Mathematical identification of diffuse and localized instabilities in fluid-saturated sands

SUMMARY: The mathematical properties of diffuse and localized failure modes in fluid-saturated sands are investigated. The granular medium is modeled as an elastoplastic solid, and a recently proposed set of scalar indices, here referred to as moduli of instability, is used to identify the onset of potential bifurcations of the incremental response. First, the analytical properties of these moduli are discussed, stressing their dependence on the kinematic constraints associated with the imposed deformation modes. Then, by using an elastoplastic model for sands, drained and undrained loading paths are simulated under axisymmetric, plane-strain and simple shear conditions. For each deformation mode, the instability moduli are computed and monitored throughout the simulations, with the purpose of elucidating the consequences of changes in control conditions. In addition, it is illustrated that suitable linear transformations allow the same strategy to be used to perform drained or undrained shear band analyses and predict the interval of possible band inclinations. The final comparison against literature experiments on loose Hostun sand shows that the instability moduli are indicators of the loss of resistance against specific modes of deformation. As a result, they can be used to identify and explain a number of failure mechanisms that can be commonly observed in experiments.