Tunnels located in seismic active areas must support not only static loads exerted by the ground under gravity but also seismic loads from earthquake events. Current analytical solutions for seismic analysis of tunnel structures are limited to circular or rectangular tunnels but not available for tunnels with other complex cross-section shapes, such as straight-wall-arch-shaped or semi-rectangular-shaped tunnels. This paper presents a unified simplified analytical solution for deep tunnels with arbitrary cross-section shapes subjected to seismic loading. Since the cross-section dimension of tunnels is normally much smaller than the wavelength of ground peak velocities, the structure can be designed using the pseudo-static approach. The ground and the tunnel liner are assumed to be elastic, homogeneous, and isotropic in plane strain condition. Two different contact conditions, no-slip and full-slip conditions, are considered at the liner-ground interface. The complex variable theory combined with the conformal mapping technique are employed to obtain closed-form solutions for tunnel deformation and stresses. The proposed solution is verified by providing comparisons between its results and those from the finite element program ABAQUS. Furthermore, parametric analyses are carried out to investigate the influence of soil-structure relative stiffness ratio, cross-section shape, height-span ratio and thickness of middle wall on tunnel responses.

位于地震活动区的隧道不仅必须承受地面在重力作用下施加的静载荷，还必须承受地震事件产生的地震载荷。目前隧道结构抗震分​​析的解析解仅限于圆形或矩形隧道，而不适用于具有其他复杂横截面形状的隧道，如直壁拱形或半矩形隧道。本文提出了一种具有任意截面形状的深埋隧道在地震荷载作用下的统一简化解析解。由于隧道的横截面尺寸通常远小于地面峰值速度的波长，因此可以使用伪静态方法设计结构。假定地面和隧道衬砌在平面应变条件下是弹性的、均匀的和各向同性的。线性地面界面处考虑了两种不同的接触条件，无滑移和全滑移条件。复变量理论结合共形映射技术被用来获得隧道变形和应力的封闭形式解。通过将其结果与有限元程序 ABAQUS 的结果进行比较来验证所提出的解决方案。此外，还进行了参数分析，以研究土结构相对刚度比、横截面形状、高跨比和中墙厚度对隧道响应的影响。复变量理论结合共形映射技术被用来获得隧道变形和应力的封闭形式解。通过将其结果与有限元程序 ABAQUS 的结果进行比较来验证所提出的解决方案。此外，还进行了参数分析，以研究土结构相对刚度比、横截面形状、高跨比和中墙厚度对隧道响应的影响。复变量理论结合共形映射技术被用来获得隧道变形和应力的封闭形式解。通过将其结果与有限元程序 ABAQUS 的结果进行比较来验证所提出的解决方案。此外，还进行了参数分析，以研究土结构相对刚度比、横截面形状、高跨比和中墙厚度对隧道响应的影响。