Analysis of Horizontal Dynamic Response of a Single Pile in Layered Foundations Based on the Timoshenko–Pasternak Model

To compensate for the deficiencies of the conventional Euler–Bernoulli beam-dynamic Winkler foundation model in analyzing the horizontal dynamic response of a single pile, in this paper, the Timoshenko–Pasternak model, which considers both the soil shear effect and pile shear deformation, is established to reveal the pile-soil dynamic interaction accurately. Based on Timoshenko beam theory and Pasternak foundation theory, the pile horizontal vibration control equation considering pile shear deformation and the soil shear effect is derived based on D’Alembert’s principle. On this basis, the transfer matrix method is applied to consider the layering characteristics of the soil, and the dynamic complex impedance frequency domain analytical solution of the pile top is obtained by using the initial parameter method combined with the pile bottom boundary conditions. A comparison with the existing model solution is carried out to verify the correctness and reasonableness of the model in this paper; finally, the parameters of the pile characteristics and soil properties around the pile are analyzed. The results show that (1) the pile bottom boundary condition and pile length have almost no effect on the pile top impedance after the single pile reaches the critical value of the length-to-diameter ratio. (2) The trend of pile top impedance becomes increasingly evident with increasing dimensionless frequency. (3) The pile top impedance increases with the decrease in the pile-soil elastic modulus ratio, and the changing trend becomes increasingly apparent; meanwhile, the influence of the elastic modulus of the surface soil on the pile top impedance is much more significant than the influence of the underlying soil on it.