Dynamic Soil-Structure Interaction Using a High Performance Scaled Boundary Finite Element Method in Time Domain

In this paper a substructure method is used for the solution of the dynamic soil-structure interaction problem in which the soil is modeled using a scaled-boundary finite element (SBFEM) in time domain, while the structure is modeled using a finite-element method. A governing equation of the SBFEM, in which the unknown is a fully populated acceleration unit-impulse response matrix, requires solution of the matrix integral equation involving convolution integrals. The original discretization scheme assumes a piece-wise constant approximation of the acceleration impulse-response matrix within time step and it is only conditionally stable, requiring a small minimum step size. In this paper we describe a new procedure developed by authors in their previous work, which brings two essential improvements to the original method: (1) A new scheme which assumes piece-wise linear change of the acceleration unit-impulse response matrix is used and in combination with an extrapolation parameter and linearization for the late times provides more robustness and efficiency to the solution. For the examples analyzed by authors no instabilities where present for a wide range of parameters. (2) Soil-structure interaction vector described by the convolution integral is evaluated using a new and efficient recursive scheme based on the integration by parts. These two enhancements lead to a very significant reduction of computation effort and a linear dependency with time. Using a new method a two-and three-dimensional examples of the dynamic wave-soil-structure interaction are analyzed. These examples show the accuracy and high computational efficiency of the proposed discretization schemes and qualify the new approach for the usage in large practical problems encountered in vibration and earthquake engineering.