考虑隧道剪切效应的隧道下穿对既有盾构隧道的纵向影响

将既有隧道简化为能考虑隧道剪切效应的Timoshenko梁，提出在隧道开挖作用下既有隧道纵向响应的解析解答.通过两阶段分析法，分析隧道开挖过程中既有隧道的变形及内力响应.基于修正的Loganathan和Polous地层位移理论，预测新旧隧道成任意夹角情况下隧道开挖引起的自由土体沉降分布；把隧道开挖引起的自由土体沉降施加于既有隧道之上，并基于Timoshenko梁理论，建立考虑隧道剪切效应的既有隧道纵向变形微分平衡方程；通过有限差分法求得在自由土体沉降作用下既有隧道纵向变形及内力数值解答.收集2个已发表工程实测数据，并与所提方法和Euler-Bernoulli法得到的计算结果进行对比.通过对比分析发现，实测结果与两者计算结果有良好的一致性；相对于所提方法，基于Euler-Bernoulli梁的计算结果明显高估了隧道的弯矩、剪力及接头张开量；所提方法能有效模拟既有隧道剪切效应，因而可进一步得到隧道开挖作用下的既有隧道错台量.研究成果可为合理预测隧道开挖对既有隧道影响提供一定的理论支持.

Longitudinal impacts of existing shield tunnel due to down-crossing tunnelling considering shield tunnel shearing effect

An analytical method considering the shearing effect of tunnel was proposed to assess the tunnel longitudinal responses induced by tunnelling. The existing shield tunnel was modeled by Timoshenko beam, which considers the tunnel shearing effect. Two-stage analysis method was applied to analyze the tunnelling-induced existing shield tunnel deformation and internal force responses. First, the tunnelling-induced free ground settlement was predicted by using the modified Loganathan and Polous's theory when there was an oblique angle between the new and old tunnels. Second, the induced free ground settlement was imposed on the existing tunnel; the equilibrium differential equations for tunnel responses considering the shield tunnel shearing effect were then established based on the Timoshenko beam theory. Eventually, the equilibrium differential equation for longitudinal displacement was solved numerically by using the finite difference method (FDM). The effectiveness of the proposed method was verified by two well-documented published case histories. General good agreement is observed between the measured data and the results obtained from the proposed and the Euler-Bernoulli beam methods. Compared with the proposed method, the theory based on the Euler-Bernoulli beam remarkably overestimates the bending moments, shear forces and joint openings of existing shield tunnel. The dislocations between the adjacent segmental linings of tunnel can be further obtained by the proposed method due to its inherent advantage of modeling the shear effect of shield tunnel. In general, the proposed method may provide a certain theoretic basis to estimate the tunnel longitudinal responses induced by beneath tunnelling.