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Abstract.Reexamination

Field and laboratory observations indicate that at seismic slip rates most shearing is confined to a very narrow zone, just a few tens to hundreds of microns wide, and sometimes as small as a few microns. Rice et al. (2014) analyzed the stability of uniform shear in a fluid‐saturated gouge material. They considered two distinct mechanisms to limit localization to a finite thickness zone, rate‐strengthening friction, and dilatancy. In this paper we use numerical simulations to extend beyond the linearized perturbation context in Rice et al. (2014), and study the behavior after the loss of stability. Neglecting dilatancy we find that straining localizes to a width that is almost independent of the gouge layer width, suggesting that the localized zone width is set by the physical properties of the gouge material. Choosing parameters thought to be representative of a crustal depth of 7 km, this predicts that deformation should be confined to a zone between 4 and 44 μm wide. Next, considering dilatancy alone we again find a localized zone thickness that is independent of gouge layer thickness. For dilatancy alone we predict localized zone thicknesses between 1 and 2 μm wide for a depth of 7 km. Finally, we study the impact of localization on the shear strength and temperature evolution of the gouge material. Strain rate localization focuses frictional heating into a narrower zone, leading to a much faster temperature rise than that predicted when localization is not accounted for. Since the dynamic weakening mechanism considered here is thermally driven, this leads to accelerated dynamic weakening.

Field observations of major earthquake fault zones show that shear deformation is often confined to principal slipping zones that may be of order 1–100 μm wide, located within a broader gouge layer of order 10–100 mm wide. This paper examines the possibility that the extreme strain localization observed may be due to the coupling of shear heating, thermal pressurization, and diffusion. In the absence of a stabilizing mechanism shear deformation in a continuum analysis will collapse to an infinitesimally thin zone. Two possible stabilizing mechanisms, studied in this paper, are rate‐strengthening friction and dilatancy. For rate‐strengthening friction alone, a linear stability analysis shows that uniform shear of a gouge layer is unstable for perturbations exceeding a critical wavelength. Using this critical wavelength we predict a width for the localized zone as a function of the gouge properties. Taking representative parameters for fault gouge at typical centroidal depths of crustal seismogenic zones, we predict localized zones of order 5–40 μm wide, roughly consistent with field and experimental observations. For dilatancy alone, linearized strain rate perturbations with a sufficiently large wavelength will undergo transient exponential growth before decaying back to uniform shear. The total perturbation strain accumulated during this transient strain rate localization is shown to be largely controlled by a single dimensionless parameter E, which is a measure of the dilatancy of the gouge material due to an increase in strain rate.

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.

[1] Detailed observations of compaction bands exposed in the Aztec Sandstone of southeastern Nevada indicate that these thin, tabular, bounded features of localized porosity loss initiated at pervasive grain-scale flaws, which collapsed in response to compressive tectonic loading. From many of these Griffith-type flaws, an apparently self-sustaining progression of collapse propagated outward to form bands of compacted grains a few centimeters thick and tens of meters in planar extent. These compaction bands can be idealized as highly eccentric ellipsoidal bodies that have accommodated uniform uniaxial plastic strain parallel to their short dimension within a surrounding elastic material. They thus can be represented mechanically as contractile Eshelby inclusions, which generate near-tip compressive stress concentrations consistent with self-sustaining, in-plane propagation. The combination of extreme aspect ratio ($10 À4 ) and significant uniaxial plastic strain ($10%) also justifies an approximation of the bands as anticracks: sharp boundaries across which a continuous distribution of closing mode displacement discontinuity has been accommodated. This anticrack interpretation of compaction bands is analogous to that of pressure solution surfaces, except that porosity loss takes the place of material dissolution. We find that displacement discontinuity boundary element modeling of compaction bands as anticracks within a two-dimensional linear elastic continuum can accurately represent the perturbed external stress fields they induce.

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