SUMMARYA number of methods have been developed for solving the dynamics of saturated porous media. However, most solutions are based on the finite element method, and only a few employ finite differences (FDM). One problem with the FDM is the difficulty in fulfilling the inf-sup (Ladyženskaja-Babuška-Brezzi) condition. This paper explores solutions with the FDM, including the development of new schemes aiming at stabilised formulations. The efficiency, accuracy and stability of several FDM and finite element method algorithms are thoroughly investigated as well. A combination of primary variables from the theory of porous media is considered, including the so-called up and uvp formulations. Six numerical schemes are produced and quantitatively studied. Simulations of 1D and 2D wave propagation problems are performed in order to reveal the advantages and drawbacks of all schemes.
SUMMARYThe complexity of formulations for the hydromechanical coupled mechanics of porous media is typically minimised by simplifying assumptions such as neglecting the effect of inertia terms. For example, three formulations commonly employed to model practical problems are classified as fully dynamic, simplified dynamic and quasi-static. Thus, depending on the porous media conditions, each formulation will have advantages and limitations. This paper presents a comprehensive analysis of these limitations when solving one-dimensional fully saturated porous media problems in addition to a new solution that considers a more general loading situation. A phase diagram is developed to assist on the selection of which formulation is more appropriate and convenient regarding particular cases of porosity and hydraulic conductivity values. Non-dimensional formulations are proposed to achieve this goal. Results using the analytical solutions are compared against numerical values obtained with the finite element method, and the effect of porosity is investigated.
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