Semi‐Analytical Solution of Time‐Harmonic Soil–Pile Interaction Using Love Numbers in Transversely Isotropic and Layered Half‐Spaces

ABSTRACT An efficient semi‐analytical approach based on the Fourier–Bessel series (FBS) system of vector functions and the stiffness matrix method is proposed to study the dynamic response of axially loaded piles embedded in transversely isotropic (TI) layered soil. The method utilizes a robust free‐field matrix formulation of layered soil that integrates with the pile matrix, enabling efficient computation of expansion coefficients, termed as Love numbers. These coefficients need to be computed only once for multilayered soil. They are then stored and reused to quickly obtain responses at multiple field points using FBS synthesis, avoiding the computational complexity of the Hankel integral transform. The proposed formulation is validated against various existing solutions, demonstrating excellent agreement. Furthermore, the effects of compressibility, slenderness, pile spacing, soil anisotropy, layering, and frequency‐dependent loading on the pile–soil interaction are investigated, offering practical insights for improved and reliable pile design.