APPLICATION OF A UNIFIED RATE AND STATE FRICTION THEORY TO THE MECHANICS OF FAULT ZONES WITH STRAIN LOCALIZATION

The formalism for rate and state friction is extended to represent fau lt zones where temperature, porosity, effective normal traction, and s train rate are functions of position (measured across the fault zone). A traditional form for the instantaneous coefficient of friction is r etained, mu(0) + a ln(epsilon epsilon)+ b ln(psi/psi(0)) where mu(0) i s the steady state coefficient of friction at shear strain rate epsilo n(0), a and b are small constants, epsilon is the shear strain rate, p si is a state variable that represents damage, and psi(0) a normalizin g factor. Percolation theory of cracked solids is used to justify a re lation between Porosity and the state variable of psi = exp[(phi(0)-f) /C-epsilon], where c(epsilon) is a dimensionless constant, and phi(0) is the porosity at a reference steady state strain rate epsilon(0) and at a reference temperature where Delta=0 and a reference effective no rmal traction Delta P-0. These relationships and percolation theory im ply an evolution law for porosity of the (normalized) form partial der ivative f/partial derivative t = (Delta P-0(n) epsilon/C-eta(0)epsilon (0)) - (Delta P-n/C-eta(Delta T)psi) where t is time, Delta P is the e ffective normal traction, C, is a material property (related to compac tion viscosity) that depends on the temperature difference Delta T fro m reference condition, 0 indicates reference conditions, and n is a po wer law rheology exponent. The first term represents creation of poros ity by frictional dilatancy while the second term represents closure o f porosity by compaction. The effects of transient changes of pressure and temperature on the coefficient of friction are represented when t he normalizing factor psi(0) is Delta (PCeta)-C-n(O)/Delta (P0Ceta)-C- n(Delta T). The theory is complete in the sense that the complete eart hquake cycle is represented and that there are no unmeasurable state p arameters. The theory was applied to investigate earthquake quenching by fluid pressure decreases associated with frictional dilatancy and t he related topic of strain localization and delocalization within faul t zones. It was found that strain localization will occur when b >a. S uch strain localization tends to destabilize sliding within drained fa ults by reducing the effective value of the critical displacement. Fau lt zones that sire hydraulically sealed from the country rock but inte rnally hydraulically connected are also destabilized because strain lo calization reduces the fluid pressure decrease from frictional dilatan cy. Two mechanisms that delocalize strain once sliding is well underwa y were investigated. Strain rate strengthening at high-strain rates le ads to a high strain zone that gradually broadens throughout An increa se in the coefficient of friction with temperature leads to a high str ain rate zone that moves through the fault zone from hot regions creat ed by frictional heating to cold regions.