基于Timoshenko梁的盾构上跨对既有隧道纵向变形影响研究

采用修正的Loganathan理论研究了盾构上跨过程中土体损失引起的既有隧道纵向位移，考虑剪切变形的Timoshenko梁理论分析隧道内力变化及管片间错台量，基于弹性力学理论中的剪切效应建立了隧道纵向变形微分方程并求解，研究了隧道剪切刚度、土体损失率对隧道弯矩、剪力、管片间错台量变化规律。将计算结果与已发表监测数据对比，分析了Timoshenko梁发生弯曲变形后梁横截面不再与中性轴垂直，与不考虑剪切变形的Euler-Bernoulli梁的差异。研究表明:考虑剪切变形的理论解能准确预测隧道纵向变形，能矫正不考虑剪切变形条件下弯矩、剪力内力值过大以及无法计算管片错台量的缺陷。研究为预测盾构近距离上跨对既有隧道影响分析提供一种有效方法。

Study on the influence of above-crossing tunneling on the existing shield tunnels based on timoshenko beam

Based on the modified Loganathan theory, the longitudinal displacement of an existing tunnel caused by the ground loss in the process of shield crossing was studied. Timoshenko beam theory considering shear deformation was used to analyze the change of tunnel internal force and the amount of the dislocation between the adjacent rings. Based on the shear effect in elastic mechanics theory, the differential equation of tunnel longitudinal deformation was established and solved. After the bending deformation of Timoshenko beam, the difference between the beam cross-section of euler-Bernoulli beam which was not perpendicular to the neutral axis was analyzed. Furthermore, the variation of tunnel bending moment, shear force, and displacement between tunnel segments on tunnel shear stiffness and the ground loss ratio was studied. The results showed that the theoretical solution considering the shear deformation of the tunnel could predict the longitudinal deformation of the tunnel accurately. The proposed theory can correct the excessive internal forces such as bending moment and shear force without considering shear deformation and make up for the defect of unable to calculate the dislocation between the adjacent ring misalignment without considering shear deformation. The research results provide an effective method for predicting the influence of shield on existing tunnels.