Induced force chain anisotropy of cohesionless granular materials during biaxial compression

This paper investigates the induced anisotropy and multi-scale shear characteristics of granular materials by quantifying force chain distribution in two-dimensional specimens of rigid particles under quasi-static loading. A new criterion is proposed and implemented into the existing algorithm which can effectively solve the identification instability of force chains at branching and merging points. Force chain is then classified into three categories according to the variation of force chain quantity and average stress with segment length: stable segments, meta-stable segments and unstable force chain segments. The stable force chain segments dominate the load-bearing behavior of the granular materials. The directional distribution of force chain segments is more anisotropic and more sensitive to the applied stress than contact normal vectors, which show obvious local peaks in both vertical and horizontal directions at high deviatoric stress. Therefore, the probability density of directional distribution of force chains needs to be described by the first two deviatoric components of Fourier expansion with deviators A(1) and A(2), which are indicators reflecting the intensity of the induced-anisotropy of the granular materials. As the absolute values of A(1) and A(2) increase, the induced anisotropy is more significant. The final shear failure types are determined by the quantities of force chains orienting in two potential shear failure directions: if there is an obvious difference between the quantities of the two directions, single shear band occurs within the direction with less force chains; otherwise, conjugated double shear bands occur and lie in the two potential shear failure directions.