分数导数黏弹性准饱和土中球空腔振动特性

在频率域内用解析方法研究分析了简谐轴对称荷载和流体压力作用下分数导数黏弹性准饱和中球空腔的稳态响应问题。将土骨架等效为具有分数阶导数本构关系的黏弹性体，基于Biot两相饱和介质模型，通过势函数推导求得了边界部分透水时分数导数粘弹性准饱和土中球空腔的位移、应力和孔压等的解析解。根据界面连续性条件，确定了待定系数的表达式。在此基础上，考察了准饱和土各参数对动力响应的影响，结果表明：轴对称荷载和流体压力两种情况时，相对渗透系数对动力响应的影响有较大的差异。分数导数本构模型更合理地描述了准饱和土中球空腔的振动特性。

Vibration characteristics of a spherical cavity in fractional-derivative-viscoelastic nearly saturated soil

By using the analytical method, the steady state responses of a spherical cavity in nearly saturated fractional derivative viscoelastic soil are investigated subject to harmonic axisymmetric load or interior water pressure in the frequency domain. The soil skeleton is treated as a viscoelastic medium with fractional derivative constitutive relations. Based on the Biot’s theory, the analytical solutions for the displacement, stress and pore water pressure of the spherical cavity in the nearly saturated fractional derivative viscoelastic soil for the partial permeable condition are obtained by the potential functions. The expressions of the undetermined coefficients are derived based on the continuity conditions. On the basis, the dynamic responses of the spherical cavity in the nearly saturated fractional derivative viscoelastic soil are analyzed for different parameters of the soil. It is shown that the influences of the relative permeability coefficient on the dynamic responses have obvious differences between the conditions of harmonic axisymmetric load and interior water pressure. The vibration characteristics of the spherical cavity in nearly saturated soil are described reasonably by the fractional derivative model.