Loading-dependent microscale measures control bulk properties in granular material: An experimental test of the stress-force-fabric relation

The bulk behavior of granular materials is tied to its mesoscale and particle-scale features: Strength properties arise from the buildup of various anisotropic structures at the particle-scale induced by grain connectivity, force transmission, and frictional mobilization. More fundamentally, these anisotropic structures work collectively to define features like the bulk friction coefficient and the stress tensor at the macroscale and can be explained by the stress-force-fabric (SFF) relationship stemming from the microscale arrangement of the forces and fabric. Although the SFF relation has been extensively verified by discrete numerical simulations, a laboratory realization has remained elusive due to the challenge of measuring both normal and frictional contact forces. In this study, we analyze experiments performed on a photoelastic granular system under four different loading conditions: uniaxial compression, isotropic compression, pure shear, and annular shear. During these experiments, we record particle locations, contacts between particles, and normal and frictional forces to measure the particle-scale response to progressing strain. We experimentally assess the SFF relation across multiple loading conditions in a two-dimensional photoelastic granular system. We track microscale measures like the packing fraction, average coordination number, and average normal force, along with angular distributions of the interparticle contacts and the interparticle forces. We then track the anisotropy in the angular distributions of contacts and forces and connect these particle-scale anisotropies to bulk behavior using the SFF relation. The SFF relation provides compact expressions for both the stress tensor and the bulk friction coefficient in terms of fabric and force anisotropies. Our results demonstrate that these expressions accurately capture the bulk stress and friction across different loading histories, validating the predictive power of the SFF framework. Additionally, we test the assumption that contact and force anisotropies contribute equally to load transmission in our granular packings and show that this assumption is sufficient at large strain values and can be applied to areas like rock mechanics, soft colloids, or cellular tissue where force information is inaccessible.