Directional interpolation infinite element for dynamic problems in saturated porous media

In this study, a directional interpolation infinite element suited to a saturated porous medium is presented to account for dynamic problems with semi-infinite or infinite domain. By employing the Galerkin method, the element property matrixes for a two-dimensional space are given. Using the governing differential equations for wave propagation in the saturated porous media, the analytical solutions for one-dimensional wave propagation are derived in detail. Then the shape functions for the infinite element based on the analytical solutions are formulated and the dynamic stiffness matrix is presented in analytical form is presented. As a result, a fully coupled 2D infinite element for the analysis of dynamic problems in unbounded saturated porous media is presented. The effectiveness and accuracy of the proposed element is well demonstrated by a comparison of the numerical results with known analytical solutions for 1D and 2D wave propagation problems. The results highlight that the proposed directional interpolation infinite element is useful and effective for addressing the dynamic problems with semi-infinite or infinite domain, with consideration of both compression and shear waves.