浅埋三孔隧道开挖的复变函数解  

Complex function solution of shallow buried three-hole tunnel excavation

作　　者：晏莉 杨海涛 YAN Li;YANG Haitao(School of Civil Engineering,Changsha University of Science&Technology,Changsha 410114,China)

机构地区：[1]长沙理工大学土木工程学院,湖南长沙410114

出　　处：《交通科学与工程》2024年第6期119-126,共8页Journal of Transport Science and Engineering

基　　金：国家自然科学基金项目(51408067);湖南省教育厅优秀青年项目(18B136)。

摘　　要：为了分析浅埋三孔隧道施工对地层的影响,利用复变函数理论和Schwarz交替法,求解半无限平面内三孔圆形隧道开挖的弹性解。建立三孔隧道开挖数值计算模型,将得到的数值解与复变函数理论解进行对比分析。针对三孔隧道两种常见的布置方式(平行布置、“品”字形布置)进行参数分析,得到不同的隧道间距和埋深条件下地层变形的分布规律。结果表明:基于应力边界条件的复变函数解与数值解的吻合度较高,两种解得到的地表沉降变形的分布规律基本保持一致;在平行布置的条件下,随着隧道间径比的增大,三孔隧道之间的施工扰动随之减弱,当隧道的间径比为2时,地层的沉降曲线在三孔隧道各自洞室的上方形成相对独立的峰值;在“品”字形布置的条件下,随着三孔隧道埋深的增加,地层的竖向位移随之减少,而地层竖向位移等值线的影响范围却随之扩大。To explore the influence of shallow buried three-hole tunnel construction on strata,this paper solved the elastic solution of three-hole circular tunnel excavation in a semi-infinite plane by employing the complex function theory and the Schwarz alternative method.Meanwhile,the finite element model for tunnels was built to obtain the numerical results,which were compared with the complex function solution.In addition,relevant parameter analysis was conducted on two layouts of the parallel three-hole tunnel layout and wedge-shaped tunnel layout to obtain the stratum deformation distribution law under different shallow three-hole tunnel spacing and burial depths.The results show that the complex function solution based on the stress boundary conditions is in sound agreement with the numerical solution,and the distribution law of surface sedimentation deformation is basically consistent.Under the parallel layout,the construction disturbance between three-hole tunnels weakens with the increasing ratio of spacing to the diameter.When this ratio is 2,the relatively independent peak value of stratum sedimentation is formed above the respective caverns of three-hole tunnels.Under the wedge-shaped layout,with the rising burial depth of the three-hole tunnels,the vertical displacement of the three-hole tunnels decreases,while the influencing range of the contour line of vertical displacement of the strata expands.

关 键 词：浅埋三孔隧道 SCHWARZ交替法 复变函数 应力边界 数值模拟 地层变形 

分 类 号：TU470[建筑科学—结构工程]