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

TL;DR

This study investigates how stress propagates in a large, ordered 2D packing of frictional beads, revealing a double-peaked response that broadens and shifts with depth and friction, aligning with stochastic stress models.

Contribution

It introduces a multi-agent computational method to analyze stress responses in large 2D bead packings, incorporating friction-induced disorder and revealing detailed response profiles.

Findings

Response profile exhibits a double-peaked structure.

Peak positions grow linearly with depth, widths scale with square root of depth.

Peak separation and width depend on friction coefficient, matching stochastic model predictions.

Abstract

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 $1000\times1000$ 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 $\sqrt{Dz}$. $c$ and $D$ are analogous to `propagation' and `diffusion' coefficients. Their values depend on that of the friction coefficient $\mu$. At small $\mu$, we get $c_0-c \propto \mu$ and $D \propto \mu^\beta$, with $\beta \sim 2.5$, 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.