考虑剪切变形下盾构隧道引起上覆管线变形分析

近邻上覆既有管线进行盾构开挖会引起管线产生附加变形，进而会影响到既有管线的安全。这方面的理论研究，大多数将既有管线简化成Euler-Bernoulli梁搁置在Winkler和Pasternak地基模型上，未考虑管线的剪切效应及三参数Kerr地基模型对管-土相互作用的影响。基于此，提出了一种可预测管线纵向变形的解析方法。采用Loganathan公式获得隧道开挖引起周围土体自由竖向位移，把土体自由竖向位移附加在既有管线轴线上，将既有管线简化成可考虑剪切变形的Timoshenko梁，管-土相互作用采用Kerr地基模型，基于提出剪切层弯矩的计算假设，结合管线两端的边界条件获得管线在盾构隧道下穿作用下受力变形响应。工程案例研究结果表明：与既有文献存在的理论分析方法比较，该方法计算得出的理论解析结果更加贴近实测数据；与Euler-Bernoulli梁计算结果比较， Timoshenko梁给出的计算结果更具有优越性。进一步参数研究表明：随着既有管线剪切刚度的增大，管线抵抗变形的能力逐渐增大，这会导致隧道下穿引起的管线变形逐步减小，但会引起管线内力反向增大；随着地层损失率增大，既有管线受到的外力逐步增大，使得管线变形及其内力也逐渐增大；随着管线直径的逐渐增大，管线在隧道下穿作用下引起的管-土相互作用力逐渐增大，最终导致既有管线所受到的应力应变也会增大。

Deformation Analysis of Shield Tunnel Undercrossing Existing Pipeline Considering Shear Deformation

The deformation of the pipeline can be induced by adjacent tunneling, in turn, the safety of the pipeline will be affected. Most of the theoretical studies in this regard simplify the existing pipelines as Euler-Bernoulli beams lying on the Winkler and Pasternak foundation models, without considering the shear effect of pipelines and the influence of the three-parameter Kerr foundation model on the pipeline-soil interaction. Based on this, an analytical method for predicting the longitudinal deformation of pipelines is proposed. Firstly, the vertical soil-free settlement around tunnel induced by tunneling can be calculated by Loganathan function, then the soil-free settlement is put upon the centerline of the existing pipeline, to simplify the tunnel as Timoshenko beam and the three-type Kerr foundation model is selected to simulate the pipeline-soil interaction, a bending moment assumption of shear layer is proposed and the response of existing pipeline can be solved by considering with the boundary conditions at the ends of the pipeline. The results of the engineering case study show that compared with the theoretical analysis method in the existing literature, the theoretical analysis calculated by the method in this paper is closer to the existing measured data. Compared with the calculation results of the Euler-Bernoulli beam, the Timoshenko beam calculation results are more advantageous. Further parameter studies show that with the increment of the shear stiffness of the existing pipeline, the ability of the pipeline to resist deformation gradually increases, which will lead to the gradual decrease of pipeline deformation but will cause the reverse increment of pipeline internal force. With the increment of volume loss rate, the external force on the existing pipeline gradually increases, which results in the increase of pipeline deformation and internal force. With the gradual increment of the diameter of the pipeline, the pipeline-soil interaction force caused by the tunneling underneath is gradually increased, which eventually leads to the stress and strain of the existing pipeline.