中文摘要：

基于流体不可压缩饱和多孔介质理论,将衬砌视为具有分数导数本构关系的多孔黏弹性体,在频率域内研究了在内水压力作用下饱和黏弹性土和衬砌系统的振动特性。通过引入与孔隙流体体积分数有关的应力系数,合理地确定了隧洞边界衬砌和孔隙水共同承担的内水压力值。利用衬砌内边界上的边界条件以及衬砌和土体界面处应力和位移的连续性条件,给出了隧洞边界部分透水条件下饱和黏弹性土和分数导数型黏弹性衬砌系统简谐耦合振动时系统动力响应的解析解。结果表明：饱和黏弹土和衬砌结构的动力响应与衬砌材料的黏性有关;应力系数合理地确定了衬砌和孔隙水共同承担的内水压力值。

英文摘要：

The lining is considered as a porous viscoelastic medium with fractional derivative constitutive relation. Based on saturated porous medium theory, the dynamic responses of saturated viscoelastic soil and lining system subject to the inner water pressure are investigated in the frequency domain. By proposing a stress coefficient depending on the volume fraetion of pore fluid, the values of inner water pressure in lining and in pore water are respectively determined reasonably. By utilizing the inner boundary condition of the lining and the continuity conditions of stress and displacement between the soil and the lin- ing, the analytical solutions of the system dynamic responses for the harmonic eoupled vibration of saturated viscoelastic soil and lining are derived under the partial permeable conditions. It is shown that the dynamic responses of saturated viscoelastic soil and lining are depending on the viscous of the lining. The values of inner water pressure in lining and in pore water on the boundary of lining are determined reasonably by the stress coefficient.