Wave propagation phenomena in unbounded domains occur in many
engineering applications, e.g., soil structure interactions. The
considered problem is often modeled by the theory of elasticity which is
in some applications a sufficient accurate approximation. Nevertheless,
the interaction of the solid- and the fluid phase attribute a time
dependent character to the mechanical response of the saturated soil,
which can be modeled by Biot‘s theory of poroelasticity. When simulating
unbounded domains, infinite elements are a possible choice to describe
the far field behavior, whereas the near field is described through
conventional finite elements. Hence, an infinite element is presented to
treat wave propagation problems in unbounded elastic and saturated
porous media. Infinite elements are based on special shape functions to
approximate the semi-infinite geometry as well as the Sommerfeld
radiation condition, i.e., the waves decay with distance and are not
reflected at infinity. To provide the wave information the infinite
elements are formulated in Laplace domain. The time domain solution is
obtained by using the convolution quadrature method as inverse Laplace
transformation. The temporal behavior of the near field is calculated
using a standard time integration scheme, i.e., the Newmark-method.
Finally, the near- and far field are combined using a substructure
technique in any time step. The accuracy as well as the necessity of the
proposed infinite elements, when unbounded domains are considered, is
demonstrated with different examples.