Stress ratio–fabric relationships of granular soils under axi-symmetric stress and plane-strain loading

This paper investigates the relationship between the stress ratio and the fabric of frictional material under three-dimensional stress. The spatial distribution function of the contact normal was derived to describe the heterogeneous distribution of the micro-structural architecture. Discrete element simulations were conducted using an assembly consisting of 10,000 spherical particles. Sixteen stress probe experiments were simulated under both axi-symmetric stress and plane-strain conditions. The numerical results show that a change in the direction of the stress probe does not significantly affect the evolution of the fabric structure in the vertical plane. Regardless of whether the material is subjected to axi-symmetric stress or plane strain, the degree of fabric anisotropy shows a unique relationship with the stress ratio. The modified stress ratio, as theoretically derived from a micromechanics formulation, is able to separately measure micro-structures in the vertical and horizontal planes. The distribution function proposed in this study generally performs well in estimating the heterogeneous distribution of the contact normal. A higher-order distribution function is required to improve the predictability of the contact normal distribution for increasing stress-ratio paths.