管凌霄 徐长节 可文海 马锡海 徐立明 虞巍巍

摘 要：采用两阶段法推导了考虑管道剪切效应时盾构隧道下穿施工引起既有管道竖向位移的解析解。在第1阶段采用Loganathan公式计算盾构隧道下穿管道施工引起的管道轴线处土体竖向位移，第2阶段采用考虑剪切效应的Timoshenko梁模型模拟管道，并结合叠加法对管道位移控制方程进行求解，提出简化计算方法。通过与工程监测、既有文献结果及离心机试验数据的对比，验证了方法的准确性，并进一步分析了管土弹性模量比、管道直径以及管道剪切刚度变化对管道变形的影响。结果表明：随着管土弹性模量比、管道直径的增大，管道的竖向最大位移值减小;管道剪切刚度对管道位移存在较大影响，剪切刚度减小可导致管道最大位移值增大。

关键词：盾构隧道;管道位移;剪切效应;计算方法

Abstract： The two-stage method is used to derive the analytical solution of the vertical displacement of the existing pipeline caused by the undercrossing construction of the shield tunnel when the shear effect of the pipeline is considered. In the first stage， the Loganathan formula was applied to calculate the vertical displacement of the soil at the axis of the pipeline caused by the construction of the shield tunnel undercrossing the pipeline. In the second stage， a Timoshenko beam model considering the shear effect was used to simulate the pipe. Combined with the superposition method， the pipeline displacement control equation has been solved， and a simplified calculation method have been proposed. Then， the accuracy of the method has been verified via comparison with engineering monitoring， existing literature and centrifuge test data. Furthermore， the influence of the pipeline-soil elastic modulus ratio， pipeline diameter and pipeline shear stiffness change on pipeline deformation has been further studied. The results show that as the pipeline-soil elastic modulus ratio and pipeline diameter increase， the maximum vertical displacement of the pipeline decreases; the shear stiffness of the pipeline has a great influence on the displacement of the pipeline， and the decrease of the shear stiffness can lead to an increase in the maximum displacement of the pipeline.

Keywords： shield tunnelling; displacement of pipeline; shearing effect; calculation method

城市地鐵盾构隧道开挖导致的地层损失会引起周围地层的变形[1]，由于城市地下存在大量的管道，紧邻管道的盾构施工必然对其产生重大影响。因此，众多学者对如何准确分析盾构隧道下穿施工对邻近管道的影响展开了研究[2]。

目前，针对盾构隧道下穿施工对邻近管道影响的研究主要采用3种方法：模型试验法[3-4]，有限元法[5-6]以及理论解析法[7-10]。Shi等[3]、Vorster等[4]采用离心模型研究了盾构隧道下穿开挖对既有管道的影响;张治国等[5]、毕继红等[6]采用有限元法分析了盾构隧道开挖引起的邻近管道变形和内力。两阶段法作为理论解析的常用方法，意义明确，计算简便，将该问题分为两个阶段进行分析：第1阶段，先计算出管道轴线处因盾构隧道掘进引起的土体竖向位移;第2阶段，采用合理的管土相互作用模型解得管道的竖向位移。……