Robert C. Viesca

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 …

We examine the circular, self-similar expansion of frictional rupture due to fluid injected at a constant rate. In a prior problem [Viesca, 2021], the author examined rupture of a planar frictional fault driven by line source of fluid injected at constant pressure. Here, fluid injection occurs at constant volumetric rate at a point on the fault and fluid migration occurs within a thin, relatively permeable layer containing and parallel to the fault plane. For the particular case when the Poisson ratio , self-similarity of the fluid pressure profile implies that fault slip will also evolve in an axisymmetric, self-similar manner, reducing the three-dimensional problem for the spatiotemporal evolution of fault slip to a single self-similar dimension. The rupture radius grows as , where is time since the start of injection, is the hydraulic diffusivity of the pore fluid pressure, and is a prefactor determined by a single parameter, , which depends on the pre-injection stress state and injection conditions. The prefactor has the range , where the lower and upper limits of correspond to, respectively marginal pressurization of the fault and critically stressed conditions, in which the fault-resolved shear stress is close to the pre-injection fault strength. In both limits of , we derive asymptotic solutions for the slip by perturbation expansion, to arbitrary order. For the critically stressed limit, the solution for slip contains an interior boundary layer and an outer solution. We perform a matched asymptotic expansion to provide a composite solution with uniform convergence over the entire rupture. The leading order of these solutions was recently used by Saez et al. [2022] to …

We assess if a characteristic length for a non-linear 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 a 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.

Microseismicity associated with fluid pressurization in the subsurface occurs during fluid injection but can also be triggered after injection shut‐in. Understanding the extent and duration of the post‐injection microseismicity is critical to limit the risk of fluid‐induced seismicity and insure the safe utilization of the subsurface. Using theoretical and numerical techniques, we investigated how aseismic slip on a fault plane evolves and stops after a fluid pressurization event. We found that the locking mechanisms controlling the arrest of aseismic slip highly depend on the initial fault stress criticality and the pressurization duration. The absolute arrest time of fault aseismic slip after injection shut‐in is proportional to the pressurization duration and increases significantly with the initial fault stress criticality. Given that microseismicity can be triggered by aseismic slip, these results provide insights into the mechanics controlling …

We investigate the quasi-static growth of a fluid-driven frictional shear crack that propagates in mixed mode (II+ III) on a planar fault interface that separates two identical half-spaces of a three-dimensional solid. The fault interface is characterized by a shear strength equal to the product of a constant friction coefficient and the local effective normal stress. Fluid is injected into the fault interface and two different injection scenarios are considered: injection at constant volume rate and injection at constant pressure. We derive analytical solutions for circular ruptures which occur in the limit of a Poisson’s ratio ν= 0 and solve numerically for the more general case in which the rupture shape is unknown (ν≠ 0). For an injection at constant volume rate, the fault slip growth is self-similar. The rupture radius (ν= 0) expands as R (t)= λ L (t), where L (t) is the nominal position of the fluid pressure front and λ is an amplification factor …

There is scientific and industrial interest in understanding how geologic faults respond to transient sources of fluid. Natural and artificial sources can elevate pore fluid pressure on the fault frictional interface, which may induce slip. We consider a simple boundary value problem to provide an elementary model of the physical process and to provide a benchmark for numerical solution procedures. We examine the slip of a fault that is an interface of two elastic half-spaces. Injection is modelled as a line source at constant pressure and fluid pressure is assumed to diffuse along the interface. The resulting problem is an integro-differential equation governing fault slip, which has a single dimensionless parameter. The expansion of slip is self-similar and the rupture front propagates at a factor , in the regime of a so-called critically stressed fault, a boundary layer emerges on the diffusive length scale, which lags far behind …

Injection-induced seismicity is usually observed as an enlarging cloud of seismic events that grows in a diffusive manner around the injection zone. These observations are commonly interpreted as the triggering of instabilities in pre-existing fractures and faults due to the direct effect of pore pressure increase (Shapiro, 2015), whereas poroelastic stressing is usually associated with the occurrence of seismic events beyond the plausible zone affected by pore pressure diffusion (Segall and Lu, 2015). However, an alternative triggering mechanism based on the elastic transfer of stress due to injection-induced aseismic slip has been recently proposed (Viesca, 2015; Guglielmi et al, 2015). Previous studies have shown that in critically stressed faults, the aseismic rupture front can outpace fluid diffusion (Garagash and Germanovich, 2012; Bhattacharya and Viesca, 2019), and in turn be the primary cause that controls the …

Fluid pressurization of preexisting faults due to subsurface energy and storage applications can lead to the onset of aseismic slip and microseismicity, and possibly to major induced seismic events. Fluid injection decreases the fault shear strength and slip occurs when the in situ shear stress on the fault exceeds its shear strength. The nature of slip (aseismic or seismic) depends on the rate at which it occurs and thus on the stability of the deformation. Understanding the mechanics controlling the onset and arrest of aseismic slip and the transition to seismic slip is therefore key to design mitigation strategies for the safe utilization of the subsurface. In this contribution, we investigate using theoretical and numerical techniques how aseismic slip on a fault plane nucleates, evolves and stops in response to fluid pressurization and its relaxation. We analyze the impacts of the stress regime and the duration of the …