Effective stress, friction, and deep crustal faulting

Studies of crustal faulting and rock friction invariably assume the effective normal stress that determines fault shear resistance during frictional sliding is the applied normal stress minus the pore pressure. Here we propose an expression for the effective stress coefficient (f) at temperatures and stresses near the brittle-ductile transition (BDT) that depends on the percentage of solid-solid contact area across the fault. (f) varies with depth and is only near 1 when the yield strength of asperity contacts greatly exceeds the applied normal stress. For a vertical strike-slip quartz fault zone at hydrostatic pore pressure and assuming 1mm and 1km shear zone widths for friction and ductile shear, respectively, the BDT is at similar to 13km. (f) near 1 is restricted to depths where the shear zone is narrow. Below the BDT (f)=0 is due to a dramatically decreased strain rate. Under these circumstances friction cannot be reactivated below the BDT by increasing the pore pressure alone and requires localization. If pore pressure increases and the fault localizes back to 1mm, then brittle behavior can occur to a depth of around 35km. The interdependencies among effective stress, contact-scale strain rate, and pore pressure allow estimates of the conditions necessary for deep low-frequency seismicity seen on the San Andreas near Parkfield and in some subduction zones. Among the implications are that shear in the region separating shallow earthquakes and deep low-frequency seismicity is distributed and that the deeper zone involves both elevated pore fluid pressure and localization.