中文摘要：

对隧洞周边土体采用饱和土Biot理论，隧洞衬砌采用考虑剪切和转动变形的曲线梁振动理论，分析地震P波作用下饱和土体中圆形隧洞衬砌的动力响应问题。对于饱和土体中的散射波场采用波函数展开法求解，对曲线梁的振动控制微分方程采用一般化的微分求积法（GDQM）求解。由饱和土体与衬砌接触处的位移协调条件，采用最小二乘法确定波函数未知系数项。计算结果表明：当入射波频率较低时，衬砌结构的入射面与背对面的动力响应几乎是对称的；随着入射频率的增加，衬砌结构的入射面与背对面不再具有对称性，且衬砌结构入射面的动力响应要大于背对面的动力响应。

英文摘要：

Dynamic response of a circular tunnel lining embedded in the saturated soil subjected to seismic P wave was investigated. The surrounding medium of the tunnel was considered as a saturated porous medium and described by Biot’s theory. The tunnel lining was treated as curved beams described by a curved beam theory, which can account for both rotary and shear deformation. The scattered wave field in the porous medium was obtained by the wave function expansion method. The differential equations governing the vibration of curved beam were discretized by the general differential quadrature （GDQ） method. The wave function coefficients in the truncated series can be obtained by using the displacement compatibility conditions between the porous medium and the tunnel lining. The displacement compatibility condition between the porous medium and the tunnel was implemented by boundary least square collocation method. The results show that for low-frequency incident waves, the responses of the liner segments at the incident side and the shelter side are almost symmetrical. With the increase of frequency, the responses of the liner pieces at the incident side and the shelter side are not symmetrical anymore. The responses of the incident side tunnel are larger than those of the shelter side tunnel.