Development of the scaled boundary finite element method for dynamic soil-structure interaction analysis in the time domain

This thesis presents the development of the displacement-unit-impulse-response-based modelling of unbounded domains for the numerical simulation of dynamic soil-structure interaction (SSI) problems in the time domain. Wave propagation in a 2D half-plane, 2D semi-infinite layers with constant depth and 3D half-space are studied where material anisotropy is also considered. Typical dynamic SSI applications include foundation-soil interaction, road-soil systems subject to traffic load, earthquake analysis, etc. The theoretical framework of this research is based on extending the scaled boundary finite element method (SBFEM), which is a semi-analytical technique. The soil-structure interaction relationship formulated in the thesis is based on the displacement unit-impulse response matrix. An accurate and efficient method for calculating the displacement unit-impulse response matrix is proposed. The convolution integral representing the interaction force-displacement relationship can be truncated due to the decaying behaviour of the displacement unit-impulse response matrix, which leads to a significant reduction of the computational effort. Meanwhile, a reliable viscous damping model is also proposed for the 2D layered case.For large-scale wave propagation problems in 3D half-space, the computational effort is reduced in two ways: (1) the unbounded domain is divided into multiple subdomains, in which the interaction force-displacement relationship is evaluated separately; (2) based on the piece-wise linear approximation of the displacement unit-impulse response matrix, a recursive formulation for calculating the interaction displacement-force relationship is proposed.For wave propagation problems in 2D semi-infinite layers, the computational effort is reduced further by performing a trigonometric interpolation of the truncated displacement unit-impulse response matrix. Therefore, the kernel in the convolution integral is substituted by a series of sine and cosine functions, which facilitate the use of an efficient recursive algorithm. The proposed techniques are applied to wave propagation problems in 2D unbounded domains with topological irregularities or multiple material interfaces. A quadtree meshing technique based on the scaled boundary finite element method is used to model the near field in an efficient and automatic way. The proposed displacement-unit-impulse-response-based formulation of the far field can be coupled seamlessly with the quadtree mesh of the near field