An analysis of strong discontinuities in a saturated poro-plastic solid

We present in this paper an analysis of strong discontinuities in fully saturated porous media in the infinitesimal range. In particular, we describe the incorporation of the local effects of surfaces of discontinuity in the displacement field, and thus the singular distributions of the associated strains, from a local constitutive level to the large-scale problem characterizing the quasi-static equilibrium of the solid. The characterization of the flow of the fluid through the porous space is accomplished in this context by means of a localized (singular) distribution of the fluid content, that is, involving a regular fluid mass distribution per unit volume and a fluid mass per unit area of the discontinuity surfaces in the small scale of the material. This framework is shown to be consistent with a local continuum model of coupled poro-plasticity, with the localized fluid content arising from the dilatancy associated with the strong discontinuities. More generally, complete stress-displacement-fluid content relations are obtained along the discontinuities, thus identifying the localized dissipative mechanisms characteristic of localized failures of porous materials. The proposed framework also involves the coupled equation of conservation of fluid mass and seepage through the porous solid via Darcy's law, and considers a continuous pressure field with discontinuous gradients, thus leading to discontinuous fluid flow vectors across the strong discontinuities. All these developments are then examined in detail for the model problem of a saturated shear layer of a dilatant material. Enhanced finite element methods are developed in this framework for this particular problem. The finite elements accommodate the different localized fields described above at the element level. Several representative numerical simulations are presented illustrating the performance of the proposed numerical methods.