Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 8 October 2018 / Approved: 9 October 2018 / Online: 9 October 2018 (05:13:57 CEST)

A peer-reviewed article of this Preprint also exists.

Viallon-Galiner, L.; Combe, G.; Richefeu, V.; Picardi Faria-Atman, A. Emergence of Shear Bands in Confined Granular Systems: Singularity of the q-Statistics. Entropy 2018, 20, 862. Viallon-Galiner, L.; Combe, G.; Richefeu, V.; Picardi Faria-Atman, A. Emergence of Shear Bands in Confined Granular Systems: Singularity of the q-Statistics. Entropy 2018, 20, 862.

Journal reference: Entropy 2018, 20, 862
DOI: 10.3390/e20110862

## Abstract

The statistics of grain displacements probability distribution function (pdf) during the shear of a granular medium displays an unusual dependence with the shear increment upscaling as recently evinced [Phys. Rev. Lett. 115 238301 2015]. Basically, the pdf of grain displacements has clear nonextensive ($q$-Gaussian) features at small scales but approaches to Gaussian characteristics at large shear window scales -- the granulence 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 pdf of grain displacements and the dependency of the $q$-statistics with the shear increment. This analysis have shown a singular behavior of $q$ 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 $q$-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.

## Subject Areas

granular materials; displacement fluctuations; $q$-gaussian; strain localization

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