深基坑开挖引起隧道纵向位移的Hermite差分法

Hermite Difference Method for Tunnel Longitudinal Displacement Caused by Deep Foundation Pit Excavation

基坑开挖会造成周边地铁不均匀沉降从而影响其正常运营,为此需要研究基坑与周边地铁隧道的影响关系,本文分析了深基坑开挖对周边隧道的纵向位移的影响。首先通过Mindlin解可以计算出基坑开挖卸荷后引起隧道的附加荷载,其次基于Pasternak地基模型建立地铁隧道纵向变形的双参数基本微分方程,根据Hermite插值方法构建七点有限差分格式,从而对微分方程进行求解,可以求出邻近隧道的纵向位移。最后针对实际工程案例,建立相应的计算模型,将理论计算结果与实测结果进行对比,可以得到较好的一致性。因此本文研究成果可以帮助工程人员分析基坑开挖对周边地铁隧道的变形影响,从而制定相关的保护措施。

The excavation of foundation pit will cause uneven settlement of surrounding subway and affect its normal operation.Therefore,it is necessary to study the relationship between foundation pit and surrounding subway tunnel.This paper analyzed the impact of deep foundation pit excavation on the longitudinal displacement of surrounding tunnel.Firstly,Mindlin solution could be used to calculate the additional load of the tunnel caused by the excavation and unloading of the foundation pit.Secondly,based on the Pasternak foundation model,the two parameter basic differential equation of the longitudinal deformation of the subway tunnel was established.According to the Hermite interpolation method,the seven point finite difference scheme was constructed,so that the differential equation could be solved,and the longitudinal displacement of the adjacent tunnel coould also be calculated.Finally,according to the actual engineering case,the corresponding calculation model was established,and the theoretical calculation results were compared with the measured results,which got better consistency.Therefore,the research results of this paper can help engineers to analyze the influence of foundation pit excavation on the deformation of surrounding subway tunnels,and then formulate relevant protection measures.