A fast and accurate hybrid green’s function-FEM approach for dynamic soil-structure interaction of arbitrarily shaped foundations in layered transversely isotropic media

A new semi-analytical method is developed to evaluate the dynamic response of arbitrarily shaped flexible foundations resting on or embedded in a transversely isotropic multilayered half-space. The formulation integrates Green’s functions (GFs) with the finite element method (FEM) within the modified subtraction approach. The GFs in the multilayered half-space are derived using the Fourier-Bessel series (FBS) system of vector functions combined with the dual-variable and position (DVP) method, while FEM is employed to discretize the foundation domain. Since the expansion coefficients (Love numbers) depend solely on the z -coordinate, a precomputation strategy is introduced to significantly reduce the computational cost associated with evaluating GFs over discrete horizontal mesh points. This strategy substantially improves computational efficiency in dynamic response analysis. Within the modified subtraction framework, the combined GFs–FEM formulation is used to construct the dynamic impedance matrix of the interacting system. The proposed algorithm is implemented and validated against benchmark solutions, demonstrating high accuracy and numerical stability. Parametric studies reveal that foundation geometry, near-surface inhomogeneity, and soil anisotropy can significantly influence the impedance response, providing useful insights for engineering design.