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

We present in this paper an analysis of strong discontinuities in fully sat urated porous media in the infinitesimal range. In particular, we describe the incorporation of the local effects of surfaces of discontinuity in the displacement held, and thus the singular distributions of the associated st rains, from a local constitutive level to the large-scale problem character izing the quasi-static equilibrium of the solid. The characterization of th e flow of the fluid through the porous space is accomplished in this contex t by means of a localized (singular) distribution of the fluid content, tha t is, involving a regular fluid mass distribution per unit volume and a flu id mass per unit area of the discontinuity surfaces in the small scale of t he material. This framework is shown to be consistent with a local continuu m model of coupled pore-plasticity, with the localized fluid content arisin g from the dilatancy associated with the strong discontinuities. More gener ally, complete stress-displacement-fluid content relations are obtained alo ng the discontinuities, thus identifying the localized dissipative mechanis ms characteristic of localized failures of porous materials. The proposed f ramework also involves the coupled equation of conservation of fluid mass a nd seepage through the porous solid via Darcy's law, and considers a contin uous pressure field with discontinuous gradients, thus leading to discontin uous fluid flow vectors across the strong discontinuities. All these develo pments are then examined in detail for the model problem of a saturated she ar layer of a dilatant material. Enhanced finite element methods are develo ped in this framework for this particular problem. The finite elements acco mmodate the different localized fields described above at the element level . Several representative numerical simulations are presented illustrating t he performance of the proposed numerical methods. Copyright (C) 1999 John W iley & Sons, Ltd.