum scale of grooving on faults

“…1;Power and Tullis, 1991;Renard et al, 2006). These observations have been used to infer mechanisms of fault resistance and wear (Scholz, 1988;Fang and Dunham, 2013;Brodsky et al, 2016).…”

The spatial distribution of earthquake stress rotations following large subduction zone earthquakes

“…The large patches of slip may represent areas of smooth fault surface, which may allow greater dynamic weakening during a large earthquake (e.g., Fang and Dunham 2013). Flat, smooth fault regions also appear to produce the largest earthquakes (Bletery et al 2016).…”