Abstract: 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.

Key words: vibration and wave, single pile, layered and saturated soil, torsional dynamic impedance, transfer matrix method

摘要： 以分层饱和土中单桩扭转振动为研究对象，将桩周土体视为分数阶黏弹性饱和土，借助分数阶黏弹性本构模型和土体运动平衡方程、应力位移关系建立分层分数阶黏弹性饱和土层扭转振动微分方程。以两层分数阶黏弹性饱和土为例，讨论主要桩土力学参数对扭转动力阻抗影响。结果表明：下上层土体本构模型阶数比对扭转动力阻抗随频率变化曲线峰值影响较大，下上层土体剪切波速比、土层厚度比和桩土模量比对扭转动力阻抗的影响与频率有关，下上层土体液固耦合系数较小时，其对扭转动力阻抗的影响很小。

关键词: 振动与波, 单桩, 分层饱和土, 扭转动力阻抗, 传递矩阵法