Soil–structure interaction (SSI) under torsional loading plays a critical role in the dynamic performance of foundations supporting offshore structures and machine foundations. However, existing simplified or semi-analytical approaches often idealize the pile tip boundary and may not adequately capture the frequency-dependent torsional impedance induced by finite soil thickness beneath the pile tip in layered deposits. This study develops a Hamilton-based variational solution for dynamic torsional soil–pile interaction in layered viscoelastic soils by explicitly incorporating a fictitious soil pile (FSP) beneath the pile tip within an energy-consistent framework. Admissible torsional displacement fields for the pile, layered soil, and FSP are adopted to establish a frequency-domain variational functional, and an iterative scheme is used to obtain the convergent frequency-dependent torsional impedance at the pile head. The formulation is verified against an existing semi-analytical solution for piles in layered soils and shows excellent agreement. Parametric results indicate that introducing a finite FSP reduces torsional stiffness and increases damping compared with a rigid base condition, while the thickness and stiffness of the bearing stratum govern the variation in impedance, providing physical insight into torsional SSI in layered ground.
Wang et al. (Wed,) studied this question.