Loading-dependent microscale measures control bulk properties in granular material: an experimental test of the Stress-Force-Fabric relation

The bulk behaviour 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 (fabric), 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. 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, and normal and frictional forces vectors to measure the particle-scale response to progressing strain. We track microscale measures like the packing fraction, average coordination number and average normal force along with anisotropic distributions of contacts and forces. We match the particle-scale anisotropy to the bulk using the SFF relation, which is founded on two key principles, a Stress Rule to describe the stress tensor and a Sum Rule to describe the bulk friction coefficient; we find that the Sum and Stress Rules accurately describe bulk measurements. Additionally, we test the assumption that fabric and forces transmit load equally through 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.