Evolution of fabric under the rotation of the principal stress axes in the simple shear test

•We developed a new formulation to account for fabric and its evolution.•The main factors for fabric evolution are included in the formulation.•The variation of inter-particle mobilized friction angle is investigated.

A mathematical relation is presented for predicting the value of the contact normal plane distribution or the anisotropy parameter “αα” (the ratio of the second invariant to the trace of fabric tensor) for granular materials under shearing loads. The changes of the contact normal planes are attributed to the mobilized stress ratio, internal friction angle, fabric principal direction and non-coaxiality between the major principal directions of stress and fabric. A new relationship between “αα” and the main factors is derived by focusing on two particles across a potential sliding plane and the peanut-shaped function for the distribution of the contact normals. This formulation is obtained by combining the contact normal distribution function and mobilized stress ratio for sliding planes in a micro-level analysis. The dependence of “αα” on the internal mobilized friction angle and the shear to normal stress ratio are the main characteristics of this relationship. The degree of anisotropy is easily obtained by applying this equation. The variation of the inter-particle mobilized friction angle in micro-level and double-shearing is briefly discussed. The variation of “αα” with shear strain is similar to the variation of the shear to normal stress ratio with shear strain. The inter-particle mobilized friction angle with shearing approaches the mobilized stress ratio on the spatial mobilized plane. A comparison with experimental tests demonstrates the validity of this formula for the evolution of anisotropy.