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Analytical solutions for seismic responses of shaft-tunnel junction under longitudinal excitations

机译：纵激作用下竖井-隧道交界处地震响应解析解

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摘要

Analytical solutions are deduced for seismic responses of shaft-tunnel junction under longitudinal excitations. The influence of the tunnel is incorporated by introducing terms of shaft-tunnel and soil-tunnel interactions into equations originally developed for rigid caissons. The shaft is simplified into a rigid body. The tunnel is represented by a continuous beam perpendicularly fixed onto the shaft. Firstly, solutions for displacements of the shaft are given. Then, solutions for the three major internal forces of the tunnel are proposed. Validity of the proposed solutions is examined by finite element method in respect of the shaft and the tunnel separately. The comparisons confirm that the proposed solutions could successfully predict the displacements of the shaft and the three major internal forces of the tunnel at the vicinity of the shaft-tunnel junction. However, they become less accurate with increasing distance to the shaft. Interactions among the shaft, the tunnel, and the soil are discussed based on the proposed solutions. A special emphasis is placed on the mutual influences between the shaft and the tunnel. Displacements of the shaft, especially the rotational displacements, are likely to decrease under longitudinal excitations when connected to tunnels. Shaft-soil relative displacement and soil-tunnel relative stiffness are the two key factors affecting the seismic responses of the tunnel. The former determines the amplitudes of the internal forces, while the latter governs how the internal forces distribute along the tunnel axis. A conceptual aseismic measure is studied by setting a pin joint at the shaft-tunnel junction. Theoretically, it could eliminate the influence imposed on the tunnel by the rotational displacement of the shaft.
机译：推导了竖井-隧道交界处在纵向激励作用下的地震响应的解析解。通过将竖井-隧道和土-隧道相互作用的项引入最初为刚性沉箱开发的方程中，将隧道的影响纳入其中。轴被简化为刚体。隧道由垂直固定在竖井上的连续梁表示。首先，给出了轴位移的解;然后，针对隧道的三大内力问题提出了解决方案。采用有限元方法分别对竖井和隧道进行了验证。对比结果证实，所提方案能够成功预测竖井位移和竖井隧道交界处隧道三大内力。然而，随着与轴的距离增加，它们变得不那么准确。根据所提出的解决方案，讨论了竖井、隧道和土壤之间的相互作用。特别强调竖井和隧道之间的相互影响。当连接到隧道时，竖井的位移，特别是旋转位移，在纵向激励下可能会减小。竖井-土体相对位移和土-隧道相对刚度是影响隧道地震响应的两个关键因素。前者决定了内力的振幅，而后者决定了内力如何沿隧道轴线分布。通过在竖井-隧道交界处设置针接头，研究了概念抗震措施。从理论上讲，它可以消除竖井旋转位移对隧道的影响。

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