Advanced 2.5D meshless methodologies to deal with soil-structure interaction problems in elastodynamics

This thesis is concerned with the development of efficient and practical numerical methodologies to deal with longitudinally invariant soil-structure interaction problems in elastodynamics. All the approaches appearing in this thesis are formulated in the frequency-wavenumber domain. Moreover, the formulations can deal with full-space and half-space models of the soil. The novel proposed methods are mainly based on meshless approaches, which provide three main benefits: simplicity on the formulation and implementation, to avoid meshing requirements and to increase the computational efficiency of the evaluation of the soil-structure system response. Generally, these approaches are employed to model the wave propagation in unbounded mediums. Thus, in this thesis, meshless methods are used to model the soil, while the finite element method is mainly used to deal with the structure modelling. However, this thesis also demonstrates that meshless methods can also be used to model homogeneous structures. The performances of the novel approaches presented have been assessed in the context of railway tunnels embedded in the soil, especially for the case studies of circular and cut-and-cover tunnels. The studies are carried out for different elastodynamic models of the soil, including homogeneous full-space, homogeneous half-space and horizontally layered half-space. Four new methodologies are presented in this thesis. Firstly, a two-and-a-half-dimensional finite element-boundary element methodology coupled with the method of fundamental solutions is developed. This approach uses the method of fundamental solutions to model the wave propagation in the soil once the soil-tunnel interaction has been determined, reducing the computational needs of computing the soil response. Afterwards, the second methodology further enhances the computational efficiency, the robustness and the simplicity of the approach, by modelling the soil response using the singular boundary method. To reach even higher computational benefits, a hybrid method that combines the singular boundary method and the method of fundamental solutions is proposed. This hybrid approach is found to be inheriting the computational efficiency of the method of fundamental solutions while keeping the robustness and accuracy presented by the singular boundary method. The hybrid methodology is finally extended to model both the structure and wave propagation in the soil, which leads to a fully meshless and efficient approach to deal with the soil-structure interaction problems.