Dynamic infinite elements for soil-structure interaction analysis in a layered soil medium

This paper presents the dynamic infinite element formulations that have been developed for soil-structure interaction analysis both in frequency domain and time domain by the present authors and our colleagues during the past 20 years. Axisymmetric, 2D and 3D layered half-space soil media were considered in the developments. The displacement shape functions of the infinite elements were established using approximate expressions of analytical solutions in frequency domain to represent the characteristics of multiple waves propagating into the unbounded outer domain of the media. The shape functions were determined in terms of the excitation frequency as well as the spatial and material characteristics of the far-field soil region. Thereby the element mass and stiffness matrices are frequency dependent. As for time domain analysis, the shape functions were further simplified to obtain closed-form frequency-dependent mass and stiffness matrices, which can analytically be transformed into time domain terms by the Fourier transform. The proposed infinite elements were verified using benchmark examples, which showed that the present formulations are very effective for the soil-structure interaction analysis either in frequency or in time domain. Example applications to actual soil-structure interaction problems are also given to demonstrate the capability and versatility of the present methodology.