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This paper investigates the torsional dynamic response of a single pile with a circular cross-section embedded in multi-layered soils. The energy principles and variational approach are employed to establish the governing equations of the pile-soil system subjected to dynamic torque applied at the pile head in the frequency domain. The proposed solution is based on the finite element method for a bar on an elastic foundation to provide the torsional dynamic subgrade reaction, angle of twist, torque along the pile and the torsional impedance at the pile head. The accuracy of the proposed method is verified by comparing the analysis results with those of existing analytical solutions. Parametric studies are also performed to investigate the influence of the soil properties and the excitation frequencies on the stiffness and radiation damping of the pile-soil system.

Variational approach for torsional dynamic response of a single pile in multi-layered soils