Stress response function of two-dimensional ordered packing of frictional beads

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 1000 x 1000 grains. We show that the average response pro le has a double-peaked structure. At large depth z, the position of these peaks grows with cz, while their widths scales like rootDz. c and D are analogous to "propagation" and "diffusion" coefficients. Their values depend on that of the friction coefficient mu. At small mu, we get c(0)-cproportional to mu and D proportional to mu(beta), with betasimilar to2.5, 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.