On the existence of a nucleation length for dynamic shear rupture

We assess if a characteristic length for an interfacial slip instability follows from theoretical descriptions of sliding friction. We examine friction laws and their coupling with the elasticity of bodies in contact and show that such a length does not always exist. We consider a range of descriptions for frictional strength and show that the area needed to support an interfacial slip instability is negligibly small for laws that are more faithful to experimental data. This questions whether a minimum earthquake size exists and shows that the nucleation phase of dynamic rupture contains discriminatory information on the nature of frictional strength evolution.Comment: 5 pages, 4 figures, and supplementary materia

Elastic Reciprocity and Symmetry Constraints on the Stress Field Due to a Surface-Parallel Distribution of Dislocations

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.Earth and Planetary SciencesEngineering and Applied Science

Nucleation of Slip-Weakening Rupture Instability in Landslides by Localized Increase of Pore Pressure

We model landslide initiation as slip surface growth driven by local elevated pore pressure, with particular reference to submarine slides. Assuming an elastic medium and friction that weakens with slip, solutions exist in which the slip surface may dynamically grow, without further pore pressure increases, at a rate of the order of the sediment shear wave speed, a situation comparable to earthquake nucleation. The size of the rupture at this transition point depends weakly on the imposed pore pressure pro file; however, the amount of slip at the transition depends strongly on whether the pore pressure was broadly or sharply elevated. Sharper profiles may result in pore pressures reaching the total slope-normal stress before dynamic rupture is nucleated. While we do not account for modes of failure other than pure slip on a failure surface, this may be an indication that additional modes involving liquefaction or hydraulic cracking may be factors in the initiation of shallow slope failure. We identify two lengthscales, one geometrical (h, depth below the free surface) and one material (l, determined by the frictional weakening rate) and a transition in nucleation behavior between effectively "deep" and "shallow" limits dependent on their ratio. Whether dynamic propagation of failure is indefinite or arresting depends largely on whether the background shear stress is closer to nominal peak or residual frictional strength. This is determined in part by background pore pressures, and to consider the submarine case we simplify a common sedimentation/consolidation approach to reflect interest in near-seafloor conditions.Earth and Planetary SciencesEngineering and Applied Science

Off-Fault Plasticity and Earthquake Rupture Dynamics: 2. Effects of Fluid Saturation

We present an analysis of inelastic off-fault response in fluid-saturated material during earthquake shear rupture. The analysis is conducted for 2-D plane strain deformation using an explicit dynamic finite element formulation. Along the fault, linear slip-weakening behavior is specified, and the off-fault material is described using an elastic-plastic description of the Drucker-Prager form, which characterizes the brittle behavior of rocks under compressive stress when the primary mode of inelastic deformation is frictional sliding of fissure surfaces, microcracking and granular flow. In this part (part 1), pore pressure changes were neglected in materials bordering the fault. In part 2, we more fully address the effects of fluid saturation. During the rapid stressing by a propagating rupture, the associated undrained response of the surrounding fluid-saturated material may be either strengthened or weakened against inelastic deformation. We consider poroelastoplastic materials with and without plastic dilation. During nondilatant undrained response near a propagating rupture, large increases in pore pressure on the compressional side of the fault decrease the effective normal stress and weaken the material, and decreases in pore pressure on the extensional side strengthen the material. Positive plastic dilatancy reduces pore pressure, universally strengthening the material. Dilatantly strengthened undrained deformation has a diffusive instability on a long enough timescale when the underlying drained deformation is unstable. Neglecting this instability on the short timescale of plastic straining, we show that undrained deformation is notably more resistant to shear localization than predicted by neglect of pore pressure changes.Earth and Planetary SciencesEngineering and Applied Science

The fracture energy of ruptures driven by flash heating

We present a model for dynamic weakening of faults based on local flash heating at microscopic asperity contacts coupled to bulk heating at macroscopic scale. We estimate the fracture energy G associated with that rheology and find that for constant slip rate histories G scales with slip δ as math formula at small slip, while math formula at large slip. This prediction is quantitatively consistent with data from laboratory experiments conducted on dry rocks at constant slip rate. We also estimate G for crack-like ruptures propagating at constant speed and find that math formula in the large slip limit. Quantitative estimates of G in that regime tend to be several orders of magnitude lower than seismologically inferred values of G. We conclude that while flash heating provides a consistent explanation for the observed dynamic weakening in laboratory experiments with kinematically imposed slip, its contribution to the energy dissipation during earthquakes becomes negligible for large events when considering the elastodynamic coupling between strength and slip evolution

Propagation of extended fractures by local nucleation and rapid transverse expansion of crack-front distortion

Fractures are ubiquitous and can lead to the catastrophic material failure of materials. Although fracturing in a two-dimensional plane is well understood, all fractures are extended in and propagate through three-dimensional space. Moreover, their behaviour is complex. Here we show that the forward propagation of a fracture front occurs through an initial rupture, nucleated at some localized position, followed by a very rapid transverse expansion at velocities as high as the Rayleigh-wave speed. We study fracturing in a circular geometry that achieves an uninterrupted extended fracture front and use a fluid to control the loading conditions that determine the amplitude of the forward jump. We find that this amplitude correlates with the transverse velocity. Dynamic rupture simulations capture the observations for only a high transverse velocity. These results highlight the importance of transverse dynamics in the forward propagation of an extended fracture

Fluid-induced faulting

Subsurface fluid injection is often followed by observations of an enlarging cloud of microseismicity. The cloudâ s diffusive growth is thought to be a direct response to the diffusion of elevated pore fluid pressure reaching pre-stressed faults, triggering small instabilities; the observed high rates of this growth are interpreted to reflect a relatively high permeability of a fractured subsurface [e.g., Shapiro, GJI 1997]. We investigate an alternative mechanism for growing a microseismic cloud: the elastic transfer of stress due to slow, aseismic slip on a subset of the pre-existing faults in this damaged subsurface. We show that the growth of the slipping region of the fault may be self-similar in a diffusive manner. While this slip is driven by fluid injection, we show that, for critically stressed faults, the apparent diffusion of this slow slip may quickly exceed the poroelastically driven diffusion of the elevated pore fluid pressure. We also examine recent field injection experiments providing time series, measured at the borehole, of both fluid pressure as well as the relative displacement of a fault cross-cutting the borehole [Guglielmi et al., 2015]. We couple a hydrogeologic model for fluid flow from the borehole with a model for an expanding shear rupture of the fault. We find that such a model reproduces the observed time history, with a Bayesian inversion providing uncertainties of the model parameters for host rock stiffness and frictional strength, fault zone storage and permeability, as well as the pre-injection stress state. Remarkably, we also find that the inferred rupture front outpaces the region of significant pore pressure increase.Non UBCUnreviewedAuthor affiliation: Tufts UniversityOthe

Slow slip and self-similar asymptotics of rate-strengthening faults

International audienc

The slow slip of viscous faults

We examine a simple mechanism for the spatio-temporal evolution of transient, slow slip. We consider the problem of in-plane or anti-plane slip on a fault that lies within an elastic continuum and whose strength is proportional to sliding rate. This rate dependence may correspond to a viscously deforming shear zone or the linearization of a non-linear, rate-dependent fault strength. We examine the response of such a fault to external forcing, such as local increases in shear stress or pore fluid pressure. We show that the slip and slip rate are governed by a type of diffusion equation, the solution of which may be found by using a Green’s function approach. We derive the appropriate long-time, self-similar asymptotic expansion for slip or slip rate, which depend on both time t and a similarity coordinate η = x/t, where x denotes fault position. The similarity coordinate shows a departure from classical diffusion and is owed to the non-local nature of elastic interaction among points on an interface between elastic half-spaces. We demonstrate the solution and asymptotic analysis of several example problems. Following sudden impositions of loading, we show that slip rate ultimately decays as 1/t while spreading proportionally to t, implying both a logarithmic accumulation of displacement as well as a constant moment rate. We discuss the implication for models of post-seismic slip as well as spontaneously emerging slow slip events