Vertical dynamic response analysis of large diameter piles in fractional viscoelastic saturated foundation

As a commonly used pile foundation, tubular piles are widely used in practical engineering, and their dynamic response analysis has important research value. Based on the principle of elastic dynamics and viscoelastic saturated soil model, the dynamic characteristics of large-diameter tubular piles in fractional-order viscoelastic saturated soil under vertical dynamic load are investigated by taking into account the immobile viscosity of the soil skeleton and the lateral inertia effect of the tubular piles. Firstly, the fluctuation equations of fractional-order viscoelastic saturated soil in column coordinate system were established based on Biot's dynamic consolidation theory and fractional-order standard linear solid (FSLS) model. Secondly, based on the Rayleigh-Love rod model and considering the lateral inertia effect of the tubular piles, the analytical solution of the pile top dynamic impedance of the tubular piles is derived. Finally, the effects of fractional order model parameters, lateral inertia effect of tubular piles, pile length and soil permeability on the dynamic impedance of pile top of tubular piles are investigated by example analysis. The results show that: the increase of fractional order and strain relaxation time and the decrease of stress relaxation time in the FSLS model parameters of saturated soil skeleton increase the dynamic impedance at the top of the pile; the transverse inertia effect of tubular piles is especially obvious in the high-frequency section to reduce the dynamic impedance at the top of the pile; and the reduction of the outer radius of tubular piles and enlargement of the inner radius of tubular piles, as well as the increase of the pile length and decrease of the permeability of the soil body all help to improve the dynamic impedance at the top of the pile.