  In this paper, we propose a numerical method for computing solutions to
Biot's fully dynamic model of incompressible saturated porous media
[Biot;1956]. Our spatial discretization scheme is based on the three-field
formulation (u-w-p) and the coupling of a lowest order Raviart-Thomas mixed
element [Raviart,Thomas;1977] for fluid variable fields (w, p ) and a nodal
Galerkin finite element for skeleton variable field (u). These mixed spaces are
constructed based on the natural topology of the variables; hence, are
physically compatible and able to exactly model the kind of continuity which is
expected. The method automatically satisfies the well known LBB (inf-sup)
stability condition and avoids locking that usually occurs in the numerical
computations in the incompressible limit and very low hydraulic conductivity.
In contrast to the majority of approaches, our three-field formulation can
fully capture dynamic behavior of porous media even in high frequency loading
phenomena with considerable fluid acceleration such as liquefaction and
biomechanics of porous tissues under rapid external loading. Moreover, we
address the importance of consistent initial conditions for poroelasticity
equations with the incompressibility constraint, which represent a system of
differential algebraic equations. The energy balance equation is derived for
the full porous medium and used to assess the stability and accuracy of our
time integration. To highlight the capabilities of our method, a variety of
numerical studies are provided including verification with analytical and
boundary element solutions, wave propagation analyses, hydraulic conductivity
effects on damping and frequency content, energy balance analyses, mass lumping
considerations, effects of mesh pattern and size, and stability analyses. We
also explain some discrepancies commonly found in dynamic poroelasticity
results in the literature.
