Stress response function of a two-dimensional ordered packing of frictional beads
Laboratoire d'Informatique de Paris 6, pôle IA (UMR 7606)
4 place Jussieu, case 169, 75252 Paris Cedex 05, France
2 Laboratoire des Milieux Désordonnés et Hétérogènes (UMR 7603) 4 place Jussieu, case 86, 75252 Paris Cedex 05, France
Accepted: 3 October 2002
We study the stress profile of an ordered two-dimensional packing of beads in response to the application of a vertical overload localized at its top surface. Disorder is introduced through the Coulombic friction between the grains which gives some indeterminacy and allows the choice of one constrained random number per grain in the calculation of the contact forces. The so-called “multi-agent” technique we use lets us deal with systems as large as grains. We show that the average response profile has a double-peaked structure. At large depth z, the position of these peaks grows with cz, while their widths scales like . c and D are analogous to “propagation” and “diffusion” coefficients. Their values depend on that of the friction coefficient μ. At small μ, we get and , with , which means that the peaks get closer and wider as the disorder gets larger. This behavior is qualitatively what was predicted in a model where a stochastic relation between the stress components is assumed.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 45.70.Cc – Static sandpiles; granular compaction / 83.80.Fg – Granular solids
© EDP Sciences, 2002