Stochastic Methods for Slip Detection in a Sheared Granular System

Abstract

We develop a flexible methodology for predicting slip events in a sheared granular system. The considered system consists of two-dimensional soft disks between two rigid horizontal walls, where the top wall is exposed to downward pressure and horizontal elastic shearing force, resulting in intermittent stick-slip regimes. The prediction methodology first uses topological data analysis to compute the persistent homology between successive force networks of the system and then quantifies the topological change by placing a metric between the respective persistence diagrams, resulting in a time series. Next, we construct a Bayesian stochastic state space model, which describes the behavior of the time series during the stick regime. We also create similar models for the stick regime behavior of the time series of more traditional measures on the granular system. A model identifies departure from the stick regime by detecting when the predictive error exceeds a specified threshold. The resulting detections demonstrate that this approach can detect the slip events in advance, with further investigation revealing a rough sequence of events. First, a local change appears in the force network and either dissipates or spreads globally. Next, the global change either triggers a slip event or a much smaller ‘micro-slip,’ depending on if its magnitude exceeds a critical threshold.