中文摘要：

在频率域内研究了内水压力作用下分数导数型黏弹性准饱和土中球空腔的稳态动力响应.通过引入与孔隙率有关的应力系数合理地确定了介质和孔隙水共同承担的内水压力值.将土骨架和衬砌分别视为具有分数导数本构模型的黏弹性体和多孔柔性材料,基于Biot两相介质模型,通过引入位移势函数解耦得到了内水压力作用下分数导数型黏弹性准饱和土中半封闭球形空腔的位移、应力和孔隙水压力解析表达式.考察了物性和几何各参数对球形空腔动力响应的影响,结果表明：分数导数本构模型更合理地描述了土体的动力学行为;饱和度对应力和孔隙水压力影响较大,而对位移影响较小.

英文摘要：

The steady-state dynamic responses of a spherical cavity in nearly saturated fractional derivative viscoelastic soil are investigated subject to the internal water pressure in the frequency domain. By a stress coefficient depending on the porosity of soil, the values of internal water pressure in medium and in pore water are determined, respectively. The soil skeleton and the lining are treated as a viscoelastic medium with fractional derivative constitutive relations and a porous flexible material, respectively. Based on Bolt＇s theory, the analytical solutions for the displacement, stress and pore water pressure of the partial sealed spherical cavity in the nearly saturated soil subject to the internal water pressure are obtained by the displacement potential functions. The dynamic responses of the spherical cavity are analyzed for different physical and geometry parameters. It is shown that the dynamic behaviors of the soil are described reasonably by the fractional derivative constitutive model. The saturation degree has great influences on the stress and pore water pressure, while it has a smaller impact on the displacement.