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In this paper, we propose a numerical method for computing solutions toBiot's fully dynamic model of incompressible saturated porous media[Biot;1956]. Our spatial discretization scheme is based on the three-fieldformulation (u-w-p) and the coupling of a lowest order Raviart-Thomas mixedelement [Raviart,Thomas;1977] for fluid variable fields (w, p ) and a nodalGalerkin finite element for skeleton variable field (u). These mixed spaces areconstructed based on the natural topology of the variables; hence, arephysically compatible and able to exactly model the kind of continuity which isexpected. The method automatically satisfies the well known LBB (inf-sup)stability condition and avoids locking that usually occurs in the numericalcomputations in the incompressible limit and very low hydraulic conductivity.In contrast to the majority of approaches, our three-field formulation canfully capture dynamic behavior of porous media even in high frequency loadingphenomena with considerable fluid acceleration such as liquefaction andbiomechanics of porous tissues under rapid external loading. Moreover, weaddress the importance of consistent initial conditions for poroelasticityequations with the incompressibility constraint, which represent a system ofdifferential algebraic equations. The energy balance equation is derived forthe full porous medium and used to assess the stability and accuracy of ourtime integration. To highlight the capabilities of our method, a variety ofnumerical studies are provided including verification with analytical andboundary element solutions, wave propagation analyses, hydraulic conductivityeffects on damping and frequency content, energy balance analyses, mass lumpingconsiderations, effects of mesh pattern and size, and stability analyses. Wealso explain some discrepancies commonly found in dynamic poroelasticityresults in the literature.

A topology-motivated mixed finite element method for dynamic response of porous media