Evolution of force networks during stick-slip motion of an intruder in a granular material: Topological measures extracted from experimental data

In quasi-two-dimensional experiments with photoelastic particles confined to an annular region, an intruder constrained to move in a circular path halfway between the annular walls experiences stick-slip dynamics. We discuss the response of the granular medium to the driven intruder, focusing on the evolution of the force network during sticking periods. Because the available experimental data do not include precise information about individual contact forces, we use an approach developed in our previous work [Basak et al., J. Eng. Mech. 147, 04021100 (2021)0733-939910.1061/(ASCE)EM.1943-7889.0002003] based on networks constructed from measurements of the integrated strain magnitude on each particle. These networks are analyzed using topological measures based on persistence diagrams, revealing that force networks evolve smoothly but in a nontrivial manner throughout each sticking period, even though the intruder and granular particles are stationary. Characteristic features of persistence diagrams show identifiable slip precursors. In particular, the number of generators describing the structure and complexity of force networks increases consistently before slips. Key features of the dynamics are similar for granular materials composed of disks or pentagons, but some details are consistently different. In particular, we find significantly larger fluctuations of the measures computed based on persistence diagrams and, therefore, of the underlying networks, for systems of pentagonal particles.

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.