Evolution of percolating force chains in compressed granular media

TL;DR

This study investigates how force chains evolve in compressed granular media using experiments and a novel fiber bundle damage model, revealing universal power law behaviors in stress and acoustic signals.

Contribution

It introduces a continuous damage model to describe force chain evolution, linking microscopic rearrangements to macroscopic behavior in granular systems.

Findings

Nonlinear constitutive behavior matches experimental data.

Universal power law divergence of stress near critical deformation.

Acoustic signal amplitudes follow a power law with exponent ~1.15.

Abstract

The evolution of effective force chains percolating through a compressed granular system is investigated. We performed experiments by compressing an ensemble of spherical particles in a cylindrical container monitoring the macroscopic constitutive behavior and the acoustic signals emitted by microscopic rearrangements of particles. As a novel approach, we applied the continuous damage model of fiber bundles to describe the evolution of the array of force chains during the loading process. The model provides a nonlinear constitutive behavior in good quantitative agreement with the experimental results. For a system of hard particles the model predicts a universal power law divergence of stress when approaching a critical deformation. The amplitude distribution of acoustic signals was found experimentally to follow a power law with exponent $\delta = 1.15 \pm 0.05$ which is in a good agreement with the analytic solution of the model.