Instabilities in a two-dimensional granular fault gouge: Particle dynamics and stress fluctuations

Predicting stress fluctuations in granular media under steady-state shear loading is crucial for applications ranging from geophysical processes to construction engineering. Stress fluctuations emerge from particle rearrangement, usually enabled by frictional slip and force-chain buckling. Existing models used to predict stress fluctuations are largely phenomenological, often accounting for the force chain phenomena implicitly through the introduction of internal variables, or explicitly through assumptions of force chain mechanics. Improper consideration of particle mechanics or mesoscale effects can lead to inaccurate predictions of shear strength and instability, making it difficult to predict the onset of yielding, shear band formation, and other instabilities. Furthermore, while recent advancements in machine learning methods have established links between microscale behavior and macroscopic stress drops in granular fault gouges, their predictive capabilities are limited due to their black-box nature. To gain a deeper understanding of stress fluctuations, and ultimately predict them in a physics-informed manner, it is necessary to examine how system energetics change with stress fluctuations. In this paper, we analyze stress fluctuations in a 2D granular fault gouge loaded under quasistatic, steady-state shear. We track the flow of potential energy between force networks and understand how energy and force networks vary with stress rises and drops. We derive an analytical, dynamic force chain model from first principles to illustrate how interactions between force networks lead to the emergence of localized instability phenomena. Finally, we offer insights into how these localized instabilities ultimately enable shear stress fluctuations at the continuum scale.