Hybrid-trefftz displacement finite elements for elastic unsaturated soils

The displacement model of the hybrid-Trefftz finite element is formulated for elastodynamic problems defined on unsaturated soils. The mathematical formulation is based on the theory of mixtures with interfaces. The model considers the full coupling between the solid, fluid and gas phases, including the effects of relative (seepage) accelerations. The hyperbolic problem is integrated in time using a step-by-step implicit scheme that transforms it into a series of elliptic problems in space. The free-field solutions of these problems are derived in cylindrical coordinates and used to construct the domain approximation of the hybrid-Trefftz displacement element. This builds relevant physical information in the approximation basis, increasing the convergence of the elements under p-refinement and their robustness to wide variations of the frequency of the propagating wave.