During the installation of rock-socketed pile, a certain thickness of sediment inevitably accumulates at the pile bottom. Given this, the influence of the pile bottom sediment on the torsional vibration of the rock-socketed pile is investigated with the aid of the virtual soil pile model. First, the bottom sediment is regarded as a virtual soil pile with the same cross-sectional area as the pile tip, and the pile and the virtual soil pile are divided into a series of segments along the vertical direction. Then, the governing equation of torsional vibration of the pile (virtual soil pile) - soil system under torsional dynamic load is established. The circumferential shear complex stiffness at the pile (virtual soil pile)-soil interface is obtained by solving the governing equation of the surrounding soil. The displacement impedance function at the top of the virtual soil pile (i. e., the circumferential complex stiffness at the pile tip) is obtained by solving the governing equation of the virtual soil pile. Furthermore, the displacement impedance function of the pile top is obtained by the recursion of the impedance function at the adjacent pile segments. Finally, the established solution derived based on the virtual soli pile model is compared with the existing solutions. A parameter analysis is conducted to investigate the influence of various factors such as the sediment thickness, shear wave velocity and density on the complex impedance of the rock-socketed pile under different pile-soil parameters.

Based on the plane strain model, the torsional vibration of a belled pile is theoretically investigated considering the construction disturbance effect. First, in view of the cross-sectional characteristics of the belled pile and the radial inhomogeneity of the surrounding soil caused by construction disturbance, the belled pile is divided into finite sections along the longitudinal direction, and the surrounding soil is divided into finite annular zones along the radial direction. The pile and soil vibration governing equations are established, respectively. Then, the soil governing equations of each zone are solved one by one through the shear complex stiffness transfer model to obtain the shear complex stiffness at the pile-soil interface, which is substituted into the governing equation of the pile. The displacement impedance function at the belled pile head is obtained in the frequency domain by virtue of the Laplace transform and impedance function transfer method, and further the amplitude-frequency response function of the twist angle at the belled pile head is obtained. Finally, the influence of bottom-expanding section parameters and construction disturbance effect on the complex impedance and amplitude-frequency of the twist angle at the pile head are analyzed in the low frequency range utilizing parametric analysis.