Effective stress, friction and deep crustal faulting

Nicholas M. Beeler, Greg H. Hirth, Amanda M. Thomas, & Roland Bürgmann

Published 2015, SCEC Contribution #1971

Studies of crustal faulting and rock friction invariably assume the effective normal stress that determines fault shear resistance during frictional sliding is equal to applied normal stress minus the pore pressure, an assumption that is known to work well at room temperature. In this paper we develop a trial effective stress relationship for friction at temperatures and stresses near the brittle ductile transition (BDT). The relationship follows from low temperature observations and theory that relates the effective pressure coefficient 0 ≤ αf ≤1, equal to 1 according to the usual assumption, to the percentage of solid-solid contact area across the fault. This contact area depends on the applied stresses, pore pressure, the yield strength, and strain rate (slip rate and degree of localization). Because mineral yield strength decreases with increasing temperature and stress and temperature increase with depth in the crust, αf depends significantly on temperature and is only near 1 when the yield strength of asperity contacts greatly exceeds the applied normal stress.
For a quartz fault zone at hydrostatic pore pressure and assuming 1 mm and 1 km shear zone widths for friction and ductile shear, respectively, the BDT is at ~13 km. αf near 1 is restricted to depths where the fault is localized and asperity strength is controlled by low temperature Arrhenius deformation mechanisms such as crack growth and dislocation glide. This regime covers the entire brittle portion of the crust in this calculation. Below the BDT αf =0 due to the dramatically decreased strain rate; the contact area becomes complete as porosity vanishes. Accordingly friction cannot be reactivated below the BDT by increasing the pore pressure alone and requires localization. If somehow pore pressure increases and the fault localizes back to 1 mm, then brittle behavior can occur to a depth of around 35 km. This interdependence among effective stress, contact scale strain rate and pore pressure allows estimates of the conditions necessary for deep low frequency earthquakes and tremor seen on the San Andreas near Parkfield [Shelly and Hardebeck, 2010; Thomas et al., 2012] and in some subduction zones. Among the model implications are that shear in the region separating shallow earthquakes and deeper events is distributed and that the zone that hosts low frequency earthquakes involves both elevated pore fluid pressure and highly localized slip.

Citation
Beeler, N. M., Hirth, G. H., Thomas, A. M., & Bürgmann, R. (2015). Effective stress, friction and deep crustal faulting. Journal of Geophysical Research,.