考虑隧道剪切效应的基坑开挖对邻近隧道纵向变形分析

 基坑施工将打破周围地层已平衡的应力场，引起应力释放，对既有下卧地铁隧道产生不利的影响。针对既有研究的不足，提出考虑隧道剪切效应的基坑开挖对下卧隧道影响的解析解。既有隧道简化为搁置于Winkler地基上的Timoshenko梁。通过两阶段分析法，考虑基坑卸荷作用下已建隧道的响应。首先基于Timoshenko梁理论，建立考虑隧道剪切效应的隧道纵向变形微分方程，然后将由Mindlin弹性解计算得到附加荷载施加于既有隧道上，最后通过有限差分法得到在附加荷载作用下隧道的纵向变形解答。收集3个已发表工程实例的实测数据，并与本文方法及Euler-Bernoulli梁法的计算结果进行对比分析，发现实测结果与2种方法得计算结果有较好的一致性。然而，在内力分析上，相对比于本文方法，Euler-Bernoulli梁法明显高估基坑卸荷引起的隧道弯矩与剪力。由于本文方法可有效模拟既有隧道剪切效应，因而可进一步给出1在卸荷作用下隧道管片间错台量。研究成果可为合理预测邻近基坑施工对既有隧道的影响提供一定的理论支持。

Analysis on the longitudinal deformation of tunnels due to pit excavation considering the tunnel shearing effect

Pit excavation changes the ground stress state which affects the existing metro tunnels. An analytical method considering the shearing effect of tunnels was proposed to assess the longitudinal responses of tunnels induced by the adjacent excavation. The tunnel was assumed as a Timoshenko beam resting on the Winkler foundation. A two-stage approach was used to analyze the longitudinal deformation of the tunnel due to excavation. Firstly，equilibrium differential equations considering the effect of tunnel shearing were established based on the Timoshenko beam theory. Secondly，additional unloading pressure on the existing tunnel due to excavation was calculated using Mindlin′s elastic solution. Finally，the longitudinal deformation of the tunnel due to the unloading pressure was solved numerically using the finite difference method. The measured results from three well-documented published cases were selected to compare with the predicted results calculated with the proposed method as well as the Euler-Bernoulli beam method. Fairly good agreements are obtained between both two methods and the measurements. However，the Euler-Bernoulli method overestimates remarkably both the bending moment and shear force induced in the tunnel when compared to the results given by the proposed method. Because the proposed method is able to effectively model the shearing effect of the tunnel，the dislocation between the adjacent segmental linings subjected to the excavation can be further obtained by the proposed method.