Vertical dynamic response of pipe pile embedded in unsaturated soil based on fractional‐order standard linear solid model and Rayleigh‐Love rod model

Abstract Considering the flow‐independent viscosity of soil skeleton and the lateral inertia effect of pipe pile, the vertical dynamic behavior of a pipe pile embedded in unsaturated soil is investigated in this work when the pipe pile is subjected to the vertical dynamic loading. In order to model this problem, the fractional‐order standard linear solid (FSLS) model is introduced to characterize the flow‐independent viscosity of the soil skeleton, the Rayleigh‐Love rod model is employed to specify the lateral inertia effect of pipe pile, while both vertical and radial soil displacement are entirely considered. The analytical solution of the pipe pile complex impedance is obtained through the rigorous theoretical derivation. Numerical results with known analytical solution are finally presented to discuss the influence of the model parameters for the FSLS model, lateral inertia effect and geometrical characteristic for the pipe pile, and saturation degree and intrinsic permeability for the unsaturated soil on the vertical complex impedance of the pipe pile. The main results indicate that enlarging the fractional‐order index, raising the strain relaxation time, or shortening the stress relaxation time will reduce the oscillation amplitude and natural frequency for the dynamic stiffness and damping of the pipe pile but will improve their mean value. The lateral inertia effect of pipe pile has effect on its complex impedance only in the high‐frequency region. The outer and inner radii of pipe pile, pile length, soil saturation degree, and soil intrinsic permeability are highly correlated with the pipe pile complex impedance.