On the Modeling of Porous Media with Emphasis on Localization
The mechanics of porous media is nowadays relevant in a broad spectrum of engineering applications. In the case of geomaterials, the description of the mechanical behavior is complicated by the fact that the deformation characteristics involve (strain) localization, which is indeed the main topic of this thesis.
In the present context, the conditions for localization are derived analytically from the concept of regularized strong discontinuity. Discontinuities for both the displacement and pore fluid pressure fields are introduced in conjunction with elastic-plastic effective stress response. The analytical analyses are used to formulate a consistent finite element procedure with the ability to capture the progressive development of a localized zone. A key issue is to embed the properly regularized discontinuous fields within the finite elements. The width of the localization zone is incorporated as an additional parameter, whereby good performance regarding mesh insensitivity is obtained.
The porous medium is as a first step analyzed with respect to the undrained condition. An analytical localization analysis for this situation leads to a more restrictive criterion for localization than for the corresponding drained porous medium. Concerning the partly drained porous medium, the analytical investigation predicts the onset of localization whenever the underlying drained "effective" material signals this. In this case, the coupling of deformation-diffusion affects the growth of discontinuities in time. These characteristics of the undrained and partly drained porous medium are also recovered by the numerical simulations.
A continuum formulation for a porous medium with a compressible pore fluid at large elastic-plastic deformation is developed. The proposed thermodynamic setting leads to a straightforward and transparent formulation. A numerical parameter study shows the influence of the permeability and the pore fluid compressibility on the occurrence of localization.