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将桩基和土体视为三维连续介质,桩基和土体的应力-应变关系采用分数阶黏弹性模型描述。在三维轴对称情况下,利用三维弹性理论和连续介质力学理论,运用分离变量法和分数阶导数的性质,得到了分数阶黏弹性土层中分数阶黏弹性桩基的三维轴对称解;并分析了相关参数对桩顶动态刚度和等效阻尼的影响。研究结果表明:与土体相比,桩基的相关参量对桩顶复刚度的影响较大;桩基和土体的密度比、模量比对桩顶复刚度都有较大的影响。
The pile foundation and soil are regarded as three-dimensional continuous media. The stress-strain relationship between pile foundation and soil is described by fractional-order viscoelastic model. In the case of three-dimensional axisymmetry, the three-dimensional axisymmetric solutions of fractional viscoelastic pile foundations in fractional viscoelastic soil are obtained by using the three-dimensional elastic theory and the theory of continuum mechanics with the help of the properties of separation variables and fractional derivatives. The influence of relevant parameters on the dynamic stiffness and equivalent damping of the top of the pile is analyzed. The results show that compared with soil, the relative parameters of pile foundation have a great influence on the complex stiffness of pile top, and the density ratio and modulus ratio of pile foundation and soil have a greater influence on the complex stiffness of pile top.