基坑开挖卸载引起下卧已建隧道的纵向变形研究

城市地下空间开发中经常遇到已建隧道上方进行基坑开挖的情况，如何提前预测已建隧道的纵向变形是目前工程界普遍关心的问题。基于能够考虑土体变形连续性的Kerr地基梁理论，分别将已建隧道简化为欧拉伯努利梁和铁木辛柯梁，将Mindlin基本解积分得到已建隧道纵向上的附加荷载，建立了基坑开挖卸载对下卧已建隧道影响的解析分析方法，探讨了隧道剪切刚度对隧道纵向变形的影响。研究发现，当隧道剪切刚度趋于无穷大时，Kerr地基上的铁木辛柯梁退化为欧拉伯努利梁，当隧道等效剪切刚度有效系数 时，已建隧道的剪切刚度对其纵向变形和纵向曲率产生显著影响，必须予以考虑。将文中的分析方法应用于郑州市某基坑工程，通过实测数据反分析得知水泥土有效卸荷系数为0.22，对快速开挖、快速等量加载的抽条开挖方式用各条基坑独立开挖，计算结果叠加的方法进行预测，将预测的结果与地铁最终上隆量进行对比，较为吻合。

Study of longitudinal deformation of existing tunnel due to above excavation unloading

The effect of above deep excavation on existing tunnel is of great concern because the excavation unloading can induce longitudinal deformation of existing tunnels. A prediction model based on the method of beam on Kerr elastic foundation is proposed. The existing tunnel is simplified as Euler-Bernoulli beam and Timoshenko beam, respectively, to consider the effect of the tunnel shear stiffness on the longitudinal uplift caused by the above excavation. The impact of unloading on the existing tunnel can be obtained based on the Mindlin Solution. The effect of tunnel shear stiffness on the longitudinal uplift of existing tunnel cause by above excavation is investigated. The results of Timoshenko beam are consistent with those of Euler-Bernoulli beam when the tunnel shear stiffness is big enough. The effect of tunnel shear stiffness is very significant when the equivalent shear stiffness ratio is less than 1/4. Based on the proposed method, cement-soil effective coefficient of unloading is proved to be 0.22 through the measured data analysis. The ribbon-unloading method of rapid excavation and equivalent load quickly is assuming to be equal to the accumulation of relatively independent excavation. The proposed method is finally validated using the field monitoring in Zhengzhou.