Helical piles are a new type of pile that has good application prospects, and researchers have carried out an in-depth investigation into their vertical uplift and compressive bearing capacity. However, there is relatively little research on the dynamic bearing characteristics of helical piles. Therefore, the lateral vibration of a helical pile embedded in the viscoelastic foundation is systematically studied in this article. Utilizing the equivalent stiffness method to transform a helical pile into a cylindrical pile of special diameter, the lateral vibration model of the helical pile considering shear deformation is established based on the Winkler foundation model and the Timoshenko beam theory. The analytical solutions for the lateral dynamic displacement, bending moment, and shear force of the helical pile are strictly derived, and the rationality of the present solutions is also verified by comparing them with existing solutions. Based on the present solutions, a parametric study is carried out to investigate the influence of the pile and soil properties on the lateral dynamic response of the helical pile. It is found that the load excitation frequency and pile–soil stiffness ratio have a significant influence on the lateral dynamic displacement, bending moment, and shear force of the helical pile with space and time response.

The dynamic characteristics of pipe piles are of considerable importance for the dynamic foundation design of offshore wind turbines. In this study, we develop an analytical model for the lateral vibration of offshore pipe piles with consideration of the inertia effect and axial loading from the superstructure. A coupled dynamic saturated soil–pile interaction model is established based on Biot’s poroelastic theory and Euler–Bernoulli theory. The potential function, operator decomposition method, variable separation method and matrix transfer method are introduced herein to obtain the lateral force of the inner and outer soil acting on the pile shaft. Then, the analytical solution of the pile dynamic impedance in the frequency domain is derived by employing the soil–pile continuous deformation conditions and the boundary conditions of the pile. The rationality and accuracy of the presented solution have were by comparing its results with those predicted by existing solutions. The influence of superstructure, pile geometry and soil plug height on the lateral dynamic impedance and natural frequency of pipe piles was thoroughly investigated based on the theoretical model. The main findings can be summarized as: (1) The dynamic stiffness of piles will be remarkably underestimated if the inertia effect of the superstructure is not accounted for. (2) The vertical load of the superstructure is main factor affecting the natural frequency, whereas the inertia effect of the superstructure will enlarge the resonance amplitude. (3) The overall lateral dynamic impedance and first-order natural frequency of the pile increase significantly with the soil plug height.

The vertical vibration of a viscoelastic pile immersed in arbitrarily layered soil is investigated by taking the interaction among pile, pile surrounding soil (PSS) and pile end soil (PES) into account. Firstly, considering both the stratification and stress wave effect of soil, a mathematical model of the pile–soil system is established based on the fictitious soil pile (FSP) model. Then, utilizing the impedance function transfer method and Laplace transform technique, the analytical solutions of the vertical dynamic impedance of pile are derived in the frequency domain. The analytical solutions are validated by comparing them with other existing solutions. Finally, a parametric study is put forward to investigate the properties of PES on the vertical dynamic impedance of pile. The results reveal that the properties of PES have a significant effect on the vertical dynamic impedance of pile, but there is a critical influence thickness for this effect. For the cases of the PES thickness exceeding the critical influence thickness, further increase of PES thickness will not affect the dynamic behavior of the pile–soil system.

A tapered pile (TP) is a new type of pile with a good bearing capacity, and scholars have conducted in-depth research on its static bearing characteristics. However, there is relatively little research on its dynamic bearing characteristics. In this paper, the horizontal vibration behavior of a tapered pile in arbitrarily layered soil is studied. Utilizing the Winkler foundation model and Timoshenko beam model to simulate pile-surrounding soil (PSS) and a tapered pile, respectively, the horizontal vibration model of a tapered pile embedded in layered soil was built. The analytical solutions for the horizontal displacement (HD), bending moment (BM), and shear force (SF) of a tapered pile were derived, and then the solutions for the horizontal dynamic impedance (HDI), rocking dynamic impedance (RDI), and horizontal-rocking coupling dynamic impedance (HRDI) of pile head were obtained. Using the present solutions, the effects of soil and pile properties on the horizontal vibration characteristics of a tapered pile were systemically studied. The ability of a tapered pile–soil system to resist horizontal vibration can be improved by strengthening the upper soil, but this ability cannot be further improved by increasing the thickness of the strengthened upper soil if its thickness is greater than the critical influence thickness.