Stabilization of rapid frictional slip on a weakening fault by dilatant hardening

Abstract

Frictional slip is often accompanied by dilatancy due to uplift in sliding over asperities and micro‐cracking in the adjacent material. If dilatancy occurs more rapidly than pore fluid can flow into the newly created void space, the local pore pressure is reduced and the effective normal stress is increased in compression, tending to inhibit further slip. This dilatant hardening is analyzed for a simple model. One surface of a slab is loaded by compressive stress and shear displacement and connected to a reservoir of pore fluid held at constant pressure. The other boundary is a frictional surface, assumed to have formed at peak stress, on which the shear stress decreases from a peak value τp to a residual value τr as slip increases from zero to δ0. In the absence of pore fluid effects an instability corresponding to an unbounded slip rate occurs when the slope of the shear stress versus slip relation is more negative than the unloading stiffness of the surrounding material. Dilatant hardening prevents this instability provided that the pore pressure in the reservoir is high enough. If the pressure in the reservoir is too low, the pressure at the fault surface can be reduced to the point at which the pore fluid bulk modulus decreases rapidly, eliminating the stabilizing effect. When the analysis is modified to include normal stress changes simulating those in the axisymmetric compression test, the prediction of the critical pressure in the reservoir agrees to within a factor of 2 or 3 with that observed by Martin in tests on Westerly granite. The predictions are also consistent with the trends observed by Martin of decreasing critical reservoir pore pressure with increasing effective confining stress and decreasing nominal strain rate.

Effects of normal stress variations on frictional stability of a fluid‐infiltrated fault

“…Hence the second term on the right-hand side of (7) are (using the parameters of section 2.8) (in MPa mm -1) 1.69 x 10 -2for normal geometry, 7.50 x 10 -2 for strikeslip geometry, and 1.89 x 10 -1 for reverse geometry. As found by Rudnicki and Chen [ 1988], the geometric coupling thus has a strong influence on the stability of the drained system: the critical stiffnesses vary by a factor of more than 10 between normal and reverse geometries. With the value of 10 -2MPa mm -1 that we estimated for the spring stiffness, all the three geometries would be unstable.…”

The Mechanical Coupling of Fluid-Filled Granular Material Under Shear

“…Similar formulations also appear in Iverson [1993], Rudnicki and Chen [1988], Miller and Nur [2000], Snieder and van der Beukel [2004] and Samuelson et al [2009].…”

“…While undrained conditions have shown to cause liquefaction when loading a loose specimen, they are also believed to cause hardening by pore volume increase (dilation) and pore pressure decrease when loading a densely packed layer [Rudnicki andChen, 1988, Scholz, 2002]. Moore and Iverson [2002] performed stress-controlled shear experiments of dilative saturated granular layers.…”

“…When the fault is sealed, porosity increase (i.e. dilation) during shear is often suggested to prohibit unstable sliding via pore pressure reduction leading to strain hardening following equation (2) [Scholz et al, 1973, Scholz, 1978, Rudnicki and Chen, 1988, Segall and Rice, 1995, Moore and Iverson, 2002, Scholz, 2002, Samuelson et al, 2009, while compaction of under-compacted gouge was shown experimentally to lead to extreme weakening and unstable sliding [Blanpied et al, 1992].…”

Volume fraction variations and dilation in colloids and granulars

“…In the geophysical literature, for example, dilation hardening has been suggested as important in earthquake response (e.g. Whitcomb et al 1973;Rice 1975;Rudnicki & Rice 1975;Rudnicki & Chen 1988). Highly shear-stressed regions of porous rocks or soil must first dilate to allow shear deformation.…”