Finite element simulation of deformation bands in saturated granular media with inhomogeneous porosities at the meso-scale

The balance of mass and linear momentum of a solid-fluid mixture furnish a complete set of equations from which the displacements of the 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 [

1

], [

2

], [

3

]. In contrast with other more traditional models, inherent inhomogeneities in the density field at the meso-scale can be easily incorporated and coupled with the macroscopic laws of mixture theory. The hydraulic conductivity is naturally treated as a function of the porosity in the solid matrix, hence 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. Numerical simulations on dense sand specimens are performed to study the effects of inhomogeneities on the stability of saturated porous media at the structural level.

Supported by National Science Foundation under Grant Nos. CMS-0201317 and CMS-0324674 to Stanford University.