Abstract
The rhombic sphere packing can be used to model the biaxial test on granular soils in a very simple way. According to the angle of assemblage, the packing is dilatant or contractive. Correspondingly, 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 only of dense soils. The band 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 to reach the full plastic state. The equilibrium of the overall stress at the line of discontinuity reveals a relationship between the peak friction angle and the coefficient of lateral pressure at rest. As long as these parameters are obtained independently of each other, they allow the validation of the theory.
Highlights
A shear band is the final effect of the location of deformation in a solid body
The most important property of these plots is the connection of the sphere packing theory with the overall mechanical behavior of granular soils
The connection between a soil and a packing is the mapping of plots. It explains the critical state of soils and the shear banding
Summary
A shear band is the final effect of the location of deformation in a solid body. The localization of the deformation is a phenomenon whose understanding cannot be achieved without taking into account the granular nature of the soil [4]. As a matter of fact, several authors have found that the assemblies of spheres used in the Distinct Element Method give results that are consistent with the experiments [5, 6]. An analytical and comprehensive theory of the mechanics of shear bands is still in development. A packing of frictionless spheres, ordered in a rhombic Bravais lattice, is proposed to model a granular soil subjected to a biaxial compression test. The assembly of grains within the shear band is modeled by a rhombic packing rotated until the limiting equilibrium is fulfilled
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