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土体具有黏弹性性质,为了更好地考虑饱和土体固相土骨架的黏弹性性质,在分数导数理论和多孔介质理论的基础上,将土体视为液固饱和两相介质,并利用分数导数模型来描述饱和土固相土骨架的应力-应变关系,建立分数导数模型描述的饱和土的控制方程。在三维轴对称情况下,利用势函数和分离变量法研究了分数导数模型描述的饱和土中桩的振动问题。分析了模型参数对饱和土中桩的竖向振动的影响。研究表明,分数导数模型描述的饱和土的控制方程应用范围更广,模型参数对桩的竖向振动有较大的影响。
In order to better consider the viscoelastic properties of saturated soils, based on fractional derivative theory and porous media theory, soil is considered as a two-phase liquid-solid saturated medium, Fractional derivative model to describe the stress-strain relationship of saturated soil solid framework, and the governing equation of saturated soil described by fractional derivative model is established. In the case of three-dimensional axisymmetric vibration, the vibration problem of piles in saturated soil, which is described by fractional derivative model, is studied by using the potential function and the separation-variable method. The effect of model parameters on vertical vibration of pile in saturated soil is analyzed. The research shows that the governing equations of saturated soil described by Fractional Derivative Model have a wider range of applications and the model parameters have a great influence on vertical vibration of piles.