Emergence of Shear Bands in Confined Granular Systems: Singularity of the q -Statistics

The statistics of grain displacements probability distribution function (<i>pdf</i>) during the shear of a granular medium displays an unusual dependence with the shear increment upscaling as recently evinced (see &#8220;experimental validation of a nonextensive scaling law in confined granular media&#8222;). Basically, the <i>pdf</i> of grain displacements has clear nonextensive (<i>q</i>-Gaussian) features at small scales, but approaches to Gaussian characteristics at large shear window scales&#8212;the <i>g</i>ranulence effect. Here, we extend this analysis studying a larger system (more grains considered in the experimental setup), which exhibits a severe shear band fault during the macroscopic straining. We calculate the <i>pdf</i> of grain displacements and the dependency of the <i>q</i>-statistics with the shear increment. This analysis has shown a singular behavior of <i>q</i> at large scales, displaying a non-monotonic dependence with the shear increment. By means of an independent image analysis, we demonstrate that this singular non-monotonicity could be associated with the emergence of a shear band within the confined system. We show that the exact point where the <i>q</i>-value inverts its tendency coincides with the emergence of a giant percolation cluster along the system, caused by the shear band. We believe that this original approach using Statistical Mechanics tools to identify shear bands can be a very useful piece to solve the complex puzzle of the rheology of dense granular systems.

Abstract licence: CC BY

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