Localization and instability in sheared granular materials: Role of friction and vibration

The Edwards volume ensemble in cyclically sheared granular experiments

We experimentally investigate the Edwards volume ensemble in cyclically sheared bidisperse disks of two friction coefficients (μ ≈ 0.3 and μ → ∞) subjected to a range of shear amplitudes γ_m. Despite the local and global anisotropy, hysteresis, and the potential long-range correlation of the free volume, the Edwards volume ensemble surprisingly provides an excellent statistical description of disk packings in cyclically sheared systems. Our finding can be better understood from the comprehensive analysis of the geometric and statistical properties of Voronoi cells of individual particles. First, the average degrees of anisotropy of Voronoi cells are weak at both the microscopic and macroscopic scales within a range of shear amplitudes γ_m of up to γ_m = 12% regardless of the inter-particle friction coefficients μ even though the azimuthal distributions of the Voronoi cell depend on μ. Second, there is only negligible hysteresis of global compactivity and volume fluctuations. Finally, the spatial correlations of the free volume and the orientation are weakly anisotropic and short ranged for practical purposes. Both results are independent of μ. Interestingly, our free-volume statistical results are consistent with the simple physical picture that the free volume is directly proportional to the compactivity.

Strain localization in dry sheared granular materials: A compactivity-based approach

Shear banding is widely observed in natural fault zones as well as in laboratory experiments on granular materials. Understanding the dynamics of strain localization under different loading conditions is essential for quantifying strength evolution of fault gouge and energy partitioning during earthquakes and characterizing rheological transitions and fault zone structure changes. To that end, we develop a physics-based continuum model for strain localization in sheared granular materials. The grain-scale dynamics is described by the shear transformation zone (STZ) theory, a nonequilibrium statistical thermodynamic framework for viscoplastic deformation in amorphous materials. Using a finite strain computational framework, we investigate the initiation and growth of complex shear bands under a variety of loading conditions and identify implications for strength evolution and the ductile to brittle transition. Our numerical results show similar localization patterns to field and laboratory observations and suggest that shear zones show more ductile response at higher confining pressures, lower dilatancy, and loose initial conditions. Lower pressures, higher dilatancy, and dense initial conditions favor a brittle response and larger strength drops. These findings shed light on a range of mechanisms for strength evolution in dry sheared granular materials and provide a critical input to physics-based multiscale models of fault zone instabilities.