SUMMARYWe present in this paper an analysis of strong discontinuities in fully saturated porous media in the in"nitesimal range. In particular, we describe the incorporation of the local e!ects of surfaces of discontinuity in the displacement "eld, 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 #ow of the #uid through the porous space is accomplished in this context by means of a localized (singular) distribution of the #uid content, that is, involving a regular #uid mass distribution per unit volume and a #uid 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 #uid content arising from the dilatancy associated with the strong discontinuities. More generally, complete stress}displacement}#uid 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 #uid mass and seepage through the porous solid via Darcy's law, and considers a continuous pressure "eld with discontinuous gradients, thus leading to discontinuous #uid #ow 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 "nite element methods are developed in this framework for this particular problem. The "nite elements accommodate the di!erent localized "elds described above at the element level. Several representative numerical simulations are presented illustrating the performance of the proposed numerical methods.
A granular soil REV located on the upstream side of the erosion pipe front is modelled numerically, at the grain scale, by coupling the Discrete Element Method (DEM) with the Lattice Boltzmann Method (LBM) for the representation of the solid and fluid phases, respectively. The implementation of DEM follows a standard molecular dynamics approach and the interactions between grains are regulated by unilateral contacts and breakable bonds. A synopsis of the LBM scheme is provided, with focus on the implementation of non-slip conditions for moving boundaries and use of the Multiple Relaxation Time approach for improved numerical stability. The coupling scheme is described along with the criteria for setting the numerical parameters of the two methods. After a "dry" preparation procedure, the numerical REV is tested under fully saturated conditions and increasing pressure difference. Backward erosion is observed and a micromechanical inspection of the granular phase suggests that arching through force chains and the breakage of tensile bonds are prominent resistance and degradation mechanisms, respectively.
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