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建立了基于三维积分型本构方程的单桩在黏弹性土体的竖向振动微分方程。利用三维分数导数Kelvin黏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黏弹性土层的竖向振动,并在此基础上求解了黏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,土体黏性系数对桩顶复刚度的实部和桩顶导纳影响较大,而对桩顶复刚度虚部影响相对较小。
The vertical vibration differential equation of single pile in viscoelastic soil is established based on three-dimensional integral constitutive equation. The relationship between stress and strain of soils is described by means of the Kelvin viscoelastic constitutive relation of three-dimensional fractional derivative. Considering the Fourier transform property of fractional derivative and convolution, the potential of fractional derivative viscoelastic soil is solved in the frequency domain by using the potential function and the separation- On this basis, the vertical vibration of single pile in viscoelastic soil is solved. The effect of constitutive model parameters on pile complex stiffness and pile top admittance was studied. The results show that the order of fractional derivative has a great influence on the complex stiffness of the top of the pile and the admittance of the top of the pile. The viscosity coefficient of the soil has a great influence on the real part of the complex stiffness of the pile top and the admittance of the pile top, Complex stiffness of the imaginary part of the impact is relatively small.