Use of DEM and elastic stability analysis to explain the influence of the intermediate principal stress on shear strength

One interesting aspect of soil response is the sensitivity of the mechanical behaviour to the intermediate principal stress. In this study, a fundamental mechanism that explains the influence of the intermediate stress ratio (b) on soil shear strength is proposed. Prior experimental, numerical and analytical studies have indicated that soil failure occurs when the strong force chains that transmit stress through the material buckle. These strong force chains are networks of contacting particles that are relatively highly stressed, and aligned in the direction of the major principal stress (sigma(1)'). The buckling resistance is thought to be determined by 'weaker' lateral networks of less-stressed contacting particles that are orthogonal to the strong force chain orientation. Discrete-element method (DEM) simulations of true triaxial tests show that as b is varied, so too is the relative support provided by the force chains orientated in the directions of the intermediate and minor principal stresses (sigma(2)' and sigma(3)' respectively). At a macro scale, the effective axial stiffnesses along these directions vary. The DEM dataset is complex, and so a conceptually simple model is used to assess the influence of lateral support on the buckling resistance of a single column of connected nodes, analogous to a single force chain. The lateral support is modelled using linear springs. When the stiffnesses of these springs are selected to reflect the variation in axial stiffness with b observed in the DEM simulations, the reduction in axial buckling load with b is found to be similar to the reduction in major principal stress with b. When combined, the DEM data and simple analytical model support a hypothesis that failure under three-dimensional stress conditions is determined by buckling of the strong force chains. It is the variation in lateral support provided by the force network aligned along the minor and intermediate stress directions that determines, in part at least, the relation between soil shear strength and b. The data presented provide a conceptually simple framework to justify the need to consider three-dimensional effects in geomechanical stress-deformation analyses, and may inform future development of constitutive models.