Force correlations and arches formation in granular assemblies

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, $P(v)\sim v^α\exp(-v/ϕ)$, strongly depend on the spatial extensions, $ξ_V$, 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, $ϕ(ξ_V)$, and the small forces power law exponent, $α(ξ_V)$, depend on the correlation length, $ξ_V$. If correlations go to infinity, weights are power law distributed.