Comparative assessment of finite element formulations for dynamic analysis in low-permeability saturated porous media

To address the issue of spurious pore pressure oscillations in equal-order finite element analyses of the dynamic responses of low-permeability saturated porous media, we compare two primary formulations: (1) a novel unequal-order interpolation element enriched with cover functions; (2) a stabilized equal-order interpolation element. To circumvent inherent linear dependence issues in the cover function-enriched formulation, specialized quadrilateral and triangular elements are developed for 1D and 2D problems, respectively. The performance of each element type is evaluated for both compressible and incompressible materials. Our results demonstrate that the cover element consistently and accurately captures pore pressure evolution for both forms of material. In contrast, the stabilized equal-order element achieves acceptable accuracy only for incompressible materials with high skeleton stiffness and exhibits degraded performance for compressible materials. Despite efforts to mitigate the influence of the stabilization term, the numerical results remain prone to either oscillatory or excessively damped responses.