Person:

Rice, James

We seek to characterize the likelihood of multiple fault activation along a branched normal-fault system during earthquake rupture using dynamic finite element analyses. This is motivated by the normal faults in the vicinity of Yucca Mountain, Nevada, a potential site for a high-level radioactive waste repository. The Solitario Canyon fault (SCF), a north–south trending fault located approximately 1 km west of the crest of Yucca Mountain, is the most active of these faults. Based on the results of previous branching work by Kame et al. (2003), branch activation in the hanging wall of a normal fault such as the SCF may be possible for fast ruptures propagating near the Rayleigh-wave speed at the branch junction. Dynamic branch activation along a splay of the SCF during a seismic event could have important effects on the rupture velocity and resulting ground motions at the proposed repository site. We consider elastic as well as a pressure-dependent elastic–plastic response of the off-fault material. We find that based on the regional stress state in the area, the only likely candidates for branch activation in the hanging wall of the SCF are more steeply westward dipping intrablock splay faults. We also find that the rupture velocity for an earthquake propagating updip along the SCF must reach supershear speeds in order for dynamic branch activation to occur. Branch activation can have significant effects on the ground motions at the proposed repository site, 1 km away from the SCF beneath the crest of Yucca Mountain, causing the repository site to experience a second peak in large vertical particle velocities. Elastic–plastic response near the branch junction reduces peak ground velocities and accelerations at the proposed repository site.

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.

Flow of glacial ice in the West Antarctic Ice Sheet localizes in narrow bands of fast-flowing ice streams bordered by ridges of nearly stagnant ice, but our understanding of the physical processes that generate this morphology is incomplete. Here we study the thermal and mechanical properties of ice-stream margins, where flow transitions from rapid to stagnant over a few kilometers. Our goal is to explore under which conditions the intense shear deformation in the margin may lead to deformation-induced melting. We propose a 2-D model that represents a cross section through the ice stream margin perpendicular to the downstream flow direction. We limit temperature to the melting point to estimate melt rates based on latent heat. Using rheology parameters as constrained by laboratory data and observations, we conclude that a zone of temperate ice is likely to form in active shear margins.

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.

Material contrasts across faults are a common occurrence, and it is important to understand if these material contrasts can influence the path of rupture propagation. Here we examine models, solved numerically, of rupture propagation through one type of geometric complexity, that of a fault branch stemming from a planar main fault on which rupture initiates. This geometry, with a material contrast across the main fault, could be representative of either a mature strike-slip fault or a subduction zone interface. We consider branches in both the compressional and extensional quadrants of the fault, and material configurations in which the branch fault is in either the stier or the more compliant material and configurations with no material contrast. We find that there are regimes in which this elastic contrast can influence the rupture behavior at a branching junction, but there are also stress states for which the branch activation will not depend on the orientation of the mismatch. For the scenarios presented here, both compressional and extensional side branches are more likely to rupture if the branch is on the side of the fault with the more compliant material versus the stiffer material. The stresses induced on the branch fault, by rupture traveling on the main fault, are different for the two orientations of material contrast. We show how the interactions between rupture on the two faults determine which faults are activated.

Fault intersections are a geometric complexity that frequently occurs in nature. Here we focus on earthquake rupture behavior when a continuous planar main fault has a second fault branching off of it. We use the finite element (FE) method to examine which faults are activated and how the surrounding material responds for both elastic and elastic–plastic off-fault descriptions. Compared to an elastic model, a noncohesive elastic–plastic material, intended to account for zones of damaged rock bordering maturely slipped faults, will inhibit rupture on compressional side branches and promote rupture of extensional side branches. Activation of extensional side branches can be delayed and is triggered by continued rupture propagation on the main fault. We examine the deformation near the branching junction and find that fault opening is common for elastic materials, especially for compressional side branches. An elastic–plastic material is more realistic because elevated stresses around the propagating rupture tip and at the branching junction should bring the surrounding material to failure. With an elastic–plastic material model, fault opening is inhibited for a range of realistic material parameters. For large cohesive strengths, opening can occur, but with material softening, a real feature of plastically deforming rocks, open- ing can be prevented. We also discuss algorithmic artifacts that may arise due to the presence of such a triple junction. When opening does not occur, the behavior at the triple junction is simplified and standard contact routines in FE programs are able to properly represent the physical situation.

We consider rupture initiation and instability on a displacement-weakening interface. It is assumed to follow a power-law relation between a component of displacement discontinuity (whether tensile opening in mode I or shear slippage in modes II or III) and the reduction from peak strength of a corresponding component of stress (normal or shear stress) on the interface. That is, the stress decrease from peak strength, as the interface discontinuity develops, is assumed to be proportional to displacement-discontinuity to some exponent (n > 0). The study is done in the 2D context of plane or anti-plane strain, for an initially coherent interface which is subjected to a locally peaked “loading” stress which increases quasi-statically in time. We seek to establish the instability point, when no further quasi-static solution exists for growth of the ruptured zone along the interface, so that dynamic rupture ensues. We have previously addressed the case of linear displacement-weakening ((n = 1)), and proven the remarkable result that for an unbounded solid, the length of the displacement-weakening zone along the interface at instability is universal, in the sense of being independent of the detailed spatial distribution of the locally peaked loading stress. Present results show that such universality does not apply when (n) differs from (1). Also, if (n < 2/3), there is no phase of initially quasi-static enlargement of the rupturing zone; instead instability will occur as soon as the maximum value of the loading stress reaches the peak strength. We first employ an energy approach to give a Rayleigh–Ritz approximation for the dependence of quasi-static rupture length and maximum displacement-discontinuity on the loading stress distribution of a quadratic form. Results, depending on curvature of the loading distribution, show that qualitative features of the displacement-discontinuity development are significantly controlled by n, with the transition noted at (n = 2/3). Predictions of the simple energy approach are in reasonable quantitative agreement with full numerical solutions and give qualitative features correctly.

Elastic reciprocity and geometric symmetry are used to constrain the expressions for stresses due to introduction of line dislocations near a half-space surface. Specifically, a relationship is shown to exist between the changes induced by dislocations of orthogonal Burgers vectors (normal and parallel to the free surface). These results are used to address inconsistencies of solutions in the literature.

The mechanics of slow slip events (SSE) in subduction zones remain unresolved. We suggest that SSE nucleate in areas of unstable friction under drained conditions, but as slip accelerates dilatancy reduces pore pressure (p) quenching instability. Competition between dilatant strengthening and thermal pressurization may control whether slip is slow or fast. We model SSE with 2‐D elasticity, rate-state friction, and a dilatancy law where porosity (\phi) evolves toward steady state (\phi_{ss}) over distance (d_c) and (\phi_{ss}=\phi_0+\epsilon ln(v/v_0)); (v) is slip speed. We consider two diffusion models. Membrane diffusion (MD) is approximated by (-(p-p^{\infty})/t_f) where (p) and (p^{\infty}) are shear zone and remote pore pressure and (t_f) is a characteristic diffusion time. Homogeneous diffusion (HD) accurately models fault-normal flow with diffusivity (C_{hyd}). For MD, linearized analysis defines a boundary (\epsilon \equiv 1-a/b) between slow and fast slip, where (\epsilon \equiv f_0 \epsilon /\beta b(\sigma-p^{\infty})), (f_0), (a), and (b) are friction parameters and (\beta) is compressibility. When (\epsilon < 1-a/b) slip accelerates to instability for sufficiently large faults, whereas for (\epsilon > 1-a/b) slip speeds remain quasi-static. For (HD), (E_p\equiv \epsilon h/(\beta (\sigma-p^{\infty})\sqrt{v^\infty / C_{hyd}d_c} )) defines dilatancy efficiency, where (h) is shear zone thickness and (v^{\infty}) is plate viscosity. SSE are favored by large (\epsilon h) and low effective stress. The ratio (E_p) to thermal pressurization efficiency scales with (1/(\sigma - p^{\infty})), so high (p^{\infty}) favors SSE, consistent with seismic observations. Model updip propagation speeds are comparable to those observed along-strike. Many simulations exhibit slow phases driven by steady downdip slip and faster phases that relax the accumulated stress. Model SSE accomodate only a fraction of pale motion; the remaining deficit must be accommodated during coseismic or postseismic slip.