Variational Elastic Solution for Dynamic Torsional Soil–Pile Interaction Using Fictitious Soil Pile Model

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.