Prediction of shear bands in sand based on granular flow model and two-phase equilibrium

Abstract

In contrast to the traditional interpretation of shear bands in sand as a bifurcation problem in continuum mechanics, shear bands in sand are considered as high-strain phase (plastic phase) of sand and the materials outside the bands are still in low-strain phase (elastic phase), namely, the two phases of sand can coexist under certain condition. As a one-dimensional example, the results show that, for materials with strain-softening behavior, the two-phase solution is a stable branch of solutions, but the method to find two-phase solutions is very different from the one for bifurcation analysis. The theory of multi-phase equilibrium and the slow plastic flow model are applied to predict the formation and patterns of shear bands in sand specimens, discontinuity of deformation gradient and stress across interfaces between shear bands and other regions is considered, the continuity of displacements and traction across interfaces is imposed, and the Maxwell relation is satisfied. The governing equations are deduced. The critical stress for the formation of a shear band, both the stresses and strains inside the band and outside the band, and the inclination angle of the band can all be predicted. The predicted results are consistent with experimental measurements.