4.03 - Fracture and Frictional Mechanics – Theory

Abstract

Fracture mechanics considers conditions for the onset, propagation, and arrest of shear and tensile ruptures. Because earthquakes can be naturally represented as elastodynamic shear instabilities, fracture mechanics forms a theoretical basis of earthquake seismology. Earthquake ruptures involve a number of mechanical processes, including yielding and material breakdown around the propagating rupture front, complex time-dependent evolution of friction on a slipping interface behind the rupture front, radiation of seismic waves, wear, communition, and heating of the fault zone material, etc. These processes are intrinsically coupled, and must be considered in a unified fashion. Recent theoretical, experimental, and field data suggest that fracture mechanics models assuming small-scale yielding and constant residual friction on a fault surface may not be an adequate theoretical description of earthquake ruptures. This is because the fault interface may undergo a continuous weakening with rapid slip (e.g., due to thermal effects), so that the effective displacement corresponding to fault weakening may (1) scale with the rupture length and (2) be non-negligible compared to the overall coseismic offset. Also, an assumption that the inelastic yielding is confined to the slip plane is likely violated, especially at high rupture speeds approaching the shear wave velocity. It follows that the earthquake fracture energy is expected to scale with the rupture size, and may not be a negligible part of the earthquake energy balance, perhaps even for large earthquakes. In the presence of significant variations in the dynamic friction during fault slip, a distinction between the fracture energy and the energy loss due to friction is not well defined. Both terms represent inelastic work done on a fault that is ultimately spent on fracturing, communition, and heating of the fault zone material. If the fracture energy is formally defined as work required to evolve friction from the maximum static level in the breakdown zone at the rupture front to the minimum dynamic level, a continuous dynamic weakening implies repartitioning of the total inelastic work between the fracture energy and the ‘residual’ frictional losses. The coseismic heating is one of the likely mechanisms that control the dynamic fault strength, and thus the stress drop and seismic radiation. The instantaneous along-fault temperature distribution is governed by the details of slip history, as well as the characteristic thickness and thermophysical properties of a slipping zone. Faults that are thin compared to the thermal diffusion length scale are predicted to produce maximum temperatures near the rupture front, while thicker faults are likely hottest in the central part of the rupture. These patterns may affect the rupture dynamics. Theoretical models that fully couple heat transfer, thermally activated friction, elastodynamics, and off-fault damage may be necessary for realistic simulations of earthquake ruptures.