Three-dimensional Soil-Structure-Interaction Applying the Coupled Integral Transform Method (ITM) – Finite Element Method (FEM) Approach

In this contribution an efficient approach to model the three-dimensional soil-structure-interaction is presented using a coupled Integral Transform Method (ITM) - Finite Element Method (FEM) approach. Using the ITM analytical solutions of the dynamic wave equation, that satisfy the radiation condition for unbounded media, can be obtained for different fundamental systems like a halfspace and a fullspace with spherical cavity. Superposing these fundamental systems, a semi analytical solution for the system halfspace with spherical cavity or excavation can be derived. Therefore, a threefold Fourier Transformation into the wavenumber frequency domain (k_x,k_y,z,ω) is applied for the quantities at the half space surface. The parameters on the spherical surface are expanded into spherical harmonics and also transformed into the frequency domain (R,m,l,ω). The domain inside the spherical cavity or excavation can be modeled using finite elements, where the outer boundary of the finite element mesh must be adapted to the spherical surface of the soil, modelled with the ITM. Simple eight node three-dimensional finite elements can be used to calculate the stiffness matrix of the spherical structure in the frequency domain. Both substructures are coupled applying the equilibrium of the forces as well as the compatibility of the displacements on the spherical interaction surface and therefore have to be described in the same coordinate system on the coupling surface. The parameters of the FEM substructure thus have to be transformed into the domain of the ITM structure. Finally, the complete system of a halfspace including an arbitrary three-dimensional structure inside a spherical cavity or excavation can be modeled.     «

In this contribution an efficient approach to model the three-dimensional soil-structure-interaction is presented using a coupled Integral Transform Method (ITM) - Finite Element Method (FEM) approach. Using the ITM analytical solutions of the dynamic wave equation, that satisfy the radiation condition for unbounded media, can be obtained for different fundamental systems like a halfspace and a fullspace with spherical cavity. Superposing these fundamental systems, a semi analytical solution for...     »