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基于Biot理论,研究了饱和土中带有衬砌的圆形隧洞在移动环形荷载作用下的动力响应。假定衬砌为弹性体,土体为饱和多孔介质,引入两类势函数来表示土体、孔隙水和衬砌的位移,使隧洞的控制方程解耦。结合边界条件及连续条件,通过傅立叶变换得到频率-波数域中衬砌和土体的应力、位移和孔隙水压力解答,最后用傅立叶积分逆变换得到时-空域中的数值解。计算并比较了3种隧洞模型(弹性土体隧洞、饱和土体隧洞和饱和土衬砌隧洞)的动力响应分析。数值分析结果说明:(1)移动荷载速度对3种隧洞动力响应均具有较大影响;(2)弹性土体隧洞和饱和土体隧洞的动力响应具有明显区别,所以在富水地区的隧洞动力响应中土体应该视为饱和土体;(3)衬砌对隧洞动力响应有较大影响,故隧洞的动力分析中不能忽略衬砌作用。
Based on the Biot theory, the dynamic response of circular tunnel with lining in saturated soil under moving circular load is studied. Assuming that the lining is an elastic body and the soil is saturated porous medium, two types of potential functions are introduced to represent the displacements of soil, pore water and lining, and the governing equations of the tunnel are decoupled. Combining the boundary conditions and continuous conditions, the stress, displacement and pore-water pressure solutions of the lining and soil in the frequency-wavenumber domain are obtained by Fourier transform. Finally, the numerical solution in the time-space domain is obtained by inverse Fourier transform. The dynamic response analysis of three kinds of tunnel models (elastic soil tunnel, saturated soil tunnel and saturated soil lining tunnel) is calculated and compared. Numerical analysis results show that: (1) The moving load velocity has a great influence on the dynamic response of the three kinds of tunnels. (2) The dynamic response of the elastic soil tunnel and the saturated soil tunnel is obviously different. Therefore, The response of soil should be regarded as saturated soil; (3) Lining has a greater impact on the dynamic response of the tunnel, so the tunnel can not be ignored in the dynamic analysis of the lining.