Modeling deformation banding in dense and loose fluid-saturated sands

Balance of mass and linear momentum of a solid-fluid mixture furnish a complete set of equations from which the displacements of the solid matrix and the pore pressures can be resolved for the case of quasi-static loading, resulting in the so-called u-p Galerkin formulation. In this work, a recently proposed model for dense sands is utilized to model the effective stress response of the solid matrix appearing in the balance of linear momentum equation. In contrast with other more traditional models, inherent inhomogeneities in the porosity field at the meso-scale are thoroughly incorporated and coupled with the macroscopic laws of mixture theory. Also, the hydraulic conductivity is naturally treated as a function of the porosity in the solid matrix, allowing for a more realistic representation of the physical phenomenon. The aforementioned balance laws are cast into a fully nonlinear finite element program utilizing isoparametric elements satisfying the Babuska-Brezzi stability condition. Criteria for the onset of localization under locally drained and locally undrained conditions are derived and utilized to detect instabilities. Numerical simulations on dense and loose sand specimens are performed to study the effects of inhomogeneities on the stability of saturated porous media at the structural level. (c) 2007 Elsevier B.V. All rights reserved.