The longitudinal seismic response of a long tunnel subjected to Rayleigh waves is investigated in this paper. The tunnel is assumed to be infinitely long, has a uniform cross section, and rests on a viscoelastic foundation. The free‐field deformation under Rayleigh waves traveling parallel to the tunnel axis is decomposed into two directions, namely, the axial motion and the vertical motion, and transformed into dynamic loads imposed on the tunnel. Based on the Fourier and Laplace integral transform techniques, the governing equations of tunnels are simplified into algebraic equations, and the analytical solutions are obtained with the convolution theorem. The final solutions of the tunnel responses in terms of deflection, velocity, acceleration, axial force, bending moment, and shear force are investigated. The proposed solution is verified by comparison of its results and those from the finite element program ABAQUS. Further parametric analysis is carried out to investigate the influence of soil‐structure relative stiffness ratio and wave frequency on dynamic longitudinal responses of the tunnel.

中文翻译：

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瑞利波作用下长隧道纵向地震响应的解析解

本文研究了长隧道在瑞利波作用下的纵向地震响应。假定隧道是无限长的，具有均匀的横截面，并位于粘弹性基础上。在平行于隧道轴线传播的瑞利波作用下的自由场变形被分解为两个方向，即轴向运动和垂直运动，并转化为施加在隧道上的动态载荷。基于傅立叶和拉普拉斯积分变换技术，将隧道的控制方程简化为代数方程，并利用卷积定理获得解析解。研究了隧道响应在挠度，速度，加速度，轴向力，弯矩和剪力方面的最终解决方案。通过将其结果与有限元程序ABAQUS的结果进行比较，验证了所提出的解决方案。进行了进一步的参数分析，以研究土-结构相对刚度比和波频率对隧道动态纵向响应的影响。