A comparison of variational formats for porous media subjected to dynamic loading

This paper presents a comparison of two variational formats for fully saturated porous media subjected to dynamic loading, whereby the general situation of relative fluid acceleration is considered: (1) the classical three-field (u, p, w)-format and (2) a novel two-field (u, p)-format, where the seepage velocity w is a spatially \u27local\u27 field whose treatment resembles that of internal variables in material models. The limited numerical comparison shows that the (u, p)-format competes well with the (u, p, w)-format. Indeed, it is consistent with the general acceleration modeling in the full range of permeabilities. Moreover, in the low permeability regime (where the magnitude of w is insignificant), the new format reflects the situation pertinent to \u27added-mass\u27 and is more efficient than the classical (u, p, w)-format. Finally, the (u, p)-format can conveniently be implemented in existing FE-codes based on the \u27added mass\u27 formulation