J. Phys. I France
Volume 7, Numéro 12, December 1997
Page(s) 1541 - 1558
DOI: 10.1051/jp1:1997155
J. Phys. I France 7 (1997) 1541-1558

Stochastic Aspects of the Force Network in a Regular Granular Piling

Christophe Eloy and Éric Clément

Laboratoire des Milieux Désordonnés et Hétérogènes URA 800 CNRS, B. 86, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France

(Received 14 May 1997, received in final form 25 July 1997, accepted 5 August 1997)

We study the influence of solid friction on the structure of the force network sustaining a regular bidimensional granular piling. We show how the mechanical equations describing local equilibrium may couple naturally with a stochastic variable. A Monte Carlo method is designed to extract the force networks satisfying static equilibrium conditions. A statistical ensemble is constructed and we study some of its structural and stochastic properties. We address, in particular, the question of the vertical load transfer in two different cases i.e. the response to a localized force excess at the top of an horizontal piling and the distribution of forces under a sand pile. Using this very simple mechanical model, we test the validity of the passage to various stochastic descriptions as well as the existence of macroscopic constitutive relations. We also address the question of the influence of a local friction bias on the macroscopic static equilibrium conditions.

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