中文摘要：

由于混凝土衬砌具有黏弹性性质,以往的弹性曲梁、弹性壳体等理论都难以描述其蠕变的全过程。将土体和混凝土衬砌分别视为饱和多孔黏弹性介质和具有分数阶导数本构的黏弹性体,在频率域内研究饱和黏弹性土和分数导数型黏弹性衬砌系统耦合振动特性。根据Biot理论和黏弹性理论,通过位移势函数,分别得到简谐荷载作用下饱和土和衬砌的位移、应力和孔压解析通解,并通过衬砌内边界以及饱和土和衬砌接触面处的应力和位移协调条件,给出待定系数的具体表达式。考察饱和土和衬砌各物性和几何参数对系统动力特性的影响,研究表明：饱和黏弹性土和分数导数型黏弹性衬砌系统的动力特性与饱和黏弹性土和经典黏弹性衬砌系统的动力特性存在较大差异。另外,随着土骨架阻尼比的增加,响应幅值逐渐减小。

英文摘要：

Since the concrete lining has viscoelastic properties,the whole process of its creep can not be described well by the previous theories such as elastic curved beam,elastic shell and so on.In this paper,the soil and concrete lining are considered as saturated viscoelastic porous medium and viscoelastic material with fractional derivative constitutive relation,respectively.The coupled vibration characteristics of the saturated viscoelastic soil and the lining system with a deep circular tunnel are investigated in frequency domain.Based on the Biot s theory and viscoelastic theory,analytic solutions of displacement,stress and pore water pressure of the saturated soil and the lining under harmonic loads are obtained by displacement potential function,respectively.Besides,the expressions of undetermined coefficients are presented according to the inner boundary conditions of the lining as well as the displacement and stress continuous conditions at the interface between the saturated soil and the lining.At last,the effects of the physical and geometric parameters of the saturated soil and the lining on the system dynamic behavior are investigated.It is shown that the dynamic characteristics of the saturated viscoelastic soil and fractional derivative viscoelastic lining system are obviously different from those of the saturated viscoelastic soil and classic viscoelastic lining system.Furthermore,the response amplitudes decrease gradually as the damping ratio of the soil skeleton increases.