盾构下穿引起上覆管线变形的解析计算方法

盾构下穿易引起周边土体产生自由位移，并进一步对邻近既有管线的受力变形产生较大影响。论文从能量角度出发，采用Rayleigh-Ritz法获得管线变形函数，并基于Pasternak地基模型建立管线在外力作用下的势能方程，采用最小势能原理对管线能量进行变分求解，获得盾构下穿引起上覆既有管线受力变形解析解。与既有文献实际工程监测数据对比，验证了该方法计算结果的合理性；与基于Pasternak和Winkler地基模型差分解进行对比分析，该方法更贴近实测数据。进一步参数研究表明：增大隧道开挖半径、地层损失率会导致管线变形及其弯矩的增大；隧道与管线的夹角的增大会减轻管线变形，但会增大管线弯矩。

Analytical calculation method of deformation of overlying pipeline caused by shield tunneling

Tunneling underneath is bound to cause the free displacement of surrounding soil, which will further have a great influence on the stress and deformation of adjacent existing pipelines. In the view of the energy relationship in this paper, the pipeline deformation function can be obtained by adopting the Rayleigh-Ritz method, and based on Pasternak foundation model, the potential energy equation of the pipeline under the action of external force is established. The principle of minimum potential energy is used to solve the variational solution of pipeline energy, and then the analytical solution of the stress and deformation of the overlying existing pipeline caused by shield tunneling is obtained. Compared with the actual measurements in the existing literature, the rationality of the proposed method is verified. Compared with the finite solutions of Pasternak and Winkler foundation model, the proposed method is closer to the measured data. Further parameter studies show that increasing the tunnel excavation radius and ground loss rate will lead to the increase of pipeline deformation and bending moment. The increase of the angle between the tunnel and the pipeline will reduce the deformation of the pipeline, but will increase the bending moment of the pipeline. Further study shows that with the volume loss and the tunnel radius increase, the deformation and bending moment of the existing pipeline will increase; By increasing the skew angle between tunnel and pipeline, the deformation of pipeline will be relieved but the bending moment of the pipeline will increase.