Simulation of Soil-Structure-Interaction Problems Using an Indirect Trefftz Approach to Solve Lamé Equations

Ground vibrations caused by dynamic loads result in root-point excitations of adjacent struc-tures. This becomes critical if the amplitudes raise beyond a certain acceptable limit for e.g. sensitive machines, or the excitations exceed critical values as in earthquakes. In order to pre-dict the effects of those loads on structures sufficiently, a calculation model that incorporates the soil-structure interaction has to be used. In the presented study an efficient and accurate solution algorithm for computing soil-structure-interaction problems is proposed. An Indirect Trefftz Approach is used to solve the Lame differ-ential equation governing the considered problem, with wave functions forming a T-complete solution set. With the help of a Helmholtz decomposition the Lame differential equation is split up in an irrotational and a solenoidal field, with each of these fields approximated by a truncat-ed set of wave functions. The used wave functions inherently satisfy the governing equation of the problem. For solving the semi infinite domain of the halfspace the Integral Transform Method (ITM) is used. The constructed ITM based solutions can represent the radiating effects of the infinite domain as well as the surface boundary conditions of the half space. By this, a homogeneous (and layered) halfspace with a cylindrical inclusion and a foundation of moderate complexity shall be considered. Both methods are solved in the frequency domain (uniform reference domain). By using a Galerkin approach, continuity of the displacement and stress field is enforced at the transition between the two models. Finally, the solution of the cou-pled soil-structure-interaction problem is validated by comparison with the solution of reference studies with an alternative approach.