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Analytical solutions for seismic responses of shaft-tunnel junction under travelling SH-wave
Tunnelling and Underground Space Technology ( IF 6.7 ) Pub Date : 2021-03-31 , DOI: 10.1016/j.tust.2021.103910
Jinghua Zhang , Mingqing Xiao , Emilio Bilotta , Chong Li , Yong Yuan

When the shaft-tunnel junction is subjected to vertically propagating SH-waves, the dominant factor is the discrepant responses between the shaft and the tunnel. However, in the case of inclined SH-waves, the travelling wave effect also has a significant influence, especially on the tunnel. To address this issue in an analytical fashion, the displacement field of the ground under travelling SH-wave is described by the stiffness matrix method and then incorporated into the solutions for the shaft and the tunnel. Some of the major assumptions include: 1) the SH-wave is a plane wave with a given incident angle; 2) the shaft is regarded as a rigid body; and 3) the tunnel is simplified into a massless Euler-Bernoulli beam. Two scenarios are considered according to the direction of the tunnel axis. When the tunnel axis is parallel to the shaking direction of the ground, the travelling wave effect is rather irrelevant, and the solutions for shaft-tunnel junction under uniform longitudinal excitations are still valid with some minor modifications. Therefore, this scenario is only briefly discussed. In the second scenario, when the tunnel axis is parallel to the horizontal propagation of the SH-wave, the travelling wave effect is no longer negligible, and a new set of solutions are offered. Validation of the solutions is made by comparison with finite element method. As demonstrated by the solutions, the displacements of the shaft and the tunnel are both affected by the travelling wave effect. The seismic distortions originate from the nonuniformities of the structure and the seismic excitation at the same time. Great internal forces at the intersection point are inevitable regardless of the direction of wave propagation, but the influence of the shaft on the tunnel diminishes exponentially with increasing distance to the shaft. Beyond the scope of the shaft influence, the responses of the tunnel are dominated by the travelling wave effect. In the case of vertically propagating SH-wave, the internal forces of the tunnel would approach to zero towards the free end of the tunnel. However, under travelling SH-wave, even at a great distance to the shaft, the tunnel would still have significant internal forces due to the travelling wave effect.



中文翻译:

行波SH波作用下竖井-隧道枢纽地震响应的解析解

当竖井-隧道交界处受到垂直传播的SH波作用时,主要因素是竖井和隧道之间的响应差异。但是,在倾斜的SH波的情况下,行波效应也有很大的影响,尤其是在隧道上。为了以解析的方式解决这个问题,通过刚度矩阵方法描述了行进SH波下地面的位移场,然后将其合并到竖井和隧道的解决方案中。一些主要的假设包括:1)SH波是具有给定入射角的平面波; 2)SH波是具有给定入射角的平面波。2)轴被视为刚体;3)将隧道简化为无质量的Euler-Bernoulli梁。根据隧道轴线的方向考虑两种情况。当隧道轴线与地面的振动方向平行时,行波效应就无关紧要了,在统一的纵向激励下,竖井-隧道连接处的解法仍然有效,但有一些小的修改。因此,仅简要讨论这种情况。在第二种情况下,当隧道轴平行于SH波的水平传播时,行波效应将不再可忽略,并提供了一套新的解决方案。通过与有限元方法的比较来验证解决方案。如解决方案所示,竖井和隧道的位移都受到行波效应的影响。地震畸变源自结构的不均匀性和同时的地震激励。无论波的传播方向如何,交点处的内力都是不可避免的,但是随着对轴距离的增加,轴对隧道的影响将呈指数减小。除了竖井影响的范围外,隧道的响应还受到行波效应的支配。在垂直传播SH波的情况下,隧道的内力朝着隧道的自由端接近零。但是,在行进SH波的作用下,即使行进到竖井的距离很大,由于行波效应,隧道仍将具有很大的内力。除了竖井影响的范围外,隧道的响应还受到行波效应的支配。在垂直传播SH波的情况下,隧道的内力朝着隧道的自由端接近零。但是,在行进SH波的作用下,即使行进到竖井的距离很大,由于行波效应,隧道仍将具有很大的内力。除了竖井影响的范围外,隧道的响应还受到行波效应的支配。在垂直传播SH波的情况下,隧道的内力朝着隧道的自由端接近零。但是,在行进SH波的作用下,即使行进到竖井的距离很大,由于行波效应,隧道仍将具有很大的内力。

更新日期:2021-03-31
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