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[Formula: see text]. 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.