Force correlations and arches formation in granular assemblies

TL;DR

This paper investigates how spatial correlations influence force transmission and arch formation in granular assemblies, revealing that microscopic correlations significantly affect macroscopic force distributions and structural properties.

Contribution

It introduces a scalar model linking spatial force correlations to force distribution parameters, highlighting the dependence of force statistics on correlation length.

Findings

Force distribution parameters depend on correlation length.

As correlations increase, force weights tend toward a power-law distribution.

Macroscopic force behavior is connected to microscopic correlation mechanisms.

Abstract

In the context of a simple microscopic schematic scalar model we study the effects of spatial correlations in force transmission in granular assemblies. We show that the parameters of the normalized weights distribution function, $P(v)\sim v^{\alpha}\exp(-v/\phi)$, strongly depend on the spatial extensions, $\xi_V$, of such correlations. We show, then, the connections between measurable macroscopic quantities and microscopic mechanisms enhancing correlations. In particular we evaluate how the exponential cut-off, $\phi(\xi_V)$, and the small forces power law exponent, $\alpha(\xi_V)$, depend on the correlation length, $\xi_V$. If correlations go to infinity, weights are power law distributed.