Hybrid-Trefftz displacement and stress elements for bounded poroelasticity problems

The hybrid-Trefftz displacement and stress elements for poroelasticity are applied here to the spectral analysis of bounded saturated porous media. The displacement model is derived from the direct approximation of the displacement and fluid seepage fields in the domain of the element and of the tractions and pore pressures in the solid and fluid phases, respectively, on the Dirichlet boundary of the element. Conversely, the stress model is obtained by the direct approximation of the total stress and pore pressure fields in the domain, while independent approximations of the displacement and fluid seepage fields are enacted on the Neumann boundaries. As typical of the Trefftz methods, for both models, the domain approximation bases are constrained to satisfy locally all field equations. The central objective of the paper is to present a consistent set of tests designed to evaluate the ability of the proposed models to accurately predict the response of saturated porous media subjected to harmonic excitation and to assess the corresponding convergence patterns. Emphasis is placed on some key advantages of the presented formulation, namely the insensitivity of the results to gross mesh distortion, to near-incompressibility of the medium and to the wavelength content of the propagating wave, which enables the use of frequency-independent finite element meshes.