Lateral-Rocking Coupled Vibration Response of Tapered Piles in Layered Foundations

Based on the Timoshenko-Pasternak model, this paper investigates the dynamic response of tapered piles in layered soft soil foundations under combined lateral and rocking harmonic excitations. Considering the pile as a linear elastic Timoshenko tapered beam-column, the model accounts for variations in pile-soil friction and foundation parameters along the pile shaft. A dynamic analytical model for tapered piles embedded in a three-parameter Pasternak viscoelastic foundation subjected to initial axial loading is developed, and the governing differential equations for lateral steady-state vibration are derived. A finite element numerical model of tapered piles in layered foundations is established through command streams. Results indicate that the lateral harmonic load at the pile head dominates the coupled lateral-rocking vibration response. Under conditions of equal pile volume, variations in taper angle significantly influence the lateral dynamic impedance at the pile head; specifically, increasing the taper angle enhances lateral dynamic stiffness and damping effectively at high frequencies, with an optimal taper angle identified at 1.5 0 . Additionally, as the pile-soil stiffness ratio decreases, the dynamic impedance at the pile head increases, amplifying the impact of soil shear effects on the pile's lateral dynamic response. Under specified pile-end constraint conditions and within the given parameter ranges, the dynamic stiffness at the pile head decreases markedly with increasing soft soil thickness, eventually converging to a stable value. In contrast, the thickness of the soft stratum is found to have only a limited influence on the dynamic impedance behavior.