A modified scaled boundary finite element method for three-dimensional dynamic soil-structure interaction in layered soil

This paper is devoted to the analysis of elastodynamic problems in 3D-layered systems which are unbounded in the horizontal direction. For this purpose, a finite element model of the near field is coupled to a scaled boundary finite element model (SBFEM) of the far field. The SBFEM is originally based on describing the geometry of a half-space or full-space domain by scaling the geometry of the near field?/?far field interface using a radial coordinate. A modified form of the SBFEM for waves in a 2D layer is also available. None of these existing formulations can be used to describe a 3D-layered medium. In this paper, a modified SBFEM for the analysis of 3D-layered continua is derived. Based on the use of a scaling line instead of a scaling centre, a suitable scaled boundary transformation is proposed. The derivation of the corresponding scaled boundary finite element (SBFE) equations in displacement and stiffness is presented in detail. The latter is a nonlinear differential equation with respect to the radial coordinate, which has to be solved numerically for each excitation frequency considered in the analysis. Various numerical examples demonstrate the accuracy of the new method and its correct implementation. These include rigid circular and square foundations embedded in or resting on the surface of layered homogeneous or inhomogeneous 3D soil deposits over rigid bedrock. Hysteretic damping is assumed in some cases. The dynamic stiffness coefficients calculated using the proposed method are compared with analytical solutions or existing highly accurate numerical results. Copyright (C) 2011 John Wiley & Sons, Ltd.