Implementation of Porous Media Formulation for Geomaterials

The mechanical behavior of saturated geomaterials is largely governed by the interaction of the solid skeleton with the fluids present in the pore structure. Traditional geotechnical analyses, commonly based on simplified effective stress theories, fail to fully describe the behavior of saturated porous materials. Hence, it has become necessary to use more robust and complete formulations. In this context, the use of multiphase theories appears to be an alternative and more appropriate approach. In this work, the governing equations of a porous media interacting with immiscible porous fluids are presented in the light of the theory of mixtures. A generalized Galekin procedure is devised to establish the coupled mixed finite-element equation set with u-p-U form. An unconditionally stable implicit solution procedure is used for the time domain numerical solution. Finally, a recently developed constitutive model based on the fuzzy set plasticity concept is described and implemented in the finite-element tool. A companion paper focuses on applications of this theory, and case studies are used to evaluate the proposed formulation.