Regarding the soil portion below the floating pile as a virtual soil pile, and the soil around the pile as a fractional derivative viscoelastic medium, the vertical vibration of the floating pile was solved. The boundary conditions of the soil and the pile and their continuity conditions were considered. The influence of main mechanical parameters of the pile and the soil on the complex stiffness at the head of the floating pile was investigated. The result indicates that the order of the fractional derivative has some influence on the real part and imaginary part of the complex stiffness. The constraint effect of the soil on the pile will be larger when the length of the pile is longer. The real part of the complex stiffness at the pile head will decrease when the model’s constitutive parameter increases. And the influence of the model’s constitutive parameter on the imaginary part of the complex stiffness is somewhat complicated.

The torsional vibration of a single pile in layered and saturated soil foundation was taken as the research object. The soil around the pile was regarded as a medium with the constitutive relation of fractional-derivative viscoelasticity. The dynamic differential equations of the soil for torsional vibration analysis were established in virtue of the dynamic equilibrium equation, viscoelastic constitutive relation and the stress-displacement relation of the soil. With a double-layered viscoelastic saturated soil foundation as an example, the influence of main mechanical parameters of the pile and the soil on torsional dynamic impedance was investigated. It is shown that the order ratio of the viscoelastic constitutive relations of lower soil layer to upper soil layer has great influence on the torsional dynamic impedance of the pile, and the influence of the ratio of shear wave velocities and the ratio of thicknesses between the two soil layers, and the influence of the ratio of moduli of the pile to the soil on the torsional dynamic impedance depends on the frequency of torsional vibration. However, the influence of these ratios is very small when the solid-liquid coupling coefficients of both soil layers are small.