分数导数模型描述的饱和土桩纵向振动分析

Analysis of vertical vibrations of a pile in saturated soil described by fractional derivative model

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。

As we know,the soil has viscoelastic characteristic,the control equations of saturated soil described by fractional derivative model are established based on the theories of porous media and theories of fractional derivatives,in which the soil is regarded as porous medium filled with water;and the stress-strain relationship is described by fractional derivative viscoelastic model for considering the viscoelastic properties of soil skeleton.The vertical coupled vibration of a pile in a saturated soil described by fractional derivative model is investigated by introducing the potential functions and separation of variables method under the three-dimensional axisymmetric condition;and the influences of the model parameters on the vertical vibration of a pile in saturated soil is analyzed.The results indicate that the control equations of the saturated soil described by fractional derivative model has a wider application;and the model parameters has great influences on the vertical vibration of a pile in saturated soil.