Janssenʹs law and stress fluctuations in confined dry granular materials

In order to clarify the mechanisms which determine the Janssenʹs law for the pressure distribution at the bottom of a silo we reconsider the so-called q-model describing an assembly of granular particles on a lattice, confined between vertical walls. We find that the expected macroscopic behavior with the correct scaling is obtained whenever a mechanism able to transfer the weight from the interior of the silo to the walls in an efficient way is present, i.e., in mean field regime. Deviations from the Janssen lawʹs found in lattice models are due to the absence of this efficient mechanism. We investigate the scaling properties of a stick-slip model recently introduced, and find that relative fluctuations do not disappear for large systems and are of the order of average values. Finally we observe that an exponential local weight distribution at the bottom of the silo is independent of the model considered.