Improvement in the computational efficiency of the coupled FEM–SBFEM approach for 3D seismic SSI analysis in the time domain

Abstract

The scaled boundary finite element method (SBFEM) is an attractive approach for modelling unbounded media because it offers the advantages of both the finite element method (FEM) and the boundary element method (BEM) avoiding their respective drawbacks. Unfortunately, being a rigorous method, the SBFEM exhibits non-locality in both time and space, which results in significant numerical effort, especially for large problems with many degrees of freedom and a long simulation time. In order to improve the performance of this method, two different approximation techniques – one in time and one in space have been combined and implemented in the present work. A three-dimensional embedded footing problem was solved for the dynamic load, including a chirp load and a sinusoidal load. The combination of the two approximation techniques implemented in the time domain-coupled FEM–SBFEM approach for 3D analysis leads to significant reduction in computational time and storage requirements with insignificant loss in accuracy. The computational time required for the approximation techniques was found to be only 5% of that required using the conventional method, whereas the loss in accuracy was found to be less than 5%. Further, numerical problems for the externally applied dynamic load as well as the seismic load demonstrate the applicability of the coupled FEM–SBFEM approach for modelling dynamic soil–structure interaction (SSI) problems.