盾构近距离下穿引起已建地铁隧道纵向变形理论研究

盾构下穿会引起邻近已建隧道附加应力的变化，使已建隧道产生变形，对已建隧道的结构和运营安全造成一定的影响。基于明德林（Mindlin）解，经数值积分可以计算出盾构产生的刀盘附加推力q、盾壳摩擦力f及同步注浆附加压力p作用下所引起的已建隧道轴线处的附加应力。同时，利用镜像法算出在土体损失作用下已建隧道轴线处的附加应力，再将已建隧道视为温克勒（Winkler）地基梁，应用Winkler地基梁理论即可算出上述4个参数作用下已建隧道的变形，根据盾构穿越的不同工况，将上述参数作用下的变形进行叠加得到已建隧道总变形。通过杭州4号线盾构隧道下穿1号线隧道的工程实例将理论计算结果与实测结果对比分析，证明了该方法的有效性。

Theoretical analysis of vertical deformation of existing metro tunnel induced by shield tunneling under-passing in a short distance

The process of shielding changes the additional stress of the above existing tunnel which causes the deformation of the tunnel and has certain influence on the structural safety of the existing tunnel. The Mindlin solution can be used to calculate the additional stress along the central axis of the existing tunnel caused by the shield driving parameters such as the compressing pressure of the cutter-head q, friction of the shield skin f, synchronous grouting pressure p. The additional stress caused by soil loss can be calculated by the image method theory. Winkler foundation model can be used to calculate the deformation of the existing tunnel. According to the different crossing processes, the total deformation of existing tunnel can be calculated by combining the above four parts of deformation. Finally, comparing the theoretical results with the measured data of metro construction project in Hangzhou, the valid of the method is confirmed.