基于积分型分数导数本构方程的粘弹性弹性土层中单桩的复刚度与导纳研究

在三维积分型粘弹性本构方程的基础上，建立了基于三维积分型本构方程的粘弹性土体的竖向振动微分方程。利用三维分数导数Kelvin粘弹性本构关系描述土体的应力应变关系，考虑分数导数和卷积的Fourier变换性质，利用势函数和分离变量法在频域内求解了分数导数粘弹性土层的竖向振动，并在此基础上求解了粘弹性土层中单桩的竖直振动。研究了土体本构模型参量对桩顶复刚度和桩顶导纳的影响，研究表明，分数导数的阶数对桩顶复刚度和桩顶导纳有较大的影响，土体粘性系数对复刚度的实部和桩顶导纳影响较大，而对复刚度虚部影响相对较小。

Complex Stiffness and Admittance Research of Single Pile in Soil Based on Integral Fractional Derivative Constitutive Equation

The vertical vibration differential equations of viscoelastic soil are established based on three dimensional integral viscoelastic constitutive equations. The stress-strain relationship of soil is described by three dimensional fractional derivative Kelvin viscoelastic integral constitutive relationship, the vertical vibration of fractional derivative viscoleastic soil is solved by potential functions and method of separation variables in frequency range by considering the properties of Fourier transform of fractional derivative and convolution integral, and from this, we solved the vertical vibration of single pile in viscoelstic soil. And the influence of constitutive model parameters on complex stiffness and admittance at pile head was investigated, the research indicated that the order of fractional derivative has great effect on the complex stiffness and admittance at pile head, the influence of viscosity coefficient of soil on the real part of complex stiffness and admittance at pile head was greater, but the effect of viscosity coefficient of soil on the image part of complex stiffness was littler.