Theory and numerics of localization in a fluid-saturated elasto-plastic porous medium

Abstract

In this contribution, we outline a theoretical and numerical approach for describing deformation localization due to hydro-mechanical coupling. In the localization analysis, the concept of “regularized strong discontinuity” is extensively used at the application to the conservation laws of momentum and mass. At the onset of localization, the displacement and pore pressure fields are assumed to contain regularized discontinuities that are superposed on the continuous fields. As a result, we obtain a coupled localization condition, whereby the partly drained situation is discussed and compared to the drained and undrained situations. As to the finite element modelling, it is proposed to capture the development of regularized discontinuities in the displacement and pressure fields it is proposed to use a finite element procedure for the mixture of soil and pore fluid based on the “embedded band approach”, where the finite element interpolation allows for discontinuities within the elements. The procedure is based on the enhanced assumed strain concept, and from the pertinent orthogonality condition a coupled set of finite element equations are obtained, where the coupling between continuous and discontinuous response is obtained at the element level. Under certain circumstances, the coupled localization condition may be shown to be preserved by the finite element formulation, and the element response may be characterized like in the continuum situation. It is shown that the algorithm is capable of capturing the onset of localization as well as the post-localized response. In a numerical example, we study the influence of the internal friction angle on the development of a slip surface within a soil slope.