A coupled FEM–SBM methodology for dynamic interaction of multiple structures and soil

In densely populated urban areas, there is a growing trend in constructing complex structural systems that include underground structures located beneath clusters of aboveground buildings. The dynamic interaction between these underground and aboveground structures, mediated by the surrounding soil, is known as structure-soil–structure interaction (SSSI). SSSI is a topic whose effects pose significant challenges to the design and analysis of such complex systems. In this paper, we propose a novel numerical methodology for addressing longitudinally invariant multi-structure-soil interaction problems in elastodynamics. The proposed approach combines the Finite Element Method (FEM) for modelling structural components with the Singular Boundary Method (SBM) for simulating wave propagation in the soil and capturing inter-structural coupling effects, all formulated in the wavenumber-frequency domain. The synergy of FEM, well-suited to complex geometries, and the computational simplicity and efficiency of SBM yields a robust and accurate framework for solving SSSI problems. The framework features a strongly coupled formulation between structures and soil, enhancing both accuracy and ease of implementation. The accuracy of the method is assessed through several benchmark studies involving cylindrical shells and cylindrical solids, while its practical applicability is demonstrated via real-scale numerical examples, with relative errors typically below 2%. Furthermore, the computational efficiency of the proposed methodology is compared with traditional hybrid approaches, in which both the structures and the surrounding soil are modelled using FEM, with the remaining soil represented via the Method of Fundamental Solutions (MFS) or Boundary Element Method (BEM). On average, the proposed approach achieves a computational performance nearly twenty times faster than that of the reference solutions. The results underscore the advantages of the proposed framework in terms of modelling simplicity, numerical efficiency, accuracy and robustness, and show that the method is scalable and capable of evaluating interactions among an arbitrary number of structures.