基于层状Mindlin解的基坑开挖引起下卧隧道变形计算方法  

Calculation Method for Underlying Tunnel Deformation Induced by Foundation Pit Excavation Based on Layered Mindlin Solution

作　　者：吕林海[1,2,3] 蒋明杰 谢忠铭 黄钟晖 王炳华 梅国雄 LV Linhai;JIANG Mingjie;XIE Zhongming;HUANG Zhonghui;WANG Binghua;MEI Guoxiong(School of Civil Engineering and Architecture,Guangxi University,Nanning 530004;Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education,Guangxi University,Nanning 530004;Nanning Rail Transit Construction Group Co.,Ltd.,Nanning 530029;Nanning Rail Transit Investment Group Co.,Ltd.,Nanning 530029;Ocean College,Zhejiang University,Zhoushan 316021)

机构地区：[1]广西大学土木建筑工程学院,南宁530004 [2]广西大学工程防灾与结构安全教育部重点实验室,南宁530004 [3]南宁轨道交通建设集团有限公司,南宁530029 [4]南宁轨道交通投资集团有限责任公司,南宁530029 [5]浙江大学海洋学院,舟山316021

出　　处：《现代隧道技术》2024年第4期95-104,共10页Modern Tunnelling Technology

基　　金：国家自然科学基金项目(51878185,52178321,52108309).

摘　　要：基坑开挖将不可避免地引起坑底一定深度范围内的土体回弹,导致下卧隧道隆起变形,而较大变形将对隧道安全构成一定威胁。为进一步探究基坑开挖对下卧隧道变形的影响规律,基于层状材料弹性理论,在考虑基坑两侧土体对坑底土体影响的基础上,运用积分变换和矩阵递推的方法,推导出多层土体内部作用轴对称荷载下土体竖向附加应力。在此基础上将隧道简化为Euler-Bernoulli长梁置于考虑土体连续性的利夫金地基模型中,推导得到基坑开挖卸荷下隧道纵向变形控制微分方程,并采用有限差分方法求解得到隧道纵向位移矩阵表达式。通过工程案例进行对比分析,发现所提出方法较Winker地基模型更加接近实测数据,验证其具有良好的预测效果。Foundation pit excavation inevitably causes rebound of the soils within a certain depth range at the pit bottom,leading to the uplift deformation of underlying tunnels,which will pose a threat to tunnel safety if the defor⁃mation is significant.To further explore the impact of foundation pit excavation on the deformation of underlying tun⁃nels,based on the elastic theory of layered materials,and considering the influence of the soils on both sides of the pit on the soils at the pit bottom,the vertical additional stress of the soils under internal action of axisymmetric loads in the multi-layered soils is derived using integral transformation and matrix recursion methods.On this basis,the tunnel is simplified as an Euler-Bernoulli long beam placed in a Lifking foundation model that considers the conti⁃nuity of soils,and the differential equations for controlling the longitudinal deformation of the tunnel under unloading of pit excavation are derived.The finite difference method is used to solve the longitudinal displacement matrix ex⁃pression of the tunnel.Through comparative analysis of engineering cases,it is found that the results by proposed method are closer to the measured data than the Winkler foundation model,verifying its good prediction effect.

关 键 词：弹性层状地基 MINDLIN解 利夫金模型 基坑开挖 隧道变形 

分 类 号：U451[建筑科学—桥梁与隧道工程] TU431[交通运输工程—道路与铁道工程]