中文摘要：

将衬砌分别视为多孔柔性材料和弹性介质，在频率域内研究内水压力作用下饱和分数导数黏弹性土一深埋圆形隧洞多孔柔性或弹性衬砌系统的耦合简谐振动。土体的宏观力学特性采用多孔介质理论来模拟。通过引入与土体体积分数相关的应力系数，利用衬砌和土体界面处位移连续，分别得到饱和黏弹性土和衬砌的位移、应力和孔隙水压力等的解析表达式。在此基础上，分析了多孔柔性衬砌和弹性衬砌结构的差异，并考察了应力系数、渗透系数、分数阶导数本构参数等对系统动力响应的影响，结果表明：多孔柔性衬砌材料条件下系统的动力响应明显大于弹性衬砌材料条件下系统的动力响应；随着分数导数阶数和材料参数比的增加，系统共振效应明显减弱；衬砌边界透水和不透水只是反映边界渗透性的两种极限状态。

英文摘要：

The lining is respectivel.y regarded as porous flexible material and elastic medium. The coupled harmonic vibration of the system of saturated fractional derivative viscoelastic soil and porous flexible or elastic lining with a deeply embedded circular tunnel with inner water pressure is investigated in the frequency domain. The macroscopic mechanical properties of soils are simulated by using the porous medium theory. By introducing the stress coefficient and utilizing the displacement continuity at the interface between lining and soil, the analytical expressions for displacement, stress and pore water pressure of saturated viscoelastic soil and lining are respectively obtained. On this basis, the differences between porous flexible lining and elastic lining structure are analyzed. The influences of stress coefficient, permeability coefficient and fractional derivative constitutive parameters on the system dynamic response are studied. It is shown that the system dynamic responses for porous flexible lining are greater than those for porous elastic lining. With the order of fractional derivative and material parameters increasing, the resonance effect of the system is significantly reduced. The available solutions of permeable and impermeable boundary conditions are only two extreme eases of this paper.