A Multiscale Model of Shear flow of Granular Materials with Breakable Particles: Role of Force Chain Instabilities and Implications for Strain Localization and Stability of Sliding

Abstract:

Quantitative prediction of the shear response and energy partitioning in granular layers with breakable particles remains a major challenge in earthquake physics. As a first step towards addressing this problem, we use the Shear Transformation Zone theory (STZ) to model irreversible plastic deformations in the gouge due to local rearrangements of the particles. To model grain breakage, we use an energy balance approach to augment the STZ theory with an equation for the grain size reduction as a function of the applied work rate and pressure.

Previous numerical and experimental work on grain breakage was inconclusive regarding whether grain breakage was a softening or a hardening mechanism. The outcome depends on the competition between evolving grain angularity and reduced particle size with both processes affecting force chain dynamics. To account for local force chain instabilities, we develop a small scale model for force chain buckling that is integrated within the STZ formulation through variations of the minimum flow stress of the system. We idealize a typical force chain as an array of particles with both translational and rotational degrees of freedom. The relative motion between the particles is resisted by sliding and rolling friction. The sliding friction is provided by a rigid-plastic element. The rolling resistance is modeled by a torsional spring. The deflection of the force chain is resisted by an array of lateral springs representing the effective confinement provided by the rest of the granular medium

Our results suggest that there exist a critical grain size below which the buckling stress for the force chain, and hence the flow stress, decreases linearly with the decrease of the particle size. Furthermore, we show that grain breakage is a potential weakening mechanism at high pressures and at strain rates high enough to reduce the grain size below the aforementioned critical limit. Grain breakage also promotes strain localization, particularly in compact layers, and may explain the long term persistence of shear bands in natural faults due to the permanent change in the layer fabric resulting from comminution. We discuss the implications of these findings on the stability of sliding of natural faults and earthquake energy budget.