Seismicity in sheared granular matter

Hidden jerk in universal creep and aftershocks

Most materials exhibit creep memory under the action of a constant load. The memory behavior is governed by Andrade's creep law, which also has an inherent connection with the Omori-Utsu law of earthquake aftershocks. Both empirical laws lack a deterministic interpretation. Coincidentally, the Andrade law is similar to the time-varying part of the creep compliance of the fractional dashpot in anomalous viscoelastic modeling. Consequently, fractional derivatives are invoked, but since they lack a physical interpretation, the physical parameters of the two laws extracted from curve fit lack confidence. In this Letter, we establish an analogous linear physical mechanism that underlies both laws and relates its parameters with the material's macroscopic properties. Surprisingly, the explanation does not require the property of viscosity. Instead, it necessitates the existence of a rheological property that relates strain with the first order time derivative of stress, which involves jerk. Further, we justify the constant quality factor model of acoustic attenuation in complex media. The obtained results are validated in light of the established observations.

Sheared granular matter and the empirical relations of seismicity

The frictional instability associated with earthquake initiation and earthquake dynamics is believed to be mainly controlled by the dynamics of fragmented rocks within the fault gauge. Principal features of the emerging seismicity (e.g., intermittent dynamics and broad time and/or energy scales) have been replicated by simple experimental setups, which involve a slowly driven slider on top of granular matter, for example. Yet these setups are often physically limited and might not allow one to determine the underlying nature of specific features and, hence, the universality and generality of the experimental observations. Here, we address this challenge by a numerical study of a spring-slider experiment based on two-dimensional discrete element method simulations, which allows us to control the properties of the granular matter and of the surface of the slider, for example. Upon quasistatic loading, stick-slip-type behavior emerges which is contrasted by a stable sliding regime at finite driving rates, in agreement with experimental observations. Across large parameter ranges for damping, interparticle friction, particle polydispersity, etc., the earthquake-like dynamics associated with the former regime results in several robust scale-free statistical features also observed in experiments. At first sight, these closely resemble the main empirical relations of tectonic seismicity at geological scales. This includes the Gutenberg-Richter distribution of event sizes, the Omori-Utsu-type decay of aftershock rates, as well as the aftershock productivity relation and broad recurrence time distributions. Yet, we show that the correlations associated with tectonic aftershocks are absent such that the origin of the Omori-Utsu relation, the aftershock productivity relation, and Båth's relation in the simulations is fundamentally different from the case of tectonic seismicity. This, we believe, is mainly due to a lack of macroscale relaxation processes that are closely tied to the generation of real aftershocks. We argue that the same is true for previous laboratory experiments.

Controlling crackling dynamics by triggering low-intensity avalanches

We examine the effect of small, spatially localized excitations applied periodically in different manners, on the crackling dynamics of a brittle crack driven slowly in a heterogeneous solid. When properly adjusted, these excitations are observed to radically modify avalanche statistics and considerably limit the magnitude of the largest events. Surprisingly, this does not require information on the front loading state at the time of excitation; applying it either at a random location or at the most loaded point gives the same results. Subsequently, we unravel how the excitation amplitude, spatial extent, and frequency govern the effect. We find that the excitation efficiency is ruled by a single reduced parameter, namely the injected power per unit front length; the suppression of extreme avalanches is maximum at a well-defined optimal value of this control parameter. analysis opens another way to control the largest events in crackling dynamics. Beyond fracture problems, it may be relevant for crackling systems described by models of the same universality class, such as the wetting of heterogeneous substrates or magnetic walls in amorphous magnets.

Dilation as a precursor in a continuous granular fault

We analyze the dilation of the system in a cylindrical granular fault consisting of one single layer of disks submitted to both normal pressure and continuous and slow shear, which results in intermittent and sudden energy release events that reproduce the main laws of seismicity. The dilation of the system can be separated into two parts: a smooth increase of dilation, plus sudden changes both contracting and dilating the medium, which are correlated to abrupt jumps -both positive and negative- in the measured resisting torque. We explain the four possible (and existing) general scenarios combining those two variables: dilation jumps and torque jumps, thanks to the assumption of an optimal local angle in the direction of force chains, and each reorganization of the structure as a replacement of the force chain holding most of the applied stress. The average rate of increase of global dilation varies monotonically with the size of the energy release event, making dilation a plausible candidate to predict catastrophic events in such earthquake-like systems.

Correlating the force network evolution and dynamics in slider experiments

The experiments involving a slider moving on top of granular media consisting of photoelastic particles in two dimensions have uncovered elaborate dynamics that may vary from continuous motion to crackling, periodic motion, and stick-slip type of behavior. We establish that there is a clear correlation between the slider dynamics and the response of the force network that spontaneously develop in the granular system. This correlation is established by application of the persistence homology that allows for formulation of objective measures for quantification of time-dependent force networks. We find that correlation between the slider dynamics and the force network properties is particularly strong in the dynamical regime characterized by well-defined stick-slip type of dynamics.

Acoustic localisation in a two-dimensional granular medium

We focus on localizing the source of acoustic emissions within a compressed two-dimensional granular ensemble of photoelastic disks, having as main information the arrival times of the acoustic signal to 6 sensors located in the boundaries of the system. By estimating, thanks to the photoelasticity of the grains, the wave speed at every point of the structure, we are able to compute the arrival times from every point of the system to the sensors. A comparison between the arrival time differences between every set of computed values to those from the actual measurements allows finding the source of the acoustic emissions.

Asymmetric Damage Avalanche Shape in Quasibrittle Materials and Subavalanche (Aftershock) Clusters

Crackling dynamics is characterized by a release of incoming energy through intermittent avalanches. The shape, i.e., the internal temporal structure of these avalanches, gives insightful information about the physical processes involved. It was experimentally shown recently that progressive damage toward compressive failure of quasibrittle materials can be mapped onto the universality class of interface depinning when considering scaling relationships between the global characteristics of the microcracking avalanches. Here we show, for three concrete materials and from a detailed analysis of the acoustic emission waveforms generated by microcracking events, that the shape of these damage avalanches is strongly asymmetric, characterized by a very slow decay. This remarkable asymmetry, at odds with mean-field depinning predictions, could be explained, in these quasibrittle materials, by retardation effects induced by enhanced viscoelastic processes within a fracture process zone generated by the damage avalanche as it progresses. It is associated with clusters of subavalanches, or aftershocks, within the main avalanche.

Seismiclike organization of avalanches in a driven long-range elastic string as a paradigm of brittle cracks

Crack growth in heterogeneous materials sometimes exhibits crackling dynamics, made of successive impulselike events with specific scale-invariant time and size organization reminiscent of earthquakes. Here, we examine this dynamics in a model which identifies the crack front with a long-range elastic line driven in a random potential. We demonstrate that, under some circumstances, fracture grows intermittently, via scale-free impulse organized into aftershock sequences obeying the fundamental laws of statistical seismology. We examine the effects of the driving rate and system overall stiffness (unloading factor) onto the scaling exponents and cutoffs associated with the time and size organization. We unravel the specific conditions required to observe a seismiclike organization in the crack propagation problem. Beyond failure problems, implications of these results to other crackling systems are finally discussed.