A sphere packing model for shear bands in dense soils

Abstract

The rhombic sphere packing can be used to model granular soils in a very simple way. According to the angle of assemblage, the packing is dilatant or contractive. Correspondingly, the overall stresses are transmitted as chains of forces or oblique forces of contact. The connection of the soil stress-strain behaviour and the packing void ratio is achieved by mapping both of the plots. The mapping shows that dense soils are dilatant and loose soils are contractive, separated by the critical state. It also shows that the bifurcation point and the peak strength are features of dense soils. The line of strain localization is analysed in the elastic regime, and its inclination is found maximizing the intensity of the mobilized stress ratio. The stresses within the shear band are obtained by assuming a partially coaxial packing rotated for reaching the full plastic state. The equilibrium of the overall stress at the line of discontinuity leads to the relationship between the peak friction angle and the coefficient of lateral pressure at rest. As long as these parameters are independently obtained from each other, they allow the validation of the theory.